ISSN:0308-6003    

DOI:10.1039/PR97572FX001

出版商:RSC    

年代:1975

数据来源: RSC

ISSN:0308-6003    

DOI:10.1039/PR97572BX003

出版商:RSC    

年代:1975

数据来源: RSC

摘要:

2 The Motion of Simple Molecules in Liquids By J. S. ROWLINSON and M. EVANS Physical Chemistry Laboratory South Parks Road Oxford OX1 302 1 Introduction In a dilute gas the molecules move freely with a spread of velocities given by the Maxwell-Boltzmann distribution. After they have moved for distances many times their diameters they collide with other molecules and are deflected into new rectilinear paths. Their mean motion over a long time is measured by the coefficient of diffusion which can be expressed in terms of the angles of deflection of the colliding pairs. In liquids matters are not so simple since each molecule is in perpetual interaction with its neighbours; there are no mean-free-paths and no binary collisions. Molecules can also rotate in an irregular manner about one or more axes under the influence of the torques exerted by their neighbours or by an external field.The molecular motions can be studied on a macroscopic scale by measuring for example rates of diffusion or dielectric relaxation but the relation of these crude macroscopic averages to what is happening at a molecular level is a difficult task. The purpose of this review is to describe the progress that has been made in this field in the past ten years. Sections 2 and 3 introduce the statistical language used to describe molecular motion the language of correlation functions and their spectra or Fourier trans- forms. Perhaps the greatest advance of the past ten years has been the systematic use of this language to describe ever-increasing regions of chemical physics statistical mechanics the scattering of light X-rays and neutrons i.r.Raman and n.m.r. spectroscopy are subjects which have gained in precision and unity from these developments. Section 4 describes the measurement and computer simulation of the correlation functions of a monatomic liquid. Sections 5-7 extend the discussion to simple molecular liquids with emphasis on the study of orientational correlation functions by far4.r. spectroscopy and light scattering. We give no derivations or proofs only statements and references. 2 The Velocity Auto-correlation Function A distribution function is an answer to a question of the following form if there is a molecule with a specified position orientation velocity etc.at a certain time t =0 what is the probability that there will be a molecule (the same or different) at a position distant by r with an orientation changed by 4,with a velocity increased by u J. 0.Hirschfelder C. F. Curtiss and R. B. Bird ‘Molecular Theory of Gases and Liquids’ Wiley New York,1954. 5 J. S. Rowlinson and M.Evans etc. at a time t? Such a function can be very complicated but often we are not interested in all these variables. Thus the equilibrium or thermodynamic properties are described by a time-averaged distribution function or what is equivalent by an average taken over an ensemble of systems at a fixed time t = 0. They are functions of r and 4 alone or in a monatomic fluid of r alone.’ The dynamic and transport properties in which we are here interested can be described only if we know the time evolution of these functions but then we can often ignore one of the other variables e.g.r or 4. The term correlation function (which we abbreviate c.f.) is used to describe a distribution function which has been normalized so as to approach zero for large values of the argument r and/or t (as is appropriate). It describes the degree of correlation between two events; such correlation is zero at large times or distances in an isotropic fluid. The most familiar distribution function is probably the radial function g(r) which describes the equilibrium probability of there being two molecules at a separation r and which can be measured from the X-ray diffraction pattern. At large separations this approaches unity (see below Section 3) and the corresponding c.f.is therefore g(r)-1 which is usually called h(r) the total correlation function. We consider below (Section 3) the generalization of h(r) to include time-dependence but start first with a more simple one-molecule c.f. the velocity auto-correlation function. If a molecule has a velocity u(0)at t =0 and a velocity u(t)at time t then a suitable measure of the degree of correlation of these velocities is the scalar product u(0) u(t). After a sufficiently long time e.g. lO-’Os the magnitude and direction of ~(t) will bear no relation to that of u(0) and so the scalar product goes to zero. The velocity auto-correlation function is defined as the average of this product over all molecules in a system at equilibrium and is denoted (u(0) -u(t)).It is convenient to use the symbol $(t) for the normalized function (~(0) u(t))/(u(0)2).The impor- tance of this function is its close relation to the coefficient of diffusion but before discussing this it is useful to examine the behaviour of correlation functions in general and this one in particular as functions of time. Consider first an almost collision-free gas in which a molecule has the same velocity at t as it has at t = 0. Hence the c.f. +(t) is a constant namely unity since (u(0)-u(t)>=(u(O>’>= 3kT/rn (1) where m is the mass of the molecule. A second idealized case is the perfect Einstein solid in which a molecule vibrates about a site at a constant angular frequency a,; here the c.f.is an oscillatory function proportional to cos (aEt).A liquid behaves in an intermediate fashion as is shown in Figure 1 which is based on a computer simulation discussed in Section 4. The c.f. is constant or gas-like at short times (typically t< s) it oscillates weakly and goes to zero at long times. The first negative region is easily explained as the rebound as a molecule reverses its velocity on colliding with a neighbour after travelling on average for the mean molecular separation. (a)H. N. V. Temperley J. S. Rowlinson and G. S. Rushbrooke ‘Physics of Simple Liquids’ North- Holland Amsterdam 1%8;(6)C. A. Croxton ‘Liquid State Physics’ Cambridge University Press 1974; (c) A. F. M. Barton ‘The Dynamic Liquid State’ Longmans London 1974.The Motion of Simple Molecules in Liquids Figure 1 The normalized velocity auto-correlation function for a collision-free gas for an Einstein solid and for a liquid. The last is based on results obtained by computer simulation discussed in Section 4 Each c.f. has a Fourier transform and if the variable of the c.f. is time as here then that of the transform is frequency. We define the transform of $(t) by . rw and conversely we have also the important relation . rw The function $(w) is called the spectrum of $(t) since it can be regarded as the 'sampling' of $(t) by a signal of frequency o.It is often easier to measure the spectra than the functions themselves. Equations (2) and (3) show that we can pass freely from c.f.to its spectrum and vice versa providing we know one of them for all values of its argument. In practice this is a considerable restriction. The spectca of the three cases considered above can be found at once. If $(t) is unity then $(o)is zero unless w = 0 and is infinite if o=0. That is &(o)= I J"OD e-'"' dt= (2~)~ S(o) (4) (2.rrY -OD where 6(o) is Dirac's delta function. This is zero everywhere except where its argument is zero where it is infinite and it is normalized to unity W W f(x)S(x -x*) dx =f(x*) 1-S(x) dx = 1 (5) 00 J. S. Rowlinson and M. Evans *E lo" o/rad s-' Figure 2 The Fourier transforms of the correlation functions of Figure 1. Those for gas and solid are delta-functions whilst that for the liquid has two broad components a difisiue mode centred on o = 0 and an oscillatory mode at frequencies comparable with oEof the solid Thus the spectrum of a collision-free gas is a sharp line at zero-frequency; it will be seen below that the diffusion coefficient is then infinite.For an Einstein solid the c.f. is obtained by integrating the product of e-'"' and cos (oEf), and this integral is zero unless o= wE,so that the spectrum is now a sharp line at the Einstein frequency or $(o)is proportional to S(o-oE).For a liquid we have again both features in the spectrum. The integration of the curve in Figure 1 produces a spectrum with two peaks characteristic of diffusional and oscillatory motion but both are now very broad (Figure 2). Thus the c.f.and its spectrum enable us to describe succinctly the essential features of translational motion in a liquid more accurately than was possible with the 'models' of the liquid state that used to be so popular; in which diffusion for example might be treated as an activated jump from one site to another. However if we are to use these correlation functions we must be able to observe them or their spectra to relate them on the one hand to macroscopic properties such as diffusion coefficients and on the other to intermolecular forces by the methods of statistical mechanics. In the rest of this section we say something of the second of these problems and touch on the fringes of the third. The first the measurement of correlation functions we cover in Section 4.The connection between correlation functions and macroscopic properties is a consequence of two broad and related generalizations which lie at the root of our present understanding of transport properties. These are linear response theory and a theorem linking dissipative processes and the regression of fluctuations. Neither is new for specialized versions of both were used for many years by Einstein Onsager and others but the realization of their power and generality is much more recent; it The Motion of Simple Molecules in Liquids stems from the work of Callen Green Kubo and during the years 1955-1965. Linear response theory describes the behaviour of two weakly coupled systems as for example when a beam of light or neutrons interacts with and is scattered by a liquid or when a beam of sound is absorbed and dispersed.Because the coupling is weak it follows that the response of the liquid can be calculated from a knowledge of its behaviour in the absence of the stimulus. This behaviour is described in terms of correlation functions of the appropriate dynamical variables (velocities energies etc.)in which the averages denoted by angle brackets are it is important to note averages over a system at equilibrium. By suitable ingenuity (sometimes called ‘indirect Kubo methods’) the stimulus can be chosen so that the response can include diffusional or viscous motion or transport of thermal en erg^,^'^ and so we are able to relate these transport or non-thermodynamic properties to averages over systems at equilibrium.The theorem on fluctuations stems from a hypothesis due to Onsager which lies behind his reciprocal relations between coupled transport processes. Every system at equilibrium exhibits small departures from the average values of unconstrained dynamical properties (e.g. fluctuations of energy in a system at fixed temperature). These fluctuations regress with time and Onsager’s result is that the average rate of their regression is governed by the usual macroscopic transport coefficients (e.g. thermal conductivity for thermal energy).’ Again we have this direct relation between a transport or dissipation process and a purely equilibrium phenomenon viz.fluctuations. These theorems lead to simple relations between the transport properties and the correlation functions relations which can now be derived in at least six different ways of different assumptions and rig~ur,~ and about whose truth there can now be no doubt.The first relation due originally to Einstein is the one most directly connected with the subject of this review for it shows that the coefficient of diffusion is the time-average of the velocity c.f. D = (~(0)u(t))dt or from equation (3) It is characteristic of hydrodynamic properties such as diffusion and viscosity that they are related to the zero-frequency intercept (Figure 2) of $ and similar functions. In fact the spectrum of a time-dependent c.f. can be regarded as a frequency- dependent transport coefficient. More recent results relate other transport coeffi- cient~~’~ to integrals over other correlation functions.R. Zwanzig Ann. Rev. Phys. Chem. 1%5,16,67. R. Kubo Reports Progr. Phys. 1%6,29 255. W. Marshall and S. W. Lovesey ‘Theory of Thermal Neutron Scattering’ Clarendon Press Oxford 1971 Chap. 11 and Appendix B. H. Mori Progr. Theor. Phys. 1%5 33 423; P. Schofield in ‘Statistical Mechanics’ ed. K. Singer (Specialist Periodical Reports) The Chemical Society London Vol. 2 1975. H. C. Longuet-Higgins Mol. Phys. 1963,6,65. P. A. Egelstaff ReportsProgr. Phys. 1%6,29 333. 10 J. S. Rowlinson and M. Evans The second problem the relationof a c.f. to the underlying molecular behaviour is more difficult and largely unsolved. One useful route which has been much followed recently is to express the c.f.in terms of so-called memory functions which are believed to have more simple structures. This idea has a lot in common with the reduction of the total (static) correlation function h(r)by expressing it in terms of the apparently more simple direct correlation function c(r) of Ornstein and Zernike.’.’’ This reduction which was re-introduced into modern statistical mechanics by Rushbrooke and Scoins,” has proved to be particularly fruitful for it is easier to make intelligent approximations for c(r) than for h(r);for example the Percus- Yevick approximation which lies behind much recent work on the static structure of liquids.2,10 The introduction of memory functions into the time-dependent correla- tion functions is leading to equally fruitful approximations.This approach is best described by discussing first the problem of Brownian motion or the diffusion of a particle of essentially infinite mass m. Its motion may be described by Langevin’s equation6 which separates the total force into two parts a frictional retardation proportional to the velocity (c is a constant) and a randomly fluctuating force K(t)which arises from the impacts of the molecules of the liquid in which the particle is suspended. The two forces are not unrelated for interaction with the molecules of the liquid is also the cause of the frictional retardation. This relation between the random and the systematic components is a very general phenomenon and when put into precise form becomes the mathematical expression of the fluctuation-dissipation the~rern.~ Since the molecules hitting the Brownian particle are light and their impacts frequent and (almost) independent it is usual to assume that K(t) is a Gaussian process with a correlation time negligibly short compared with the time steps of the Brownian motion.That is It follow~~,~,~ that the velocity c.f. of the Brownian particle is an exponential in the magnitude of the time (~(0) u(t))=(u2>exp (-clrl) (10) and where c is the constant in equation (8). Such exponential decay is a valid solution for a massive particle but it will not do if the particle is itself one of the molecules of the liquid. The results in Figure 1 show that $(t) is more complicated than (lo) and moreover it is an even function of time whose derivative vanishes at t =0 for at infinitessimally short times u(t) must be the same as u(0).Langevin’s equation has 9 L. S. Ornstein and F. Zernike Roc. Acad. Sci. Amsterdam 1914 17 793 reprinted in ‘Equilibrium Theory of Classical Fluids’ ed. H. L. Frisch and J. L. Lebovitz Benjamin New York 1964. lo A. Munster ‘Statistical Thermodynamics’ Springer-Verlag Berlin 1%9 Vol. 1 Chap. 10. 11 G. S. Rushbrooke and H. I. Scoins Proc. Roy. SOC.,1953 A216,203. The Motion of Simple Molecules in Liquids therefore been generalized for the discussion of molecular motion by the replace- ment of the constant c by what is in effect a frequency-dependent coefficient of friction. We write -m lo‘ m6(t)= u( t -t’)M,(t’) dt’ +K(t) where Mo(t)is a memory function which describes the past history of the friction which is itself a correlation function and which therefore has in turn a memory function which describes its own evolution.6 That is there exists a function Ml(t) defined by hi,(t)= -6’Mo(t- t’)Ml(t’) dt’ This argument can be extended indefinitely to M2(f) M3(t) etc.If we take the correlation of (12) (13) etc.with u(O),use the fact that this velocity is not correlated with K(t) (v(0)* K(t))=0 (14) and take Laplace transforms* of each expression then Mori showed that we obtain the transform $(p) of the original c.f. $(t) as a continued fraction.6 This approach is useful only if the memory functions are more simple than the original c.f. The first Mo(t)will show a peak at t=0 representing the quasi- Brownian or inertial motion of the molecule and a tail at longer times representing the damped oscillatory motion.(The memory function of an oscillator of frequency oEis a constant mi.) One might hope that if not the first then one of the low-order memory functions could be adequately approximated by a 6(t),thus truncating the continued fraction of Mori. In Section 4 we discuss the computer simulation of the velocity c.f. and in Section 5 extend the discussion to the rotational velocity c.f. and its memory functions but first introduce in the next section a more general two-particle c.f. 3 The Density-Density Correlation Function The velocity c.f. of the last section describes the motion of one molecule. It is equally important to be able to discuss the motions of pairs for two reasons; first the intermolecular forces in a liquid are to a first approximation the sum of the interactions of the molecules in pairs only and so we must know the static c.f.for pairs even to obtain the thermodynamic properties of internal energy pressure etc. and secondly because the observed scattering of electromagnetic radiation by matter is a coherent interference of the scattering from two different centres. Let the limiting? density on a molecular scale at point r =0 and at t =0 be denoted * A Laplace transform differs from a Fourier transform by the replacement of the oscillating function exp (-iot) by the monotonically decaying function exp (-pt) so that $(p) can be regarded as the result of sampling $(r) by a probe with a relaxation time of p-’.The integration in a Laplace transform is over all t>O. The limit is the ratio (SN/SV) of the number of molecules 6N with centres in a volume GVcontaining the point r = 0 as 6 V goes to zero. J. S. Rowlinson and M. Euans n(O,O) and that at r and t by n(r t). We define a density-density distribution function g*(r t) by g*(r t) = n-'(n(O 0) n(r t)) (15) where n is the mean number density or N/ V. If we average over an ensemble at a fixed time say t =0 then we obtain the static or as it is commonly called the radial distribution'*2g(r) ng(r)= n-'(n(O) n(r)) (r # 0) (16) We have however specified that there is a molecule at r = 0 and so we have there a density described by the delta-function S(r),and we have shown in (16) that the probability that there is a second molecule at r is proportional to ng(r).Hence g*b 0) = S(r)+ngb) (17) The two terms are called the self and the distinct parts of g*. As time passes the first broadens out into a curve as the molecule originally at r = 0 diffuses away and this curve finally collapses to a line gz, = 0. The second term also loses its structures with time and goes finally to the constant value%(r) = 1,(Figure 3). We therefore form the c.f. corresponding to g* by subtracting this long-time limit and the result G(r,t) is called the van Hove c.f." G(r,t) = g*(r t) -n (18) The Fourier transform of this c.f. over the three dimensions of space and one of time is S(k,w) the structure factor 00 S( k,w)=2 G(r,t)exp [i(r * k -of)] dr dt (19) I (2d v -a r Figure 3 The self and distinctparts of van Hove's correlation function G(r t).At zero time the self part is a delta-function at r =0 and the distinct is the (static) pairc.f. h(r) = g(r)-1. At infinite time both parts go to zero 12 L.van Hove Phys. Rev. 1954,95 249. The Motion of Simple Molecules in Liquids 13 It is the structure factor which is measured by the radiation (electromagnetic or neutron) scattered by the liquid. An incoming wave of length A is characterized by a vector k which has the direction of the wave and a magnitude of 27r/A. The wave scattered with vector k has an intensity which is proportional to S(k,a),where k = k,-k,and w is the change of angular frequency.Alternatively we can say that this wave has suffered a change of momentum of hk and of energy ha. Neutrons scattered from a monoenergetic (or monochromatic) beam can be analysed for change of angle and speed and so S(k,w)can be measured as a function of both variables at least over limited ranges. The scattering can be either incoher- ent (from one centre) or coherent (from a pair of centres) according to the nature of the nucleus. Different isotopes of one atom behave differently in this respect. The former arises from the self-part of the c.f. and the latter from the distinct and so in particularly favourable cases both parts of the transforms of G can be studied experimentally. Thermal neutrons have a wavelength of ca. 1A and so k-’ is comparable with the intermolecular spacing and the coherently scattered beam yields useful information on Gdistinct(r, t) on taking the inverse If the analysis by speed (or energy) is omitted then what is obtained is an integral of S(k,o)over all w,which is therefore a function of k only S(k).Information on the time dependence of the c.f. has now been lost and the transform of S(k)yields only the static distribution function g(r). With a beam of X-rays all the scattering is coherent analysis by energy is virtually impossible and so only S(k)and g(r) can be observed. Neutron scattering has therefore told us about the dynamics of liquids in a way which was not possible with X-rays. Visible light is scattered coherently with negligible change of momentum and the spectrum observed is therefore S(0,w).The change of frequency is small but observable if the incident light is from a laser and so highly monochromatic. Measurement of the intensity and angle but not the spectrum of the scattered light tells us only about the static properties. In particular S(k=0) is related to the Such scattering is small in a normal liquid but intense near the critical point where (dn/dP),is infinite. The spectrum of the scattered light is more useful for it has three distinct peaks,14 a Rayleigh line at o = 0 and two Brillouin lines at w =fWs, where W is the speed of sound in the liquid and s the wavenumber of the particular sound wave responsible for the scattering. The Rayleigh line arises from density (or more properly refractive index) fluctuations arising from fluctuations of local entropy at fixed pressure.Such fluctuations do not propagate through the fluid and so the Rayleigh line is centred on o = 0. It may also contain a weak and very broad depolarized component discussed in Section 6. The Brillouin lines arise from fluctuations of density due to fluctuations of pressure at fixed entropy. Such fluctuations propagate as sound waves which are l3 J. G. Powles in ‘Chemical Applications of Thermal Neutron Scattering’ ed. B.T. M. Willis Clarendon Press Oxford 1973. 14 D. McIntyre and J. V. Sengers in ref. 2(a);H. L. Strauss in ‘Chemical Applications of Lasers’ ed. C. B. Moore Academic Press New York 1974. 14 J. S. Rowlinson and M. Evans present in all liquids at equilibrium and which diffract the light at the appropriate Bragg angle.The frequency shift is a Doppler effect of the moving 'grating' and since the sound wave of appropriate length and orientation can be moving in either direction a pair of lines is produced one on each side of the incident frequency. The Rayleigh and Brillouin lines provide a wealth of information even for a monatomic liquid. The total intensity yields the compressibility (20) the ratio of intensities yield CJC, the width of the Rayleigh line yields the thermal diffusivity and the displacement and width of the Brillouin lines yield the speed and coefficient of absorption of sound at frequencies above 10"Hz that is above the range accessible by mechanically generated sound waves.l5 4 The Simulation and Measurement of Correlation Functions in Monatomic Liquids The study of the dynamics of liquids by computer simulation started with the work of Alder and Wainwright16 in 1959 who solved Newton's equations of motion for 32 hard spheres moving in a cubical box. It has progressed rapidly hand-in-hand with the advances in computer speed and capacity but even now it is clearly impossible to handle systems of molecules; the present practicable limit is about lo3 or perhaps up to lo4for particularly simple systems. In a sample of liquid of this size many molecules would be near a wall and so not representative of those in a bulk liquid. This problem is solved by surrounding the cubical sample on all sides by replicas of itself so that even molecules at a side or edge interact only with molecules in a similar en~ir0nment.l~ In these conditions even a sample of 1000molecules is amply large enough to study the dynamics and thermodynamics of a liquid since correlation functions decay virtually to zero over lengths of the order of 10molecular diameters except for liquids near their critical points.Before we can solve the equations of motion we must choose an intermolecular potential and the most popular for simulating the liquefied inert gases has been the Lennard-Jones (1 2,6) potential,' which is a reasonable compromise between simp- licity and realism. Geometrically more complicated potentials are now being used to simulate diatomic molecules;'8 one of the most complicated that has so far been used is that chosen by Rahman and Stillinger" for a simulation of water.The first and still perhaps the most informative simulation of the properties of a monatomic liquid was Rahman's study2' of 864 Lennard-Jones (12,6) particles confined to a cubic cell of side 10.2 c at a reduced temperature of kT/&= 0.786 where u and E are the collision diameter and depth of the Lennard-Jones potential. The density and temperature were chosen to simulate argon at 1.374 g cm-3 and 94.4 K. The velocity c.f. and its transform are shown in Figures 1 and 2. From the area under the curve in Figure 1 or equivalently from the intercept at zero frequency in Figure 2 we get a diffusion coefficient of 2.43 X lop9m2s-' which is the D. Sette in ref. 2(a).l6 B. J. Alder and T. E. Wainwright J. Chem. Phys. 1959 31 459. l7 B. J. Alder and W. G. Hoover and W. W. Wood in ref. 2(a). l8 J. Barojas D. Levesque and B. Quentrec Phys. Rev. 1973 A7,1092;P. S. Y. Cheung and J. G. Powles Mol. Phys. 1975 30 921. I9 A. Rahman and F. H. Stillinger J. Chem. Phys. 1971,55 3336. 20 A. Rahman Phys. Rev. 1964 136 A405. The Motion of Simple Molecules in Liquids Figure 4 The mean-square displacement as a function of time (schematic) same as that of liquid argonz1 at a temperature of 90 K. However the full curves give much more detailed information on the molecular motion than the value of the macroscopic or hydrodynamic coefficient of diffusion and in particular show the inadequacy of the unmodified Langevin equation.It is instructive to calculate the mean-square displacement (r2) of any one molecule as a function of time (Figure 4).This was computed directly by Rahman or in principle could have been obtained from the self-term of van Hove’s c.f. (r2(t)>= Jo r2Gs(r,t) dr At short time (r2)grows quadratically with time; that is the motion of the molecule is unretarded as in a perfect gas. For a crystal in which the average is taken from a fixed zero time over the unrelated phases of the oscillators (r‘) settles down to a constant value. For a liquid the initially unretarded motion quickly passes into a linear dependence of (r2)on time which corresponds to a constant rate of diffusion. For ‘argon’ this linear or hydrodynamic regime is reached after ca. 2.5 x 1O-l2s a time in which a molecule has moved on average through a distance of about 0.The hydrodynamic regime is thus reached surprisingly quickly. At high temperatures or at densities substantially lower than those of a typical liquid the negative region of the velocity c.f. disappears and there is a monotonic fall with this increasing time. In this region the dissection of the c.f. into memory functions has proved Much recent interest has centred about this decay to zero at long times of this positive c.f. in a fluid of moderate density. The decay is slow 21 J. Naghizadeh and S. A. Rice J. Chem. Phys. 1962,36 2710. z2 D. Levesque and L. Verlet Phys. Rev. 1970 A2,,2514. 16 J. S. Rowlinson and M. Evans (k7 not exponential) and the consensus of opinion23 is that at long times it goes as t-$.Such a slow decay gives rise to an anomalously large coefficient of diffusion at these densities. The cause of the tail is probably to be found in a weak vortex pattern which a moving molecule apparently generates. If a molecule is moving along say the x-axis at a particular time then its very motion will tend to establish a pattern of motion in the neighbouring molecules which resembles a vortex ring with cylindrical symmetry about the x-axis. The motion of the molecules in this ring gives an impetus to the first molecule along the x-axis thus tending to prolong its motion in that Such long tails in the c.f. and the complicated molecular motions which give rise to them are clearly going to make it difficult to develop a statistical theory of transport for fluids of densities between those of the dense liquid and the dilute gas.That is no early truncation of the memory function expansion is likely to do justice to the complexity of the motions. The measurement of correlation functions for a real liquid is more difficult than their computer simulation. In Section 3 we saw that their spectra can be obtained from scattering experiments but these rarely cover a sufficiently complete range of k or o for their successful Fourier inversion. If we want to study the one-molecule correlation functions then we must use incoherent neutron scattering and so are restricted to substances containing atoms at least one of whose isotopes has a large incoherent cross-section.The best is the proton with an incoherent cross-section of 79.7 barn and a coherent of 1.8 barn and after that the best is apparently sodium for which both areas are 1.7 barn. For argon (incoherent 0.4 barn and coherent 0.5 barn) Dasannacharya and Ra024 have obtained Gs(r,t) at 85 K but only with an accuracy of ca. 15%. From this result we could go to the diffusion coefficient by calculating (r2)from equation (21) and then obtaining D from the limiting slope of Figure 4 or we can use the fact that if G,at time t has a Gaussian shape (as they aver) then its width w(t)is related to the velocity c.f. by 5.13.25 w(r)=$[ (u(O)-u(t))(t-t’)dt’ For liquid sodium the results are more extensive although judging by the agreement between different not necessarily more accurate.Figure 5 shows a spectrum of the velocity c.f. which resembles that for a liquid of Lennard-Jones molecules (Figure 2) more closely than either resemble the Lorentzian form predicted by a simple Langevin equation. The coefficient of diffusion calculated from the intercept of the spectrum at zero frequency is ca. 2.8 x mz s-’ which is in only rough agreement with the experimental valuez6 of 4.3 x mz s-’. 23 B. J. Alder and T. E. Wainright Phys. Rev. 1970 Al 18; T. E. Wainright B. J. Alder and D. M. Gass Phys. Rev. 1971 A4 233; R. Zwanzig in ‘Statistical Mechanics-New Concepts New Problems New Applications’ ed. S. A. Rice K. F. Freed and J. C. Light University of Chicago Press Chicago 1972 p. 241; Papers by B. J. Alder and J. M. Deutch and the discussion on them in ‘Transport Phenomena- 1973’.ed. J. Kestin American Institute of Physics 1973. z4 B. A. Dasannacharya and K. R. Rao Phys. Rev. 1965,137 A417. 25 B. J. Berne and G. D. Harp Adv. Chem. Phys. 1970 17 63; B. J. Berne in ‘Physical Chemistry an Advanced Treatise’ ed. D. Henderson Academic Press New York 1971 Vol. 8B; B. J. Berne and D. Forster Ann. Rev. Phys. Chem. 1971 22 563; R. T. Bailey in ‘Molecular Spectroscopy’ ed. R. F. Barrow D. A. Long and D. J. Millen (Specialist Periodical Reports). The Chemical Society London 1974 Vol. 2 p. 173. 26 p. A. Egelstaff ‘Introduction to the Liquid State’ Academic Press London 1967 p. 4. The Motion of Simple Molecules in Liquids 1 2 3 0/10” rad s-’ Figure 5 The experimental Fourier transform of the velocity c.f.for liquid sodium’ compared with the form of this function predicted by Langevin’s equation 5 Absorption in Molecular Liquids In this Section and the next two we describe how we can study the rotary motion of molecules by means of the bandshapes of their spectra which are linked to orientational auto-correlation functions. Let u be a unit vector along a convenient axis of the molecule (usually along the permanent dipole moment if any) and J the angular velocity vector which is perpendicular to u in a diatomic molecule. We shall use the following correlation functions; the first in this section the second in Section 6 and the third in Section 7. UR)$(t) =(u(0) dt)> (R) +(t) =;(~[u(o)u(~)I~ -1) (23) ‘J’rL(t) =(J(0) J(f)>/(J2(O)> Here (IR) stands for infra-red and (R) for Rayleigh rather than Raman since we shall be considering scattered light that is symmetrically disposed about the exciting line and not about a line displaced from it.The Fourier transform of (IR)+(?) is related to the dielectric abs~rption~’*~~ that arises from the attempt of dipolar molecules to respond to a small perturbing electric field which may oscillate over a wide range of frequencies. Energy is absorbed because they cannot follow the applied field F instantaneously. More than fifty years ago Debye discussed this phenomenon in terms of a rotational Langevin equation in which the torque on a dipole p at an angle 8 to the field F is opposed by a frequency-independent microscopic coefficient of friction { which arises from the force-fields of neighbouring molecules.pXF=-l9 (24) 27 N. E. Hill A. G. Price W. E. Vaughan and M. Davies ‘Dielectric Properties and Molecular Behaviour’ Van Nostrand Reinhold London 1969. 28 S. Kielich in ‘Dielectric and Related Molecular Processes’ ed. Mansel Davies (Specialist Periodical Reports) The Chemical Society London 1973 Vol. 1 p. 192. 18 J. S. RowEinson and M. Evans The Langevin equation per unit moment of inertia is then (cf. equation 8) e(t)= -&t)+r(t) (25) where r(t)is the random torque imposed on a molecule by the motion of its neighbours. If 4(t)is the angle between u(0)and u(t)then25’29 (40) 4t)>=(cos 4(t)) (26) These equations describe adequately the rotational dynamics and so the absorption up to field frequencies of ca.10” Hz. As we move into the far4.r. region3’of lOI3 Hz (i.e.,for molecular motion at times of s)then the same limitations apply to these equations as applied before to the translational Langevin equation. An obvious weakness appears if the absorption is expressed in terms of a(o),the absorption coefficient per unit path length. Integrati~n~~ of equation (25) gives an absorption coefficient a(@)proportional to 02(1 +02)-’,which means that at high frequencies a(@)has a plateau and spectral transparency is not regained. The trouble lies as before in the neglect of molecular inertia and so the assumption that the random torque r(t)has an infinitely small correlation time. Only then is l independent of time.Equation (25) is the truncation of the rotational equivalent of Mori’s continued fraction6 (Section 2) so that the memory function is a peak at t = 0; (IR)M( t) =D6 (t) (27) where D is a rotational diffusion coefficient equal to kTl/1. If r(t)is to be non-Gaus~ian,~~ and if l is to be a function of time then we must generalize Langevin’s equation in the same way as we went from equation (8)to equation (12); This equation has been used recently to describe the far4.r. absorption of furan and chlor~form.~~ t) which replaces the delta-function of The memory function ‘IR’Mo( the simple Langevin equation is the c.f. of the random torque (IRkO(t)=(r(o)r(t)) (29) Since ‘IR)Mo(t) defined by the is itself a c.f. it has its own memory function (IR)Ml(t) analogue of equation (13) and we can again extend the series indefinitely.Mori’s continued fraction for the Laplace transform starts Table 1summarizes how this series can be used as a framework into which to fit some of the widely used models for molecular rotation. The rotational like the transla- 29 G. Wyllie in ref. 28 p. 21; G. Williams Chem. Rev. 1972 72 55. 30 C. Brot in ‘Dielectric and Related Molecular Processes’ ed. Manse1 Davies (Specialist Periodical Reports) The Chemical Society London 1975 Vol. 2 p. 1. 31 B. Quentrec and P. Bezot Mol. Phys. 1974 27 879. The Motion of Simple Molecules in Liquids tional velocity c.f. is necessarily an even function of time,32 and has a Taylor expansion t2 t4 -(u(0) * u(t))= 1-(ri2(0))+-(ii2(0))-' (31) 2! 4! The mean angular velocity (u2(0))of a linear molecule is 2kT/I.The mean square acceleration (u'(0)) comprises two terms; a radial or centripetal acceleration due to the fact that the vector u is of fixed length and a tangential acceleration. The first is independent of the molecular interactions and is 8(kT/1)' and the second is (02( V))/I where O(V) is the torque that the environment exerts on the molecule via the intermolecular potential V. The substitution of these expressions into equation (31) gives the equation of motion of an ensemble of interacting molecules. The equation shows the value of the c.f. representation in isolating the short-time behaviour from that at long times. The former can be followed analytically but the latter can be obtained only by invoking statistical arguments which usually lead to an exponential tail in the c.f.Gordon3* and othersz5 have calculated the first few terms of the expansions of (IR)$(t) '"'$(t) and ")+(t);each contains the torque a functional of the intermolecu- lar potential V (0(V)) or its time derivative. The true c.f. is even in time and Table 1 shows the degree to which particular models satisfy this condition. Gordon's M and J diffusion models are zeroth-order truncations of Mori's series and so have a term in t3,and all higher odd terms. In these models the torque is not defined at the moment of impact (it?.,it becomes instantaneously infinite) and so although transparency is regained in the far4.r.(as o-'),it is regained more slowly than is found experimen- tally33 for many dipolar liquids and for those solid phases in which translational freedom is lost but rotational is retained. More the truncation at M,(t) shown in the last section of Table 1 has been used to ensure evenness to t4. The torque (0(V)) is now well-defined at all times although its derivative (6(V)) which is part of the term in t6,is not. This is because the truncation at M,(t)implies that the angular acceleration is randomized in direction at each impact so that its derivative has an infinite singularity. The absorption spectrum a(w)is the Fourier transform of (IR)+(t) and behaves asymptotically as 0-4at high frequency. It reduces3' to a Debye curve when 04<< w2,as is shown in Figure 6 where it is compared with experimental results33 for liquids and rotationally-free solids.Further comparisons with experi- ment can be found in the papers of Quentrec and Bezot3' and Evans and Evans.35 It is remarkable that although the agreement of a(@) with the experimental results is good over several decades of frequency the overall memory function 'IR'M(f),is even only to t2. This function is another equilibrium property and so should be even in time. One possible remedy would be to truncate Mori's series at R. G.Gordon J. Chem. Phys. 1%6,44,1830; Ado. Magn. Resonance 1%8,3,1;R. E. D. McClung J. Chem. Phys. 1972,57 5478. I. W. Larkin J.C.S. Faraday Symposia 1972,6 112; R. Haffmanns and I. W. Larkin J.C.S. Faraday ZZ 1972,68,1729;M.Evans M. Davies and 1. W. Larkin ibid. 1973,69,1011;I. W. Larkin ibid. 1973,69 1278;I. W. Larkin and M. Evans ibid. 1974,70,477;I. W. Larkin ibid. 1974,70,1457;M. Evans ibid. 1975,71,2051. F. Bliot C. Abbar and E. Constant Mol. Phys. 1972 24 241; F. Bliot and E. Constant Chem. Phys. Letters 1973,18,253; 1974,29,618. G.J. Evans and M. Evans J.C.S. Faraday II 1976,72 in press. Table 1 Some dynamical models in Mori’s formalism ‘IR’Mn(t) (IR)Mn(PI ‘IR)Mo(t) =D6(t) (IR)MOW =D (IR) Mo( t) =MFR(t)e-YJltl where MFR( t) is the memory function of a free rotator (IR)M1 (t) =(‘R)Ml(o) e-71‘ Model and references Debye 25,27-30 Gordon M-diffusion 30 32 33 Gordon J-diffusion 32,34 25 31 35 N Description and comment (IR)#(t) where T is the Debye Molecular inertia neglected; infini- exp (-t/~~) tesimal angular displacement in relaxation time.infinitely short time. Used to Not an even function of t describe dielectric absorption at low frequencies but leads to a ‘Debye plateau’ in the far4.r. Instantaneous elastic collisions This has a Taylor expansion perturb the rotation at random 1-ut2+O(t3)and so starts as an times. Angular velocity vector is even function of t randomized in direction; torque is infinite at impact. A slow return to transparency in the far-ix. As for M-diffusion except that A complicated function whose angular velocity is randomized Taylor expansion has a term in both direction and magnitude. in t3 An ‘inertia-corrected’ Debye model Torqueis always finite.Taylor expansion is even to t4 Describes both low-frequency and but contains a term in t5. far-i.r. absorption more Exponential at long times satisfactorily than previous models. oscillatory at short -a The past history of molecular reflection of molecular movements and interactions libration and the origin of the influences future behaviour far-i.r. Poley absorption i.e. a non-Markovian model The Motion of Simple Molecules in Liquids 21 higher and higher order but this introduces an inacceptably large number of averages (IR)M2(0), . . . ,"R)M,(0),which cannot be obtained analytically and which would therefore remain as phenomenological coefficients. A limitation of Mori's approach is that it does not give a natural picture of the long-time or hydrodynamic tail of the c.f.of angular velocity (J)t,b(t),as emphasized in many papers at a conference in Paris.36 The long-time behaviour of (J)t,b(t)appears to go as t-* as for the translational case discussed in Section 4.Such a limit is expected also for (IR)t,b(t) at least for spherical tops but this tail would distort the spectrum only on the low-frequency side of the Debye absorption. It is natural to expect i.r. absorption associated with the rotation of a dipolar molecule in a liquid but not so obvious that non-dipolar molecules also absorb in the far-i.r. and high microwave region.37 This arises from the small temporary dipole induced in a normally non-polar molecule by the fluctuating fields of moving neighbours.The reciprocal of the half-width of the absorption band is of the order of the lifetime of the induced dipole which is generally ca. 0.2 X s. The associated c.f. is one of orientation coupled with interaction and it falls to zero much more rapidly than its purely orientational dipolar counterpart (IR)t,$(t). Mori's approximation injects a unity into the description of both permanent and induced dipolar absorption as can be seen by the ease with which the truncation at M, which was successful in reproducing the permanent dipole absorption (Figure 6) also reproduces the induced dipole absorption in a range of liquids from nitrogen to benzene (Figures 7 and 8). For these liquids both Mo(0) and M,(O) are multi- molecular in origin since an isolated molecule would not absorb.Both averages are related to (02(V)) although not in a simple way and so can be used as rough probes for the change with pressure and temperature of the mean-square 6 Depolarized Rayleigh Scattering-a Study of ("'Nt) We saw in Section 3 that light scattered from a monatomic liquid had two compo-nents a Rayleigh line of the same frequency as the incoming light and surrounding it on either side a pair of Brillouin lines shifted by an amount proportional to the speed of sound in the liquid. In a molecular liquid there is usually also a weak very broad depolarized band centred on the incident frequency which leads to the so-called Rayleigh wings. It is now generally agreed that this band arises from the re-orientation of single molecules an interpretation which differs from that of collective (shear-wave) modes which prevailed39 before the c.f.formalism was introduced about ten years ago. However both mechanisms may be involved in the long-time tails on the c.f. '")t,b(t)which molecular dynamic studies have shown to be present. As with the corresponding tails in the translational velocity c.f. (Section 4) these probably arise from a coupling of the motion in this case orientational of a single molecule with the hydrodynamic transverse velocity gradient^.^' j6 'Molecular Motions in Liquids' ed. J. Lascornbe Reidel Dordrecht 1974. 37 M. Davies Ann. Reports 1970,67,65;M. Davies G. W. F. Pardoe J. Chamberlain and H. A. Gebbie Trans. Faraday SOC.,1970,66,273; G.W. F. Pardoe ibid. p. 2699; G.J. Davies J. Chamberlain and M. Davies J.C.S. Faraday ZZ 1973,69 1223; G. J. Davies and J. Chamberlain ibid. 1973,69 1739; G.J. Davies and M. Evans ibid. 1975,71 1275. 38 G. J. Davies and M. Evans J.C.S.Faraday ZZ 1976,72 in press. 39 I. L. Fabelinskii 'Molecular Scattering of Light' Plenum Press New York 1968. 40 J.-L.Greffe J. Goulon J. Brondeau and J.-L. Rivail in ref. 36 p. 151. 35r T 'r T I I I I I 20 40 60 80 100 120 140 OO 1 2 3 4 5 140-141-120 -40 -20 -' ?I I I I I I I Oh 20 40 60 80 100 I 126 140 Figure 6 The absorption (top left) and dielectric loss (top right) of t-butyl chloride in the rotator solid phase at 238 K. The abscissae are wavenumbers (cm-') and the ordinates are a in neper cm-1 and d'.The dashed lines are the experimental absorption33 and the points the experimental measurements of dielectric loss ,in the microwave region.33 The full lines are calculated from the truncation in the last line of Table 1. '7kc lower figures are similar resultsfor the absorption ad loss in liquid Me2CCIN02at 296 K. The arrows in the lower right-hand figure mazk tk?pasit'rox and knW%Tityof the ptdk in he cfiebcmc bss .-. 'r Fwe7 The absorption3" a in neper cm-'for non-dipolar substances as a function of wavenumber in cm-'. Liquid N2at 76.4 K (top left) liquid Cot at 273 K (top right) liquid CH4 at 98 K (bottom left the broader band) solid CH4 at 77 K (bottom left the narrower band) and liquid (CN) at 301 K (bottom right). The experimental results are shown by the full curves and the theoretical calculations from the truncation in the last line of Table 1 by the dashed cuws.J. S. Rowlinson and M Evans Figure 8 The absorption^^^ a in neper cm-' as a function of wavenumber in cm-' for the non-dipolar liquids CC14 (left) and GH6 (right) If the incoming light is travelling in the x-direction if it is polarized in the z-direction (vertically) and is observed in the y-direction polarized in the x-direction (horizontally) then the scattered spectrum is Im(o) and it arises from a dipole induced in the x-direction by a field along the z-direction. Such a dipole is proportional to the xz-element of the electric polarizability of the scattering volume. For a system with isotropically polarizable molecules (e.g.CCl,) this element is zero. Gordon3* showed in 1966 that this depolarized component is the Fourier transform of the average motion of the polarizability tensor and so for self-correlation in a linear or symmetric top molecule of the c.f. '"'ll/(t). The depolarized light scattered from liquids with anisotropic polarizability arises from local fluctuations of the orientation from the random isotropic average. If it is assumed that the movement of neighbouring molecules is uncorrelated then the scattered intensity at frequency o from the exciting line is This expression is similar to the quanta1 equation32 for the rotational absorption in the microwave and far-i.r. bands; Im(o) and A(@)have quantitatively the same features.The low-frequency Lorentzian4' of the scattered light corresponds to the low-frequency Debye relaxa- tion in dipolar absorption. This Lorentzian is imposed on a broader background which extends to ca. 100-150cm-' corresponding to the far-i.r. Poley absorp- ti~n.~'?~' Beyond this the intensity falls exponentially with frequency. The Lorentzian behaviour at low frequencies implies that the long-time behaviour of both (IR)t,b(t) and (")ll/(t) is exponential with relaxation times of T~ and rR respectively the reciprocals of the half-widths of the Lorentzians. Details of the 41 D. A. Pinnow S. J. Candau and T. A. Litovitz,J. Chem. Phys. 1%8,39,347; H. Dardy V. Volterra and T.A. Litovitz J.C.S. Faraday Symposia 1972,6,71; J Chem. Phys. 1973,59,4491. The Motion of Simple Molecules in Liquids 25 molecular motion are reflected in the deviations from the exponentials at short times and give rise to an added background or shoulder in the scattered light and to the Poley absorption in the i.r.A simple comparison of TM with TR tells us something of the mechanism of re-orientation; for example whether it is by large rotational jumps or Thus if motion about an axis can be described by a model of rotational diffusion with individual time steps of a short time T then Hubbard's equation43 links T,TM and TR r = I/6kTrR= I/2kTrM (34) If the Rayleigh scattering is observed as a function of temperature4' then in principle the different contributions to the scattering can be assigned different energies of activation which can be compared with those obtained from viscosity and dielectric measurements.For the substituted benzenes41 good agreement with experiment can be obtained by attributing the spectrum of linearly anisotropic molecules to a single mechanism of re-orientation. However the far wing of the Rayleigh scattering contains also information about intermolecular properties since a weak exponential scattering is observed here even with molecules with scalar p~larizabilities~~ used a simple binary-collision such as CCI,. Bucaro and Lit~vitz~~ approach to model this scattering for spherically polarizable molecules. However the spectra of anisotropic liquids show the same quasi-exponential tail and also a shoulder around 50-90cm-' which cannot be accounted for by this simple distortional binary mechanism.After subtracting the collision-induced component of m)t+b(t) Dardy et al.41 found that a molecule such as benzene behaves much as a free-rotator at short times. There is an average rotation of ca. 15" between collisions. The long-time behaviour of (")&(t)is found to be exponential reflecting the ultimate diffusional behaviour. It can be that the short-time behaviour of a c.f. is revealed in greater detail by an analysis of its second derivative; for example (R)$(t) is related to the correlation of angular momenta and angular orientation. This c.f. s~~ws~~,~~ that there is not a complete loss of memory during collisions in molecules like benzene and so the simple diffusion model which lies behind the Hubbard equation is inadequate.The Rayleigh scattering has been observed also as a function of pressure47 and from these measurements the change with density of (R)t,$(t) and (R)q$(t)can be obtained. The mechanism of re-orientation appears to involve rotation which is randomly affected by collisions but it is a process which is not described accurately by the J-diffusion model. The c.f. ("'q$(t)has a negative region and oscillates [as is well for (lR)$(t)] thus showing that there is not a complete randomiza- tion of the angular velocity at each collision. There is also evidence that memory of 42 F. J. Bartoli and T. A. Litovitz J. Chem. Phys. 1972,56 413. 43 P. S. Hubbard Phys. Reu. 1%3,131 1155. 44 J. P. McTague and G. Birnbaum Phys.Reu. Letters 1%8,21,661; W. S. Gornall H. E. Howard-Lock and S. P. Stoicheff Phys. Reu. 1970 Al 1288. 45 J. A. Bucaro and T. A. Litovitz J. Chem. Phys. 1971,553846. 46 T. Keyes and D. Kivelson,J. Chem. Phys. 1Y72,56 1057; ibid. 1972,57,4599; A. G. St. Pierre and W. A. Steele J. Chem. Phys. 1975 62 2286. 47 J. F. Dill T. A. Litovitz and J. A. Bucaro J. Chem. Phys. 1975,62,3839; P. van Konynenburg and W. A. Steele ibid.,p. 2301; M. Perrot J. Devaure and J. Lascombe Mol. Phys. 1975,30 97. J.S. Rowlinson and M. Evans one impact is carried through to the next and beyond. The oscillations in (“)$(t) are most pronounced in strongly anisotropic molecules such as benzene and suggest that such strong anisotropic forces lead towards molecular librati~n.~~ This mechanical anisotropy is accentuated at high molecular densities.The J-diffusion model is qualitatively adequate only for the simplest molecules such as N and CO. From the Mori series for depolarized Rayleigh scattering we see that the trunca- tion (R) MO(t)= DR s(t) (35) is equivalent to the Debye model of dielectric absorption and leads to the Loren tzian which is adequate only at long times. The ~houlder~~,~~ found at higher frequencies in moderately and highly anisotropic liquids can neither be described by a Lorentzian nor fitted by the distortional mechanism of Bucaro and Lit~vitz.,~ The truncation yields on Fourier transformation of the corresponding (R)$( t) the scattering func- tion of the M-diffusion model which is proportional to o-,at high frequencies and reduces to a Lorentzian when o4<< 02.The equilibrium average (R)Mo(0) is still for this model a property of a single molecule (no torque involved); for a linear molecule it is 3kT/I.The limitations of the M-and J-diffusion models in their treatment of torque (Section 5) and the false assumption of complete randomization of angular velocity at each collision have been revealed by the measurements at high pressure. Thus the J-diffusion model is adequate for the Rayleigh scattering in liquid CO,up to 100bar but fails at higher pressures when the index n of the frequency dependence (w-”) changes to higher n at intermediate and high frequencies. This sharper asymptotic fall-off with osuggests that the truncation might lead to a suitable function for IVH(u).A finite torque is now implied in ‘R’Ml(0); for a linear molecule The function IvH(w)is again Lorentzian at low frequencies but now has a peak2* around 50 cm-’ near the shoulder found by Dardy et al.,’ in anisotropic liquids.The complete spectrum of depolarized scattered light can be written as the sum of three terms; I(@)= 140)+ &mL(m) + IvH-coL(o) (40) where ICoL(o) is the collisional part of the intensity observable in molecules with isotropic polarizability such as CCI,. The theoretical expressions from which the sign and magnitude of the cross-term can be calculated are only crude but its The Motion of Simple Molecules in Liquids 27 does not seem to affect the consistency of the subsequent analysis of the results.In anisotropic molecules Iw(w) accounts for almost all the intensity and IcoL(o) is restricted to the wings. Bucaro and Lit~vitz~~ predict lCoL(o)012/7 exp (-w/oo) (o>oo) (41) where wo is calculated from a chosen intermolecular potential usually of the Lennard-Jones form. IcoL(w) is a Lorentzian if w <wo. The equivalent expression in the far-i.r.41 is acoL(w)~ w26/7exp (-o/oo) (o>wo) (42) but this fits the results much less satisfa~torily~~ than the anisotropic term shown in Figures 7 and 8. Bucaro and Lit~vitz~~ emphasize the similarity between IcoL(o) and the population-corrected dielectric loss factor in non-polar liquids viz. They have shown that both are fairly well described by semi-empirical equations such as (41)and (42).Both have separate high- and low-frequency portions whereas the generalized Langevin theory of Kubo Mori and others stresses that these peaks in the i.r. (or shoulders in the Rayleigh spectrum) are to be treated as part of the lower frequency orientational processes -a unifying formalism for both dipolar (aniso- tropic) and non-dipolar (isotropic) molecules. It would therefore seem to be fruitful to treat IcoL(o)by invoking Mori's truncation at first-order with both (R)Ml(0) and (R'Mo(0)as torque dependent parameters. 7 N.M.R. Spin-Rotation Relaxation-a Study of "'Ht) The relaxation of nuclear spins is determined by their coupling with the translational and rotational motions of the molecule. For a nucleus of spin i,the spin-rotation interaction of a linear molecule has a Hamiltonian of the form -cI J where Iis the angular momentum of the nucleus J is that of the molecule and c is the spin- rotation coupling con~tant.~~,~~ When this is the only part of the total energy which leads to relaxation of the spins then the spin-relaxation time TI is 1 c2 OD -=-(J(0).J(t))e-'%' dt (42) Tl 3H2 -oo where (')$(t) is the third c.f.defined in equation (23) and wois the Larmor precession frequency. In a typical liquid w;' is of the order of s and this is so much longer than the time for the angular momentum c.f. to decay to zero (say lO-"s) that the exponential term in (42) can be put equal to unity. For a linear molecule the expan~ion*~.Of (')t+h(t)in powers of t2 resembles those of the ratios (IR)$( t)/('")$(O) and (R)$(t)/(R)$(0).Gerschel Darmon and Brat"showed that the (IR)ratio oscillated at short times and measurements of light scattering from 48 M.Evans J.C.S. Faraday II 1975,71,71. 4y J. A. Bucaro and T. A. Litovitz J. Chern. Phys. 1971 55 3585; T. A. Litovitz in ref. 36 p. 613. 50 A. Gerschel I. Darmon and C. Brot Mol. Phys. 1972,23 317. 28 J. S. Rowlinson and M.Evans liquids at high pressures4’ have shown that the (R) ratio does also. There has been little if anything reported from n.m.r. studies of the full time dependence of (J)t,!t(t) but Berne and Harp25 have made computer calculations which show that it is negative for an interval of time if the pair potential is anisotropic.It remains positive and changes little over an interval of s if the pair potential is of the Lennard- Jones form. If there is no molecular interaction then (02( V)) is zero the c.f. (J)t,!t(t)is unity and its memory function (J’M(t) is zero. Hence “’M(t)can be looked upon as a molecular memory of the interactions. In contrast (IR’M(t)and ‘R’M(t)are non-zero decaying functions even in the absence of torque since there is always a distribution of frequencies of rotation. If ‘J)J/(t) is at any time negative then ‘J’M(t)must be non-zero; that is a molecule retains some memory of its interactions. Berne and Harp25 find that in simulated CO ‘J’M(t) goes almost to zero within 0.3 X s and that there is then a much slower decay with a final positive tail.The time of 0.63 x s is roughly that taken by a molecule to move from the centre of its ‘cage’ and meet one of its neighbours at the ‘wall’. An example of an n.m.r. study of spin-rotation relaxation is the work of Rigny and Virlet51 on the relaxation of the fluorine nuclei in UF, WF, and MoF, all of which are liquid at temperatures little above room temperature. They are unusual in that contrary to the behaviour of most the spin-rotation interaction is the dominant mechanism of relaxation even at temperatures well below the critical. The molecules retain their angular momentum for a long (correlation) time but the rotation is not free since they can move only about 1 radian at 343 K before their angular momentum changes. These conclusions are revealed by using the generalized Langevin equation which now takes the form .f(f)=-c “’M(f-f‘)J(f’)df’+rj(f) (43) where rJ(t) is the random torque and M the memory function.The associated spectrum is then O‘ ‘“J(io) (J(0) J(f))e-’”O‘dr O>= (44) = ‘J’tj(~)[ioo + (J)~(oo)l-’ where a,,is the Larmor frequency of spin precession. This is again sufficiently small to be neglected so the exponential term is unity. That is rJ(t) fluctuates so rapidly that its c.f. which is related to “’M(w)by is a delta function. The simple Langevin equation is thus regained with (J)M independent of frequency. Therefore 51 P. Rigny and J. Virlet J. Chem. Phys. 1%7,47 4645. 52 J. G. Powles in ‘Molecular Relaxation Processes’ ed. M. Davies Academic Press New York 1%6.The Motion of Simple Molecules in Liquids 29 where ?J is the angular momentum correlation time inversely proportional to TI,the spin-rotation relaxation time. As the temperature is raised the torque fluctuates more rapidly the ‘friction’ is reduced and so Tl decreases. It is found in practice that this decrease follows an Arrhenius law.27 For spherical tops such as CH4 CF4 SF, and the hexafluorides above the contribution of spin-rotation interaction to the n.m.r. lineshape is comparable with and greater than at high temperatures that of spin-spin magnetic dipole interaction. The latter is the contribution to spin resonance relaxation from the interaction of a pair of identical nuclei in the same molecule of spin quantum s and a separation defined by the vector u and the scalar distance b.The spin-spin relaxation time is where y is the gyromagnetic ratio. This relaxation time provides therefore a method of measuring the area under the ‘R’JI( t) curve which is a correlation time and is to be compared with a diffusion coefficient in the translational case equation (6). It does not however tell us anything about ‘”’Jl(t) itself as a function of time. Such n.m.r. results can be compared usefully3o with those of dielectric meas~rements,~”~~ particularly at temperatures near the triple point where rotational diffusion might be a useful concept. At the boiling point and at higher temperatures the mechanism of reorientation is generally interpreted with the help of the spin-rotation component of TI thus taking advantage of the increased periods of rotation.The principal interest of such work is to study any anisotropy of motion; sometimes the rotation is almost free about one axis and diffusional about another perpendicular to it.53 The integral of ‘“’+(t) over all time defines a correlation time ?R. In the limit of rotational diffusion this is related to ?J by Hubbard’s TRrJ = I/6kT (48) and in the limit of a rarely perturbed free spherical-top rotation by For the intermediate region M~Clung~~ has discussed the relation between ?R and 75 for spherical tops in terms of the M-and J-diffusion models. These approach the limits of equations (48) and (49) when ?J is very small and very large. Sillescu has extended54 the Debye model of Brownian motion and the random jump of rotation to take account of temporal fluctuations in their rates.Further develop- ments in the use of n.m.r. in this field can be found in the comprehensive reports edited by We conclude by applying the formulation in terms of memory functions to spin resonance relaxation. From the equipartition of kinetic energy over two degrees of 53 D. K. Green and J. G. Powles Proc. Phys. SOC.,1965,85,87; T. T. Bopp J. Chem. Phys. 1967,47,3621; D. E. Woessner B. S. Snowden and E. T. Strom Mol. Phys. 1%8 14 265; J. Jones and T. M. Di Gennaro J. Chem. Phys. 1%9,50,2392;A. A. Marryot,T. C. Farrar and M. S. Malmberg ibid. 1971 54,64. 54 H. Sillescu J. Chem. Phys. 1971 54 2110. 55 ‘Nuclear Magnetic Resonance’ ed.R. K. Harris (Specialist Periodical Reports) The Chemical Society London 1971-1975 Vols. 1-4. J. S. Rowlinson and M.Evans rotational freedom we have kT=(J2(0)>/21 so that cn T~= I (J)$(r) dt When ‘J’Mand ‘R)Mare both delta functions we have and TJ and rR are linked by Hubbard’s relation. The mean field of force due to the neighbours tends to hold a given molecule in a fixed orientation for a variable time while superimposed on this time-smoothed field is a rapid fluctuation due to the actual molecular motions. This is approximated in Brownian theory by a random torque of simple character superimposed on a steady orientating field. If the constraining field is strong the molecule moves as a damped gyrostatic pendulum. If the constant is highly anisotropic the motion about one axis may approach free rotation.If the molecule is a spherical top its components of rotation behave independently. All these different modes are not describable by a simple exponential c.f. and the introduction of memory functions will probably lead to more satisfactory descriptions. Thus =‘J’~o(~) ‘J)Mo(t) exp (-t/T;) (53) is likely to lead to a better account of the dependence of the correlation time TJ on temperature. In the M-diffusion model the product TJTRgoes through a minimum dependent on (02(V)) which is more realistic than Hubbard’s relation equation (48). With the truncation (J)Ml(t)=“’~~(0) exp (-t/T;) (54) we have that depends both on (02(V))and its time-derivative so that the product TJTR might behave ever more realistically.These applications have how- ever still to be explored.

