摘要:

J. Chem. SOC.,Faraday Trans. 2, 1982, 78, 1-15 Analysis of the Molecular Electronic Absorption Spectra of Shock-heated Aromatic Compounds BY WILLIAM BYRON RICHARDSON? AND SHENG HSIEN LIN* Department of Chemistry, Arizona State University, Tempe, Arizona 85257, U.S.A. AND DONALDL. EVANS Department of Mechanical Engineering, Arizona State University, Tempe, Arizona 85257, U.S.A. Received 3rd February, 1981 Advantage has been taken of the rapid and homogeneous heating of a sample in a shock wave to record the electronic absorption spectra of the 'Al, + lBzutransition in benzene and the corresponding 'Al +'B1 transition in toluene as a function of temperature over the range 700-1300 K, prior to thermal decomposition. A model for the band-shape function of electronic absorption spectra of symmetry-allowed and symmetry-forbidden transitions in the context of the Herzberg-Teller theory is proposed based upon the assumption of harmonic oscillators.For symmetry-forbidden transitions, frequency changes in the promoting modes are ignored and only the linear Herzberg-Teller terms are considered to account for the dependence of the electronic transition moment upon nuclear coordinates. Explicit attention is paid to the temperature dependence of the band-shape function and it is shown, in conjunction with a moment analysis of the band-shape function, how important molecular parameters may be deduced in favourable instances, which are determined chiefly by the inherent molecular complexity and symmetry point group of the molecule.It is shown by a moment analysis of the shock data that the induced and allowed transition moments in toluene are of comparable magnitude. There have been several studies of the temperature dependence of the benzene, spectrum over moderate temperature ranges. lv2 Radle and Beck' studied the variation in intensity of the main band of the A, B and D progressions (A, B, D) at temperatures up to 250°C in order to resolve the assignment of these bands; their results indicated that the analysis of Sponer and collaborators3 was correct. Almasy and Laemme12 extended this study, experimentally observing the tem- perature dependence of the band intensities of members of several of the major progressions. Their results clearly illustrate the loss of fine structure and the broadening of the absorption band as a function of temperature.There have been few studies of the high-temperature molecular electronic absorption spectra of polyatomic molecules obtained under conditions in which the molecules are stable and prior to decomposition. Bauer et al.4undertook a study of the absorption spectra of cis-and trans-1,2-dichloroethylene at selected frequen- cies between 37 000-43 000 cm-' over the temperature range 800-1055 K. The compounds of interest were highly diluted with argon (97%) and shock heated. They assumed that the samples attained full thermal equilibrium within the time required (3-10 ps) to record the data oscillographically. This work was then extended by Bauer and Aten5 in a study of shock-heated dilute (1-10%) mixtures of benzene and hexafluorobennene in argon at t Present address: Unidynamics/Phoenix Inc., Phoenix, Arizona 85062, USA.1 ELECTRONIC SPECTRA OF AROMATIC COMPOUNDS temperatures ranging from 700 to 1900 K. In particular, they reccrded the absorp- tion spectrum of benzene vapour at 690, 810 and 1150 K. Pyrolysis was observed only at temperatures >1400 K. They observed that the spectrum became a struc- tureless continuum at 800 K and above 850 K another band (‘Alg ‘BlU)-+ ped the ‘A1,-+ ’& band of interest. overlap-The first part of the present work consists of an experimental determination of the absorption coefficients as a function of temperature for two compounds (benzene and toluene) which are representative of symmetry-forbidden transitions and transi- tions of mixed symmetry, respectively, and their interpretation.Advantage is taken of the rapid and homogeneous heating of a compound provided by shock compress- ion as a tool for the determination of spectral properties in times so short as to preclude decomp~sition.~’~ The second part of this work is concerned with the synthesis of a model capable of predicting the band shape (envelope of the absorption curve) of polyatomic electronic absorption spectra. The main emphasis will be placed upon the sym- metry-forbidden but vibronically allowed transitions, using the conventional Herzberg-Teller theory. Primary importance will be placed upon developing explicit temperature-dependent expressions for the zeroth, first and second moments of the absorption spectrum, in addition to the band-shape function itself.These will suffice to expose the principles required to explain the major observable features of broad structureless spectra: the mean frequency, bandwidth and the skewness sometimes observed. In addition it will be shown in principle how measurement of the absorption spectrum as a function of temperature allows the determination of the dependence of the transition moment upon each of the inducing modes. EXPERIMENTAL The basic approach employed here for obtaining high-temperature absorption coefficients in the visible-ultraviolet region utilizes the method originated by Davidson and coworkers.6-8 From the Beer-Lambert law we may writeg I(v)= I()(v)lo-c“”’x (1) where C is the concentration of absorbing molecules in moldm-3, X is the optical path length in cm, E(V) is the molar (decadic) extinction coefficient with units of dm3 mol-’ cm-’ and I(v)and Io(v)are the transmitted and incident light intensities, respectively, at the frequency v.We may convert the above relation into a form suitable for shock-tube measurements as follows: in the unshocked gas we have I’(Y) = I&) lo--cEo(”)x while in the shocked gas I2(v)=I&) lo-c’ET(”)x (3) where E~(v) are the values of the molar extinction coefficient at room temperature and E~(v) and the temperature T,respectively. The vacuum transmission Io(v) is normally unobserved in the usual shock-tube experiment. Solving eqn (2) for Io(v)we obtain I&) = IJV) locEo(”)x (4) and substituting this into eqn (3)to eliminate Io(v)results in the relation log10 [12(v)/Il(v)l=[cEO(v>-c’&T(v)Ix (5) where C’= (p2/p1)C.Solving for eT(v)yields &0(4 +log10 [L(v)/L(v)I (6)&T(V)=-P2IP1 CX(P*/Pd * W.B. RICHARDSON, S. H. LIN AND D. L. EVANS Eqn (6) was used for the reduction of the shock-tube data in this study. The temperature and shock compression ratio p2/p1 for a particular shock are determined by standard methods as discussed elsewhere." The experimental methods and equipment required to determine the high-temperature absorption coefficients are discussed below. SHOCK TUBE The shock tube used in this work is of the double-diaphragm type and consists of three separate sections: a high-pressure driver section 1.8m long and of 10cm inside diameter made of stainless steel, a dual-diaphragm section and a driven section 4.6m long with a square cross-section of 5 cm inside width and made of extruded aluminum.To take advantage of the inherently good reproducibility of the double-diaphragm shock tube, the driver section was routinely evacuated with a Cenco Hyvac 2 roughing pump. Pressures achieved in this fashion were typically 0.01 Torr. The high pressures in the driver and diaphragm sections were monitored with a pair of Heise high-pressure gauges. The shock-tube optical observa- tion system was comprised of the following components: light source, fused quartz windows and lenses on both sides of the shock tube, monochromator, photomultiplier and an oscillo- scope as a recording device.OPTICAL OBSERVATION SYSTEM The Tadiation source used in this work was a 1000 W xenon lamp (Hanovia 976-C1) operating between 20 and 26 V and at 43 A. The light dispersing agent was a Jarrell-Ash (JACO) model 75-000 grating spectrograph with a Czerny-Turner mount. It was fitted with a reflecting grating for which the reciprocal lhear dispersion was 22.5 A mm-' and all measurements were taken in the first order. The radiation detection used was an RCA7200 photomultiplier with a fused silica window, responding to radiation below 2000 A, with an S-19 spectral curve, the