ISSN:0300-9238    

DOI:10.1039/F298480FX001

出版商:RSC    

年代:1984

数据来源: RSC

ISSN:0300-9238    

DOI:10.1039/F298480BX003

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

J. Chem. SOC.,Faraday Trans. 2, 1984, 80, 31-41 The Huggins Coefficient as a Means for Characterizing Suspended Particles BY WILLIAMB. RUSSEL Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544, U.S.A. Received 6th April, 1983 This theory determines the dependence of the Huggins coefficient kHon the interaction potential between rigid spheres. Hard-sphere interactions represent a minimum, with k, increasing for either attractive or longer-range repulsive potentials. Although derived for model potentials, the sticky sphere for short-range attractions and the excluded shell for repulsions, the results for kH, when plotted against A2NA/Mw[q],should characterize other potentials as well. Furthermore, this interpretation should distinguish the effects of interac- tion potentials from those of anisotropy or permeability of the individual particles.INTRODUCTION Light-scattering and viscosity measurements on dilute suspensions or solutions form a classical means of characterizing the suspended particles or dissolved macromolecules.’ In particular, these determine the four coefficients in the virial expansions for the osmotic compressibility d7r NkT----[1+2A2(N/MW)c+. . .] dc M, and the viscosity where N is Avogadro’s number, kT is the thermal energy and c is the weight concentration. The molecular weight M, together with the intrinsic viscosity [q] yields the apparent hydrodynamic volume, while the second virial coefficient A2 indicates the thermodynamic volume. Generally the two are unequal, i.e.the particles/macromolecules do not behave simply as hard spheres. This paper illus- trates how the fourth parameter, the Huggins coefficient, kH, which is generally discarded or not estimated accurately, can elucidate the reason for this discrepancy. The theory of dilute solutions of rigid spheres, including pair interactions, is now firmly established. The thermodynamic properties are well known and predict- able, even to extreme concentration^.^'^ Hydrodynamic consequences have been resolved only relatively recently. The work of Bat~helor,~,’who successfully assimi- lated both hydrodynamic interactions and Brownian motion into a rigorous theory for the low-shear limiting viscosity, forms the basis for the theory developed herein.Interest in the thermodynamic properties of dense fluids has focused attention on potentials with short-range attractions or soft repulsion^.^ The square well and the sticky sphere,6 convenient idealizations of the Lennard-Jones potential, permit 31 THE HUGGINS COEFFICIENT AND SUSPENDED PARTICLES analytical solutions at high densities. At the pair-interaction level the general theory can handle any potential with ease. Interaction potentials also affect the dynamics of colloidal suspensions quite significantly. Batchelor7 resolved the 6(c)correction to the sedimentation velocity for hard spheres. It was thens-" demonstrated that attraction should enhance, and repulsion retard, the sedimentation process.Here the interaction potentials merely alter the equilibrium radial distribution function, thereby changing the importance of the positive contribution from the near-field relative to the negative one from far-field hydrodynamic interactions. The mutual-diff usion coefficient follows from the generalized Stokes-Einstein relation' ',12 as the product of the sedimentation coefficient and the osmotic compressibility. Generally the direct contribution of the potential to the driving force embodied in the latter outweighs the effect on the hydrodynamics; hence repulsions increase and attractions decrease the diff usivity. Little is known, however, about the effect of such potentials on the Huggins coefficient. Only with long-range electrostatic repulsions, which increase kH dramatically, does a satisfactory theory exist.l3 The following sections describe an analogous theory which includes the more subtle short-range attractions and repul- sions between rigid spheres, together with hydrodynamic interactions and Brownian motion. At the end we combine these results with extant treatments of non-spherical particles and flexible macromolecules to demonstrate that kH, when taken together with [q],M, and A2,can distinguish between the various possible deviations from hard-sphere behaviour. INTERACTION POTENTIALS AND THE SECOND VIRIAL COEFFICIENT The two interparticle potentials of interest here are the simplest possible addi- tions to the classical hard-sphere interaction. Baxter6 proposed sticky spheres with O<r<2a fOO (3) R <r as a convenient model for short-range attractions, where kT is the thermal energy, a is the hard-sphere radius and r is the stickiness parameter.This pair potential V(r)produces a population of doublets in addition to the random distribution of singlets characteristic of hard-sphere suspensions. At dilute concentrations the Boltzmann distribution of pairs determines the radial distribution function as g(r)=H(r-2a)+(a/6~)6(r-2a) (4) with H(x)the Heaviside step function and S(x) the Dirac delta function. Baxter actually solved the Percus-Yevick equation for g (r) at arbitrary concentrations. For repulsive interactions extending beyond the hydrodynamic radius we use an excluded shell, i.e.W. B. RUSSEL with R 22a. This trivial extension of the hard-sphere potential clearly indicates g(r)=H(r-R) (6) at dilute concentrations while the standard theories provide values at higher con- centrations as well. The thermodynamic consequences of these interactions are well known. The second virial coefficients of interest here follow from3 T =nkT(1+A2n) dV=nkT-n2 J rg(r)--d3r (7)dr with rz =cN/M, the mean number density of spheres. The results are 167ra3 1-1/47 sticky sphere A2=-3 { (R/2a)3 excluded shell. We recall that the infinite-dilution intercepts of turbidity and viscosity data provide the molecular weight and the hydrodynamic radius, respectively. Measure- ment of the second virial coefficient then fixes the single parameter, r or R, characterizing the interaction potential in these models.Clearly the sticky sphere is appropriate if A2CAYS= 167ra2/3and the excluded shell applies for A2 BAYS. In the following sections we derive the corresponding contribution of pair interac- tions to the viscosity, characterized by the Huggins coefficient, to provide an independent test of the pair potential. NON-EQUILIBRIUM PAIR DISTRIBUTION FUNCTION The convection of particles relative to one another in a shear flow with rate of strain E perturbs the microstructure of a suspension from the isotropic equilibrium state. Consequently, the pair distribution function P(r), reflecting the probability of finding a second particle at r relative to the test particle, deviates from the equilibrium value ng(r). This equilibrium structure contributes to the stress even in the low-shear limit and bears full responsibility for non-Newtonian behaviour at high shear rates.In the dilute limit the pair distribution function satisfies the conservation eq~ation’”~ aP-+v*j =o (9)at in which the flux j =PU -D [VP+ (l/kT)PVV] includes contributions from convection, diffusion and the pair potential, respec- tively. The relative velocity U = E r -r (r)+[I-(rr/r2)]BE {(rr/r2)A (r)} (10) and the diffusion tensor depend on known scalar functions A, B, G and H of the separation r = (r r)1’2. THE HUGGINS COEFFICIENT AND SUSPENDED PARTICLES A 1-4.077(p -2) (12) B =.0.406 where p = r/a.The importance of convection relative to diffusion is measured by the Pklet number 37rpa3E/kT, where E = (E E)1’2.For weak flows 37rpa3E/kT<< 1 and the departure from equilibrium can be extracted via the regular perturbation expansion P = ng(r)[l -(3npa3/kT)(r E r/r2)f(r)]. (13)9 Substitution into eqn (9)and omission of higher-order terms produces 2 dVW+p3(l-A)--dp kT (14) with the boundary conditions dfp(l-A)+G---=O (15)dP at p=2 and f + 1 as p+a,and W = 3B-(l/p2)[d(p3A)/dp]. For hard-sphere interactions, considered previously by Batchel~r,~ V ZE 0 except at p = 2, where G =0 and A = 1. Hence the terms containing the interaction potential disappear from eqn (14) and the boundary condition at contact reduces to lim G -df = 0.p+2 dp The two potentials considered here lend themselves to similar simplifications. For the sticky-sphere potential dV-=-kT lim In dr R+2a so that dV dVlim [l-A(R)]-(R)= lim G(R)-(R)=0.R+2a dr R +2a dr Hence f for sticky spheres coincides with that for hard spheres. The doublets present in the former case orient slightly toward the plane of shear but are immobile and cannot separate. W. B. RUSSEL For the excluded-shell potential V = 0 for r > R while P = 0 for r < R. Thus the hard-sphere form of eqn (14) holds for r > R with the boundary condition eqn (15) replaced by at p = R/a. Numerical solution of the resulting boundary-value problem is straight- forward except for p = 2.0.5 Alternatively, an accurate approximation to f can be constructed from the far-field solution to eqn (14) C 3C-25 f=3+---.P 2P4 Application of eqn (18)directly to eqn (19) determines C= 50~~)+ ri -A(wG(R)I(R/~)5 3(1+2a/R) with A and G calculated from the far-field limits, eqn (11).For R/a = 2 this leads to C = 13.1 and f(2)= 2.07, compared with the exact results for hard spheres of 9.41 and 1.41,’ respectively. As demonstrated in the next section, a cancellation of errors provides an accurate result for the stress despite the significant discrepancy in f. BULK STRESSES GENERAL FORM Previous ~ork~~’*~’ has identified three distinct contributions to the bulk stress and provided means for avoiding the non-convergent integrals ubiquitous to prob- lems involving the averaging of hydrodynamic interactions.Below we review briefly these developments before presenting specific results. Hydrodynamic stresses, originating with the viscous nature of the fluid, are enhanced by non-deformable particles. Volume averaging of the local stresses yields thereby identifying the extra stress with the viscous dipoles {(x -xi)uH n -$I(x -xi) uH n}dA (22)Sr = I,! induced in the individual particles. For a homogeneous suspension the sum over all N particles in the representative volume V is equivalent to the ensemble average over all configurations, i.e. lN -C SH=n(SH)..Ir i=, At dilute concentrations Batchelor and Green demonstrated the proper virial expansion of eqn (23)to be THE HUGGINS COEFFICIENT AND SUSPENDED PARTICLES The first term, comprising the dipole in an isolated sphere 207T 3Sy=-a puoE3 generates the Einstein correction to the viscosity.The dipole in the second term, caused by hydrodynamic interactions between two spheres, decays as (a/r)3,as does the additional rate of strain [e(r)-El at a position r relative to an isolated sphere. In fact, that is the origin of the excess dipole so that 207rlim [SH(r)-S,"]=-a3pa[e(r)-El. r+oO 3 \ Hence the two terms cancel as r -+ a,leaving an unconditionally convergent integral. This renormalization simply recognizes that the divergent far-field interactions serve to increase the effective rate of strain experienced by the test sphere. In the low-shear limit P(r)= ng(r)[l+ O(Pe)],so that4 (SH)= 54PoE[ 1+4 + 34 Ii"J (p>g(P >P2 dpI[ 1+0(Pe11 (27) where J(p),which decays as J = yp-" as p + a,accounts for near-field hydrody- namic interactions.The preceding term accounts for the far-field interactions mentioned above, an increase of 4E in the apparent rate of strain experienced by an individual sphere. The hydrodynamic stress clearly is affected by Brownian motion and the inter- particle potential through g(r). Both, however, can also contribute directly to the bulk stress. Although only addressing the Brownian stress EB explicitly, the treat- ment of Batchelor' applies to that generated by the interparticle potentials X1as well. The derivation identifies two kinds of local stresses which must be averaged to obtain either bulk stress.One, mechanical in nature and arising from the motion of the particles due to the non-hydrodynamic forces, has the form IN with Si calculated from eqn (21). The other is purely thermodynamic, caused by the increase in free energy associated with the configurational charge accompanying flow. An analysis of the effect of a small virtual strain establishes IN with Fi the non-hydrodynamic force on the ith sphere. The sum of the two can be rewritten formally in terms of the forces as with Ci remaining unspecified. For forces decaying faster than (~z/r)~ direct reduction to the pair interaction limit is possible. Then C2= -C1= C and W. R. RUSSEL so that X'=&Z r[fIA+(~/r')(l-A)]%(,)dr.I dr In the limit p +a,A +0 and the integrand reduces to (rVV)P,clearly indicating the dipole nature of this contribution to the bulk stress, eqn (13).In the low-shear limit eqn (13)gives The isotropic term coincides with the pair interaction term in the virial series for the osmotic pressure obtained from McMillan-Mayer theory. The deviatori: term disappears for hard-sphere interactions, as assumed implicitly by Batchelor, since A = 1at p = 2, as noted above. The Brownian forces, Fi= -kTVi In P, decay as (~x/r)~,precluding the same approach. Hence Batchelor converted eqn (30)to the convergent form W(r)[(rr/r2)-$I]P(r)dr. (34) Unlike the interparticle potential, Brownian forces do not contribute to the osmotic pressure and contribute directly to the deviatoric stresses ogly through near-field hydrodynamic interactions. In the low-shear limit this yields completing the three contributions to the bulk stress.In the following two subsections we present results for the Newtonian zero shear viscosity p defined by XH+ XB +XI= -TI+ 2wE. (36) RESULTS FOR STICKY SPHERES As noted above, stickiness generates a population of doublets without affecting the singlets present with hard-sphere interactions alone. The latter contribute a hydrodynamic stress 2pOE(1+$4 +5.2 4') (37) and a Brownian stress of5 2poE 0.99 4'. The doublets add a hydrodynamic stress from eqn (4)and (27)of THE HUGGINS COEFFICIENT AND SUSPENDED PARTICLES and a Brownian stress from eqn (13) and (35) of The interparticle force does not produce a stress in either case.Together these determine the viscosity as -=1+-4+ (6.2+-3782)42+. . ..P 5 Po 2 The ratio of the Brownian to the hydrodynamic stress at 0(42)differs notably for the two cases. For singlets Brownian motion exerts a small effect, accounting for only ca. l6%0of the total, while ca. 40% comes from the far-field hydrodynamic interactions. With doublets, however, it amounts to ca. 71% of the total, reflecting the amplification of near-field and the absence of far-field interactions. This closely resembles the behaviour of rigid rods, for which rotary Brownian motion accounts for ca. 75% of the intrinsic viscosity at zero shear.16 Expressing eqn (40) in terms of weight concentration identifies the intrinsic viscosity as 107ra3 N [TI=--3 Mw and the Huggins coefficient as k~ = 0.99 +-.0.611 7 RESULTS FOR THE EXCLUDED-SHELL POTENTIAL The various contributions to the bulk stress for the excluded-shell model are illustrated best via the far-field approximation for f(p). Substitution of eqn (18) and the far-field forms of the hydrodynamic functions into eqn (27), (33) and (35) produces with C from eqn (20). For hard spheres (R = 2a), this approximation yields P 5-~1++-4+6.444~ (44)Po 2 or kH= 1.03. The surprisingly small deviation from the exact results is due to a cancellation of errors shown in table 1. The hydrodynamic and Brownian portions of the Huggins coefficient fall below the exact values of 0.83 and 0.16, respectively, W.B. RUSSEL Table 1. Numerical results 2.0 13.1 2.07 0.77 0.113 0.14 1.03 2.1 16.7 2.45 0.72 0.114 0.29 1.13 2.2 20.6 2.72 0.68 0.110 0.49 1.28 2.3 25.0 2.95 0.65 0.104 0.70 1.45 2.4 29.6 3.16 0.62 0.096 0.96 1.67 2.5 36.1 3.38 0.59 0.093 1.25 1.94 2.7 51.7 3.85 0.55 0.090 2.03 2.67 but the interparticle force term, which is non-zero because of the far-field approxi- mation used for A, compensates. With increasing R > 2a the error in the far-field approximations decreases. The hydrodynamic and Brownian stresses fall off slowly, since the hydrodynamic interac- tions become weaker, but X1increases sharply. In the limit of r/a >> 1 ZH=: 2poE(1 + $4+ $4*) ZB-0 (45) in acco d with earlier asymptotic solutions for long-range electrostati interac-tion~.~~Clearly the Huggins coefficient is quite sensitive to repulsive potentials.DISCUSSION The derivations of the preceding sections illustrate the dependence of the Huggins coefficient, characterizing the effect of pair interactions on the zero-shear viscosity, on the interaction potential between spheres. The specific potentials examined are clearly idealized but should model at least semi-quantitatively more complex attractive or repuIsive potentials. Each contains a single parameter reflect- ing either the strength or the range of the interaction. In contrast to their effects on sedimentation and diffusion, each causes the Huggins coefficient to increase above that for hard spheres.With the attractive potential Brownian and hydrody- namic stresses associated with the doublets are responsible for the excess. The repulsive potential, on the other hand, contributes directly to the stress while reducing the hydrodynamic and Brownian portions. To generalize these results we can express kH as a function of the departure from hard-sphere behaviour as measured by A2/AyS =A2N/l.6[q]Mw. Fig. 1 illustrates the minimum in kHcorresponding to hard spheres. Since light-scattering and viscosity measurements on dilute suspensions yield M,, A2, [q]and kH, this plot serves to test whether deviations from hard-sphere behaviour can be attributed solely to the interaction potential.A common alternative explanation cites the effect of non-sphericality.’ Only partial theoretical results are available but the qualitative trends are clear. For ellipsoids of aspect ratio e without additional potentials the intrinsic viscosity’6 and the second virial coefficient” both have minima at F = 1. However, A2/AFS=s 1 for both prolate and oblate spheroids. The Huggins coefficient is known only for THE HUGGINS COEFFICIENT AND SUSPENDED PARTICLES Fig. 1. Master plot of Huggins coefficient against A,/AyS:(-) sticky-sphere and excluded-shell models; (---) slender rod limit; (. -.) correlation of experimental results for flexible macromo1ecules.19 E +00, slender rods, where kH=r 0.40.’* Thus the trend, sketched qualitatively in fig.1,runs counter to that for spheres with attractive potentials. For flexible macromolecules at theta conditions A2 0 and kH=0.4-0.7. Improving the solvent quality causes the molecule to expand from a random coil because of intramolecular interactions, i.e. excluded v01ume.’~ Intermolecular repulsions increase A2from zero and contribute directly to the stress, as with rigid spheres, but also produce a slight shrinkage of the coil.’’ This concentration- dependent reduction in the hydrodynamic volume appears in the stress at O(c2) and outweighs the direct contribution for high-molecular-weight species with small excluded volume. Hence the Huggins coefficient decreases as the solvent quality improves. The curve shown in fig.1is merely a sketch indicating the trend suggested by the existing theory,” as yet incomplete, and the data.20 The master plot indicates that measurements of kH,in conjunction with [q], M, and A2,should indeed be useful in characterizing the thermodynamic nature of the suspended species. The effects of attractive or repulsive potentials, non- spherical geometries and solvent quality for flexible macromolecules are reasonably distinct. Hence the magnitude of kH and its variation with A2N/[q3Mwis fairly definitive. This work was supported by grant no. CPE-8116339 from the U.S. National Science Foundation. ’ C. Tanford, Physical Chemistry of Macromolecules (John Wiley, Chichester, 1961). W. R. Smith and D. Henderson, Mol. Phys., 1970, 19, 411.W. B. RUSSEL 41 D. A. MacQuarrie, Statistical Mechanics (Harper and Row, New York, 1976). G. K. Batchelor and J. T. Green, J. Fluid Mech., 1972, 56, 375; 401. G. K. Batchelor, J. FluidMech., 1977, 83, 97. R. J. Baxter J. Chem. Phys., 1968 49,2770. G. K. Batchelor J.Fluid Mech., 1972, 52, 245. C. C. Reed and J. L. Anderson AIChE J., 1980,26,816. R. Finsy, A. Devriese and M. Lekkenkerker, J. Chem. SOC., Faraday Trans. 2, 1980, 76, 767. I0 C. van der Broeck, F. Lostak and H. Lekkerkerker, J. Chem. Phys., 1981,74, 2006. 11 G. K. Batchelor J. Fluid Mech., 1976, 74, 1. 12 W. B. Russel, Annu. Rev. Fluid Mech., 1981, 13, 425. W. B. Russel, J. Fluid. Mech., 1978, 85, 209. 14 W. B. Russel, J. Rheology, 1980, 24, 287. '' G. K. Batchelor, J. Fluid Mech., 1970,41, 545. 16 E. J. Hinch and L. G. Leal, J. Fluid Mech., 1972, 52, 683. 17 H. Yamakowa, Modern Theory of Polymer Solutions (Harper and Row, New York, 1971).18 D. H. Berry and W. B. Russel, J. Fluid Mech., 1983, in press.19 M. Muthukumar and K. Freed, Macromolecules, 1977, 10, 899. 20 G. C. Berry, J. Chem. Phys., 1967, 46, 1338. (PAPER 3/529)