ISSN:0308-6003    

DOI:10.1039/PR9757200005

出版商:RSC    

年代:1975

数据来源: RSC

摘要:

3 Liquid Crystals By T. E. FABER Department of Physics The Cavendish Laboratory Cambridge C65 OH€ and G. R. LUCKHURST Department of Chemistry The University Southampton SO9 5NH 1 Introduction Liquid crystals are a state of matter existing between the crystal and the amorphous liquid phases. At the microscopic level the characteristic property of a liquid crystal is the existence of long-range orientational order in contrast with the short-range order typical of liquids. This ordered phase may be obtained from certain solids by heating and also destroyed by further heating; such liquid crystals are known as thermotropic. However various solids may also be made to yield an orientationally ordered phase by the addition of the appropriate solvent; the resultant phase is known as a lyotropic liquid crystal.Although these two classes of liquid crystals have certain features in common we shall be concerned largely with thermotropic liquid crystals in this Report. The behaviour of liquid crystals stems from molecular interactions both with each other and with external fields; in this sense all of their properties are molecular. However many of the bulk properties are adequately described by continuum mechanics which does not need to refer to the existence of molecules. This Report is therefore divided somewhat arbitrarily into two parts; the second of these deals with continuum studies of liquid crystals while the first considers other aspects which are loosely described as molecular. We shall not therefore describe their applica- tions in electro-optic display devices or as solvents in spectroscopy; neither will we refer to the synthesis of new liquid crystals.This is the first account of thermotropic liquid crystals to appear in Annual Reports even though this fascinating state of matter was discovered over eighty years ago. Consequently although much of the literature surveyed appeared in 1975,we shall also refer to earlier publications when this seems appropriate. A number of texts on liquid crystals are available; these include the pioneering account by Gray,’ the masterly treatise on their continuum behaviour by de Gennes,’ and the more recent volumes edited by Gray and win so^.^ The liquid-crystal state seems to have come of age for it now merits a series describing recent advances in both our G.W. Gray ‘Molecular Structure and the Properties of Liquid Crystals’ Academic Press New York 1962. P. G. de Gennes ‘The Physics of Liquid Crystals’ Oxford University Press 1974. ‘Liquid Crystals and Plastic Crystals’ Vols. 1 and 2 ed. G. W. Gray and P. A. Winsor Ellis Horwood Ltd. Chichester 1974. 31 32 T.E. Faberand G.R. Luckhurst understanding and application of liquid crystal^.^ Two general reviews of thermo-tropic liquid crystals have appeared re~ently.~.~ In addition the RCA Review contains a number of good in-depth accounts of many specialized areas of liquid crystals; these include the molecular field theories of nematic' and smectic A phases,' the hard-rod me~ophase,~ the determination of order parameters," con-tinuum theory," and their optical properties.'' The number of papers concerned with liquid crystals continues to grow and it would be impossible to review all of these in the space available. We have therefore selected those publications which we believe to be of particular importance as well as close to our own interests. PART I Molecular Behaviour 2 Orientational Order A complete description of both the orientational and spatial order in a liquid crystal is provided by a hierarchy of distribution functions which give the probability of finding clusters of molecules with particular positions and orientations. The simplest of these is the singlet orientational distribution function but even this has proved to be particularly elusive.The singlet distribution can be determined for a paramag- netic spin probe dissolved in a supercooled nematic me~ophase'~ but has not been obtained for a pure mesophase. The singlet distribution for uniaxial phases may be expanded in terms of spherical harmonics with expansion coefficients proportional to the orientational order parameters. For rigid cylindrically symmetric molecules this expansion reduces to a sum of Legendre functions where 0 is the angle between the molecular symmetry axis and the director. The series is slowly convergent and so many order parameters pLwould be required to yield the true distribution. Unfortunately only the first parameter 4 may be determined with any certainty; in principle the next order parameter P4may be obtained from Raman light-scattering experiments but as we shall see there is some controversy as to the reliability of these values.In the following sections we shall discuss the determination and interpretation of the order parameters p and P4for the various liquid-crystal phases. Nematics. Rigid Rod-like Molecules. Provided we are prepared to assume that the molecules constituting liquid crystals are rigid and possess a three-fold or highzr symmetry axis then a wide variety of techniques is available to determine P2. These include measurement of the partially averaged diamagnetic susceptibility 'Advances in Liquid Crystals' Vol. 1 ed. G.H.Brown Academic Press New York,1975. M. J. Stephen and J. P. Straley Rev. Mod. Phys. 1974,46,4.G.Durand and J. D. Litster Ann. Rev. Mafer. Sci. 1973 3 269. P. J. Wojtowicz RCA Rev. 1974,35 118. 8 P. J. Wojtowicz RCA Rev. 1974,35 388. 9 P.Sheng RCA Rev. 1974 35 132. 10 E.B.Priestley RCA Rev. 1974,35 144. P. Sheng RCA Rev. 1974 35,408. '2 E. B. Priestley RCA Rev. 1974 35 584. '3 P.Krebs and E. Sackmann Mol. Phys. 1972 23 437. Liquid Crystals tensor dielectric tensor and refractive index the order parameter then occurs in the relationship between these tensors and the appropriate molecular parameters. The form of this relationship is well defined for the diamagnetic susceptibility although there are considerable difficulties with the refractive index because the magnitude of the internal electric field is still the subject of some debate.There are those who prefer the Vuks formulation," whereas others prefer the more acceptable Neugebauer prescription,16 although the justification for either approach seems to be largely empirical. Despite the potential uncertainty in the order parameter extracted from measurements of refractive index there has been some effort to improve the accuracy with which the birefringence can be determined.'6y17 A more reliable technique is provided by observation of the dipolar splitting in the 'H n.m.r. spectrum although under low resolution only one order parameter may be determined." The results provided by these various methods may differ in the fine detail but all agree that at the nematic-isotropic transition pz is ca. 0.4 and it increases to approximately 0.7 at 40"C below the transition.The basic features of these results are adequately accounted for by the Maier-Saupe theory and the deviations from this theory are explained by employing a more general anisotropic intermolecular p~tential.~ This success is surprising because by analogy with normal liquids strong repulsive forces might be expected to play a dominant role in determining the molecular organization whereas the theory employs a relatively weak potential. The unimportance of the repulsive part of the anisotropic potential is further supported by approximate statistical mechanical theories such as the Onsager approach,' which show that although an order-disorder transition is predicted for hard particles the order parameter p2of 0.84at the transition is much too large.Other approxima- tions based on lattice models lead to similar discrepancies when compared to the behaviour of real nematics. Of course this failure could always be ascribed to the approximations rather than to the inappropriateness of the repulsive potential. The need for approximations in statistical mechanical calculations of dense ensembles may often be removed oy resorting to the powerful computer-simulation techniques. Thus Vieillard-Baron's Monte Carlo calculation for an ensemble of spherocylinders with length to breadth ratio of 3 is particularly important." Temperature plays no role in determining the static properties of hard particles and so the system is studied as a function of the density which is defined as the number density multiplied by the molecular volume.No evidence was found for an order-disorder phase transition even at densities as high as 0.54,whereas the scaled particle theory predicts a transition for a density of 0.518.20 The absence of a phase transition is particularly disappointing especially for the proponents of the repulsive potential. However it may be that the system has not come to equilibrium because the particles become locked in unrealistic configurations. It may therefore be significant that a preliminary molecular dynamics configuration for ellipsoids interacting with a continuous hard l4 Y.Poggi,J. Robert and J. Borel Mol. Cryst. Liquid Cryst. 1975. 29 311. Is R. Chang Mol. Cryst. Liquid Cryst. 197530 155. l6 H.S. Subramhanyam,C. S. Prabha and D. Krishnamurti Mol. Cryst. Liquid Cryst.,1974,28 201. W. Kuczynski and B. Stryla Mol. Cryst. Liquid Cryst. 1975,31 267. E. Boilini and S. K. Ghosh J. Appl. Phys. 1975,46 78. l9 J. Vieillard-Baron Mol. Phys. 1974,28 809. 2o M. A. Cotter and D. E. Martire J. Chem. Phys. 1970,52 1909. 34 T.E. Faber and G.R. Luckhurst potential does yield an orientationally ordered phase.’l However like the approxi- mate theories this calculation also gives an order parameter pzwhich is unrealisti- cally large. The molecular field approximation is most reliable when applied to the long-range properties of a mesophase; as a consequence there is some interest in seeing if the Maier-Saupe-like theories are as successful in predicting p4as in accounting for p2.Since most anisotropic molecular properties transform under rotation as second rank spherical harmonics the majority of experiments can only provide p2.However the intensity of light scattered in a Raman experiment is proportional to the mean- square polarizability and so depends on the order parameter p4as well as pz.The theoretical relationship between the scattered intensity and p4is quite straightfor- ward,22 although considerable precautions must be taken in the spectral analysis especially if the contribution of director fluctuations to the scattering is to be avoided. The technique has been applied to 4’-n-heptyl-4-cyanobiphenyl,using the cyano vibration which is well removed from other molecular vibration^.'^ The parameter p4is found to be lower than that predicted by either the Maier-Saupe theory or the Humphries-James-Luckhurst extension.The departure of P4 from the predicted values is still more marked for a mixture of 4-n-butyloxybenzylidene-4’-cyanoaniline and 4-methoxybenzylidene-4‘-n-butylaniline, where negative values of P4have been dete~mined.~~ The failure of theory is still unexplained but the discrepancy could stem from error in the experimental values of p4.This view is supported by linewidth variations in the e.s.r. spectra of a spin probe dissolved in the nematic mesophase of Merck Phase IVZ5which give values of p4in support of the Maier-Saupe theory. The order parameter P4is available from such measurements because the linewidths depend on the mean-square value of the relevant magnetic tensors which are also second rank.26’27 Clearly further experimental investigations employing both techniques are required preferably of the same system before we can be certain ofeither the success or failure of the simplest molecular field theories.Deviations from Cylindrical Symmetry. Of course the molecules of most mesogens are neither cylindrically symmetric nor rigid as is so often supposed. Since the molecules do not possess a three-fold or higher symmetry axis the single order parameter p2must be replaced with the Saupe ordering matrix defined by sab =(3 cos 0 cos 6 -6&)/2 (2) where 0 is the angle between the molecular axis a and the director. There has been one attempt to determine S for a nematogen,28 but this was not entirely satisfactory because it involved the combination of results from different experiments.The reason for this lack of detail is quite straightforward for techniques (such as measurement of the partially averaged refractive index tensor) only provide a single 21 J. Kushick and B. J. Berne J. Chem. Phys. 1976,64 1362. 22 E. B. Priestley and P. S. Pershan Mol. Cryst. Liquid Cryst. 1973 23 369. 23 J. P. Heger J. Phys. (Paris) 1975,36 L-209. 24 S. Jen N. A. Clark P. S. Pershan and E. B. Priestley Phys. Rev. Letrers 1973 31 1552. 25 G. R. Luckhurst and R. Poupko Chem. Phys. Letters 1974 29 191. 26 G. R. Luckhurst M. Setaka and C. Zannoni Mol. Phys. 1974,28,49. 27 G. R. Luckhurst R. Poupko and C. Zannoni Mol. Phys. 1975 30,499.28 R. Alben J. R. McColl and C. S. Shih Solid State Comm. 1972 11 1081. Liquid Crystals 35 piece of independent information and so cannot be expected to yield the five independent elements of the ordering matrix. Thus most experiments can give some average of S or if the appropriate molecular interaction is cylindrically symmetric one of its components. The complete matrix can be measured by n.m.r. spectros- copy and this is part of a standard procedure for determining the geometry of solutes dissolved in a liquid-crystal The same approach cannot be readily applied to a pure mesophase because the large number of dipolar interactions make it virtually impossible to resolve the complex ‘H n.m.r. spectrum. One solution to this problem is to replace certain protons by deuterons.Then the proton spectrum may be readily resolved after decoupling any deuteron-proton interactions. A successful analysis of the spectrum would then yield several partially averaged dipolar interac- tions from which S can be determined. Although the proton spectra of partially deuteriated mesogens have been reported there was no attempt either to simplify the spectra or to obtain a quantitative anal~sis.~’ Alternatively the ’H n.m.r. spectrum may be recorded; this is usually dominated by pairs of quadrupole-split lines from each deuterium with some secondary structure from dipolar splittings. This technique has been applied to perdeuterio-4,4’-dimethoxyazoxybenzene,and both the partially averaged quadrupole splittings and dipolar coupling between the ortho-deuterons were ~btained.~’ The analysis of these splittings provides useful geometrical information but cannot give the ordering matrix because the coupling between nuclei in different rings was too small to be resolved.Consequently only the local ordering matrix for each ring could be determined and these are found to be essentially cylindrically symmetric about the para axis presumably because of internal rotation about this axis. Since the molecules constituting nematogens are biaxial there is the possibility that the mesophase itself might also be biaxial. The factors influencing the transition from a uniaxial to a biaxial nematic phase have been studied in some detail using a variety of theoretical approaches.However such a transition has yet to be observed; nonetheless it is important to see how the molecular biaxiality will influence the properties of the uniaxial mesophase. Straley3’ has tackled this problem for an ensemble of hard rectangular particles but as we have seen the use of a repulsive potential may well invalidate the quantitative aspects of his calculation. A compar-able theory has been reported which employs a general expansion of the pair potential for molecules of arbitrary ~hape.’~ The number of parameters in the resultant pseudopotential is reduced by restricting the summation to second-rank interactions and further assuming that the remaining coefficients may be equated with those expected for dispersion forces. The pseudopotential parametrized in this way contains two arbitrary parameters; one of these is proportional to the nematic- isotropic transition temperature while the other is related to the deviation of S from cylindrical symmetry.By using the data available for the nematogen 4,4‘-dimethoxyazoxybenzene it is possible to predict the temperature dependence of the major element of S at constant volume in excellent agreement with ex~eriment.~~ 29 J. W. Emsley and J. C. Lindon ‘NMR Spectroscopy using Liquid Crystal Solvents’ Pergamon Press Oxford 1975. 30 J. J. Visintainer E. Bock R. Y. Dong and E. Tomchuk Cunad. J. Phys. 1975 53 1483. 31 P. Diehl and A. S. Tracey Mol. Phys. 1975,30 1917. 32 J. P. Straley Phys. Reu. (A) 1974 10 1881. 33 G. R. Luckhurst C. Zannoni P. L. Nordio and U.Segre Mol. Phys. 1975,30 1345. 36 T. E. Faber and G. R. Luckhurst Departures from predictions of the Maier-Saupe theory appear to be attributable to deviations from molecular cylindrical symmetry but more accurate measurements of the total ordering matrix are required before we can be certain of the success claimed for the theory. Nun-rigid Molecules. Although there is scant experimental support for deviations of S from cylindrical symmetry there is ample evidence for the profound influence of molecular non-rigidity. For example the flexible alkyl chains which form a vital part of many mesogens are known to be responsible for the alternation in the nematic- isotropic transition temperature along an homologous series. 1,3 This odd-even effect can be reconciled with the Maier-Saupe theory because the molecular interaction parameter is expected to alternate when averaged over the various chain configura- tions.However the theory cannot explain the observed alternation in the entropy of transition which is predicted to be constant. MarEelja was the first to develop a quantitative theory of such effects by specifically including the influence of the chain configurations on the intermolecular potential.34 He proposed a pseudopotential which contains terms similar in form to the Maier-Saupe potential where 0 is the angle between the director and the supposed symmetry axis of the ith unit. The order parameter for the jthunit is denoted by Py)and the coefficients vj are related to the strength of the interaction between various units; these are usually the rigid aromatic core and the flexible alkyl chains.MarEelja then includes another term in the total pseudopotential to represent the dependence of the internal energy on the chain configuration. The resulting single-particle pseudopotential is then employed to determine the various order parameters from the usual consistency equations as well as the Helmholtz free energy to obtain the transition temperature. Since the orientation of a unit in the alkyl chain depends on that of the rigid core the total number of distinct chain configurations is unmanageably large; this number is reduced by restricting the rigid core to either three or five configurations. Despite this drastic approximation the calculated alternation in both the transition tempera- tures and entropy of transition is in agreement with experiment.The complexity of MarEelja’s calculations tends to obscure those factors which are basically responsible for the various odd-even effects that are observed for most homologous series. This has prompted Pink to simplify MarEelja’s theory;35 the philosophy of his simplification is to treat the interactions of the alkyl chains both with each other and with the rigid aromatic core as perturbations. This has the advantage that averages over the chain configurations may be evaluated for a single particle in the absence of the molecular field; some influence of the field is in fact retained because configurations outside a cylinder generated by rotating an all-trans configuration of the chain are ignored.Despite some of the questionable assump- tions necessary for the simplified theory its predictions are comparable to those of the Mar5elja theory and hence in reasonable accord with expzriment. The two theories also predict that the order parameter P2for the rigid core evaluated at the transition temperature should exhibit an odd-even effect. N.m.r. spectroscopy provides virtually the only method for testing this prediction. For 34 S. Mareelja J. Chem. Phys. 1974 60 3599. 35 D. A. Pink J. Chem. Phys. 1975,63 2533. Liquid Crystals 37 example it the ordering matrix for the rigid unit is cylindrically symmetric then p2 could be determined from the dipolar splitting between the ~rtho-protons.~ An alternative route has been proposed by Pines and Chang;36 this involves measure- ment of the 13Cn.m.r.spectrum from which the dipolar interaction with protons has been removed by noise decoupling. The remaining spectrum is particularly simple because each nucleus in the carbon skeleton can only contribute one line whose frequency is determined by the partially averaged chemical-shift tensor and hence by the ordering matrix. This technique has been applied to the homologous series of 4,4’-di-n-alkyloxyazoxybenzenes; unfortunately no attempt was made to see if S for the rigid core was cylindrically symmetric and so only the order parameter at the transition was obtained for this series.37 The order parameter was found to exhibit an odd-even effect as predicted with the maximum value of 0.455 found for the ethoxy-derivative and the minimum value of 0.365 observed for propyloxy.These results reveal that the quantitative aspects of MarEelja’s theory are not quite so satisfactory since the predicted maximum and minimum values are 0.455 and 0.399.34 The MarEelja theory but not Pink’s simplification may also be used to calculate the order parameters of the methylene groups along an alkyl chain. As we might have anticipated these order parameters may be determined from the 2Hn.m.r. spectrum of the mesogen with deuteriated chain^.^^.^' The spectrum is dominated by a series of doublets each of which come from the methylene groups or the terminal methyl group. The unambiguous assignment of a splitting to a particular group is impossible in the absence of specifically deuteriated mesogens but it seems reason- able to suppose that the order parameter decreases along the chain.The results shown in Figure 1 for 4-cyan0-4’-n-pentylbiphenyl,~’ terephthalylidene-bis(4-n-b~tylaniline),~’ were obtained with and 4-n-butyloxybenzylidene-4’-n-octylaniline38 this assumption The behaviour of the chains in these compounds shows similar trends and is in qualitative agreement with MarEelja’s calculations for 4,4’-di-n- octyloxyazoxybenzene,34 although values are not yet available for the compounds studied. An alternative technique is to attach a paramagnetic group such as 2-N-oxyl-3,3-dimethyloxazolidine,at specific positions along the chain and to determine the ordering matrix for this group from the partially averaged g and hyperfine tensors.This approach has been used with several 4,4’-dialkyloxyazobenzenes dissolved in the smectic B and C phases of 4,4’-di-n-octadecyloxyazoxybenzene~o the order parameter is found to decrease along the chain in the manner similar to that shown in Figure 1. However the order parameters exhibit a more pronounced odd-even effect which may be attributed to the perturbing influence of the spin label on the configurations adopted by the chain. The orientational order in a mesophase makes it possible to observe a n.m.r. dipolar echo following an in-phase pulse sequence.41 The echo amplitude exhibits a gaussian dependence on the time 7between 90”pulses E(T,90”)=E(O,9Oo)exp {-iM272} (4) 36 A.Pines and J. J. Chang Phys. Rev. (A),1974,10 946; B. Clin Compr. rend. 1975,280 C 73. 37 A. Pines D. J. Ruben and S. Allison Phys. Rev. Letters 1974,33 1002. 38 B. Deloche J. Charvolin L. Liebert and L. Strzelecki,J. Phys. (Paris),1975,36 C1-21. 39 J. W. Emsley J. C. Lindon and G. R. Luckhurst Mol. Phys. 1975,30 1913. 40 F. Poldy M. Dvolaitzky and C. Taupin J. Phys. (Paris) 1975 36 Cl-27. 41 N. Boden Y. K. Levine D. Lightowlers and R. T. Squires Chern. Phys. Letters 1975 31 511; ibid. 1975,34,63. T.E. Faberand G.R. Luckhurst 0.2 sc-D 0.1 0 12345678 carbon number Figure 1 The orderparameters SC-, for the alkyl-chain segments in the mesogens 4-cyano-4'-n- pntylbiphenyl (O) terephthalylidene-bis(4-n-butylaniline) (0),and 4-n -butyloxybenzylidene-4'-n-octylaniline(0).where Mz is the second moment between pairs of strongly coupled protons. For example in an alkyl chain the methylene protons are strongly coupled and it is the interactions between protons in different methylene groups which contribute to M2. This second moment reflects the chain statistics but the extraction of detailed information concerning the orientational order of the chain is clearly a difficult task. However qualitative information is available from such experiments. For example the echo amplitude for the nematic mesophase of even members of the series of 4,4'-di-n-alkyloxyazoxybenzenesis found to follow a single decay whereas the decay for the odd members can only be represented by a sum of two decays.This observation is taken to imply a discontinuous flexibility gradient for the odd members of the series; although this information is potentially valuable experiments with simpler systems in which protons are replaced by deuterons are required to prove this conclusion. Cho1esterics.-The characteristic feature of the cholesteric mesophase is the helical arrangement of the director. Since the pitch of the helix is large compared with the range of the intermolecular potential responsible for the angular correlation the helical structure should not influence the magnitude of the order parameters. The constituent molecules of most cholesterogens contain a steroidal residue and are devoid of the aromatic groups found in most nematogens.It is likely therefore that the anisotropic forces responsible for the orientational order in the phases are quite different and that this difference would be reflected in the order parameter pz. Liquid Crystals 39 However the apparently important problem of determining p2for steroidal choles- terogens appears to have been neglected. There do not seem to be any measure- ments of p2for the pure phase even though the birefringence has been defe~mined.~~ The only other measurements are for the ordering matrix of aromatic solutes dissolved in a compensated mixture of steroidal cholester~gens.~~ SmecticA.-Experimental studies of the smectic A phase were much stimulated by the Kobayashi-McMillan theory.* One intriguing prediction of the theory is that the nematic-smectic A transition should become second-order when it occurs at or below a certain reduced temperature.If the theory is restricted to a purely anisotropic intermolecular potential as in the Maier-Saupe theory then this tricriti- cal point is shown to occur when TS-N/TN-I equals 0.85. However the results of various experiments suggest that this estimate is too low. For example the order parameter of a spin probe dissolved in 4’-n-octyloxy-4-cyanobiphenylhardly changes at the nematic-smectic A transition which would therefore appear to be essentially second-~rder.~~ Since the transition occurs at a reduced temperature of 0.96 the theoretical prediction of 0.85 or less is clearly in serious error. A more refined test of the theory would be to vary the reduced temperature for the nematic-smectic A transition in order to locate the tricritical point exactly and two ingenious experiments have been devised to accomplish this aim.In the first study the transition temperatures TS-Nand TN-Ifor the mesogen 4-cyanobenzylidene-4’-n-nonylaniline were varied by increasing the pressure.45 The two transitions have different pressure coefficients and it was possible to decrease the reduced nematic- smectic A transition temperature while monitoring the order parameter with n.m.r. The discontinuity in p2was found to vanish when the reduced transition temperature was 0.92 corresponding to a pressure of 2.89 kbar. The transition temperature TS-N was varied in the second investigation by changing the composition of a binary mixture of 4-n-octyloxybenzylidene-4’-n-propylaniline and its ethoxy-hom01ogue.~~ The order of the transition was determined from the enthalpy of transition after due correction for the contribution from pretransitional effects.The tricritical point was then identified at a reduced temperature of 0.96. These high values of the reduced nematic-smectic A transition temperature can be explained if the scalar contribution to the intermolecular potential is included. The observed values of TS+/TN-,would then appear to indicate that this scalar term tends to dominate the potential. SmecticC.-The smectic C phase differs from the A phase because the constituent molecules prefer to be tilted away from the normal layer. Consequently any molecular theory of the smectic C phase must start from a pairwise potential which constrains the molecules to be inclined to the intermolecular vector in the minimum energy configuration.This contrasts with the situation in a nematic or smectic A where the minimum in the intermolecular potential occurs when the molecules are orthogonal to the vector. McMillan forces the molecules to tilt by the addition of 42 M. Evans R. Moutron and A. H. Price J.C.S.Faraday II 1975 71 1854. 43 E. Sackmann,P. Krebs,H. U. Rega,J. Voss and H. Mohwald,Mol. Cryst.Liquid Cryst. 1973,24,283. 44 G. R. Luckhurst and R. Poupko,Mol. Phys. 1975,29,1293. 45 T. J. McKee and J. R. McColl Phys. Rev. Letters 1975 34 1076. 46 D. L. Johnson C. Maze E. Oppenheim and R.Reynolds Phys. Rev. Letters 1975,34 1143. 40 T. E. Faber and G.R. Luckhurst electric dipoles which are not parallel to the molecular long axis.47 He then considers a particularly simple system of a layer of particles with this dipole-dipole interaction and using the molecular field approximations discovers a second-order transition from smectic A to a tilted smectic C phase. The rotational motion about the long axis is predicted to be quenched in the smectic Cphase but as yet there is no experimental evidence for such quenching. Indeed many experiments suggest that the rotational motion in the C phase is as unhindered as in the preceding smectic A phase.48 Wulf has proposed that it is the interactions between the alkyl chains which are responsible for the tilt in the smectic C phase because the chains are of necessity not parallel to the molecular long axis.49 The chains are assumed to be rigid entities and so the problem of chain statistics is avoided; their interaction is represented by an empirical term in the intermolecular potential.This is then treated in a manner analogous to that in the Kobayashi-McMillan theory of the smectic A phase. The theory successfully predicts a second-order phase transition between the smectic A and C phases. Unlike the smectic A phase a smectic C is predicted to be biaxial and the extent of the biaxiality is related to the tilt angle. In fact the deviation from cylindrical symmetry is predicted to be large and some evidence for this can be gleaned from a careful analysis of n.m.r.spectra of smectic C phases." 3 Molecular Dynamics The molecular structure of most mesogens is relatively complex and so there are a wide variety of motions which a molecule may execute. These include translation rotation vibration and internal rotation; the situation is further complicated by the possibility of coupling between these various modes. However the motions are invariably assumed to be independent and so we shall discuss them separately. TranslationalDiff usion.-The macroscopic anisotropy of a liquid crystal demands that the translation motion be described by a second-rank tensor D rather than a scalar as in normal liquids. For uniaxial systems such as a nematic or smectic A mesophase the diffusion tensor has cylindrical symmetry whereas for a smectic C it should be biaxial although the departure from cylindrical symmetry appears to be negligible for terephthalidene-bi~(4-n-butylaniline).~~ Of the several techniques available for the determination of D probably the most reliable involves direct observation of the motion in an aligned mesophase.For example Yun and Fre- dricks~n~~ monitored the diffusion of 14C-labelled4,4'-dimethoxyazoxybenzene at 122"Cand found Dll=4.0X cm2s-' with a ratio of Dll/D,equal to 1.25. These results clearly demonstrate the relative ease of diffusion parallel rather than perpendicular to the director although the difference is not as large as anticipated. Two other ingenious methods have been devised to monitor mass migration of a probe molecule in a mesophase; in one experiment the probe is a dye and so its progress may be observed dire~tly.~~ In the other the probe is optically active;54 this 47 W.L. McMillan Phys. Reu. (A) 1973,8 1921; R. J. Meyer and W. L. McMillan ibid. 1974 9 899. 48 Z. Luz R. C. Hewitt and S. Meiboom J. Chem. Phys. 1974,61 1758. 49 A. Wulf Phys. Reu. (A) 1975,11 365. 50 A. Wulf J. Chem. Phys. 1975,63 1564. st R. Blinc M. Burger M. Luzar J. PirS I. ZupanEiE and S. iumur Phys. Reu. Letters 1974 33 1192. 52 C. K. Yun and A. G. Fredrickson Mol. Cryst. Liquid Cryst. 1970 12 73. 53 F. Rondelez Solid State Cornm. 1974 14 815. s4 H. Hakemi and M. M. Labes J. Chem. Phys. 1974,61,4020. Liquid Crystals converts the nematic into a cholesteric phase with a pitch related to the probe concentration.The magnitude of the pitch is readily gauged from the distance between the Grandjean lines which gives the required time dependence of the concentration. The technique has been applied to a racemic mixture of (l),using one of the optical isomers as a probe," so removing the objection that the results are not directly relevant to the behaviour of the pure nematic phase. Here the enhanced molecular anisotropy results in a greater anisotropy in D;thus DI1/D1 ranges from 2.25 at 45 "C to 1.70 at 86 "C while Dllgoes from 0.5 x cm2s-' to 4.10X cm2s-' for the same change in temperature. N.m.r. spectroscopy may also be employed to determine the diffusion tensor by observing the influence of either a static or a pulsed gradient in the applied magnetic field on the form of the spin echo.The technique is difficult to apply to liquid crystals because of their complex spectra caused by the dipolar splittings although this difficulty has been circumvented in a number of ways. For example the structure may be removed by using a multiple-pulse experiment in conjunction with partial deuteriation; this procedure has been employed for 4-methoxybenzylidene-4'-n-butylaniline where Dll/D is found to be 1.4 at 25 "C with Dllequal to 6.9 X lo-' cm2s-'.~~ The smectic C and A phases of terephthalidene-bis(4-n-butylaniline) have been studied with the same technique,'l and in the A phase Dll is 14~ cm2s-' while Dll/D,is 0.3. This demonstrates the ease of motion within the smectic layers in contrast to movement across the layers; again the difference is not as large as might have been anticipated.An alternative procedure to spin decoupling is to align the mesophase with the director at the so-called magic angle (cos-' 1/J3)for then the dipolar splitting vanishes and the spectrum collapses to a single line. Kruger et ~11.~~ have employed this trick to study translational diffusion in the smectic A and B phases of 4-n-dodecanoylbenzylidene-4'-aminoazobenzene. At the start of the smectic A Dll/D,is only 0.6 but this decreases to 0.2 at the transition to the smectic B phase where the anisotropy in D increases still further. In principle incoherent quasi-elastic scattering of neutrons from a liquid crystal can also be used to determine the translational diffusion tensor.However the major difficulty and possibly the strength of this technique is that all kinds of molecular motion can contribute to the scattering. Indeed many of the earlier measurements of D using neutron scattering are now known to be in error because the scattering vector Q employed in these experiments was so large that there was rotational broadening of the quasi-elastic peak." It seems that the broadening comes entirely 55 H. Hakemi and M. M. Labes J. Chem. Phys. 1975,63,3708. 56 I. ZupanEiE J. PirS M. Luzar R. Blinc and J. W. Doane Solid State Comm. 1974 15 227. 57 G. J. Kruger J. Spiesecke and R. Weiss Phys. Letters (A) 1975 51 295. 58 J. Topler B. Alefeld and T. Springer Mol. Cryst. Liquid Cryst. 1974,26 297.42 T.E. Faberand G.R. Luckhurst from translational motion only if the scattering vector is less than 0.3 k’;under these conditions the width of the peak Aq is AW; = D,,COS’ e +D sin2 e (5) where 6 is the angle between the director and Q.59 The diffusion tensor determined for 4,4‘-dimethoxyazoxybenzene,for low Q values is found to be in good agreement with that determined from tracer experiments. Similar studies have also been reported for 4-n-pentyl-4’-cyanobiphenylusing material with and without the alkyl chain completely deuteriated.60 Since the scattering cross-section of deuterium is far less that that for a proton it is possible to see if the chain motions contribute to the broadening. In fact the linewidth was the same for both samples and so the broadening may be ascribed entirely to translational motion.The ratio D,,/D, determined from the slopes of a plot of Awa uersus Q2 was found to be 1.3 which is close to the value for 4,4’-dimethoxyazoxybenzene.The nematogen 4- methoxybenzylidene-4’-cyanoanilinewas also studied and at 112 “C the ratio Dll/D,was determined to be 2.2. The relatively large difference between these values was taken as further evidence for some sort of association in 4-n-pentyl-4’- cyano biphenyl. Despite the considerable effort on the part of experimentalists to determine the translational diffusion tensor for nematics and other liquid crystals there are remarkably few theoretical models to rationalize their results. One of the earliest attempts to develop a theory was made by Franklin,61 who modified the Kirkwood theory to allow for the anisotropy in the bulk viscosity of the nematic.Of course this is an over-simplification because in the Leslie formulation of the hydrodynamics of nematics there are five viscosity coefficients. Accordingly Franklid2 has modified the original theory to take account of all these coefficients and claims to find good agreement with the experimental temperature dependence of D for 4,4’-dimethoxyazoxybenzene. Although it is helpful to have a relationship between the translational diffusion tensor and the various Leslie viscosity coefficients a theory involving the molecular interactions might be more illuminating. Any such molecu- lar theory must start with the autocorrelation function of the momentum p since the scalar diffusion constant is .OD D = (k~/m7) p(0) -p(t) dt (6) J 0 This approach has been adopted by Chu and Mor~i,~~ although they only expand the correlation function for small times and then evaluate p’ and p’ by invoking the molecular-field approximation.The theory appears to work reasonably well although the assignment of various parameters occurring in the theory is not clear. A more reliable route to an understanding of the molecular factors determining D should be provided by the powerful computer-simulation technique of molecular dynamics. One calculation is available for highly anisotropic particles interacting sy K. Rokiszewski Acta Phys. Polon. (A),1972 41 549. 6o A. J. Leadbetter F. P. Temme A.Heidemann and W. S. Howells Chem. Phys. Letters 1975,34,363. W. Franklin Mol. Cryst. Liquid C.yst. 1971 14 227. 62 W. Franklin Phys. Rev. (A),1975,11 2156. 63 K. S. Chu and D. S. Moroi J. Phys. (Paris) 1975 36 CI-99. Liquid Crystals 43 with a continuous but strongly repulsive potentiaL2' However the orientational order in this system of ellipsoids with the major axis three and a half times the minor axis was found to be much larger than that in a real nematic. Nonetheless the translational diffusional tensor can be scaled to allow for this high order according to the common (but suspect) rule where the superscript indicates the diffusion tensor for the completely aligned mesophase. Then the ratio Dll/D,,for an order parameter pzof 0.56 is calculated to be 3.35 which is considerably higher than the values determined experimentally.There are two possible explanations for this major discrepancy between theory and experiment. One is the difficulty of knowing whether the system has reached thermodynamic equilibrium because with highly anisotropic potentials it is possible for the system to become isolated in such metastable regions of configurational phase space. Alternatively the purely repulsive anisotropic interaction may not be appropriate for real liquid crystals. Rotation.-The molecular reorientation in a liquid crystal must be highly aniso- tropic for while rotation about the long axis is essentially unhindered the motion of the long axis is constrained by the long-range orientational order.Nordio and his colleagues have developed a theory of rotational diffusion to describe these motions by extending the Debye theory to allow for the torques experienced by a molecule as a consequence of the orientational order.64 The theory therefore relates the various rotational correlation times to the parameters in the orientational pseudopotential as well as to the components of the rotational diffusion tensor. However the theory does not attempt to describe those factors which determine this tensor and as we shall see these have yet to be assigned. The strong-collision model has also been applied to the evaluation of various rotational correlation functions involving liquid crystals; however its only merit would appear to be its mathematical simplicity for it is unable to relate the collisional correlation times to the order in the mesophase.26 Dielectric relaxation provides a valuable technique for investigating molecular reorientation in liquid crystals and has been applied to a variety of systems.Of course the permittivity is now a second-rank tensor and for most liquid crystals it possesses cylindrical symmetry. The component parallel to the director normally shows a low-frequency dispersion associated with long-axis reorientation as well as a high-frequency dispersion coming from rotation about the long axis. The low- frequency dispersion can normally be fitted to a single Debye rela~ation~~ or a narrow Fuoss-Kirkwood distribution,66 and the relaxation time obtained is iden- tified with the correlation time for rotation of the Iong axis.For example the low-frequency dispersion for 4-n-pentyl-4'-cyanobiphenyl can be explained in terms ofa single relaxation time which decreases from 8.5 X lo-' s at 14 "Cto 2.7 x lo-' sat 28 0C.65Similarly recent measurements for certain 4,4'-di-n-alkoxyazoxybenzenes can be interpreted with a single relaxation time.67 The temperature dependence of 64 P. L. Nordio and P. Busolin J. Chem. Phys. 1971,55,5485;P. L. Nordio G. Rigatti and U. Segre ibid. 1972,56,2117. 65 P. G. Cummins D. A. Dunmer and D. A. Laidler Mol. Cryst. Liquid Cryst. 1975 30 109. 66 V. K. Agarwal and A. H. Price J.C.S. Faraday Il 1974 70 188. 67 A. Mircea-Roussel and F. Rondelez J. Chem. Phys. 1975,63 231 1. 44 T.E.Faber and G.R.Luckhurst the rotational correlation times for this series was analysed with the aid of a simple Arrhenius plot and the resulting activation energies were employed to support the idea of significant pretransitional effects for those members of the series which possess a smectic C phase following the nematic.However considerable caution must be exercised when applying such a simple approach to the analysis of the temperature dependence of the correlation time because two quite different factors contribute to this time. The first is the long-range orientational order while the second is the rotational diffusion tensor. By employing Nordio's theory this first contribution may be removed from the correlation time to leave the diffusion tensor. For many normal liquids this tensor is proportional to the bulk viscosity and so there is now some effort to find which if any of the Leslie viscosity coefficients may be involved for a mesophase.It has been suggested that the twist viscosity coefficient may be important,68 but the determination of the rotational correlation time in the nematic and smectic A phases of 4-cyanobenzylidene-4'-n-octyloxyanilineseems to rule out this po~sibility.~' Thus the correlation time is continuous through the second-order nematic-smectic A transition whereas the twist viscosity coefficient diverges at the transition. Reorientation about the long axis in a mesophase has not received as much attention as motion of the long axis probably because the dispersion in the permittivity occurs in an experimentally difficult frequency range.In addition this motion is not significantly affected by the long-range order that is characteristic of a liquid crystal. However Evans et al.have studied this motion for cholesteryl oleyl carbonate in the isotropic cholesteric and smectic phases.42 They find that the correlation time is continuous at the isotropic-cholesteric transition but increases discontinuously when the smectic phase is formed. The far-i.r. spectra of the cholesteric and isotropic phases were also recorded; a broad absorption centred at ca. 75 cm-' was detected for both phases. By analogy with similar studies of 4-methoxybenzylidene-4'-n-butylan~l~ne70 this Poley-like absorption has been attri- buted to a librational motion of the rigid part of cholesteryl oleyl carbonate.These particular measurements probe the local structure of the system and it would appear that this does not suffer any major changes on going from the isotropic to the cholesteric mesophase. Of course the major difficulty of studying molecular rotation by dielectric relaxation is knowing the exact relationship between the frequency-dependent permittivity and the dipole-moment autocorrelation function. This problem is particularly severe for liquid crystals because both the permittivity E and the correlation function @( t) are second-rank tensors. However linear-response theory has been employed in an attempt to allow for this anisotropy and the following expression is obtained for the permittivity parallel to the director where n(w) is a frequency-dependent depolarization The autocorrelation 68 F.Rondelez and A. Mircea-Roussel Mol. Cryst. Liquid Cryst.,1974,28 173. 69 Y.Galerne Compt. rend. 1974,278 B 347. 70 M. Evans M. Davies and I. Larkin J.C.S. Faraday ZZ 1973,69 101 1. 71 G. R. Luckhurst and C. Zannoni Proc. Roy. SOC. 1975 A343,389. Liquid Crystals function @(t) is defined in terms of the dipole moment of an ellipsoidal cavity embedded in the mesophase. Consequently the problem of relating this to the single-particle autocorrelation function remains unless correlations between dipole moments in different molecules are ignored. Nonetheless this theory is an improve- ment over the relationships implicitly adopted for &(a), but in view of its complexity it remains to be seen if experimentalists consider that their data merit such an analysis.There are far fewer theoretical problems in obtaining rotational correlation times from the line broadening in electron resonance although this dynamic information relates to the motion of the spin probe and so unless the probe is carefully chosen day not reflect the behaviour of the pure mesophase. The theory governing the linewidths caused by the rotational modulation of the g and hyperfine tensors is reasonably well established for doublet-state spin probes.26 It has recently been extended to triplet-state species where the dominant interaction is the zero-field ~plitting,~’ The macroscopic anisotropy of a mesophase results in an angular dependence of the linewidths and this should be exploited to maximize the informa- tion available from line-broadening studies.These techniques have been employed to study the rotational motion of the spin probe (3-spiro-[2’-N-oxyl-3‘,3’-dimethyloxazolidine])-5a -cholestane in the smectic A phase of 3-N-(4’-ethoxybenzylideneamin0)-6-n-butylpyridine.~~ Using the diffusion model the ratio Dll/D,for the components of the rotational diffusion tensor was found to be about 50for an order parameter p2of 0.89. This ratio is extremely large and contrasts with a value of three predicted by a purely hydrodynamic model; departure from this prediction is taken to indicate essentially unhindered rotation about the long molecular axis. The same spin probe has also been employed to study the nematogen Merck Phase IV;25in this mesophase the order parameter p2for the spin probe is only 0.62 and this may account for the reduction of Dll/D,to 35.Most experimental and theoretical investigations of line broadening in e.s.r. spectra have been confined to the fast-motion limit partly because the spectral analysis is far simpler in this regime. The theory has been extended to the.slow-motion limit and employed to analyse the line broadening in the spectrum of perdeuteriated 2,2,6,6-tetramethyl- 4-piperidone- 1-oxyl dissolved in the nematic mesophase of Merck. Phase V.72 Because the spin probe is not cylindrically symmetric the diffusion model developed by Nordio and his c011eagues~~ for symmetric-top molecules was modified for asymmetric rotors.This complicates the spectral analysis which is also inhibited by the low degree of order found for the spin probe. However a detailed analysis is possible and it is found that parameters obtained in the fast-motion limit cannot be used to predict their values at lower temperatures. This discrepancy can be removed by replacing the Debye-like spectral densities j(w)= T/(I +w2~2) (9) by the semi-empirical expression j(w)= T/(I+w2T2) (10) The magnitude of E is rationalized in terms of coupling of the molecular reorienta- tion to other degrees of freedom of the spin probe’s environment. 72 C. F. Polnaszek and J. H. Freed J. Phys. Chem. 1975,79,2283. 46 T.E.Faber and G. R. Luckhurst There have been few studies of the rotational motion in liquid crystals by incoherent quasi-elastic neutron scattering possibly because the exact theory neces- sary to interpret the scattering is still being de~eloped.~’*~~.~~ The central problem is the evaluation of the intermediate scattering function Ii”c(Q t) =exp {-iQ * r(O)}exp {iQ -r(t)} (11) where r is the position vector of the scattering centre.Provided the various motions are uncorrelated this scattering function may be written as a product of scattering functions and for rotation If:,!(Q t) =exp {-iQ a(0)) exp {iQ -a(t)} (12) where a is the position vector of the scatterer with respect to the centre of rotation. Unlike the situation in magnetic resonance it is difficult to evaluate this correlation function except for very special situations.For example if the long molecular axis is fixed and the molecule undergoes rotational diffusion about this axis the correlation function can be evaluated as a series expansion.74 A Fourier transform in time then gives the so-called scattering law for rotation as where J is an 12‘’-order Bessel function of the first kind and D is the rotational diffusion constant. The angle between Q and the long molecular axis is denoted by 8. When 8 is 7r/2 the width of the quasi-elastic peak is found to pass through a maximum at Qa equal to about 3.9. Similar results are found for other models describing reorientation about the long axis.74 The assumptions employed in this derivation are likely to be realistic for a smectic H phase or a solid where the long molecular axes are completely ordered.Indeed such notions have been employed to study motion in the smectic H phase of terephthalidene-bis(4-n-butylaniline) and to show the absence of any correlation between the short molecular axes.75 The same mesogen has been studied in the solid phase using material with deuteriated chains; apparently the scattering is caused by chain motion and an analysis in terms of a jump-diffusion model gives a correlation time of ca. lo-’* s.76 However in a nematic phase and certain smectic phases the orientational order is not high but provided the rotation of the long axis can be ignored then the scattering law can be obtained by taking the appropriate average over 8. Such averaging complicates the resultant scattering function even in the simplifying situations with Q either parallel or perpendicular to the director.There is however a more serious problem with this approach for it is by no means certain that the motion of the long axis can be ignored when evaluating the scattering law. Indeed although e.s.r. studies confirm the expected anisotropy in the rotational diffusion tensor this is not sufficiently large as to justify the neglect of long-axis motion. It would appear that we must await further theoretical developments before incoherent quasi-elastic neutron scattering can be employed to study rotational motion in a nematic. 73 K. RoSciszewski Physica 1974,75 268. 74 A. J. Dianoux F. Volino and H. Hervet Mol. Phys. 1975 30 1181. ’5 H.Hervet F. Volino A. J. Dianoux and R. E. Lechner Phys. Rev. Letters 1975 34,451. 