maximum sensitivity of this tube being at 3300 A.Power supply for the phototube was a high-voltage Fluke power supply, model 412 A. A Tektronix 565 dual beam oscilloscope was fitted with a Tektronix oscilloscope camera (modelC-12) and all oscillograms were recorded on Polaroid type 107 film (ASA3000, black and white). SHOCK-V EL0 CITY D ETE RM IN AT1 ON The method used to determine shock velocity employed thin-film resistance gauges," which-proved to be simple in construction and reliable in operation. Three such gauges, spaced 0.72 and 0.79 m apart, were used to determine sbock velocities. The amplified signals were fed into a pair of Hewlett-Packard digital counters (model 523 CR) and the transit times determined within a microsecond. The use of three such gauges made possible two separate determinations of the shock velocity and, assuming a simple linear model, the shock deceleration rates.G AS-MIXTU RE PRE PA RAT1 ON The aromatic hydrocarbons used in this study, benzene and toluene, were supplied by Matheson, Coleman and Bell and were of spectroquality and chromatoquality, respectively. The gas mixtures were prepared and stored in a 160 dm3 glass-lined tank. The tank was first evacuated by many hours of pumping to a pressure of lop5Torr with a CVC 5.08 cm oil diffusion pump backed by a Cenco Hyvac 14 roughing pump. Pressures of this magnitude were measured with a NRC cold-cathode ionization gauge (NRC 524-2). The sample was distilled under vacuum into the storage tank and diluted with Matheson high-purity argon to the desired composition.The gas mixtures thus prepared were allowed to mix by diffusion overnight. ELECTRONIC SPECTRA OF AROMATIC COMPOUNDS ROOM-TEMPERATURE SPECTRA From eqn (6) we see that values of the room-temperature molar extinction coefficients as a function of frequency are required to determine the absorption coefficients at elevated temperatures. Since the spectra of the shock-heated gases were obtained at a nominal bandwidth of 5 8, over nearly the entire wavelength regions of interest, the room-temperature spectra of both benzene and toluene were recorded at a comparable resolution. All spectra were recorded with a Varian Techtron recording spectrophotometer with a scanning rate of 100 8, min-' and with a fixed bandwidth of 5 A.The absorbances so determined could be accurately read to k0.02 absorbance units. STRAY LIGHT After many data had been collected it became apparent that the results had been systematically biased because of stray radiation. For the detection of stray radiation we employed a method suggested by Bauman12 and found no stray radiation at 3300A, but 2.2, 11.1 and 16.6% stray radiation from the unfiltered source at 2941, 2632 and 2381 A, respectively. In order to suppress stray radiation, a Kasha filter was used, consisting of an aqueous solution of NiSO4-6H20and CoS04.7H20with an optical path length of 5.0 cm. Subsequent tests indicated that with the Kasha filter no stray light was detectable at any wavelength and all the measurements reported herein were taken with this filter as an integral part of the optical system.NOMINAL OPERATING CONDITIONS Typical operating conditions and average thermal parameters and deceleration rates are summarized in tables 1 and 2. Note that no pyrolysis was observed in any of the incident shocks, decomposition occurring only behind the hotter reflected shocks. This is in accord with the observations of Bauer and ~o-workers.~*~ TABLE1.-TYPICAL CONDITIONS FOR BENZENE-ARGON SHOCKS diaphragm diaphragm/driver test shock shock thickness gauge pressure pressure temp. compression deceleration IPm /kPa Imm /K ratio rate ("/om) 38.1 24 1 /482 180 718 3.11 1.89 38.1 2411482 65 999 3.89 1.72 76.2 4481896 50 1292 4.36 1.62 TABLE 2.-TYPICAL CONDITIONS FOR TOLUENE-ARGON SHOCKS diaphragm thickness lw diaphragm/driver gauge pressure 1kPa test pressure Imm shock temp.IK shock compression ratio deceleration rate ("/om) ~ ~ ~~~~ ~~~ 38.1 2411482 180 735 3.06 1.76 38.1 2411482 75 979 3.73 1SO 38.1 2411482 50 1102 4.02 1.63 76.2 4141828 50 1244 4.20 1.38 W. B. RICHARDSON, S. H. LIN AND D. L. EVANS THEORY BAND-SHAPE FUNCTION SYMMETRY-FORBIDDEN TRANSITIONS The molecular absorption coefficient from the vibronic state lau) to the vibronic state Ibv‘) is given in the adiabatic approximation kab(a)= (4n2m/3fic) c c pav1(8avlRablobo’ )l2a(Wbv‘,au -0) (7) u v‘ where? o(= 27~)is the radiation frequency, Wbv’,av is the resonance frequency for the transition ao +bv’,Rab is the electronic transition moment (Rab = (Qa [xierilQb), @ are electronic wavefunctions), Pa, is the Boltzmann factor and is required to account for hot bands while the Dirac &function1’ insures that the transitions are consistent with the Bohr frequency rule, and 8ku are vibrational wavefunctions in the kth electronic state.16 For symmmetry-forbidden transitions the electronic transition moment is a function of the normal coordinates of one or more inducing modes Qiand may be expressed as1’ Rab = Rho2 +c(aRab/aQi)oQi =I(aR,b/aQi)oQi (8) I I where the sub- and super-scripts imply evaluation at the equilibrium position.Assuming that the normal coordinates are independent the vibrational wavefunc- tions 8,” and 8bu‘ are expressed as products of individual harmonic oscillator wavefunctions18 8av =nXau,(Qj>;i 8bu’ =nXbv’,(Qj’)i (9) where = xCZt& Nuk exp (-Pk?t/2)Hv, (PkQk), ~k = (Wk/h)’/2, H,, are the Hermite polynomials and N,, = (Pk/2”kvk!J.r>1/2.The vk designate the vibrational quantum numbers of the kth normal mode and the product is over all vibrational modes of the molecule. The molecular absorption coefficient may be written as (K=4r2/3hc) kab(m) = 1cpa, I(~av1c(aRab/dQi)ooilsbr.‘)( a(mbv’,au-a)* (10) v u’ Neglecting frequency changes in the inducing modes and introducing the integral expression for the S-fun~tion’~ we have 202 kab(0)= (KU/2T)c I(aRab/aQi)ol I dt exp [it(mba-w>]Ki(t) n Gj(t> (11) 1 --oo j#i where hoab is the energy difference between the two electronic states and Ki(t)and Gj(t)are defined by t Primed and unprimed quantities denote the excited and initial electronic states, respectively.ELECTRONIC SPECTRA OF AROMATIC COMPOUNDS and Since the inducing modes are not displaced we can anticipate the approximate 1result that (XauiQi IXb,;) = 0 unless v I = ui * 1and thus Ki(t) will reduce to just two terms Ki(t)= (h/2wi){$ exp (itmi) [coth (hwi/2kT) + 11+$ exp (-itoi)[coth (A~i2kT) -11). (14) The expression for Gj(t) is complicated but it has been evaluated previously.20 The result is Gj(t)= exp {(-itpjoj/2) coth (A42kT) -(P;AQ:/2) coth (h~j/2kT) + (p,”AQ,”/2) cosech (kwj/2kT)cos [ojt-(ihwj/2kT)]} (15) where AQj is the normal coordinate displacement of jth oscillator between the initial and excited states and pj = (oj-wi)/oj.Substituting eqn (14) and (15) into eqn (1 1) yields nexp { -(itp,~j/2) coth (Aoj/2kT)-(p;AQ;/2) coth (hojl2kT) j#i + (P;AQ;/2) cosech (Aojl2kT) cos [wit -(iAoj/2kT)]}. (16) For the case in which Cj$P,”AQ,”>> 1, eqn (16) may be transformed into a recognizable form by expanding the function cos [ojt-(iAoj/2kT] in a Maclaurin series: cos [ojt -(iAoj/2kT] = cash (Awj/2kT) + iqt siph (A~j/2kT) -(u;t2/2) cash (hwj/2kT) + * * * . (17) After expanding and simplifying we find that k,b (a)can be expressed in the Gaussian forms where GI and G2 are Gaussian functions of the form = d$ exp [Gl(w +mi) -(Li + wi -w)~/D] G2(0 -oi)= pgexp [ -(0-oi-U)~/D] W.B. RICHARDSON, S. H. LIN AND D. L. EVANS with and If we consider the special case of only one inducing mode at T = 0 K, we find and the band shape is a symmetric function with a maximum occurring at the frequency urnax= (3 +mi.Note that AQj = 0 unless the jth normal mode is totally symmetric if the geometry of the molecule is the same in the ground and excited states.21 Eqn (18) implies that two Gaussian functions with maxima displaced by 2oi originate from each active inducing mode and the absorption coefficient at any frequency will be a superposition of temperature-dependent Gaussian curves with temperature-dependent pre-exponential factors. TRANSITIONS OF MIXED SYMMETRY In the case that both RZi and (aRab/aQi)oQi are non-zero we can express the absorption