ISSN:0300-9238    

DOI:10.1039/F29848000031

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

J. Chem. SOC.,Faraday Trans. 2, 1984, 80, 43-49 Laser Excitation Spectra A” 2113/2+r? 2113/2of the Bromoacetylene and Deuterobromoacetylene Cations in the Gas Phase BY JOHNP. MAIER*AND LIUBOMIR MISEV Physikalisch-Chemisches Institut der Universitat Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland Received 6th June, 1983 Laser excitation spectra of the 2113/2+-221J3/2electronic transition of rotationally cooled bromo- and deuterobromo-acetylene cations in the gas phase have been obtained. The cations were produced by Penning ionisation in a liquid-nitrogen-cooled environment. The vibronic band systems have begn analysed and the vibrational frequencies of the funda- mentals for these cations in their A 2113,2states inferred. The ground and the lower excited electronic states of the bromoacetylene cation were first loc3ted by pJotoelectron spectroscopy.’ This information was used to identify the A 211n-,X 211n(R = 3/2, 1/2) emission spectrum of this cation which was observed with a crossed electron-effusive-sample beam apparatus.2 It was hoped that the much higher resolution of the optical approach would lead to an accurate determination of the vibrational frequencies of the cation.However, the ap earance of a large number of vibronic transitions from excited levels of the A 2:II, state, and the profuse overlap of the R = 3/2 and 1/2 band systems, precluded a reliable interpretation of the spectrum or even the identification of the origin bands. The extensive Franck-Condon profile is characteristic of band systems connecting two mutually displaced electronic potential surfaces.These obstacles have now been surmounted using two more refined techniques. In one, the emission spectrum of supercooled cations is obtained using a helium- seeded supersonic free jet excited by an electron beam.3 Due to the cooling of the rotational degrees of freedom, the bromoacetylene cation bands are sharpened-up and isotope splittings become clearly discernible. These features allow an interpreta- tion of the band systems to be made.4 The second technique, the one applied in this study, yields the laser excitation spectrum of the cation in the gas phase,s and it aim is to identify the origin band and to infer the vibrational frequencies of the cation in the excited electronic state.It also offers a high resolving power (ca. 500 000) in order to probe the rotational structure of_the bands.: In this paper we focus our attention on the vibrational structure of the A 2r13/2+ X 2113/2excita-tion band system of the bromoacetylene cation. The corresponding spectrum of deuterobromoacetylene cation enables us to follow the frequency changes on isotopic substitution and, in turn, to identify the vibrational modes excited. EXPERIMENTAL The excitation spectra of bromo- and deuterobromo-acetylene have been recorded using the laser-excited fluorescence apparatus already described in Cations in their ground state are produced in the gas phase by a Penning ionisation process at an ambient temperature 43 LASER EXCITATION SPECTRA OF BrCCH(D)+ of ca.100 K using discharge-excited Ar metastables thermalised by a liquid-nitrogen bath surrounding the gas-flow system. The cations are excited by a tunable and pulsed nitrogen-pumped dye laser offering resolution of 1cm-' and the resulting spontaneous fluorescence is detected by a photomultiplier. The fluorescence signal, along with two photodiode signals representing laser intensity and frequency marker output, are digitised (Tektronix 7912 AD) and processed by a dedicated microcomputer system (LSI 11/23). The dye-laser scan is also controlled by the computer, The wavelength calibration of the spectra was accomplished using an argon transition (452.232 nm) in conjunction with frequency markers from a Fabry-Perot etalon, the thickness of which was spectroscopically determined.The samples were introduced from a glass vessel held at -80 "C.The synthesis and purification of bromo- and deuterobromo-acetylene were carried out as described in ref. (1). RESULTS AND DISCUSSION In fig. 1 and 2 are shown the laser excitation spectra, A 2n3/2 +-22n3/2, of bromo- and deuterobromo-acetylee cations. The band systems are assigned to the R = 3/2 component because the X 2111/2state cannot be significantly populated at an ambient temperature of 100-150K. The spin-orbit separation in the ground state is 1000f160 cm-' according to the photoelectrQn spectrup"2 and causes the complete absence of the R = 1/2 component of the A 211n+X 211n transition.The most conspicuous feature of the band system is the long progression in the u3[v,(C-Br)] vibrational mode, for which seven quanta are observed, and some combination bands involving this mode in the excited cationic state. Such a broad Franck-Condon profile is characteristic of transitions between electronic states having considerably displaced equilibrium positions. In the case of the bromoacety- lene cation it is presumed that linearity is retained in both the states and the main change is a lengthening of the C-Br bond on passing from the ground to the excited cationic state. The latter is also the prediction made using a quantitative Franck- Condon analysis of the band profiles in the photoelectron spectrum of bromoacetylene.8 Because of the unfavourable Franck-Condon factor, the assignment of the vibrational origin of the band system (i. e.0; R = 3/2) is not immediately apparent. The assignment made (fig. 1 and_2) is based on several grounds: knowledge of the vibrational frequencies in the X2113/2state from the emission spectrum of the supercooled cations4 and the intensities of the first members of the 30, and 5:n progressions in the excitation spectra, the isotope shift between the corresponding bands in the bromo- and deuterobromo-acetylene cations and the isotope splittings of the bands of the 3," progression due to the equally abundant 79Br and 81Br species. For the latter, the separation between the R heads was found to be a minimum for the band assigned as 0," and was found to be 0.30k0.05 cm-' from high-resolution recordings (AA = 0.001 nm) for both bromo- and deuterobromo- acetylene cations.' In tables 1 and 2 are given the maxima ( Cvvac)of the more intense bands in the two excitation spectra as well as the assignments made.The numbering of the five fundamentals (3Z+, 2II) is according to the order given in table 3 for the molecular ground-state values. lo For the bromoacetylene cation the_ frequencies of four of the five fundamental vibrational modes in the excited A2113/2state have been inferred from the data, whereas for the deuterated species all of them could be determined. These sets of frequencies are compiled in table 3. The determinations of the vibrational frequencies are based on the observation of progressions and combination bands, which are most apparent for the u2, v3 and vs (in double quantum excitation) modes.In the case of the v4 bands, these are I I I 1 20000 20500 21000 21500133, I 22000 22500 23000 231500 24600 ;/crn-l Fig. 1. Laser excitation spectrum of the A 2113/2+-22113/2transition of the bromoacetylene cation in the gas phase recorded with 0.02 nm band-width. The vertical markers, intermit- tently numbered, dsnote the bazds listed in table 1. The bands marked with a dot belong to the A 2113/2,g +X 2113/2,usystem of the dibromoacetylene cation. /3; 4; I/ -7 I 1 1 1 20000 20500 21000 21500 I I I I I 22000 22500 23000 23500 24000 v"/ cm-Fig. 2. Laser excitation spectrum of the A2113/2+%2113/2transition of the deutero- bromoacetylene cation in the gas phase recorded with 0.02 nm band-width.The vertical markers, intermittently numJered, denoie the bands listed in table 1. The bands marked with a dot belong to the A 2113/2,g+X 21'13/2,u system of the dibromoacetylene cation. LASER EXCITATION SPECTRA OF BrCCH(D)' Table 1. Prominent bands in the 2 2113/2tr? 2113/2excitation system of the bromoacetylene cation. Isotopic splittings and other multiplet structures are bracketed. All values k1 cm-' label Vvac/crn-' assignment label Vvac/crn-' assignment - 1 19 876 19 22 602 2 20 371 3 20 468 20 22 851 4 5 6 20 551 20 966 21 043 21 22 22 896 22 890 22 950 22 954 1 7 21 389 23 22 988 8 21 465 24 23 093 9 21 535 25 23 328 10 21 809 26 23 393 11 21 823 27 23 438 12 21 886 21 891 1 28 23 472 13 21 965 29 23 578 14 22 020 30 23 758 15 22 323 31 23 829 16 22 384 22 390 22 394 22 397 32 33 23 881 23 914 23 920 17 18 22 460 22 4991504 34 35 23 978 24 058 weak for the bromoacetylene cation but become much stronger for the deutero-bromoacetylene cation, presumably because they gain intensity by Fermi resonance with the now much nearer lying, intense 3: transitions (cf.fig. 1 and 2). The intensities of the 31;5ifl combinations and 5;' bands are also enhanced due to their proximity to the respective 3; bands. Note also that there are appreciable irregularities in the frequencies of the excited-state progressions.For example, the frequencies of the v3 progression first decrease in a regular manner but cease to do so after the 3; member for the non-deuterated cation. J. P. MAIER AND L. MISEV Table 2. Prominent bands in the 2 2113,2+-k2113,2excitation system of the deutero- bromoacetylene cation. Isotopic splittings and other multiplet structures are bracketed. All values *I cm-l label fivvac/cm- assignment label fiV&m-' assignment 1 20473 27 22 901 2 3 20 546 20 946 28 22 936 4 21 030 21 436 29 22 950 5 21 444 30 22 966 21 450 31 22 983 6 21 511 32 33 23 094 23 175 7 8 21 521 21 777 34 23 245 9 10 11 21 860 21 925 21 936 35 36 37 23 248 23 311 23 316 23 321 1 12 21 988 38 23 366 13 14 22 003 22 272 39 23 372 15 16 17 22 341 22 353 22 408 40 41 42 43 23 383 23 406 23 417 23 442 18 22 413 44 23 579 19 20 22 462 22 475 45 46 23 729 23 791 23 798 21 22 22 484 22 752 47 23 836 23 843 23 22 763 48 23 864 24 22 828 49 23 888 25 22 837 50 23 919 26 22 893 51 24 058 Most of the bands in the spectra could be assigned to the A 2113,2+221J3,2 band system of the bromoacetylene cation.The remaining series of weak bands occur at the same frequencies for both species (cf.bands between 19 700 and LASER EXCITATION SPECTRA OF BrCCH(D)' Table 3. Vibrational frequencies (cm-') of the X+ _and I3 fundamentals of bromo- and deuterobromo-acetylene cations in the X 2113/2and A 'II3/2 electronic states inferred from the excitation spectra; all values *3 cm-l.The molecular ground-state frequencies are taken from ref. (10) C' n Br-CrC-H 6'C+ 3325 2085 618 618 Br-CEC-H+ < 2n[3,2 674 290 A 2n3/* 2051 493 629 207 Br-C=C-D X 'C+ 2600 1950 606 480 283 Br-CrC-D' 'I33/2 273 A '133/2 2548 1939 484 488 200 20 900 cm-' in fig. 1 and 2) and belong to the 2113/2,g+-22113/2,u sBstem of the dibromoacetylene cation.' The strongest band of this transition, Oo, occurs at 19 856 cm-l (vvac). A, comparisp of the vibrational frequencies of the bromoacetylene cation in the X 211and A 211 states in the framework of the molecular-orbital description of the electronic structure' predicts a much lower frequency for the v3[v(C-Br)] stretching mode for the excited state.Also, a slightly lower frequency is to be expected for the degenerate bending modes v4[8(CCBr)] and v5[S(CCH)], but practically the same values for the v2[v(C=C)] mode. This qualitative scheme is confirmed by all the frequencies available either from the present ezcitation spectra or from the emission spectra of the supercooled cations for the X211 ~tate.~The main influence of deuteration is on the v4 bending and v,[v(C-H)] stretching modes (cf.table 3). Finally, it is apparent that the bands are red-shaded. This implies that the rotational constant for the ground state is larger than for the excited state. This is again in accord with the relative vibrational frequency changes and the predictions made by the Franck-Condon analysis of the photoelectron spectra.' A large change in the rotational constant is also indicated by the broad profile of the band system.In the higher-resolution recordings the rotational structure of the 79Br and 81Br isotopes is clearly discernible and a rotational analysis is in progress.9 This work is part of project no. 2.419-0.82 of the Schweizerischer National- fonds zur Forderung der wissenschaftlichen Forschung. Ciba-Geigy SA, Sandoz SA and F. Hoffmann-La Roche & Cie. SA, Basel, are also thanked for financial support. H. J. Haink, E. Heilbronner,V. Hornung and E. Kloster-Jensen,Helv. Chim. Acta, 1970,53,1073.* M. Allan, E. Kloster-Jensen and J. P. Maier, J. Chem. SOC., Faraday Trans.2, 1977, 73, 1406. A. Carrington and R. P. Tuckett, Chem. Phys. Lett., 1980, 74, 19; T. A. Miller, B. K. Zegarski, T. J. Sears and V. E. Bondybey, J. Phys. Chem., 1980,84, 3154; D. Klapstein, S. Leutwyier and J. P. Maier, Chem. Phys. Lett., 1981, 84, 534. D. Klapstein, R. Kuhn and J. P. Maier, to be published. T. A. Miller and V. E. Bondybey, J. Chim. Phys., 1980, 77, 695 and references therein. D. Klapstein, J. P. Maier and L. Misev, in Molecular Ions: Spectroscopy, Structure and Chemistry, ed. T. A. Miller and V. E. Bondybey (North-Holland, Amsterdam, 1983), p. 175. J. P. Maier and L. Misev, Chem. Phys., 1980, 51, 3 11. J. P. MAIER AND L. MISEV E. Heilbronner, K. A. Muszkat and J. Schaublin, Helv. Chirn. Actu, 1971, 54, 58. J. P. Maier and L. Misev, to be published. lo G. R. Hunt and M. K. Wilson, J. Chern. Phys., 1961, 34, 1301; J. K. Brown and J. K. Taylor, Proc. Chern. Soc., 1961, 13. (PAPER 3/934)