76 F. Volino A. J. Dianoux R. E. Lechner and H. Hervet J. Phys. (Paris) 1975,36 CI-89. Liquid Crystals 47 Internal Rotations. There have been relatively few investigations of the dynamics of internal motion for molecules within a liquid-crystal mesophase. However the situation might well get better because the improvement in spectrometer design has removed many of the experimental difficulties in measuring nuclear spin relaxation times. In addition preliminary observations suggest that deuterium relaxation times for the alkyl chains of the mesogen are dominated by internal rotations. At present neutron scattering has been employed to study alkyl-chain motions in 4-methoxybenzylidene-4'-n-butylaniline.77The correlation time governing the motion is said to be 3 X s but we have seen that the analysis of neutron-scattering experiments is fraught with difficulties.Ultrasonic absorption would appear to provide an alternative technique.78 Close to the order-disorder transition the attenuation is governed by critical fluctuations but at lower temperatures the absorption by internal modes is important. Thus for the nernatogen Merck Phase V a single absorption at 2 x 1O7 Hz is observed and attributed to trans-gauche isomeri-zation in the alkyl chains. PART11 Continuum Behaviour 4 Continuum Theory for Nematics and Cholesterics Curvature Elasticity.-A nematic specimen is never a perfect single crystal; the axis with respect to which the molecules are preferentially aligned never points in exactly the same direction throughout.Even if it is not deliberately distorted by strains imposed at its surfaces or by the application of electric or magnetic fields it may still be riddled by disclinations; and even if the disclinations are eliminated by careful annealing distortions are bound to arise through thermal agitation alone. Let us describe the local axis of alignment by a unit vector n known as the director bearing in mind that since the molecules in nematics never seem to distinguish up from down the states described by n and -n must be treated as equivalent. Now suppose we choose a Cartesian co-ordinate system (the director frame) such that n lies along the z-axis at the origin.To specify the degree of distortion around the origin we need to specify the local derivatives of n such as dn,/dx and the first objective of the continuum theory of nematics is to generate an expression for the free-energy density in powers of these. Much the same problem arises in the theory of elasticity of solids. There we describe the local strain by specifying the derivatives such as dX/dx of a displacement vector with components (X Y,Z),and any reader who is familiar with the subject should be able to convince himself that if the solid is uniaxial if its symmetry axis coincides at the origin with the z-axis and if the distortion is such that 2 is everywhere zero then the free-energy density is given in terms of the usual elastic constants by ax aY 77 J.A. Janik J. M. Janik K. Otnes and K. RoSciszewski PhySlCQ 1974 77 514. 78 S. Nagai P. Martinoty S. Candau and R. Zana Mol. Crysr. Liquid Cryst.,1975 31 243. T.E.Faber and G.R.Luckhurst The answer for nematics is almost identical if we replace dX/ax by dn,/dx and so on;; the first-order derivatives of n necessarily vanish because A is a unit vector which can vary in direction but not in length and that is why there was no need to include in equation (14)any terms involving 2. It seems that in the nematic case the coefficients of the fourth and fifth terms in the formula equivalent to equation (14) are not necessarily related but this is scarcely relevant because the fifth term can in any case be discarded. We discard it because from which it follows that an integral of the fourth term over any sheet that is everywhere normal to n is completely specified by the boundary conditions at the edge of that sheet.A term in the free energy that depends only on boundary conditions can have no influence on the direction of A somewhere in the interior* The starting point for the continuum theory of nematics is therefore the formula in the director frame or in any frame of reference f =fo+4Kl(div n)2+4Kz(n-curl n)’+$K3(n xcurl n)’ (16) The three Frank stiffness constants which feature in this formula are in practice very much smaller than the elastic constants of a typical solid which is why nematics distort so easily. It is also the reason incidentally why we may safely assume that unless the distortion is very marked indeed (e.g.in the core of a disclination) it has no effect on the degree to which the molecules are aligned i.e.on the local value of F2 and hence on other properties -such as the stiffness constants themselves -which in principle may depend upon the degree of alignment.In the materials so far investigated the stiffness constants lie in the range 10-7-10-6dyn; they decrease on heating and K33K1>K2.t K1 is known as the splay constant K2 as the twist constant and K as the bend constant. Left to itself a nematic specimen minimizes its total free energy by letting its director relax to the least distorted configuration that is consistent with the boundary conditions. In principle however we may prevent the director from relaxing by applying a suitable torque to each molecule from outside.The torque required may readily be calculated from equation (16) by application of the principle of virtual work and hence we may calculate the equal and opposite torque which is exerted on the molecules internally by the distortion of the director. The general expression is too complicated to be worth writing out here. Cholesteric liquid crystals closely resemble nematics but because they are com- posed of optically active molecules they like to adopt a configuration in which the * Nehring and Sau -P have shown that terms in the free energy of nematics depending on second-order derivatives such as d. n,/dyaz introduced by Oseen but lost sight of by most later authors may in practice be discarded for much the same reason.t Some theories suggest that K and K3 should become equal in the limit p2 + 0. Liquid Crystals director twists in a spiral fashion about an axis perpendicular to itself. For choles- terics the appropriate generalization of equation (16) is f=fo+iKl(div n)2+iKz(n'curl n*q0)'+$K3(n Xcurl n)* (17) where 27r/q0 is the pitch of spiral that the cholesteric likes best. The sign to be attached to qo in (17) depends upon whether the spiral is right- or left-handed. Viscosity.-Naturally enough extra stresses and torques develop in a nematic as soon as it begins to flow. Let us treat it as Newtonian and assume the stresses to be related in a linear fashion to the gradients of the flow velocity V=(u u w). If the director is rotating they may also be affected by the speed of its rotation but for the moment we shall suppose n to be fixed despite the flow.Symmetry considerations then allow us to write down equations for the shear stress components which once more in the director frame take the following form* au av fxy = fyx = 773 (G+Z) For an ordinary isotropic fluid the four coefficients introduced above would all be equal to the conventional shear viscosity q. In principle we can measure ql,q2,and q3by using a simple viscometer in which the flow is planar and only one component of the velocity gradient tensor is non-zero. Suppose for example that we fix n (e.g.with the aid of a large magnetic field) so that it lies along the direction of the flow and the aligned molecules are made to slide over one another in a lengthwise fashion then we shall measure ql.If we fix n so that it lies perpendicular to the flow planes and the molecules are made to slide over one another end to end then we shall measure qz.In the third principal configuration with n fixed in the flow planes but perpendicular to V we shall measure q3.It generally turns out in practice (for recent measurements on 4-methoxybenzylidene- 4'-n-butylaniline see ref. 79) that q2> q33 ql,which is perhaps hardly surprising. Incidentally the difference between q1and q3means that if we do the experiment with n in the flow planes but at some angle to V other than 0 or ~/2,then the tangential stress experienced by the viscometer must have a component perpendicu- lar to V.Furthermore if a nematic fluid is forced to undergo Poiseuille flow between flat plates while the director is held at an angle a transverse pressure gradient should develop.The latter effect reminiscent of the Hall effect perhaps has recently been demonstrated by Pieranski and Guyon." 79 1.w.Summerford J. R. Boyd and B. A. Lowry J. Appl. Phys. 1975,46 970. p. Pieranski and E. Guyon Phys. Letters (A),1974,49 237. * The reader conversant with elasticity theory may again find it helpful to explore the analogy of a uniaxial solid to persuade himself that equations (18)-(20) are correct. In elasticity theory the coefficients relating tzxto aX/azand rxz to aZ/ax are necessarily identical as can readily be proved by appealing to the law of conservation of energy.It can be proved by the methods of irreversible thermodynamics that the v4 which occurs in (18) is necessarily identical to the v4 which occurs in (19). T.E. Faberand G.R. Luckhurst The importance of q4 is apparent when we come to consider viscous torques. Given the shear stresses described by equations (18) and (19) it follows that a nematic fluid undergoing shear flow experiences a torque per unit volume the component of which about the y-axis say is given in the director frame by For an ordinary isotropic fluid this evidently vanishes. It need not do sofor a nematic fluid because any amount of torque can be absorbed as it were by whatever external agency is used to fix the director. Let us now decompose the fluid motion about the y-axis into a solid-body rotation with angular velocity my and a pure shear compo-nent ty;this means writing Then we may write Gy = YlOy -Y26y (23) where Y1 = 771 +7?2-2774 Y2= 11-12 (24) At this stage let us admit the possibility that the director is not fixed but is rotating about the y-axis with angular velocity say Ry.The appropriate generalization of equation (23) is clearly which ensures that in the absence of shear and when the whole specimen is rotating as a solid body director and all the viscous torque vanishes. The coefficient q4 therefore plays a role in determining the so-called torque coefficient or twist viscosity yl. This is of particular importance in experiments where for example a nematic sample is allowed to oscillate as a solid body in a magnetic field strong enough to hold n fixeds1782 or alternatively where the nematic is stationary and the magnetic field is changed in direction.It is y1which determines the decay rate of the oscillations in one case and the rate at which n relaxes to its new equilibrium configuration in the other. The twist viscosity has an additional significance for cholerestics because it controls the rate of permeation. Suppose we have a cholerestic specimen in which the axis of the cholerestic spiral points along the y-axis in the director frame and suppose that the fluid is in uniform motion in this direction with velocity V while for some reason the phase of the cholerestic spiral is unable to change. The fact that n is fixed in space means that in each element of fluid it is rotating with angular velocity 0,= Vq,.This implies a viscous torque per unit volume Gy=-yl Vq, and to provide the energy dissipated against this torque there must be a pressure gradient. A simple calculation shows that P. J. Flanders Mol. Cryst. Liquid Cryst. 1974 29 19. 82 S. Meiboom and R. C. Hewitt Phys. Rev. Letters 1975,34 1146. Liquid Crystals The smallness of the permeation coefficient A defined by equation (26)may explain as Helfrich originally pointed out the anomalously high apparent viscosities reported for cholerestics by some of the early experimenters who measured rates of flow through tubes. So far we have four independent viscosity coefficients for a nematic uiz.ql,q2,q3 and q4 or yl.The need for a fifth becomes apparent when we have occasion to consider the normal stress components in the director frame. If we regard the nematic as incompressible and therefore ignore the complications associated with bulk viscosity equations for the normal stresses may be written thus au av aw txx=-p+2q3-; tyy= -p+2q3-;JY tzz=-p+2q5-ax az where p is the pressure that would exist in the absence of velocity gradients. It may be added that many authors prefer to use a set of Leslie coefficients al to as rather than the q’sdefined above. The relationships between the a’s and the q’sare set out by Stephen and Straley.’ 5 Applications of Continuum Theory The ability of the theory which has been summarized above to explain a vast range of intriguing phenomena was amply demonstrated in the years before 1973 and little that is essentially new has emerged since then except in relation to flow instabilities and to the effects of smectic ordering.These matters will be dealt with in Sections 6 and 7 respectively. In the present section a survey of the pre-1973 work on nematics and cholerestics will be conducted and a number of elegant experiments that have been carried out since 1973 by way of extension of this work will be described. The reader should bear in mind that many of these experiments lead in the end to values for the stiffness and viscosity coefficients of the material under investigation. To improve our stock of information about these coefficients is a worthwhile objective by itself for any investigator since the information will no doubt be needed shortly for comparison with microscopic theories.FreederickszTransitions.-While liquid crystals still cost El per gram or more there is some incentive to devise experiments that can be done on small samples and in fact many of the experiments to be described in this section were done on thin films Contained between two glass (or similar) slides. In a thin film the boundary conditions for n are naturally of overwhelming importance. The boundary condi- tions depend upon the treatment of the glass. If it has been carefully rubbed over a sheet of paper always in the same direction then where the liquid crystal makes contact with the glass n is obliged to lie parallel to the surface and in the rubbing direction.The same condition can be achieved more easily and reproducibly by evaporating onto the glass at a slanting angle a thin film of say silicon monoxide. If the glass has been treated with suitable surfactants then n is obliged to lie perpen- dicular to the surface. Thus we can obtain between two glass slides a film of nematic that is almost a single crystal aligned either in a planar (nparallel) or a homeotropic (n perpendicular) sense. T.E. Faber and G.R. Luckhurst Now suppose that we subject such a film to a magnetic or electric* field. Because the susceptibility of a nematic is anisotropic the field adds a term of the form -&ll(n H)’-ixL(n XW2 to the free-energy density in the magnetic case and something similar in the electric case.Now the difference (xrl-xl),denoted by xa,is almost invariably positive for nematics. Hence in the presence of a magnetic field a nematic can lower its free-energy density by an amount $xaHZby allowing n to point along H rather than perpendicular to it and for intermediate orientations the nematic experiences a magnetic torque. This means that if we start with the planar nematic field shown in Figure 2 with n oriented initially along the x-axis and apply a Figure 2 Cross-section through a planar nematic film above the Freedericksz transition induced by the application of a magnetic field along the y-axis. Cylinders are drawn to indicate schematically the local orientation of the director. magnetic field along the y-axis the single-crystal configuration becomes unstable at a certain critical field Hc.Above this critical field it pays for n in the interior of the film to swing round into the y-direction even though this introduces some twist distortion in the neighbourhood of the surfaces. If the twist is confined to two thin layers of thickness 6 small compared with the thickness of the film d then the free energy per unit area should be something like Fo-haH2(d -6) + where Fois the free energy per unit area in the untwisted state. From this expression it is easy to see that above the transition we should expect 6 (K~/x~H’)’ (28) in equilibrium and that ~c (~2/xad~P (29) In a film of thickness 20 pm the critical field might be ca. 10kG. This type of transition is known as a Freedericksz transition.The reader must be left to imagine for himself the variety of different geometries in which similar transitions can be studied using planar or homeotropic films and parallel or perpendicular fields and to consult de Gennes’s book’ concerning the possibilities that exist for cholerestics where a large enough magnetic field is capable of unwinding the spiral. In many of these geometries of course the distortion of n near * A.c. electric fields with frequencies in the kHz range are to be preferred in this context. Low-frequency or d.c. fields may trigger off the electrohydrodynamic instabilities discussed in Section 6. Liquid Crystals 53 the surface of the film involves splay or bend rather than twist and H,therefore depends upon K1 or K3 rather than K2.When an electric field is employed rather than a magnetic one it is of course the anisotropy of the dielectric constant which matters and it should be noted that this quantity (E = ql-E~) is sometimes positive and sometimes negative. Most Freedericksz transitions are easy to detect (e.g.with a polarizing microscope) but the one illustrated in Figure 2 is not readily spotted,83 which is why K2is less often determined than K1 and K3. Recently however methods have been devised involving tilted fields,84 or crossed magnetic and electric fields applied simultane- ~usly,~~ whereby all three stiffness constants can be found. Other recent works6 concerns the dynamics of the transition which is of technical importance in relation to display devices.Under this heading may be included an experiment where the transition is stimulated by application of a continuously rotating magnetic field,87 from which y1can be deduced. Finally something very like a Freedericksz transition can be brought about in planar films of some nematics by twisting one surface with respect to the other in the absence of any field. When the twist exceeds a critical value that may be as high as 6~, n in the interior of the film suddenly tilts into the perpendicular configuration and the twist can then relax. A careful study of this effects8 suggests that very close to the nematic-isotropic transition 2K2+ (K2+K3)in these materials. Disc1inations.-Disclinations are line defects somewhat resembling the edge and screw dislocations that occur in solid lattices.In a nematic film that has recently been subjected to some mechanical disturbance they are normally to be seen in great abundance and they are indeed the threads or nema which give the nematic phase its name. A dislocation is defined of course by its Burgers vector. The equivalent quantity for a disclination is an angle namely the angle by which n would appear to a Maxwell demon to rotate during a journey round the disclination and back to his starting point. The disclination may be classified by an index s which is *i if the angle is &T,f1if the angle is *2~, and so on. In addition we need to distinguish two principal types of disclination depending upon whether the rotation occurs about an axis parallel to the disclination or perpendicular to it.Some authors refer to these loosely perhaps as screw and edge disclinations respectively. Figure 3 may help the reader to visualize some of the disclinations that arise most frequently in practice. It was originally thought that all disclinations had some sort of core in which perhaps the liquid was isotropic since the simple two-dimensional models illustrated in Figure 3 suggest singularities in div n or curl n on the axis. It is now recognized however that round disclinations of integral s n usually tilts into the third dimension and thereby adopts a configuration that is everywhere non-~ingular.~~-~~ The nature of the core in s = * disclinations remains an interesting question about which very little is known.83 R. Dreher Z. Naturforsch.,1974,29a 125. 84 H. J. Deuling M. Gabay E. Guyon and P. Pieranski J. Phys. (Paris),1975,36 689. 85 H. J. Deuling E. Guyon and P. Pieranski Solid State Comm. 1974 15 277. 86 D. W. Berreman Appl. Phys. Letters 1974 25 12. 87 F. Brochard L. Uger and R. B. Meyer J. Phys. (Paris) 1975,36 C1-209. 88 R. Turner and T. E. Faber Phys. Letters (A) 1974,49,423. 89 S. I. Anisimov and I. E. Dzyaloshinskii Souiet Phys. (J.E.T.P.),1973 36 774. 90 R. Turner Phil. Mag. 1974,30 13; 31 719. 91 C. Williams and Y. Bouligand J. Phys. (Paris) 1974,35 589. T.E. Faber and G.R. Luckhurst I I I I I 1 0 0 I Figure 3 Orientation of the director around some common disclinations. In each case the disclination itself is perpendicular to the plane of the diagram.(a) screw s = ++;(b) screw s = -3; (c) edge s =$; (d) screw s =+l;(e) screw s =+l. Continuum theory may be used to make predictions about the line tension of disclinations about the way they should interact with each other and with solid surfaces and about the direction and speed at which they should move when the nematic is sheared or subjected to a magnetic field. A start has been made on the task of verifying these predictions e~perimentally.~~,~~ To classify the line defects that may arise in cholesterics is a more complicated task. Because a cholerestic has a structure with layers in it dislocations can occur as well as disclinations similar to the dislocations in smectics that will be mentioned in Section 7.Their topology has been discussed in detail by B~uligand~~ and Ra~lt.~~ Flow Alignment.-If a nematic specimen containing no disclinations is undergoing steady planar shear flow as shown in Figure 4 in which direction will the director choose to set itself boundary conditions permitting? Presumably in some direction such that the viscous torque vanishes. One such direction is along the y-axis in Figure 4 but there is another possibility suggested by equation (24). Suppose we choose our z-axis to lie at an angle 8 to the flow velocity (see Figure 4). Then clearly ry= -my for 8 =0 and cy= +o for 8 = ~/2.In general ty= -my cos 28 which means that Gy vanishes when cos 28 =-Yl/Y2 = 1 -2h-771)/(772-771) (30) 92 J.A. Guerst A. M. J. Spruijt and C. J. Gerritsma Phys. Letters (A) 1973,43 536. 93 G. Malet J. Marignan and 0.Parodi J. Phys. (Paris),1975,36 L-317. 94 Y. Bouligand J. Phys. (Paris) 1974 35 215 959. 95 J. Rault Phil. Mag. 1974,30,621. Liquid Crystals Figure 4 Stable orientation of the director in a nematic undergoing uniform planar shear flow. Arrows indicate the flow velocity. It turns out on closer examination and has now been demonstrated experimen- tally,96 that it is the second of these possibilities which represents the stable configuration. The experimental results are rather well described by a microscopic theory due to For~ter,~~ which suggests -71/72 = 3p2/(p24-(31) where (Y depends upon the shape of the molecules. For molecules which can be treated as rigid ellipsoids with a length to breadth ratio of a/b (Y = (1+2b2/a2)/(1-b2/a2),so the theory turns out to imply that tan 8 = b/a for perfect alignment (p2= 1) 8+n/4 for poor alignment (F2+0) Thus in most nematics at most temperatures 8 is a modest angle a typical value being in the region of 15”.We shall discover in Section 7 however that in a nematic which is on the point of going smectic qlmay become very large and once it becomes larger than q4there ceases to be any real solution for equation (30).What is thought to happen in that event is that the director adopts a non-uniform configuration in which the angle 8 changes continuously from one shear plane to the next. The viscous torque is then balanced locally by a torque due to the bend and splay in the nematic.This ‘tumbling’ pattern of steady flow (not to be confused with the convective patterns to be discussed in Section 6) may have been observed recently by Cladis and T~rza.~* Ultrasonic Attenuation.-A theory for the attenuation of both longitudinal and transverse sound waves in nematics has been worked out and by comparing it with 96 P. Pieranski and E. Guyon Phys. Rev. (A),1974 9 404. 97 D. Forster Phys. Rev. Letters 1974 32 1161. yu P. E. Cladis and S. Torza Phys. Rev. Letters 1975 35 1283. T.E. Faber and G.R. Luckhurst experimental results it is possible to obtain values for the viscosity coefficient^.^^-^'^ The theory is not straightforward because the shear component of the flow pattern in the sound wave is liable to cause some realignment of n,quite apart from complica- tions associated with thermal conduction and bulk viscosity.When sound is propa- gated along the spiral axis of a cholesteric it may affect the pitch of the spiral in a periodic fashion and when the wavenumber of the sound wave coincides with qo there is a 'Brillouin zone' effectlo' and a discontinuous jump in the attenuation ~oefficient."~ Surface Ripples.-The ripples of short wavelength or Rayleigh waves which are excited thermally on the surface of any liquid and which can be studied by light-scattering techniques are of considerable interest in liquid crystals. A ripple is liable to introduce splay or bend (depending on the boundary conditions at the free surface) and potential energy may be stored in this distortion as well as in the more usual surface-tension term.For nematics the extra energy is likely to be negligible but it could be detectable in cholesterics and ~mectics.'~~~~~~ The most recent experimental work in this field is described in ref. 106. Rayleigh Scattering.-By Rayleigh scattering is meant the quasi-electric scattering of laser light that is such a marked feature of nematics and cholesterics -hence their milky appearance. It is not to be confused with inelastic Brillouin scattering. Both types of scattering are due to fluctuations in the body of the specimen and in both cases the fluctuations can be described theoretically in terms of a set of periodic modes thermally excited and with a mean-square amplitude proportional to temperature as required by the law of equipartition of energy.But the modes responsible for Brillouin scattering are the ordinary Debye modes of the system i.e. sound waves. The modes responsible for Rayleigh scattering are distortion modes in which the fluid remains almost stationary while it is the direction of n which varies in a periodic fashion. Because nematics and cholesterics are strongly birefringent any periodic variation in the direction of n is likely to mean a periodic variation in the refractive index seen by a plane-polarized light beam passing through the specimen and it is this that causes the strong scattering. By measuring the scattered intensity as a function of angle for various geometries one may determine the mean-square amplitude of each mode and by analysing the frequency spectrum of the scattered beam one may determine the frequency spectrum of the modes.One of the principal achievements of continuum theory has been the detailed explanation of data obtained from experiments of this kind (for a recent example see ref. 107). The modes are of course to be labelled by a wave-vector q and for each value of q there are two possible polarizations; the distortion is a mixture of splay and bend in one case and of twist and bend in the other (becoming pure splay or pure twist when 99 J. C. Bacri J. Phys. (Paris) 1974 35,601. loo K. Miyano and J. B. Ketterson Phys. Rev. (A) 1975,12,615. S. E. Munroe G. C. Wetsel M. R. Woodard and B. A. Lowry J. Chem.Phys. 1975,63 5139. lo* J. D.Parsons and C. F. Hayes Solid Stare Comm. 1974,15,429. lo3 I. Muscutariu S. Bhattacharya and J. B. Ketterson Phys. Rev. Letters 1975,35 1584. J. D. Parsons and C. F. Hayes Phys. Rev. (A) 1974 10 2341. lo5 A. Rapini Canad. J. Phys. 1975 53 968. Iw D.H.McQueen and V. K. Singhal J.Phys. (D), 1974,7 1983. lo' H.Fellner W. Franklin and S. Christensen Phys. Rev. (A) 1975,11 1440. Liquid Crystals q is perpendicular to n and pure bend when these two vectors are parallel). The mean-square amplitude predicted by the theory expressed as the mean-square angle through which n is rotated when the mode is thermally excited is where K is an appropriate combination of K1 K2,and K3. Naturally all three stiffness constants can be deduced from the scattering data if they are not already known.The modes are heavily overdamped by viscosity of course the rotational inertia of the molecules being negligible in virtually every context such as this. Their frequency spectra are therefore Lorentzian centred about o=0 and with a width of order Kq2/q (much less than the frequency qu of a Debye mode of the same wavelength). Scattering experiments can therefore yield values for the viscosity coefficients as well. Nuclear Magnetic Relaxation.-The distortion modes discussed briefly in the previ- ous section are also relevant to the theory of the anomalous relaxation times that are observed in n.m.r. experiments on protons in nematics and cholesterics these relaxation times Tl and T2,are generally a good deal shorter than for the same material in its isotropic phase and they become shorter still as the magnetic field in which the experiment is done is reduced.There may of course be a number of relaxation processes at work but the one that is normally blamed for the anomalies just described has to do with the dipole-dipole interaction between protons attached to adjacent carbon atoms in the same molecule. As the molecule librates and the angle between the line joining the two protons and the magnetic field changes the strength of this interaction varies. In the isotropic phase it varies rapidly with a coherence time that may be lO-'Os or less and its frequency spectrum is therefore a rather broad Lorentzian. Out of this frequency spectrum only the components in two narrow bands centred on oLand 2uL(where oLis the resonant Larmor frequency always much less than 10" s-') contribute to the spin relaxation rate l/Tl.The shorter the coherence time the less intensity there is in these bands and the slower the relaxation rate. We have the usual motional narrowing situation where Tl is long and where -because the Lorentzian spectrum has a flat top -it is independent of wLand therefore of the strength of field used. The situation is different for a nematic because the librations of the molecule are constrained. If we think first of the case of perfect alignment (p2= l),the only motions allowed to each molecule are rapid rotations about the local direction of n and the relatively slow co-operative rocking motions which correspond to excitation of distortion modes.This was first pointed out by Pincus who found that the rocking motions should contribute to the relaxation rate a term proportional to [see equation (32) and the remarks that follow it]. If the upper limit to this integral may be taken as infinity the result is proportional to @it. T.E. Faberand G. R. Luckhurst Later authors have tried to extend this theory to the case of imperfect alignment and have obtained a result of the form 1/T1=A+Bp22 (34) where the frequency-independent term A takes care of other relaxation processes. This has been fitted to some sets of experimental data with fair success but there are serious discrepancies. Something of a controversy has therefore blown up between those who argue that a Pincus-type theory modified perhaps by application of a cut-off to the integral in equation (33)at a finite wavenumber qC,lo8 is ~ufficient~~~*~~~ and those who believe that an altogether different frequency-dependent relaxation mechanism involving diffusion of the molecules is at work.'11 To the present author it seems clear that there must be a cut-off qc,and that its magnitude can be established by the same argument that is used to establish the cut-off in the Debye theory one cannot have more distortion modes than there are degrees of freedom in the system. But by specifying the amplitude and phase of every mode up to this cut-off one provides a complete description (within the framework of a continuum model) of the misalignment of the molecules and it is quite inappropriate to suppose that there is enough order left on the microscopic scale to justify the addition of a factor p2*to the Pincus formula.A more elaborate treatment is required. It leads to formulae for l/Tl and 1/T2which include terms proportional to and In oLas well as the conventional term proportional to wLf.It looks as though they may explain the data rather 6 Dynamic Instabilities Thermal Convection.-Readers may be familiar with the Benard convection cells which are liable to develop in an ordinary fluid when it is heated from below with the not-unrelated cells that may develop between two coaxial cylinders rotating at different angular velocities and with the phenomenon of turbulence in shear flow.These can all be classed as dynamic instability effects. Liquid crystals also become unstable in many circumstances and much ingenuity has been devoted to attempts to discover just when and how they do so. Some very curious results have been established. To take a particularly spectacular example it is now known that a nematic layer can be set into convection by heating it from the top. In a layer a few mm thick a temperature difference between top and bottom of only one degree may be sufficient. The effect was first predicted and observed for layers with homeotropic alignment (i.e. with n vertical) of any nematic material whose thermal conductivity is aniso- tropic in a positive sense (ie. KII>Kl). The explanation for it is indicated by Figure 5(a).In this Figure the rods which are used to indicate the local alignment of n show that this has acquired a small tilt in the central region initially as the result of a chance fluctuation.Because the thermal conductivity is anisotropic the heat current in this central region is not entirely vertical; it has a component from left to right. As a J. W. Doane C. E. Tarr and M. A. Nickerson Phys. Rev. Leners 1974,33,620. 109 S. D. Goren C. Korn and S. B. Marks Phys. Reu. Letters 1975 34 1212. 110 W. Wolfel F. Noack and M. Stohrer Z. Naturforsch. 1975,3Oa 437. R. Blinc M. Vilfan and V. Rutar Solid State Comm. 1975 17 171. 112 T. E. Faber to be published. Liquid Crystals result heat is being drained from the regions marked '-' in the figure and is accumulating in those marked '+'.The resultant density difference has started a circulation of the liquid as suggested by a dotted line. The flow associated with this circulation is exerting a clockwise torque on the director and is therefore enhancing the fluctuation with which the process began. Space does not permit further discussion of the thermal convection problem but at least three interesting papers on the subject describing results for cholesterics as well as nematics have been published in the past two years.'13-l15 hot cold Figure 5 Convection in nematic films. (a) Thermal convection induced by heating the top of a homeotropic film; + and -indicate regions which are hot and cold respectively. (b) EHD convection induced by an a.c.voltage across a planar film; + and -now indicate space charge in the fluid during the half cycle when the top of thefilm'is positive with respect to the bottom; the circulation originates from the force exerted on the space charge by the field. (c) Convection induced by uniform shearpow in a homeotropicfilm ; the top surface of the film is moving along the y-axis into the paper. (N.B.In this instance the co-ordinate system used is not the director frame.) 60 T.E. Faber and G.R. Luckhurst Electrohydrodynamic Convection.-Rolling convective cells of much the same appearance as the ones caused by temperature gradients may be set up in planar nematic and cholesteric films by the application of transverse electric fields either d.c.or audiofrequency a.c. for reasons that may be apparent from Figure 5(b). The effect is known as electrohydrodynamic or EHD convection and the cells are known as Williams domains. The a.c. effect is easier to make sense of because under d.c. conditions charge-injection from the electrodes may complicate the situation. With a.c. there is a threshold voltage of the order of 10V independent of film thickness which increases up to some critical frequency of the order of 100Hz. Above this frequency a different type of instability is found where the domains are narrower and the liquid within any one domain chooses to move up and down with the frequency of the field rather than roll continuously in the same sense. The threshold conditions for both types of EHD convection are now well under~tood."~~"~ They depend not only on the anisotropy of the electrical conduc- tivity cr but also on the sign and magnitude of E, and the theoretical predictions have been checked for a range of materials in which crll/crl and E take widely different values."*,' l9 Above the threshold however some curious and beautiful domain patterns have been observed especially with cholesterics,'20,'21 which are still not fully understood.Nor is it known why the Williams domains in a nematic film rock slowly to and fro when the voltage is above threshold or why the narrow domains in the high-frequency regime adopt a herringbone or chevron structure. Well above threshold moreover one sees a gradual transition to a generally turbid state of motion which has received little attention as yet though it is in this turbid state that dynamic-scattering display devices work.Convection Induced by Shear Flow.-Circulation patterns resembling Williams domains are also liable to arise when a nematic is sheared as has recently been demonstrated in some elegant experiments by Pieranski and Guy~n.~~,'~* In one of these experiments a planar nematic film between flat plates treated so as to favour alignment in the x direction is uniformly sheared by moving one plate in the y direction. Were it not for the boundary conditions the shear would make n swing round into the favoured orientation (see Section 5)at a small angle 8 to the y-axis in the yz plane and in fact n does start to swing round in the centre of the film; it is prevented from swinging very far however by the twist that develops in the structure [see Figure 5(c)].Now remember that planar shear in a nematic generates a sideways component in the shear stress if A is aligned more or less in the flow planes but at some angle to the flow velocity other than 0 or ?r/2 (see Section 4). In the present instance there are bound to be shear stresses t, acting in the x-direction. Because C. R. Carrigan and E. Guyon J. Phys. (Paris) 1975,36 L-145. I14 E. Dubois-Violette Solid State Comm. 1974 14 767. I15 J. D. Parsons J. Phys. (Paris) 1975,36 1363. I16 P. A. Penz Phys. Rev. (A),1975,10 1300. I. W. Smith Y. Galerne S. T. Lagerwall E. Dubois-Violette and G.Durand J. Phys. (Paris) 1975,36 C1-237.M. I. Barnik L. M. Blinov M. F. Grebenkin S. A. Pikin and V. G. Chigrinov Phys. Letters (A),1975 51 175. lI9 M. Goscianski and L. Uger J. Phys. (Paris) 1975; 36,C1-231. H. Amould-Netillard and F. Rondelez Mol. Cryst. Liquid Cryst.,1974,26 11. 121 M. de Zwart and Th.W. Lathouwers Phys. Letters (A) 1975,55 41. 122 E. Guyon and P. Pieranski J. Phys. (Paris) 1975,36,C1-203. Liquid Crystals the orientation of n depends on z these tranverse stresses also vary with z which means that a layer of the liquid of thickness Az experiences a finite force per unit area of (dt,,/dz)Az tending to move it sideways. The force acts in the +y direction in one half of the film and in the -y direction in the other half. The result is to set the nematic rolling about the direction of flow as suggested by the dotted circles in Figure 5(c).It is already clear that there are a great variety of flow convection patterns of this sort to be explored. It is also clear that as the shear rate is increased the rolling domains become unsteady as the Williams domains do in EHD convection and that turbulence ensues at Reynolds numbers far below those which mark the onset of turbulence in normal fluids. One may speculate that when a nematic fluid is forced at any substantial speed through a tube or past an obstacle turbulence is inevitable and that disclinations are created in abundance. The next challenge facing theoretical physicists or applied mathematicians in this area is surely to develop a statistical theory to describe the flow properties of a bulk nematic permeated by disclina- ti on^.'^^ The next challenge for the experimentalist is to devise experiments to prove the theory inadequate! 7 Smectics Continuum Theory of the Smectic A Phase.-Our picture of the smectic A phase in its undistorted state is of molecules arranged in regular layers of thickness t say each layer being perpendicular to the director n -which still describes as in nematics the axis with respect to which the molecules are preferentially aligned.It seems intuitively likely that (a) to tilt n away from the layer normal or (b) to change t without tilting n,will cost a lot in free energy and the continuum theory of smectics in its most primitive form is based on the assumption that both these operations are forbidden.Granted this assumption it follows that we may use the line integral t-’jIn *dl to measure the number of layers that separate B from A. Since the answer must be the same whatever route between these two points we choose it follows that the integral of (n -dl) round any closed contour must vanish and hence by Stokes’ theorem that curl n must vanish. Thus [see equation (16)] a’primitive smectic can sustain no twist or bend*. This is equivalent to saying that K2and K3are infinite in the smectic A phase. We are then left with the possibility of splay distortion and a distortion free- energy which depends only on (div n)’. Now imagine an initially flat layer rep- resented by the equation z =0 in the local director frame which is bent about the origin in some way until z = l(x y).Since n coincides everywhere with the layer normal it follows that in the neighbourhood of the origin n = -dl//ax and n = -dc/ay so that div n = -(d2[/dx2+a2[/dy2). Hence we can write the free-energy density of a primitive smectic in terms of the principal radii of curvature of the layers in the region of interest thus f =fo++&(R;+R ;I)’ (35) Left to themselves therefore the layers in a smetic prefer either to lie flat or to curve in opposite directions like a saddle so as to make R1= -R2. * If operation (a)is forbidden but not (b),then twist is forbidden but not bend. 62 T.E. Faber and G.R. Luckhurst The assumption that (a) or (b) are totally forbidden is rather a drastic one and many situations can be envisaged where the director has no option but to tilt a little or the layers to contract or expand given rigid boundary conditions.It can be shown however that in thermal equilibrium the resultant twist or bend is necessarily confined to regions near the surfaces of the sample or to the cores of disclinations and dislocations and that it should not infect the bulk. It is nevertheless desirable to add to equation (35) a term to allow for the finite compressibility of the layers of the form where t is the local layer thickness and to its equilibrium value. This determines for example the velocity of second sound in smectics a type of wave motion detectable by Brillouin scattering experiments in which t varies in a periodic fashion while the density stays almost constant.The theory of second sound in smectics has been discussed by Br0~hard.l~~ It is believed that permeation can occur in smectics i.e.that if a pressure gradient is established across the layers the liquid will flow through them at a steady rate described by equation (26). The permeation coefficient A must be much smaller than in cholesterics however and no experiment has yet been devised to measure it. The mechanism for the process is presumably akin to the mechanism of vacancy diffusion that in principle allows a crystal which is acted on by a pressure gradient to advance at one end and retreat at the other even when there is no motion of the lattice as a whole. Finally what can be said about the viscosity coefficients in the smectic A phase? The layers can slide easily enough over one another so presumably q2is no larger than in the nematic phase.Likewise q3 should be quite small; there is little to prevent the layers from shearing in their own plane though in this respect a smectic B phase could be very different. But the type of shear flow associated with q1can only take place if n tilts away from the layer normal. If K2and K3 are to be regarded as infinite in a smectic then ql and y1should be too. Pre-Smectic Behaviour in Nematics.-It is now known that if a nematic liquid is liable to transform into a smectic on cooling the transition is always heralded by a marked increase in just those coefficients which we expect to be infinite in smectics namely K2 K3 and yl.A dozen papers have been published since 1973,too many to be listed here reporting experiments in which such an increase has been observed.The subject has attracted much interest because it is one to which the Landau theory of phase transitions can be applied. This theory has already been shown to give a good account of pre-transitional effects in isotropic liquids just above an isotropic- nematic transition.. There have in fact been two varieties of Landau theory developed for the nematic-smectic transition. One due primarily to McMillan 124 is of the classical mean-field type. It predicts that K3 and y1should diverge as the temperature of the transition is approached like (T-T*)-$. The other due originally to de Gennes but carried further by Jahnig and Bro~hard,'~~ is based on an analogy with theories **3 F.Brochard Phys. Letters (A) 1974,49 315. 124 W. L. McMillan Phys. Rev. (A) 1974,9 1720. 125 F. Jahnig and F. Brochard J. Phys. (Paris) 1974,35 301. Liquid Crystals 63 established for superconductors and liquid helium. It predicts that K3should diverge like (T-T*)-3and y3like (T- T*)-3. Which of them agrees best with experiment is not yet clear. It is difficult for the experimentalist to determine an exponent unambiguously from his results because there is often a non-divergent but neverthe- less temperature-dependent term in the measured quantity to be allowed for and because he is never quite sure what to choose for T*. An added complication is that the exponents observed experimentally seem to depend very much on purity.'26 One matter for controversy is whether the transition from nematic to smectic A is second-order or weakly first-order if it is second-order then r* should coincide with the transition temperature T, but otherwise r* may be slightly below T,.The material most often studied is 4-cyanobenzylidene-4'-n-octyloxyanilineand for this at any rate the most direct evidence available from thermal measurement~'~' and density measurements,'28 indicates a weak first-order transition. That was a surprise to some until it was pointed that the twist and bend which are present due to thermal fluctuations in the nematic phase above the transition and which must be frozen out when the material turns smectic can play much the same role that a magnetic field does with a superconductor.By the same token L~bensky'~~ argues that the cholesteric-smectic transition should always be first-order because of the intrinsic twist in the cholesteric phase. Experiments on cholesteryl oleyl carbonate under pressure seem to falsify this prediction ho~ever.'~~,'~~ Perhaps the argument fails because the cholesteric spiral has unwound itself before the transition is reached. Certainly the pitch has been observed in two cases to Dislocations and Flow in Smectics.-It is much easier to persuade a smectic specimen to adopt what is virtually a single-crystal configuration than to do the same for a nematic. One has only to hold a bottle full of 4-cyanobenzylidene-4'-n-octyloxyaniline for example in a magnetic field and allow it to cool slowly through the nematic-smectic transition to obtain a sample in which the director is so well aligned that the milkiness which characterizes the nematic phase is almost com- pletely removed.If the bottle is now slightly tilted the sample will be seen to flow -a little reluctantly perhaps but enough to convince most observers that they are looking at a proper liquid. By what processes does the flow occur? There is of course no problem in understanding the type of flow in which the smectic layers slide over one another but suppose they lie at right angles to the direction of shear flow as shown in Figure 6(a),what then? The work of Williams and Klerna~~'~~ has provided most of the answers. To begin with (as the upper surface of the smectic film shown in Figure 6 is moved to the right) the layers may deform elastically as suggested by Figure 6(b);the thickness of each layer is now necessarily 126 P.E. Cladis Phys. Letters (A) 1974,48 179. 12' D. Dyarek J. Baturif-Rub~E and K. FranuloviE Phys. Rev. Letters 1974 33 1126. S. Torza and P. E. Cladis Phys. Rev. Letters 1974 32 1406. 129 T. C. Lubensky J. Phys. (Paris),1975,36 C1-151. I3O P. H. Keyes H. T. Weston W. J. Lin and W. B. Daniels J. Chem. Phys. 1975 63 5006. 131 R. Shashidhar and S. Chandrasekhar J. Phys. (Paris) 1975.36 C1-49. 132 C.-C. Huang R. S. Pindak and J. T. Ho Phys. Letters (A),1974 47 263. 133 R. S. Pindak C.-C. Huang and J. T. Ho Phys. Rev. Letters 1974 32 43. 134 C. E. Williams and M.KICman J. Phys. (Paris),1975,36 C1-315. T.E.Faber and G.R.Luckhurst Figure 6 Layer structures in a smectic specimen; the orientation of n is suggested by double arrows. (a) An undistorted film. (6) and (c) The same film after shear; edge dislocations have appeared in (c). (d) A bulk specimen initially oriented as in (a) which has been stretched horizontally; between the dotted lines there are focal conic walls. less than to in the interior of the film and n may not everywhere be normal to the layers so there is excess free energy stored in the layers. To release this free energy the smectic layers strive to return to toin thickness which is possible if and only if the number of layers in the specimen changes. Somehow by a process that must involve permeation but has not yet been studied adjacent layers must coalesce in the interior to leave the configuration sketched in Figure 6(c).There are now edge dislocations regularly spaced along the upper and lower surfaces of the film and running at right angles to the direction of flow. Williams and KlCman have shown (see also refs. 135-137) that once dislocations have been nucleated it is energeti- cally favourable for them to run together to form the type of linear defect that is illustrated in Figure 7 -equivalent to an edge dislocation of large Burgers vector but strictly speaking a pair of disclinations (s = &) Where the smectic layers are strongly curved in the neighbourhood of these defects div n is large. It therefore pays for the layers to buckle (to make R1=-R2).The defects curve into ellipses and a focal conic structure develops of the sort that has been understood for many years. The layers may now be almost parallel to the shear direction in the interior and further flow can proceed without impediment. 135 M. Kkman J. Phys. (Paris) 1974,35 595. 136 P. S. Pershan J. Appl. Phys. 1974,4S 1590. l3’ P. S. Pershan and J. Prost J. Appl. Phys. 1975 46 2343. Liquid Crystals Figure 7 The layer structure around two disclinations of opposite sign corresponding to an edge dislocation of Burgers vector 8t0. Related things probably happen when a smectic single crystal is stretched along its director a type of strain that can of course be regarded as a combination of two shear strains at 45" to the director.Very small extensions suffice to distort the layers in a periodic fashion and one can imagine this distortion developing into the structure sketched in Figure 6(d),with focal conic walls separating each domain. What happens when a smectic is squeezed along its director is a different question. Presumably the layers must get fewer in number as they grow in area and nucleation of edge dislocation loops must be required. The process has been discussed in a paper by members of the Orsay groups.138 This paper incidentally contains some intriguing speculations about flow phenomena dominated by permeation which might be observable in smectic systems where nucleation of dislocations is very difficult. The speculations have yet to be confirmed experimentally.13* Orsay Group on Liquid Crystals J. Phys. (Paris) 1975,36 C1-305. 139 J. Nehring and A. Saupe J. Chem. Phys. 1971,54,337. 140 B.I. Halperin and T. C. Lubensky Solid State Comrn. 1974,14 997. 141 P.G.de Gennes J. Phys. (Paris),1974,35 L-217.