cofficient as The second term has been previously evaluated and the band-shape function from the first term (corresponding to a symmetry-allowed transition) may be expressed as -(cs-w)X exp [Xi AQ;u; coth ;Aui/2LT) From eqn (24)one can readily deduce an expression equivalent to the frequently used Sulzer and Wieland equation.22 In the general case of electronic transitions of mixed symmetry we conclude that the absorption coefficient at any frequency will be a sum of Gaussian functions [see eqn (18)and (24)].RESULTS AND DISCUSSION To analyse our experimental results, we shall employ the method of moment analysis; this method will be presented first and then applied to analyse our experimental results.ELECTRONIC SPECTRA OF AROMATIC COMPOUNDS MOMENT ANALYSIS It has been found useful to characterize broad, featureless spectra in terms of the moments of the band-shape function. We will, as with Lax,23 Moffitt and Moscowit~~~ define the nth moment of the spectrum as and Jw where the dipole strength fd = I [kab(w)dw/w] plays the role of a normalizing factor. The most general case, that of transitions of mixed symmetry, occurs when neither IRril2 nor CiI(dRab/dQi)012 (h/20i)are negligible. Special cases of interest are those corresponding to purely symmetry-allowed and symmetry-forbidden transitions. In the general case, the dipole strength is given as This result clearly indicates that the dipole strength of a symmetry-forbidden transition is temperature dependent, while the dipole strength of an allowed transition is relatively independent of temperature.FIRST MOMENT By definition, we have J w(y) do Jo and the denominator has been evaluated above. The calculation of eqn (27) is straightforward and we find that the mean frequency of the transition (w) is given by where (3 = oab +I(p;AQ;/2)oj -C (pi~j/2)coth (h~j/2kT). (29)i i In the case of a symmetry-allowed transition, (w)=C3. Even though the dipole strength is constant, we would expect the mean frequency of the absorption band to shift to higher wavelengths (red shift) as the temperature is increased, since ordinarily I,.piwj> 0.If we consider the case of a symmetry-forbidden transition and assuming only one effective inducing mode, we find (0)= C3 + wi tanh (ti~i/2kT) (30) and again we anticipate a red shift with increasing temperature. W. B. RICHARDSON, S. H. LIN AND D. L. EVANS BANDWIDTH The function Aw = [(w2)-(w)~]~’~is ordinarily taken as a measure of the width of the absorption band. According to the definition, the second moment (w2)is given by (w’)= and the result for the second moment is given by (w2)= IRfL12(W2 +D/2)+xi I(aR,b/aQi)012(h/2~i){2(3~i+ coth (hwi/2kT)[D/2+ G2+ @TI} IRzi1’ +xi I(dR,h/aQi)o12(~/2~i)coth (h~i/2kT) (32) The general result for Aw is unwieldly and complicated, but for the case of the symmetry-allowed transition we find (w’)= (3’ +D/2 and thus (P’AQ;w’/2) coth (hoJ2kT) (33) For the case of a symmetry-forbidden transition, if there is only one inducing mode, we obtain (w2)=D/2+W2+w: +2Owi tanh (h~j/2kT) and consequently Aw = {D/2+wT[1-tanh2 (h~i/2kT)]}~’~.(34) In each case, we note that the bandwidth is determined essentially by the totally symmetric modes and is temperature dependent. ANALYSIS OF EXPERIMENTAL RESULTS The absorption spectra of benzene and toluene, recorded at elevated tem- peratures, are reproduced in fig. 1 and 2, respectively. The graphs for benzene are similar to those depicted by Bauer et aL5 at similar temperatures. For each compound we note the following qualitative trends as the temperature is increased: both the breadth and spectral intensities increase and there appears to be a shift of the entire spectrum to lower frequencies (that is, to longer wavelengths).In addition, it is seen that another, higher-frequency band begins to overlap the transitions of interest even at the lowest temperatures at which the spectra are recorded. Standard methods are available for the resolution of overlapping bands26-28 but all require that the complete spectrum of these bands be available and also a priori that the distribution function of the bands are known (e.g.Gaussian or Lorentzian). In a situation such as occurs here, common practice is to either assume fixed ELECTRONIC SPECTRA OF AROMATIC COMPOUNDS 125.0, ” I FIG. 1.-Absorption spectra of benzene obtained behind incident shocks.150.0. I 125.0.5 I I 100.0. 300 330 360 390 420 450 frequency/ lo2em-’ FIG. 2.-Absorption spectra of toluene obtained behind incident shocks. W. B. RICHARDSON, S. H. LIN AND D. L. EVANS integration limits5 or terminate the spectrum of interest at the floating minimum of the overlapping bands. We have followed a suggestion of J~rgensen~~ and have attempted to fit the spectra of interest assuming a skewed Gaussian distribution. We believe this to be more accurate than either of the last two alternatives mentioned but recognize that no unequivocal resolution of the overlapping bands is obtained, the error increasing with increasing temperature. Using this method, the moment analyses of the benzene and toluene shock data are presented in tables 3 and 4, respectively.TABLE 3.-MOMENT ANALYSIS OF BENZENE DATA nominal temperature, TIK dipole strength, fd/dm3 mol-' cm-' mean frequency, (w )/cm-' bandwidth, Ao/cm-' 718 9.05 39 514 1866 999 15.41 38 515 2359 1292 20.5 38 208 2591 TABLE 4.-MOMENT ANALYSIS OF TOLUENE DATA nominal temperature, dipole strength, mean frequency, bandwidth, TIK fd/dm3 mol-' cm-' (w ) / cm-' Awlcrn-' 735 13.8 38 597 1619 979 18.1 37 835 1915 1102 19.5 37 568 1995 1244 22.1 37 279 2161 This uncertainty in the band resolution is reflected most obviously in the calculation of the transition moments induced by the various normal modes of appropriate symmetry. Consider benzene, for which there are four EZg modes of the proper symmetry to distort the nuclear framework and thus contribute to the induced transition moment.Complete vibrational data on benzene are known and the four E2Rmodes are designated Vg, v7, v8 and v9 with ground-state frequencies of 606,3042,1584 and 1174 cm-l, respectively. The mode of frequency 1174 cm--' has, however, been shown to be inactive in the spe~trum.~' From eqn (26) it can be seen that in principle measurements of the dipole strengths at three temperatures should suffice for the simultaneous determination of the quantities (dRab/aQ6)0,(dRab/dQ7)o and (dRab/dQ~)O.However, our results for benzene do not yield a sensible value for I(aRab/dQ&l2.Previous studies have established the fact that the EZg mode of frequency 606 cm-' is largely responsible for the appearance of the benzene 2600 A spectrum. We may therefore, in oodapproximation, analyse benzene assuming only one effective inducing mode.51-34 Using the values of dipole strength listed in table 3 we find, with v6 = 606 cm-', hv6/2k = 436 K, eqn (26) gives an average value of l(dRUb/dQ6)l2= 1.19x 104cm3s-', in remarkably ood agreement with the recent value of 1.08~lo4cm3sK2 obtained by Volk & using a different method. A molecule as complex as toluene and of such low symmetry presents formidable difficulties in analysis. It is apparent that the value of I(dRab/dQj)ol for toluene is smaller than that for benzene. An estimate of this quality can be obtained as follows.As the symmetry is lowered from D6h in benzene to C2" in toluene, the ELECTRONIC SPECTRA OF AROMATIC COMPOUNDS degenerate EZg606 cm-' mode in benzene is split into a pair of modes of symmetry A1 and B2in toluene. The latter non-totally symmetric mode with a ground-state frequency of 622cm-' may be identified as the mode responsible for the vibra- tionally induced spectral intensity in toluene. From eqn (26) we have [K, = (N/2303)(4* / 3tic)] fd = K,{/Rril2 + I(aR,b/aQi)o12(ti/2wi) coth (hoi/2kT)}. (35) Differentiating with respect to 1/ T yields dfd --K, (ti2/4k) cosech2 (ti~i/2kT)l(aRab/dQi) Ol2. d(l/T) (36) However, a linear least-squares analysis of the toluene dipole-strength data yields a value of the slope of -1.42x lo4.Equating the two corresponding expressions gives K,l(aR,b/aQi)o12(ti2/4k)cosech2 (tioi/2kT) = 1.42 x lo4. (37) An identical analysis for benzene yields K,l(aR,b/aQs)o12(ti2/4k)cosech2 (A~6/2kT) = 1.82X lo4. (38) Since the temperature range over which these results (slopes) were obtained are similar and the vibrational frequencies do not differ appreciably, we find for toluene the result I(aR,b/aQi)o12 = 9.32 x lo3cm3sP2. This result for toluene, in conjunction with the tabulated dipole strengths at the appropriate shock tem- peratures listed in table 4 and eqn (26) then allows us to obtain an average value for the quantity IRhOb)I2,which is IRz212= 6.74 x J cm3. It is interesting to compare the magnitudes of lRr2 l2 and I(aR,b/aQi)o12(r?