ISSN:0300-9238    

DOI:10.1039/F29848000043

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

J. Chem. SOC.,Faraday Trans. 2, 1984, 80, 51-65 Microwave Rotational Spectrum of a Weakly Bound Complex formed by Hydrogen Sulphide and Hydrogen Chloride BY ELIZABETH AND A. C. LEGON"J. GOODWIN Christopher Ingold Laboratories, Department of Chemistry, University College London, 20 Gordon Street, London WClH OAJ Received 7th June, 1983 A weakly bound dimer formed by hydrogen sulphide and hydrogen chloride has been identified in the gas phase by means of its rotational spectrum which has been detected with the aid of the sensitive technique of pulsed-nozzle, Fourier-transform microwave spectros- copy. The spectra of eight isotopic species have been analysed to give rotational constants (B,+ C,),centrifugal distortion constants Dj and C1 nuclear quadrupole coupling constants xna as follows: (B,+Co)IMHz D,/kHz XaaIMHZ (HZ3'S, H35Cl) 4014.5339 (2) 5.348 (3) -53.499 (4) (H2"2S, H"C1) 3909.9929 (5) 5.06 (1) -42.1 69 (3) (H234S, H35Cl) 3902.6704 (2) 5.060 (4) -53.54 (3) (HD"S, ~~"1) 3945.6136 (9) 5.27 (2) -53.48 (2) (D~s,H~~CI) 3880.2976 (9) 5.02 (2) -53.63 (4) (H232S,D""C1) 4015.407 (2) 5.20 (3) -55.58 (5) (HD3'S, D35Cl) 3946.459 (2) 4.97 (6) -55.67 (8) (D2"S, D35Cl) 3881.1878 4.88 -55.70 The listed spectroscopic constants allow us to establish that the weak intermolecular linkage occurs through a hydrogen bond, with HCl acting as the proton donor and the S atom acting as the proton acceptor.The S-..H-Cl nuclei are collinear (or nearly so) with r(S. * * *Cl)= 3.8092 A, and the plane of the H2Smolecule is almost perpendicular (4 = 93.8') to the line of the hydrogen bond.Conclusions about the relative strength of the hydrogen bond are drawn from analyses of the constants DJ and xaa. Rotational spectroscopy has recently proved to be a powerful technique for the investigation of hydrogen-bonded dimers at low pressure in the gas phase and hence effectively in isolation. Thus it has been possible by this means to determine, for example, some important details of the geometry, the intermolecular potential- energy function and the electric charge distribution of the simple hydrogen-bonded species (Hz0,HF),'-3thereby fulfilling some of the aims of our work in this area. Another aim of our investigations of weakly bound complexes is to identify any systematic changes that occur in their properties when the proton-acceptor atom in the Lewis base is systematically varied.In particular, for the series (H2Y, HX), where Y is an atom from Group VI of the Periodic Table and X =F, C1 and Br, we aim to establish whether systematic changes occur in the geometry and in the quantities, such as the hydrogen-bond stretching force constant k,, that measure the strength of the hydrogen bond. Investigations of the dimers (H20, HF)'-' and (H20,HCl)4 have already been reported by us, while Viswanathan and Dyke have studied (H2S,HF).s 51 MICROWAVE SPECTROSCOPY OF H2S-HCl DIMER We have taken advantage of the new technique of pulsed-nozzle, Fourier- transform microwave spectroscopy in order to identify the weakly bound species (H2S,HCl) by means of its rotational spectrum in the vibrational ground state.We report here the rotational constants ( Bo+ Co),the centrifugal distortion constants DJ and the C1 nuclear quadrupole coupling constants xaa for eight isotopic species of this dimer, as obtained from analyses of their rotational spectra. A detailed consideration of the spectroscopic constants so reported allows us to draw con- clusions about the geometry of the dimer and the nature and strength of the intermolecular binding. A comparison with other members of the (H2Y, HX) series is also presented. EXPERIMENTAL Rotational spectra of various isotopic species of the dimer (H2S, HC1) were detected by means of a pulsed-nozzle, Fourier-transform microwave spectrometer.The instrument con- structed at University College London is similar to that described by Balle and Fl~gare,~,’ and a preliminary account of it has been given elsewhere.8 A gas mixture consisting of ca. 2% each of hydrogen sulphide and hydrogen chloride in argon, and having a total pressure in the range 1-2.5atm, was expanded in a short pulse through the 0.7mm orifice in a solenoid valve into an evacuated, microwave Fabry-Perot cavity. When the cold dimer molecules (effective temperature ca. 3-10 K) so created were in collisionless expansion between the Fabry-Perot mirrors, they were polarized by means of a 1 ps pulse formed from monochromatic microwave radiation of frequency v.The macroscopic polarization is appreciable only if the molecules have rotational transition frequencies falling within the bandwidth (ca. 1 MHz) of the cavity when tuned to the frequency v. The subsequent emission at a rotational transition frequency v, was detected, after a suitable delay and in the absence of the polarizing radiation, by two superheterodyne stages to give a mixed-down time-domain signal that consisted of the beat (v-vml between the molecular emission and the polarizing radiation. This signal was then digitized, typically at a rate of 0.5 ps per point for 512 points, and stored. Where necessary, repetition of the gas pulse and averaging of stored signals allowed a sufficiently high signal-to-noise ratio to be achieved.Fourier transformation of the averaged time-domain signal gave the intensity of the rotational emission as a function of its frequency offset from v. As an example of the nature of rotational transitions detected, we show in fig. 1 the emission resulting from the unresolved F = 3, 3 +-pair of 35Cl nuclear quadrupole hyperfine components in the 202-101 transition of (H232S, H3’Cl). The time-domain signal from which this was obtained was recorded at a digitization rate of 0.5 ps per point, and accordingly the points in fig. 1 are offset at a rate of 3.90625 kHz per point from v= 8029.9039 MHz. The doublet nature arises from a Doppler splitting that has its origin in the distributior of the emitting molecules within the polarized gas pulse and has been fully discussed.’ The true molecular emission is thus a singlet with its frequency equal to that of the doublet centre.We note from fig. 1that detected transitions have a full-width at half-height of ca. 10 kHz. As a result of making six measurements per transition we were able to achieve a precision of 1 kHz in measurement of the transition fre uency. An accuracy of 1 kHz was ensured by 9measuring the J = 1+-0 transition of l60l2C 2S from time to time. This transition occurs at a calculated frequency” of vo= 12 162.9790(1) MHz and could be measured by us with a precision of better than 0.5 kHz. Throughout the course of the work reported here our measurements of vo were always within 0.5 kHz of the above value. The sensitivity of the pulsed-nozzle, Fourier-transform spectrometer is clearly illustrated by fig.2. This shows a Cl nuclear quadrupole component of the 303t-202 transition in the isotopic species (H234S, H35Cl), which has a natural abundance of 3%. Except for a longer averaging time for the weaker signal, both transitions were recorded under the same condi- tions. E. J. GOODWIN AND A. C. LEGON 0 50 100 I50 200 250 300 frequency offset/ kHz Fig. 1. Unresolved pair (F=5 +-8and 8-3) of 35Cl nuclear quadrupole components in the 202+-lo, transition of (H232S,H35Cl). This results from Fourier transformation of the corresponding time-domain signal digitized at a rate of 0.5 ps per point. Frequencies are offset at a rate of 3.906 25 kHz per point from Y = 8029.9039 MHz.The doubling is a Doppler effect (see text). i 0 50 100 I50 200 250 300 350 400 frequency offset/kHz Fig. 2. Unresolved pair (F=g +-;+-g) of 35Cl nuclear quadrupole components in the and 303+202 transition of (H234S,H3’Cl). Frequencies are offset at a rate of 3.906 25 kHz per point from v = 11 707.9239 MHz. MlCROWAVE SPECTROSCOPY OF H,S-HCl DIMER Hydrogen sulphide and hydrogen chloride gases, supplied by B.D.H. Chemicals Ltd, were used without further purification. DC1 gas was prepared by dehydrating a solution of 40% DCl in D,O (Merck, Sharp and Dohme) with P205. On mixing H2S and DC1 the exchange of deuterium was sufficiently rapid to allow the rotational spectra of all possible deuterated species of (H2S,HCl) to be observed.RESULTS ROTATIONAL SPECTRA AND SPECTROSCOPIC CONSTANTS Any weakly bound dimer formed between H2S and HC1 in the gas phase will necessarily be a nearly prolate asymmetric rotor if, as it is likely, the intermolecular separation r(S---Cl) of the subunits is large compared with the intramolecular distances r(H-S) and r(H-Cl). We demonstrate below that, in fact, the inter- molecular binding involves a hydrogen bond formed by the H atom of HCl with the S atom and that the geometry of the complex has the form shown in fig. 3. The rotational spectra recorded in mixtures of isotopically normal H2Sand HC1 when using the pulsed-nozzle, Fourier-transform spectrometer consisted of sets of equally spaced transitions that could be attributed to the vibrational ground state of each of the three isotopic species (H232S,H%), (H2”S, H3’Cl) and ( H234S,H3’Ci).Each rotational transition carried a characteristic hyperfine struc- ture arising from coupling of the C1 nuclear angular momentum (I = $) with the overall rotational angular momentum (J) by means of the interaction of the C1 nuclear electric quadrupole moment and the electric-field gradient at the C1 nucleus. Except in the case of the various deuterated species discussed below, no further sub-structure, such as might arise from spin-spin coupling among the nuclei in the molecule that have I2 $, was detected in transitions. The various spin-spin coupling constants are, in fact, readily estimated geometrically and are found to be too small to generate any observable extra splitting at the preqent level of resolution, in agreement with experiment.Observed rotational transitions were unambiguously assigned as of the type (J + 1,K-, = 0) +-(J,K-, = 0) by means of their C1 nuclear quadrupole hyperfine patterns. Such transitions are allowed by the component pa of the electric dipole moment. Whatever the detailed geometry of the complex, the inertial axis a will be almost coincident with the S...Cl internuclear line and hence pa will have a substantial value [see fig. 3 for the principal inertial axes of (H22S,H3’C1)]. Although pc# 0 for the model shown in fig. 3, no transitions allowed by this component are predicted to fall within the frequency range of our spectrometer. In addition, a careful search for transitions originating in rotational levels having f 0 was unsuccessful, presumably because such levels are higher in energy by ca.(Ao-B,JK?l than the corresponding = 0 level and hence have negligible population at the low effective temperature of the gas issuing from the pulsed nozzle.A similar investigation of ( H2S,HF),l for which observed rotational transitions are consider- ably stronger than those of (H2S,HCI), has shown that the J = 2 +-1,K1= 1 transitions are observed but only very weakly, a result consistent with the present conclusions. For the same reasons, only vibrational ground-state transitions are observed in both cases. The frequencies of the C1 nuclear quadrupole hyperfine components of transitions were analysed to give unperturbed transition frequencies vo and the component xaa of the nuclear quadrupole coupling tensor by using a method correct to second order of perturbation theory.For an asymmetric rotor, the first-order expression for the energy shifts of the hyperfine components of a given rotational level, when E. J. GOODWIN AND A. C. LEGON ‘. I \ I Fig. 3. Molecular geometry and orientation of principal inertial axes for the dimer (H~~’S,H~~c~). the nuclear quadrupole interaction is treated as a perturbation, is’* E(1)= [J(J+l)]-l(Xaa[J(J+1)+E(K)-(K + l)aE(K)/K]+2XbbaE(K)/aKQ +xc.[J(J+~)-E(K)+(K-~)~E(K)/~K]}Y(I, (1)J,F) where xgg(g= a, b or c) are the components of the nuclear quadrupole coupling tensor, Y(I,J,F) is Casimir’s function and E(K)is the reduced energy of the unperturbed rotational state.Unfortunately, the rotational constant Ao,and hence Ray’s asymmetry parameter K, is not available from the experiments reported here. It is readily shown, however, that for K1= 0 rotational levels of a nearly prolate asymmetric rotor, eqn (1) can be recast as E:’ = -xuay(I, J, F)+f(Xbb -xcc) y(I, J,F, (2) where f is a function of J and K. Using the final geometry determined below, the value of K = -0.999 97 can be calculated for (H232S,H35Cl) and this leads, for example, to values of f=O.O, -7.5 X and -18.7X lop6for J = 1, 2 and 3, respectively. In view of the remoteness of the HCl subunit from H2S in the complex and the fact that the S.* .C1 intermolecular line is almost coincident with the a axis (see below and fig. 3), it follows that Xbb-xcc will be little different from its value of zero in free HCl. Consequently, for K-, =O transitions, the second term in eqn (2) leads to contributions to the hyperfine frequencies that are negligible in com- parison with the accuracy of frequency measurement (1kHz). Hence, eqn (2) truncated after the first term, which is the expression appropriate to the symmetric- top limit, is sufficient for the first-order expression for C1 nuclear quadrupole coupling in (H2S,HCl). If the symmetric-rotor form is adequate for the first-order correction, it follows that the second-order corrections, which are s10 kHz in transitions investigated here, can be obtained by using the symmetric-rotor-type expression E(2)= “xau)21(Bo+ Co)IdL J, K,F) (3)0 where the g(1,J,K,F) have been tabulated.12 The following procedure was then applied to determine values of vo and xaa.For a given isotopic species of (H2S,HCl), the hyperfine component frequencies of all observed (J+ 1, K1= 0)+-(J,KP1= 0) transitions were first corrected for MICROWAVE SPECTROSCOPY OF H2S-HCl DIMER Table 1. Observed and calculated rotational transition frequencies of (H232S,H3’Cl) transition observed obs.-calc. unperturbed J+ltJ F’tF’’ frequency /MHz frequency /kHz“ frequency, vo/MHz 2-1 8030.0481 3.4 8015.5349 -1.6 8016.6739 0.5 8028.8964 (10) 8039.6143 0.1 8028.8940 -2.3 3+2 12 043.6643 2.6 12 040.3443 -3.9 12 043.0239 (10) 12 030.2912 2.2 12 049.9138 -0.2 12 053.7114 -0.7 4-3 16 057.1749 1.9 16 055.6198 0.7 16 056.7671 (10) 16 043.7987 -0.9 16 061.8694 -1.5 16 068.9899 -0.1 5+4 20 070.2776 -1.2 20 069.6390 (15) 20 069.3562 1.2 a Differences of second-order corrected frequencies and those calculated in the first-order analysis of the nuclear quadrupole coupling (see text).second-order effects by subtracting the corrections calculated from eqn (3) using initial estimates of xaa and (Bo+Co). The truncated eqn (2) was then used to fit the corrected frequencies in a least-squares analysis to give xaa and the vo values. The initial guesses of xaa and (Bo+C,) were sufficiently close to the final values that further cycles of this procedure were unnecessary.Observed hyperfine com- ponent frequencies, the differences between the second-order corrected frequencies and those calculated in the least-squares analysis, and vo values are given in tables 1,2 and 3 for the isotopic species (H232S, H3‘C1), (H2”2S,H”Cl) and (H234S, H”Cl), respectively. The values of xaa so determined are included in table 4. When mixtures were made from H2S and DCl, the rotational spectrum of each of the possible deuterated species (H2S, DCl), (HDS, DCl), (D2S, DCl), (HDS, HCl) and (D2S,HC1) of the weakly bound complex was observed, indicating that a rapid exchange of the deuterium label had occurred. The spectrum of each of these E.J. GOODWIN AND A. C. LEGON Table 2. Observed and calculated rotational transition frequencies of (H232S, H3'Cl) transition observed obs.-calc. unperturbed frequency frequency frequency, J+l tJ F'+-F" /MHz / kHz" u,/MHz 7820.7307 2.7 7809.28 8 1 -2.3 7810.1888 0.7 7819.8232 (7) 7828.2692 0.7 7819.8215 -1.7 34-2 24-;\ 11 729.9363 1.2 11727.3211 -1.4 11 729.4325 (7) 11 719.3949 0.8 11734.8620 0.7 11737.8624 -1.3 15 638.9959 0.9 15 637.7713 0.8 15 638.6751 (8) g4-g 15 642.6960 -1.1 ;4-; 15 648.3092 -0.6 Differences of second-order corrected frequencies and those calculated in the first-order analysis of the nuclear quadrupole coupling (see text). Table 3. Observed and calculated rotational transition frequencies of (H234S,H3'Cl) transition observed obs.-calc.unperturbed frequency frequency frequency, J+l tJ F'+-F" /MHz /kHz" u,/MHz 24-1 $4-5 }24-i 7806.3283b 0.0 7805.1791 (14) 34-2 ;t;} 11708.1032 -0.4 11707.4644 (10) ;t; 54-2 11704.7839 0.4;ti} 44-3 +;} 15609.7917 -0.8 54-3 ;4-; 15 609.3862 (9) 44-2 } 15608.2380 0.8 " Differences of second-order corrected frequencies and those calculated in the first-order analysis of the nuclear quadrupole coupling (see text). Only one component observed. MICROWAVE SPECTROSCOPY OF H2S-HCl DIMER Table 4. Spectroscopic constants of various isotopic species of (H2S,HC1)" -53.499 (4) 4014.5339 (2) 5.348 (3) -42.169 (3) 3909.9929 (5) 5.06 (1) -53.54 (3) 3902.6704 (2) 5.060 (4) -53.48 (2) 3945.6136 (9) 5.27 (2) -53.63 (4) 3880.2976 (9) 5.02 (2) -55.58 (5) 4015.407 (2) 5.20 (3) -55.67 (8) 3946.459 (4) 4.97 (6) -55. 