ISSN:0308-6003    

DOI:10.1039/PR9757200031

出版商:RSC    

年代:1975

数据来源: RSC

摘要:

4 The Effect of a Magnetic Field on Chemical Reactions By P. W. ATKINS and T. P. LAMBERT Physical Chemistry Laboratory South Parks Road Oxford 1 Historical Background The ways in which magnetic fields can affect chemical reactions have long been the subject of investigation but only recently with the theoretical insight given by the interpretation of chemically induced magnetic polarization,’ has significant progress been made. The early work which because of the frequency of rebuttal and retraction is very hard to disentangle and even then to rely on has been summarized in a number of Mare recently the subject has been analysed by Buchachenko in his book9 on chemically induced polarization and in a brief simplified artic1e,lo but most of the work we describe has been reported only in primary journals.The magnetic field effects that have been reported (if not substan- tiated) range from the physiological7 to the purely chemical. This review ignores the former but includes in the scope of the latter the effect of magnetic fields on the fluorescence intensity of various types of fluid sample. We shall therefore devote some attention to electrochemiluminescence phenomena but refer elsewhere’ to reviews that assess the field in detail and relate it to its solid-state analogues. The turmoil of the early literature is illustrated very.wel1 by the summary given in the review by Figueras Roca.’ For instance in 1908 Ro~enthal’~ reported an effect of a magnetic field on the hydrolysis of starch but this was rapidly refuted by Cegiel~ky’~ and Heimrod.” Selwood6 came to the conclusion that the catalytic activity of various ions in solutions which according to several reports was modified by the application of a modest was more likely to be due to the local agitation of the ions by the field than by any direct modification of their activity.More 1 ‘Chemically Induced Magnetic Polarization’ ed. A. R. Lepley and G. L. Closs Wiley London 1973. * S. S. Bhatnagar and K. N. Mathur ‘Physical Principles and Applications of Magnetochemistry’ Macmillan London 1935. S. S. Bhatnagar K. N. Mathur and R. N. Kapur Phil. Mag. 1929,8,457. E. Miller Natunviss. 1937 25 545. R. Delhez Rev. Quest. Sci. 1957 18 176; Bull. Soc. my. Sci. Litge 1957,27 161. P. W. Selwood Chem. Rev.1946,38,41. ‘Biological Effects of Magnetic Fields’ ed. M. Barnothy Plenum New York 1964. F. Figueras Roca Ann. Chim. 1967 2 255. A. L. Buchachenko ‘Chemical Polarization of Electrons and Nuclei’ Nauka Moscow 1974. lo P. W. Atkins Chem. inBritah 1976 12 214. l1 P. Avakian and R. E. Merrifield Mol. Cryst. 1968,5 37. l2 P. Avakian Pure Appl. Chem. 1974,37 1. l3 I. Rosenthal Sitzber. Akad. Wiss. Berlin 1908 1 20. l4 R. Cegielsky Ber. Phys. Ger. 1908 15 566. l5 G. W. Heimrod 2.Elektrochem. 1914,19,812. l6 S. N. Basmanova Trudy Inst. prikad. Khim. i Electrokim. Akad. Nauk Gruz. S.S.R. 1962 3 117. A. Krause F. Domka and B. Marcieniec Monatsh. 1966,97 99. 67 68 P.W.Atkins and T.P. Lambert recently' the reported magnetic inhibition of the polymerization of styrene'' appears to be ~ontradicted,'~*~~ although a patent based on a 5% increase in the rate of polymerization of propene21 appears to survive.It is not in the least unlikely that commercially sensitive work continues in this field. Figueras Roca's review' is an excellent source of this type of information for it concentrates on the magnetic influence on catalytic activity. Probably the most poignant summary of the early days of this type of work is provided by Mulay and Mulay,22 who make the following remark on the electrochemical studies carried out over more than a decade by Sh~hukarev~~ at the beginning of this century '. . . .after finding that the phenomena of the action of a magnetic field on chemical reactions [were] more complicated than he had originally suspected and that they were too complex for individual observa- tion he decided to give up his study of the phenomena and to retract his former statements.' The reason for the hope and scepticism of the early years lay in two rules advanced by Bhatnagar et aL,2,3one for predicting the effect of a magnetic field on the equilibrium position of a chemical reaction and one for predicting the effect on its rate.The former although not phrased as such was essentially the recognition of the possibility that the magnetic susceptibility of the reactants and the products might differ and therefore that the standard molar reaction Gibbs function AGE would depend on the strength of the applied field B. If the molar susceptibilities differ by Ax this contributes iAxB2 to AGE,24and in principle leads to some concomitant change in the equilibrium constant through AGZ = -RTIn K.It is not difficult however to dismiss this effect as negligible. Even for a generous difference of susceptibilities it is hard for to exceed ca. 1mJ mol-' in magnetic fields available in the laboratory and the resulting shift in the equilibrium is nugatory. The early explanation of the kinetic effect (if by then it had been observed) is also untenable on the grounds of the weakness of the interaction. It was suppo~ed~*~ that the field favoured some molecular orientations thereby altering the effectiveness of collisions. What experimental results were available at the time and which appeared to support the rules seem to be accounted for either by agitation of the mixture or by some photochemical activity.' There is one further type of magnetic activity which might play a role but it remains to be substantiated by reliable experiments and we shall pay no more attention to it than it receives in this paragraph.It is known that the presence of a magnetic field can influence the band structure of conductors and semiconductors (e.g.the de Haas-van Alphen effect) and some authors have reported changes in the work function of metals by as much as 0.1V in quite low fields25 (can that really be so?),and significant changes in their If these results are depend- H. Schmidt G. Muhr and H. Marek 2. Elektrochem. 1945,51 37. l9 J. Breitenbach and F. Richter Monatsh.1949,80 315. 20 S. Collins and W. A. Bryce J. Chem. Phys. 1950,18 1297. 21 W. B. Reeves U.S.P.2 663 394 1953 (Chem. Abs. l954,48,434OE). z2 I. L. Mulay and L. N. Mulay ref. 7 p. 146. 23 A. N. Shchukarev,J. Russ. Phys. Chem. Soc. 1915-1926. 24 S. Kaneko J. Soc. Chem. Znd. Japan Suppl. 1931,34,133. 25 R. Bedos Compt. rend. 1964,259 1695. 26 E.E. Kolosov and P. V. Sharavski,Fiz.Doklady Nauchn. Konf. Leningrad,lngh. Stroit Inst. Leningrad Sb. 1961,31. z7 E. Weisshaar and H. Welker 2. Nuturforsch.,1958,8a 681. The Effect of a Magnetic Field on Chemical Reactions 69 able they certainly suggest that heterogeneous catalytic activity might be changed by a magnetic field and Figueras Roca' has drawn attention to reports in the literature on the rate of oxidation of iron at 580 "Cand the inhibition of the oxidation of formic acid in the presence of a magnetite-Cu2+ mixture.Nevertheless the actual proof of magneto-catalytic activity remains extraordinarily difficult on account of the irre- producibility of samples and the elimination of extraneous complications. Although these effects are of considerable technological importance we shall devote this review to the effects that have been fully substantiated experimentally and which can be accounted for on the basis of moderately reliable theories. Some magnetic field effects have been known and established for many years. Probably the most famous is the interconversion of ortho- and para-hydrogen this was studied originally by Farkas and Sachsse28 and explained by Wigner.29 The basic idea underlying the explanation is closely related to that behind the modern theories of magnetic field effects and a brief account will set the stage.The interconversion of ortho- and para-hydrogen depends on the relative realign- ment of the two proton spins in the molecule. In ortho-hydrogen the proton spins are mutally parallel and the total nuclear spin is unity this is the nuclear triplet state. In para-hydrogen the nuclear spins are antiparallel and the total nuclear spin is zero this is the nuclear singlet. As a result of the requirements of the Pauli exclusion principle3' only the odd rotational energy levels may be populated if the nuclear spins are arranged as the triplet (we shall call this 'triplet phased') and only the even levels if the nuclei are singlet phased.The rotational energy levels are sufficiently different in energy for the nuclear statistical effects to have significant ther- modynamic consequences and the rate of interconversion is so low that ortho- and para-hydrogen constitute two distinct species. In order for an ortho molecule to be converted into a para molecule (or vice versa) the nuclear spins must be realigned. One way of doing this is to dissociate a collection of molecules and then to allow random recombination. This is the dissociative mechanism and is not the one expected to be influenced by a magnetic field (but see below p. 72). Another way of bringing about relative realignment is to subject the molecule to a magnetic field that is inhomogeneous on the scale of the molecule.In that case the two protons will be in different magnetic fields and will precess at different rates. Precession at different rates means relative reorientation of the two nuclear spins and so ortho switches into para and vice versa. One way of generating a sufficiently inhomogeneous magnetic field is to allow collisions between hydrogen molecules and either paramagnetic specie^^^*^'-^^ (ions or neutral molecules) or magnetic surfaces.34 Theory suggests that the rate of interconversion should be proportional to the square of the magnetic moment of the paramagnetic species and this accords with experiment. The interconversion process has recently been the 28 L. Farkas and H. Sachsse 2. phys. Chem.,1933,23B 1 19.29 E. P. Wigner Z. phys. Chem. 1933,23B 28. 30 P. W. Atkins 'Quanta a Handbook of Concepts' Clarendon Press Oxford 1974. 3' H. Sachsse Z. phys. Chem. 1934,24B 429. 32 W. K. Wilmarth and M.K. Baes J. Amer. Ckm. Soc.,1953,75 2237. 33 G.-M. Schwab J. Voitlander and V. Penka Z. phys. Chem. 1963,36,378. 34 D. D. Eley and D. Shooter J. Catalysis 1'963 2 268. 70 P.W.Atkinsand T.P. Lambert subject of renewed aftenti~n~~-~~ and detailed theories of the process in the gas and liquid phases are now available. One chemical application has been to the estimation of the size of hydration spheres of ions in solution.36 Many important chemical reactions involve two electron spins either paired (as in a singlet) or parallel (as in a triplet).The significance of the ortho-para interconver- sion work should now be clear local inhomogeneous magnetic fields can interchange singlet and triplet electron spin phasings as well as nuclear spin phasings and can thereby affect the course of the reaction. Since the electron spins have much stronger magnetic moments than the protons we can expect the difference in precession frequency to be greater for a given magnetic field difference. There is every hope therefore that the local field inhomogeneities can modify the course of reactions and this is confirmed by experiment. The remainder of this review explores this idea for radical reactions and fluorescent processes involving excited triplet states of molecules. We shall see that the various types of spin rephasing process are the central reasons for the response of chemical reactions to magnetic fields.2 The General Theoretical Background Modern theories of the effects of magnetic are based on two effects and both are related to the interconversion of spin multiplets. The problem can be illustrated by considering the simple case of the homolysis of a bond in the molecule A-B to give two doublet radicals 'A and 2B.We suppose first that the homolysis occurs from a singlet state of AB and that the bond cleavage occurs without alteration of the overall spin of the molecule. This means that the two spins of the bond remain antiparallel even though they are now confined to spatially separated radicals. In other words homolysis leads to a singlet radical pair 1{2A-.-2B}.If the homolysis proceeds through a triplet state of AB (as it might in a photochemical cleavage) the same argument implies the formation of a radical pair in an overall triplet spin state 3{2A***2B}. The components of the radical pair diffuse apart but they have a significant probability of re-encountering each other. If they re- encounter they may form a bond this is geminate recombination and the product is called the cage product. The bond will form however only if the radicals have singlet-phased electron spins when they re-encounter if the electrons are triplet phased (parallel) the bond will not form and the encounter will be unproductive. If a mechanism exists for destroying the initial singlet phasing of the radical pair it follows that the probability of geminate recombination is reduced.In that case the proportion of cage products declines relative to the escape products. If the magnetic field can influence the rate at which the singlet character of the radical pair is lost it will affect the proportions of cage and escape products. The loss of singlet phasing implies a gain in overall triplet phasing. The process by which this comes about is the same as in the ortho-para interconversion process 35 S. E. Nielsen and J. P. Dahler J. Chem. Plays. 1967,46 732. 36 P. W. Atkins and M. J. Clugston Mol. Phys. 1974,27 1619. 37 E.-A. Reinsch Mol. Phys. 1974,28,683. 38 R. Kaptein Thesis Leyden 1971. 39 R. Lawler and G. T. Evans Ind. Chem. Belges 1971,36 1087. 40 R.Sagdeev Yu. N. Molia K. M. Salikhov T. V. Leshina M. A. Kamha and S. M. Shein Org. Magn. Resonance 1973,5,603. 41 A. L. Buchachenko and Sh. A. Markarian React. Kinetics Catalysis Letters. 1974 1 157. The Effect of a Magnetic Field on Chemical Reactions (which was for nuclei -now we deal with electrons) and is illustrated in Figure 1.The singlet state of a pair of electrons can be depicted as in Figure l(u):we see that not only does the state consist of an a and a p spin but their relative azimuth is such that the resultant spin angular momentum is zero.3o On the other hand a triplet state of two electron spins can be constructed in three ways. One uses an equal mixture of a and /3 spins but their relative azimuth is such as to give a resultant spin angular momentum of unity (actually d2R),Figure l(6).The difference between the arrange- ments in Figures l(a) and l(b) illustrates what is meant by the difference of the ‘phasing’ of the a and /.? spin orientations in the singlet and triplet states.There are twoother ways of obtaining a total spin of unity. One is to use two a spins this gives a state with S = 1 M = +1 (Figure l(c)),which is denoted T+l.The other uses twop spins this gives S = 1 M = -1 (Figure l(d)),a state denoted T-l. S Figure 1 A singlet-phased pair of spins can be induced to switch into a triplet if their individual precession frequencies differ. For example if the Larmor precession frequencyof spin A in Figure l(a)differs from that of spin B they will not maintain their initial singlet phasing but will evolve into the phasing characteristic of To.If the (circular) frequencies differ by A@,complete conversion will occur in a time T/Ao.A difference of Larmor precession frequencies about the z-direction depends on the two spins experiencing different fields along z. It is also quite possible for the spins to experience different local fields pointing along the x-and y-directions. Such fields exert torques about their directions (about the x and y axes) and tend to twist aspins into p and p spins into a.It follows that a singlet state may have its (Y spin twisted into p (if the field is sufficiently different at the twoelectrons) and soevolve into T-l or its p spin twisted into a,which takes it into T+l.In summary therefore we see that local magnetic fields different at the two electrons of a radical pair can induce singlet- triplet interconversions and the triplet state generated (its M value) depends on the orientation of the local field inhomogeneity.72 P. W.Atkins and T.P. Lambert This qualitative discussion can be made more quantitative as follows. If the energy of spin A is determined by a termf,*s in a Hamiltonian and that of spin B by a term fB*sB the total Hamiltonian can be written H=fA'SA+fB.SB =g(fA+fB)'(SA+sB) +i(fA -fB)'(sA -sB) (1) For our purposes the important term is the second. This is antisymmetric in the spins and so it contributes to matrix elements (qH(S)because the singlet is antisymmetric in the spins the triplet is symmetric and the whole matrix element must be symmetric if it is not to be zero.The term proportional to S -sBvanishes if fA =fB and this is the basis of the earlier assertion that the individual Larmor precession frequencies (which are proportional to fA and fB) must differ if singlet-triplet transitions are to occur. In order to identify what contributions to the Hamiltonian may induce singlet- triplet rephasing we have to find interactions of the form f-s that are different for the two radicals. One candidate is the Zeeman interaction. If the g-values of the radicals are gA and gB their interaction with the external field B is and the antisymmetric part of this is proportional to (gA-gB)B. Its magnitude increases with B and so the rate of singlet-triplet conversion should increase as the applied field is increased.Notice that this interaction has operators relating to only the z-direction and in terms of the qualitative picture of the process corresponds to a relative rephasing of the two spins around the z-direction. In other words the g-factor differences allow S-To crossing but not S-T,,. (This restriction can be lifted in some special cases.42) In a field of 1 T (10kG) taking gA -gB -loA3(which is a reasonable choice for a range of organic radicals) the time for complete rephasing is about 3 X lo-* s. We shall return to explore the significance of this remark. Another candidate for the spin-rephasing interaction is the hyperfine interaction of each electron with the magnetic nuclei in the radicals. The antisymmetric part of the interaction aAIA*sA+aBIB*sBis H(-) =+(~AIA-MB) * (sA -sB) =;(a,+ ~B)(IA-IB) '(~A-sg) +b(aA-aB)(rA+~g) * (sA-s~) (3) and so this interaction can operate even if the radicals are identical (a = aB)but their nuclear spin orientations differ (I # IB).The rate of interconversion under the influence of H(-)depends on the nuclear spin states of the radicals because of the involvement of nuclear ,spin operators in H(+ and this is the reason why chemical reactions are a potential technique for the separation of isotopes on the basis of their spins rather than their masses.The hyperfine Hamiltonian has components of magnetic field in all three directions (because the nuclear moments can take up various orientations) and so it can induce transitions between the electronic singlet and all three substates of the triplet.At first sight however does not appear to depend on the strength of an external magnetic field. This is indeed true but the effectiveness of H(-)in causing S-T interconversions does depend on the applied field and this introduces one of the most important sources of a magnetic field effect. 42 P. W. Atkins A. J. Dobbs and K. A. McLauchlan Chem Phys. Letters 1973 22 209. The Effect of a Magnetic Field on Chemical Reactions 73 The explanation of the role of the external field in governing the effectiveness of the perturbation H(-)is as follows. When a perturbation acts its success in causing a transition depends on the ratio of its strength to the energy separating the states it is tending to This can be illustrated explicitly by a very simple calculation.Suppose a perturbation of strength k V acts on a system which at t = 0 is known to be in a state $l; then the probability that it will be in another state q52 (the only other state available) at a later time t is p(t) = (2V/u> sin2 Ut (4) where U2= A2+ 4 v‘,A being the separation in energy of q1and q2.If A is very small 2 V/ U -1 and the probability oscillates between 0 and 1 the latter implying total transfer to q2.If A is large in the sense V<cA the value of P(t)does not rise above ca. 2V/A which is small and implies that the perturbation is unable to induce a significant transition into the other state. In the present case the To,T,l substates of the triplet do not lie at the same energy when a magnetic field is present and so the efficiency with which can induce transitions from S to To,T, will be different in each case.The simplest situation that arises is when the singlet and triplet lie at the same mean energy (which is the case if exchange interactions between the components of the radical pair are very small this is often the case for radicals that are significantly separated in the solution but not when they are actually in contact). In this case and in the absence of an external field the hyperfine interaction can induce transitions from S to To,T, at about the same rate (so long as it has non-vanishing matrix elements) because the triplet substates lie at the same energy. When a field is applied the T- substate drops to an energy A -gp,B below To(and therefore below S which remains degenerate with To),and T, rises to an energy A above To.Therefore although the S-To crossing may continue as before the extent of the S -T, crossing is decreased by a factor of ca. 2 V/A (where V-El(-)in this case). Since V-0.1 mTand A -1T it follows that the crossings to and from T, are effectively quenched in a high field. This discussion may be summarized as follows. The proportion of cage and escape products in a radical reaction in solution depends on the rate at which the spins of the radical pair change their relative orientations. The rate of S-T, crossing is decreased on the application of a magnetic field and in regions of high field only the S-To crossing plays a significant role.All three crossings may be induced by hyperfine interactions. The S-To crossing may also be induced by a g-value difference in the two radicals of the pair the strength of this interaction is proportional to the magnetic field and the rate of S-To crossing is increased by a field. Being in an overall singlet is a necessary but not a sufficient criterion for recombination the two radicals of the pair must also be in contact (in some sense). Therefore the probability that the pair is in a singlet at a time t has to be multiplied by the probability that at that time it has a spatial conformation corresponding to If the latter probability is denoted G(t) the total recombination probability depends on the value of the integral gdtG(t)P,(t) P,(t) being the probability of being in a singlet at time t.For simple three-dimensional translational diffusion G(t)a t-9 exp (-t/~),and the integral can be evaluated; this gives the characteristic $ and thence (q/7‘)j behaviour of such diffusional processes and explicit expressions have been reported in several 43 P. W. Atkins ‘Molecular Quantum Mechanics’ Clarendon Press Oxford 1970. 74 P. W.Atkins and T.P. Lambert 3 Experimental Examples Substantial experimental evidence is a~ailable~~.~~ for magnetic field effects along the lines of the theory described so far. For instance Sagdeev et uL40have examined the dependence on a magnetic field ofthe proportions of cage and escape products in the liquid-phase reaction between various fluorinated benzyl chlorides and n-butyl- lithium.The cage product formed from benzyl+ butyl radicals is phenylpentane and the escape products include diphenylethane. The reaction involves a singlet precursor and so we expect the proportion of cage products to increase as the field increases (S-Tinhibited). The report indicates that for benzyl chloride itself the ratio of phenylpentane to diphenylethane does indeed increase and changes from 4.7 f 0.3 to 5.6*0.5 when the applied field is changed from 50 pT (0.5 G) to 1.5 T (15 kG). The same authors also studied the effect of temperature and solvent on the field dependence. Typical results are those relating to pentafluorobenzyl chloride and n- butyl-lithium. The ratio of products rose from 4.5f0.5 to 6.2 h 0.3 when the solvent was n-hexane at 70 "C and the field was increased from 50 pT to 2.5 T (25 kG) an increase of cu.37% but it changed from 4.0h0.3 to 6.1*0.5 in cyclohexane at 70 "C,an increase of ca. 54% (probably the record so far). In cyclohexane at 80 "C the ratio changed from 3.7 f0.3 to 5.3 f0.5. The magnetic field is expected to have a smaller effect at high solvent mobilities because the diffusional trajectory terminates more quickly than at low mobilities and the rephasing effects are less pronounced because they have less time to operate. Another class of examples is pravided by the work of Gupta and Hamm~nd,~~ who reported some intriguing results on the effect of a magnetic field on the photosen- sitized isomerization of piperylene (penta- 1,3-diene) and stilbene (1,2-dip hen yle t hene).They found that the photos ta tionar y state concentrations changed when a 0.9 T field was applied and that the effect depended on the nature of both the substrate and the photosensitizer. For instance the ratio of translcis photostationary state concentrations of the isomeric piperylenes was 1.08 (ben-zophenone as sensitizer) 1.13 (m-methoxyacetophenone) 1.08 (fluorenone) 1.16 (2-acetonaphthone) 1.07 (Michler's ketone) but 0.91 for stilbene (with ben- zophenone) and 0.95 (2-acetonaphthone). They pointed out a number of features of their results which would need to be accommodated by any theory. In the first place they considered that some kind of relaxation time must be involved but that this could not be radiative decay of sensitizer triplets because the substrate concentra- tions are much greater than are needed to capture virtually all the excited triplets and an effect on the sensitizer alone would be unlikely to influence the different isomers to different extents.They concluded that the explanation probably lay in the ability of the magnetic field to influence the relative rates of radiationless decay of triplet exciplexes. An explanation of these experiments which conforms to the suggestions outlined here has been ~uggested.~~ It was proposed that the triplet exciplex should be regarded as having the nature of a radical ion pair. In that case the application of the magnetic field can stimulate an intersystem crossing because the two components of the exciplex have different g-values and therefore different precession frequencies in 44 A.Gupta and G. S. Hammond J. Chem. Phys. 1972,57 1789. 45 P. W. Atkins Chem. Phys. Letters 1973 18 355. The Eflect of a Magnetic Field on Chemical Reactions 75 the same applied field. Furthermore the rate of deactivation of the exciplex (the rate at which it is switched from triplet to singlet) will depend not only on the field strength but also on the nature of the components as the experimental results require. The theory was expressed in simple quantitative and speculations about the g-value differences and the unperturbed lifetimes of the exciplex showed that it could account for the order of magnitude of the effect observed. The crucial difficulty of the theory is the magnitude of the exchange interaction between the two components of the exciplex the theory would fail if it were much larger than the Zeeman interaction energies.Therefore if the theory is valid it points to a structure of the exciplex that has the two components separated by at least one solvent molecule and possibly more. There is clearly room for a closer analysis of the effect and note should be taken of a brief comment46 which suggests that triplet quenching by other radicals produced in the reaction might be another explanation. (Why that should be field dependent we shall explain in Section 4.)If however the orbiting model of the exciplex is tenable the development of the theoretical description could take the form of structuring the relative translational motion of the two components to take into account their mutual Coulomb interaction and some features of their exchange interaction (as has been done for some aspects of chemically induced magnetic p~larization~~).Some crude potential energy surfaces are available4' but it is most doubtful that they would be applicable to the present problem. There has been some peculation^^ about the possibility that a high-frequency magnetic field can play a special role in influencing the rate of recombination of radicals but there appears to be no experimental support for the suggestion. Strong static fields at low temperatures can play a role and the recombination of hydrogen atoms has been The authors showed that the rate of recombination was inhibited by a strong field and accounted for it on the basis that the atoms all tended to adopt /3 as their spin state and the parallel electrons were unable to form bonds.A similar type of problem has been studied in connection with ion recombination processe~,~ as is described below. 1-54 When solutions of aromatic compounds such as naphthalene and anthracene in aliphatic solvents are exposed to high-energy radiation excited states of molecules are produced as a result of the ion-recombination process. At high solute concentra- tions the main reactions are s + S++e-S++M + S+M+ M++M-+ M*+M 46 H. van Willigen Chem. Phys. Letters 1975 33 540. 47 J. B. Pedersen and J. H. Freed J. Chem. Phys. 1963,58,2746. 48 J.N. Murrell and J. Tanaka MoZ. Phys. 1964,7 363. 49 S. I. Kubarev and E. A. Pshenichnov Chem. Phys. Letters 1974,28 66. J. T. Jones and M. H. Johnson U.S. Gout. Res. Reports 1959,32 110. 51 B. Brocklehurst Nature 1969,221 921; Chem. Phys. 1973 2,6. 52 B. Brocklehurst Chem. Phys. Letters 1974 28 357. 52aB. Brocklehurst Chem Phys. Letters 1974 29,635. 53 B. Brocklehurst R. S. Dixon E. M. Gardy V. J. Lopata M. J. Quinn A. Singh and F. P. Sargent Chem. Phys. Letters 1974,28,361. R. S. Dixon E M. Gardy V. J. Lopata and F. P. Sargent Chem. Phys. Letters 1975,30 463. P. W.Atkins and T.P. Lambert where M is the solute and S the solvent. The question that arises is the multiplicity of the excited solute molecule M*. Both singlets and triplets may be formed and Brocklehurst has predicted,” that the proportion of excited states may be altered by the application of a magnetic field.The argument is as follows. If the encounters between the reacting species M’ M- were random then a triplet singlet ratio of 3 would be expected since of the four arrangements of the two electrons three are triplet and one is singlet. Generally however the encounters are not random the low relative permittivity of the solvent in these systems means that in only a few cases do the ions escape from their mutual Coulombic interaction and the majority undergo geminate recombination. In such a situation if the recombination is very fast the triplet singlet ratio will be zero because the initial state is a singlet and there is insufficient time for significant rephasing.On the other hand if the recombination is slow the arguments of Section 2 lead one to expect total relaxation and therefore approach to a triplet singlet ratio of 3. The relative recombination and rephasing times can be discussed in a variety of ways and the theories outlined earlier are applicable. It is helpful for instance to be precise about the meaning of ‘S~OW’ and ’fast’ recombination times. If the time for recombination is TR,by fast recombination is meant TR<<T, T2,where T and T2are the longitudinal and transverse electron- spin relaxation times (the former corresponding to S-T, rephasings and the latter to S-To).Clearly slow recombination is when TR >> T, T2.We can also distinguish an intermediate case when T2<<TR<< T,,and in this case a triplet :singlet ratio of unity is expected because of the S-To equilibration.In summary TR<<T, T2should give a ratio of 0; T, T2<< TRa ratio of 3; and T2<<TR<<T a ratio of 1. In zero magnetic field there is no distinction between T and T2(all three triplet levels are mutually degenerate and degenerate with the singlet at significant separations) but in high fields the situation changes to the intermediate case. (This is the same argument as used in Section 2 but expressed differently.) Therefore we expect the triplet singlet ratio to drop from 3 to 1as high fields are reached. On these arguments and with some consideration of the mobility of the substrates in the solvents Brocklehur~t~’ proposed that magnetic field effects should be observable in solvents with viscosities in the range 1-10 poise.It was found53 that the intensity of emission from the singlet excited state of fluorene in the solvent squalane was enhanced by a magnetic field in accord with the theory. Subsequent experiment~~~ examined the continuous y-irradiation of fluorene. In squalane solutions application of a magnetic field again significantly enhanced the emission from singlet excited fluorene. In cyclohexane solutions a magnetic field effect was also observed but it was much less marked as expected on the basis that cyclohexane is much less viscous than squalane. No magnetic field effect was observed when benzene was the solvent and it is believed that excited states of fluorene are not formed by ion recombination in this case.Brocklehurst has pointed out” that an implicit assumption in this work is that the rates of formation of the singlet state and the triplet substates are all equal. Since Franck-Condon factors and densities of states in the singlet and triplet manifolds are unlikely to be the same this is unlikely to be true and the pure triplet singlet ratios of 0,3 or 1are unlikely to be obtained even when the conditions predict them. There is reason to hope however that deviations from them are likely to be and magnetic field effects should be an acceptable technique of studying the recombina- tion process (and perhaps even of elucidating that very point). The Effectof a Magnetic Field on Chemical Reactions 77 On to the basic account of atom and ion recombination may be grafted a number of significant extra features.In the first place Brocklehurst has e~amined’~*’~~ the problem from the point of view of coherent rephasing of the electron spins rather than stochastic relaxation. If the general ideas of Section 2 are borne in mind it is easy to understand that the S-To rephasing can be brought about by the nuclear hyperfine interaction with the two electron spins. If only one magnetic nucleus were involved the overall state would oscillate harmonically between singlet and triplet in accord with equation (4). In the present case there are many magnetic nuclei in each species of the pair and so the hyperfine interactions have to be summed over.This summation has the practical effect of making the singlet probability decay rather than oscillate (unless the coupling constants happen to be in simple ratios as in perylene52T52a or the magnetic nuclei are sparse) on the time-scale of interest (generally less than the Poincare cycle time). The singlet probability is therefore predicted to fall to an average value (at slightly greater than $) and then to remain constant. In zero field however the rate of decay of the singlet under the coherent but multiple hyperfine perturbation should be greater than in the high-field case for reasons that we have already explained. A quantitative calculation is difficult because the angular momenta are orientated at random but it has been done on the basis of a number of approximation^.^^ The overall result is again that decay rather than oscillation occurs but in this case the singlet population falls to a value of slightly less than $.The difference between the two results one at high field the other at low is the basis of the experimental results for the magnetic field effect on singlet recombination yields.54 The other feature to graft on to this work is the problem of the allowed multiplicities when a number of ions or neutral molecules can take part in a recombination (as in a spur). On the basis that the spins do not relax or rephase there have been two conflicting sets of expressions quoted for the probability that the recombination product is a singlet (or a A recent analysis of the problem5’ shows it to be more complex than either of the earlier results had suggested but the singlet recombination probabilities can be calculated for any number of participants.It is now also possible to account for spin rephasing within the spur and the consequent effects of a magnetic field but that work remains incomplete. There are three examples of the effects of magnetic fields on fluorescence from the molecules in the gas phase but as these lie at the limits of the boundaries of the present report we shall deal with them only briefly. The quenching of the fluores- cence of iodine ~apour’~,’~ is a result of a magnetic-field-induced dissociation of an excited state and arises from the ability of the applied field to mix the 0; state with the unbound 0 state.Similarly the fluorescence from nitrogen(1v) oxide (NO,) is quenched by a magnetic field.60 In that case the field appears to operate in the collisional quenching step NO;(B)+NO2 + 2N02 rate =B2[NO2][N0;] 55 J. L. Magee and J.-T. J. Huang J. Phys. Chem. 1972,76 3801. 56 B. Brocklehurst and T. Higashimura J. Phys. Chem. 1974,78,309. 57 P. W. Atkins and T. P. Lambert in press. 58 E. 0.Degenkolb J. I. Steinfeld E. Wasserman and W. Klemperer J. Chem. Phys. 1969,51,615. 59 L. A. Turner 2.phys. 1930,65 464. 6o R. Solarz S. Butler and D. H. Levy J. Chem.Phys. 1973 58 5172. 78 P. W.Atkins and T.P.Lambert and the Lorentzian field dependence of the overall fluorescence is reproduced by the inclusion of this rate step.It has been suggested that the excited states of NO are heavily perturbed by vibrational levels of the ground 2A1state and magnetic mixing of the quenched state with the ground state followed by radiationless collisional relaxation down the vibrational states of 'A1 would account for the observations.60 Collisions play an essential role because of the low density of states in the small molecules. Matsuzaki and Nagakura61a have reported equally interesting results on the gas-phase fluorescence from carbon disulphide. They recorded the time-dependence of the fluorescent emission from gaseous CS excited by a nitrogen gas laser and observed three band systems of which one was due to the 'Azexcited state. Particular attention was paid to the 'A2(0,5,0)vibronic state and its lifetime and integrated emission intensity were measured for applied magnetic fields of up to 1.5T.They found that both the lifetime and the integrated intensity are reduced by half when the field is ca. 1.3 T; this indicates that the non-radiative processes are enhanced by the magnetic field. They also found that the extrapolated collision-free lifetimes shortened with increasing field strength but the collisional quenching constant remains unchanged within the limits of experimental error. At low magnetic fields (<70 mT 700 G) the opposite effects were observed. Once again the effects can be accounted for in terms of magnetic-field-induced mixing the influence on a singlet molecule being possible because of the large spin-orbit coupling present.Very recent work61b reports virtually the same behaviour for glyoxal. 4 EIectrochemiluminescence Electrochemiluminescence has turned out to be rich in examples of magnetic field effects. The processes that occur are closely related to exciton mechanisms in the solid state and the way that these involve applied magnetic fields has received considerable attention and has been largely elucidated through the work of Mer- rifield,11,62,63 Frankevit~h,~~~~ and others.12 We shall give a brief description of the solid-state processes and then pass on to concentrate on theories and experimental results for fluids. The theory advanced by Merrifield62 and Johnson and Mer~-ifield~~ runs as follows. In a pair of colliding triplets there are nine possible spin states and these will occur with equal probability when the temperature is high.The rate of production of each of the nine composite states is therefore $kln2,where n is the concentration of triplet excitons. There are two possible outcomes of the collision one is scattering the rate being k-l and for which there are no collision rules. The other is annihilation with a rate that may be written k,S where S =I(Slt,hl)l is the modulus of the amplitude of the singlet component in the state labelled 1. It follows that the probability of annihilation from the Z'th composite exciton state is k,S:/[k_ +k2S:].The annihila- tion rate constant k is then the product of the collision rate constant and the total O1 A. Matsuzaki and S. Nagakura (a) Chem.Letters 1974,7,675;(b)Chem. Phys. Letters 1976,37,204. 62 R. E. Merrifield J. Chem. Phys. 1968,48 4318. O3 R. C. Johnson and R. E. Merrifield Phys. Rev. 1970 B1 896. 64 B. M. Rusin and E. L. Frankevitch Phys. Status Solidi 1969,33 885. 65 E. L. Frankevitch B. M. Rurnyantsev and B. I. Lesin Optics and Spectroscopy 1974,37,376. 66 E. L. Frankevitch and B. M. Rusin J.E.T.P. 1972,63,2015. The Efect of a Magnetic Field on Chemical Reactions annihilation probability 9 k =$kl 1 k2S:/[k_,+k2S?] 1=1 The qualitative manner in which k depends on the pair spin states can be seen by considering the two limiting cases. In one limit all nine states have equal singlet character; in the other only one state is a singlet. If the annihilation rates are denoted k(9) and k(l) respectively their ratio is given by the last equation together with the requirement that S? must sum to unity as This indicates that k is greater the more uniformly the singlet character is distributed over the nine pair states.The next problem therefore is the assessment of this distribution and its dependence on an applied field. The spin-Hamiltonian for a triplet exciton consists of two terms one is the Zeeman interaction the other the spin-spin interaction. In the zero-field case the spin vectors of each triplet are aligned along one of the principal directions of the zero-field splitting tensor and we speak of the T, Ty,and T states depending on the orientation of the spin with respect to these axes. The averall singlet state of two triplets can be constructed by analogy with the scalar r2=x2+y2+z2 and is (1/./3){~T,T,)+~T,Ty)+(T~T,)}.Thus at zero field three of the pair states have a singlet component (by inversion of this state). As the field is turned on the zero-field states are contaminated because the Zeeman interaction provides an alternative and increasingly important quantization axis. It follows that the zero-field states begin to mix. This disperses the singlet character over more states and so according to the above discussion the annihilation rate constant should increase in a magnetic field. This behaviour is confined to low magnetic fields where the spin-spin interaction although suffering competition from the Zeeman interaction is dominant.At high magnetic fields the Zeeman interaction is dominant and in the limit of infinite field strength the spins are quantized exactly along its direction. Three of the joint triplet states 10,0),1+1,-l) 1-1 +1) (labelled now as IMs,M>) have a total projection of 0 and so may contribute to a singlet. Nevertheless we have to take not? of the relative phasing of the If 1)states (just as in the case of the construction of singlets and triplets out of spin-; components Figure 1) and only the in-phase combination 1+1 -l)+ 1-1 +1) can contribute to the singlet. (This can be seen explicitly by examining the vector coupling coefficients.) It follows that in the high-field case there are only two states with singlet character and therefore a smaller annihilation rate constant than at zero field.The general dependence of the annihilation rate constant is therefore as fol-low~.~~~~~ At low fields it should increuse with increasing field pass through a maximum and then decrease at high fields to a value lower than the zero-field value. Detailed analysis of the degeneracies and level crossings involved also leads to the conclusion that the high-field annihilation rate constant should be anisotropic with minima in field directions for which the energies of the 10,O) and l*l 71) states are the same. These conclusions conform to experiment11T12 in the solid state and are a basis for explanations of processes in fluids. 80 P.W.Atkins and T.P. Lambert The Johnson-Merrifield scheme has been adapted for fluid solutions by averaging the interactions over a random but stationary en~emble.~' This is obviously a restricted view of the actual dynamical situation and the model based on mobile species has been examined by a different technique.68 The sequence of events treated by Atkins and Evans6' is as follows The triplet species diffuse from their points of generation by charge transfer from pairs of radical ions and encounter each other at some point in the fluid medium.Since each triplet has unit spin the total spin angular momentum of the colliding pair is 0 1,or 2 (giving respectively an overall singlet triplet or quintet). The overall singlet pair may pass on to give fluorescence because the energy transfer step is permitted by the overall spin. This is because the energy transfer takes 3A* +3A* to 'A* +'A and the latter can be only an overall singlet; therefore on the basis of the conservation of spin angular momentum during the energy exchange only the 1{3A* +3A*} can give rise to 'A* +'A.Neither the overall triplet 3{3A* +3A*} nor the overall quintet 5{3A* + * 3A } can redistribute their energy to give '{'A" +'A} without violating spin conser- vation and so pairs in these overall states survive the encounter. There is in fact some possibility that the overall triplets and quintets do change into an overall singlet during the encounter. This can come about because of the different spin-spin dipolar interactions within each triplet (different not because the triplets are not identical but because they are in general at different orientations to the applied field and compete with its quantization direction).The overall quintet can switch into the singlet (the triplet-singlet switch is forbidden by symmetry for this mechanism -the spin-spin interaction is of second rank) and do so with a rate ps(t) =&(1 i-c)D2I,'dt(1+2 cos wt+2 cos 2ot)exp (-t/~& (7) where o =p,B/A is the Larmor frequency of the spins D the spin-spin interaction within each triplet and 7R the rotational correlation time of the pair (c = 1 if they rotate as though stuck together; c =0 if the two triplets rotate independently). The cos ot and cos 2wt terms represent the mixing of the singlet with the M =*1 and M,=*2 states of the quintet and we. see that they contribute less to the integral at high fields (because they oscillate to positive and negative values) than at low fields.This is the effect of the removal of degeneracy already described in the earlier sections. At short times the integrand varies as 1-02t2 and so the crossing rate is inhibited by a field. The expression for P,(t) shows that the magnetic field effect vanishes when the triplets rotate rapidly (because the exponential term quenches the integrand if TR is short) the physical reason for this being that the spin-spin interaction averages to zero and ceases to compete effectively with the Zeeman interaction. The difficulty with this mechanism is that the two colliding triplets might remain together for only a short time and the interconversion rate be so slow that only an insignificant amount switches into the singlet.What we seek is a way of permitting a long interval during which the spins are able to rephase significantly. The same requirement is needed in chemically induced magnetic polarization experiments,' 67 P. Avakian R. P. Groff R. E. Kellogg R. E. Merrifield and A. Suna 'Organic Scintillators and Liquid Scintillation Counting' Academic Press New York 1971,499. 68 P. W. Atkins and G. T. Evans Mol. Phys. 1975,29,921. The Effect of a Magnetic Field on Chemical Reactions 81 where the spin rephasing is allowed to take place during a diffusional trajectory which has a high probability of bringing the two components back to a re-encounter configuration. We therefore consider the following sequence of events.68 During the initial encounter the two triplets may fluoresce if they are relatively singlet phased but will survive as individual triplets if they are overall triplet or quintet.The encounter pair breaks up and the two triplets drift apart. Although separate they still possess their initial phasing but over the whole sample there is a depletion of overall singlet-phased pairs. During the translational diffusion that takes them apart the two triplets rotate. This rotation is a very efficient cause of spin relaxation on account of the strong anisotropic spin-spin dipolar interactions within each triplet. (A few trriplet spin-relaxation times in fluids have been and found to lie in the range 2-20 ns.) The triplet spins relax independently.When therefore their diffusive motion brings them back into contact (or whatever a ‘re-encounter’ involves) there is some probability that they have replenished the depleted overall singlet phasing and have regained more or less the thermal equilibrium distribution which had been distorted by the first encounter. If overall singlet phasing has been replenished contact between the two species may lead to energy transfer and thence to fluorescence. The point to emphasize at this stage is that the observed fluorescence is the totality of emission from the first encounter and the re-encounter and the latter can contribute more effectively if spin relaxation has occurred before it takes place. The magnetic field plays its role during the diffusional excursion.Efficient spin relaxation depends not only on the strength of the perturbative coupling (for example the anisotropy of the dipolar interactions and in particular the spin-spin interaction) but also on the rate at which they are modulated by molecular motion (e.g. molecular rotation). Relaxation between different m states is most efficient when the relaxing perturbations are modulated at a rate comparable to the Larmor frequency. If the Larmor frequency is changed by an alteration of the strength of the applied field the rela,xation rates will change. This is the core of the magnetic field effect on this type of fluorescent reaction the field changes the relaxation rates and so the extent of replenishment of the singlet is changed. This change affects the probability of energy transfer on a re-encounter and so the fluorescence intensity depends on the applied magnetic field.These ideas have been expressed quantitatively68 and the following is a brief outline of the calculation. In the beginning there are two independent triplets with their spins at thermal equilibrium. The state of each is described by the thermal equilibrium density matrix a*.Immediately before the first encounter both triplets are described in this way and the overall state at that instant is p(0J =a*(A)g*(B). Immediately after the collision the overall density matrix is p(0,). This differs from p(0-) in as much as some of the overall singlets have been eliminated. If Psis an operator that selects singlets and A is a parameter that measures the effectiveness with which an overall singlet undergoes energy transfer we can write the final state of the triplet pair just as it breaks up as p(0,) =(1-APs)p(O-).From this point the states of the two triplets evolve independently and each one obeys the equation of motion a(t) =i[u(t),W+ Ru(t) (8) 69 P. W. Atkins A. J. Dobbs and K. A. McLauchlan Chem. Phys. Letters 1974,29 616. P. W.Atkinsand T.P. Lambert 2is the Hamiltonian representing the effect of the applied field and R is an operator that takes relaxation into account. This equation can be solved for each triplet using as initial conditions the joint singlet-depleted density matrix p(0,). In this way it is possible to calculate the probability Ps(t) that the pair of triplets is in an overall singlet at some t>0+.In order to contribute to the fluorescence the two triplets must re-encounter each other at some stage. The probability that they do so G(t),can be evaluated on the basis of a diffusion equation and the total contribution to the fluorescence is determined by the product of probabilities P,(t)G(t) integrated over all possible excursion times. Explicit expressions are given in the original paper,68 and in the limit of rapid molecular motion in a strong magnetic field one finds I(B)/I(O)= 1 -0.61(-)Dd(+,s) A 1-A (9) where D is the spin-spin interaction (zero-field splitting) rR the rotational correla- tion time and r the translational diffusion correlation time. This is the asymptotic behaviour and it predicts that the intensity falls off with increasing field as observed.The role of stable doublet quenchers is easy to explain qualitatively but much more difficult to deal with quantitatively. Once again the solid-state mechanisms are a guide to those operating in the fluid if the rudiutionless quenching by the doublets is inhibited by the application of a magnetic field the fluorescence radiation will be enhanced. We shall describe the qualitative model but not go as far as describing the actual calculation68 (which follows much the same scheme as that outlined above). Consider the collision of a doublet (S= 5) and an excited triplet (S= 1).Their overall spin may be either doublet (S= +) or quartet (S =;). If it is the former radiationless energy reorganization from 2{3A*+ 'Q} to 2{1A+ 'Q} may occur with- out change of total spin angular momentum but 4{3A*+ 'Q} may not so reorganize.When the initial encounter pair breaks up it is depleted in overall doublet. The two components diffuse apart but have a significant re-encounter probability. During the diffusion spin relaxation replenishes the overall doublet and so on re-encounter the quenching is more likely to occur than if no relaxation had occurred. The spin relaxation depends on the Larmor frequencies involved (this time of both doublet and triplet species) and so it depends on the strength of the applied field. It turns out that the significant relaxation is inhibited by the applied field and so the radiationless quenching is also inhibited. That is just the situation necessary in order to lead to enhancement of the fluorescence because more triplets survive doublet encounters and live long enough to meet triplet partners.These triplet encounters are also field dependent (as described earlier) but the observed increase in fluorescence indicates that the quenching responds to the magnetic field in the dominant way. The calculational d@culty in the quantitative formulation of the model is the need to treat it as at least a three-particle collision (doublet triplet and another triplet). Nevertheless the overall effect has been estimated and the observed increase in fluorescence intensity with field strength can be accounted for.68 There are of course many loose ends in both calculations and there is room for a much more detailed analysis of the quenching sequence.Furthermore the descrip- tion of the processes going on during the encounters themselves remain to be unified into a single coherent calculation rather than remaining in their present disjointed The Effect of a Magnetic Field on Chemical Reactions 83 form. When this is analysed in more detail the type of argument used by Perisamy and Santhanam7' on the Marcus description of the electron-transfer step may play a role in the overall scheme. The type of experimental information available can be illustrated by the following selection of papers. For instance Faulkner and Bard71 examined the magnetic field dependence of the chemiluminescence from electron transfer reactions involving the ion-radicals of a variety of aromatic hydrocarbons.In particular they studied the reaction of the radical cation formed from NNN'N'-tetramethyl-p-phenylenediamine (Wursters' Blue WB henceforth) with the anion radicals of anthracene and 9,lO-diphenylanthracene (DPA). From the standard electrode potentials it is clear that the energy available from the ion-radical annihilation involving WB' and a hydrocarbon radical anion is insufficient to produce the hydrocarbon in its first excited singlet (such systems are called 'energy deficient'). This excited state is attainable from the reaction between DPA' and DPA- (an 'energy sufficient' system). In a magnetic field the authors found that for solutions containing WB the emission intensity from the excited singlet increases with applied field (by ca.20% in 0.6 T for anthracene-WB) but in the solution containing only DPA the field had no effect on the emission intensity. Faulkner and Bard draw two conclusions from these first that paramagnetic species are involved in at least one rate-determining step for light emission from the energy-deficient system and that the rate of that step is field- dependent and secondly either that no paramagnetic species are involved in the rate-determining steps for fluorescence in the case of DPA alone or that paramagne- tic species are involved but that behaviour is unaffected by the field. Furthermore unless one supposes that the magnetic field can influence the diffusional characteris- tics (e.g.the diffusion constants) the rate of a diffusion-controlled reaction cannot be altered by the field in the manner observed and the rate-determining steps for the energy-deficient system studied are probably not diffusion controlled.The DPA energy-sufficient system however may or may not have diff usion-controlled rate- determining steps. The results for the energy-deficient system were rationalized by supposing that if the hydrocarbon triplet is formed in the radical annihilation step then triplet-triplet annihilation leads to the first singlet-excited state by the energy-exchange process discussed in the earlier part of this section. In contrast the reaction involving annihilation of DPA' and DPA- is believed to result in the direct formation of an excited singlet DPA molecule.The magnetic field dependence occurs as we have already described and the increase in fluorescence intensity is compatible with the inhibition of radiationless triplet quenching by the presence of stable doublets (WB'). It has also been pointed out in support of this mechanism7' that Parker et aZ.72have provided substantial evidence to support the view that triplet-triplet annihilation is not generally a diff usion-controlled process for aromatic hydrocar- bons and might occur by means of a resonance energy transfer mechanism that can operate over a great distance. 'O N. Perisamy and K. S. V. Santhanam Chem. Phys. Letters in press. 71 L. R. Faulkner and A. J. Bard J. Amer. Chem. Soc. 1969,91 209. 72 C. A. Parker in 'The Triplet State' ed. A B. Zahlan Cambridge University Press 1967.84 P.W.Atkins and T.P. Lambert This early work was followed by a series of studies on related systems. In the case of anthracene in dimethylformamide (DMF)73 for example it was observed that the fluorescence intensity decreased with increasing field and was proportional to the square of the incident excitation intensity. The intensity of delayed fluorescence under steady-state illumination is expected to obey the expre~sion’~ I = $dfka(1a+t7)* (10) where +fis the fluorescence efficiency k the annihilation rate constant I the rate of light absorption 4 the triplet formation efficiency and r is the triplet lifetime. The three quantities 4f,+t I,,it was argued,73 are unlikely to be field-dependent because they are properties of diamagnetic materials (although the peculiar properties of carbon disulphide referred to above indicate that that may be a false argument in special circumstances).In support of this view Faulkner and Bard draw attention to solid-state results which show that magnetic fields do not affect the intensity of the prompt fluorescence from crystalline anthracene. The concentration dependence of the fluorescence and its magnetic field dependence allows this argument to be taken further. In solutions containing an anthracene concentration of > ca. mol dm-3 anthracene triplet lifetimes are shortened drastically by self- or impurity-quenching. At lower concentrations the lifetime is virtually constant. Any field dependence of the lifetimes would probably be concentration dependent in the range where the quenching term begins to be significant in determining the value of 7.Thus the field effect that arose from this source would be expected to be concentration dependent in this range. Since the experimental results show that the field variation is indepen- dent of concentration in the range where the lifetime begins to change markedly it is most unlikely that the lifetime r is the field-dependent quantity. Faulkner and Bard also go on to eliminate 4t as the field-dependent quantity.73 They examined the fluorescence of a solution of 5 X lo-’ mol dm-3 anthracene plus 7 x mol dm-3 phenanthrene in DMF and found that the field dependence of the anthracene-delayed fluorescence was the same as in the absence of the phenanthrene sensitizer.In this case the anthracene triplet is populated by energy transfer rather than intersystem crossing from anthracene singlet and therefore +t cannot be the field-dependent factor. The elimination of 7 4f,I, and 9 as the field-sensitive quantities leaves only k, and the theoretical reasons for its dependence have already been explained. The role of doublet species in modifying the field dependence of the delayed fluorescence has also been elucidated74 and as indicated previously centres on the suggestion made by Hoytink7’ that ion radicals might be effective triplet quenchers in fluid solution. Faulkner and Bard74 measured the intensities and lifetimes of the delayed fluorescence from anthracene and WE3 perchlorate in methylene chloride solution.The effectiveness of WB’ as a quencher of anthracene triplets was indicated by the shortening of their lifetimes. For example a 1.8X mol dm-3 WB perchlo-rate and 8x lo-’ mol dm-3 anthracene solution showed a delayed fluorescence lifetime of 1.4ms in contrast to a lifetime of 6.4 ms in the absence of WB’. The quenching rate constant was ca. 2 X lo9dm3 mol-‘ s-’ which is comparable to the triplet-triplet energy-transfer rate constant in solvents of similar viscosity. As for the 73 L. R. Faulkner and A. J. Bard J. Amer. Chem. Soc. 1969,91,6495. 74 L. R.Faulkner and A. J. Bard J. Amer. Chem. Soc. 1969,91,6497. 75 G. J. Hoytink Discuss. Faraday Soc. 1968,45 14. The Efect of a Magnetic Field on Chemical Reactions 85 magnetic field effect it was found that the fluorescence intensity was enhanced (by ca.2% in 0.8 T) as would be expected on the basis of the theory already explained. The longer lifetimes that result from this effect dominate the opposing effect on the annihilation rate. The results also suggest that the quenching rate is not entirely diffusion contr~lled,~~ and the authors suggest a tentative upper limit of 2.6~ 10" dm-3 mol-' s-' on the rate constant. Magnetic field effects on the fluorescence intensity from anthracene DPA rubrene 1,3,4,8-tetraphenylpyrene (TPP) and fluoranthrene have also been reported.76 Enhancements of the emission to the extent of up to 27% were noted for energy-deficient oxidations of anthracene DPA rubrene and TPP anions by WB+ for the energy-deficient oxidation of fluoranthrene anion by the radical cation of 10-methylphenothiazine and for the energy-deficient reduction of the rubrene radical cation by the p-benzoquinone radical ani~n.'~ In contrast (but in conformity with theory) no field effect was observed for the fluorescence arising from the energy-sufficient DPA'/DPA- reaction.The field enhanced the luminescence from the reaction between the rubrene anion and cation radicals but had no effect on the TPP anion and cation reaction. All these results are compatible with the inhibition of the triplet-triplet step by a magnetic field the inhibition of the triplet-doublet radiationless quenching step and the absence of involvement of triplet species in energy-sufficient systems.The rubrene'/rubrene- and the TPP'/TPP- systems are marginal cases and it was suggested76 that the former gives rise to luminescence predominantly uia the triplet mechanism but the latter is essentially energy- sufficient and forms the emitting state directly. The paper includes a useful list of reaction enthalpies and spectroscopic data and rationalizes the magnetic field effects by reference to the Johnson-Merrifield solid-state mechanism. Oxygen is an obvious candidate for the examination of magnetic field effects on triplet species and its role in the production of delayed fluorescence from anthracene and pyrene in fluid solution has been studied.78 The triplet quenching can be represented by the simple scheme 3~+3~2 + 'M+~O~ and its rate should be field dependent.The authors observed that the usual decrease of fluorescence intensity with applied field was modified when oxygen was admitted to the solution. At first no delayed fluorescence signal was detected but after several minutes its intensity increased to a measurable level. The same kind of time- dependent increase has also been noticed in solid samples and is probably caused by oxygen depletion arising from the formation of a transannular peroxide. The delayed fluorescence signals from both anthracene and pyrene increased with increasing field indicating a magnetic inhibition of the quenching reaction just as in the case of radical ion quenching. On the other hand in acetonitrile solution no change in the fluorescence was observed for either species although oxygen quenching was shown to be occurring by the decrease in lifetime of the aromatic triplet.Further papers in this series deal with a series of related observations. Onen 76 L. R. Faulkner H. Tachikawa and A. J. Bard J. Amer. Chem. Soc. 1972,94,691. 77 H. Tachikawa and A. J. Bard Chem. Phys. Letters 1974,26 10. 78 H. Tachikawa and A. J. Bard J. Amer. Chem. Soc. 1973,95 1672. 79 C. P. Kesthelyi N. E. Tokel-Takvoryan H. Tachikawa and A. J. Bard Chem. Phys. Letters 1973,23 219. 86 P. W.Atkins and T.P. Lambert examines the effect of the supporting electrolyte concentration and the magnetic field effect on a 9,lO-dimethylanthracene (DMA) -tri-p-tolylamine (TPTA) system dissolved in tetrahydrofuran (THF).The magnetic field enhanced the fluorescence for all concentrations of the supporting electrolyte tetra-n-butylammonium perchlo- rate (TBAP) and extrapolation to zero TBAP concentration gave results in accord with those of Weller and Zachariasse." Although quenching of intermediates by TBAP ions might be important the authors believe that the effect on the reaction enthalpy as the concentration of TBAP decreases is probably more important.This increase in AH can be traced either to a decrease in the extent of formation of the ion pairs (TBAP)'. -.(DMA)- or (TPTA)'. * .ClO (formation of ion pairs would facili- tate the oxidation of TPTA and the reduction of DMA and hence reduce AG* for the ion annihilation reaction) or to a change in the nature of the solvent system with an effective increase in relative permittivity at higher TBAP concentrations.Thus at low TBAP the reaction is strongly energy deficient and proceeds through the magnetically sensitive triplet annihilation route but at high TBAP concentrations the reaction may proceed through the direct production of singlets and be less magnetically sensitive. The effect of solvents has been by measuring the emission intensity of rubrene ions generated electrochemically. The intensity increases with applied field and the effect is strongest when the solvent is DMF and then progressively weaker along the sequence acetonitrile benzonitrile THF. The results were interpreted" in terms of a model in which the electron-transfer route produces both singlet and triplet excited states of rubrene with the triplets being quenched by radical ions or oxygen The authors examined the energetics of the reaction on the basis of Marcus's theory of electron transfer and suggest the possibility that two triplet states may be formed in the electron-transfer step.Wyrsch and Labhart,82 Tachikawa and Bard,83 and van Willigen46 have all examined the delayed fluorescence from monomer and excimer species. Wyrsch and Labhart investigated 172-benzanthracene in ethanol van Willigen investigated pyrene in 3-methylpentane and in ethanol and Tachikawa and Bard pyrene and 172-benzanthracene the pyrene-TMPD system and the 9-methylanthracene- TPTA system. Wyrsch and Labhart observed different magnetic quenching behaviour of the monomer and excimer emissions and concluded that there is no common triplet annihilation process generating the two types of fluorescent species.On the other hand van Willigen observed the same behaviour when 3-methylpentane was the solvent. van Willigen ascribes his results to a scheme proposed by Stevenss4 which involves the reaction sequence -B 'M*+ 'M* '&*+ 'M0 'Mg+'Mo+ 'D* '&*+'M -D 'D* A. Weller and K. Zachariasse Chem. Phys. Letters 1971 10 424 590. H. Tachikawa and A. J. Bard Chem. Phys. Letters 1974,26 246. 82 D. Wyrsch and H. Labhart Chem. Phys. Letters. 1971,8 217. 83 H. Tachikawa and A. J. Bard Gem. Phys. Letters. 1974,26 568. 84 B. Stevens Chem. Phys. Letters. 1969,3 233. The Eflect of a Magnetic Field on Chemical Reactions 87 The first step is common to excimer ('D*)and excited monomer ('M,*) formation; it is a spin-selective step and therefore the magnetic field ought to affect the two fluorescent intensities equally.He attempts to account for the discrepancy between the two sets of results on two grounds. First that the mechanism depends on the species involved. Second and much more speculatively that the exciplex formation step (the second of the three steps in the scheme above) depends on the relative orientations of the species orientations that are influenced by the magnetic field. It is hard to believe that this could be the explanation even at low temperatures where rotational correlation times are quite long but it is at least an interesting suggestion.Tachikawa and Bard observe that the magnetic field effects on the excimer and monomer delayed fluorescence intensities are essentially the same for pyrene in cyclohexane and for 1,2-benzanthracene in cyclohexane and also conclude that there must be a common precursor in these systems. van Willigen46 has also reported a peculiar field dependence when ethanol is used as solvent. At low temperatures the monomer and dimer fluorescences increase with magnetic field. He suggests that the reason might lie in the formation of doublet radicals in the system and that these act as triplet quenchers (the remark on p. 75 arose from this suggestion). Magnetic field effects have also been observed in tetracene-TMPD," this energy- deficient system showing an intensity increase of up to 19.5% in fields of up to 0.75 T and the results were interpreted as evidence for the production of triplet tetracene by charge transfer between tetracene radical anion and TMPD cation.The delayed fluorescence of carbazole in DMF with t-butylammonium iodide as supporting electrolyte shows a sharp increase in intensity up to ca. 0.4 T and this is followed by a gradual decline.86 Perisamy and SanthanamS7 have also examined the elec- trochemiluminescence of mixed systems in which phenanthrene and perdeuteriated phenanthrene provide the radical anion and propose a triplet-triplet annihilation step on the basis of the magnetic field effect observed. A magnetic field effect-on an energy-sufficient system has also been reported." The authors studied the rubrene tetracene phenanthrene and cation-anion systems and found an increase in fluorescent intensity of the order of 10% in 1T.The overall scheme can be summarized by the sequence 3M*+3M* -+'M*+M; 'M* + M+hv t (c) 'M*-3M*; 'M* -+ M+hv Step (b) is the conventional magnetic-field-sensitive step but triplet species gener- ated by the singlet step (c)may also take part in it and give rise to an overall magnetic field dependence especially if step (c)is itself magnetic field dependent. Thus if a magnetic field can inhibit the crossing involved in step (c)more of the initial singlets can produce fluorescence. H. Tachikawa and A. J. Bard Chem. Phys. Letters. 1973 19 287. 86 K. S. V. Santhanam Canad. J. Chem. 1971,49,3577. 87 N.Perisamy and K. S. V. Santhanam Canad. J. Chem. 1975,53 76. 88 N. Perisamy S. J. Shah and K. S. V. Santhanarn,J. Chem. Phys. 1973,58 821. 88 P. W.Atkins and T.P. Lambert Finally we report an interesting application of this type of magnetic field effect on a solid polymer (which is as close to true solids as we allow ourselves to come in this review). Avakian et uLg9have found that the rate of fusion of triplet exciton pairs in polymers such as poly(vinylnaphtha1ene) can be changed by a magnetic field of a few kilogauss. The delayed fluorescence following exciton generation was found to increase monotonically to 3% above the zero-field value at 0.09 T (900 G),and then to drop back to its zero-field value at 0.4 T. The emission continues to decrease to an asymptotic value ca.2% below the zero-field value when the field reaches 1.O T. This behaviour contrasts with the observation of a similar phenomenon in naphthalene at 77 K where the low-field peak (of 6%)occurs at 0.06 T the zero-field value is passed at 0.17 T and the saturation value (of -12%) is attained above 1.0 T. The authors explain these observations in terms of the local orientations of the naphthalene units along the polymer chain and reach the significant conclusion that they are spread over a range of orientations such that S:-S; averages to zero but that the normal axes of each naphthalene unit remain approximately aligned. This magnetic field dependence therefore constitutes a novel method for investigating the conformation of polymer molecules.Essentially the technique consists of deducing the fine- structure parameters D and E from the magnetic field dependence of delayed fluorescence Deviations from the known parameters of the isolated molecules can then be accounted for by assuming a conformation and then allowing for the averaging of differently ordered side-groups by the exciton motion. 5 Conclusion It should be clear at this point that there are many well-authenticated examples of the effect of magnetic fields on chemical reactions; effects that range from the inhibition of spin-multiplicity crossings and the consequent effects on fluorescent activity (and presumably on reactions themselves) to the actual modification of the concentra- tions of the product species.A magnetic field is potentially an influence on any reaction involving the change of multiplicity of some intermediate and whether that change of multiplicity leads on to a physical consequence (fluorescence) or to a chemical consequence (cage escape reactions) is not of itself of interest. The rate constants of all the steps in the overall scheme must be appropriate but in many cases that is happily the case. So many reactions involving doublet and triplet (and presumably higher multiplets) are magnetically sensitive that the best advice a theoretician can give to the experimentalist with a likely candidate is try it! Although we have emphasized the academic and theoretical aspects of magnetic field effects it should be clear that they may have considerable industrial significance.We shall have to wait in order to see whether this will emerge through their application to polymerization reactions or to the separation of nuclear isotopes or simply to the warping of a reaction in favour of one stereoisomer or product of a radical reaction. Note added in proof. Although an earlier analysis of the singlet and triplet photosen- sitized decomposition of dibenzoyl peroxide showed no field effect,” a new study using much higher fields’’ has shown that there is one. 89 P. Avakian R. P. Groff,A. Suna and H. N. Cripps Chem. Phys. Letters 1975,32,466. 90 H. Sakuragi M. Sakuragi T. Mishima S. Watanabe M. Hasegawa and K. Tokumaru Chem. Lerfers 1975,8 231. 91 Y. Tanimoto H. Hayashi S. Nagakura H. Sakuragi and K.Tokumaru in press.