/2wi).The value of the latter is 4.19 x J cm3. It is seen that the allowed and induced moments do not differ greatly in magnitude. For simplicity, we shall assume the equality, in which case it can be shown that the mean frequency is given by (0)= (3 + mi/[ 1+ Coth (A~i/2kT)] (39) and the bandwidth as As expected, we note that the mean frequency is shifted toward higher wavelengths as the temperature is increased. Inclusion of the room-temperature values (40 070 cm-' for benzene, 39 332 cm-' for toluene) indicates a slight cur- vature as well. For benzene, a least-squares analysis of these data yields an intercept (extrapolated T = 0 K) of 40 729 crn-l. From eqn (30), we have At T = 0 K, we have then W. B. RICHARDSON, S.H. LIN AND D. L. EVANS An additional relation is provided by the equation for the 0, 0 transition (vibration- less transition), i.e. or, dividing by hc to convert it to cm-' @O,O = ma6 +I -@j>/2= @a6 -c (pi@j/2)* (44)i i Since the value of the latter is known35 (o~,~= 38 086 cm-'), substitution into eqn (42)yields I(p;AQ?/2)wi = 40 629 -38 086 -606 = 2037 cm-'. (45)i Of the 30 normal modes of benzene, only two are totally symmetric and values for their displacements have been given by Burland and Robinson36 as AQ1= 3.06 x (amu1/2 cm) = 3.94x g1/2 cm for the C-C stretching mode (v'= 990 cm-') and AQ2 = 3.45 x lo-'' (arnu'I2 cm) =4.45 x g'" cm2fOr tbe C-H stretching mode (v'= 3063 cm-'). Using their values we find xi(piAQi /2)0i = 1526 cm-'.Since the results of Burland and Robinson indicate that the displacement of the totally symmetric C-H stretching is an order of magnitude smaller than that of the C-C stretching mode, we may neglect the former and obtain, from eqn (45) the result AQ1= AQc-c = 4.83x g1/2cm, a value comparable to that of Burland and Robinson. For toluene, our least-squares analysis of the toluene data indicates an intercept of 40 077 cm-', which in conjunction with the known value37 for the 0, 0 transition of 37 474 cm-' yields the result x,(ppAQ7/2)wi =40 777 -37 474 -31 1 = 2292 cm-'. This value exceeds that found for benzene and is reasonable since toluene has more totally symmetric normal modes which may suffer a displacement upon excitation. From tables 3 and 4 we note that the bandwidth of the toluene absorption spectrum is less than that of benzene.For the latter we have, from eqn (34), (Ao) = C p?AQ&; coth (Fl42kT)+O?[l-tanh2(hoi/2kT)] (46)i and at T = 0 K, eqn (46) becomes (Am) = [Ijp;AQ707]~/~ = 1006 cm-l, the value of (Am) = 1006 cm-l being the result obtained from a linear least-squares analysis of the data, extrapolated to 0 K. The analogous value for toluene, using eqn (40),is (Ao)~= (p?AQf/2)0; +$wf = (8.57X 102)2 (47)i or, with wi = 622 cm-', [xi(P7AQ~/2)w~]'/2=798 cm-'. This indicates that despite the increased number of totally symmetric normal modes which may potentially undergo a displacement upon excitation, they must be of rather low frequency.The sensitivity of the moments to the band-shape function has recently been emphasized25 and it is evident that a potential source of error in this work is due 14 ELECTRONIC SPECTRA OF AROMATIC COMPOUNDS to our inability to resolve the overlapping spectral bands, an effect which becomes increasingly severe at elevated temperatures. We have, nevertheless, been able to obtain values of the major contribution to the vibrationally induced transition moment for benzene and the displacement of the totally symmetric C-C stretching mode which are in good agreement with previous estimates of this quantity and, in addition, we have obtained values for both the allowed and vibrationally induced transition moments in toluene. It is of interest to discuss two major approximations which we have adopted.Our model has been based upon the linear (first-order) Herzberg-Teller correction, which amounts to assuming that the electronic transition moment is a linear function of Q, regardless of the displacement of the latter. This point has been discussed by Ziegler and Albre~ht,~~ who found that this assumption holds well for the vibronically active v6 mode for displacements up to twice the root-mean-square displacement. An additional assumption, that of the vibrations being strictly har- monic, has been discussed by both Craig3' and Burland and Robinson.36 For the totally symmetric A', normal modes, the latter have derived the values for the anharmonicity constants of Xeae = 0.28 cm-I (993 cm-' A', mode) and Xeae = 12.6 cm-' (3063 cm-' Al, mode).Thus, for large polyatomic molecules, the assumption of harmonic vibrations appears to be an accurate one. It is evident that a moment analysis of high-temperature absorption data can, in favourable instances, yield important molecular data, especially when applied to intermediate size molecules of high symmetry or to smaller molecules of arbitrary symmetry. W. F. Radle and C. A. Beck, J. Chem. Phys., 1940,8, 507. F. Almasy and J. Laemmell, Helv. Chim. Acta, 1951, 34, 462. H. Sponer, G. Nordheim, A. L. Sklar and E. Teller, J. Chem. Phys., 1939,7, 207. S. H. Bauer, H. Kiefer and N. C. Rol, 9th Syrnp. Combust., (Carnell University, 1963). S. H. Bauer and C. F. Aten, J. Chem. Phys., 1963, 39, 1253.D. Britton, N. Davidson and G. Schott, Discuss. Faraday SOC., 1954, 17, 58. D. Britton and N. Davidson, J. Chem. Phys., 1956, 25, 810. G. Schott and N. Davidson, J. Am. Chem. SOC., 1958,80, 1841. H. F. Hameka, Advanced Quantum Chemistry (Addison-Wesley, Reading, Mass., 1956).10 W. B. Richardson, Ph.D. Thesis (Arizona State University, 1976); R.L. Belford and R. A. Strehlow, Annu. Rev. Phys. Chem., 1969, 20, 247. 11 J. N. Bradley, Shock Waves in Chemistry and Physics (Methuen, London, 1962).12 R. P. Bauman, Absorption Spectroscopy (Wiley, New York, 1962).13 M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Oxford University Press, New York, 1954).14 S. H. Lin, Theor. Chim. Acta, 1968,10, 301. 1s W. Heitler, Quantum Theory of Radiation (Oxford University Press, London, 1954).16 J.J. Markham, Solid State Physics, S8 (Academic Press, New York, 1966).17 S. H. Lin, L. Colangeio and H. Eyring, Proc. Natl. Acad. Sci. USA, 1971, 68, 2135. 18 H. Eyring, J. Walter and G. Kimball, Quantum Chemistry (Wiley, New York, 1944). l9 E. Butkov, Mathematical Physics (Addison-Wesley, Reading, 1968).20 S. H. Lin, J. Chem. Phys., 1966, 44, 3759. 21 H. Sponer and E. Teller, Rev. Mod. Phys., 1941,13,75.22 P. Sulzer and K. Wieland, Helv. Phys. Acta, 1952, 25, 653. 23 M. Lax, J. Chem. Phys., 1952, 20, 1752. 24 W. Moffitt and A. Moscowitz, J. Chem. Phys., 1959, 30,648. 25 L. J. Volk, Ph.D. Dissertation (Arizona State University, 1975).26 J. R.Morrey, Anal. Chem., 1968,40,905.27 B. D. Saksena, K. C. Agarwal, D. R. Pahwa and M. M. Pradhan, Spectrochim. Acta, Part A, 1968,24,1981.28 R. D. B. Fraser and E. Suzuki, Anal. Chem., 1969,41, 37. 29 C. K. Jorgensen, Acta. Chem. Scand., 1954,8, 1495. W. B. RICHARDSON. S. H. LIN AND D. L. EVANS 15 30 F. M. Garforth, C. K. Ingold and H. G. Poole, J. Chem. SOC., 1948,406.31 W. F. Radle and C. A. Beck, J. Chem. Phys., 1940,8,507.32 S. Harnung, E. C. Ong and 0.E. Weigang, J. Chem. Phys., 1971,55,5711.33 J. N. Murrell and 3. A. Pople, Proc..Phys. SOC., London, Sect. A, 1956,69, 245. 34 A. C. Albrecht, J. Chem. Phys., 1960, 33, 169. 35 J. H. Callomon, T. M. Dunn and I. M. Mills, Philos. Trans. R. SOC.London, Ser. A, 1966, 259, 499. 36 D. M. Burland and G. W. Robinson, J. Chem. Phys., 1969,51,4548.37 C. S. Burton and W. A. Noyes, J. Chem. Phys., 1968,49, 1705. 38 L. Ziegler and A. C. Albrecht, J. Chem. Phys., 1974, 60, 3558. 39 D. P. Craig, J. Chem. SOC., 1950, 2146. (PAPER 1/163)