70b 3881.187gb 4.8gb For species containing D only two vo values are available to give (B,+ Co)and DJ. The error quoted for these cases is half the range of values allowed by the extremes of the two vo values. No error estimate available. See footnote b of table 5. deuterium species was analysed, although attention was restricted to the' most abundant combination of sulphur and chlorine isotopes (32S,35Cl). For all species, the effects of D nuclear quadrupole coupling were apparent in the transitions investigated through a slight splitting or broadening of a given C1 nuclear quadrupole coupling component.Since these effects were always incompletely resolved, they were ignored and the frequency of the unperturbed Cl hyperfine components was taken at the centre of the broadened or partially resolved transition. As an illustra- -$, % +-tion of the extent of the approximation involved, the F = (unresolved) component of the 404+-303transition of (D:*S, H35Cl) is shown in fig. 4. Under the above assumption, the Cl nuclear quadrupole coupling in the D species was then analysed in the same manner as for the species involving only protium. Observed and calculated hyperfine frequencies and vo values that result are collected in tables 5 and 6 for deuterated species containing D35Cl and H35Cl, respectively, while the xaa values are included in table 4.Because of a smaller number of data and the above-mentioned line broadenings, xaa and vo are probably less well determined for the various D species, especially for those containing two or more D atoms. The asymmetry parameter K of each isotopic species of the complex is so close to the limiting prolate value of -1 [for example, for (H22,H35Cl) the estimated value is K = -0.999 971 that the vo values of each species can be expressed to a very high degree of approximation by v,(J+l,K-1=0 tJ,K-, =0)=(B,+Co)(J+1)-4Dj(J+1)3 (4) where DJ is the centrifugal distortion constant. Model calculations using the set of rotational constants derived from the geometry for ( H2S, HC1) determined below show that, for all transitions considered here, the error involved in employing eqn (4) for yo is less than the estimated accuracy (1kHz) of the frequency measurement.Values of (Bo+C,) and DJ determined from a least-squares analysis of the set of vo for each isotopic species using eqn (4) are recorded in table 4. MOLECULAR GEOMETRY The rotational constants (Bo+Co) given for the various isotopic species of (H2S, HC1) in table 4 can be used to establish the geometry of the dimer. First, we 0 50 100 I50 200 250 300 350 400 450 500 frequency offset/kHz Fig. 4. Unresolved pair (F =; 6;and +2) of 35Clnuclear quadrupole components in the 404t303 transition of (DZ3*S,H3w). Frequencies are offset at a rate of 3.906 25 kHz per point from v=15 518.5348 MHz. The splitting (other than the Doppler doubling of ca.50 kHz) arises from D nuclear quadrupole coupling. note that (Bo+Co)increases by a small and similar amount (ca.0.9 MHz) when D is substituted in the H35Cl subunit of each of the three species (H232S,H35Cl), (HD32S, H35Cl) and (D232S,H3'Cl). It is well known that isotopic substitution close to the centre of mass of a molecule can lead to an increase in rotational constants, because changes in the equilibrium moments of inertia are swamped by changes in zero-point motion. The above observations consequently establish that the H nucleus in question lies close to the centre of mass of the complex and thus must lie between the S and Cl nuclei, so providing a hydrogen bond between the two component molecules. As discussed below, the involvement of the HC1 molecule in a hydrogen bond is also consistent with the small operationally defined angle 8,,==22" between the HC1 direction and the a axis. Since the angle between the a axis and the S-..Cl internuclear line can be only a few degrees, this small average angle between the HCl and S...Cl directions implies a linear or nearly linear hydrogen bond at equilibrium.In the arguments that follow, the nuclei S.-.HCl are assumed collinear. Given the above conclusion, the geometry of the dimer can be shown to be of the form given in fig. 3. If we assuAe that the component molecules have their geometries r,(S-H) =1.3356 A, HSH =92.11' l3 and r,(H-Cl) =1.274 57 A l4 unchanged on dimer formation and that the dimer has a plane of symmetry containing the bisector of HSH and the HC1 internuclear line, only the distance r(S--.Cl) and the angle 4 remain to be determined.In fact, the conclusions discussed below are relatively insensitive to small changes in the component geometries. The quantities 4 and r(S.-.Cl) are then readily established from the (B,+C,) values of (H232S, H3'Cl), (HD32S, H3u) and (D232S,H3%l) as follows. MICROWAVE SPECTROSCOPY OF H,S-HCl DIMER Table 5. Observed and calculated rotational transition frequencies of (H232S, D35Cl), (HD3’S, D35Cl) and (D232S, D35Cl) isotopic species transition J + 14-J F’+-F” observed frequency /MHz obs.-calc. frequency/ kHz“ unperturbedfrequency , v,/MHz (H~~~s,D~~CI) 3 4-2 g +-;I 12 046.3237 -0.9 12 042.8656 -12.6 12 045.660 (4) 12 052.8172 -0.9 16 060.7233 3.8 16 060.298 (3) 16 059.1012 -3.8 11839.5157 12.1 11836:0467 -8.2 11838.841 (7) 11845.9941 -3.9 15 784.9888 -1.7 15 784.568 (8) 15 783.3752 1.7 11643.6962 -11643.036b 15 523.9240 0.0 15 523.501 15 522.3058 0.0 “ Differences of second-order corrected frequencies and those calculated in the first-order analysis of nuclear quadrupole coupling (see text).Estimated using the observed component frequency and xaadetermined from J = 4 3 transition. If, for a given value of the angle 4, we adjust r(S. .Cl) so that (Bo+Co)of the first species is reproduced, the changes, A( B + C),in (B+ C) that accompany isotopic substitution to give each of the two remaining species can be calculated.Repetition of this procedure for a range of angles 4 allows A( B + C) to be plotted against (6, with the results shown in fig. 5. The appropriate experimental values A(Bo+Co), also indicated in fig. 5, then lead to (6 = 93.81(4)O and r(S.-.Cl) = 3.809 22(3) A, where the error quoted is merely the range of the two determined values of each quantity about the mean. A similar calculation using the A(Bo+Co)of the corre- sponding set of three isotopic species that contain D3’Cl instead of H35Cl gives E. J. GOODWIN AND A. C. LEGON Table 6. Observed and and calculated rotational transition frequencies of (HD32S, H35Cl) and (D232S, H35Cl) observed obs.-calc. unperturbed isotopic species transition J + 1+-J F' 4-F" frequency /MHz frequency/ kHz" frequency, v,/MHz 11836.9100 0.4 11833.5949 -4.4 11836.272 (2) 11843.1596 -0.4 15 781.5135 1.4 15 781.106 (1) 15 779.9588 -1.4 11637.6708 -0.6 11640.351 (2) 11640.9876 0.6 15 520.3121 -1.3 15 519.906 (1) 15 518.7567 1.3 " Differences of second-order corrected frequencies and those calculated in the first-order analysis of nuclear quadrupole coupling (see text). 4 = 94.28 (2)" and r(S..C1) = 3.8066 (1)A.The mean geometry determined from the first set of three molecules has been used to predict (B+ C) for each isotopic species of (H2S, HCl) investigated. The results are shown in comparison with the observed quantities in table 7. The agreement between observed and calculated values is excellent, except that D35Cl species are always predicted to have (B+ C) lower than the observed values, for the reasons discussed above.We note that the above conclusions are relatively insensitive to the assumption of a linear hydrogen bond. We now assume a model in which the rigid H2S and HCl molecules are rotated about their respective centres of mass. The HC1 molecule is rotated anticlockwise (see fig. 3) by 21.91", the magnitude of the operationally defined angle O,, determined below from the coupling constant xaaof (H232S, H3'Cl), while the H2S molecule is rotated through the angle 4 as previously defined. A repetition of the above calculation of A(B+ C) values for (HD32S, H3vl) and (D232S,H3'Cl) as afunction of 4 then allows 4 = 92.99(4)" and r(S-*Cl)= 3.8069 A to be estimated from the experimental quantities A( Bo+ Co).Of course, xaaactually leads only to the magnitude of 6,,, but this example illustrates that the geometrical results are not strongly dependent on assumptions about the angle and hence about the linearity of the hydrogen bond. MICROWAVE SPECTROSCOPY OF H2S-HCl DIMER 0 20 40 60 80 100 41° Fig. 5. Calculated variation of the quantities A(B+ C) with the angle 4 for (H,S, HCl). The quantity A(B+ C) is the difference of the rotational constant (B+ C) between a deuterated species of the dimer and the parent species (H232S, H3'Cl). In the upper curve, the deuterated species is (D232S, H3'Cl) while in the lower curve it is (HD3,S, H35Cl). Observed values of A(&+ C,) are indicated on the dashed lines.Table 7. Observed and calculated values of (B+ C) for isotopic species of (H2S,HCl) observed calculated" isotopic species (B,+ C,)/MHz (B+C)/MHz 4014.534 40 14.52 3909.993 3 90 9.40 3902.670 3901.13 4015.407 4008.96 3945.614 3945.57 3946.459 3939.70 3880.298 3880.36 3881.188 3874.19 " Model assumes component geometries are unchanged on dimer formation, 4 = 93.81", r(S--CI) = 3.8092 8, and the arrangement of fig. 3 (see text for discussion). E. J. GOODWIN AND A. C. LEGON Table 8. Some molecular properties of (H2S,HC1) isotopic species O,,/O k,/N rn-l V,/cm-’ (H2”S, H”Cl) 21.91 6.93 82.0 (H~~~S,~”7~1) 21.90 6.94 81.1 (H~”s,H~~c~) (H232S,D”C1) (HD”S, H”C1) 21.87 19.99 21.92 6.93 7.23 6.78 80.8 83.2 80.5 (HD32S, D”C1) 20.07 7.28 83.0 ( D~~~s,H~~c~) ( D~~~s,D~~c~) 21.80 19.88 6.86 7.16 80.5 81.6 STRENGTH OF THE INTERMOLECULAR BINDING FROM Xaa AND OJ The C1 nuclear quadrupole coupling constants xaaand the centrifugal distortion constants OJcan be used to obtain a measure of the strength of the intermolecular binding in (H2S,HCl).We have established above a geometry for (H2S,HCl) which shows that the C1 nucleus is remote from the H2S molecule. We can therefore assume in reasonable approximation that the electric-field gradient at the C1 nucleus, and hence the equilibrium value of xaa,is unchanged from the free HCl molecule. Then, the change in xaaon dimer formation results from changes in the zero-point motion of the HC1 subunit alone and we can write where xo is the C1 nuclear quadrupole coupling constant of free HCl, 8 is the instantaneous angle between the a inertial axis of the dimer and the HCl direction and the average is over the zero-point motion.Eqn (5) can then be rearranged to define operationally an average value, 8,,, of the angle 8 according to 8,” = arc cos [(2xaa/3xO)+3]1’2. (6) Values of 8,, so determined from the xaavalues of table 4 and the appropriate quantities xo= -67.618 93, -53.294 45 and -67.393 38 MHz for H”C1, H37Cl and D3‘Cl, re~pectively,’~ are recorded in table 8. The definition of 8 is such that it is zero when the H nucleus in HCl lies along the a axis and between the S and C1 nuclei. The acute angle value is chosen when using eqn (6)because of the conclusion of the preceding section and because the change from H”Cl to D3’Cl species is small.The obtuse angle would imply that the H atom of HC1 was not involved in a hydrogen bond and should be accompanied by a larger change on deuteration. The small decrease of 6,, on deuteration is consistent with a small decrease in the amplitude of the motion of the D nucleus in excursions away from the a axis. We note that because of the large mass of S and C1 compared with H, the a axis will make an angle of, at most, 2 or 3 degrees with the S...Cl internuclear line and accordingly 8,, can be used as a measure of the average deviation of the hydrogen bond from the S.-.Cl line. The smallness of this angle is consistent with the previous assumption that the hydrogen bond is linear or nearly linear in the equilibrium conformation. The angle 8,” is clearly related to the restoring force constant for bending the hydrogen bond and as such can be taken as a measure of its strength. On this basis, the order of the stren th of the intermolecular binding in the series B. * .HC1 is B = H204> H2S=: PH3.16g 64 MICROWAVE SPECTROSCOPY OF H,S-HCl DIMER Another measure of the strength of intermolecular binding is the quadratic force constant k, associated with stretching ef the hydrogen bond. For weakly bound molecular complexes like (H2S, HCl), for which A. >> Bo== Co, ( Bo-Co== 2 MHz while A. = 100 GHz in the present case) and for which Bo is very much smaller than the rotational constants of either of the component molecules of the complex, it has been indicated17 that the centrifugal distortion constant DJ is related to ku to a reasonable degree of approximation by the expression where p = M(H,S)M(HCl)/[M(H,S)+M(HCl)].We have used the Dj and (go+ Co)values recorded in table 4 to calculate k, for each isotopic species with the aid of eqn (7). The results are recorded in table 8. The wavenumbers V, for the hydrogen-bond stretching vibration, calculated on the basis of the pseudodiatomic formula Fm = (2nc)-'( ku/p)'", are also recorded in table 8. The increase in k, from the HCl to the DC1 species that is evident in table 8 is an effect noted previously in similar investigations6 and its origins have been discussed in terms of a coupling between hydrogen-bond bending and stretching modes.6 DISCUSSION The investigation of the rotational spectrum in the vibrational ground state of the weakly bound complex (H2S,HC1) reported here has demonstrated that the intermolecular linkage is through a hydrogen bond, with the HCl molecule acting as the proton donor and the sulphur atom of H2S as the proton acceptor.We have established that the dimer has a geometry in which the nuclei S--SH-Cl are collinear (or nearly so) in the order given and in which the plane of the H2S subunit is very nearly perpendicular to the S-..Cl internuclear line, with the appropriate angle 4 (see fig. 3) having a value of ca.94". A similar conclusion has been reached for (H,S,HF) by means of an investigation of its rotational spectrum using the molecular-beam electric-resonance te~hnique,~ when it was found that 4 = 89". A simple rationalization of these results is possible if we accept the hypothesis'* that, in such weakly bound dimers, the axis of the HX molecule lies at equilibrium along the axis of a non-bonded electron pair on the proton-acceptor atom, as conven- tionally envisaged. Thus, we conclude that the axes of the non-bonded pairs on S are nearly collinear and lie perpendicular to the H2S plane. This is consistent with the simple valence-shell electron-pair repulsion mode119 applied to H2S, w&h implies a larger than tetrahedral angle between the non-bonded pair-f the HSH angle is considerably less than tetrahedral.On the other hand, the HOH angle in water is much closer to tetrahedral, and a nearly tetrahedral angle between the non-bonded pairs on oxygen is then expected. This prediction is in accord with the result' that 4 = 46"in (H20, HF). The nearly right-angled value of 4 for V2S,HCl) can also be interpreted on the basis of an alternative simple model. In H2S, the fact that the mH angle is close to 90" implies that the sulphur 3s orbital is not involved in the bonding orbitals and thus that the non-bonded electron pairs can be described as occupying 3s and 3p orbitals. Formation of a hydrogen bond by HCl along the axis of the 3p non-bonded orbital would then result in an angle 4 = 90", as observed.It is of interest to collect together in table 9 the heavy-atom distances in a number of hydrogen-bonded complexes formed by hydrides of elements in Groups E. J. GOODWIN AND A. C. LEGON Table 9. Heavy-atom distances r(X-.-Y) (A) in hydrogen- bonded dimers H, Y-* .HX HF 2.662" 3.249' 3.309' HCl 3.215d 3.809" 3.880f " Ref. (2); ref. (5); ref. (8); ref. (4); " this work; ref. (16). V and VI of the Periodic Table with the hydrogen halides (X =F and Cl). We note that in passing from the first to the second row within Group VI the expected substantial increase in the heavy-atom distance occurs between H20* * -HX and H2S...HX, both for X=F and C1. A change from Group V to Group VI within the second row, however, leads to little change in the corresponding distances.We note also that the order of the strength of binding among this group of complexes B* .HX is B =H20>H2S=PH3when X =F or C1, as measured by the hydrogen- bond stretching force constant k, which has the values 20.7,T 12 and 12.5 N m-l,' respectively, when X =F and 12.8,t 6.9 and 6.1 N m-',$ respectively, when X =C1. A research grant from the S.E.R.C. to construct the pulsed-nozzle, Fourier- transform microwave spectrometer is gratefully acknowledged. Z. Kisiel, A. C. Legon and D. J. Millen, Proc. R. SOC.London, Ser. A, 1982, 381,419; J. Chem. Phys., 1983, 78, 2910. J. W. Bevan, Z. Kisiel, A. C. Legon, D. J. Millen and S. C. Rogers, Proc. R. Soc. London, Ser. A, 1980, 372, 441. A.C. Legon and L. C. Willoughby, Chem. Phys. Lett., 1982, 92, 333. A. C. Legon and L. C. Willoughby, Chem. Phys. Lett., 1983, 95, 449. R. Viswanathan and T. R. Dyke, J. Chem. Phys., 1982, 77, 1166. T. J. Balle, E. J. Campbell, M. R. Keenan and W. H. Flygare, J. Chem. Phys., 1980, 72, 922. T. J. Balle and W. H. Flygare, Rev. Sci.Instrum., 1981, 52, 33. * A. C. Legon and L. C. Willoughby, Chern. Phys., 1983,74, 127. E. J. Campbell, L. W. Buxton, T. J. Balle, M. R. Kennan and W. H. Flygare, J. Chem. Phys., 1981, 74, 828. lo A. Dubrulle, J. Demaison, J. Burie and D. Boucher, 2.Nuturforsch., TeilA, 1980, 35, 471. l1 A. J. Fillery-Travis, A. C. Legon and L. C. Willoughby, to be published. l2 C. H. Townes and A. L. Schawlow, Microwave Spectroscopy (McGraw-Hill, New York, 1955).l3 R. L. Cook, F. C. de Lucia, P. Helminger and W. Gordy, J. Mol. Struct., 1975, 28, 237. l4 J. K. G. Watson, J. Mol, Spectrosc., 1973, 45, 99. l5 E. W. Kaiser, J. Chem. Phys., 1970,53, 1686. xo for H37Cl was calculated from the H35Cl value by dividing it by the ratio Q35/037of the C1 nuclear electric quadrupole moments. l6 A. C. Legon and L. C. Willoughby, J. Chem. SOC.,Chem. Commun., 1982, 997. l7 W. G. Read, E. J. Campbell and G. Henderson, J. Chem. Phys., 1983,78, 3501. l8 A. C. Legon and D. J. Millen, Faruduy Discuss. Chem. SOC.,1982,73, 71. l9 R. J. Gillespie and R. S. Nyholm, Q. Rev. Chem. SOC.,1957, 11, 339. (PAPER 3/944) ?Values of k, for (H20,HF) and (H,O,HCl) are calculated from the data in ref. (2) and (4), respectively, using eqn (7). $ Value of k, calculated using eqn (7) and data of A. C. Legon and L. C. Willoughby (to be published).