ISSN:0308-6003    

DOI:10.1039/PR9757200067

出版商:RSC    

年代:1975

数据来源: RSC

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PART II INORGANIC CHEMISTRY 5 Introduction By M.F. LAPPERT School of Molecular Sciences University of Sussex Brighton BN 1 9QJ The general form of the 1975 Annual Reports (Vol. 72) on Inorganic Chemistry shows significant changes from previous years. Even greater note than hitherto is taken of the existence of the Specialist Periodical Reports series. Individual volumes of these now provide comprehensive coverage of inter alia Main-group Element Chemistry Inorganic Chemistry of the Transition Elements Organometallic Chemistry Electronic Structure and Magnetism of Inorganic Compounds Inorganic Reaction Mechanisms Spectroscopic Properties of Inorganic and Organometallic Compounds and Radiochemistry. Furthermore the Publications Committee of the Chemical Society has recommended a substantial decrease in the size of the Annual Reports.A deliberate attempt has therefore been made to offer a quite distinct form of coverage of progress in inorganic chemistry from that of the Specialist Periodical monographs which give a comprehensive-but inevitably terse -summary of advances in the subject and provide a particularly convenient secondary source of literature for the researcher. Our aim is to appeal more to generalists including the members of staff of University or Polytechnic Chemistry Departments in their capacities as teachers rather than as research workers who wish to keep themselves and their students abreast of important developments in all branches of the subject. We have tried to cover rather fewer areas than in former years but in greater detail than has been possible hitherto.Selected topics rather than papers have been chosen and in the main these represent areas in which there has been a considerable activity during the year. Where feasible for each topic chosen for comment one or two key references to work prior to 1975have been made. Each author was asked to restrict the number of references cited relative to the amount of descriptive material. For this reason there is very limited mention of books or review articles. The choice of material is necessarily subjective and to some extent reflects the interest of the contributors. We are conscious of the fact that much fine work has not been covered and we wish to have this contribution considered as the first of a short series.In subsequent years a deliberate attempt will be made to cover fields which have been neglected in the present volume. Aspects of the non-organometallic chemistry of the lanthanides and actinides are omitted this year but will be dealt with in the 1976 Reports. In the organometallic section we have kept in mind that Annual Reports Section B also deal with this topic although there the appeal is intended to be primarily to the organic chemist. We do not particularly accept the desirability for boundaries between the various areas of chemistry but simply recognise that with limited space 91 M.F.Lappert duplication of coverage is undesirable. Drs. Cardin and Dixon have therefore concentrated on aspects of structure and synthesis and less on the use of organometallic compounds as reaction intermediates or as catalysts.For example the topic of hydroboration is omitted from this volume. Discussion of metal carbonyls and aspects of transition-metal hydride chemistry is found in this section. Among the books published in 1975 or to the close of 1974 are the SI edition of an important undergraduate text,’ and a monograph2 on inorganic solids also princi- pally of interest to teachers and students. The Pergamon multivolume reference work3 ‘Comprehensive Inorganic Chemistry’ written by a formidable international group of inorganic chemists has now been made available in 27 separate titles in hard- and soft-backed editions often ca. 150 pages long dealing with single elements groups of elements or groups of compounds e.g.tungsten bronzes. In addition to the Specialist Periodical Reports 1975 saw the publication of a parallel series published comrner~ially.~ We also note the appearance of a number of specialist monographs.’-13 J. E. Huheey ‘Inorganic Chemistry; Principles of Structure and Reactivity’ Harper and Row New York 1975 1972 edition with SI unit alterations. 2 D. M. Adams ‘Inorganic Solids’ John Wiley New York 1974. ‘Comprehensive Inorganic Chemistry’ ed. J. C. Bailar H. J. EmelCus R. S. Nyholm and A. F. Trotman-Dickenson Pergamon Press Oxford 1974 (Vols. 1-5). M.T. P. International Review of Science Inorganic Chemistry Series 2 eds. M. F. Lappert D. W. Sowerby V. Gutmann B. J. Aylett D.W. A. Sharp M. Mays K. W. Bagnall A. G. Maddock M. L. Tobe and L. E. J. Roberts of Vol. 1-10 respectively Butterworths London 1975. D. E. Corbridge ‘Structural Chemistry of Phosphorus’ Elsevier Amsterdam 1974. S. A. Cotton and F. A. Hart ‘The Heavy Transition Elements’ Macmillan London 1975. Gmelin ‘Handbuch der Anorganische Chemie’ Vol. 24 Part 3 ‘Perfluorohalogenoverbindungenvon P As Sb and Bi’ Springer Berlin 1975. ‘Dynamic Nuclear Magnetic Resonance Spectroscopy’ ed. L. M. Jackman and F. A. Cotton Academic Press New York 1975. ‘Techniques and Topics in Bioinorganic Chemistry’ ed. C. A. McAuliffe Macmillan London 1975. lo F. J. McQuillin ‘Homogeneous Catalysis in Organic and Inorganic Chemistry’ ed. R. Ugo D. Reidel Dordrecht-Holland 1975. II ‘Boron Hydride Chemistry’ ed. E. L. Muetterties Academic Press New York 1975. 12 T. Onak ‘Organoborane Chemistry’ Academic Press New York 1975. l3 M. J. Taylor ‘Metal-to-Metal Bonded States of the Main Group Elements’ Academic Press New York 1975.

ISSN:0308-6003    

DOI:10.1039/PR9757200089

出版商:RSC    

年代:1975

数据来源: RSC

摘要:

The Typical Elements By A. J. CARTY Guelph- Waterloo Centre for Graduate Work in Chemistry Departmentof Chemistry University of Waterloo Waterloo Ontario Canada N2L 3G7 R. H. CRAGG Department of Chemistry University of Kent Canterbury CT2 7NH J. D. SMITH School of Molecular Sciences University of Sussex Brighton BN 1 9QJ PART I Groups I and II By R. H. Cragg 1 Group1 One of the major areas of interest in Group I chemistry has been the detailed study of the reactions of alkali metals with hydrogen. The significance of this work arises from the knowledge that in the reactions of alkali metals with hydrocarbons the metal hydride is a possible significant intermediate and it is therefore of importance to have some understanding of these alkali-metal hydrides.For example in the self-hydrogenation of alkynes and alkenes at the surface of liquid sodium molecular hydrogen is formed and the rate at which it is subsequently converted into metal hydride is influenced by the nature of the hydrocarbon. Liquid alkali metals react with hydrogen to form hydrides at the surface and because the reaction is moderately slow at temperatures just above the melting point of the metal it is relatively easy to measure the rate of the reaction by following the decrease in hydrogen pressure manometrically M(1) + iH,(g) +MH(s) The results for the reaction between hydrogen and liquid sodium have been previously reported and in order to obtain comparisons with other alkali metals the rate of adsorption of hydrogen at liquid lithium and potassium surfaces has been determined in the absence of hydrocarbons.The experimental technique used for the study of the reaction of hydrogen with alkali metals is relatively straightforward. A jet of the clean metal is continuously injected into hydrogen and the rate of reaction of hydrogen with the metal surface is measured over a selected temperature and pressure range e.g. in the case of potassium 22.24.3 kNm-' and 210-333 OC.' The reaction between hydrogen and potassium is observed to follow first-order kinetics with an activation energy of 66.5 kJ mol-' a slightly higher value than that reported for sodium (see Table). In contrast potassium is observed to react ' G. Parry and R.J. Pulham J.C.S. Dalton 1975,446. 93 A.J.Carty,R. H. Cragg and J. D. Smith with hydrogen approximately four times faster than with sodium which is a little surprising in view of the chemical similarities of the two metals. It was therefore suggested that in view of the similar activation energies of sodium and potassium the rate-determining step in their reaction with hydrogen is the same and probably involves electron transfer from the metal to adsorbed hydrogen atoms. This proposal is consistent with the observation that the free energies of formation of the two hydrides are similar and that the dissociative adsorption of hydrogen is usually rapid. The mechanism of the reaction is suggested to proceed by successive steps uiz.the conversion of gaseous molecular hydrogen into crystalline potassium hydride with dissociation into atoms and the formation of hydride anions.The adsorbed hydride ions can either dissolve in the metal or alternatively if the potassium is saturated potassium hydride crystals nucleate and grow on the sdrface of the potassium H,(g) -+ H(ads) + H(ads) H(ads) + e-+ H-(ads) It therefore seems reasonable to suggest that the difference in the rates of reaction of hydrogen with potassium and with sodium is mainly due to the relative strength of hydrogen adsorption; the more strongly the atom is adsorbed the easier becomes the electron transfer and the results indicate that hydrogen is more strongly adsorbed on potassium than on sodium. The rates of reaction of hydrogen with a clean liquid lithium surface have also been studied; the reaction is first order with an activation energy of 52.8 kJmol-'.* Lithium was found to react at 250°C about forty times faster than sodium with hydrogen and this result supports previous observations which showed that the addition of small amounts of lithium to sodium increases the rate of hydrogen adsorption.As in the case of potassium the rate-determining step in the reaction of hydrogen with lithium is assigned to the electron transfer from the metal to adsorbed hydrogen atoms. In view of the faster reaction in the caseaf lithium it appears that hydrogen is more strongly adsorbed on lithium than on either sodium or potassium. The reaction of hydrogen with solutions containing lithium strontium or barium is faster than with The rate is directly proportional to the hydrogen pressure and the reaction is first order with respect to the hydrogen pressure provided that the solution composition and the liquid-metal surface remain constant throughout the reaction.The results suggest that the hydrogen molecule is directly involved in the rate-determining step. However it is important to note that the observed changes in the rate constants are not accounted for only by the activation energy changes as the pre-exponential factor changes with both the solute metal and its concentration. Reported values for the activation energies and rate constants for the reaction of liquid metals with hydrogen are given in the Table. Table Metal E*/ kJ mol-' k(250 'C)/mrn s-' (kN m2)-' Na 72.4 2.505 X Na-Li (5.0%) K 64.1 66.5 5.860 X 9.010X Li 52.8 1.065 X Na-Ba (5.0%) 45.0 4.821 X G.Parry and R. J. Pulham J.C.S. Dalton 1975 1915. M. R. Hobdell and A. C. Whittingham J.C.S.Dalton 1975 1591. The Typical Elements Recently the reaction of liquid potassium with ethylene has been investigated over the range 503-67 1K by measuring the pressure changes and analysing the gas as the metal is injected into hydrogen using an electrical pump.4 It is observed that at lower temperatures self-hydrogenation takes place. The amount of ethane produced decreases as the temperature increases and it is suggested that this is due to the loss of hydrogen from the surface by dissolution in the metal. 2 Group11 Alkoxy-derivatives of beryllium are usually associated in keeping with the general property of beryllium to be four-co-ordinate where possible.For example dimethoxyberyllium is polymeric and insoluble in hydrocarbon solvents. Even di-t-butoxyberyllium which is soluble in hydrocarbon solvents is trimeric (1) and the only monomeric alkoxide so far reported is bis(2,6-di-t-butyl-phen0xy)beryllium. Recently a dimeric alkoxide of beryllium bis(nonafluor0-t- butoxy)beryllium(2),one of the most volatile alkoxides known (it sublimes in vacuo at room temperature) has been obtained from the interaction of nonafluoro-t-butyl alcohol and diethylberylli~m.~ Although insoluble in benzene (2) dissolves without reaction in nitrobenzene and is dimeric in hexafluorobenzene. The.lack of extensive association can be attributed to the increase in steric hindrance about the beryllium atom.Rather surprisingly the bridge Be-0 bond in the dimer is cleaved by diethyl ether. This is in contrast to the lack of reaction with pyridine or quinuclidine of (l) the hydrogen analogue of (2). But I Bu' I 0 0 0 /\ /\ \/\/0 0I I Bu'O -Be Be Be-OBu' (CF,),CO-Be /\ I Be-OC(CF,) \O/ But Bu' C(CF3)3 (1) (2) The reaction of sodium nonafluoro-t-butoxide with beryllium(I1) chloride in diethyl ether results in the formation of a distillable liquid Be[(CF,),CO], OEt, which is monomeric in benzene and only the second example of a three-co-ordinate monomeric beryllium alkoxide. On reaction with pyridine or ammonia the first examples of 1:2 beryllium complexes are obtained.