ISSN:0300-9238    

DOI:10.1039/F29827800001

出版商:RSC    

年代:1982

数据来源: RSC

摘要:

J. Chem. SOC.,Faraday Trans. 2,1982, 78, 17-26 Weak Peaks in the Electronic Spectra of One-dimensional Semiconductors with a Metal-Halide Chain BY GEOREGE C. PAPAVASSILIOU* Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, 48 Vassileos Constantinou Avenue, Athens 501/ 1, Greece AND RENA RAPSOMANIKIS AND STAMATIS MOURIKIS Department of Physics, University of Athens, 104 Solonos Street, Athens 144, Greece AND CLAUS S. JACOBSEN Physics Laboratory 111, Technical University of Denmark, DK-2800 Lyngby, Denmark Received 3rd March, 1981 The weak peaks in the electronic spectra (reflectance, absorption, luminescence) of one-dimensional (1-D) semiconductors with a metal-halide chain are described. It is found that the positions and intensities of the peaks depend on the method of observation (reflectance, absorption, etc.) and on the size or the shape of the crystalline particles.Peaks inside the gap frequency are attributed to excition or impurity localized states and peaks near the plasma frequency are attributed to indirect excitation of plasmons. These effects are similar to those observed in the past from other conducting solids. A large number of compounds of the type [M(L-L)2][M(L-L)2X2]Y4 (where M =Pt or Pd, L-L =diamine, 2C2HsNH2 or 2NH3, X =C1, Br or I, Y =C1, Br, I, c104, BF4, HSO, or +SO4), of the type Mh[M(L)X3] [M(L)XS] (where M' =K or NH4, L=NH3 or pyridine) or of the type [M(L-L)X2][M(L-L)X4] have been prepared.'-3 Most have been found to be one-dimensional semiconductors.The one-dimensional conductivity is due to the chain ---MI1---X-M'"-X which is a metal-halide chain. Single-crystal reflectance spectra4 show a broad band in the visible or near-infrared spectral region when the electric vector of the light is parallel (E11 2) to the chain (conducting) axis (Z),while in the perpendicular polarization (E12)they do not show maxima in this region. Besides the main band, some weak peaks also appear in the reflectance and absorption spectra. In this paper we describe the behaviour of the peaks which occur inside the gap or near the plasma spectral regions. We also report the luminescence spectra of the materials. EXPERIMENTAL Mixed valence compounds were prepared according to methods previouslyRecrystallization was performed by slow cooling of concentrated solutions. Measurements were made on small single crystals of dimensions ca.0.2 x 0.1 x 3 mm3 because larger crystals were imperfect. The particle sizes of deposits were measured with a Siemens Elmiscop 101 electron microscope. The reflectance and absorption spectra were recorded with instrumentation described in our previous The luminescence (and Raman) spectra were recorded with a Jobin-Yvon Ramanor model HG-2S spectrometer. Exciting 17 ELECTRONIC SPECTRA OF METAL-HALIDE CHAINS radiation was provided by a Spectra Physics model 165 argon laser and model 125 helium-neon laser. The luminescence spectra of the powders and suspensions in CC1, were recorded with a Perkin-Elmer model 3000 fluorescence spectrometer.RESULTS AND DISCUSSION Fig. 1 shows the reflectance spectra of a greenish single crystal of [Pt(en)2] [Pt(en)2C12](C104)4(where en is 1,2-diaminoethane) observed at room temperature with the wave vector of light parallel [fig. l(a)]and perpendicular [fig. l(b)] to the A/nm 2000 1000 666 500 400 333 0.2 hmc1 .-C 0.1 .-x Y m C +I -0-.-1 I I 5 10 15 20 25 30 w/ 10~cm-' FIG. 1 .-Polarized reflectance (a$) and fluorescnce (c,d)spectra of [Pt(en)2][Pt(en)2C12](C10& single crystal with E 1) 2 (a,c) and E IZ(b,d).Excitation, 514.5 nm. chain axis. One can see that in the case of E 11 2 the reflectance spectrum shows a broad band, due to charge transfer, at 465 nm, another band at 1492 nm, a weak shoulder at ca.730 nm and some very weak shoulders at ca. 606 and 495 nm. These shoulders become more evident at low temperature [see also ref. (9)]. In the case of E I2 the reflectance spectrum does not show a maximum in the region from 5000 to 30000cm-'. Fig. 1 also shows the polarized luminescence (and Raman) spectra of [Pt(en)2][Pt(en)2C12](C104)4observed at room temperature with 514.5 nm excitation and the wave vector parallel [fig. l(c)] or perpendicular [fig. l(d)] to the chain axis. In the case of E 11 2 the luminescence tail in the visible region indicates a maximum in the mid-infrared region and shows a shoulder at 730nm and some sharp lines (Raman liness) at shorter wavelengths. In the case of E I2 there is no maximum in the long-wavelength region but some sharp weak lines (Raman lines) have been observed in the short-wavelength region [for details see ref, (5)].Using excitations from 632.8 to 450nm we observed the same luminescence spectra. The absorption spectra of polycrystalline deposits show considerable differences from the reflectance spectra. Thin deposits of [Pt(en)2][Pt(en)2C12](C104)4on quartz plates are reddish-brown in colour (small needles) and become yellow (small spheres) after rubbing with a soft paper. Fig. 2 shows the absorption spectra of a G. C. PAPAVASSILIOU etal. A/nm 1 .o C 0.5 0,2 I 1 I I0 ) 10 15 20 25 30 w/ 103cm-1 FIG. 2.-Absorption spectra of thin [Pt(en)2][Pt(en)2C12](C104)4deposits before (a) and after (6) rubbing with a soft paper.The absorbance values were normalized to the same concentration (g cmP3). thin deposit before [fig. 2(a)] and after [fig. 2(6)] rubbing. We found that before the rubbing 85% of the deposit consisted of small needles ca. l500A in length and 15% of small spheres of diameter lOO0A.t Almost all the particles became small spheres ca. 150 A in diameter after rubbing. The spectrum of small needles [fig. 2(a)] shows a maximum at 480nm and some weak shoulders at 666, 1042 and 370 nm, while the spectrum of small spheres [fig. 2(6)] shows a maximum' at 410 nm. The absorption spectra also show some peaks in the U.V. region. The luminescence spectra of small particles deposited on quartz plates or suspended in CC14 are the same as in fig. l(c) but the shoulder occurs at 705 nm.~)Table 1 gives the values of real (E~,)and imaginary part ~2 of the dielectric constant (E,) of [Pt(en)2][Pt(en)2C12](C104)4obtained by a Kramers-Kronig analysis of the reflectance spectrum of fig. l(a) (E11 2).Using these values we calculated, as in ref. (8),the absorption spectra of small needles and small spheres (fig. 3). One can see that there is a qualitative agreement with the experimental spectra of fig. 2. Fig. 3 shows how the spread of the particle shape effect the intensity of the shoulders. The spread of the particle size has a similar effect [see ref. (lo)]. The imaginary part (c2=)shows a maximum at 20 200 cm-' (495 nm) which is the gap frequency of [Pt(en)2][Pt(en)2C12](C104)4.The absorption spectrum of small needles shows a maximum near the gap frequency which is in agreement with the Gan's theory [see, for example, ref. (lo)]. The contributions of the refractive index, given by ELECTRONIC SPECTRA OF METAL-HALIDE CHAINS TABLE1.