ISSN:0300-9238    

DOI:10.1039/F29848000051

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

J. Chem. SOC.,Faraday Trans. 2, 1984, 80, 67-83 Influence of Surface Heterogeneity on the Luminescence Decay of Probe Molecules in Heterogeneous Systems Clayson 5' bpy)Ru( BY ABDELMAJIDHABTI, DIDIER KERAVIS,PIERRE LEVITZ AND HENRIVAN DAMME* Centre de Recherche sur les Solides, Organisation Cristalline Imparfaite, C.N.R.S., 1B Rue de la Fkrollerie, 45045 Orleans Cedex, France Received 13th June, 1983 The decay of a luminescent probe [Ru( bpy) ",] adsorbed on solids (clays) containing quenching impurities (Fe3') has been examined. The time law is a multi-exponential function which stems from (i) the quasi-total translational immobility of the probe on the microsecond scale, and (ii) the heterogeneous nature of the surface, which is influenced by the local concentration of iron in the clay lattice.An elementary model has been proposed based on a randomly decorated 2-dimensional lattice for the probe and a second underlying and randomly decorated 2-dimensional lattice for the quencher ions. Assuming that the quenching probability for an excited probe is linearly related to the number of neighbouring quenchers, a decay function has been derived which, for very low quencher concentrations, reduces to the Infelta-Gratzel-Thomas equation for quenching in micellar solutions. The parameters of the decay function have been correlated to the chemical composition of the clays and to their swelling properties. The photochemistry and photophysics of molecules in inhomogeneous systems are currently areas of much interest.Micellar solutions and related surfactant-based systems have been extensively studied from this viewpoint.' In particular, time- resolved fluorescence measurements of probe molecules dissolved in micelles have led to a detailed kinetic model for excimer formation and for quenching reactions in this environment.2 Similar interest has been shown in polymers3 and molecules adsorbed on polymer^.^Much less work has been done on the photophysics of molecular species in inorganic heterogeneous systems, although the amount of possible phenomena is potentially ~onsiderable.~ One point which seems to emerge from the few reported studies is the multi-exponential character of the decay time law of adsorbed lumines- cent probe molecules.This was first reported by de Mayo and coworkers6 for pyrene adsorbed on silica. It was also found for other aromatic hydrocarbons on y-alumina by Kessler et d7and for Ru(b y);' impregnated on silica and various oxide !semiconductors by Kajiwara et al. Our contribution to this field has been mainly devoted to sheet silicate interca- lates.'3"' Steady-state measurements showed that the luminescence quantum yield of Ru(bpy)S' intercalated in solid samples of swelling clays was dependent upon the amount of co-adsorbed water and was strongly depleted by transition-metal impurities such as Fe3+ or Cr3' in the clay crystal lattice.' Very recently, Dellaguar- dia and Thomas" showed that the decay of Ru(bpy);' bound to colloidal kaolin and montmorillonite clays is also of a multi-exponential form.Using a double- 67 LUMINESCENCE DECAY ON HETEROGENEOUS SURFACES exponential function to fit their data, these authors confirmed the influence of the iron content of the clay on the decay. When taken together, these various observations suggest that the decay of luminescent probe molecules adsorbed on solid materials containing quencher impurities is perhaps liable to a general treatment which would take into account the characteristics of these systems. In this paper we present a simple lattice statistics treatment of this roblem based on experimental results obtained for the lumines- cence of Ru( bpy) Eintercalated in swelling clays or adsorbed on the external surfaces of non-swelling clays.The single-photon counting method has been used in order to be able to analyse the shape on the decay accurately. As far as the problem of quenching reactions in heterogeneous media is concer- ned, clays seem to form a particularly interesting class of compounds since they exist in a variety of forms with different chemical compositions (transition-metal content), morphologies and colloidal and surface properties. Most of the clays that we choose to study are swellingoclays of the smectites group.12 Each elementary smectite layer, which is ca. 9.6A thick, is com osed of a central octahedral sheet of oxygen and hydroxyl ions coordinating A&, Fe3+ or Mg2+ ions, sandwiched between two tetrahedral sheets coordinating Si"' ions.Smectites are therefore classified as 2 :1clays. Isomorphic substitutions within the lattice lead to a negative residual charge which is compensated by exchangeable cations on the surface of the layers. One of the fundamental properties of smectites is of course their ability to form an expanding layer structure. Even in very dilute aqueous suspensions, smectite layers form face-to-face associations. l3 The average number of layers per stack depends upon the nature of the clay and of the exchangeable cations.I4 In the 'dry' state, i.e. in solid samples containing only a small fraction of adsorbed water, the spatial extension of these ordered stacks may increase considerably to several hundred layers, as shown by X-ray diffra~tion.'~ In addition to the exchange- able cations [which may be almost any kind of inorganic, organic or organometallic cations, such as Ru(bpy):+], the interlayer space is able to accommodate water and/or a remarkably wide variety of organic species." Such systems are adequately described as intercalation compounds.Closely related to smectites are the fibrous minerals polygorskite and sepiolite. l7 They are made up of building blocks similar to those of smectites, but their different arrangement leads to a ribbon structure, The individual fibres (in fact, laths) are made of a rigid network of ribbons and channels. Unlike the interlamellar space of smectites, these channels cannot be expanded by foreign species. Their limited cross-section allows only for the penetration of very small molecules such as water (zeolitic water).Bulky organic and organometallic species are therefore forced to remain adsorbed on the external surface of the laths. Although electron microscopy shows that the sepiolite laths agglomerate in bundles, no ordering seems to occur in these systems. Therefore, the intercalation concept can hardly be applied to them. Another important group of layer silicates is formed by the kaolin minerals,18 which are classified as 1:1clays since each elementary layer contains one octahedral sheet and only one tetrahedral sheet. Unlike the smectites, they are not expandable in aqueous media, although some of them are able to intercalate a limited variety of organic species (hydrazine, dimethylsulphoxide etc.).16 Their cation-exchange capacity is also much lower than that of smectites.Organometallic ions such as Ru(bpy):+ are not intercalated and therefore remain on the external surface of the crystallites. In order to investigate the influence of the clay's composition, its structure and its swelling properties on the excited-state decay of Ru(bpy):', we will compare A. HABTI, D. KERAVIS, P. LEVITZ AND H. VAN DAMME 69 Table 1. Clays used in this study clay mineralogical group [Fe]" (ppm) So/m2 g-' c.e.c./meq g-l hectorite smectite, 500 -750 0.85 2 :1, trioctahedral laponi t e smectite, 1000 -750 0.80 2: 1, trioctahedral sepiolite fibrous, 4300 -250 0.15 1 :I, trioctahedral kaolinite kaolin, 8770 26.7 0.10 1: 1, dioctahedral montmorillonite smectite, 27 000 --750 0.95 2 :1, dioctahedral non troni te smecti t e , 250 000 -750 0.95 2 : 1, dioctahedral a Almost entirely in the form of Fe3+ ions in octahedral positions.'' Specific surface area.For sepiolite and kaolinite, the values quoted are the values obtained from N2adsorption at 77 K. For the smectites, 750 m2 8-l is the ideal value for an infinite sheet 9.6 A thick.13 Cation-exchange capacity. four smectites with a large span of iron contents (laponite, hectorite, montmorillonite and nontronite), with a fibrous clay (sepiolite) and with kaolinite. The influence of the hydration state of the system will also be studied. Two extreme situations will be considered: dilute colloidal aqueous suspensions on the one hand, and solid deposits containing only a fraction of adsorbed water on the other.As will be shown below, the excited-state decay of our probe molecule in these systems is typical of a low-mobility medium with a distribution of local situations. EXPERIMENTAL MATERIALS As mentioned above, six cla minerals were studied. Four of them are smectites which are able to intercalate Ru(bpy)$ and water within the interlayer space: montmorillonite, a natural mineral from Upton, Wyoming; hectorite from Hector, California; nontronite from Gardfield, Washington; and laponite, a synthetic hectorite from Laporte Industries. Sepiolite, from Spain, was taken as an example of fibrous clay, whereas kaolinite, from Charentes, France, was taken as a typical example of the non-swelling kaolin minerals.Some properties of these clays, including cation-exchange capacity (c.e.c.), B.E.T. surface area and iron content," are summarized in table 1. Laponite, sepiolite and kaolinite were mineralogically pure and used as such. Montmoril- lonite, hectorite and nontronite were first purified as described elsewhere.' The pure clays, in the Na+-exchanged form, were suspended in water. When a good colloidal dispersion was obtained an aqueous solution of the ruthenium complex was added to the clay suspension 'and the mixture was shaken. After a few hours the suspension was centrifuged in order to verify that the complex was completely adsorbed (as evidenced by a clear supernatant}. The clay was then resuspended in water and used as such.Alternatively, this suspension was filtered on a Millipore filter. This procedure led to a thin clay deposit (2.5 mg dry clay per cm2) which, in the case of hectorite, nontronite, sepiolite and montmorillonite, could be peeled from the filter to yield an homogeneous self-supporting film well suited for spectro- scopic studies. However, in order to have a good quality film which was not too brittle, the Ru(bpy)z' loading of the clay had to be kept below 10meq per 100g of clay. Higher loadings led to increasingly hydrophobic clay particles and to powdery films. LUMINESCENCE DECAY ON HETEROGENEOUS SURFACES PROCEDURES The luminescence decays were measured using an Applied Photophysics single-photon counting spectrometer, equipped with a PM2233B photomultiplier cooled at -40 "C.Excita-tion was performed at 337 nm and emission was monitored at 620 nm. Particular care was taken to avoid scattered light by doubling the excitation and emission monochromators with narrow-band-pass, short-pass and long-pass interference filters. The decays were accumulated over 1024 channels and a span of 2 ps. The colloidal suspensions were stirred and deaerated in the sample compartment of the spectrometer by continually bubbling N2 through them. The clay films were examined in a specially constructed sample cell, equipped with quartz and ZnS windows, which could be connected to a classical gas-handling system. This allowed the sample films to be outgassed and equilibrated at a given water vapour pressure.The water content was calculated from the integrated intensity of the 1630cm-' water deformation band in the i.r. spectrum, as described previously.8 No convolution of the observed decays was performed. On the time-scale of the decay, the excitation pulse (f.w.h.m. = 5 ns) was indeed negligibly narrow. The data, starting from the channel of maximum intensity, were fitted to the theoretical expressions using a non-linear least-squares procedure. THE DECAY LAW GENERAL BEHAVIOUR As shown in fig. 1, the time decay of Ru(bpy)i' adsorbed on the various clays that we studied is not a simple exponential function of time. In the long-time limit (>ca. 1ps) the curves approach an exponential form, with lifetimes ranging from 0.82 to 1.57 ps at room temperature, but at shorter times a faster and complex decay is observed, which cannot be satisfyingly fitted by merely adding a second exponential to the decay function.The amplitude of the fast multi-exponential part can be estimated from the intercept at time t = 0 (A,) of the extrapolated exponential limit of the normalized decay. As shown in fig. 1, A, seems to be related to the iron content of the clay, whereas the lifetime associated with the exponential limit at long time (7,) does not. This complex behaviour was also observed for solid samples. A natural approach to the analysis of a multi-exponential decay is to fit it with a sum of i exponential components and to analyse the behaviour of the i amplitudes and i lifetimes.The rationale behind such an approach is that the observed decay is a sum of contributions from i populations of luminescent species. In the present case, the existence of several populations of luminescent species could correspond to (i) several types of surface-induced perturbations which would modify the intrinsic excited-state properties of the probe (an extreme case could be an emission resolved into components from i excited states), or (ii) several surface environments which would not perturb the electronic properties of the probe molecule to various degrees, but which would modify its lifetime via one or more quenching reactions. Point (i) can safely be ruled out here since we were unable, by u.v.-visible spectroscopy, steady-state fluorescence measurements, i.r.spectroscopy or X.P.S., to detect more than one type of adsorbed Ru( bpy) :+ species on montmorillonite and hectorite.' In addition, it is extremely unlikely that several deeply perturbed species would emit at the same wavelength. Point (ii), which is more likely, is in fact equivalent to the classical concept of surface heterogeneity widely shown by thermodynamic or relaxation methods. The local iron concentration might be the factor affecting heterogeneity in our case. A. HABTI, D. KERAVIS, P. LEVITZ AND H. VAN DAMME 200 LOO 600 800 1000 channel number 1.6 ns per channel) Fig. 1. Normalized luminescence decay curves, P(t),of Ru(bpy)z' adsorbed on (a)hectorite, (b)laponite (100 ppm), (c)sepiolite (4300 ppm), (d)kaolinite (8770 ppm), (e) montmorillonite (27 000 ppm) and (8) nontronite (25 000 ppm) in aqueous suspensions.The meaning of the parameters A. and T,, is illustrated for kaolinite. LUMINESCENCE DECAY ON HETEROGENEOUS SURFACES It is clear, however, that introducing the concept of spatial heterogeneity in the dynamics of a quenching reaction is meaningful only if the mobility of the reactant molecules is low enough to prevent the luminescent probe from probing a large number of local environments during its excited-state lifetime. Otherwise 'averag- ing' of the multi-exponential character is expected. This has been seen in micellar solutions.2 The system we are dealing with here is characterized by the fact that, on the time-scale considered, the quencher molecules, which we presume are the iron ions, are entirely immobile within the crystal lattice of the clay.On the other hand, the luminescent probe, Ru(bpy):', is, in principle at least, allowed to diffuse on the surface (either the external surface or the interlayer space) of the clay particles. In fact, the observation that the long-time limit of the decay is not correlated with the iron content of the clay suggests that, on the time-scale we are ions is smaller than 5' considering, the mean displacement of the adsorbed Ru( bpy) the spatial scale of the heterogeneity. Indeed, if the surface mobility of the probe was high enough to allow it to probe several local environments ( i.e. several quencher distributions) during its excited-state lifetime, one would expect the long-time limit of the decay to reflect a diffusion process and, consequently, to be correlated to the quencher content of the clay. This is not the case. We may therefore consider that the T~values in fig. 1reflect the decay of probe molecules in a virtually quencher-free environment. A fundamental point in this discussion is the spatial scale of the surface heterogeneity. A priori, the various local environments of our system could be associated either with rather large subunits, such as the individual clay layers, fibres or their aggregates, or with much smaller areas at the molecular level. The first possibility can be discarded on the basis of simple statistical considerations.Indeed, the occurrence of totally iron-free particles is extremely unlikely with clays such as montmorillonite or nontronite, where the probabilities for a single octahedral site to be occupied by Fe3+ are ca. 0.1 and ca. 1.0, respectively. The second possibility is more in line with the classical view of surface heterogeneity. It is also more in accord with estimates of the diffusion coefficient, D, of cations in clays. Little is known about the translational mobility on the surface of clays of bulky organometal- lic cations such as Ru(bpy) :+,but self-diffusion measurements performed by Calvet2' using radioactive tracers show that D for a small divalent cation such as Ca2' in dehydrated montmorillonite plugs (ca.5% water, w/w) may be as low as cm2s-l at room temperature. In extensively hydrated samples (gels), D increases by a few orders of magnitude. The values for Ru(bpy):+ are, however, probably much smaller, because of its larger size. A rough numerical estimate is useful. With D = lo-'" cm2s-', a simple 2-dimensional random-walk calculation shows that the r.m.s. displacement within 1ps is smaller than 2 A, which seems too small to average a number of local situations. On the other hand, with D of the order of lo-' cm2s-' some averaging would be expected. We are thus left with the plausible conclusion that the decay we observe is occurring in a medium with very restricted translational freedom and with a range of local environments at the molecular level.Since we are unable to identify several well defined environments on the surface of clays, it seems arbitrary to fit the data with a sum of two, three, four etc. exponential components. A more satisfying approach would be to consider a model which, from a distribution of quencher ions in the solid adsorbant, enables one to derive the decay function of the adsorbed probes, and vice versa. In a totally rigid medium containing N quencher molecules, the probability for a probe molecule excited at time t = 0 to be in the excited state A. HABTI, D. KERAVIS, P. LEVITZ AND H. VAN DAMME at time t would be given by N P(t)=exp (-kot)exp where ko= 1/~~is, as usual, the unimolecular rate constant for radiative and non-radiative decay and k,(ri) is the unimolecular quenching rate constant for a probe-quencher pair at centre-to-centre distance ri.The decay described by eqn (1) corresponds to one particular configuration of the quencher molecule in the system. The observed decay in the actual heterogeneous sample is the ensemble average of eqn (1) over all the possible configurations: (2) where u(rl, r2,.. .,r,) is the probability density of finding quencher 1 at position rl, quencher 2 at position r, etc. Eqn (2) has been solved by Inokuti and Hirayama2l for energy transfer by the exchange mechanism, and by Tachiya and Mozumder22 for electron scavenging in low-temperature glasses, assuming (i) a totally random distribution of particles u(r1,r2,. . . ,r,) = 1/ VN (3) and (ii) an exponential dependence of k,(r) on r k,(r) = u exp (-ar).(4) Using slightly different methods, both derivations led to a final result of the form =exp[-k,t-(c/c,,)g(vt)l (5) where co=3a3/4r and g is an integral function which, for sufficiently large ut, reduces to [In ( ~t)l'.Z'-~~ Attempts to fit our data to (5)using three adjustable parameters (k,, c/c, and v) were unsuccessful. Although a good fit can be obtained over a limited range at short times, the general agreement over the entire range is poor. An attempt was also made to fit the data with the equation obtained by Inokuti and Hirayama2' for energy transfer by the Forster mechanism in a rigid solution, with an inverse power rate law, and much the same behaviour was found as with eqn (5). In fact, it seems to us that the decrease of k,(r) with r is so fast in energy- and electron-transfer reactions that, with T~ of the order of lop6s, the decay law might be entirely dominated by the quencher distribution at short distances around the adsorption sites, i.e.in a region where the actual shape of the probe-quencher pair-correlation function cannot be neglected. Thus, passing to the continuum limit and assuming a homogeneous distribution function may be a bad approximation in our case. Therefore, we will derive a simple localized model based on the assumption that, on each clay particle, the quenching process can be described as occurring in an ensemble of small independent subsystems, each subsystem being composed of an excited probe molecule and the nearest lattice sites of the solid, which may be occupied by the quencher ions.For the sake of simplicity we will assume that the adsorbed probe molecules are not totally randomly distributed on the surface, but occupy the sites of a superlattice which matches the lattice of the quenchers, as LUMINESCENCE DECAY ON HETEROGENEOUS SURFACES 0 empty site @excited probe0probe molecule quencher ion Fig. 2. Sketch of the model with a square lattice for the quencher ions and a (4,;) translated and superimposed square lattice for the probe molecules. shown in fig. 2. The spatial extent of the systems is in fact determined by the physical nature of the quenching reaction, i.e. by k (r). In aqueous solution, Fe3'(a )q4is known to quench the excited state of Ru(bpy)fby an electron-transfer reaction with a theoretically estimated or experimentally inferred value of a in eqn (4)ranging from 2.6 to 1.1 Taking an average value of 1.5 a simple calculation shows that even with v as high as 1013 k,(r) should become negligibly small (ca,.1YO)compared with ko (ca.lo6s-', fig. 1)at a centre-to-centre distance of ca. 14 A. Considering the large radius of Ru(bpy);' (ca.7 A 25), this suggests that only the nearest-neighbour sites of the quencher lattice should be taken into account. The assumption of subsystem independence is reasonable for a similar reason. Indeed, even in a compact monolayer of Ru(bpy)$+ (ca. 1014 molecule cm-2), a pulse of light of ca.lo7photons on a 1cm2 sample would produce excited molecules more than lo3A apart on average, i.e. at centre-to-centre dist- ances much larger than the interaction range that we just considered. A. HABTI, D. KERAVIS, P. LEVITZ AND H. VAN DAMME In a system of N ions distributed over M lattice points, the average occupancy is w = N/M. In the absence of interactions, the probability of an excited probe being in a subsystem containing n quencher ions distributed over the rn sites of the subsystem at time t=O is given by the binomial law p; = w"(1-w)"-"Wll, (6) where W; is the number of distinguishable configurations W; = rn!/n!(rn-n)! (7) each configuration being equally probable. The decay law for probe molecules in subsystems containing n quencher ions in a given configuration is given by an equation analogous to eqn (1) where the summation is performed over the n quenchers: P(t>=exp (-kot) exp [-t k,(ri)J.i=l The experimentally observed decay is obtained by averaging eqn (8) over all configurations, <p, and n values, up to n = rn P(t>=exp (-k,,t) i P; c (1/Wzt ) exp [-t i k:(ri)]* (9)n=O cp i=l On the basis of the above considerations on the size of the subsystems, we will assume that all the sites in a subsystem are equivalent. All the ri and k,(ri) are equal and the observed decay becdmes Ili P(t)= exp (-kot) 1 Plz, exp (-nk,t) (10) n =o or rn 1 P(t)= exp (-k,t)~: 1+ c n=l which, for t -+ CO, becomes, in logarithmic form In P(t)= -kot+ In Thus eqn (1 1) correctly predicts single-exponential behaviour at long times and multi-exponential behaviour at short times (t< T~).It can easily be seen that the extrapolated intercept of eqn (12) at time t = 0, i.e. A. in fig. 1, is just the logarithm of the probability for a subsystem to contain zero quencher at t = 0. In the limit of very low quencher concentration (w---+ 0), the binomial law turns into a Poisson distribution P; =exp (-ii)ii"/n! (13) where ii = rnw is the average number of quencher ions per subsystem, and the decay can be put in the form P(t)=exp(-k,,t) exp{-ii[l-exp(-k,t)]). (14) -Ao is now just the average number of quencher molecules per subsystem. Eqn (14) is a well known three-parameter equation (k,, ii, k) which was derived by Infelta, Gratzel and Thomas for fluorescence quenching in micellar solutions.2 In this latter case the physical meaning of the subsystems is obvious, and it can be LUMINESCENCE DECAY ON HETEROGENEOUS SURFACES I 200 LOO 600 800 channel number (1.6 ns per channel) Fig.3. Best fit of eqn (14) to the normalized decays, Pft), for Ru(bpy):+-sepiolite (A) and Ru(bpy)5'-montmorillonite (€3) suspensions. shown that the Poisson distribution is the expected distribution law for the solubili- zates.'6 Eqn (14) has been successfully used to describe the 24uenching kinetics of Ru(bpy,)-;+ by 9-rnethylanthracene in SDS micellar solutions. We found that eqn (14) also fits the decay of laponite-Ru(bpy):+, hectorite-Ru( bpy) :+and sepiolite-Ru(bpy):+ samples in aqueous suspensions [fig.3(A)]. It is significant that these are also the clays with the lowest iron content, i.e. those with the smallest w (table l), and those where the distribution of iron ions around the excited probes is the most likely to follow a Poisson law. Going to kaolinite- Ru( bpy) :', montmorillonite-Ru( bpy) :+ and nontronite-Ru( bpy) :+ suspensions, increasingly large departure from eqn (14) is found at short times (t<50 ns) [fig. 3(B)]. That some departure is found is not unexpected since, as pointed out above, a binomial distribution should replace the Poisson distribution as w increases. The effect of passing from a Poisson distribution to a binomial distribution is shown in fig.4(A) for a subsystem of four sites with an average occupancy per site w =0.75. A. HABTI, D. KERAVIS, P. LEVITZ AND H. VAN DAMME 1 2 3 4 number of occupied sites 0 1 2 1/70 Fig. 4. (A) Comparison of the binomial (m) and Poisson (U)distribution laws for occupancy probability in a system of four sites, with an average occupancy of 0.75. (B) Comparison of the decay curves calculated from the previous distribution. The main result is that the Poisson distribution underestimates the probability for the subsystem to contain a larger than average number of quenchers. In terms of decay this leads, with the binomial distribution, to a larger contribution of the fast decreasing exponentials in eqn (12), and therefore to faster decay at short times [fig.4(B)]. This is precisely what we observed for the clays with a large iron content. COMPARISON WITH EXPERIMENTAL RESULTS INFLUENCE OF THE CLAY STRUCTURE AND IRON CONTENT We will first compare the results obtained with the aqueous suspensions of the six clays at the same Ru(bpy)z+ loading (table 2). The absence of a correlation LUMINESCENCE DECAY ON HETEROGENEOUS SURFACES Table 2. Decay parameters obtained by fitting the data with eqn (14) clay WbPY):+ /meq g-' sample R T~/lo-' s -Ao k,/ lo6 s-l 1 2 3 4 5 6 7 8 9 hectorite laponite sepiolite kaolinite montmorillonite nontronite hectorite hectorite hectorite 0.05 0.05 0.10 0.05 0.05 0.10 0.20 0.a0 0.07 susp. susp. susp. susp. susp. susp. susp. susp. film 5 x 10-3 5 x 10-3 5 x 10-3 5 x 10-3 5 x 10-3 5 x 10-3 5 x 10-3 5 x 10-3 39.7 1.52 1.20 0.84 0.75 1.20 1.98 1.12 1.12 1.31 0.57 0.22 0.41 1.02 1.46 2.87 0.53 0.59 1.051 5.3 4.15 4.15 4.3 5.9 5.8 5.0 4.2 3.8 10 hectorite 0.07 film 24.7 1.07 0.923 4.2 11 hectorite 0.07 film 19.5 1.13 0.756 4.1 12 hectorite 0.07 film 18.2 1.12 0.712 4.0 13 hectorite 0.07 film 12.8 1.11 0.684 3.8 14 hectorite 0.07 film 10.4 1.12 0.705 3.6 15 hectorite 0.07 film 9.7 1.11 0.644 4.0 16 hectorite 0.07 film 9.0 1.28 0.756 3.5 17 hectorite 0.02 film 45.2 1.56 1.150 3.5 18 hectorite 0.02 film 32.7 1.39 1.010 3.9 19 hectorite 0.02 film 22.6 1.17 0.771 4.3 20 hectorite 0.02 film 18.7 1.31 0.726 3.7 21 hectorite 0.02 film 14.7 1.32 0.684 3.6 22 hectorite 0.02 film 8.7 2.33 0.631 3.6 23 montmorillonite 0.05 film 50.5 0.75 1.81 5.8 24 montmorillonite 0.05 film 45.2 1.29 1.77 6.6 25 montmorillonite 0.05 film 32.8 0.93 1SO 6.9 26 montmorillonite 0.05 film 16.4 0.97 1.26 6.9 27 28 29 30 31 sepiolite sepiolite sepiolite sepiolite kaolinite 0.10 0.10 0.10 0.10 0.05 film film fllm film powder 23.9 12.1 9.81 0.01 50 0.75 0.78 0.84 0.68 0.78 1.05 0.96 0.91 0.78 1.07 4.6 4.8 4.7 4.7 4.5 between T()and the iron content of the clay has already been pointed out.It is one of the basic points of our model and it is evidence for the absence of long-range translational motion in our medium on the microsecond time-scale.On the other hand, there seems to be some correlation between ro and the mineralogic class of the clay. Indeed, T~is significantly longer when Ru(bpy)z+ is intercalated in smectites than when it is adsorbed on the external surfaces of a non-swelling clay. Also, note that all the ro values are larger than the lifetime of Ru(bpy):' in aqueous solution at room temperature (ca.0.65 ps28)or even in crystalline form as the dichloride salt (0.43 ps, this work).? This is likely to stern from the reduced vibrational freedom of the bpy ligands, expected in the adsorbed state and even more so in the intercalated statc8 The most surprising point is the behaviour of Ao,the intercept at t=O of the exponential limit of the decay at long times.As pointed out above, with a Poisson distribution of quenchers, A. is just (minus) the average number of quencher i-The decay of crystalline Ru(bpy),Cl, is a single exponential. A. HABTI, D. KERAVIS, P. LEVITZ AND H. VAN DAMME 25 20 LO 60 (ppm)"3 Fig. 5. Correlation of the -A, parameter of the decay function with the iron concentration [Fe] (A) and with (€3): (a) laponite, (b)sepiolite, (c) hectorite, (d) kaolinite, (e) montmorillonite and (f) nontronite. molecules per subsystem. It is therefore expected to be linearly related to the iron content of the clay: -Ao ti = mw -[Fe]" (15) with x = 1. A simple numerical calculation shows that the more rigorous expression which is derived from a binomial distribution (Ao=In P:) can hardly be distinguished from eqn (15) up to w =0.5.The observed [Fe]dependence of A. is much weaker than predicted from eqn (15) [fig. 5(A)]. Going from hectorite to nontronite, i.e. increasing [Fe] by almost three orders of magnitude, A. increases by a factor of 12 (see table 2, rows 1-6) with a pronounced tendency to saturation. LUMINESCENCE DECAY ON HETEROGENEOUS SURFACES Note that the prediction that -Ao should be linearly increasing with quencher concentration is not an artifact due to our particular model, in which we considered the quenching probability only in a small domain around the excited probe. Indeed, even in the continuous model considered above, where integration of the quenching probability was performed over the whole sample, -Ao is predicted to be linearly related to c, the quencher concentration.In fact, a satisfying linear relationship exists between -Ao and [Fe]0.3, as shown in fig. 5(B). Considering this relationship, there is little doubt that the iron of the clay is directly related to the multi-exponential character of the decay: there is quenching only when iron is present. However, the exponent ~~0.3seriously questions the assumption that quenching occurs through a one-to-one electron- transfer reaction between adsorbed Ru(bpy) f’ and lattice Fe3+ ions. At the moment, we see no clear explanation for this exponent (interestingly, for co-adsorbed quenchers, x is close to one, as will be shown in a forthcoming paper29). Iron ions are found in clays in several forms, differing from one another in oxidation state, first coordination sphere, nearest-neighbouring cations etc.Superparamagnetic clusters have also been detected. In addition to the iron ions of the clay lattice, one has also to consider the presence of iron oxihydroxide particles associated with the clay mineral. A more detailed study is clearly needed to establish the precise nature of the ‘quencher’ species. Another point to analyse is the behaviour of k,, the unimolecular quenching rate constant for an isolated probe-quencher pair in one subsystem. In our model, all the probe-quencher pairs within one subsystem were assumed to be equivalent. A critical test for this is that the measured k, values should be independent of the average quencher concentration, unless the physical nature of the P*-Q interaction changes with concentration. As shown in table 2, rows 1-6, k, is indeed constant within experimental error from hectorite to nontronite, with an average value of ca.4 x lo6s-l. The influence of the Ru(bpy);+ density on T(),A. and k, for a given clay was analysed in the case of hectorite suspensions (table 2, rows 1,7 and 8). No important changes were observed for Ru(bpy);+ loadings ranging from 6 x 10l8 to 6 X 10l9 ion g-’. Assuming that each probe ion covers an area of ca. 80 81* (on each side) within an infinitely thick stack of hectorite sheets, this corresponds to a surface coyerage 8 ranging from 1.2 to 12%. INFLUENCE OF HYDRATION STATE AND SWELLING PROPERTIES In this section we will compare the decay parameters obtained from suspensions of hectorite, niontmorillonite, sepiolite and kaolinite with those obtained from solid samples with variable water content.The results (table 2) can be summarized as follows: (i) neither T()nor k, is seriously affected by changing the hydration level of a given clay, and (ii) only A()is affected, but to a variable extent which depends on the nature of the clay. As shown in fig. 6(a),there is a remarkably simple linear relationship between A. and the cla -water ratio in hectorite samples. This relation- ship is independent of the Ru( bpy) [’ loading of the clay, within experimental error. Interestingly, the A. value obtained with hectorite suspensions is in excellent agreement with the value predicted from the results obtained with film samples, showing that there is no discontinuity in going from solid samples to colloidal suspensions.This represents a change in clay : water ratio of approximately four orders of magnitude; from ca. 5 X 10 to ca. 5 X lop3. Similar sample behaviour is observed with montmorillonite samples [fig. 6(b)]. For sepiolite samples, the A. HABTI, D. KERAVIS, P. LEVITZ AND H. VAN DAMME 0.5l-okII-LIl 10 20 30 40 50 R Fig. 6. Influence of swelling properties on the water content dependence of -An for (a) hectorite, (b) montmorillonite, (c) sepiolite films and (d) kaolinite powders. R is the clay: water ratio (w/w). clay: water ratio dependence of A.is already much weaker [fig. 6(c)], and for kaolinite samples no change occurs at all [fig. 6(d)]. The gradual progression displayed in fig. 6 strongly suggests that the swelling character of the clay is involved in these observations. Indeed, hectorite and montmorillonite are typical swelling clays, whereas kaolinite is not expandable at all in water. Sepiolite has intermediate properties. Because of the small size of the individual laths (ca.65X 65 A average cross-section, estimated from the B.E.T. surface area), some disentanglement of the fibre bundles is indeed expected upon increasing the hydration state of the system. Hence, the clay :water ratio dependence of A. is at first sight directly related to the swelling properties of the clay. Since there is no concomitant variation of k, there seems to be no variation of the average probe-quencher distance within one subsystem.For the same reason, LUMINESCENCE DECAY ON HETEROGENEOUS SURFACES any influence of the dielectric constant on A,, can hardly be invoked. In fact, it seems to us that the increase of A. upon dehydrating the samples is simply related to the increased probability for a probe molecule to be in contact with more than one clay particle, and hence to have 2m, 3m,. . . sites in its subsystem. This would imply a representation of the particle arrangement in solid smectite samples ‘looser’ than the classical ordered-stack picture.12 However, no matter how disordered the system could be, it is hardly conceivable that A.would increase by more than a factor of 2-3. This is what we observed. CONCLUSIONS In this paper we have shown that the excited state of Ru(bpy):+ adsorbed on clays decays according to a multi-exponential time law which stems from (i) the quenching effect of the ions within the lattice of the mineral and (ii) the essentially immobile character of adsorbed Ru(bpy) s’ on the microsecond time-scale. The mathematical form of the decay function and the observed behaviour of the para- meters of this function suggest that each adsorbed probe molecule is able to interact with a very limited number of neighbouring quencher ions in the solid around the adsorption site. The total quenching probability for a particular probe is determined by the quencher-ion concentration in the solid and by the number of solid particles in contact with the probe.In swelling systems this number is a function of the degree of swelling. Potentially, this description could apply to other heterogeneous systems. Whether it is general behaviour remains to be investigated. Further work on the form of the decay law in more mobile systems will be published (a)M. Gratzel and J. K. Thomas, in Modern Fluorescence Spectroscopy, ed. E. L. Wehry (Heyden, London, 1976), vol. 2, p. 169; (b) N. J. Turro and A. Yekta, J. Am. Chem. Soc., 1978, 100, 5951; (c) M. Almgren, F. Grieser and J. K. Thomas, J. Am. Chem. 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Fripiat, to be published. (PAPER 3/991)