ISSN:0308-6003    

DOI:10.1039/PR9757200093

出版商:RSC    

年代:1975

数据来源: RSC

摘要:

The Typical Elements PART 11 Group III By A. J. CARTY 1 Boron Boron Hydrides and Borane Anions.- Theoretical Studies of Bonding and Structure. It is refreshing to find a paper in which theoretical calculations are used to predict G. Parry and R. J. Pulham J.C.S. Dalton 1975 2576. R. A. Andersen and G. E. Coates J.C.S. Dalton 1975 1244. A.J. Carty,R. H. Cragg and J. D. Smith chemical behaviour rather than to rationalize postfacto experimental observations. In an important contribution from Lipscomb's laboratory ground-state charge distributions derived from minimum basis set Slater orbital calculations using the PRDDO approximation have been employed to predict likely sites of electrophilic and nucleophilic attack in BgHlZ BI0Hl4 [BllH13]z- related boranes and car- baboranes.la Reactivity predictions are based on relative values of inner-shell eigenvalues Mulliken atomic and group charges and in addition sums of popula-tions over the several highest occupied MO's. Such calculations can be an invaluable aid in rationalizing reaction sequences or devising routes to boron hydride deriva- tives although it must be remembered that orbital symmetry correlations are ignored. In the past similar calculations have proved of significant value in decaborane( 14) chemistry. For BgH'Z electrophilic attack is predicted to occur preferentially at B-2 while B-7 is most susceptible to nucleophilic substitution. For [B8Hl3]- electrophilic substitution should occur in the order B-4 >B-2 =B-1>B-3>B-7 and a facile loss of H- from either B-4 or B-5 should yield BgHI2.In several cases [e.g. in BgH1 (C symmetry) where charge criteria indicate B-3 as a site for nucleophilic attack but eigenvalue differences do not differentiate between B-3 and B-7 sites] an unequivocal distinction between two possible sites of attack cannot be made. Here experimental results will be particularly significant in refining the model. The same paper analyses structural interrelationships between several Bg-B hydride species on the basis of detailed examination of localized molecular orbitals (LMO's). Topological and LMO descriptions generally correlate quite well. In the context of ab initio LMO theory for boron hydrides it is significant that experimental confirmation of the validity of this approach has been obtained from measurements of the Compton profile of decaborane( 14)? There is excellent agreement between the experimental and calculated electron momentum distribu- tions in this molecule showing that the wavefunctions used in constructing LMO's are 'good'.Ab initio MO calculations on seventeen small boron compounds have been carried out for comparison of geometries bonding preferences and stabilities with isoelectronic carbocations. These calculations lend quantitative support to many intuitive predictions. Thus for example substitution of H in BH by a w-donor group X (NH, OH or F) stabilizes BHzX relative to BH by 53-58 kcalmol-' while hyperconjugation in H,BCH gives only 12 kcal mol-' of stabilization energy and adduct formation H,N,BH 21 kcal mol-'.Similarly H2NBH2 and H2BOH are predictably planar with B-N and B-0 multiple bonds and with non-rigid rota- tional barriers about B-N and B-0 bonds of 29 and 144 kcal mol-' respectively. Geometries of boron compounds and isoelectronic carbocations (e.g. HB=CH and the classical vinyl cation CH,=& are generally similar but in terms of bonding boron is a stronger 0-donor and weaker w-acceptor than positively charged carbon. This comparison is best represented by the major resonance structures (1)and (2). Where experimental data are available for comparison the 6-3lG* calculations appear to give a better overall level of agreement than previous calculations. * (a)J. H. Hall jun. D. A. Dixon D. A. Kleier T. A. Halgren L.D. Brown and W. N. Lipscomb,J. Amer. Chern. SOC.,1975,97,4202; (b)I. R. Epstein P. Pattison M. G.H. Wallbridge and M. J. Cooper J.C.S. Chern. Cornm. 1975,567;(c) J. D. Hill P. von R. Schleyer and J. A. Pople J. Amer. Chern.Soc. 1975 97,3402; (d)E. L. Muetterties E. L. Hoel C. G. Salentine and M. F. Hawthorne Znorg. Chem. 1975 14 950; (e)E. L. Muetterties and B. F. Beier Bull Soc. Chim. belges. 1975 &I 397. The Typical Elements The borane anions [BnH,I2- present a unique opportunity for the study of rearrangement mechanisms and dynamics among the various classes of stereochemi-cally non-rigid molecules. These ions incorporate two nuclei ('H and "B) which are excellent n.m.r. probes and in atomic and electronic terms are relatively simple molecules lending themselves to sophisticated MO calculations.Several experimen- tal observations'd concerning rearrangement barriers in these ions have been clarified via extended Huckel MO calculations." Key features of polytopal isomer- ism for the family [B,H,]'- are (i) [B8H8]2- dodecahedra1 in the solid state fluxional in solution with rearrangement occurring between square-antiprismatic and bicapped trigonal-prismatic isomers; (ii) [B lH1 1]2- subject to rapid intramolecular rearrangement in solution even at low temperatures; (iii) [B7H7]'- a rigid pentagonal-bipyramidal structure in solution over a wide temperature range; (iv) [B,H,]'- a much larger rearrangement barrier than for [B8H8]'- being essen- tially rigid up to 200 "C. These apparently conflicting facts can be rationalized by consideration of MO energies in the various polyhedral forms of the ions.For [B8H8I2- calculations indicate a small energy gap between the highest occupied and lowest unoccupied MO's in all of the possible DZd,D4d,and c2u forms. Facile rearrangement of all three forms can occur via normal vibrational modes. By contrast the gap is large for D5h[B7H7]2- and this anion cannot rearrange via the degenerate C,,isomer. The most likely intermediate (C4, [B,H,]'-) in the re- arrangement of ground-state [B,H,]'- is degenerate. This may explain the apparently anomalously high barrier to interconversion in this species. However for [BllHll]*- the presence of a degeneracy in the C5uform suggests that the lower- symmetry C isomer may be a more reasonable transition state.It will be interesting to see whether predictions of fluxionality in co-ordination compounds ML7 ML8 and ML based on generalization of the borane anion rearrangement processes are borne out in subsequent work; there is evidence that ML8 complexes have very low rearrangement barriers. Incorporation of heteroatoms (carbon or metal atoms) into a closoborane framework might be expected to complicate rearrangement processes. This appears to be the case for metallocarbaboranes (see below). Structure of Boranes. The new boron hydride tetradecaborane(20) synthesized via reaction of excess octaborane( 12) with potassium nonahydrohexaborate in ether followed by treatment with HCl at -78 "C is a yellow crystalline solid for which X-ray data collected at -164 "C indicate structure (3).'" The molecule consists of two fragments fused at the B-7-B-12 positions with their open faces cis to one another.This molecule thus joins a growing number of boranes with structures built up by fusing two different borane fragments across a common edge. Examples include B13H19 B16H20 n-BI8Hz2 and i-B18H2'. The hydride B14H18 recently (a) J. C. Huffman,D. C. Moody and R. Schaeffer,J. Amer. Chem. Soc. 1975,97,1621; (b)S. Hermanek K. Felter J. Plesek L. J. Todd and A. R. Garber Znorg. Chem. 1975 14,2250; (c)J. D. Weiser D. C. Moody J. C. Huffman R. L. Hilderbrandt and R. Schaeffer,J. Amer. Chem. Soc. 1975,97 1074. A.J. Carty,R.H. Cragg and J. D.Smith characterized by ''B and 'H n.m.r.may be of this type,2b with decaborane and hexaborane frameworks fused across one edge. The existence of other hydrides with decaborane fragments linked to lower polyhedra seems possible. Interesting structural results relevant to the problem of boron-substituent bond- ing in substituted boranes have been obtained. Thus the postulate that m-bonding interactions between fluorine (2p,) silicon (3p and 3d,) and the boron cage may be responsible for the known stability sequences 2-FB,H8> 1-FB5H8 and 1-SiH,B,H >2-SiH,B,H8 has been supported by extended Huckel MO calculations. (The 1-SiH,-isomer is favoured over the 2-isomer by ca. 0.4 eV.) In direct contrast whereas isomerization studies show a stability order 2-MeB,H8 >1-MeB,H, calcu- lations yield a negligible r-bond order for the B-C bond; hence B-C m-bonding is an unlikely source of stabilization.It is comforting to know that these results are borne out by subsequent electron diffraction results.2c The Si-B bond length in l-SiH,B,H [1.98l(5) A] is indeed significantly shorter than the corresponding length in the 2-isomer [2.006(4)A] while the B-C bond lengths in 1-MeB,H8 [1.595(5) A] and 2-MeB5H [1.592(5) A] are essentially identical. Synthesis and Structures of Borune Anions. The Bronsted acidity of boron hydrides is now well established. Abstraction of a bridging proton followed by insertion of an electrophile into the 'bare' boron-boron bond results in polyhedral expansion and is a useful synthetic method for borane anions or indeed metalloboranes.The nido carbaborane anion [2,3-C2B,H,]- undergoes quite analogous reaction sequences. Recent Annual Reports have illustrated the scope of these insertions. An important paper pertaining to properties and structures of borane anions derived in this way has now appeared. Thus B,H, can be deprotonated by potassium hydride or ammonia according to equations (1) and (2). R. J. Remmel H. D. Johnson jun. I. S. Jaworiwsky and S. G. Shore J. Amer. Chem. Soc. 1975,97 5395. The Typical Elements The competing hydrogen abstraction and cleavage implied in the latter reaction are notable and perhaps more general than previously suspected (cf. Annual Reports 1971-73). The anion [B4H9]-is dynamic at room temperature on the n.m.r.time-scale. The structure represented in terms of Lipscomb's fractional three- centre B-B-B bonds is shown in (4). More importantly the same paper describes H' 'H HHHH (4) (5) the anions [B5H12]- [B6H1J and [B7H12]-,produced via addition of BH3 to the corresponding species [B4H9]- [BSHS]- and [B6H9]-. The triphenylmethylphos- phonium salts of [B5HI2]-and [B6Hll]-are white solids stable at room temperature for short periods. "B and 'H n.m.r. spectra show that [B5H12]-is fluxional above -90 "C but a static structure is apparent at -135 "C. Topologically this ion has been represented as (5) and is a member of a new class of boron hydride species the hypho-boranes containing 2n +8 skeletal electrons. The hypho (Greek for net) structure can be compared with the increasingly open frameworks closo (2n +2) (e.g.[Bl2Hl2I2-),nido (2n+4) (e.g. B5H9),and arachno (2n+6) (e.g. B5Hil) as the number of skeletal electron pairs increases. The phosphine adducts B5H9(PMeJ2 described in last year's report (p. 181) and B6H10(PMe3)2are also members of the hypho-boranes. The structure of the latter not available at the time of writing is apparently an open fragment of the equatorial belt of an icosahedron. Shore and co-workers3 also give details of their high-yield synthesis of B5Hll and [equations (3) and (4)]briefly mentioned in the 197 1Annual Report. Finally it has become clear from recent work that the relative acidities (Bronsted) of boron hydrides of a given class (e.g. nido or arachno) increase with increase in framework size.-110°C KB,H, + HCl 'BSH11 + H + KCl (3) KB,H, + HCl B,H,2 + KCI (4) Metalloboranes.-An excellent review of metalloborane chemistry published in 1974,4" together with last year's Report gives perspective to this rapidly expanding (a) N. N. Greenwood and I. M. Ward Chem.SOC.Rev. 1974,3,231;(b)B. P. Sullivan R. N. Leyden and M. F. Hawthorne J. Arner. Chem. Soc. 1975,97 455; (c)R. N. Leyden and M. F. Hawthorne J.C.S. Chem. Comrn. 1975,310;(d)K. Wade Chem. inBritain 1975,11,177; (e)K. Wade Adv. Inorg. Chern. Radiochern. 1975,18 in the press; (f) J. T. Gill and S. J. Lippard Inorg. Chern. 1975,14 751. A.J. arty R. H. Cragg and J.D. Smith field of research. The major advance this year has been the synthesis of several closo-nickelaboranes derived from [B9HI2]- [B10H10]2- and [B 1H13]2-.4b,4c Syntnetic methods generally involve reduction of an anion with Na-Hg in the presence of nickelocene or for derivatives of [B10H10]2- direct reaction of the anion with [q-C,H,Ni(CO)] or [(q-C5H5)3Ni2]2+.Of the four compounds characterized two Bu:N[( q -C,H,)-1-Ni( B ,H 1)] and [(7-C5H5)2-1,2-Ni2( B loHlo)] have while Me4N[(q-C,H,)-2-Ni-(B9H9)] icosahedral ~tr~cture~~* and Me4"( q-C5H5)-1-Ni-(B9H9)] have bicapped square-antiprismatic structures with the nickel atoms in equatorial and apical positions respectively.& By analogy with related metallo- carbaboranes (see below) it might be expected that Me,N[(q-C,H,)- l-Ni-(B9H9)] would thermally rearrange to the 2-isomer where the metal has a higher-co-ordinate position.Rearrangement does occur photochemically and thermally but in the opposite sense indicating that not only co-ordination number but also the charge densities on the boron atoms in the cage may be pertinent to the stability sequence. The existence of these polyhedra is predictable from electron-counting For example the hypothetical anion [BloH,,]b- contains 13 skeletal electron pairs suitable for a 12-vertex polyhedron with two sites vacant. Incorporation of two formally [q-C5H5Ni]3' units (a neutral q-C,H,Ni fragment contributes three elec- trons to a cluster) would be expected to produce a closo-icosahedron. Similarly the anion [(B11H11)Ni(C5H5)]- is derived from the nido-species with one vacant site in an icosahedron.Clearly the existence of a vast number of metalloboranes can be predicted using electron-counting rules and unquestionably there will be major developments in this area paralleling the burgeoning chemistry of metallocarba- boranes. Finally attention is drawn to a conceptually useful correlation4' between the structures of nido-metalloboranes and the boron hydride species which can be derived from the complexed hydroborate ion by addition or elimination of H' or BH;. For example [B3H8]- formally derived from B4HIo by elimination of BH,' forms a complex [Cu(PPh3)2B,H8] with a structure quite analogous to B4H10. Similarly the molecule forms a complex [Fe(CO),(B6Hl0)] with a structure derived from that of [B6H11]+ by removal of the proton bridging a basal B-B bond.Whether this model has general predictive utility remains to be seen. Metal Complexes of the Tetrahydroborate Ion.-It has been known for many years that the 'H n.m.r. spectra of metal tetrahydroborate complexes provide little structural information since the bridge and terminal protons appear to be magneti- cally equivalent as a result of rapid intramolecular rearrangements. Structural assignments have thus been based mainly on vibrational spectroscopy and where possible X-ray analyses. Two groups have now independently observed separate resonances for bridge and terminal hydrogens in complexes containing bidentate [BH4]- ions. Marks and Kolb5" had previously observed that paramagnetism induced sufficient energy separation between exchanging proton sites in [(C,H,),UBH,] that the n.m.r.coalescence point could be approached at low temperatures. Subsequently a vibrational analysis of the paramagnetic molecule s(~)T. J. Marks and J. R. Kolb J. Amer. Chem. Soc.,1975,97,27; (b) T. J. Marks and W. J. Kennelly J. Amer. Chem. Soc. 1975,97,1439; (c) H. D. Empsall E. Mentzer and B. L. Shaw J.C.S. Chern.Cornrn. 1975.861. The Typical Elements [(C5H,),VBH,]56 indicated considerable covalency in the V-H(BH,) bonds. At -90 "C the fluxionality of this molecule was arrested; resonances due to bridge and teminal hydrogens were evident below this temperature. A free energy of activation of 7.6 f0.3 kcal mol-' compares with a barrier of ca. 5.0* 0.6 kcal mol-' estimated for [(C,H,),UBH,].The small size of these barriers emphasizes the facility of the intramolecular rearrangement which may well involve a bidentate-terdentate con-version. In view of the above results the iridium and rhodium complexes [IrH2(BH4)L2] (L=PBu',Me PBu PBu\Bu" or PBuiPh) prepared from [IrHCl,L,] by treatment with sodium borohydride are remarkable.," These com- pounds all exhibit typical i.r. spectra for doubly bridged metal-BH bonding but are non-fluxional in solution with resonances at ca. 6 = -6.5 for bridging [IrH2B] and at S =6.8-7.8 for terminal BH protons. Perhaps the bulky phosphines prevent the attachment of a third BH hydrogen in the intermediate [IrH,BH] species necessary for the bridge-terminal exchange. It should be noted that despite the obvious difference in structural types the terminal protons in static [(C,H,),VBH,] and [IrH,(BH,)L,] resonate at lower field than the bridging hydrogens.Carbaboranes and Metallocrubaboranes.-This is one of the most active areas of inorganic research and a great deal of interesting work is published each year. A small number of topics have been singled out for specific mention. Intramolecular Rearrangements. The facile intramolecular rearrangement of borane carbaborane and metallocarbaborane molecules is amply documented. Mechanistic understanding of these processes many of which have no precedent in other areas of chemistry is however in its infancy. An important paper which complements earlier work by Hawthorne and co-workers on large may provide an initial basis for rationalizing thermal isomerization processes for small metallocarbaboranes.6' Thermolysis of [1,2,4-(r)-CSH5)CoC2B3H5] produced no isomerization to the 1,2,3- or 1,2,6-~ystems.~' The seven-vertex cage [1,2,3-(q-C,H,)CoC,B,&] however isomerized in high yield at 400 "C to the 1,2,4-isomer.Rearrangement of [1,7,2,3-(q-C,H,),Co2C2B3H5] occurred stepwise yielding [1,7,2,4-(~-C5H,),Co2C2B3H5] via the intermediate 1,2,4,5- and 1,2,3,5-isomers as shown in Scheme 1. While it should be remembered that the isolation of inter-mediates does not prove a reaction mechanism the formation of all three sequential products in this reaction can be accomodated if (a)atoms permutate by a triangular rotation on the polyhedron surface [as opposed to a less likely diamond-square- diamond (dsd) mechanism] (6) carbon atoms may not move from a low to a high (apex) co-ordination position (c) carbon atoms will not decrease their mutual separations (d) rotation of B2C or B2Co triangles is preferred and (e) the metal atom prefers an apex position provided that rules (6)-(d) are followed.It is clear at least for [(q-C,H,),Co,~B,H,] that cobalt is not restricted to positions of high co-ordination number (cf. 1,2,4,5- and 1,7,2,3-isomers) although for cages with 26 boron atoms such a restriction has generally been {Note however (a)D. F. Dustin W. J. Evans C. J. Jones R. J. Wiersema H. Gong S. Chan and M. F. Hawthorne J. Amer. Chem. Soc. 1974 96 3085; (b) M. F. Hawthorne K. P. Callahan and R. J. Wiersema Tetrahedron 1974,30,1795;(c)V.R. Miller and R. N. Grimes J. Amer. Chem. SOC.,1975,97,4213; (d) G. D. Mercer M. Tribo and F. R. Scholer Inorg. Chem. 1975,14,764;(e) C. G. Salentine and M. F. Hawthorne J. Amer. Chem. Soc. 1975,97,6382; cr)B. J. Meneghelli and R. W. Rudolph Inorg. Chern. 1975,14 1429. A.J. Carty,R. H. Cragg and J. D.Smith 5 Scheme 1 that [~,~,~-(~-C,H,)CO(CM~~)~B&~] is converted into [1,2,3-(q-C,H,)Co(CMe,)B,H,] via [10,2,3-(q-CSH,)Co(CMe2)B8H,]6d and that [2,10,1-(q- C,H,),CoNiCB,H,] and [6,10 1-(q-CSH5)2CoNiCB7H8]6e contain nickel atoms in low-co-ordinate vertices.} Grimes" suggests that while the driving force for the 1,7,2,3+1,7,2,4 conversion is the separation of carbon atoms strong cobalt-cobalt bonding lowers the activation energy for apex+equatorial migration of cobalt thus allowing a facile reaction path via a series of trigonal rotations.Pyrolysis of the and eight-vertex cobaltacarbaboranes [3,1,7-(q-C5H,)CoC2BsH7][3,5,1,7-(q-C,H,),Co,C,B,H,] resulted in considerable cage fragmentation (boron and cobalt transfer) but no isomerization to the [3,1,8-(q-CSH,),CoC2BsH7] or [3,5,2,8-(q- C,H,),Co,C,B,H,] isomers predicted if the number of Co-C bonds was to be minimized. If the structures of these compounds have been correctly assigned (no X-ray data are available) these results may imply that the thermal stabilities of the 3,1,7-monocobalt and 3,5,2,8-dicobalt cages are higher than those of any other isomer. Alternatively there may be a kinetic barrier to interconversion.Conversion of the nine-vertex cage [1,7,5,6-(q-CSH5)2C02C2BSH7], in which two cobalt atoms are adjacent into the isomer [1,8,5,6-(q-C,H,),Co,C2BsH7] produced an equilibrium the first such example for closo-metallocarbaboranes. The AH for the 1,8,5,6+1,7,5,6 process is -2 kcal mol-' perhaps indicating a fine balance between competing steric and electrostatic repulsion effects on the one hand and strong cobalt-cobalt bonding on the other. The Typical Elements / 450"c 450 "C -95 % BH .C ,1L 111 IV Scheme 2 A second important paper this year on polyhedral rearrangements deals with the synthesis and thermal isomerization of the mixed-metal bimetallocarbaborane [(C,H,),CoNiCB,H,] (Scheme 2).6e The presence of a direct nickel-cobalt bond in the thermally most stable [6,9,l-(~-CSH,),CoNiCB,H,l isomer IV and preference of nickel for a high-co-ordinate position in IV was established although nickel atoms in I and I11 occupy low-co-ordinate sites.Rearrangement processes were discussed in terms of the dsd mechanism (cf. ref. 6c). This year's work thus establishes clearly that in metallocarbaboranes of inter- mediate stability the presence of metal atoms in low-co-ordinate positions is not precluded. Furthermore strong metal-metal bonds are possible and may play an important role in determining relative stabilities for other di- and polymetallocar- baboranes. Rearrangements of metallocarbaboranes incorporating second- and third-row transition elements will be interesting in this regard.It is also clear that a definitive experiment to distinguish between the alternative dsd and trigonal- rotational mechanisms for metallocarbaborane interconversion has not yet been described. A. J.Carty R. H. Cragg and J.D. Smith The reduction of closo-carbaborane cages with subsequent cage-opening and insertion of a metal ion into the vacant site is a valuable synthetic route to metallocarbaborane complexes. The mechanisms of ring-opening are generally obscure. Evidence is however accumulating that two-electron reduction of closo-carbaboranes occurs via conversion of deltahedra to nido counterparts. Thus extended Huckel MO calculations confirm that D3,,[C2B3H5lz- should not be stable and that trigonal-bipyramidal isomers are energetically inaccessible.6f However square-pyramidal isomers of [GB,H,]’-have appreciably higher stabilities with the stability order trans -basal-basal >cis-basal-basal >apical-basal.Accessible and symmetry-allowed interconversion pathways between these three isomers are avail- able (Figure 1).Addition of two protons to give C,B,H changes the relative stability ordering to apical-basal >trans-basal-basal >cis-basal-basal such that the two hydrogens can be accomodated in bridging positions on non-trigonal faces of the apical-basal isomer. The known isomer of C,B,H (isoelectronic with [C,B,H,]’-) has this stereochemistry. For the six-vertex carbaborane anions [C,B,H$ derived from CzB4& all pentagonal-bipyramidal isomers are more stable than octahedral species.Hence open pyramidal forms of [CzB3H,l2- and [CzB,H,]2- appear favoured over their closo analogues. The rearrangements closo =nido and -2e nido 7arachno provide a rationale for polyhedral expansion. Metal fragments capable of accomplishing these conversions can be predicted.4d.‘ -370 -374 -378 4 Rearrangement co-ordinate Figure Energy as a function of geometry for [C2B3H,]2-. The solid line represents the intercon- version of isomeric forms of [CzB3H5]2-via symmetry-allowed arcing movements of the designated atoms. The broken line designates interconversion via a dsd mechanism (Reproducedby permission from Inorg. Chem. 1975,14,1429) The Typical Elements Synthesis. There has been very little information relating to the mechanism of formation of carbaboranes.The kinetics of formation of derivatives of 1,2-dicarba- closo-dodecaborane(12) from B10H12(Me2S) and acetylenes RCGCH show that the rate determining process is attack by the acetylene on B10H12(Me2S) forming the adduct BloHl2(Me2S)(RC-CH). Subsequent loss of a molecule of Me,S from B-9 and co-ordination of the acetylne to B-9 adjacent to B-10 yields a geometry favourable to closo-carbaborane f~rmation.'~ Importantly isolable BloHl,L species synthesized by other workers are not intermediates and hence not identical to the active species BloHl,L formed in situ by reversible dissocation of BloH12L2. Clearly positive identification of these active species which may also be implicated in [B,oHlo]2- formation is desirable.The general synthetic methods namely cage expansion by carbaborane reduction in the presence of metal halide and sodium cyclopentadienide direct insertion of metal fragments (e.g. d" complexes) into a polyhedral cage and the polyhedral subrogation reaction have been described in detail in previous Annual Reports and recent survey^.^^*^ These methods have been extended this year. Only a few novel examples can be mentioned. Until this year the only v-hydrocarbon ligand which had been extensively utilized as a capping ligand in metallocarbaboranes was CSH5-. Derivatives with 778-Cg&7d and q6-CloHg6' have now been synthesized. Thus reaction of [(C,H,)TiCl] with Na,C,B,H, followed by treatment with Et,N' yielded [Et,N][3,1,2-(q8-C,H,)TiC,B,Hll].Reaction with H202gave [3 1,2-(q8-C,H,)Ti~B,Hll].7d Reaction of [2,1-(q5-C5H5)CoCBloHll]sodium with naphthalide followed by treatment with C5H5- and Co" gave orange diamagnetic [2,1-(q6-CloH,)CoCBloHll], formulated as (6) {cf.[(C,,H,)Cr(CO),J) and the first metallocarbaborane with a neutral q6-arene ligand.6" There are other metallocar- baborane complexes purported to contain qz-and q4-arene ligands in the recent literature but these must be considered highly speculative. In view of the interest and (a)W. E. Hill F. A. Johnson and R W. Novak Inorg. Chem. 1975,14,1244; (b)M.F.Hawthorne,J. OrganometaNicChem.,1975,100,97;(c)F.G.A. Stone J. OrganometallicChem. 1975,100,257;(d)C. G.Salentine and M. F. Hawthorne J.C.S.Chem. Comm. 1975 848; (e) C.G.Salentine and M. F. Hawthorne,J. Amer. Chem.SOC.,1975,97,426;(f) F.Y.Yo,C. E. Strouse,K. P. Callahan C. B. Knobler and M. F. Hawthorne,J. Amer. Chem. Soc. 1975,97,428;(g)P.L.Timms,Angew. Chem. Internut. Edn. 1975,14,2/3;(h) E.L.Hoe1 and M. F. Hawthorne J. Amer. Chem. Soc. 1975,97,6388. A.J.Carty,R. H. Cragg and J.D. Smith controversy surrounding the structures of 'titanocenes' and related complexes the characterization of [Me4NI2[{ 1,6-C2B10H10Me2}2Ti] as a 14-electron titanacar- baborane is From the few studies presently available it appears that metallocarbaborane complexes of the early transition metals are considerably more stable than the &responding cyclopentadienyl complexes. Whether these metallo- carbaboranes undergo the facile thermal rearrangements typical of the cyclopen- tadienyl titanium complexes remain to be established.The use of metal vapours in the cage expansion of carbaboranes is a potentially useful but to date little used synthetic method. Thus nickel vapour reacts with the closo-carbaborane C2B9H11 to give the known complex [(C2B9H 1)2Ni] derived from the nido-anion [C2B9Hll]2-.7g A variety of B-a-carbaboranyl complexes of iridium have been obtained by oxidative addition of terminal B-H bonds to iridium@ ~pecies'~ [equations (5)and (611. [Ir(C8H14),C1] + 6 1-PMe,-1,2-C,B,,Hll -+2[IrL,Cl] (5) (L) [IrL,Cl] + [IrL,( 1-PMe,-1,2-C2B,,,H ,)HCl] (6) (7) The complex (7) has a cis-octahedral stereochemistry at iridium with three phos- phorous atoms cis to the hydride and the chloride trans.The carbaborane cage is probably attached to the metal via a boron atom in the 3- or 6-position. Intermolecu- lar oxidative addition is also possible. Thus reaction of 1,2-C2B10H12 with [(Ph,P),IrCl] gave small amounts of 3-[(PPhJ2IrHC1]- 1 2-C2BloHl Substitution on the cage was at the 3,6-sites. These reactions thus complement the methods discussed in last year's Report for synthesizing B-a-carbaboranyl complexes. Structures of Carbaboranes and Metallocarbaboranes. With the availability of auto- mated diffractometers X-ray analysis has become a rapid analytical tool not least in the field of metallocarbaboranes. Structures are too numerous to list. We mention only a few important structural trends.X-ray data are now available for a wide variety of twelve-vertex metallocar- baboranes in which the metal d-electron configurations vary from d2to d9.Electron-rich d8 and d9 complexes e.g. [( 1,2-C2B9H11)2Ni"]2-,have 'slipped' sandwich structures with the distortion largest in the d9 cases. For electron-deficient metal- locarbaboranes of which the 15-electron complex Cs[{C2B9H9Me2},Cr] is an exam- ple a symmetrical structure with long metal-ring distances is observed. Long metal-ring bonds are also evident in the 14-electron 13-vertex cage complex [Me4FJ12[( 1,6-~BloHloMe2)2Ti]. An alternative explanation of the slippage in the electron-rich species has now been proposed.8" Basically comparison with the MO energy-level diagram of ferrocene is useful.In the bis-dicarbollide systems the orbitals corresponding to the 2el MO's of ferrocene are antibonding with respect to (a)P. A. Wegner Inorg. Chem.,1975,14,212;(b)W. T. Robinson and R. N. Grimes,Znorp. Chem.. 1975 14,3056;(c)G. K. BarKer M. Green J. L. Spencer,F. G. A. Stone B. F. Taylor and A. J. Welch J.C.S. Chem. Comm.,1975,804;(d)K. P. Callahan W. J. Evans F. Y. Lo,C. E. Strouse and M. F. Hawthorne J. Amer. Chem. Soc. 1975,97 296. The Typical Elements both the metal-ring interactions and the icosahedral cage framework. In d8and d9 complexes two and three electrons occupy these antibonding MO’s. Distortion and eventually cage-opening (closojnido) ensue. The process is analogous to that occurring on reduction of CZ~SO-C~B~~H~~ systems.Although the author mentions that similar distortions do not occur for electron-rich [(C,H,),M] complexes it should be pointed that there are some unusual features in the structure of gaseous nickelocene (a 20-electron complex) in particular that the Ni-C bonds may not all be equivalent. The structure of [2-Me-1,7,2,4-(q-C5H,),Co2GB3H4]consists of a triple-decked sandwich analogous to the [(T-C,H~)~N~~]+ ion. The planar [C2B3H,I4- ring system in 1,7,2,3- and 1,7,2,4-[(q-C,H,),Co2C2B3H5] is isoelectronic and isostructural with [C,H,]-. Development of metallocene-like polymers based on [C2B3H,l4- thus seem possible.86 P(21’) P(31’) (8) A.J. Carty,R. H. Cragg,andJ. D.Smith The reactions of cZoso-2,4-~B5H7 and doso-1,6-C2BsHlo with [Pt(styrene) (PEt3),] and [Pt(C,H,,)(PMe,),] respectively afforded the novel complexes (8) and (9)." Compound (8) has a closed nine-atom bimetallocarbaborane structure but illustrates that M-M bonds in metallocarbaboranes can be very weak.The Pt-Pt bond length of 3.051(4) A is barely a bonding distance. In (9) an unusual exocyclic Pt-Pt bond is present which can readily be removed to generate nido-[8,8- ((Me3P),}-7,8 lO-CPtCB,H,,]. Despite much effort it does not yet seem possible to predict the course of these d10insertions. It is also becoming obvious (cf. refs. 6c and 6e) that metal-metal bonds in metallocarbaboranes can vary enormously in strength. The frequent occurrence of unusual structures in the products derived from insertion of electron-rich metal fragments into carbaborane cages should not mask the utility of electron-counting rules for rationalizing the basic polyhedral geomet- ries of metallocarbaboranes.For example the structure of [(q-CsH5)2Fe2~B6Hs] is that of a capped tricapped trigonal prism and differs from the idealized bicapped square antiprism of other ten-vertex borane species. However this molecule does not have the 22 electrons required for skeletal bonding according to the 2n +2 With 20 electrons only [(q-CSH5),Fe2C2B6Hs] should be derived from a nine-vertex polyhedron as is observed.8d Boracarbocycles and "heir Metal Complexes.-The search for carbocycles with aromaticity as predicted by the Huckel 4n +2 rule together with the notable stabilization of reactive molecules which can often be achieved by attachment to a suitable transition-metal fragment has motivated much research on metal-hydrocarbon v-complexes.The isoelectronic character of CH and BH- and C-C and B-N units is well recognized and has been exploited in the developing chemistry of carbaboranes and borazines. Substitution of B-H- or B-N for C-H fragments in (4n +2)v carbocycles gives rise to boracarbocycles (10)-(15) or borazacarbo- cycles [e.g. (16)-(17)]. Although derivatives of a few of these are known [e.g. pentaphenylborole corresponding to the polyene of (12Jsa and (14) (15) (16) (17) (a)J. J. J. Eisch H. K. Hota and S. Kozima J. Amer. Chem. SOC.,1969,91,4575; (b)M. F. Lappert in 'The Chemistry of Boron and its Compounds' ed. E. L.Muetterties Wiley New York 1968 Ch. 6; (c) A. J. Ashe tert. E. Myers P. Shu T. V. Lehmann and J. Bastide J. Amer. Chem. SOC.,1975,97,6865;(d) G. E. Herberich and H. J. Becker Angew. Chem. Infernat.Edn. 1975,14,184; (e)G. E. Herberich G. Greiss and H. F. Heil Angew. Chem. Zntentat.Edn. 1970,9,805;cr)R. N. Leyden and M. F. Hawthorne Znorg.Chem. 1975,14,2018; (g) G. E. Herberich H. J. Becker and G. Greiss Chem. Ber. 1974,107 3780; (h)J. J. Eisch and J. E. Galle J. Amer. Chem. SOC.,1975,97,4436. The Typical Elements borazaronaphthalenes related to (16)"] synthesis of other boracarbocycles has been very limited. Recently two have characterized phenyborinate (boraben- zene) anions by two different routes (Scheme 3). Ashe and co-workers have also made alkyl- and bromo-substituted anions.The anions are pyrophoric. Originally the phenylborinate anion was trapped as the [(q5-C5H5)(q6-C,H5BPh)Co]', [(7'-C,H,)( q6-C,H,BPh)Co] or [(q5-C,H,Ph),Co] complexes by ring expansion of q5-C5H5 rings of cobaltocene with phenylboron dichloride." A dicarbollylphenylborinate-cobaltcomplex [3,1,2-{ 1-C6H5( q6-C5BH5)}CoC2B9H has been prepared in analogous fashion.'' For the synthesis of other transition- metal derivatives ligand transfer from the cobalt complexes can be used (cf. transfer of cyclobutadienes) but prior generation of the anion would seem preferable. The 6~-aromatic system (13) can be compared to the cyclopentadienide ion. Indeed the air-stable bis(b0rabenzene)iron complexe~~~~~ appear to resemble ferrocene quite closely.In particular the chemical isomer shift 6 is identical (0.72 mm s-') to that of ferrocene indicating that differences in 0-,T-,and S-components to the bonding if any compensate one another so that no net change in s-electron density at the nucleus is apparent. A comparison of S and A values with those of the known isoelectronic [(v6-C6H&Fe]2' species would be rewarding. The bis(boraben- zene)iron complexes also undergo electrophilic substitution; a monoacetyl deriva- tive has been characterized.'" Ferrocene is however approximately four times more reactive than bis-( 1-methylborabenzene)iron. Although the borabenzene ring is bis-( 1-methoxyborinato)cobalt is asymmetrically bonded to the metal atom with substantially longer Co-B than Co-C bond lengths it must be remembered that the cobalt complex is formally a 19 electron species; a distortion might therefore be expected.An X-ray structure of the corresponding iron complex will be interesting. In view of the stability of these systems it seems clear that attempts to generate complexes derived from other boracarbocycles may well be feasible. In this context the recent synthesis of heptaphenylborepin (18) by a suprafacial sigmatropic re- arrangement of heptaphenyl-7-borabicyclo[2,2,llheptadiene followed by a disrota- tory ring-opening of the bicyclic intermediate is of intere~t.'~ The borepin (18) with six .rr-electrons may well be planar and aromatic; spectra of (18)compare well with spectra of the heptaphenyltropenium ion. Nevertheless corroborative X-ray data seem necessary especially in view of the propensity of other seven-membered heterocycles to undergo valence tautomerism.Diene triene or boratrienyl com- plexes of (18) seem possible. The electron deficiency of boron could also be satisfied by a metal lone pair with interesting sterochemical consequences. 0qpo B-Ref. 9c Bu/\Bu RI I R Ref. 9d Scheme 3 A.J. Carty,R.H. Cragg and J. D.Smith Boron-Carbon m-Bonding in Viny1boranes.-Last year's Report (p. 193) men- tioned briefly evidence for B-C v-bonding in vinylboranes. Spectroscopic support for electron delocalization in vinylboranes has now been summarized.'oa Unfort- unately previous assessments of B-C bond shortening have been hampered by a lack of accurate structural data.The gas-phase structure of trivinylborane has now been determined."' The molecule is dynamic having a planar BC skeleton but with extrfme thermal motion of the vinyl groups. The B-C bond length of 1.558(3) A is shorter at the 4a level than the B-C bond length in triphenylborane [1.577(5) A av]. Comparison of these distances is valid since both compounds have Bsp2-Csp2 links. The inference of B-C 7r-bonding appears justified although the extent of bond shortening per vinylgroup is slight. Carbon-13 n.m.r. data have been interpreted as indicating that electron drift from carbon to boron is maximized in the monovinylboranes despite the presence of competing w-donors on boron."" In view of the predicted strongly mesomeric v-donor properties of fluorine in species such as H2BF," it seems unusual that B-C w-bonding should fall off in the sequence F2B(C2H3)>FB(C,H,) >B(C,H,),.Indeed ab initio studies show that the absolute charge on C of the vinylboranes F,B(C,H,),- decreases with increased vinyla- tion."' Delocalization of vinyl 7r-density is thus greatest in trivinylborane. It is unfortunate that structural data for F,B(C2H3)'Od are not sufficiently accurate to allow a comparison with B(C,H,),. Comparison of calculations for vinyl- and methyl-boranes shows that a vinyl group donates more than twice as much w-density to boron in F,B(GH,) FB(C,H,), or B(C2H3)3 than a methyl group in F2BMe FBMe, or BMe,. Hence B-C (pm-pm)interactions in vinylboranes are considerably more important than hyperconjugation in methylboranes.Boron Halides.-The extent of B-X (p,-p,) bonding in the boron halides has intrigued inorganic chemists for years and is directly pertinent to discussion of relative Lewis acidities. An attractive approach to this problem would be compari- son of structural and spectroscopic properties of the mixed halides BXAXZ- where competitive B-X' and B-X2 p,-p interactions might be expected. Unfortunately the pure mixed halides are not isolable. Despite this an elegant study"" has recently shown that from a statistical equilibrium mixture of BCl,F,- (n = 0-3) photo- electron and microwave spectra of individual species can be obtained. For example for BClF2 IP's of 12.85 (4b,) 13.00 (2b1) 15.1 (5a1) 16.93 (3b2 a2),and 18.35 (lb,) eV were experimentally observed.Ionization from 4a1 (calc. 18.58 eV) and (a)L. W. Hall J. D. Odom and P. D. Ellis J. Amer. Chem. Soc. 1975 97 4257; (b) A. Foord B. Beagley W. Reade and I. A. Steer J. Mol. Structure 1975 24 131; (c) N. J. Fitzpatrick and N. J. Mathews J. Orgunometuific Chem. 1975 94 1; (d)J. R. Durig R. 0.Carter and J. D. Odom Znorg. Chem. 1975 13,701. The Typical Elements 2b2(calc. 19.32 eV) wasnot detected. AB-Clbondlengthof 1.71(1) AandanFBF angle of 116.6(1)0 were derived from the microwave spectrum of this compound. The B-Cl bond has 14% ?r-character; ab initio calculations agree with this estimate and indicate that the B2p,-C13pT overlap population is greater than B2p,-F2pT. This result agrees with earlier EHMO calculations on the trihalides BX where n-charge transfer from halogen to boron decreased in the order BI > BBr > BCl > BF although the c7-charge drift X+B dominates contributions to the overall bond polarity."' This opinion is not shared universally however.The a priori prediction of a more compatible p,-p, overlap in the B-F bond has usually led to the text book inference of greatest 7-bond order in the fluoride. This view still persists.10a Nevertheless the order of n-back-donation from ligand to boron B-N > B-S = B-I > B-0 =r B-Br >B-Cl> B-F deduced earlier seems realistic and can be compared with B-N > B-0 > B-F calculated for H,BX species." While halogen bridging is common for the heavier Group I11 metal halides it is rare in boron chemistry.At very low temperatures (-155 "C)1 1mixtures of BF3 and [Bu",N]'[BF,]-give 19F n.m.r. spectra consisting of a high-field doublet (JFBF 95f10 Hz)and a broad low-field resonance with area ratios of 1 6 consistent with the presence of the very labile single-fluorine-bridged species [B2F7]- the first time this ion has been observed in The Boron-Phosphorus Bond.-The nature of the co-ordinate bond between boron and phosphorus in simple co-ordination compounds has been a source of considerable controversy. Some of the more puzzling aspects which appear to have largely defied logical explanation to date are the variations in P-B bond lengths which accompany changes in the substituents on boron and phosphorus together with some rather unusual stability sequences.Thus H3P,BH3 and F,P,BH3 have P-B bond lengths [1.937(5) and 1.836(6) A] near the extremes for borane (BH,) adducts yet these compounds are considerably less stable than HF2P,BH3 [B-P 1.832(9)A] Me,P,BH [B-P 1.901(7)813 or HMe2P,BH [B-P 1.906(6) A]. The P-B bond lengths of 1.921(7)w and 1.84(2) 8 recently determined for H3P,BH312a and MePF2,BH3l2* respectively the former a compound of low dis- sociative stability shed no further light on this matter. The most that can be said at present is that for BH adducts the B-P bond lengths lie in two groups with B-P bonds in fluqrophosphine adducts ca. 0.06A shorter than in the phosphine and methylphosphine series. For boron trihalide complexes the situation is clearer. Crystal structures have been determined for Me,P,BX3 (X= C1 Br or I) this year.'2c Boron-phos horus bond lengths are 1.957(5) 8 (X= Cl) 1.924(12) 8 (X= Br) and 1.918(15) 8 (X= I).There is a significantly shorter B-P bond in the chloride complex compared with the bromide or iodide. Thus the pattern of donor-acceptor bond strengths and (a)H. W. Kroto M. F. Lappert M. Maier J. B. Pedley and M. Vidal J.C.S. Chem. Comm. 1975,810; (b)M. F. Lappert M. R. Litzow J. B. Pedley P. N. K. Riley and A. Tweedale J. Chem. Soc. (A) 1968 3105; (c)M. F. Lappert M. R. Litzow J. B. Pedley P. N. K. Riley T. R. Spalding and A. Tweedale J. Chem. Soc. (A),1970,2320; (d)J. S. Hartman and P. Stilbs J.C.S. Chem. Comm. 1975,566. l2 (a) J. D. Odom V. F. Kalasinsky and J. R. Durig Inorg. Chem.1975,14,2837; (6)R. A. Cresswell R. A. Elzaro and R. H. Schwendeman Inorg. Chem. 1975,14,2256;(c)D. L. Black and R. C. Taylor Acta Cryst.,1975 B31 11 16; (d)D. C. Mente and J. L. Mills Inorg. Chem. 1975,14,1862;(e)P. Cassoux R. L. Kuczkowski P. S. Bryan and R. C. Taylor Inorg. Chem. 1975,14,126;cf) P. M. Kuznesof F. B. T. Pessine R. E. Burns and D. F. Shriver Inorg. Chim. Acta 1975 14 271. A.J. Carty,R.H. Cragg and J. D. Smith possibly Lewis acidities evident in the Me,N,BX and MeCN,BX series is followed with BI LBBr >BCl,. This order receives direct support from gas-phase calorimetric measurements.'2d Furthermore the B-P bond length in Me,P,BH [1.901(7) A] is shorter than in any of the halide complexes Me,P,BX whereas for Me,N,BX (X = H C1 NF) the distances are virtually identical.'" The B-N bond length in Me,N,BH [1.638(10) A] is longer than in Me,N,BX (X =Br or I).Thus the greater affinity of BH3 than the boron halides towards phosphine donors predicted chemically seems substantiated. CNDO-2D calculations of dipole. moments for Me,H,-,E and Me,H,-,E,BH (E =N or P; x = 0-3) provide evi- dence for substantial differences in B-N and B-P bonds in these simple adducts.12f Co-ordination of NH to BH results in charge transfer primarily between N-bound and H-bound hydrogens (0.33e) but for phosphine complexes the transfer is largely from phosphorus to boron (0.27e). Whereas the B-N bonding MO remains essentially unchanged on methyl substitution (46% covalent character in the B-N bond with essentially sp2.' hybridization at nitrogen) substantial changes in hybridi- zation at phosphorus (from ~p'.~ in PH,,BH to spl.' in Me,P,HB,) occur on formation of B-P bonds.The B-P bond has considerably more covalent character ((51%) and a higher s-character. It also appears from these calculations that distortion of the lone-pair electrons of Me,P and PH by BH is more favourable for the former ligand. The Boron-Nitrogen Bond.-Research in boron-nitrogen chemistry is focused to a large extent on compounds where B-N n-bonding plays a major role. This year synthetic methods have been developed for several molecules whose ground-state properties should be interesting. Thus the first 1,3,2,4-diazaboretidineshave been synthesized [equation (7)].13" X I R XR B /\ R,N-P=NR + BX3 + \/N-P-N I \ +RN \/NR (7) I R BX2 P I Y Convenient routes to dialkylaminohydridophenoxyboraneshave been described.13' Restricted rotation about B-N bonds in these molecules is expected and experi- mentally observable by means of n.m.r.Aminodifluoroborane H2NBF2 has been characterized as a volatile product of the purolysis of H3N,BF3 at 185°C.'3c Polycyclic borazines (19) have been prepared from thioborane~.'~~ X = 0,NH or NMe n = 2 or 3 (19) l3 (a) E. Niecke and W. Bitter Angew. Chm. Internat. Edn. 1975 14 56; (b) R. A. Kovar and G. G. Waldvogie Inorg. Chem. 1975 14 2239; (c) E. F. Rothgery H. A. McGee jun.,and S. Pusatcioglu Znorg. Chem. 1975 14 2236; (d) R. H. Cragg and A. F. Weston J.C.S. Dalton 1975 1961; (e) A.Serafini and J. F. Labarre J. Mol. Structure 1975,26 129; (f) D. T. Haworth and V. M. Scherr J. Inorg. Nuclear Chem. 1975,37 2010; (g)A. DeStefano and R. F. Porter Inorg. Chem. 1975 14,2882. The Typical Elements As regards cr-and n-components to bonding between boron and first-period elements borazine B3N31& and boroxine B303H3 are key compounds. The influence of n-delocalization on the electronic structures of these planar six- membered ring compounds has been examined by ab inifio SCF-LCAO-MO calculations.13c In borazine there is a formal a-charge transfer from HB and B towards nitrogen (1.02e) and a much smaller n-charge transfer from N to B (0.35e). Thus nitrogen is more negatively charged. For boroxine the a-transfer from H and B to 0is 1.14e and there is a reverse .rr-transfer of only 0.26e.Hence the direction of polarity of the B-0 bond is similar to that of the B-N bond the n-overlap population of the B-0 bond is less and the total charge transfer along the ring bonds is much larger in boroxine. In fluorinated boroxines the total ring population is decreased. Electron withdrawal through the cr-system is not counterbalanced by F2p,-B2pT bonding.13' These calculations thus support the inferences made for these molecules on the basis of their chemical reactivities. In this context the likely structures (20) and (2 1) for the protonated borazine cation (cf.protonated benzene) have the proton located at a site close to nitr~gen.'~~ H H (20) (21) -Boron Carbides.-The history of the boron carbide crystal structure goes back 35 years to the initial description of a 15-atom unit cell containing a nearly regular icosahedron of boron atoms and a linear chain of supposedly three atoms linking icosahedra.Much later it was realized that the central atom of the three-atom chains was boron. This can be represented as (B12) [CBC]. The chemical composition B,C can then be attained by the average substitution of a carbon atom for boron in each icosahedron uiz. (B,,C)[CBC] a feature which was very recently revealed by careful X-ray work. With the ideal rhombohedral (B12)[CBC] and carbon-rich (BllC) [CBC] structures established the question remains as to structural modifications accompanying carbon depletion of the ideal B13C2 structure.The boron-carbon phase diagram indicates a single phase in the solubility range 9-20 atom YOcarbon. Several solutions to this problem have been suggested none of which corresponds to the structure of a boron-rich boron carbide determined this year.14 The crystal system of this carbide (containing 8k1atom O/O C) is rhombohedral (Rjrn)but unit cell parameters are significantly larger than for the material with 20% C. Icosahedra (B,2) are still present but one fourth of the linear [CBC] chains in the (B,,)[CBC] structure are replaced by planar [B4] groups. Both terminal and bridge atoms of these [B4] units have five-fold co-ordination. Thus the following changes may accompany decreases in carbon content for boron carbide l4 H. L.Yakel Actu Cryst.1975 B31,1695. A.J. Carty,R.H. Cragg,and J. D.Smith The extent to which the presence of increasing numbers of [B4] units in boron carbides contributes to the known solubility limits in the boron-carbon phase diagram remains to be deciphered. 2 Aluminium Gallium Indium,and Thallium Structure and Bonding in Aluminates.-Two particular studies are singled out for mention. Few inorganic compounds are as essential to our society as tricalcium aluminate 3Ca0,A1203 (C,A) a major component of Portland cement. Despite the efforts of numerous laboratories dating back to 1929 the structure of C,A remained unsolved until this year. The structure (22) finally elucidated by Mondal and Jeffrey"" after 12 attempts must stand as a monument in cement and aluminium- oxygen chemistry and consists of six A10 tetrahedra (AlhOI8) eight to a cell surrounding holes of radius 1.47 A with Ca2+ ions in distorted six-fold co-ordination holding the rings together.The presence of rather short Ca-0 contacts (2.26 A) and the observed compression of CaO octahedra may indicate that strain together with the availability of large holes in the lattice facilitates a rapid break-up of the structure on reaction with water to give the initial hydration product 2Ca0,A1203,8H20 and finally the hexahydrate 3CaO,AI2O3,6H,O. This structure should form the basis for an understanding of the effects of impurities on the reactivity of cement. The SCF-X method has been used for the first time to calculate the electronic structure of the aluminate ion [A1O4I5- for comparison with the isoelectronic and (u)P.Mondal and J. W. Jeffrey Actu Cryst.,1975 B31,689; (b)J. A. Tossell J. Amer. Chem. SOC.,1975 97,4840. The Typical Elements 115 isostructural [Mg0,I6- and [SiO,]"- ions.156 The calculated MO energies agree qualitatively with the separations of the Ks. (assigned to the 3t2 MO) and Ks (assigned to the 41 MO) peaks in the X-ray emission spectrum. The calculations also indicated that peaks at 9.3 and 11.1eV in the U.V. spectra of a natural phlogophite mica are due to the [AlO,]'- unit. Si3d-02p (u-and ?r-types) bonding does occur in the [SiO,]"- ion but it is relatively small in magnitude compared with Si3s-02p and Si3p-02p bonding. For [AlO,l5- the 51 MO is of similar energy to that in [S'iO,]".Thus a small A13d-02p bonding component may still be present. A sharp decrease in the strength of M3s-02p (M =Si Al or Mg) bonding is largely responsible for decreasing covalency and increasing instability of the tetrahedral clusters in the sequence [SiO,]"- >[AlO4I5->[Mg0,I6-. The Co-ordination Sphere of Aluminium in Solution.-The n.m.r. probes 'H 27Al 31 P and I3C have all been utilized to investigate the inner co-ordination sphere of A13+. Solvation numbers of 6 are the rule. However in ethanol [Al(EtOH)4]3+ is the dominant species. By utilizing both 27Aland ,'P n.m.r. Delpuech and co-workers'6 have demonstrated the existence of octahedral [AIL6],+ [L =(MeO),PO,(EtO),PO (MeO),MePO,(EtO),EtPO or (MeO),HPO] and the tetrahedral solvate [L = (Me,N),PO] in anhydrous nitromethane.Kinetic data are indicative of a dissociative SN1 ligand-exchange mechanism for [AIL6],+ while conversely an associative SN2 mechanism is applicable to [Al{(Me,N),P0},]3'. The activation energy for the associative process is dramatically smaller by ca. 12 kcal mol-' and ligand exchange on A13+ in (Me,N),PO is five orders of magnitude faster than in systems where A13+ is six-co-ordinate. These observations may have important implications for the synthetic and solution chemistry of A13+, especially if they can be generalized for other solvent systems. It is interesting that whereas activation enthalpies for exchange in [AlL6I3+ (L =DMF or DMSO) seem to indicate dissocia- tive pathways for [GaL6I3+ (L=H20 or DMF) associative mechanisms may be operative.Halide ion exchange on [GaCl,]- is also associative. Aluminium-Halogen Compounds.-The heats of reaction of Group I11 halides and organometallics with neutral ligands containing Group V and VI donor atoms have been measured over the past 20 years in an attempt to compare acceptor properties. Recently Wood and ~o-workers~~~ have determined the necessary heats of forma-tion crystal structures and lattice energies for M1[M2X,] salts (M' =Na or Cs M2=A1 or Ga X =C1 or Br) to calculate M2X3-X- donor-acceptor bond energies. (Average heats of dissociation DMzx3-x-(kcal mol-l) are 82 ([GaCl,]-) 87 ([AICl,]-) 75 ([GaBr,]-) and 80 ([AlBrJ). Hence the halide ions form stronger donor-acceptor bonds than the neutral ligands.An estimate of the InCl,-Cl- bond energy by a newly developed method suggests that towards the halide ions the order of acidities is InCI >AICI >GaCI,. These results can be compared with the relative acidity order BCl >AlCl >GaCl >InCl towards ethyl acetate as the reference base the order A1 >Ga >In for Ph3M2 towards pyridine and the common sequence l6 J. J. Delpeuch M. R. Khaddar A. A. Peguy and P. R. Rubini J. Amer. Chem. Soc. 1975,97 3373. l7 (a)R. C. Gearhart jun. J. D. Beck and R. H. Wood Inorg. Chem. 1975,14,2413;(b)G. K. Barker M. F. Lappert J. B. Pedley G.J. Sharp and N. P. C. Westwood J.C.S.Dalton 1975,1765; (c)J. L.Dehmer J. Berkowitz L. C. Cusachs and H. S. Aldrich J. Chem.Phys. 1974,61,594;(d)K. Wittel and R. Manne J.Chem. Phys. 1975,63 1322; (e)R. G. S. Pong R. A. Stachnik A. E. Shirk and J. S. Shirk J. Chem. Phys. 1975,63 1525. 116 A.J. Carty,R.H. Cragg,and J. D.Smith Al > B -Ga > In for bulky amines. Additional information on M-X p,,-p, bonding and Lewis acidities for monomeric Group I11 acceptors has been sought using p.e. ~pecfro~copy.'~~ For gaseous MCl (M = B Al Ga or In) the relative orbital energies increase in sequence u; e' e" a e' a;. The a; orbital which is primarily responsible for .rr-bonding in MX has energies indicative of greater M-X T-bonding in the boron compounds. These authors suggest that the baricentre of the first two IP's for the MX species provides an estimate of residual charge on the halogen atom and the relative .rr-density on the central metal atom.Thus A1 > B -Ga >> In if this is considered a measure of Lewis acidity. However the same criterion yields BCI >>BBr3 contrary to the usual order of affinities. As a general observa- tion changes in electronic and structural properties for both donor and acceptor occur on complexation and reliable orders of acidities cannot generally be expected from a single physical measurement. A further item of interest is the splitting observed in the e" ionization energies of the iodides. Although Lappert et al. favoured a second-order spin-orbit interaction as an explanation of this effect this has been rejected earlier.'" Instead it was proposed that GaI had a pyramidal ground state. A reinterpretation of the phenomenon has since appeared confirming the spin-orbit origin of the ~p1itting.l~~ Moreover in argon matrices all of the gallium halide monomers are planar D3h molecules as intuitively expe~ted.'~' Compounds with Aluminium-Hydrogen Bonds.-One notable development in the past five years has been the synthesis and characterization of a series of poly-(N-alkyliminoalanes).Several routes to these compounds are available e.g. 1 MAlH + RNH hydrocarbon* -(HAlNR) + 2H2 + MH A simpler direct method has been developed:18" 1 1 A1 + RNHZ + -(HAlNR) + -Hz (9) n 2 These polyiminoalanes have fascinating cage structures. A typical structure that of the alane adduct [HAINPr'],AlH is shown in (23).18* Finally mention should be made of an important study on the mechanism of hydroalumination of Group IV substituted alkynes.18c For trimethyl(pheny1- ethynyl)silane a kinetically controlled cis-hydroalumination by R,AlH is followed by a rapid isomerization to the trans-adduct.Carbon-silicon and/or carbon- aluminium p,,-d bonding as in (24) and (25)may promote cis-trans isomerization. Transition Metal-Gallium,-Indium and -Thallium Bonds.-The chemistry of compounds with transition metal-M (M = Ga In or Tl) bonds has been developed. Reaction of Me,Ga with [q-C5H5W(C0),H] gave [q-C5H5W(CO),]3Ga.1y~ The 18 (a)S. Cucinella A. Mazzei and G. Dozzi J. Orgunometullic Chem. 1975,84 C19; (b)G. Perego M. Cesari G. Del Piero A. Balducci and E. Cernia J. Orgunomefullic Chem.,1975,87,33;(c)J. J. Eisch and S. G. Rhee J. Amer.Chem.SOC.,1975,97,4673. 19 (a)A. J. Conway P. B. Hitchcock and J. D. Smith J.C.S. Dalton 1975 1945; (b)A. T. T. Hsieh Inorg. Chim. Acfu 1975,14,87;(c)H. J. Haupt. F. Neumann and H. Preut. J. Orgunometullic Chem. 1975,99 439; (d)S. G. Pedersen and W. R. Robinson Inorg. Chem. 1975,14,2360;(e)S. G. Pedersen and W. R. Robinson Inorg. Chem. 1975,14,2365. 117 The TypicalElements OAl OC ONOH (23) stereochemistry of gallium is as expected trigonal planar. This complex completes the series [q-C5H5W(C0)3]3M (M =Ga In or Tl).19b Interestingly the correspond- ing aluminium complex [q-C5H5W(C0),]A1,3THF does not contain Al-W bonds. Treatment of indium metal with [Re,(CO),,] in a bomb afforded [Re,(CO),(p- InRe(CO)5)21(cf. [Mn,(CO),{p-InMn(CO)5},1) and [Re4(Co>12{p3-InRe(c0),),1 having a tetracapped tetrahedral structure.19' There is an obvious analogy between the terminal transition-metal moieties in these species and bulky alkyl groups. Furthermore the instability usually associated with Tl' organometallics is apparent in the behaviour of Tl'-transition metal Thus reaction of Tl[Co(CO),] with a phosphine (L) causes disproportionation to thallium metal and Tl[Co(CO),L],. Only less basic phosphites yield Tl' derivatives. Thallium(1)-iron -vanadium or -chromium bonds are only stable when the corresponding transition- metal anion is weakly basic.lge Synthesis of Indium (111) and Indium (I) Compounds.-The development of a direct electrochemical synthesis of indium compounds warrants special mention.20a The method which can be used to produce neutral anionic or cationic complexes uses a cell with an indium anode a platinum cathode and a non-aqueous solvent system Ph SiMe Ph SiMe, \+ \+ / /c-c' // c-c, \ H AIR; (24) (25) 2o (a)J.J. Habeeb and D. G. Tuck J.C.S.Chem. Comm. 1975,808;(b) J. J. Habeeb and D. G. Tuck J.C.S. Dalton 1975 1815. 118 A.J. Carty,R.H. Cragg,and J. D.Smith (usually benzene-methanol). Applied voltages of 50-100 V at 20-100 mA for 1-3 h gave gram quantities of complexes. The facile synthesis of anhydrous InCl (cf.burning indium metal in an atmosphere of dry chlorine gas) and Et,N[InI,] (from Et4NI Iz and In) are notable. Apparently the method can be extended to the synthesis of transition-metal halide compounds e.g.CrCl and may therefore be applicable to organometallics. Developments will be awaited with interest. The co-ordination chemistry of indium(1) has been slow to develop owing principally to the intractability of potential percursors such as InCl InzO and In,S. This is in marked contrast to the isoelectronic tin(I1) species such as SnCl which have been extensively investigated both as Lewis acids and as useful synthetic reagents. Structural data for indium(1) compounds are very sparse when compared to those available for tin(r1). Habeeb and Tuck2" have used cyclopentadienylin- dium(1) as an organic solvent-soluble starting material. The reaction CSH,In + HX -P InX + C5H (10) yielded various indium(1) complexes including 4,4,4-trifluoro- 1-(thien-2- yl)butane-1,3-dionatoindium(1) quinolin-S-olatoindium(I) and 2-mercap-togentan-3-onatoindium(1).These indium(1) compounds e.g. quinoline-8-olatoindium(1) [In(qno)] may in their own right be useful starting materials for indium(II1) complexes. Thus acetylacetone yielded [In"'(qno)(acac),] and iodine [In(qno)I,]. The availability of soluble In' compounds such as [In(qno)] may be of considerable use in extending the range of compounds having indium-transition metal bonds via oxidative addition reactions (see above). Pentahalogenometallates(m).-New vibrational data for single crystals of the square-pyramidal ions [MCl,]'- (M = In or TI) together with low-temperature Raman and i.r. studies of polycrystalline samples allow a reassignment of vibrational spectra.21 In the isomorphous tetraethylammonium salts [MC151Z- ions reside on sites of Czsymmetry rather than C4as assumed in previous analyses based on X-ray data.Rerefinement of the earlier X-ray data in the space group P4 including anisotropic temperature factors gave an improved R value of 0.067. However the basic structural features of the molecules remain unchanged. Stereochemical Activity of the Thallium(I) Lone Pair.-Although the ions Ga' In+ and Tl' have ns2configurations there has been little structural evidence to indicate whether this pair of electrons is 'inert' or stereochemically active. X-ray studies of hexafluoroacetylacetonatothallium(I),22" (BU'~NCS~)TI,~~~ and TlzS522c have now shown unequivocally that the 6s' pair plays a major role in dictating the co- ordination geometry around the thallium atom.21 G. Joy A. P. Gaughan jun. I. Wharf D. F. Shriver and J. P. Dougherty Inorg. Chem.,1975,14,1795. 22 (a)S. Tachiyashiki H. Nakayama R. Kuroda S. Sato and Y. Saito Acru Cryst. 1975 B31,1483; (b) H. Pritzkow and P. Jennische Actu Chem. Scand. 1975 A29,60; (c)B. Leclerc and T. S. Kabre Acru Cryst. 1975 B31 1695.