-OPTICAL CONSTANTS OF [Pt(en)2][Pt(en),C12](c104)4FOR E 112 AT ROOM TEMPERATURE 4 600 8.28 2.67 16 600 3.03 3.52 5 000 8.30 3.05 17 000 3.02 3.54 5 400 8.27 3.62 17 400 3.00 3.59 5 800 7.87 3.93 17 800 2.98 3.65 6 200 7.61 4.20 18 200 2.94 3.80 6 600 7.38 4.65 18 600 2.84 3.94 7 000 6.91 4.92 19 000 2.70 4.09 7 400 6.44 5.02 19400 2.49 4.24 7 800 6.04 5.18 19 800 2.23 4.34 8 200 5.58 5.23 20 200 1.90 4.43 8 600 5.15 5.13 20 600 1.56 4.37 9 000 4.80 5.05 21 000 1.21 4.26 9 400 4.47 4.90 21 800 0.80 3.90 9 800 4.20 4.74 22 600 0.36 3.23 10 200 3.97 4.54 23 000 0.35 2.99 10 600 3.81 4.33 23 400 0.31 2.77 11000 3.71 4.18 23 800 0.31 2.54 11400 3.62 4.02 24 200 0.33 2.33 11800 3.58 3.90 24 600 0.37 2.14 12 200 3.54 3.84 25 000 0.43 1.96 12 600 3.50 3.78 25 400 0.50 1.80 13 000 3.45 3.78 25 800 0.59 1.65 13 400 3.38 3.73 26 200 0.69 1.52 13 800 3.32 3.72 26 600 0.79 1.41 14 200 3.24 3.70 27 000 0.88 1.33 14 600 3.17 3.61 27 400 0.97 1.27 15 000 3.13 3.57 27 800 1.05 1.22 15 400 3.10 3.52 28 200 1.13 1.18 15 800 3.08 3.52 28 600 1.20 1.15 16 200 3.06 3.52 29 000 1.25 1.15 and of the corresponding absorption index, given by to the reflectance and absorption are different [see, for example, ref. (lo)].SOthe peaks which appear in the reflectance (and luminescence) spectrum at lower than the gap frequencies become weak (or disappear) in the absorption spectra of small particles because k, < n, in this spectral region. Rapidly grown single crystals of [Pt(en)2][Pt(en)2C12](C104)4are sometimes red in colour7 and show reflectance spectra with a maximum at ca. 440 nm [see also ref. (1l)]and some shoulders at longer wavelengths. The reason of this behaviour in the red crystals is due to small particles on the surface and/of defects or dislocations in the bulk.There is no difference in crystalline structure between the greenish and red forms.7 The spectra calculated via the Maxwell-Garnett equation [see, for example, ref. (lo)]for small aggregated spheres show maxima around 440 nm. Consequently, we can consider G. C. PAPAVASSILIOU etal. 21 A/nm 2000 666 400 333 I I I I Q) 666C -fi $4' n d?'/0 1 I 5 10 15 20 25 30 "/ 10~~m-l FIG. 3.-Calculated absorption spectra of [Pt(en)2][Pt(en)2C12](C104)4small particles: (a) 100% needles, (b) 100% spheres, (c) 50% needles and 50% spheres. The absorbance values were normalized to the same concentration (g cmP3). the crystals as an aggregated sample of parallel oriented crystalline particles.These particles are large in the greenish form and small in the red form and are connected together by impurities or vacations. The luminescence spectra of polycrystalline pellets do not show considerable differences from those of single crystals. Fig. 4(a) shows the luminescence spectra of a [Pt(en)2][Pt(en)2C12](C102)4 pellet. The constituents Pt(en);?C12 and [Pt(en)2C12]C12 do not show luminescence peaks. However, after illumination of [Pt(en)2C12]C12 with a 454.5 nm laser-line in a moist atmosphere, a luminescence peak at 660 nm and a resonance Raman spectrum are A/nm 1000 714 555 454.5 1 1 I I I L 10 14 18 22 o/103cm-1 FIG. 4.-Luminescence (and Raman) spectra of polycrystalline pellets of [Pt(en)2][Pt(en)2C12](C104)4 (a),of [Pt(en)2C12]C12 before (b) and after (c) illumination with 454.5 nm laser line, and of [Pd(en)J-[Pt(en)2C12](C104)4(d),(e).Excitation, 454.5 nm for (a)-(d)and 514.5 nm for (e). ELECTRONIC SPECTRA OF METAL-HALIDE CHAINS observed [fig. 4(6) and (c)]. The reason for this is that after illumination of [Pt(en)2C12]C12,some of the chlorine is removed and a mixed-valence compound is formed. That the peak occurs at a shorter wavelength may be due to the effect of very small particles. We have obtained the same results for [Pt(C2HsNH2)4]- [Pt(C2H5NH2)4]C14.2H20(Wolffram's red) and similar results for other compounds with the chain ---M1l---CI-PtlV-, where M = Pt or Pd. The compound [Pd(en)2] [Pt(en)2C12](C104)4 gives a reflectance spectrum with a maximum in the U.V.region and a luminescence spectrum with a maximum at 702nm [fig. 4(d) and (e). The compound [Pd(en)2][Pd(en)2C12](C104)4gives a reflectance spectrum with a maximum at 590 nm, a weak peak at 1282 nm and a weak shoulder at cu 670 nm, but it does not give luminescence spectra in the visible or near-infrared regions. The peaks observed inside the gap are attributed to the impurity or Wannier exciton localized states. The behaviour of these peaks is analogous to that of simple semiconductors such as CdS'2-'4 and AgI. l3 The characteristic behaviour inside the gap seems to be the reason why the Raman excitation profile of small needles of [Pt(en)2][Pt(en)2C12](C104)4occurs at a frequency lower than the gap frequency [see ref.(4)]. The reflectance and absorption spectra of all the above-mentioned compounds and of their bromide and iodide analogues also show weak peaks near their plasma frequency. Some of these peaks also appear in the spectra of the constituents. The origins of the peaks of the constituents are described elsewhere [see ref. (15) and (16) and references therein]. The absorption spectra of [Pt(en)2][Pt(en)2C12]- (C104)4 show a shoulder at 370 nm (fig. 2) and a weak shoulder at 330 nm, while the spectrum of its constituent [Pt(en)2C12]C12 shows a weak peak at 370 nm and a strong peak at 330 nm. The inversion of intensities and the appearance of new peaks near the plasma frequency are more evident in the bromides and iodides [see also ref.(8)] which are better conductors than the chlorides. The conductivity (0) in pellets of [Pt(en)2][Pt(:!)2C12](C104)4 and [Pf(en)2][Pd(en)2C12](C104)4, for example, has values of 10- and 5 x 4,' cm-,respectively. This was found to be larger in single-crystal measurements. Fig. 5 shows the reflectance spectra A/nm 10 0.5 0 5 1 5 10 15 20 25 30 w/i03cm-1 FIG. 5.-Polarized reflectance spectra of [Pd(en),l[Pd(en)2Br2](C10,), single crystal with E 11 Z (a) and E 12 (b). Dotted curve (c) shows 11 2)in the visible region. G. C. PAPAVASSILIOU etal. A/nm 2000 1000 666 500 400 3331.0 -I I I I 1300 8 cd -e 0.50,2 I 0 5 10 15 20 25 30 w/i03~m-1 FIG.6.-Same as fig. 2 but for [Pd(en)2][Pd(en)2Br2](C10& of a single crystal of [Pd(en2][Pd(en)2Br2](C104)4 and the ~2~ curve in the high- frequency region.Fig. 6 shows the absorption spectra of small needles [fig. 6(a)] and small spheres [fig. 6(b)] and table 2 give the E~~ and ~2~ values of [Pd(en)2}- [Pd(en)2Br2](C104)4 obtained by a Kramers-Kronig analysis of the reflectance spectrum with E 11 2. We see (table 2) that &Iz has the value zero at 18 500 cm-’ (540.5 nm) which is the plasma frequency (0;)of the semiconductor, while E~~ has a maximum at 7800 cm-’ (1282 nm) which is the gap frequency of the symiconduc- tor. The c2, curve (fig. 5) shows a weak peak at 545 nm 18 348 cm- ), near the iplasma frequency, and another one at 460 nm (21 740 cm- ). The peak at 545 nm is shifted to shorter wavelengths in the spectrum of small needles [fig.6(a)] and becomes very weak in the spectrum of small spheres [fig. 6(b)]. This peak near the plasma frequency peak is attributed to indirect excitation of plasmons. The results are analogous to those obtained from a good one-dimensional conductor (a= lo2n-’cm-’) such as K2Pt(CN)4Br0.3 3H2017-” and K1.62Pt(C204)2 2H202’ or-from a three-dimensional conductor (i.e. an elemental Weak peaks near the plasma frequency have been observed in a large number of compounds with a metal-halide chain [see also ref. (23)-(35)]. In the following we show that the appearence of weak peaks near the plasma frequency is related to the degree of valence delocalization. The integral intensity of the mixed-valence absorption (charge-transfer band) can be used for an approximate calculation of the valence delocalization parameter (Y according to36 4.24 x 10-4~,axA (y2 = (3)VMVd2 where cmaxand A are the molar extinction coefficient at the band maximum and the half-width (in cm-l) and d is the metal-metal distance (in&.Assuming that the above equation is valid for infinite-chain compounds, the authors of ref. (29) found values typically between 0.01 and 0.1 for compounds with a metal-halide ELECTRONIC SPECTRA OF METAL-HALIDE CHAINS TABLE2.