ISSN:0300-9238    

DOI:10.1039/F29848000067

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

J. Chem. SOC.,Faraday Trans. 2, 1984, 80, 85-95 Temperature Variation of the Intervalence Absorption Band of Hexachloroantimonate(rI1, v) Ions in a Crystal Lattice BY KOSMAS PRASSIDES AND PETER DAY* University of Oxford, Inorganic Chemistry Laboratory, South Parks Road, Oxford OX1 3QR Received 28th June, 1983 The bandshape of the intervalence absorption of SbC12- and SbC1, has been measured from 300 to 4K in a crystal of (CH3NH3)2SbxSnl-xC16 in order to study the variation of the zeroth, first and second moments. At all temperatures the bandshape is Gaussian, as required by the vibronic model of Piepho, Krausz and Schatz (P.K.S.) in the weak-interaction limit. From the temperature dependence of the second moment, we estimate the electron- phonon coupling constant (and hence the displacement in vibrational coordinate from the ground state to the intervalence charge-transfer state), together with the effective phonon frequency coupled to the transition.The latter is ver _y close to the mean of the ground-state totally symmetric Sb-C1 stretching modes of SbC16- and SbCl,, and the displacement in the vibrational coordinate is also about half the difference between the Sb-CI crystallographic bond lengths in the two complex ions. To explain the temperature dependence of the zeroth and first moments anharmonicity must be involved. A simple model for the variation of intervalence excitation energy with interionic distance, combined with an isotropic model of the thermal lattice expansion, gives a quantitative account of the change in first moment with temperature and a qualitative description of the change in zeroth moment.One of the most characteristic features of class 111 mixed-valency compounds is the appearance of an intervalence optical transition as a structureless broad absorp- tion band in the visible or near-infrared. Considerable theoretical work on these transitions has appeared'-' and in particular Piepho, Krausz and Schatz4 (P.K.S.) developed a vibronic coupling model for calculation of mixed-valency absorption profiles. Their one-dimensional model for the potential-energy surf ace of mixed-valency systems can be solved exactly, and consequently it is possible to describe the whole range of behaviour of such systems as they vary from strongly localized to strongly delocalized.As examples of weak-interaction mixed valency, the hexachloroantimon-ates(111, v) are valuable prototypes with high-symmetry structures. Cs2SbC16 is the parent member of this series and its crystal structure5 reveals a superlattice of SbCli- and SbCl,. A great deal of spectroscopic evidence (e.g. Mossbauer,' far-infrared,7 Raman,' ultraviolet' and photoelectron spectra") also confirms the existence of distinguishable SbCl, and SbCli-, while semiconductivity" and visible- ab~orption~-~~measurements show that Cs2SbC16 and related hexachloroantimon- ates(111, v) are classical Robin-Day 'class I1 mixed-valency compounds. Their colour is usually dark blue and arises from the intermolecular charge transfer: hv Sb"'Clz-(A) +SbvC1,(B) -SblVC1g-(A)+SbIVC12-(B).Dilution of the effective chromophore concentration can be successfully achieved by using isostructural non-absorbing host lattices like the hexachlorostannates( ~v). 85 INTERVALENCE ABSORPTION OF SbC12-AND SbCl, 0.2 0.0 12 14 16 18 20 22 24 13103 crn-1 Fig. 1. Mixed-valency band in (CH3NH3)2SbxSnl-xC16 at 55.5 K (baseline subtracted). In view of the development of the P.K.S. model we have re-examined in greater detail the temperature dependence of the single-crystal absorption-band profile of the (CH3NH3)2Sb"',~2SbVx~2Sn1vl-xCldcompound (0 < x < l), whose properties were first investigated by Atkinson and Day,' with the aim of testing the application of both the configuration coordinate modelI3 and the P.K.S.model to Sbv-Sb"' charge transfer. EXPERIMENTAL Crystals of (CH3NH3)2Sb"'x~2SbVx~2~n1vl~x~~6were synthesized by previously published methods' from HC1 solutions of the constituent ions. Their colour ranged from purple to light green, depending on the antimony concentration, and high antimony concentration was sought. Their integrity was checked by examining them under a polarizing microscope and single crystals of exceptionally high quality were found. The absorption spectra were recorded at ca. 5 K intervals between room temperature and 4 K using a McPherson R.S.10 spectrophotometer and an Oxford Instruments CF 100 liquid-helium cryostat. The temperature of the crystal was measured with a compensated linear-temperature-sensor resistance thermometer and the temperature varied by an Oxford Instruments 'Harwell' temperature controller.The spectral output was digitized by a Stogate A/D converter. The choice of baseline to be subtracted from the digitized spectral output was of major importance. The baseline was estimated by least-squares fitting a straight line to a portion of the spectrum to the low-energy side of the intervalence absorption which was then extrapolated to the higher-energy side. The resulting spectrum after the subtraction of the baseline (fig. 1) can be considered as resulting from the superposition of two components: the intervalence band at low energy and the tail of a second high-energy charge-transfer band.A computer program was used to fit two Gaussians to the absorption spectra of the form (O.D.), = (l/~l/*A,)exp[-(hv-hvo,,)2/At]; k = 1,2 (1) where (O.D.)is the optical density, vo is the energy in cm-l of the maximum absorption and A is the half-width at the point where the optical density is l/e of the maximum absorption. The quality of the fits were excellent (fig. 1) through the whole temperature range. The K. PRASSIDES AND P. DAY R-factors? were between 4 and 5%, mainly limited by the uncertainty arising from the small number of spectral points available for the high-energy band. THEORY CONFIGURATIONAL-COORDINATE MODEL The intervalence absorption band can be considered as consisting of a series of lines arising from transitions to and from different vibrational levels of the ground and excited electronic states.Every line has a finite width due to a variety of interactions and the absorption consists of a series of bands which merge into a single broad structureless profile. The intensity of a transition of energy hvUUfis proportiona! to the square of the Franck-Condon factor of vibrational levels v, 0’. In order to carry out the summation over all the possible vibrational states of the electronic ground and excited states, the configuration-coordinate model can be used. This assumes that the optical electron is firmly trapped on an ion and interacts with a small number of local vibrational modes and that there are one or several ‘effective’ frequencies associated with these eigenmodes.The absorption band shape can be analysed by the method of moments.14 If a(E)is some function describing the line shape, the nth moment of a(E)is given by M, = (r(E)E”dE. The zeroth moment is simply the area under the band. The mean band energy is given by I? = (Ml/M(,),while the mean band width is given by m2=(1/Mo) a(E)(E-E)2dE. In the case of a Gaussian band shape: E =Em,,and m2= (1/8 In 2)H2,where Em,, is the maximum band energy and H is the full halfwidth of the band. On the assumption that the ground and excited potential-energy surfaces are harmonic: =Eo(g)+ hvj(g)(u+!i) EL!= Eo(u)+hvj(u)(v’+$) the expressions for the moments become13 t The R-factor was defined by 88 INTERVALENCE ABSORPTION OF SbClz-AND SbCl, and m2=ISj[hvi(u)12coth [hvi(g)/2kT] where Sj is the Huang-Rhys" factor, with the zeroth moment independent of temperature.THE P.K.S. MODEL In the P.K.S. formalism4 a mixed-valency system consists of two subunits desig- nated by A and B, which in the case of the SbCl:-(A)-SbCl,( B) dimer are associated with formal oxidation states III and v, respectively. Making the harmonic approxi- mation and assuming that the subunits have the same point-group symmetry in all oxidation states, one need only consider the totally symmetric normal coordinates QA, OR.In the harmonic approximation the vibrational potential energy of subunit i in oxidation state j can be written as Wf ( Q,)= Wy + lfQ, +ik;Qf. By introducing new dimensionless variables qf,A and W,and assuming kf = k for all i = A, B and j = 111, IV, v and Ifv = :( IfII+ It), the potential surfaces in q-( = q) space consist of three parabolas, each one corresponding to an Sbv-Sb"', an SbIv-SbIv and an Sb"'-Sbv oscillator.Note that q+does not enter the calculations in the case of equal force constants and when lIv is the average of l,,, and lv. The Sbv-Sb"' and Sb"'-Sbv energy surfaces are displaced horizontally and are sym- metrical about the SbIv-SbIv energy minimum while the SbIv-SbIv surface is displaced vertically from the other two surfaces (fig. 2). Furthermore if the electronic coupling is switched on and if it is assumed that there is no interaction between the (v, HI) and (HI,v) surfaces, then the vibronic matrix is of the form gq + 2h)2 &;q2+2w1; :I & ;(q -)2, with all energies expressed in units of v = (2v)-'Jk, the fundamental vibrational frequency associated with q, and where E is the electronic coupling constant, W measures the difference in zero-point energy between the Sb"'.V (or SbV'"') and SbIV,IV surfaces and A is related directly to the differences (assumed to be equal) in the equilibrium displacement between Sb'", SbIV and SbIV, SbV.The intervalence band4 is the totality of vibronic lines II+ u' arising from transitions between the surfaces, and the effect of temperature is incorporated through the Boltzmann population factors of v, v'. By using a theoretical absorption profile IKSl m,I 4I2fgu(E1 where jfgu(E)dE = 1, explicit expressions for the moments of the intervalence band can be ~btained.~ 89K.PRASSIDES AND P. DAY 1 350 -20 -15 -1 0 -5 0 5 10 15 4 Fig. 2. Potential-energy surfaces for the oscillator Sbll'C1~--SbvC1~-+SblvCl~--SblvCl~-in (CH,NH3)2Sb,Sn,-,C16 (A = 4.3, W = 10.5,E = -1.8 and v = 298 cm-'). RESULTS A typical single-crystal absorption spectrum of (CH3NH3)2Sb',:'2Sb~,2sn~~~c16 is shown in fig. 1. As already discussed, the intervalence band can be described very well by a Gaussian shape over the entire temperature range. In addition, in fig. 3 and 4 we given the variation of the halfwidth and the band maximum with tem- perature. The zeroth moment of the band (integrated intensity) increases consider- ably (ca.20%) on going from 280 to 8 K. The observation of a second intermolecular charge-transfer band at 27 500 cm-' by Day" is also confirmed in the more dilute crystals of (CH3NH3)2Sb,Snl-,C16. DISCUSSION It is clear from fig. 1 that the intervalence charge-transfer band shows no vibrational fine structure, although it becomes narrower by ca. 1500 cm-l. Since INTERVALENCE ABSORPTION OF SbCl2-AND SbCl, 3-40. N I E m2 3.20-. h c.l--. 5: v 2.80 1 ,2.60 , , 0 I00 200 300 T/ K Fig. 3. Variation in halfwidth of the intervalence band with temperature. The line is calculated from eqn (4)with v = 290 cm-’ and A = 5.8. intramolecular vibrational modes and lattice modes are well separated in frequency in the Sb mixed-valency salt, the assumption that the major contribution to the broadening of the optical absorption results from the difference in equilibrium geometry between SbCli- and SbCl, in the ground state and SbC12- in the excited state is immediately justified.Recognizing the difficulty of deciding which of the many vibrational modes in a solid interact with the optical electrons, we limit ourselves to a single ‘effective’ frequency, v. The P.K.S. model uses the parameters E, A, W and Y to define the potential-energy surfaces between which the optical transitions occur and to describe the shape of the intervalence band. We shall use these parameters throughout our discussion. Based on the above assumptions, consider the situation where the system is in the lowest vibrational state, i.e.at 0 K. If A =0, the only transition that is allowed is to the lowest vibrational level of the excited state and the spectrum consists of a single line. If, however, A2 + W >> IBI, then the quantization of vibrational levels in the upper state can be neglected. In this case a continuum of energy levels can be postulated in the upper state and the probability of the vertical Franck-Condon transition is simply proportional to Ixo12.At finite temperatures the P.K.S. model approaches the semiclassical treatment and the expression for the second moment of the band becomes m2=2A2(hv)2coth (hv/2kT) (4) on the assumption of equal force constants in the ground and excited states. K.PRASSIDES AND P. DAY 100 200 300 T/K Fig. 4. Variation in maximum energy of the intervalence band with temperature. The line is calculated from eqn (6) and (7). Eqn (4) was used to fit the observed halfwidths by employing a derivative-free non-linear regression computer program. The best fit? was obtained for the follow- ing parameter values: (H0/2) = 2801 f6 cm-'; v = 290* 3 cm-'; A = 5.8 fO.1. This fit is shown in fig. 3 and the agreement between observed and fitted values is very good. The value of the 'effective' frequency, v, falls within the range of intramolecular vibrations of the SbCl, and SbCl2- s ecies. More s ecifically, the A', modes of SbCl, and SbCl2- (327 and 267 cm-f respectively) Pfall on either side of the observed 'effective' frequency, v.For the hypothetical ion SbCl;-, a value for A', equal to [+(v&, + Y;)]I/~ = 298 cm-' is not unreasonable and indeed is very close to the observed effective frequency. Further, the oscillator considered here is SbvC16-Sb"'C16 + Sb'vC16-Sb1vC16, and hence from the electron-phonon coupling constant, A, we can get an estimate of Ar,which represents half the difference between the SbV-Cl and Sb"'-Cl equilibrium bond lengths. If the point symmetr of the SbC1,"- species is assumed to be octahedral, a value of Ar equal to 0.19 f0.01 K is obtained. Structural studies of Cs2SbC12 give a value for Ar of 0.131 A at 4.7 K, while in (C3H7NH3)4Sb:'f2Sby,,2C16(C1)2,16which has a rather different structure, Ar is 0.14 A at room temperature.In Cs2SbC165 also the deviation from Ohsymmetry is small (a 0.5 O angular distortion of SbC1, and a 2.5 O DZddistortion of the lone-pair t The smallest value of the sum x::l (H&d was 1.1976. INTEKVALENCE ABSORPTION OF SbC12-AND SbCl, SbCl2-ion). Thus besides all the drastic approximations the results show an encouraging agreement between theory and experiments, indicating that coupling of the electron transfer to antisymmetric combination of the Al, totally symmetric modes of the subunits plays a major role in determining the broadening of the intervalence charge-transf er band and that indeed the SbvC16-Sb"'C16 solids belong to the valency-trapped case (Robin-Day class 11). However, the situation changes dramatically if we continue the interpretation one stage further. If the band shape is a Gaussian, then the first moment of the band is exactly equal to the maximum band energy; hence by elementary considg- ation of the potential-energy surfaces in the case of A2+ W >> IEI we obtain E = Em,,=2(A2+ W)(hv).However, E,,,(O K) =: E,,,(8 K) = 17 290 cm-', and the value of W which measures the energy difference between the potential minima of the ground and excited states can be evaluated by substituting values for A and v. This gives values of W which are negative (W = -3.8); obviously this is not acceptable since the equilibrium energy of the ground state should be less than that of the excited state. However, we note that W is very sensitive to the value of the vibronic coupling constant A, which in turn is a very sensitive function of the difference in equilibrium bond lengths of the SbC1,"- subunits.Thus if Ar is varied from 0.19 to O.l8A, A changes from 5.5 to 5.8 and W from -3.8 to 0. Further, for the value of Ar=0.13 found from the crystal structure A is 4.0 and W is 13.8. So even if we are not able to assign a value to W, we may nevertheless conclude that the difference in energy between the equilibrium configurations of the ground- state oscillator SbCli--SbCl; and the excited-state oscillator SbClZ--SbCli- is very small. Using a two-dimensional P.K.S. model" by including a second 'effective' frequency led to an unacceptably high value of v2 or A2 and no improvement in the value of W.From fig. 4 it is noticeable that the band in the Sbv-Sb"' compound shifts monotonically to lower energy as the temperature is lowered. The shift between 300 and 8 K is ca 1500cm-l. The P.K.S. model predicts that the temperature dependence of the first moment of the band will be small in all cases.' The semiclassical treatment predicts a blue shift with decreasing temperatures. One way of introducing temperature dependence into the first moment is by considering the ground- and excited-state potentials to have different curvatures. Then in the case of a single 'effective' frequency in both ground and excited states, eqn (2) transforms into Hence a red shift with decreasing temperature is predicted when the excited-state potential-energy surface has a larger curvature than the ground-state one.Fitting eqn (5) to our data yields unreasonably large values for the ratio [ v2( u)/v2(g)],SO the explanation for the temperature dependence of E must be sought in the term AE(T).All attempts to discuss the variation of the bandshape of the intervalence charge transfer have been limited in the potential energy to terms quadratic in the inter- atomic displacements. This is the harmonic theory and a major consequence is the prediction of no thermal expansion of the crystal lattice. In real crystals, however, this prediction is not accurately satisfied. The deviations may be attributed to the neglect of anharmonic (higher than quadratic) terms. We present here a very approximate and empirical treatment of the effect of temperature on thermal K.PRASSIDES AND P. DAY 93 expansion of the crystal and consequently on the mean band energy of the charge- transfer band. The empirical nature of the treatment stems from the fact that no data are available on the thermal properties of molecular ionic crystals of Sb. Powers and Meyer18 have reported a study of the optical and electron-transfer properties of a series of Ru"-Ru"' compounds in solution. By changing the distance 1 of RuII-RuII' in successive complexes they established that the maximum energy of the intervalence charge-transfer band in solution increases as the Ru"-Ru*" distance increases. To explain their results, they considered a dielectric continuum model3 and used the relationship" 111 where Do, and D, are the optical and static dielectric constants of the solvent medium, respectively, and a, and a2 are radii of two charged spherical ions: E~ is the inner-sphere contribution to the vibrational trapping free energy of the electrons in the localized mixed-valency ion.A plot of Em,,against (11 1) gave a straight line. In our case the crystal lattice is considered as the dielectric medium. Again the lattice environment of the two ions between which electron transfer occurs is regarded as continuous dielectric. Hence the maximum band energy can be separ- ated into a part arising from lattice vibrational modes of the medium and a part arising from localized (metal-ligand) vibrational modes. Again for an ion in an octahedral hole in a lattice, eqn (6) applies with a,, a2and I identified as the SbV-Cl, Sb"'-Cl and Sb"'-Sbv distances, respectively.The temperature dependence of I can be approximately established by considering the thermal expansion of the lattice to be isotropic. Then2' l=l"(l+DoE) (7) where fis the distance between nearest neighbours at 0 K for the harmonic approxi- mation, Dois a constant which depends on the lattice type and i? is the mean energy per oscillator. For the variation of the internal energy E with temperature the Debye spectrum is taken as a basis with a Debye temperature of ca. 100K. A plot of Em,,against (1/ 1) gives a straight line (fig. 5). The exact values of the slope and the intercept are not of importance since they are very approximate, but it is noticeable that Em,,is a very steep function of I( T).The curve drawn through the experimental points in fig. 4 was calculated from eqn (6) and (7), and it can be seen that the level of agreement is satisfactory. Still, however, [(l/Dop)-(11D,)] is evaluated to be ca. 4.4, which is of the correct order of magnit~de.~ Unfortunately if the localized contribution E~ is evaluated, it turns out to be negative. So while anharmonic contributions appear to play a role in determining the behaviour of the band maximum as a function of temperature, their contribution is probably overesti- mated in the above approach. Any anharmonic contributions will be expected to manifest themselves to a lesser degree in the temperature dependence of the second moment, but they should be more visible in the temperature dependence of the integrated band intensity.Thus contraction of the lattice will increase the overlap between adjacent SbCl2- and SbCl, units, on which the dipole strength of the transition depends. So the integrated band intensity will increase as the temperature is lowered. This is indeed observed; as mentioned above, this increase is ca. 20%, well beyond experimental error that might have arisen due to uncertainties in the baseline subtraction. Note that both the semiclassical treatment and the P.K.S. model in general predict negligible temperature dependence of the zeroth moment of the band. INTERVALENCE ABSORPTION OF SbClz-AND SbCl, 17-51 I I 0.140 0-143 0.146 (I/ WA-I Fig.5. Variation in maximum energy of the intervalence band with inverse distance between nearest Sb"' SbV neigh bours. Finally, Atkinson and Day9 have calculated an upper limit for the degree of delocalization of the optical electron between the SbCl, and SbC1;- sites of ca. 0.001. Using this value we may calculate an upper limit for the value of the electronic coupling constant 14"of the P.K.S. model between the subunits in the case of strong localization of ca. 1.8. CONCLUSIONS We have shown that between 300 and 4 K the intervalence absorption band in a hexachloroantimonate( 111, v) crystal approximates very closely to a Gaussian bandshape, as required by the P.K.S. model for a weakly interacting system.Moreover, the temperature dependence of the second moment follows a hyperbolic cotangent law, leading to a value of the effective vibrational frequency coupled to the transition which is very close to the mean of the totally symmetric stretching frequencies of SbCl2- and SbC1, in their electronic ground states. The difference in bond lengths between SbCl,, SbC12- and the hypothetical excited-state SbC1:- derived from the optical spectrum is also near to half the difference between the observed bond lengths in Cs2SbC16. On the other hand both the first moment and the zeroth moment vary considerably with temperature, a result which is not compatible with the P.K.S. model if one retains the harmonic approximation. A simplified treatment of the variation of intervalence band energy with interionic spacing,*' combined with an isotropic model for the lattice expansion, provides a satisfactory picture of the temperature dependence of the first moment.The sense of the variation of the zeroth moment with temperature is compatible with the lattice expansion model, but to explain it quantitatively requires precise knowledge of the way in which the donor and acceptor orbitals overlap, which is not available at the present time. K. PRASSIDES AND P. DAY 95 We thank S.E.R.C. for partial support of this work. K.P. thanks Christ Church, Oxford, for a Senior Scholarship. We acknowledge many helpful discussions with Dr P. A. Cox. M. B. Robin and P. Day, Adv. Inorg. Chem. Radiochem., 1967, 10, 248.Proc. NATO-ASI on Mixed-valence Compounds in Chemistry, Physics and Biology, ed. D. B. Brown (D. Reidel, Dordrecht, 1980). N. S. Hush, Prog. Inorg. Chem., 1967, 8, 391. S. B. Piepho, E. R. Krausz and P. N. Schatz, J. Am. Chem. SOC.,1978,100, 2996; K. Y. Wong, P. N. Schatz and S. P. Piepho, J. Am. Chem. SOC., 1979, 101, 2793; K. Y. Wong and P. N. Schatz, Prog. Inorg. Chem., 1981, 28, 369. K. Prassides, P. Day and A. K. Cheetham, J. Am. Chem. SOC., 1983, 105, 3366. G. Longworth and P. Day, Inorg. Nucl. Chem. Lett., 1976, 12, 451. H. W. Clark and B. I. Swanson, J. Am. Chem. SOC., 1981, 103, 2929; T. Barrowcliffe, I. R. Beattie, P. Day and K. Livingston, J. Chem. SOC. A, 1967, 1810. R. J. H. Clark and W. R. Trumble, J. Chem. SOC.,Dalton Trans., 1976, 1145.L. Atkinson and P. Day, J. Chem. SOC. A, 1968, 2423. 10 P. Burroughs, A. Hamnett and A. F. Orchard, J. Chem. SOC., Dalton Trans., 1974, 565. l1 L. Atkinson and P. Day, J. Chem. SOC. A, 1968, 2432. l2 P. Day, Inorg. Chem., 1963, 2, 452. l3 J. J. Markham, Rev. Mod. Phys., 1959, 31, 956; J. J. Markham, F-Centres in Alkali Halides, Solid State Physics, Supplement 8 (Academic Press, New York, 1966). l4 M. Lax, J. Chem. Phys., 1952, 20, 1752. K. Huang and A. Rhys, Proc. R. SOC. London, Ser. A, 1950, 204, 403. l6 G. Birke, H. P. Latshcha and H. Pritzkow, Z. Naturforsch., Teif B,1976, 31, 1285. l7 K. Y. Wong and P. N. Schatz, A.C.S. Symp. Ser., 1982, 198, 281. l8 M. J. Powers and T. J. Meyer, J. Am. Chem. SOC., 102, 1289. l9 N. S. Hush, Trans. Faraday SOC., 1961, 57, 557. 2o G. Leibfried and W. Ludwig, Solid State Phys., 1961, 12, 276. (PAPER 3/ 1 1 17)