ISSN:0308-6003    

DOI:10.1039/PR9757200095

出版商:RSC    

年代:1975

数据来源: RSC

摘要:

The Typical Elements PART111 Groups IV and V By J.D. Smith 1 Reactions of Hydrides The pyrolysis of silanes is proving as complicated and difficult to sort out as the pyrolysis of hydrocarbons but interest in the subject is maintained by the differences between the chemistry of carbon and that of the other Group IV elements. For example the initial step in the thermal decomposition of hydrocarbons is the breaking of a C-H or C-C bond with formation of radical intermediates R,C*. However it has been shown e.g. by deuterium substitution studies that the initial step in the decomposition of polysilanes results in elimination of silenes :SiH or :SiHR:'" RSiH,SiH -+ :SiHR + SiH or :SiH + RSiH3 Activation energies for this process (ca. 210 kJ mol-') are less than Si-Si bond energies (ca.340 kJ mol-') and it seems that the reaction must involve a 1,2-hydrogen shift with a transition state (1) A similar transition state for hydrocarbon decompositions would involve quinque- valent carbon and this is apparently energetically unfavourable. The detailed mechanism of the decomposition of monosilane SiH is still not clear but evidence from pyrolysis in the presence of acetylenelb shows that silyl radicals -SiH, rather than silene species :SiH, are the predominant intermediates produced in the first step. It has been suggested that formation of ground-state singlet :SiH from SiH is forbidden by orbital symmetry unless the reaction path is such as to add considerable strain energy to the activation energy; .SiH formation is thus favoured.Ground- state :SiH could be generated by an orbitally allowed process from disilane and ethynylsilane HCECSiH, from :SiH2 +HCGCH is indeed found as a major product in the pyrolysis of disilane-acetylene mixtures. After further studies on the pyrolysis of hexamethyldisilane a mechanism has been proposed'' which accounts for some of the divergent results obtained under a variety of conditions in earlier work. Initial steps in the decomposition give trimethylsilyl radicals Me,Si* or dimethylsilene Me,Si both of which react further to give a complicated mixture. 2Me,Si-+ Me,SiSiMe + Me,Si + Me,Si A new value of 337 kJ mol-' for the bond dissociation energy D(Me,Si-SiMe,) has been deduced. The thermal decomposition of hexamethyldilead in toluene can be (u)A.J.Vanderwielen M. A. Ring and H. E. O'Neal J. Amer. Chem. Soc. 1975,97,993; (b) C. H. Haas and M. A. Ring Inorg. Chem. 1975,14,2253; (c)I. M. T. Davidson and A. V. Howard J.C.S. Furuduy I 1975,71,69 and references therein; (d)D. P. Arnold and P. R.Wells J.C.S. Chem. Comm.,1975,642. A.J. Carty,R.H. Cragg and J. D.Smith explained in terms of the following reaction sequence Me,PbPbMe + Me,Pb + Me,Pb Me,Pb + Me,Pb + Me8Pb + 2Me,Pb + Pb In this case no evidence for methyl or trimethyl-lead radicals Me,Pb* was obtained.ld Information about reactive species may also be obtained from reactions of metal atoms obtained by evaporation at high temperatures (>lOOO"C) and in high vacuum (<1Torr). The atoms and molecules of volatile compounds are brought together at a cold surface on which products are condensed (see also p.179).'" Particular attention has been given to the chemistry of carbon silicon and transition- metal atoms but the first reports2b9c of reactions of thermally generated germanium atoms have now appeared. The halides of carbon and silicon react with germanium atoms to give trihalogenogermyl derivatives and trimethylsilane reacts to give the new compound Me,SiGeH,SiMe, Ge + 3MX,+ MX,- ,GeX + (MX,-There is interest in whether the initially produced atoms are in the ground ('P) or excited (IS or 'D) states and whether the electrons in intermediates such as HGeSiMe or ClGeCCl remain unpaired or relax to a paired configuration before further reaction.Silyl compounds react with tin tetrachloride in two distinct ways.,= With SiH, SiH3F SiH,Cl (SiH,),N [SiH,Mn(CO),] or Si21& chlorine is substituted for hydrogen and SiH2Cl derivatives are isolated. With SiH,Br [SiH,Co(CO),] (SiH3),S or (SiH3)3P the predominant reaction is exchange SiH3X + SnC1 + SiH,Cl +XSnCl The compounds XSnCl sometimes undergo further reactions. With (SiH3)20 there is evidence for both substitution and exchange. In general the exchange reaction occurs when the silyl starting materials SiH,X have heavier less electronegative groups x. The germyl derivatives H,GeM (M =Li Na K Rb or Cs) have been made from germane and the alkali metal in dimethoxyethane and the potassium rubidium and caesium compounds have been isolated as crystalline solids.3b Solvent-free H,GeLi and H,GeNa could not be obtained.A single-crystal X-ray investigation has shown that germyl-potassium and -rubidium like silyl-potassium -rubidium and -caesium have the sodium chloride structure in which germyl anions show free rotation at room temperature. Germylcaesium has the rare thallium iodide structure in which 2 (a) P. L. Timms Adu. Inorg. Chem. Radiochem. 1972,14 121; (6)M. J. McGlinchey and T.-S. Tan Inorg. Chem. 1975,14 1209; (c)R. T. Conlin S. H. Lockhart and P. P. Gaspar J.C.S. Chem. Comm. 1975,825. (a)S. Craddock E. A V. Ebsworth and N. Hosmane J.C.S. Dalton 1975 1624; (b)G. Thirase E. Weiss H. J. Hennig and H. Lechert Z. anorg. &m. 1975,417,221; (c)P. C. Angus and S. R. Stobart J.C.S.Dalton 1975,2342; (d)A. R. Dahl C. A. Heil and A. D. Norman Inorg. Chem. 1975,14,1095. (e) A. R. Dahl A. D. Norman H. Shenav and R. Schaeffer J. Amer. Chem. SOC.,1975,97,6364; cr)A. R. Dahl and A. D. Norman Znorg. Chem. 1975,14,1093; (g)A. R. Dahl C. A. Heil and A. D. Norman Inorg. Chem. 1975,14,2562; (h)J. E. Drake and C. Riddle J. Chem. SOC.(A),1968,2709; Quart. Rev. 1970,24,263. The Typical Elements each germyl ion has seven caesium neighbours and each caesium seven germyl neighbours. At low temperatures (below -100°C for H,GeK -120°C for H,GeRb and -170 "C for H,GeCs) rotation of the germyl anion is frozen as shown by broad-line n.m.r. experiments. The GeH3- ionic radius (assuming values of K+ 1.33A; Rb+ 1.48A) is 2.29A only a little larger than that of the H3Si- ion (2.26 A).Bond angles (from broad-line n.m.r.) are for SiH3- 94 * 4" (cf.,PH3 94") and for GeH3-93*4" (cf. ASH, 92"). The conversion of bromogermane into a variety of germyl derivatives by use of lead salts has been e~plored.~' In general the conversions are cleaner and the yields are higher than with the more reactive silver salts. Good yields of germyl formate and acetate have been obtained and digermyl ether has been made from bromogermane and lead oxide. Reactions with lead cyanate or thiocyanate gave germyl isocyanate or isothiocyanate (Scheme 1). Germyl trifluoroacetate was made from bromogermane and silver trifluoroacetate. (H,Ge),O ,PbO H,GeBr 5H,GeX (X = HCO or MeC0,) 1PQNCSh H,GeSCN H,GeY [Y = C1 SMe or Mn(CO),] Scheme 1 The chemistry of phosphinogermanes R,Ge(PH,),- (R = alkyl or H) made from the chlorogermanes and LiAl(PH2)4 in glyme solvents has been investigated in some For example redistribution reactions have been studied by n.m.r.spectros~~py.~~ The products from dimethyl(phosphino)germane Me,Ge(PH,)H at equilibrium showed roughly statistical distribution of phosphino- and hydrido- substituents at germanium Me,Ge(PH,)H Me,GeH + Me,Ge(PH,) Redistribution reactions of methyldiphosphinogermane were also clearly detected 2MeGe(PH,),H + MeGe(PH,)H + MeGe(PH,) 2MeGe(PH,)H -+ MeGeH + MeGe(PH,),H From phosphinogermane H,GePH, the products indicated redistributions both at germanium and more slowly at phosphorus. New ternary hydrides H,Ge(PH,) and HGe(PH,), as well as Geh were formed rapidly and the products (H,Ge),PH (H3Ge)3P and PH3 after long reaction times.Pyrolysis of the more thermally stable dialkyldiphosphinogermanesR,Ge(PH,) (R=Me or Et) resulted in elimination of phosphine and formation of the cage compound hexa(dialky1germa)tetraphosphide (2) characterized by spectral data by reaction with hydrogen chloride (which confirms the presence of Ge-P and the absence of Ge-Ge and P-P bonds) and by an X-ray study3' (see next section). The Ge-P distance is 2.317 A. By careful separation of products twointermediates (3) and (4) were characterized but the detailed mechanism of the condensation process was not completely established. Me,GeCI LiAI(PH2), HCI Me,Ge(PH,) 12% 140"C +Me,GeCl + PH, -(Me,Ge),P (2) A.J.Carty,R.H. Cragg,and J.D.Smith H I P Me,Ge Me2Ge/\GeMe Me,Ge /’\\GeMe2 I I &I -1 bH2 PH2 PH2 PH2 PI4 (3) (4) Since oxidation products appeared to be catalysts in the formation of the cage compound (2) the reactions between trimethyl(phosphino)germane,Me,GePH, or dimethylbis(phosphino)germane Me,Ge(PH,), and oxygen in chloroform solution were studied in more detail. The products were intractable solids phosphines or phosphine oxidation products but traces of new germyl phosphonates (5) and (6) were obtained. One of these (6)has been made in 70% yield from the dimethylger- manium oxides (Me,GeO) and a ten-fold excess of anhydrous phosphorous acid.3f /-\ /O O\ Me,Ge GeMe Hydroly~is~~ of the methyl(phosphino)germanes Me,GePH and Me,Ge(PH,) appears to be quantitative e.g.2Me,GePH2 + H20 -+ (Me,Ge)20 + 2PH No evidence has been obtained for redistribution reactions at phosphorus such as those observed earlier for unsubstituted germylph~sphine:~” H,GePH (H,Ge),P + PH Hydrolysis of dimethyl(phosphino)germane,Me,Ge(PH,)H was more complex as the Ge-H bond was labile under the reaction conditions. With short reaction times (20-100 min) and a deficiency of water the compound (Me2GeH),0 was formed but this was thermally unstable at 32°C and readily converted by water into (Me,GeO),. With reaction times greater than 2 h the hydrolysis could be described by the following equation 1 2Me2Ge(PH2)H+ H20 + -(Me,GeO) + 2PH + Me2GeH2 n No Me2GeH2 was detected until after (Me,GeH),O had begun to disappear.3g 2 Cage Compounds A large number of molecules X,Y (7) where X =RE’ or E2,Y =R2E1 RE2 or E3 and E’ E2,and E3are elements from Groups IV V and VI respectively are known.Most of these have the adamantane structure with symmetry Tdor close to Td. The Typical Elements Full details of the crystal structure of (MeSi),S have been p~blished:~" the molecule is of a well established series and the germanium and tin analogues are isostructural. Hexa(dimethy1germana)tetraphosphide (2) has a similar structure (7; X = P Y = Me2Ge).3" The phosphorus atom of the cage compound P406(7; X = P Y = 0)is a donor towards some transition metals. Under a carbon monoxide atmosphere the carbonyl [Fe,(CO),] reacted with the oxide P406 in THF to give a series of compounds [{(C0)4Fe},(P40,)] (n= 1-4) which was characterized by n.m.r.Reactions with pentacarbonyl iron were more complicated and the products included the oxides P,O and P40,. Another new cage compound synthesized during 1975 is the selenide P4Se4 made by fusing together the elements at 300-350 0C.4cIts i.r. spectrum was consistent with the structure (9) similar to those of the known selenides P4Se (8) and P4Se 3 Polyatomic Anions Alloys of the post-transition metals Sn Pb Sb or Bi with alkali metals are remarkably soluble in liquid ammonia and a series of potentiometric and prepara- tive studies more than 40 years agoSa suggested that the coloured solutions contained the cluster anions Sng4- Pb7,94- Sb3,5,73- and Bi3,53-.Confirmation of these clusters by X-ray crystallography has so far proved impossible because on evaporation of the ammonia the Na' and M,"-ions revert to the metallic alloys. The isolation last yea? of the crystalline compound Na(crypt)'Na-[crypt = N(CH2CH20CH2CH20CH2CH2),N] has suggested a new approach to a long- standing problem. Small alloy samples have been treated with the crown ether in ethylenediamine. Crystalline compounds [Na(crypt)'],M,"- have been obtained (a)J. C.J. Bart and J. J. Daly J.C.S. Dalton 1975,2063; (b)M. L. Walker and J. L. Mills Inorg. Chem. 1975,14,2438;(c)Y. Monteil and H. Vincent Z. anorg. Chern.,1975,416,181; (d)G. J. Penney and G. M. Sheldrick,J. Chern. SOC.(A),1971 245; E.Keulen and A. Vos Acta Cryst 1959,12,323. (a)E. Zintl J. Goubeau and W. Dullenkopf Z. phys. Chem. l931,154A 1; (b) F. J. Tehan B. L. Barnett and J. L. Dye J. Amer. Chem. Soc. 1974,% 7203; (c) J. D. Corbett and P. A. Edwards J.C.S. chem. Cornm. 1975 984; (d) A. Hershaft and J. D. Corbett Znorg. Chem. 1963 2 979; (e) R. M. Friedman and J. D. Corbett Znorg. Chem. 1973,12,1134;v> J. D. Corbett Znorg. Chem. 1968,7,198; (g)J. D. Corbett D. G. Adolphson D. J. Merryman P. A. Edwards and F. J. Armatis J. Amer. chem. Soc. 1975,97,6267;(h)W. Dahlmann and H. G. von Schnering Natunviss. 1972,59,420; ibid. 1973 60 429; (i)U. Frank and W. Miiller Z. Natutforsch. 1975 Mb,313. A. J. Carty R. H. Cragg and J.D. Smith and the structures of three anions Sng- PbS2- and Sb,,- have been deter- mined.Although the anion Sn94-has the same valence electron structureSC as the trigonal-bipyramidal (D3h) Big5+ isolated in 'bismuth monochloride' [(Bi,5+)2(BiC152-)4(Bi2Clg2-)],'" the structure (1 1) is and in [Bi+(Bi95+)(Hfc162-),]5e an antiprism capped on one square face (C4,)(Sn-Sn = 2.93-3.31 A). That such a configuration is obtainable in a crystalline compound is consistent with the molecular orbital scheme proposed earlier.5f The green Pb94- established in liquid ammonia and isoelectronic with Big5+ has not yet been obtained in a crystalline derivative but Pb5,- also with D3h symmetry (12) and Pb-Pb 3.00-3.23 A has been obtained.'" This ion is isoelectronic with the well established BiS3+ ion. The Sb,,- ion found 5g in [Na(~rypt)+],Sb,~- has approximate C, symmetry (13) (Sb-Sb 2.69-2.88 A); the cluster is similar to the P$- cluster in Sr3PI4 and Ba3P14'h and the valence structure is presumably the same as in the well-established compounds P4S3 P4Se, and As& [cf.structures (13) and (S)]. Planar five- membered rings Ge have been characterized" in the new lithium germanide LillGe6 made by fusing the elements in a tantalum vessel but there are no metal clusters in Lil,Sn and a number of other solid phases in the lithium-tin and lithium-lead systems. 4 Alkylamido-derivatives and &oxides The chemistry of dialkylamido-compounds of tin(1v) has been extensively studied but simple dialkylamido-derivatives Sn(NR2) are rare. Most of those reported contain large R groups e.g.Sn[N(SiMe,),] or S~[N(S~M~,)BU'],.~" It has now been found,66 however that bis(dimethylamido)tin(II) is accessible from the reaction between tin(I1) chloride and LiNMe,. It is a white crystalline solid m.p. 91-93 "C subliming at 70 "C under Torr and very reactive towards air and moisture. Only peaks from fragmentation of monomer are observed in the mass spectrum but bis(dimethylamido)tin(II)appears to be dimeric in cyclohexane. The n.m.r. spectrum at 40 "Cshows only one line but at -40 "Cthere are two equal intense signals and at least three weaker peaks. The spectrum suggests that the dominant species is the trans-isomer (14) which has two non-equivalent sets of methyl groups. There may (14) (a) D. H. Harris and M. F. Lappert J.C.S.Chem.Comm. 1974,895; (6) P.Foley and M. Zeldin Inorg. Chem. 1975,14,2264; (c)R. Gsell and M. Zeldin J. Inorg. Nuclear Chem. 1975,37,1133; (d)P. F. R. Ewings and P. G. Harrison J.C.S. Dalton 1975 2015. The Typical Elements be smaller concentrations of the cis-isomer also. At 40 "C exchange of alkylamido-groups between isomers and between bridge and terminal positions must be rapid on the n.m.r. time-scale to account for the single peak. The reactions of bis(dimethylamido)tin(II)appear to be similar to those of the tin(1v) compounds. For example dimethylamine is rapidly eliminated in reactions with ethanol or N-methyldiethanolamine EtOH MeN(CH,CH,OH) 1 Sn(oEt)Z '-ZMe,NH Sn(NMez)z -2Me,NH Sn(OCH,CH,),NMe Spectroscopic properties of tin(@ alkoxides and phenoxides Sn(OR) (R =alkyl or aryl) have been reported; some of these compounds may be sublimed but most are insoluble in organic solvents and are thought to have polymeric solid-state structures.Sn(OBu), made by the well established procedure from tin(I1) chloride butanol and triethylamine is dimeric in dichloromethane.6c Phenoxides may be made in quantitative yield from bis(methylcyclopentadieny1)tin and phenols.6d 5 Lone-pair Stereochemistry The valence-shell electron-pair repulsion (VSEPR) theory provides one of the simplest interpretations of the shapes of many compounds of the main-group elements. It is usually illustrated by use of compounds with electronegative atoms such as oxygen fluorine or nitrogen and it successfully predicts the unsymmetrical environments in compounds of elements with lone pairs such as Sn" Pb" SbII' or Bi"'.In solid compounds with the heavier non-metals however post-transition metals in low oxidation states often have symmetrical environments in which lone pairs do not appear to occupy co-ordination positions. The compound CsSn"Br has now been by a single-crystal X-ray study to have the ideal perovskite structure at room temperature so each tin atom is surrounded by six bromine atoms at the corners of an octahedron as suggested earlier from '"Sn Mossbauer data. The compound is a black semiconductor and thus differs from the white compounds MSnBr (M =Na K Rb or NH,). It is suggested that the colour the electrical properties the low Mossbauer chemical shifts and the symmetrical environment of the tin(I1) can all be accounted for by postulating that the 5s2 electrons are delocalized into a band formed by the bromine orbitals.Low-temperature Mossbauer data indicate that the tin(@ environment becomes less symmetrical at low temperatures. Coloured high-temperature phases of other caesium bromostan- nates(r1) e.g. CsSn",Br or Cs4SnI1Br6 may also be obtained and their properties are accounted for in the same way. At 20 "C the colours fade and the crystal symmetry becomes non-cubic; it is suggested that this indicates depopulation of the conduction band. The white compound CS,S~'~B~~ has a cubic structure closely related to that of CsSn"Br, and a series of'solid solutions ~&'"Br6-CSSn"Br may be obtained.The intense colours of these substances which contain both SnIV and Sn" may also result from delocalization of the SnII lone pair into a conduction band formed by the bromine atoms. Electronic structures of mixed-valence compounds of antimony7' and hexahalogenotellurates(~v)~~ may be discussed in similar terms. (a)J. D. Donaldson J. Silver,S. Hadjiminolis and S. D. Ross,J.C.S. Dalton 1975,1500;(b) L.Atkinson and P. Day J. Chem. SOC.(A) 1969,2423 2432; (c) J. D. Donaldson S. D. Ross J. Silver and P. J. Watkiss J.C.S. Dalton 1975 1980. A.J. Carty,R. H. Cragg and J. D. Smith 6 Trends in Bond Order The value of structural information is considerably enhanced where data are available for a closely related series of molecules. This point is illustrated by two examples.Reactions between the lithium salt of diphenylketimine and the appropriate Group IV tetrachlorides yield the derivatives E(NCPh,) (E = Si Ge or Sn) ECl + 4Ph,CNLi -+ E(NCPh,) + 4LiCl Surprisingly these compounds are not isomorphous and there is a systematic variation in the E-N distances and E-N=C angles in the series (Table 1).8a Table 1 E-N Bond lengths and E-N=C angles in the compounds E(NCPh,) Mean Mean E E-N/A E-N=C/O E-N/A (calc.) DiferencelA Si 1.7 17( 10) 137.0 1.879 0.162 Ge 1.872(5) 127.0 1.928 0.056 Sn 2.06(4) 121.3 2.108 0.048 Each molecule has a tetrahedral arrangement of nitrogen atoms about the Group IV element. The structural differences between the silicon and germanium compounds cannot be attributed simply to differences in size as the radii of silicon and germanium are quite similar.A possible explanation is that in the series from tin to silicon the hybridization at nitrogen changes from sp2 to sp as the lone pair is transferred to a p-orbital which can more effectively interact with silicon through (p-d)~ bonds. Single-bond lengths may be estimated (Table 1)by combining well established E-C C-C and C-N bond lengths and there is a systematic shorten- ing decreasing in the series Si > Ge > Sn in accord with the n-bonding hypothesis. The (p-d)n overlap may be achieved by a variety of combinations of the four E-N orbitals and it is noticeable that the E-N=C bond angles are extremely variable especially in the silicon and germanium compounds.The choice of angles in a given crystal thus seems to depend on packing considerations -which explains the variety of molecular conformations found. In the silicon compound there are two crystallo- graphically independent molecules with a range of E-N=C angles. Another example of a systematic study designed to detect trends in molecular parameters has involved the trimethyl-phosphine and -arsine oxides and sulphides. Table 2 Molecularparameters for Me,EY (E = Por As Y = 0 or S) Me3P0 Me3PS Me,AsO Me3AsS E-Y/A 1.476(2) 1.940(2) 1.631(3) 2.059(3) E-CIA 1.809(2) 1.8 18(2) 1.937(2) 1.940(3) LYEC/" 114.4(7) 114.1(2) 112.6(3) 113.4(4) Electron diffraction measurements (Table 2)8b show that the E-C distances decrease very slightly but systematically in the series X3E X,ES and X3E0 (a)N.W. Alcock M. Pierce-Butler G. R. Willey and K. Wade J.C.S. Chem. Comm. 1975 183; N. W. Alcock and M. Pierce-Butler J.C.S. Dalron 1975 2469; (b) G. J. Wilkins K. Hagen L. Hedberg Q. Shen and K. Hedberg J. Amer. Chem. SOC.,1975,97,6352. The Typical Elements 127 (X = Me) as has been found for X = F or CI. There is also a systematic decrease in P-0 and P-S distances in the series Me3PY Cl,PY and F3PY. Trends are attributed to changes in bond polarity. By making reasonable assumptions about the lengths of E-Y single bonds it is found that P=S and As=S bonds have orders close to two but P=O and As=O bonds appear to have higher orders. The rotational freedom of the methyl group increases in the series Me3P0 <Me3PS-Me3As0<Me3AsS.7 Gas-phase Basicities One of the major problems in the interpretation of results of preparative experi- ments in terms of molecular properties is in the allowance which should be made for solvation effects. The availability in recent years of measurements made on molecules in the gas phase e.g. by ion cyclotron resonance spectro~copy,~~ has enabled much progress to be made. The gas-phase basicity of trimethylarsine has now been measured and this may be placed in the context of various amines and phosphines (Table 3)?' Table 3 Proton affinities A ionization potentials I and bond dissociation energies D(B'-H) (all in kJ mol-l) Base B NH3 MeNH2 A 841 878 I 983 865 D(B+-H) 512 431 Me2NH 904 795 387 Me3N 921 754 364 PH3 MePH2 783 841 961 879 432 408 Me2PH 889 817 394 Me3P 926 773 387 ASH^ 756 954 397 Me3As 876 761 326 For all three groups of compounds amines phosphines and arsines the gas-phase basicities increase as hydrogen atoms are replaced by methyl groups.The effect is greater in phosphines and arsines than in amines in which it is suggested rehybridi- zation energy in going from unprotonated to protonated amine opposes the effect of methyl substitution. Ion-molecule reactions of trimethylarsine are very like those of trimethylphosphine . Another approach which leads to detailed information about bonding in simple molecules is exemplified by studies" on the phosphines R,PX3- (R =Me or But; X= H C1 or F; n = 1-3) and on related compounds such as (Me2N),PC13- (n = 1-3) and R2NPF (R = Me or Et).The measurement of the He(1) photoelec- tron spectra of a complete series of similar compounds enables many of the (a)J. L. Beauchamp Ann. Rev. Phys. Chem. 1971,22 527; (b)R. V. Hodges and J. L. Beauchamp Inorg. Chem. 1975,14 2887; (c)M. F. Lappert J. B. Pedley B. T. Wilkins 0.Stelzer and E. Unger J.C.S. Dalton 1975,1207;(d)0.Stelzerand E. Unger Chem. Ber. 1975,108,1246;(e) D. C. Mente and J. L. Mills Inorg. Chem. 1975 14 1862; (f) L. J. V. Griend and J. G. Verkade J. Amer. Gem. Soc. 1975,97,5960;(g) K. 0.Christe C. J. Schack and R. D. Wilson Inorg. Chem. 1975,14,2224;(h) R. Savoie and P. A. Gigukre J. Chem. Phys. 1964,40,2698; (i) K. 0.Christe Inorg. Chem. 1975,14 2230 2821; 6)S. P. Mishra M.C. R. Symons K. 0.Christe R. D. Wilson and R. I. Wagner Znorg. Chem. 1975,14 1103. A. J.Carty,R. H. Cragg and J.D.Smith complexities which result from band overlap to be resolved so that a detailed picture of molecular orbital energies may be built up. The first band in the p.e. spectrum is assigned to the phosphorus lone pair and by plotting the values of the corresponding ionization potential against parameters such as J(PB) in phosphine-borane com-plexes or the A carbonyl-stretching frequencies in complexes ci~-[Mo~(CO),l,~~ the conclusion is reached that the lone-pair ionization potential provides a good measure of relative basicities within a related series. Correlations with Hammett constants XuPhor are less clear (except for alkyl phosphines R,-,,pH,,).One of the attractions in using ionization potential data from p.e. spectra as a measure of basicity is that information may be obtained about a very wide range of compounds. The basicity of the trimethyl derivatives of the Group V elements towards a series of boron Lewis acids has been studied by classical methods. The expected trends in complex stability have been ~onfirmed.'~ One of the manifestations of amine and phosphine basicity is in the ready formation of onium salts in acidic media and interest in these continues. For example in solutions usually in liquid sulphur dioxide containing HS0,F-SbF and phosphorus halides the species PHF3+ PHF2CI' PHC13+ PHC12Br+ PHClBr,' and PHBr,' have been identified by their 31P n.m.r. spectra from which one-bond P-H coupling constants may be clearly mea~ured.'~ The spectrum of PHF3+ for example shows a doublet of quartets with 'J(PH) = 1190.6 Hz.The new salts OH,'[EF,]-(E =As or Sb) obtained as well-defined crystalline solids from the H,O-HF-EF system," appear to be the most stable oxonium salts known and the most suitable for detailed study of the cation. Thus OH,+[SbF,]- decomposes only above 350 "C. X-Ray powder data suggest that OH,'[AsF,]- has a structure similar to that of Ag+[AsF,]- and that OH,+[SbF,]- is similar to KMF,(M = Re W,or Mo). The i.r. spectra of the cations are assigned by comparison with the isoelectronic ammonia; the bands are somewhat affected by cation-anion interactions but much less so than those of mineral acid hydrates such as H30+c104-.9h The sulphonium salt SH,'[SbF,]- was made similarly by condensing hydrogen sulphide on to a frozen solution of SbF in HF but attempts to make SH3+[AsF6]- were not successful hydrogen sulphide reacted quantitatively with arsenic(v) fluoride to give arsenic&) sulphide." By careful experiments it was possible to obtain both i.r.and Raman spectra of the cation SH3+ and to assign peaks by comparison with the isoelectronic PH,. The peaks are much better defined than those of OH3+. Protonation of HCI was also almost certainly achieved in HF-SbF but the white solid adduct decom- posed below room temperature and so full characterization of the cation was not possible. Attempts to make the analogous NHF3+ salts from NF and SbF,-HF were apparently unsuccessful and starting material was recovered from the reaction mixture at -78 'C." The difluoroammonium cation NH2F2+ was however isolated in hexafluoro-antimonate(v)or -arsenate(v) salts and in spite of frequent explo- sions n.m.r.i.r. and Raman data were recorded. The n.m.r. parameters for the NF2H2+ ion are in good agreement with those already formed for ions in the series Nb' NH3F' and NF,+ and the vibrational spectra (except for solid-state effects) were assigned by comparison with CH,F2. The dangerous instability of the difluoroammonium salts at roem temperature was attributed to exothermic elimina- tion of hydrogen fluoride. Irradiation of NF4+[AsF6]- and NF,'[SbF,]- with 6oCo y-rays gave samples with e.s.r. signals assigned to the NF3+ radical cation.9j The Typical Elements 8 Diphosphines Conditions have been described"" for the synthesis of diphosphine H2PPH2 in ca. 30%yield by passing phosphine through an electric discharge. This seems to be an improvement on the more usual method from the hydrolysis of calcium phosphide which gives unpredictable yields. Methylphosphine under similar conditions gives the new diphosphines MePHPH and MePHPHMe. Methyldiphosphine was ther- mally unstable and could not be isolated pure but its formation was clearly charac- terized by n.m.r. spectroscopy. 1,2-Dimethyldiphosphine was apparently formed as two diastereoisomers (15 and 16; R=H) with a gauche conformation. When a mixture of phosphine. and acetylene was passed through the discharge small amounts of buta- 1,3-diyne HCr C-CECH and the new compound ethynyl- phosphine HCrCPH, (yield 9Yo) were found.Isolation of these products is interesting since their formation involves the breaking of the H-C bonds in acetylene. .. R RBMe=fi R-0.R Me R Me R R (15) (17) The factors which determine the conformations of diphosphines are still not clear. Analysislob of the vibrational spectra of H,PPH in gas liquid and solid phases suggests that the only conformation is gauche; the microwave study described in 1974"' was ambiguous on this point since any trans-isomer (17; R = H) would have no dipole moment and so be undetected. The hydrogen atoms in diphosphine appear to be too far apart to have much effect on the conformation which must be dominated by lone-pair interactions.Further evidence for the predominantly trans conformation (17) in P2F4 and P,(CF,) has been obtained from electron diffraction studies:'Od the P-P distance in P2F4 (2.281 A) is the longest yet determined. There is clearly no evidence for n-delocalization across the P-P bond in contrast to the situation in molecules such as Me2NPF2 or H2NPF2 where the P-N bonds are short. It is strange that although the N-C bonds in N,(CF,) are comparable with those in other amines the P-C bonds in P,(CF,) are longer [1.914(4) A] than in most phosphines. Trends in bond lengths and angles in diphosphines (Table 4) cannot be predicted by VSEPR theory which suggests that angles adjacent to more electronegative substituents should be decreased.Table 4 Structural parameters for diphosphines P2X4 X P-P/A LPPXP LXPXI" Me 2.192(9) 101.1(7) 99.6( 10) H 2.218(4) 95.2(6) 91.3( 14) CF3 2.182(16) 106.7(7) 103.8(8) F 2.28 l(6) 95.4(3) 99.1(4) lo (a) J. P. Albrand S.P. Anderson H. Goldwhite and L. Huff Inorg. Gem. 1975 14 570; (b) J. D. Odom C. J. Wurrey L. A. Carreira and J. R. Durig Inorg. Chem. 1975,14,2849; (c) J. R. Durig L. A. Carreira and J. D. Odom J. Amer. Chem. Soc.,1974,96 2688; (d) H. L. Hodges L. S.Su and L. S. Bartell Inorg. Chem. 1975,14,599 and references therein; (e) H. C. E. McFarlane and W. McFarlane J.C.S. Chem. Comm. 1975 582; (f)R. K. Harris E. M. McVicker and M.Fild J.C.S. am. Comm. 1975,886; (g) G. R. Newkome J. D. Sauer and M. L. Erbland J.C.S. Chem.Comm. 1975,885. A. J. Carty R. H. Cragg and J.D. Smith Conformations in diphosphines have also been investigated by n.m.r. spectroscopy. An analysis of the spectra of Bu'MePPMeBu' indicated that only the gauche-isomer with the conformation (16; R = But) was present in appreci- able concentrations at the temperatures studied. Replacement of methyl by t-butyl groups gives a much more negative value for the coupling constant 'J(PP) and it has been suggested that this indicates a change in hybridization at phosphorus with an increase in the CPC angle and an increase in s-character of the P-P bond. It has also been shownlof that in diphosphines R1R2PPR1R2 the parameter ['J(PC) + 2J(PCC)] which is easily found from the 13C n.m.r. spectrum may be used to assign conformations.For the series (MeEtP), (MePr'P), and (MeBu'P), the proportion of the meso-diastereoisomer (15) (in which the larger groups cannot adopt a trans configuration) relative to the racemic (16) decreases showing the effect of steric interactions between the larger groups. A new preparation of diphosphorus tetraiodide in 75-80% yield from potassium iodide and phosphorus(II1) chloride has been described. log 9 Methylidynephosphine Modern instrumentation allows detailed data to be obtained on short-lived species. Methylidynephosphine HCP which may be obtained by passing phosphine at low pressure through a carbon arc rapidly polymerizes above -70 "C. If however the gaseous reaction products with or without vinyl chloride as solvent are condensed at -100"C the n.m.r.spectrum may be recorded at that temperature.'lU The value of 'J(13CH) (21 1Hz) is in the range expected for C(sp)-H bonds and *J(HCP) 43.9 Hz)is much larger than is normally found in phosphines or phosphonium salts. These results are consistent with the proposal that the molecule in solution is best described by the structure HCS-EPs+ as suggested by earlier microwave data.llb 10 Phosphinidene and Arsinidene Complexes A number of phosphine complexes may be metallated by butyl-lithium to give yellow crystalline lithio-derivatives as indicated in Scheme 2.12u These compounds may be kept as solids for several days but they are sensitive towards moisture and are pyrophoric and decompose even at -20 "C in THF or dioxan.The dilithiophos- phine complex (18) reacts12b with NN-dichlorocyclohexylamine to give the red [(PhPH,)Mn(CO),(CsH 511 1BuLi-pentane [(PhPHLi)Mn(CO),(C5Hs)]+ [(PhPLi,)Mn(CO),(C5H5)] 1D2O 1D*O (18) [(PhPDH)Mn(CO),(C 5H s)1 [(PhPD 2)Mn(CO),(C 5 Hs11 Scheme 2 (a) S. P. Anderson H. Goldwhite D. KO,A. Letsou and F. Esparza J.C.S. Chem. Comm. 1975,744; (b) J. K. Tyler J. Chem.Phys. 1964,40 1170. l2 (a) G. Huttner and H.-D. Muller 2. Narurforsch. 1975 30b 235; (b) G. Huttner H.-D. Muller A. Frank and H. Lorenz Angew. Chem.Inremar. Edn. 1975 14 572; (c) M. Baudler and M. Bock 2. anorg. Chem. 1973,395 37; (d) G. Huttner H.-D. Muller A. Frank and H. Lorenz Angew. Chern. Inremar. Edn. 1975.14,705; (e)G. Huttner and H.-G. Schmid Angew. Chem. Internat. Edn.1975,14 433; G. Huttner J. V. Seyerl M.Marsili and H.-G. Schmid ibid. p. 434. The Typical Elements compound [(C5H5)(CO)2MnPPh]3 (19) and this has been shown by an X-ray study to contain the ligand (PPh)3. Free triphenylcyclotriphosphine may be isolated'2c but it rearranges above -20 "C to the pentaphosphine (PhP),. The complex [(C,H,)- (C0)2MnPPh]3 is stable in air. It decomposes on heating to give a new compound PhP[Mn(CO),(C,H,)] (20); the X-ray structure shows that the co-ordination at phosphorus is planar and the Mn-P bonds (2.184 f0.002 A) are unusually short (cf. 2.26-2.40 8 in Mn-phosphine complexes). The compound thus appears to be the first example of planar phosphorus in which electrons from the manganese are used to complete the valence shell.A similar complex of arsenic has been isolated. The phenylarsine complex (21) may be metallated with n-butyl-lithium and the resulting dilithio-derivative (22) reacts with NN-dichlorocyclohexylamine to give the intensely coloured arsinidene complex PhAs[Cr(CO),12 (23). An X-ray study shows that the co-ordination at arsenic is planar and that the As-Cr bonds (2.38 A) are short compared with those in R,As complexes. The Mn-P-Mn groups in (20) and Cr-AsZCr group in (23) may be described as three-centre 4~-systems; the intense (E = 20 000) absorption involving charge transfer from metal to ligand is then ascribed to the 'A + 'B2 transition (Figure 1). Cr As Cr Figure 1 Molecular orbital diagram for the arsinidine complex PhAs[Cr(CO),12 A.J.Carty,R.H. Cragg and J. D. Smith 11 Phosphazenes After the silicones the phosphazenes constitute the most important group of polymers based on inorganic backbones. The P-CI bond in polydichlorophosphazene (24) is hydrolytically unstable but high molecular weight polymers (NPX,) (25; e.g. X = OPh or OCH,CF,) have important uses as elastomers or water repellants. These materials which cannot be made by direct polymerization of cyclic (NPX2)3-5 are accessible by nucleophilic substitution reactions on polydichlorophosphazene. Substitution however is more simply studied in cyclic derivatives; for example the reaction between (NPCI,) and sodium 2,2,2-trifluoroethoxide has yielded the first complete set of products N3P3Cl,(OR)6- (R = CH2CF3,n = 0-6).13' Successive substitution is non-geminal and trans and the sequence of reactions appears to be determined mainly by steric factors.Substitution reactions of ortho-diphenols however may lead to degrada- tion of P-N rings; it is thought that the introduction of a five-membered exocyclic ring as in the undetected (26) increases the susceptibility of the N3P3 ring to nucleophilic attack as the steric strain is relieved with formation of phosphoranes such as (27) or (28). Support for this suggestion comes from the isolation of the intermediate (27) from the reaction between N3P,Cl6 and o-aminophenol. 13' Reac-tions are complicated by scrambling of cyclic ligands during the degradation. Many derivatives N3P3Xn(NR2)6-n(X = halogen) have been made either by the reaction between hexachlorocyclotriphosphazene and amines or by treatment of the hexakisamido-derivativesN3P3(NR2)6with hydrogen halides 13d N3P,Cl NRzH N3P3CIn(NR2)6-n N3P3(NRZ)6 The importance of steric effects in shielding chlorine atoms from nucleophilic attack by amine has been illustrated by isolation of the compound N3P3CI[N(CH2Ph),]- NMe2)4 from the reaction between N3P3CI5N(CH2Ph) and dimethylamine in t~luene;'~' in many aminations the final chlorine is rapidly displaced with formation of the hexakisamido-derivative,but forcing conditions are required here Me NH N 3p3cls"(CH2 Ph)21 75-bo ' N3P3Cl"(CHzPh)z] (NMez) l3 (a)H.R.AUcock Chem.Rev.1972,72,315; R. Chem.inBritain 1974,10,118;(b)J.L.SchmutzandH. Allcock Inorg. Chem.1975,14,2433;(c)H. R. Allcock R. L. Kugel and G. Y. Moore Inorg. Chem. 1975,14 2831; (d) S.N.Nabi R. A. Shaw and C. Stratton J.C.S. Dalton 1975,588;(e)Masood-ul-Hasan R. A. Shaw and M. Woods J.C.S. Dalton 1975 2202; cr) T. S.heron K. Mannan S. S. Krishnamurthy,A. C. Sau A. R. V. Murthy R. A. Shaw and M. Woods J.C.S. Chem. Comm. 1975,975; (g) D.W.J. Cruickshank Acta Cryst. 1964,17,671;(h)H. T. Searle J. Dyson T. N. Ranganathan and N. L. Paddock,J.C.S. Dalton 1975,203;(i)H.P. Calhoun and J. Trotter,J.C.S. Dalton 1974,377,382; (j)H.P. Calhoun R. H. Lindstrom R. T. Oakley N. L. Paddock and S. M. Todd J.C.S. Chem. Comm. 1975,343;(k)H.P. Calhoun,R. T. Oakley and N.L. Paddock,J.C.S. Chem. Comm. 1975,454;(I) 0.J. Schemer and N. Kuhn Chem. Ber. 1974,107,2123;R.Appel and M.Halstenberg J. Orgunometalfic Chem.,1975,99,C25. The Typical Elements aNH2 OH \ N II /P HN aN”’ OH H I / oNH* OH (27) (28) The reaction be tween hexachlorobis(e thy1amino)cyclote trap hosp hazene (29) and an excess of dimethylamine yields among other products the unusual bicyclic phosphazene N,P,(NMe,),(NHEt)(NEt) (30).13’ The P-N bonds in the ring (mean 1.602A) are comparable with those in other phosphazene rings in which the bond order is considered to be greater than one. The P-N bonds at the bridgehead however appear to be inequivalent; the longer bond has a length (1.77 A) compara-ble with that in sodium phosphoramidate’3g (1.769 A) which is normally considered to be a P-N single bond.A further group of phosphazene derivatives may be obtained by replacement of the chlorine atoms in chlorophosphazenes by alkyl or aryl groups. These phos- phazenes are characterized by longer P-N bonds and greater charge localization so that the nitrogen atoms become Thus the cyclic methylphosphazenes (NPMe2)3-5 form salts such as N,P,Me,,HCl N,P4Me,,2HC10, and N5P5Me10,H2CuC14,H20 or complexes such as N,P,Me8,2HgC12 N4P,Me8,4AgN0, and N,P,Me8,HC1,CuC1,. All three phosphazenes form quater- nary salts N,P,Me,,RI (n= 3-5; R =Me or Et) with iodoalkanes. The properties of these alkylphosphazenes are attributed to the less electronegative substituents at NHEt c1 NHEt NMe, \ / \ / CI-P-N=P-CI P-N= P-NMe II I II\ I N N N NEt N I I1 I \II CI -P=N-P-CI Me,N -P=N -P\ / \ CI NHEt Me,N / NMe 134 A.J.Carty R. H. Cragg and J. D. Smith phosphorus so that the d-orbitals are more diffuse than in the halogenophos- phazenes and less suited to overlap with nitrogen p-orbitals. Some of the structural inf~rmation’~~” on protonated or quaternized phosphazenes is shown in Figure 2. The high-energy of the allowed transition at ca. 190nm associated with ring electrons confirms that the phosphorus and nitrogen orbitals have appreciably different electronegativities. Me H H I 1.70 ’ I pON. 1.69 I .69 1.541 1.56/ 9 1.561 p,N. p\ N N N N 1.611 / I .60\ / I.!; N .-i.??N” Figure 2 Mean bond lengths (A) in (a) N4P4Me9+,(b) N4P4Me8H+,(c)N4P,Me8,HCuC13,and (4 NJ’sM~IoH~~+ The reaction between octamethylcyclophosphazene and methyl-lithium in dimethyl ether gives the new carbanion [N,P,Me,(CH,-),] which has been identified by its reactions with iodomethane and the halides Me3EX (E= Si Ge or Sn).13’ N4P4Me8 MeLi-Et,O b [N4P,Me4(CH2-),] 5N4P4Et8 JMe,ECI N4P4Me4(CH 2EMe3) Deprotonation occurs at P-methyl rather than at N-methyl groups and it is thought that the carbanion may be stabilized by conjugation within the r-system of the ring.Deprotonation of N-phosphazenium iodides is more complicated. 13k Thus the compound P,N,Me,I (31) reacts with sodium bis(trimethylsily1)amide to give the ylidic diazaphosphorin (32) confirmed by hydrolysis to the phosphine oxide (33) and protonation to the C-hydriodide (34). The Typical Elements The initial step in the reaction appears to be deprotonation at a P-methyl group as in the phosphazenes.With potassium t-butoxide however the phosphazenium iodide (31) is converted into a linear phosphine oxide (35) by a process which appears to involve nucleophilic attack of t-butoxide on phosphorus followed by elimination of isobutene. The reaction between lithium bis(trimethylsily1)amideand phosphorus(II1) halides gives 50-70% yields of the iminophosphine (Me,Si),NP=NSiMe (36).13' This compound which is very reactive towards air or moisture may be converted into a 1 :1 adduct (37) with trimethylsilyl azide and on distillation the bisiminophos- phorane (Me3Si),NP(=NSiMe3)2 (38) is obtained This may then be treated with more of the iminophosphine to give a four-membered ring compound (39) with both tervalent and quinquevalent phosphorus.2(Me,Si),NLi + PCl Et,O (Me,Si),NP=NSiMe (36) 4 ZMe,SiN, -N (Me,Si),NP(=NSiMe,) t--(Me,Si),NP( =NSiMe,) ,Me,SiN (38) J(Me,Si),NP=NSiMe (37) SiMe SiMe (39) 12 Reactions of Phosphorus Esters More experiments to identify intermediates in the conversion of phosphites into phosphonates by alkyl halides or halogens have been described. In earlier studies much information was obtained by use of optically active corn pound^.^^^ The X -R'X *(RIO),&OR1)+ (R10),PR2+X-(R10),P(0)R2 I R2 -R'X T (40) I (41) observed stereospecificity which depends on the groups R' and R2,is thought to be a function of the lifetime of the five-co-ordinate intermediate (40).If this is short and alkyl halide R'X is rapidly eliminated either directly or via a phosphonium salt (41) optical purity is maintained; if the five-co-ordinate intermediate persists long enough to allow pseudorotation optical purity is lost. Five-co-ordinate species may be stabilized in cyclic phosphites [e.g. (42)]. Intermediates in Arbuzov-type reactions have now been detected directly14' by 31Pn.m.r. spectra of samples at -85 "C in chloroethane solution. The peak due to the five-co-ordinate intermediate (43) l4 (a)C. L. Bodkin and P. Simpson J.C.S. Perkin ZZ 1972,2049; (6) A. Skowronska,J. Mikolajczak and J. Michalski,J.C.S. Chem. Comm. 1975,791,986;(c) W. J. Stec,T. Sudol and B. Uznanski J.C.S.Gem. Comm. 1975,467. A.J. Carty R. H. Cragg andJ.D. Smith c1 (-SCI,) T weakens when the sample is warmed to -40 "C and a new peak corresponding to the phosphorokhloridate product (44)appears. Both phosphonium and five-co-ordinate intermediates have been detected in chlorinations of phosphorus thioesters. The cis-cyclic thionate (45) is converted via the phosphonium intermediate (46) into the trans-sulphenyl chloride (47) with full retention of configuration. Chlorination of the five-membered cyclic phosphorothionate (48) proceeds uia five-co-ordinate intermediates (49) and (43). The easy rearrangement of the isocyano-derivative Me,C(CH,O),P(O)NC to the corresponding cyano-compound was described last year. The prediction that the corresponding isocyano-derivative of tervalent phosphorus (50) should rearrange even more easily has been confimed,'qC since attempts to isolate the compound from the deselenization of the isoselenocyanate compound (51) by reaction with methyl diphenylphosphinite Ph,POMe yielded only the cyano-compound (52).The crude compound obtained from Me2C(CH20),PCl and potassium isoselenocyanate was used in the deselenization reaction since attempts to distil the compound Me2C(CH20)2PNCSe gave only the rearranged product (53). >c>p<N >c4PNCSe +40"C vacuum (53) Ph,POMe (51) I