-oPTICAL CONSTANT OF [Pd(en)2][Pd(en)2Br2](C104)4FOR E 1) AT ROOM TEMPERATURE 4 600 17.30 0.07 17 400 -0.39 0.44 5 000 2 1.02 0.21 17 800 -0.24 0.45 5 400 24.08 1.41 18 200 -0.10 0.45 5 800 27.62 2.59 18 600 0.02 0.45 6 200 38.53 9.66 19 000 0.12 0.44 6 600 37.85 16.32 19 400 0.23 0.42 7 000 45.09 40.45 19 800 0.35 0.41 7 400 28.52 53.20 20 200 0.45 0.40 7 800 5.70 63.49 20 600 0.55 0.40 8 200 -23.38 53.52 21 000 0.63 0.40 8 600 -27.55 34.24 21 400 0.68 0.40 9 000 -27.76 19.96 21 800 0.74 0.40 9 400 -22.66 13.01 22 200 0.79 0.38 9 800 -19.48 7.11 22 600 0.84 0.36 10 200 -15.54 4.74 23 000 0.90 0.33 10 600 -12.85 3.04 23 400 0.96 0.30 11000 -10.62 1.90 23 800 1.01 0.27 11400 -8.83 1.35 24 200 1.07 0.24 11800 -7.36 0.64 24 600 1.14 0.22 12 200 -6.04 0.46 25 000 1.20 0.21 12 600 -5.00 0.36 25 400 1.28 0.20 13 000 -4.15 0.31 25 800 1.36 0.19 13 400 -3.48 0.39 26 200 1.44 0.19 13 800 -2.94 0.37 26 600 1.52 0.20 14 200 -2.48 0.38 27 000 1.59 0.22 14 600 -2.09 0.38 27 400 1.67 0.23 15 000 -1.74 0.37 27 800 1.75 0.27 15 400 -1.44 0.39 28 200 1.81 0.30 15 800 -1.18 0.40 28 600 1.88 0.35 16 200 -0.95 0.40 29 000 1.92 0.42 16 600 -0.73 0.42 30 000 2.00 0.58 17 000 -0.55 0.42 31 000 2.01 0.71 chain.This means that the delocalization is weak. The single-crystal resonance Raman spectra of K2[PtNH3X3][PtNH3X5] show weak delo~alization~~ but the X.P.S. of [Pt(en)2][Pt(en)2X2](C104)4powders do not show delocalization. It is not known what happens in the X.P.S. of large crystals.We found that the optical absorption spectra of [M(en)2][M(en)2X2](C104)4are superpositions of the spectra of their constituents [see also ref. (9) and (23)], except if the materials are divided in small particles. However, traces of the peaks of their constituents appear in the spectra of strongly delocalized system^.'^-^' Fig. 1-3,5 and 6 show that the parameter LY depends on the state of the materials (i.e. size and shape of the particles). From eqn(3) one finds ~~~ ~ A,,,(needles) A(need1es) vMv(spheres) (4)LY (spheres) = JA,,,(spheres)h(spheres)vMv(needles) where A,,, is the absorbance at the band maximum. From fig. 2 (or fig. 3) and eqn (4) we found LY (needles) /a(spheres) = 1.7 for [Pt(en)2][Pt(en)2C12](C104)4. G.C. PAPAVASSILIOU etal. 25 From fig. 5 and eqn (4) we found a(needles)/a(spheres)==2for [Pd(e~~)~l-[Pd(en)2Br2](C104)4. This means that the delocalization in needles is stronger than that in spheres, or the delocalization is stronger in the infinite chain. The peaks near the plasma frequency are more evident in delocalized systems. These appear in the solid state and disappear in However, the position and the intensity of the peaks in the solid state depends on the size of the particles. The present and the previous investigation^^'^ explain the large variety of the spectra observed by us and ~ther~.~-~~~*~,~~~~~-~~ This variety is due to the different methods of observation (reflectance, absorbance, scattering), the temperature, the size of the particles, etc.The room-temperature spectrum of Wolff ram’s red powder, for example, reported in ref. (24), shows a shoulder at 625 nm which incorrectly was assigned to the intervalence transition. This shoulder appears at 675 nm in the single-crystal absorption spectrum at 4 K9 A weak shoulder appears at 570 nm in the diffuse powder reflectance ~pectrum,~’-~~ but it does not appear in the spectrum of small spherical particles as in the case of [Pt(en,][Pt(en)2C12](C104)4 [fig. 2(6)]. The shoulders which sometimes appear on both sides of the charge- transfer band are due to the spread of the particle size and shape. This explains the spectra of [Pt(en)2][Pt(en)2X2](C104)4in a KBr matrix after exposure to moist air.28 Some particles react with the water of the moist air and become smaller.So after the partial reaction the absorption band and the r.e.p. of the particles are shifted to higher frequencies and sometimes the absorption spectrum shows a trace of the “before-reaction” band. The amount of impurities introduced during the different methods of preparation of samples may play a considerable role in the spectral behaviour of this kind of semiconductor. We observed that the colour of [Pt(en>2][Pt(en)2C12](C104)4changes after doping with Ni(en)*Cl:’. Changes in colour have been observed in Magnus green salt doped with Pt’V.38 H. J. Keller, Linear Chain Platinum Haloumines, to be published; H. Endres, M. El Sharit and and H. J. Keller, in Synthesis and Properties of Low-Dimensional Materials, ed.J. S. Miller and A. J. Epstein (The New York Academy of Sciences, 1978) and references therein. D. Layek and G. C. Papavassiliou, 2. Naturforsch., Teil B, 1981, 36, 83; G. C. Papavassiliou and D. Layek, 2.Naturforsch., Teil B, 1980, 35, 676 A. V. Babaeva and E. Ya. Khananova, Dokl. Adad. Nauk SSSR, 1964, 159, 586; G. C. Papavassiliou, to be published. G. C. Papavassiliou and C. S. Jacobsen, J. Chem. Soc., Faraday Trans. 2, 1981, 77, 191; G. C. Papavassiliou, Proc. VIIth Int. Conf. Raman Spectrosc. Ottawa, Canada, ed. W. F. Murphy (North-Holland, Amsterdam, 1980), p. 100. G. C. Papavassiliou, D. Layek and T. Theophanides, J. Raman Spectrosc., 1980, 9, 69; Can. J. Spectrosc., 1980, 25, 151. N. Matsumoto, M.Yamashita and S. Kida, Bull. Chem. Sac. Jpn, 1978, 51, 2334. ’0.Bekaroglou, H. Breer, H. Endres, H. Keller and H. N. Gung, Inorg. Chim. Acta, 1977, 21, 1836. G. C. Papavassiliou and A. D. Zdetsis, J. Chem. SOC.,Faraday Trans. 2, 1980, 76, 104. P. Day, in Low-Dimensional Cooperative Phenomena, ed. H. J. Keller (Plenum Press, New York, 1975), vol. B7, p. 191. 10 G. C. Papavassiliou, Prog. Solid State Chem., 1979 12, 185. l1 G. C.Papavassiliou, T. Theophanides and R. Rapsomanikis, J. Raman Spectrosc., 1979,8, 227. 12 A. G. Stasenko, Sou. Phys.-Solid State, 1968, 10, 186. 13 C. R. Berry, Phys. Reu., 1967, 153,989; 1967,161, 848. 14 G. C. Papavassiliou, J. Solid State Chem., 1981, in press. l5 A. J. Poe, J. Chem. Soc., 1963; W. R. Mason, Inorg.Chem., 1973, 12, 20. 16 M. Yamashita, N. Matsumoto and S. Kida, Inorg. Chim. Acta, 1978, 31, L381. 17 P. F. Williams, M. A. Butler, D. L. Rousseau and A. N. Bloch, Phys. Reu. B, 1974, 10, 1109. l8 H.R. Zeller and P. Bruesch, Phys. Status Solidi B, 1974, 65, 537. 19 D. Kuse, Solid State Commun., 1973, 13, 885. 20 G. C. Papavassiliou, J. Phys. C, 1977, 10, 489. 26 ELECTRONIC SPECTRA OF METAL-HALIDE CHAINS 21 J. J. Hopfield, Phys. Rev. A, 1965,139, 419. 22 E. G. Wilson and S. A. Rice, Phys. Rev., 1966, 145, 55. 23 S.Yamada and R. Tsuchida, Bull. Chem. SOC.Jpn, 1956,29, 894. 24 L. V. Interante, K. W. Browall and F. P. Bundy, Inorg. Chem., 1974,13, 1158. 25 R. J. H. Clark, M. L. Franks and W. R. Trumble, Chem. Phys. Lett., 1976,41, 287.26 R. J. H. Clark and M. L. Franks, J. Chem. SOC.,Dalton Trans., 1977, 198. 21 J. R. Campbell, R. J. H. Clark and P. C. Turtle, Inorg. Chem., 1978, 17, 3622; R. J. H. Clark and P. C. Turtle, Inorg. Chem., 1978, 17, 2526. 28 R. J. H. Clark and M. Kurmoo, Inorg. Chem., 1980,19, 2523. 29 M. Albin and H. Patterson, Chem. Phys. Lett., 1980,73, 451. 30 H. Endres, H. J. Keller, R. Martin and U. Traeger, Acta Crystallogr., Sect. B, 198, 36, 35. 31 R. J. H. Clark, M. Kurmoo, H. J. Keller, B. Keppler and U. Traeger, J. Chem. SOC.,Dalton Trans., 1980, 2498; R. J. H. Clark and M. Kurmoo, J. Chem. Soc., Dalton Trans., 1981, 524. 32 N. Ohta, M. Kozuka, K. Nakamoto, M. Yamashita and S. Kida, Chem. Lett., 1978, 843. 33 R. J. H. Clark, in Mixed-Valence Compounds, ed. D. B. Brown (D. Reidel, Dordrecht, 1980), vol. C58, p. 271. 34 R. J. H. Clark, in Synthesis and Properties of Low-Dimensional Materials ed. J. S. Miller and A. J. Epstein (The New York Academy of Sciences, 1978),vol. 313, p. 672. 35 G. C. Papavassiliou and T. Theophanides, J. Raman Spectrosc., 1978,7, 230. 36 Mixed-Valence Compounds, ed. D. B. Brown (D. Reidel, Dordrecht, 1980), vol. C58, pp. 1-519. 37 G. C. Papavassiliou, unpublished results. 38 F. Mehran and B. A. Scott, Phys. Rev. Lett., 1973, 31, 99.