ISSN:0300-9238    

DOI:10.1039/F29848000085

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

J. Chem. SOC.,Faraday Trans. 2, 1984, 80, 97-1 13 Collisional Quenching of Electronically Excited Chlorine Atoms, C1[3p5(2P,,2)], by Atmospheric Gases Studied by Time-resolved Atomic Resonance Absorption Spectroscopy in the Vacuum Ultraviolet BY RICHARDH. CLARKAND DAVID HUSAIN* The Department of Physical Chemistry, The University of Cambridge, Lensfield Road, Cambridge CB2 1EP Received 29th June, 1983 The collisional quenching of electronically excited chlorine atoms, C1[ 3p5( 2P,/2)],has been studied by time-resolved atomic resonance absorption spectroscopy in the vacuum ultraviolet at A = 136.34 nm (C1[3p4 ~s(~P,,,)] was generated +C1[3p5(2Pl12)]}. Cl(3 2P1/2) by the repetitive pulsed irradiation of CCl, in the presence of excess helium buffer gas.The excited atom was then monitored photoelectrically using signal averaging in the short-time domain before the onset of Boltzmann equilibrium. The following absolute second-order rate constants for the removal of Cl(3 2P1/2),882 cm-' above the 3 2P3/2ground state, are reported ( kQ/cm3 molecules-' s-l, 300 K, errors 1u)for a wide range of gases of atmospheric interest: N2, (6.3* 1.O)X C02, <5x 02,(2.3k0.3) x lo-"; N20, (3.7*0.6) x H2, <6X H20, (2.6k0.5) X HCl, (1.1*O.l)x CH4, (3.9k0.8) x 10-l2; CO, ca. 6X These rate data are compared with the collisional-quenching rate constants for the other gases that we have reported previously using this technique which is, at present, the only practical method for monitoring Cl(3 2P112+)out of Boltzmann equilibrium for fundamental reasons discussed in this paper.General considerations of the chemistry of a Boltzmann system of Cl(3 2PJ)and the roles of the specific spin-orbit states, Cl(3 'Pl12)and Cl(3 2P3/2),are presented with special reference to CH, and the atmospheric gases in general. Relative rate data for the quenching of the transient precursor, generated from the photolysis of CCl, and from which Cl( 3 2P1,2)is derived, are also presented for most of the gases studied. Of the fundamental properties of the low-lying electronically excited chlorine atoms, C1[3p5(2P1/2)], two may be considered as dominant in governing the nature of experimental investigations in which direct monitoring of this atomic state leads to absolute rate data for its removal by different collision partners.First, the 2P1/2 state is located only 882cm-'(AE) above the ~P'(~P~,?)ground state,' a result relatively recently established by diode-laser spectroscopy,' modifying the spin-orbit splitting of 881 cm-' derived hitherto from optical spectroscopy.' Hence, purely in terms of empirical considerations of the energy to be transferred on c~llision,~ a matter which will be considered for individual gases later in this paper, experimental measurements on Cl(3 'PI,,>must be carried out under carefully chosen conditions of composition, pressure and time domain before the onset of Boltzmann equilibra- tion. The large body of rate data for atomic chlorine developed in the literature in recent years4 does not normally differentiate between the kinetic roles played by 97 COLLISIONAL QUENCHING OF c1[3p5(2P1/2)] the specific spin-orbit levels, C1( 3 ’P3/2) and C1( 3 2P1/2),essentially because rate measurements are generally carried out under conditions of Boltzmann equilibrium.Monitoring of either spin-orbit level will then yield identical kinetics for each atomic state and a measured second-order rate constant, kR, will be given by kR= (k,+ kbK)/(1+K) where k, and kb are, respectively, the specific rate constants for the 2P3/2and 2P1/2states and K is the equilibrium constant connecting these states. Thus monitoring of Cl(3 2P3/2) under such conditions may well, in fact, reflect the reactivity of the Boltzmann fraction of Cl(3 2P1/2),0.7% at 300 K.Further, for some collisional processes, the chemistry of the 2P3/2and 2P1/2states through k, and kbmay be significantly different as exp (--AE/kT)= 1.47 X at 300 K, quite apart from other effects such as orbital correlation. Similarly, direct monitoring of Cl(3 2P1/2)in a flow system under conditions of Boltzmann equilibrium as reported by Clyne and Nip’ using vacuum ultraviolet atomic resonance fluorescence measure- ments or by electron paramagnetic resonance as described by Carrington et al? does not yield absolute rate data for the 2P1/2state, a matter fully recognised by those Secondly, Cl(3 2P1/2)is highly optically metastable and characterised by an Einstein coefficient, A,,, for spontaneous emission to the 2P3/2 ground state of 0.012 s-’.~-’~)This calculated property is theoretically consistent7-’ with the lifetime of the analogous transition of atomic fluorine derived from line-shape measurements using diode-laser spectroscopy.l1 Hence, this Einstein coefficient, coupled with the low densities of Cl(3 2P1/2)that may be generated photochemically even in the pulsed mode (see later), prohibits the use of either time-resolved spontaneous emission or laser emission as a kinetic tool for this atomic state. This is, of course, in marked contrast to the study of the higher energised, heavier halogen species, I[5p5(2P1/2)]and Br[4p5( 2Pl./2)]. A final technical consideration which arises from the relatively small spin-orbit splitting is that a standard microwave-powered atomic chlorine emission s~urce’~-’~ will optically excite both the 2P3/2 and 2P1/2states simultaneously to a common upper state and hence prevent the use of time-resolved atomic resonance fluorescence as a kinetic tool for rate measurements specifically on Cl(3 Notwithstanding experimental limitations arising from time-resolved atomic resonance absorption experiments on low concentrations of C1(3 2P1/2)in the vacuum ultraviolet on a rapid time scale prior to the onset of Boltzmann equilibrium, this method, which we have employed previously mainly for the study of collisional quenching by the noble gasesI5 and chlorofluoromethanes (‘freons’ or ‘arctons’)I6 and also for C12 and 02,14 remains the only available practical technique for the kinetic study of C1( 3 2P1/2)..Earlier measurements using flash photolysis coupled with kinetic absorption spectroscopy on C1( 3 2P1/2)using photographic monitoring in the vacuum ultraviolet at a fixed time delayI7 were subsequently shown16 to describe experimental conditions close to Boltzmann equilibrium.More recently, Heaven etal.’ have described laser-induced fluorescence measurements from atomic chlorine in a flow system following two-photon excitation at h =210 nm. The sensitivity was found to be in the region of 1013molecule cm-3 operating on the 2P3/2state. The technique has not yet been extended to the time domain nor the sensitivity appropriate for Cl(3 2P1/2).In this paper we describe an investigation of the collisional behaviour of Cl(3 2P1/2)in the presence of a wide range of simple gases of atmospheric interest for both fundamental reasons and on account of the role of atomic chlorine in a stratosphere polluted by chlorofluorocarbons.19-22 Absolute rate data are reported for these gases. In most cases, particularly for those collision partners exhibiting relatively low collisional-quenching efficiency R. H. CLARK AND D. HUSAIN 99 towards Cl(3 2P1/2)and hence which involve the use of relatively high pressures of the quenching gas, the photochemistry of the precursor molecule, CC14, is affected. The results also yield relative quenching rates of the transient precursor fragment leading to Cl( 3 'P,/*). EXPERIMENTAL The experimental arrangement for monitoring C1( 3 'P1/') in the 'short-time domain' by time-resolved atomic absorption spectroscopy at A = 136.34 nm {C1[3p4 4s('P3/')] + C1[3~~('P,,.~)l}following the pulsed irradiation of CC14 employed a combination of the two data-handling systems that we have described previ~usly'~-'~ together with modifications to experimental detail.Cl(3 'P,J was generated by the repetitive flash photolysis of CCl, at low pressure (typically 4 X 1013molecule cmP3) in the presence of excess helium buffer as (pHe/pCCIJ=1.2X lo4) in a flow system kinetically equivalent to a static system.lE'" Photolysis was effected through the common wall of the high purity Spectrosil quartz (A > 165 nm) of the coaxial lamp and vessel assembly, the vacuum ultraviolet absorption spectrum for CC14 having been given by Russell et We have recently reported a detailed series of investigations of the collisional quenching of C1( 3 2P1/2)by chlorofluoromethanes,' including CCl,, which was found to be the photochemical precursor yielding the largest concentrations of the electronically excited atom and demonstrating a high collisional- quenching efficiency ( kCcl, = 2.0 f0.2 X lo-'" cm3 molecule-' s-l, 300 K).l5,I6 This latter property facilitates the necessary use of a short time scale over which Cl(3 2PI/2)must be monitored in the present kinetic investigations before the onset of Boltzmann equilibrium.Quenching by the buffer gas is negligible (kHe= 3.8f0.6 X cm3 molecule-' s-', 300 K).14,15 This may be contrasted with quenching by Ar (k,, = 1.1i0.3 X cm3 molecule-' s-l, 300 K),15 which was the prime cause of the rapid Boltzmann equilibration between C1( 3 2P1/2)and C1( 3 'P3/2) in the earlier kinetic absorption measure- ments at a fixed time delay of 10 ps using photographic monitoring and which resulted in low values of the collisional quenching constants of Cl(3 2PI12)by various gases including CC14.l7 The spectroscopic resonance source was similar to that employed hitherto,16 being derived from a stabilised microwave-powered discharge (incident power = 25 W, E.M.I.microwave generator type T1001) through an atomic emission flow lamp12 (pCl,= 2.0 N m-', pHe= 130N mP2) employing a cavity of the type described by Fehsenfeld et Special care was taken in the present measurements to minimise the major effect of colour centres that develop in the lithium fluoride window between the microwave-powered spectroscopic source and the reactor and which arise from the large number of individual decay measure- ments on the low concentrations of C1(3 'P1/')necessary to construct a signal-averaged result.This effect is manifest through the magnitude of the unattenuated signal-to-noise ratio at A = 136.34 nm (lo)and is critical in these measurements, which involve low degrees of light absorption. Hence an O-ring system supported by brass couplings was constructed and replaced the Araldite arrangement normally used for supporting this LiF windo~,'~-'~ permitting its regular replacement following cleaning, repolishing and removal of the colour centres by annealing. The resonance transition was optically isolated by means of a 1m concave-grating vacuum ultraviolet monochromator (Hilger and Watts), and following pulsed irradiation the time-resolved resonance absorption signal was monitored photoelectrically using a 'solar blind' photomultiplier (p.m.) mounted on the exit slit (p.m.tube Gencom GE-26E315, CsI photocathode, MgF2 end-window; p.m. voltage = 2.2-2.4 kV, Wallis power supply, 5 kV, 6 mA). The resonance absorption signals at A = 136.34 nm representing the decay of C1(3 towards Boltzmann equilibrium were amplified by means of a current-to-voltage converter employing a fast settling operational amplifier to avoid di~tortion.'~ Further, only limited amplification could be employed because of the restriction on the RC components imposed by the rapid time scales used.Two data-handling systems were employed with capture in a transient recorder where the signals were digitised and then transferred to a signal averager, summed, averaged and transferred onto paper tape. The first system was the combination COLLISIONAL QUENCHING OF c1[3p5(3P1/2)] of a Biomation transient recorder (type 610) interfaced to a 200-point signal averager (Data Laboratories, DL 102A) together with a Data Dynamics tape punch (type 1132), as used in a number of time-resolved resonance absorption investigations on atomic ~hlorine.~',~' The accuracy of measurements for decays of Cl(3 2P1,2)with this system is primarily limited by the number of digitised data points in individual decay profiles for the 'short-time' domain.Greater accuracy, particularly with smaller degrees of light absorption, may be achieved with the second system used previously for measurements of quenching of Cl(3 2P1,2)by the noble gases15 and described initially for resonance absorption studies of the present type on P(3 4S3/2).28This involves the combination of a relatively rapid response transient recorder (Data Laboratories DL 920, 2048 digitised data points), interfaced to a Data Laboratories DL 4000 signal averager (1024 point memory), the resulting output again being transferred to a Data Dynamics tape punch (type 1183) in ASCII code for direct input into the University of Cambridge IBM 3081 computer.All materials were essentially prepared as described in previous publications: He (buffer gas) and Kr (flash lamp);29 C12 and Cc14;30 H2, N20 and CH4;31N2, 02,CO, C02 and H20;32HCl.33 RESULTS AND DISCUSSION In our previous study of the collisional quenching of Cl(3 by the C1- substituted chlorofluoromethanes16 we have shown that whilst all the chlorinated species give rise to the electronically excited atom on pulsed irradiation in the Spectrosil region (A > 165 nm), CC14 yields the largest concentrations of Cl(3 'Pl12). Since all the molecules, CF,Cl4_,, quench Cl(3 2P1/2)at rates of the order of unit collisional efficiency, l6 CC14 is clearly the most convenient photochemical precursor for the investigations of the present type.However, molecules exhibiting relatively low quenching efficiencies towards C1( 3 2P1/2),and hence which are employed at high densities in the kinetic investigations, in turn affect the photochemistry of CC14 through the observed yields of Cl(3 2P1/2)and this aspect of the present study is thus initially described. Fig. l(a) shows an example of the di itised time-variation of the transmitted 52 0light intensity, It,,at A = 136.34 nm {CI[3p $ ~S(~P~/~>] indicating-+ C1[3p ( the decay of resonance absorption by Cl(3 2P1/2)following the pulsed irradiation of CC14 in the presence of excess helium buffer gas using the 200-point data recovery system (see Experimental section). Fig.1(b) and (c) give examples of the effect of two quenching gases, O2and N2, on the lifetime of the electronically excited atom. Considerable improvement in the quality of the decay profiles using the 1024-data recovery system can be seen in fig. 2, where only 25% of the experimental data points are presented for the purpose of clarity. Computerised fitting (see later) was, of course, applied to all the data points. This system was found to be particularly convenient when monitoring low degrees of light absorption in the Presence of gases which are found to be relatively inefficient for quenching of Cl(3 employed at relatively high concentrations, and which also significantly reduced [C1( 3 2P112)]r=a.Analyses of _plots of It,from both data-handling systems that yield time profiles of Cl(3 2P1/2)must take into account kinetic behaviour of the excited atom in what are effectively, and fortunately, two distinct time domains, namely (i) rapid decay of Cl(3 2P1,,2)to the Boltzmann population on a time scale of ca.0-500 ps or less as shown and (ii) a decay of the Boltzmann fraction of Cl(3 2P:i2) on a much longer time scale (ca.10-20 ms), as shown in earlier kinetic studies. The effect of these two domains can readily be seen in the published decay traces for Cl(3 2P1,2)from CC14+He mixtures as reported by Fletcher and Husain [ref. (14), fig. 21. The use of the A/B mode of the DL 902 transient recorder to demonstrate this is clearly ~een;'~ h = 136.34 nm) the initial plateau reached for Itr( ,-.0.28 * Y .I 9 0.26 e 2! 0.24 >2 0.22-f 0.20 t/ 0.1 81/ I 100 I 150 I 200 I 2 50 tlw Fig. 1. Digitised time variation of the transmitted light intensity, It,, at A = 136.34 nm {C1[3p 44s(2p3/2)] --* C1[3~’(~fl/~)]}indicating the decay of resonance absorption by C1( 3 2Pl/2)following the pulsed irradiation of CC4 in the presence of O2and N2 with excess ptotalhelium buffer gas. [CC14] = 4.0 X loi3molecule ~m-~; with He = 2.0 kN m-2; E = 180 J; repetition rate = 0.2 Hz; +, digitised data points; (-) computerised fitting of raw data to the form I,, = I&exp {-A[exp (-k’t)]}; average of 32 individual experiments. (a) CCl,+He (sweep rate =2 ps per Channel); (6) CC14+He, [O,]= 4.7X loi4molecule cmP3 (sweep rate = 1ps per channel); (c) CC14 +He, [N2] = 8.1 X lOI5 molecule cm-3 (sweep rate = 1 ps per channel).COLLISIONAL QUENCHING OF c1[3p5(2P1/2)] is that following relaxation of C1( 3 'PI/*)to the Boltzmann equilibrium concentra- tion and the infinite-time value represents the unattenuated signal, Io(A= 136.34nm). It is the former that is relevant in the present analyses. Its value describing It,.(A = 136.34 nm) for [C1(3 2P,/2)](equilibrium) (=I;) can be seen by inspection of fig. 1(a)or 2( a)but it is, in fact, computed. The first-order coefficient, k', for the decay of Cl(3 is quantitatively determined by the following. (a) Consideration of the first-order kinetic equations for Cl(3 'Pllz)and Cl(3 2P3/2) out of Boltzmann equilibrium gives rise to concentration profiles for each state described by the sum of two exponentials.