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DOI:10.1039/PR9757200119

出版商:RSC    

年代:1975

数据来源: RSC

摘要:

me Typical Elements PARTIV Groups VI-VIII By R. H. Cragg 1 GroupVI During 1975 a considerable amount of work has been published concerning the chemistry and properties of compounds of the Group VI elements. Two major areas which merit special mention are (i) the continuing interest in 'crown' ethers and (ii) the synthesis and properties of organic polymers such as (SN), which have metallic properties. A major characteristic of crown ethers is their ability to stabilize anions. For example dibenzo-18-crown-6 and 18-crown-6 ethers have been reported to facili- tate a simple and direct route to anionic derivatives of Group VI metal hexa- carbonyls.' The crown ether-[W(CO),OH]- compound is obtained in 57% yield from a mixture of hexacarbonyltungsten crown ether and potassium hydroxide in methylene dichloride which has been irradiated for two hours using a mercury lamp.The analogous fluoride compound is obtained in 27% yield by substituting potassium fluoride for the hydroxide. However if tetraethylammonium fluoride is used only 7% of the anion is obtained. Other complex anions reported are [M(CO),X]-(M = Cr X =For OH). One of the major problems in the development of the properties of crown ethers has been the lack of a convenient method of synthesis. However recently optically pure configurationally chiral 18-crown-6 and 9-crown-3 cryp- tands have been synthesized from L-tartaric acid and D-mannitoL2 In order to obtain an assessment of the complexing power of the 18-crown-6 derivatives the stability constants defined as equilibrium constants (K in 1mol-l) \for the equilibrium M'X-+ cryptand $ cryptate'x-have been measured for metal and primary alkylammonium cations.The results given in Table 1 indicate that the 18-crown-6 cryptands form strong cationic constants defined as equilibrium constants (K in 1 mol-l) for the equilibrium Table 1 Stability constants for cryptate complexes Cryptate K Cryptate K LL-a ButNH3+ 2 x lo4 DD-c Na+ 3.9 x lo3 LL-b ButNH3+ <l.OX lo4 DD-c K+ 3.0X lo4 DD-c Bu'NH3+ <30 DD-cRb+ 4.6X104 DD-c PhCH2NH3+ 1.5%.lo6 One important property of these crown ethers is their ability to differentiate in complex equilibria between (f)(RS)-a-phenylethylammonium hexafluorophos- hate.^ This is observed when the substituent groups on the configurationally chiral J.L. Cihonskii and R. A. Levenson Inorg. Chern.. 1975,14,1717. 2 W. D. Curtis D. A. Laidler J. F. Stoddart and G. H. Jones J.C.S. Chern. Cornrn. 1975,833. 3 W. D.Curtis D. A. Laidler J. F. Stoddart and G. H. Jones J.C.S. Chern. Comm 1975,835. A.J. Carty,R.H. Cragg and J. D. Smith LL-a R =CH20CH2Ph LL-b R =CH20CPh3 DD-c R = LL-d R = CH20Ac Me DD-d R =CH~OAC DD-e R = DD-fR= MeO Rgure 18-crown-6 cycle are bulky. For example host (S)-LL-b HPF is ca. 1.00kJ mol-' more stable than (R)-LL-b HPF6. In contrast (R)-DD-c HPF6 is ca. 1.25 kJ mol-' more stable than the (S)-DD-c HPF complex. The important property of crown ethers in chiral recognition has been further extended. The cyclic ether (l),containing two 2,2'-substituted- 1,l'-binaphthyl units as chiral barrier has been synthesized and observed to complex somewhat selectively the enantiomers of the hexafluorophosphate salt of racemic methyl phenylgly~inate.~ (1) R = H or Me Analogous macrocyclic ethers (2) are observed to complex differently with the enantiomers of the hexafluorophosphate salts of racemic methyl phenylglycinate or methyl ~alinate.~ Compounds (3) or (4)are obtained by condensation of a diaza-18-crown-6 ether with an acid chloride followed by reduction with diborane of the resulting cyclic diamide,6 and have been found to catalyse nucleophilic substitution reactions as well G.W. Gokel J. M. Timko and D. J. Cram J.C.S. Chern. Comm. 1975,394. G. W. Gokel J. M. Timko and D.J. Cram J.C.S. Chern. Cornm. 1975,444. M. Cinquini F. Montanari and P. Tundo J.C.S. Chem. Comm. 1975 393. The Typical Elements as alkylation at carbon cyclopropanation and borohydride reduction. Table 2 gives some idea of the catalytic effect in the reaction of an alkyl bromide with potassium iodide. (2) e.g.,X = Y = CH,OCH X = CH,0CH2 Y = CH,CH,CH R (3) R = n-C,,H, (4) R = n-C,,H, (5) R = H i-(6) n-C,,H,,PBu",Br - (7) crown ether Table 2 Relative catalytic effects of the compounds (3)-(7) in the reaction n-C,H,,Br + KI +n-C,H,,I +KBr Yield of Catalyst T/"C Reaction time/h n-CsHl71 (YO) (3) 60 0.2 100 (4) 60 0.5 92 (5) 60 14 90 (6) 60 1 93 (7) 80 3 100 The molecular recognition of the spherical alkali- or alkaline-earth cations by an organic ligand should ideally be achieved by a system containing a spherical intramolecular cavity into which the cation may be included.Recently the macro- cyclic system (8) has been synthesized. When solid CsBr is added to a CDCl solution of (8) the salt dissolves slowly and the initial n.m.r. spectrum is slowly replaced by a new spectrum of the 1 1 complex. Complex formation is also observed by n.m.r. with KBr CsBr or BaBr in D20 as well as with NH,I in CDCl,. As all the bridges in the ligand are equivalent in the exchanging complex in CDC13 the complex must have a centre of symmetry. This strongly suggests that the cation is trapped inside the cavity of the ligand. The cryptate has a cavity radius of about 1.8 A and its high connectivity introduces considerable rigidity in the molecule.7 E. Graf and J. M. Lehn J. Amer. Chem. Soc. 1975 97 5022. A.J. arty R.H. Cragg,and J. D.Smith Preliminary measurements show that the stability constants for the K' Rb' and Cs' complexes are about 3.4,4.2 and 3.4 respectively (log k in water at 25 "C) and the Cs' complex is probably the most stable to date. The cation exchange rates (determined from 'H n.m.r. coalescence temperatures) are amongst the lowest observed with free energies of activation of 64.8 (at 28 "C) 69.8 (51 "C) and 67.3 (41 "C) kJ mol-' for the K' Rb' and Cs' complexes respectively. The structures of a number of crown ethers have been reported. X-Ray diffraction studies of two of the five possible isomers of dicyclohexyl-18-crown-6 show that the oxygen atoms lie approximately in a plane with the cavity elliptical in shape and the shorter distance across the ellipse slightly more than 4 A.*In both isomers the cavity surrounded by the six oxygen atoms is elliptical in shape with the two axial oxygen atoms pointing out of the cavity.The structures of three macrocyclic thioethers 1,4,7-trithia-( 12-crown-4) 1,4-dithia-( 15-crown-5) and 1,lO-dithia-( 18-crown-6) with ring sizes varying from 12 to 18 atoms have been determined by X-ray diffraction and the donor atoms have been found to be nearly coplanar with all the sulphur atoms directed out of the cavitie~.~ The oxygen atoms are directed into the cavities with the exception of one oxygen atom in the crown-5 compound.The average C-C distances in the ring are 1.49 1.51 and 1.50 A shorter than the expected 1.54 A. Polyether antibiotics are important monocarboxylic acid isophores owing to their ability to solubilize cations and facilitate their passage through membranes. The absolute configuration and constitution of the polyether antibiotic R021-6 150 has been established by X-ray crystallographic analysis of the silver salt." The co- ordination about the silver ions is irregular with eight Ag-0 contacts which are less than 3.01 A. Carbon-based polymers such as polyacetylene are known to exhibit electrical insulating properties. In contrast it has recently been recognized that polymers containing sulphur and nitrogen or sulphur and selenium often have properties similar to those of a metal.The observation of superconducting phenomena in the fluctuation region in the 'organic metal' tetrathiafulvalene-7,7,8,8-tetra-cyanoquinodimethane (TI'F-TCNQ) has aroused considerable interest in the use of T-donors with TCNQ in the hope of obtaining new 'organic metals'. Recently the 8 N. K. Dalley J. S. Smith S. B. Larson J. J. Christensen and R. M. Izatt J.C.S.Chem. Comm. 1975,43. 9 N.K.Dalley J. S. Smith S. B. Smith S. B. Larson K. L. Matheson J. J. Christensen and R. M. Izatt J.C.S. Chem. Comm. 1975 84. lo J. F. Blount R. H. Evans C. Liu T. Hermann and J. W. Westley J.C.S. Chem. Cbmm. 1975 853. The Typical Elements 141 cis-(9) and trans-forms (10) of diselenadithiafulvalene (DSeDTF) have been reported and on mixing with TCNQ in acetonitrile a black 1:lcharge-transfer salt is instantly precipitated." Single-crystal electrical conductivity measurements show a metallic-like temperature dependence with a room-temperature conductivity of ca.550 i2-' cm-'.Charge-transfer salts containing the organic donor TTF or a derivative have the highest electrical conduction of organic solids presently known and it has been observed that the selenium analogue has led to an improvement in the metallic-like properties of its charge-transfer salt with TCNQ. Other workers have found the d.c. electrical conductivity to be 700* 300 K1cm-' at room temperature; the conductivity has a negative temperature coefficient upon cooling.12 The TCNQ salts of TTF and its selenium analogues form an isostructural series of highly conducting organic salts l3 having remarkably similar electrical conductivities with peaks at 59 40,and 64K respectively.(9) X' = X3= S x2= x4= Se (10) X' = X4 = S X2= X3 = Se The X-ray diffraction pattern and unit cell constants for the TCNQ salts of TIT (ll) DSeDTF (9) and (lo) and TSeF (12) show these three materials to be isostructural and the 'H n.m.r. spectra show the presence of equal amounts of the cis- and trans-isomers in neutral DSeDTF. (1 1) (12) Another organic system has been observed to have similar proper tie^;'^ 1,2-dithiolylium 5-thioxo-l,2-dithiole-3-thiolates have been observed to be charge- transfer salts with semiconducting electrical properties.The specific d.c. resistance pzOwas ca. 10f-108 i2 cm-' for 3,5-diphenyl-1,2-dithialylium 4-phenyl-5-thioxo-1,2-dithiole-3-thiolate (13). This is a little surprising since the corresponding salts derived from 3-phenyl-l,2-dithiolylium salts and 3,4-diphenyl-1,2-dithiolylium salts were found to be insulators. I s-s s-s s-s S-Ph S S* H Ph H Ph (13) l1 E. M. Engler and V. V. Patel J.C.S. Chem. Comm. 1975,671. l2 M. V. Lakshmikantharn M. P. Cava and A. F. Garito J.C.S. Chem. Comm. 1975,383. l3 S. Etemad T. Penney E. M. Engler B. A. Scott and P. E. Seider Phys. Rev. Lmers 1975 34,741. l4 N. Loayza and C. T. Pedersen J.C.S. Chem. Comm. 1975,496. 142 A.J. Carty R.H. Cragg and J. D.Smith An all-valence-electron CND0/2 MO calculation predicts that the boat form of cyclohexasulphur is the stable conformer and that its potential energy is ca.16.7 kJ mol-' less than that of the chair form which is found in the rhombohedra1 crystals. The interconversion has a barrier of 96.1 kJ m01-l.'~ The crystal structures of Ba2S and Bas, determined from three-dimensional single-crystal X-ray diffraction data show that the former contains a sulphide ion and an S22-polysulphide ion with S-S $stance 2.32 A.16In the latter a poly- sulphide anion with S,2-has S-S 2.074 A and an SSS angle of 114.8'. The Ba2S phase is apparently formed only at elevated temperature. The volume available per S atom by subtracting the volume of Ba2' from the unit cell volumes of Bas Ba2S, and Bas gives the values 54.84 42.78 and 29.37A3 respectively.Thus at high pressures the formation of polysulphide anions is favoured becaise more of the available space is utilized by the S atoms. Perhaps the most significant contribution to Group VI chemistry during 1975 has been the synthesis of analytically pure single crystals of the metallic conductor polymeric sulphur nitride (SN), polythiazyl in a convenient form for solid-state inve~tigafion~.'~"~ The significance of this work may be seen as an extension of the study of 'organic metals' and inorganic conductors the electrical properties of which are quasi-one-dimensional to potentially conducting polymeric materials. Polymeric (SN) was first reported in 1910 but the potential of this polymer as a metallic conductor has only recently been recognized.This is because the intrinsic electronic properties of anisotropic solids are extremely sensitive to impurities and defects. Ultra-pure polythiazyl is obtained by the following method. The vapour of S4N4is passed over heated silver wool S2N2collecting on the surface of a cold-finger containing liquid nitrogen. Polythiazyl is then obtained by slowly growing crystals by 8Ag + S4N4 --+ 4Ag2S + 2N2 A%*S S4N4(g) + 2S2N2(g) sublimationof S2N2at 0 "Cover a period of two days followed by room-temperature solid-state polymerization over a period of three days and then completing the polymerization by heating at 75 "Cfor two hours. During the formation of (SN) the colourless tabular monoclinic crystals of S2N2 turn dark blue and become paramagnetic (g = 2.005) and then change to gold diamagnetic crystals which are pseudomorphous with and have the same space group (P2Jc) as the S2N2crystals from which they are obtained.The purity of (SN) can be confirmed by the fact that the polymer is diamagnetic has not the characteristic iodine-like odour of S2N2and there is no vapour pressure of S2N2above the polymer at room temperature. Scanning electron micrographic studies indicate that the .crystalline polymer is composed of an ordered array of parallel (SN) fibres. At room temperature the d.c. conductivity is ca. 2.5 X lo3R-' cm-' in a direction parallel to the fibre and this value compares favourably with those obtained for metals such as mercury. The value of the conductivity is temperature-dependent a characteristic property of a 15 2.S. Herman and K. Weiss Znorg. Chem. 1975 14 767. 16 S. Yamaoka J. T. Lemley J. M. Jenks and H. Steinfink Znorg. Chem. 1975. 14 129. 17 C.M. Mikulski P. J. Russo M. S. Saran A. G.MacDiarmid A. F. Garito and A. J. Heeger J. Amer. Chem. SOC.,1975,97,6358. 18 A. G.MacDiarmid C.M. Mikulski P. J. Russo,M. S. Saran A. F. Garito and A. J. Heeger J.C.S. Chem. Comm. 1975,476. The Typical Elements metal and on decreasing the temperature to 10K the conductivity increases ca. 225-fold. Indications that (SN) remains metallic at low temperature have been obtained from heat-capacity studies and at 0.26 K (SN) is superconducting. Careful experimental technique is needed to obtain pure (SN) since the polymerization of S,N appears to take place at the surface of the crystals and consequently incom- pletely polymerized crystals can be obtained which appear to be identical with (SN) but have the same X-ray intensity data and cell dimensions of pure S2N2.Although the polymer can be sublimed in uucuoat 140-150 "C when heated above 208 "C or in an evacuated vessel at 40-50 "C (SN) decomposes into sulphur nitrogen and other as yet unidentified compounds.No change is observed in the X-ray diffraction pattern when (SN) is exposed to the atmosphere for two weeks or after exposure for six days to an atmosphere of one mole of dry or moist oxygen. However slow decomposition takes place when the polymer is added to degassed distilled water. Polythiazyl consists of an almost planar chain of alternating sulphur and nitrogen atoms (14) with intrachain distances of Sa-N 1.593(4) S,-Nb 1.628(7) sa-sb 2.789(2) N,-N, 2.576(7) and S,-N 2.864(5) A.The bond angles SNS and NSN have values of 119.9(4) and 106.2(2)" respectively. ?=-T I S-Nc ,Nb S-N sb (14) An X-ray single-crystal study of S2N2,at -130"C shows that the molecule is square planar the S-N bond lengths having approximately the same value [1.65 1( 1) and 1.657(1) A] as in (SN) the values of the SNS and NSN angles being 90.42(6) and 89.58(6)" respectively. 2 Group VII The main areas of importance in the chemistry and properties of the halogens have been the synthesis and structural assignments of polyhalogen species. An X-ray crystallographic structure determination of (theobromine),H,I shows that the compound is a polyiodide salt containing cationic and anionic layers the cation consisting of hydrogen-bonded protonated theobromine species and the anion being 1164-.19This polyiodide ion is the largest polyanion to be reported.The shortest distance between adjacent 1164-anions is 3.54 A which is of the same order as that observed in the tri-iodide chains in (benzamide) HI3. The large distance between the anions is indicative of there being only a weak interaction and suggests that the 11$-species can be regarded as a discrete polyiodide anion. The C1,-anion has been identified by Raman and i.r. studies from the products of alkali-metal atom matrix reactions with molecular chlorine.2o The yellowish M' C1,-species produced resonance Raman spectra and the dissociation energy of the C12- anion ranges from 1.19 *0.06 eV for LP3'C12- to 1.38 f0.06 eV for Cs' 35Cl,-.The vibrational assignments to the (vl)and intraionic (v2)symmetric modes of M' C1,-based on a triangular geometry are given in Table 3. F. H. Herbstein and M. Kapon J.C.S. #em. Comm. 1975,677. W. F. Howard and L. Andrews Znorg. Chem. 1975,14 767. A.J. Carty,R. H. Cragg and J. D. Smith Table 3 Vibrational assignments for alkali-metal dichlorides Species u1 (waoenurnber/cm-') u2 (wuuenurnber/cm-') 6~i~12 246 552 7~i~12 246 518 NaC12 225 (270)* KC12 264 (200)* RbC12 260 (160)* csc12 259 (140)* * Estimated. Salt-molecule reactions in a matrix have been found to be very effective for the synthesis of polyatomic ionic molecules for spectroscopic study.Reaction of the chloride of sodium potassium rubidium or caesium with hydrogen chloride in an argon matrix results in the formation of the HCl anion in the species M' HCl,-.'l A comparison of the u3 frequencies and the observed shifts for the deuterium com- pounds has led to the conclusion that this species is in fact the isolated HC1,- anion and not the HC1 radical as previously assigned. A similar reaction of a Group I metal salt with chlorine results in the formation of the M' C1,- species identified by the u3 of the C13- anion. Argon-matrix reactions of alkali-metal atoms with molecular fluorine have been studied using laser Raman and i.r. spectroscopy.22 The Raman signals appropriate for the ul intraionic (F-F)- mode in the M' Fa-species show an alkali-metal shift because of the interaction with the v2 intraionic M+-F2- mode.The vibrational assignments for the symmetric modes of the M'F,-species based on a triangular geometry are given in Table 4. Table 4 Vibrational assignments for alkali-metal dijluorides Species v1(wuuenurnber/cm-') v2(wavenurnber/cm-') 6LiF2 452 708 7LiF2 452 NaF 475 454 KF 464 342 RbF2 462 (266)* CSF~ 459 (248)* * Possibly due to (MF),. The HF2-anion has aroused considerable attention owing to the possibility of a double minimum potential for the hydrogen atom. Structural studies by X-ray analysis of p-toluidinium bifluoride show the anion to be linear and symmetric in contrast to the results from neutron diffraction studies which found the (F..-H-F)- ion to be linear but with different H-F bond lengths.However calculations based on the effect of an external point charge on the bifluoride geometry have been made,23 and show that both fluorine atoms move towards the positive charge hence shortening one H-F bond and lengthening the other. A point charge therefore will affect the geometry of the HF2- anion and hence the asymmetric geometry of the HF2-anion in p-toluidinium bifluoride can be partly explained by its asymmetric crystal field. 21 B. S. Ault and L. Andrews J. Amer. Chem. SOC.,1975,97 3824. 22 W. F. Howard and L. Andrews Inorg. Chem. 1975 14 409. 23 N. S. Ostlund and L. W. Ballenger J. Amer. Chem.SOC.;1975,97 1237. The Typical Elements 145 The products of the argon-matrix reaction of iodine and an alkali metal have been investigated by Raman The six-membered vibrational progression beginning near 115cm-' decreases in intensity and increases in bandwidth in a regular manner with inckeasing vibrational quantum number for lithium sodium potassium rubidium and caesium. The values obtained for the dissociation energies for lithium sodium and potassium are 88 84 and 75 kJ mol-' respectively. The chlorine hexafluoride radical has been obtained by y-radiolysis of sulphur hexafluoride containing 5 mole '/o of chlorine pentafluoride at -196 0C.25 The e.s.r. spectrum has been assigned and ClF has been found to have a large 35Cl coupling of 77.1 mT which is more than twice the value for CIF,.It is concluded that the unpaired electron in ClF must populate the chlorine 3s-orbital. The i.r. spectrum and force field of the hexafluorobromine cation obtained by the action of excess BrF and a 2 :1 molar ratio of KrF,-AsF, has been recorded.26 The stretching force constant for the [BrF,]' cation has a value of 4.9 mdyn A-' which is the highest value observed for any BrF bond. As these bonds are much stronger than in other bromine fluorides the reactivity of [BrF,]' salts must be due to its high oxidizing power. The chlorine n.q.r. frequencies have been reported for Ph,AsCl, Et4NC13 Me,NBrCl, and Me,NICl,." In the trichloride ion the negative charge is divided evenly between the two terminal atoms with the central chlorine atom having a slight positive charge The negative charge on the chlorine atom increases as the central atom varies from chlorine through bromine to iodine.The charge distributions observed are consistent with Rundle delocalized three-centre four-electron bonds involving s-and p-orbitals and are indicative of little or no d-orbital contribution. The i.r. and Raman studies on the 1 1 complex between iodine heptafluoride and antimony pentafluoride are consistent with the complex having the ionic structure [IF6]+[SbF6]-.28 In contrast to most halogenofluorine-metal fluoride complexes which usually react violently with water [IF,]'[SbF,]- undergoes a smooth exo- thermal hydrolysis [IF6]+[SbF6]-+ 4Hz0 + HIO4 + HSbF + 6HF Although [IF,]'[SbF6]- reacts with carbon monoxide 7CO + 2[IF6]+[SbF6] + 7COFz + I + 2SbF5 there is only a slight reaction with methane or sulphur dioxide and no reaction with carbon dioxide.Both nitric oxide and nitrogen dioxide react to form stable non- volatile complexes 2NO 4-[IF,]+[SbF6]-+ NO+[SbF6]-+ NO+[IF6]-1 FNO + IF 24 W. F. Howard and L. Andrews J. Amer. Gem. SOC.,1975,97,2956. 25 K. Nishikida F. Williams G. Maniantov and N. Smyrst J. Amer. Chem. SOC.1975,97 3526. 26 K. 0.Christie and R. D. Wilson Inorg. Chem. 1975,14,694. 27 E. F. Riedel and R. D. Willet J. Amer. Chem. Soc. 1975,97 701. ** F. A. Hohorst L. Stein and E. Gebert Inorg. Chem. 1975 14 2233. A.J. Carty,R.H. Cragg,and J. D.Smith However the most significant property of [IF6]+[SbF6]- is its reaction at ambient temperature with radon forming'an unidentified non-volatile Rn compound.This has important implications for the analysis of radon in air and also for gas purifica- tion. However although the oxidation potential of [IF6]+is high enough to oxidize Rn no reaction with Xe was observed. 3 GroupVIII Xenon difluoride forms adducts with some metal pentafluorides and these adducts have been assigned ionic structures. However recent spectral evidence suggests that in many of these compounds there is considerable covalent bonding involving fluoride bridges between the cation and the anion. For example from the reaction of xenon difluoride with the pentafluorides of antimony tantalum and niobium three types of adduct have been identified having the XeF :MF mole ratios 2 :1,l 1 and 1 :2.On the basis of Raman and X-ray crystallographic studies the adducts have been formulated as [Xe,F,]' [MF6]- [XeF]+[MF6]- and [XeF]'[M,F,,]-. However recent Raman spectroscopic studies strongly suggest some covalent bonding in that the spectra of the XeF,,MF adducts can be more satisfactorily assigned on the basis of c4"symmetry for the hexafluoro-anion than oh symmetry. The results are consistent with a significant lowering of the symmetry of the octahedral anion by fluoride bridging to the [XeF]' cation. As the v(XeF) is totally symmetric the splitting of v(XeF) in many adducts has been attributed to factor-group splitting. However the mean value of the stretching frequency associated with v(XeF+) for the XeF2,2MF and XeF,,MF series of adducts decreases in the order SbF >TaF > NbF,.These results are consistent with the suggestion that the XeF bond length in [XeF]' is progressively increasing. A comparison of the peaks which have been assigned to v(Xe..-F) shows a progressive increase in value of the mean frequency which is indicative of an increasing strength of the bridging bond.29 Previously the spectrum of XeF,,SbF5 was assigned on the assumption of oh symmetry for the anion. However definitive assignment for the anion modes has proved difficult since in the case of the Sb and Ta adducts more than six anion modes were observed. If the adducts which were previously formulated as the ionic species [XeF]'[MF,]-are reformulated as having a fluoride-bridged structure of the type XeF+,FMF,- in which the anion can be regarded as distorted from oh to C4" symmetry then the observed spectral bands can be assigned more satisfactorily.The bands in all the spectra in the region 450-490cm-' are not easily assignable to vibrations of octahedral [MFJ anions and are better assigned to additional v (Me* * F). In conclusion the i.r. and Raman spectra of the adducts 2XeF2,MF (M =Sb or Ta) XeF,,MF, and XeF2,2MF (M = Sb Ta or Nb) have been measured and although the spectra have been interpreted in terms of an ionic formulation involving [XeF]' and [Xe,F,]' the results indicate an increasing covalent character in the series XeF,,SbF <XeF,,TaF <XeF,,NbF <XeF2,2TaF <XeF2,2NbF, and 2XeF2,SbF <2XeF2,TaFS.The Typical Elements Further evidence for the covalent nature comes from a Raman and 19F n.m.r. study of adducts of xenon difluoride with WOF4.30 Stoicheiometric amounts of XeF and 'WOF react in HF at room temperature and in the melts at 30-75 "C to give stable crystalline solids at room temperature. Two possible structures are the ionic form (15)and the partially covalent form (16). The low-temperature 19Fn.m.r. spectra of FOF \$/ + [XeF] [WOF,] -F/i\ (15) iF solutions in BrF and S0,ClF support the covalent stru~ture,~" which is further supported by bands in the Raman spectrum which can be assigned to a fluoride- bridged structure. In XeF,,WOF the struc!ural unit has approximately C' sym-metry. The terminal XeF bond length (1.89 A) is shorter than that of XeF (2.00 A) while the Xe...F bridge bond length (2.04 A) is longer than the XeF bonds in XeF,.The W-.-F--Xe bridge angle is 147". The Raman spectrum of XeF,,2WOF4 is also consistent with a bridged structure (17). However the 19Fn.m.r. spectrum of a S0,ClF solution of XeF,,2WOF4 is complex and in addition to lines associated with the fluoride-bridged structures lines were also observed consistent with an oxo-bridged structure. Xe \ F (17) Krypton difluoride is a very powerful oxidative fluorinating agent and has been used to synthesize gold(v) species:31 7KrF + 2Au 'i 2[KrF]+[AuF6]-+ 5Kr Raman studies at -80 "C under a layer of HF are consistent with a formulation in which the [KrF]+ cation is fluoride-bridged to a [AuF6]- anion with lines assignable to a C, symmetry for [AUF,]-.[KrF]'[AuF,]-on pyrolysis gives AuF, a powerful oxidative fluorinating agent which react with an excess of XeF, [KrF]+[AuF,]-60~~ocb AuF + Kr + F XeF LHF .[Xe,F3]+[AUF6] -30 J. H. Holloway G. J. Schrobilgen and P. Taylor J.C.S. Chem. Comm. 1975 40. 31 J. H. Holloway and G. J. Schrobilgen J.C.S. Chem. Comm. 1975,623. A.J. Carty,R. H. Cragg,and J. D.Smith Raman and 19Fn.m.r. studies on the products of the reaction of [KrF]' salts with excess of XeOF show them to be 02'and [XeOF,XeF,]' salts and not XeOF as previously reported. Relativistic quantum mechanics applied to radon (or element 118) fluoride structures indicates that ionic crystalline forms are probably more stable for the fluorides of these elements in contrast to the molecular forms of xenon An ionic crystalline form of RnF would be expected to be non-volatile as found and show the observed migration of Rn as a cation upon electrolysis.32 K. S. Pitzer J.C.S. Chem. Comm. 1975 760.

ISSN:0308-6003    

DOI:10.1039/PR9757200137

出版商:RSC    

年代:1975

数据来源: RSC