(b)Neglect of the contribution of the diffusional loss for Cl(3 in the short-time domain demonstrated in fig. 1 and 2, a fully justified assumption in the light of the measured diffusion coefficient for Cl(3 2PJ)in He reported by Andr6 et a1.,2sreduces the profile for [C1(3 2P1/2)]to a single exponential. This, together with (c)the assumption of the Beer-Lambert law for the A = 136.34 nm resonance transition, yields decay traces described by the form Itr(A = 136.34 nm), =Id exp (-A exp -k't) (9 where A = rl{[C1(3 2P1/2)],z0-[C1(3 2P1/z)]eq}, and 1 have their usual meaning in E the context of light absorption, Id is defined above and k' is the first-order decay coefficient for the decay of Cl(3 2P,/2),the prime object of kinetic interest.The full curve in each diagram (fig. 1 and 2) represents the computerised fit derived from a NAGLIB routine to the form of eqn (i). This procedure was applied to all the decay traces obtained in this investigation. Apart from the variation of k' with the pressure of an added quenching gas, it was noticed immediately that for most of the quenching gases, Q, employed at high pressure, the computed value of In (I~/Itr)tzo(A= 136.34 nm) decryased with increasing pressure of Q. This quantity is a linear measure of [C1(3 -P1/2)],z0-[C1( 3 2P1/2)]eq as the equilibrium and, in turn, can be approximated to [Cl( 3 2P1/2)],=() term only accounts for 0.7% of the total atomic concentration.The observations may be formalised in terms of a simple kinetic scheme: CCI4+ hv (pulse) -+ P* + P* Cl(3 2P1/2)+ * * * P*+Q * products. Here the precursor, P*, yielding Cl(3 2P1/2),presumed to be an energised species of the type CCl:, is undefined. Putting [P*] in stationary state and assuming a linearity between [P*] and [CCl,], it may readily be shown that the ratio of the slope to the intercept of the plot of l/ln (I&/Itr)t=o against [Q] is given by kp*/ k,. Examples of such plots are shown in fig. 3 and 4 for the gases CH4, N20, N2, H2, HC1 and H20. The resulting values of kp*/ kl and the relative values are presented in table 1. This type of observation is analogous to the measurements on C(2 'So) derived from the flash photolysis of C302 described by Husain and Kirsch34 where the energised intermediate is considered to be an excited singlet state of C20. The scatter in the data in fig.3 and 4 arises, in part, from the necessity of carrying out decay measurements on Cl(3 'P1/Jusing a fixed low pressure of CC14. Speculation on the detailed nature of P* is not justified especially as the photochemistry of CC14 is certainly not developed in such detail as to include the source of Cl(3 2P1/2),3s-39 in spite of the detailed collisional behaviour of CC1 and CC12 reported from the 0.30 0.28 hv)c).3 c 0.26 W > 0.24 +-0.22 100 200 300 400 500 ‘/‘LE. 0.28 G 0.27 CI.3 1 0.26 -+-‘ai-cd v 0.25z+* 0.24 0.23 I I I I 1 100 200 300 400 500 tlw 0.26 -.s 0.25 1 d2 0.24 W 0.22 100 200 300 4 00 500 tlw Fig.2. Digitised time variation of the transmitted light intensity, It,, at h = 136.34 nm {C1[3p 44s(2p3/2)] +C~[~P~(~P$?)]}indicating the decay of resonance absorption byCl(3 2P112)following the pulsed irradiation of CC14 in the presence of H20 and N20 with excess helium buffer gas, [CClJ = 4.1 x 1013 molecule cmP3; PtotalwithHe = 2.1 kN mP2; E = 180 J; repetition rate = 0.2 Hz; +25’/0 density of 1024 digitised data points; (-) com-puterised fitting of raw data to the form I,, = Ib exp {-A[exp (-k’t)]}; average of 32 individual experiments. (a)CC14+ He; (b)CC14+ He, [H20]= 1.4X 1015 molecule ~rn-~; (c) CC14+ He, [N,O] = 4.0 X lo1’ molecule cmP3.COLLISIONAL QUENCHING OF c1[3p5(2P1/2)] Table 1. Rate data for the collisional quenching of the precursor, P*, leading to Cl(3 2P,,2) by various gases (errors la) gas (kp*/k1)/cm3 molecule-’ relative kp*/ k, (9.6k2.8)X lo-’’ (2.3k0.5)X (1.3f0.3) X (1.6f0.3) X (1.7k0.3) X (3.0k0.8)X (2.2k0.4) x (2.8+ 1.2)x 10-l~ 1 2.3 f0.8 2.4 f0.9 13.4f3.9 17.1f5.8 31.2* 12.2 16.4* 5.6 29.2 f15.0 excimer laser-photolysis studies of CC14 described by Tiee et aL4”and the uni- molecular decay data for CClf by Simons and coworker^.^^ Within the context of the simple formal mechanism used to present the data (fig. 3 and 4) one can only consider the limiting case of H20or C02 (table 1)where kp*might be approximated to the collision number.This yields an estimate of k, ==: los s-’ and hence a mean lifetime of P* of ca. 10 ps, which constitutes some guide to the atomicity of the species. The effect of P* on measurements of the kinetic decay of Cl(3 in the presence of the quenching gas is apparent. Gases demonstrating a high quenching efficiency with the excited atom, such as the chlorofluoromethanes,’6 and O2I4(and this work, see later) are thus studied at relatively low pressures and quenching of P* by Q is not significant, For such gases, decay measurements are carried out for those systems where [C1(3 2P1/2)]r,ois sensibly unaffected by added gases, and where the degree of light absorption is relatively large. By contrast, gases showing inefficient quenching of Cl(3 2P1/2)and which are employed at relatively high pressure involved decay measurements at lower degrees of light absorption at h = 136.34 nm through quenching of P*.This can be seen in the quality of the raw data for N2 [fig. l(c)], which are very scattered. The foregoing is the main source of the scatter in the data for the decay of Cl(3 2P1/2)when analysed in the form k’ = K + ko[Q] (ii) to determine absolute collisional-quenching rate constants, ko, for the removal of C1(3 2P1/*) itself, particularly for those gases which are relatively inefficient in this context. Whilst K in this type of investigation is generally taken to be a constant in a series of experiments in which [Q] alone is varied, this is a crude approximation for some gases studied in these measurements primarily for the reasons indicated above.Fig. 5 and 6 show the plots for the decay of Cl(3 2P1/2)in the presence of the gases 02,N2,N20 and H20, the slopes of which yield the absolute values of ko. However, as expected from extension of the discussion of the effect on P* of Q, and the photochemistry of CC14, the blanks ([a]= 0) are generally higher than the intercepts of the plots of the type given in fig. 5 and 6. Such effects were noted in some cases in the earlier measurements on Cl(3 2P1/2)by Fletcher.42 In the present measurements the values reported for kCH4and kHC,are derived solely from the limited portions of the plots of k’ against [Q]at the higher ranges of concentra- tions for these two gases which demonstrate a positive linear variation {[CH,] == (14-28) X lOI4 molecule cmP3; [HCl] -(3-6) X 10’’ molecule cm-’}.For both [CH,]/ lo', molecule ~rn-~ 0 0 3 6 9 [N20]/ 10lSmolecule cmP3 I n 1 1 1 0 3 6 9 12 [N2]/ 10l5 molecule cmP3 Fig. 3. Plots of l/ln (I&/Itr)t=o{A = 136.34 nm, C1[3p +-C1[3ps(2P~12>]}against [CH,], [N,O] and [N,] derived from extrapolation of first-order decay measurements on Cl(3 following the pulsed irradiation of CCI4, E = 180 J; [CCl,] = 4.0 X 1013 molecule cmP3;ptotalwith He = 1.9 kN rn-'. (a)CH4, (b)N,O (c) N2. 0 2 6 8 0 3 6 9 12 [HCI]/ 10'' molecule cm-3 I 0 9 18 27 [H,0]/10'* molecule cm-3 Fig. 4. Plots of l/ln (Ib/ltr)t=o{A136.34 nm, C1[3p *4s(*P~/~)]= +Cl[3pS(2e/2)]) against [H,], [HCl] and [H20]derived from extrapolation of first-order decay measurements on Cl(3 following the pulsed irradiation of CC14, E =180 J; [CC14]= ptotal ,4.0 x loi3molecule ~rn-~; with He= 1.9ICNIQ-~.(a)~2 (b)HCI, (c) H2O.R. H. CLARK AND D. HUSAIN these gases, the data at lower concentration initially yielded a decrease in k' with [Q] before reaching the same minimum value of k'. In view of the effects ascribed to P", further speculation on the factors yielding such initial variations of k' with [CH,] and [HCl] would not be justified in our view. For the molecules H2 and C02, only upper limits for ko are reported for similar reasons described for CH4 and HC1 but where there was no strong positive increase of k' with [a].Table 2 gives the results for ko derived from measurements on Cl(3 with the added gases studied in the present investigation, together with previous data reported for collisional quenching of this electronically excited atom principally determined by this research group using time-resolved atomic absorption measurements in the vacuum ultraviolet.Before considering the significance of individual quenching rate constants for Cl(3 2P1/2)by the gases studied here, brief consideration will be given to the overall body of rate data itself. The data for the noble (table 2) demonstrates the importance of the choice of He as the buffer gas in the investigations for monitoring the decay of Cl(3 in the time-resolved mode with added quenching gases.The use of Ar as the buffer gas in earlier photographic measurement^'^ is now seen to effect rapid Boltzmann equilibrationy6 and hence quenching rate constants reported from such measurement^'^ (e.g. for CCl, and CF3C1, table 2) are low for this reason. For the same reason, it is difficult to compare the limit reported for H2derived from the present investigation and the rate constant resulting from the photographic method17 (table 2). The photographic method is also seen to have yielded a low quenching rate constant for HCl by comparison with the present studyI7 (table 2). It may further be emphasised that the large value of kH (table 2) obtained in the photographic method17 resulted from an estimate of the atomic hydrogen concentration generated from the flash photolysis of HCl itself and from attributing the observed optical density due to Cl(3 2P1/2)at t = 10 ps as entirely resulting from quenching by atomic hydro 5en. The data for the collisional quenching of Cl(3 P1,2)by chlorofluoromethanes derived by time-resolved atomic resonance absorption spectros~opy'~-'~ (table 2) emphasise the limited densities of these gases that may be employed as photochemical precursors for the measurements on Cl(3 2P1/2)in the time-resolved mode.The present result for ko, is in good agreement with that reported by Fletcher and Husain. l4 From the experimental viewpoint, considered against the broad back- ground of a large range of techniques and studies of electronically excited atoms in general by time-resolved methods that have been reported in recent years, it is clear that there are severe limitations imposed by the present method for the study of C1( 3 2P1/2)in particular, notwithstanding the use of signal averaging.However, it is also clear that whilst various techniques have been employed and, indeed, could be further developed simply to monitor C1(32P~/2) such as the extension of the multiphoton excitation studies of Heaven et d.,'the monitoring of the excited atom in the short-time domain described here could not reasonably be achieved by some minor variation of existing methods but by a highly sophisticated, extensive and expensive technique employing a combination of lasers that is not fully apparent in detail at present.In spite of the limitations of the present investigation, it is at the moment the only practical method available for rate measurements on Cl(3 Table 2 represents a new body of fundamental quenching constants for Cl(3 2P1/2)which is of particular relevance to the fate of these atoms in the stratosphere when they are generated from the chlorofluorocarbons. l6 From the stratospheric viewpoint, collisional quenching of Cl(3 2P1/2)by the major atmospheric constituents, N2 and 02,are the most important results for COLLISIONAL QUENCHING OF Cl[ 3p'( 2P1/2)] 0 2 4 6 a LO,]/ 1014molecule cmP3 n 8 0 3 6 9 [N2]/ lOI5 molecule cm-3 Fig, 5. Plot of pseudo-first-order rate coefficient (k') for the decay of Cl(3 2P1,2)in the presence of O2 and N2.ptotalwith He = 1.9 kN mP2. (a)02,(b)N2. the gases investigated here. The present result of kN2= 3.7 * 0.6 X cm3 molecule-' s-' (300 K) is sensibly consistent with electronic (E) to vibrational (V) energy transfer of the type Cl(3 2Pr,2)+N2(~"=0) -+ Cl(3 2P3/2)+N2(~"=l), AE = 1448cm-' (1) (for N2, w: -2w,"x,"= 2300 cm-').43 This would imply unit collisional efficiency for the reverse of process (1) on the basis of a collision number of ca. 2X lo-'' cm3 molecule-' s-l in terms of detailed balancing and would be significantly R. H. CLARK AND D. HUSAIN 109 6cI -I 12 [N,O]/ 10' molecule ~111~~ Fig. 6. Plot of pseudo-first-order rate coefficient (k') for the decay of C1(32P,,2) in the presence of N20 and H20.pfotalwith= 1.9 kN mP2. (a)N20, (b)H20.He faster than reported rate data for the relaxation of HC1 ( u = 1) and DC1 (u = 1) byCl(3 2PJ),which are the only analogous processes with which we may compare our results.44 Estimates of the collision number of Cl(3 'PJ)+N2 based on DI2[c1(3 'PJ)-He] of 0.43+0.01 cm2 s-I at atmospheric pressure measured by .~~Andr6 et ~1 would yield a collision efficiency of the reverse of reaction (1) of magnitude ca. one in three. Similar considerations could equally apply to O2 where relaxation of 02((w,"-2w,"xI = 1556CM-')~~ u"= 1) by Cl(3 2P3/2)would be expected to proceed at a collisional efficiency comparable to that of the reverse of reaction (1) as described for N2.It would be surprising, however, if E -+ V transfer with O2 were not facilitated by chemical interaction, a mechanism which must account for E -+ R (rotational), T (translational) transfer with the gases CO and HCl where considerations of the energetics (0:-20,Nx: = 2143 and 2885 cm-', re~pectively)"~indicate that the observed quenching rates for these two gases are too rapid for E -V transfer. In the case of HCl, whilst C1 atom exchange with COLLISIONAL QUENCHING OF c1[3p5(2P1/2)] Table 2. Absolute rate constants, kQ (cm3 molecule-' s-', 300 K, errors la)for the collisional quenching of Cl(3 2P1,2) by different gases Q kQ ref. He Ne Ar Kr Xe H (3.8k0.6) X (4.0k0.5) X (1.1 *0.3) X (1.4f0.2) x (1.8k0.2) x ca. 7 X lo-'' 14,15 15 15 15 15 17 H2 <6 x a N2 02 c12 HC1 7 x 10-l2 (6.3* 1.0)x 10-l~ (2.1f 0.5) x lo-' (2.3*Oo.3)Xlo-" (4.5f0.4) X lo-' * (1.1 fO.1)X 10- 17 a a 14 14 a 6 X 17 ca.6 X a <5 x 10-13 a (3.7f0.6) X a (3.9f0.8) X (2.1 f0.4) X lo-'' 5 X lop1' (2.6k0.5) x (2.0f0.2)x lo-'' a a 16 14 17 CFC13 CF2C12 CF3C1 (3.1k0.6) X (2.1f0.4) X lo-'' (2.2f 0.4) x lo-'' 2.5 x 10-l~ (1.5* 0.4) X lo-'' 16 16 16 17 16 a This work.the chemical release of Cl(3 2P3/2)is energetically favourable, one would expect an activation energy for such a process to lead to a quenching rate lower than observed. Excitation of the low-energy v2modes4s of both C02 and N20 are consistent with the observed quenching rates of Cl(3 2P1,2)by these molecules.For the latter molecule, 0-atom abstraction with Cl( 3 2P1/2)to yield C10( X 2rIj) would be highly exothermic {AH= -1.19 eV, Di[ClO(X 'rIi)] = 2.7505 eV,43 D(N2-0) = 1.677 eVa5}. However symmetry-allowed and energetically favourable 0-atom abstraction reactions from N20 and C02 by a range of atoms are generally charac- terised by significant activation energies on account of the linear 18-electron closed- shell structures of these m01ecules,~~-~~ and this is presumed to be the case here although the detailed roles of physical quenching and chemical reaction are not resolved in the present studies. The value of kHzO(table 2) is consistent with excitation of the v2band (1595 cm-') corresponding to a reverse efficiency of V --* E transfer between H20(0,1,O) +C1(3 2P1/2)of ca.1 in 5 collisions or less. Chemical interaction is presumed to facilitate the overall quenching process. Quenching of Cl(3 2P,/2)by CH4 merits individual consideration because it highlights the general problem of the experimental interpretation of combining 111R. H. CLARK AND D. HUSAIN quenching rate data for the excited atom with the overall chemical removal of the Boltzmannised Cl(3 2PJ). First, whatever the nature of the interaction of Cl(3 2P1/2)+CH, on collision and the relative roles of physical quenching and chemical reaction, excitation of the low-energy v2 mode (1526 cm-1)45 would be consistent with the observed quenching rate of the excited atom. Secondly, we may consider the rate data for the chemical process C1( 3 2PJ)+ CH4 -+ HCl+ CH3 (2) which is discussed here in terms of the very recent compilation of Baulch et aL5' yielding k2= 9.6 X exp (-1350,' T) cm3 molecule-' s-l over the temperature range 200-300 K, with a preferred value of k2(298K) = 1.OX cm3 molecule-' s-'.The above temperature dependence corresponds to an activation energy of 938cm-'. Within the ran e of errors in the rate data of measurements employed to yield a preferred value!') this activation energy can be considered in accord with the electronic energy of C1(3 2Pl/2)of 882 cm-I.' For example, a recent and highly detailed investigation of reaction (2) by time-resolved atomic resonance fluorescence reported by Ravishankara and Wine5' and which was prominent in the compilations0 yielded k2= 3.2 f0.44 X exp (-1063 f34/ T) cm3 molecule-' s-' for a similar temperature range.This result" corresponds to an activation energy of 739 f24 cm-'. The thermochemistry of the reaction for C1(3 2P3/2)is given by AH = -223 cm-' and hence yields -1 105 cm-' for C1( 3 'P1/:){D(CH3-H) = 4.406 eV:' DE[HCl(X 'Z+)]= 4.4336 eV43}. Thus, even if the initial and rapid removal of C1(3 2P1/2)were attributed entirely to physical quenching, the chemistry of the resulting Boltzmannised population of Cl( 3 2PJ)with CH, could be dominated by the subsequent chemical removal of Cl(3 2P1/2)as indicated in the relation k2 = (k, + k,K)/(1+ K) (see Introduction). Whilst the observed results described here and those of Ravishankara and Wine" are consistent with this, these considerations alone do not settle the matter unequivocally.However, Ravishankara and Wine" have observed non-Arrhenius behaviour for reaction (2) at higher pressures and have quantitatively analysed this behaviour in terms of the then available collisional quenching data for Cl(3 2P1/2)repprted by Fletcher and H~sain.'~"~ Hence, Ravishankara and Wine concluded that at higher pressures of CH4, for example, chemical removal of Cl(3 *PlI2)by CH4proceeded at a rate which was sufficiently fast to disturb the Boltzmann equilibrium between C1(3 *P3/2) and C1( 3 2P1/2).51 This type of kinetic variation will only arise if kb> k, (see Introduction). This approach, which employs what is presumed to be the physical quenching data of Cl(3 2PY2) with a given gas, is clearly necessary before the studies of the chemistry of Cl(3 P1/2)in the Boltzmannised system can proceed.Our observed overall quenching rate for Cl(3 2P1/2)(table 2) is approximately three times faster than the chemical rate for Cl(3 2PJ)according to process (2). In future investigations it will be necessary to monitor both Cl(3 2P1/2)and C1(3 2P3/2) by time-resolved atomic resonance absorption spectroscopy in the vacuum ultraviolet in systems where the lack of Boltzmann equilibrium in the 'long-time domain' (see earlier) arises from chemistry specific to Cl(3 2Pl/2).In the simplest cases, the resulting decays for these two spin-orbit states will reflect the effect of four competing processes, two of which will employ the physical quenching data for Cl(3 2P1/2)of the present type using rate data for the reverse processes calculated on the basis of detailed balancing.The chemical rate constants specific to Cl(3 2P3/2) namely k, and kb,may then, in principle, be extracted. and Cl(3 2Pl/2),This is of course complimentary to simultaneous measurements of the decay of 112 COLLISIONAL QUENCHING OF C1[3p5(*P,/2)] Cl(3 ’PI,,) and the growth of Cl(3 ‘P3!’) during the short-time domain in order to determine the branching ratio for physical quenching and chemical reaction for the excited state. 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(PAPER 3/ 1123)

ISSN:0300-9238    

DOI:10.1039/F29848000097

出版商:RSC    

年代:1984

数据来源: RSC