ISSN:0300-9238    

DOI:10.1039/F29827800017

出版商:RSC    

年代:1982

数据来源: RSC

摘要:

J. Chem. SOC.,Faraday Trans. 2, 1982,78,27-37 Photophysics of 4a,5,10,15-Tetra-azabenzo[a]naphth-[1,2,3de]anthracene (NTCQ, the Ring-nitrogen Isostere of Tricycloquinazoline) BY ROBERTB. CUNDALL,~ DAVIDJ. W. GRANT$ AND NORMANH. SHULMAN~ Departments of Pharmacy and Chemistry, University of Nottingham, Nottingham NG7 2RD Received 27 th March, 1981 The absorption spectra and the fluorescence and phosphorescence spectra, polarization, quantum yields and lifetimes of the ring-nitrogen isostere of tricycloquinazoline (NTCQ) have been investigated over a range of solvents and temperatures. The properties of the lower energy excited states and of the ground state of NTCQ are discussed in terms of the above data. S1 is n, T* and transforms with A", whereas S2 is T,T* and transforms with A'.Vibronic coupling occurs through arrperturbing vibrations. With increasing polarity, dielectric constant and viscosity of the solvent the S1 state undergoes an increasing blue-shift and becomes quasi-degenerate with S2, presumably on account of a pseudo-Jahn- Teller coupling. The ring-nitrogen isostere of tricycloquinazoline (4a,5,10,15 -tetra-azabenzo- [a]naphth[l,2 3-delanthracene; NTCQ) is a potent carcinogen when applied to the skin of mice.1' NTCQ possesses 89% of the carcinogenic activity of the parent compound tricycloquinazoline (TCQ). NTCQ TCQ The potent biological effects have prompted structure-activity studies,lP5 investi- gations into the physicochemical properties of the molecules6-8 and related theoreti- cal By analogy with TCQ,6 the isostere, NTCQ, is probably planar. Carcinogenesis may arise from intercalation of the molecule between adjacent base iPresent address: Department of Biochemistry, University of Salford, Salford M5 4WT.$ Present address: Faculty of Pharmacy, University of Toronto, Toronto, Ontario MSS 1A1, Canada. § Present address: Department of Pharmacy, Stobhill General Hospital, Glasgow G21 3UW. 27 PHOTOPHYSICS OF THE RING-NISOSTERE OF TCQ pairs of DNA,'-'' but whatever the nature of the interaction, electronic excitation may be involved and so knowledge of the properties of the excited states may further an understanding of biological activity. The three peripheral N-atoms of NTCQ are pyridine-like, with unhybridised p-orbital electron pairs contributing to the aromatic delocalised IT-electrons. Elec- trons of a sp2 orbital act as a non-bonded pair in which most of the charge is directed away from the ring.The bridgehead N-atom of NTCQ is pyrrole-like with its three sp2 hybrid orbitals forming a-bonds and with an electron pair in an unhybridised p-orbital contributing to the aromatic delocalised T-electrons. Con- sequently, this N-atom gives rise to IT* +IT but not to T* +n transitions. The electronic asymmetry of NTCQ confers polarity on the molecule. For excited states and for the S1 state a change in the electronic charge distribution results in a change in dipole moment and the spectral properties are therefore sensitive to the dielectric constant and viscosity of the solvent.l2 EXPERIMENTAL MATERIALS NTCQ' was kindly supplied by Dr H. J. Vipond and was purified by vacuum sublimation in subdued light. The high purity of the samples was shown by t.1.c. using 0.5 mm layers of silica gel G (Merck) and by the invariance of fluorescence emission and excitation spectra at a number of different excitation and emission wavelengths. Other materials and solvents were obtained and purified as previously de~cribed.'~ TECHNIQUES Fluorescence and phosphorescence spectra were obtained with a corrected instrument based upon the design reported by Cundall and Evans.14 Fluorescence lifetimes were measured by the single photon counting pulse technique and data processed by an iterative convolution method.The viscosities of glycerol +ethanol mixtures were determined by means of a suspended level U-tube viscometer at 25 f0.1 "C. RESULTS ABSORPTION SPECTRA Room-temperature absorption spectra of NTCQ in methylcyclohexane, ethanol and toluene are shown in fig. l(a). In toluene, as the temperature was increased from 297 to 369 K, absorption decreased at the absorption maxima but increased at the long-wavelength edge (>500 nm; <20 000 cm-'). EXCITATION SPECTRA The fluorescence excitation spectra in methylcyclohexane, ethanol or toluene were the same as the corresponding absorption spectra [fig. l(a)]. In carbon tetrachloride there was a sharper resolution of the vibrational structure and a red-shift of ca. 650cm-I compared with that in chloroform the first long- wavelength peak being at 19 900 cm-l (CC4) and at 20 600 crn-' (CHCl3).In the room-temperature excitation spectra no peak shifts were observed on increasing the viscosity of the alcoholic solutions of NTCQ by addition of glycerol (0-80% v/v). R. €3. CUNDALL, D. J. W. GRANT AND N. H. SHULMAN wavenumber/103 cm-’ I-D wavenumber/103 cm-’ m c wavenumber/103 cm-’ FIG. 1.-(a) Absorption spectra of 4a,5,10,15-tetra-azabenzo[a]naphth[1,2,3-&]anthracene (NTCQ) (-) at room temperature in methylcyclohexane (E =2.020); (---a) toluene (E = 2.379); (----) ethanol (E =(-) temperature in at room NTCQofFluorescence emission spectra (b)24.55). methylcyclohexane (E =2.020); (--*) toluene (E = 2.379); (----) ethanol (E = 24.55). (Excitation wavelength = 426.0 nm = 23 474 cm-’; emission band pass = 6.6 nm, slit width = 2.00 mm.) (c) Fluores-(-) at room temperature in NTCQofcence emission spectra (-* -* ) chloroform (E =4.806); (----) acetonitrile (E = 37.5). (Excitation wavelength = 23 474 cm-’; emission band pass = 6.6 nm, slit width = 2.00 mm.) carbon tetrachloride (E = 2.238);426.0 nm = PHOTOPHYSICS OF THE RING-NISOSTERE OF TCQ The phosphorescence excitation spectra in EPA at 77 K were exactly superim- posable on the fluorescence excitation spectra.FLUORESCENCE EMISSION SPECTRA Room-temperature fluorescence spectra are shown in fig. l(b) and (c). The room-temperature emission of NTCQ in toluene [fig. 1(b)] was independent of concentration up to mol dm-3.On decreasing the temperature the fluorescence emission spectrum in toluene became more intense but no frequency shifts were observed (fig. 2). In EPA solvent decreasing the temperature through the glass (-1 wavenumber/ lo3cm-' FIG. 2.-Influence of temperature on the fluorescence emission spectrum of NTCQ in toluene at -a299, (----) 320, (. -.) 340 and (-. ) 370 K. (Excitation wavelength =425.8 nm= 23 485 cm-'; emission band pass =6.6 nm, slit width = 2.00 mm.) transition temperature (ca. 150 K) brought about a pronounced blue-shift as shown in fig. 3(a)and (6). In glycerol+ethanol mixtures at room temperature, increasing proportions of glycerol, which cause a progressive increase in viscosity, also gave rise to a blue-shift in the fluorescence emission spectra shown in fig.4. PHOSPHORESCENCE EMISSION SPECTRA Fig. 5 presents the phosphorescence emission spectrum of NTCQ in EPA and in a 10%(v/v) solution of ethyl bromide in EPA. At 77 K the ratio phosphorescence quantum yield/fluorescence quantum yield (&T/&M), for NTCQ in EPA was ca. 0.003 and that in a 10% (v/v) solution of ethyl bromide in EPA was ca. 0.005, the phosphorescence lifetime, rT,in the latter solvent mixture being 200-219 ms. The phosphorescence of NTCQ in EPA itself at 77 K was, however, too weak to allow TT to be estimated. R. B. CUNDALL, D. J. W. GRANT AND N. H. SHULMAN At? c wavenumber/103 cm-' 22 20 18 16 14 wavenumber/ lo3cm-' FIG.3.4~)Influence of temperature on the fluorescence emission spectrum of NTCQ in EPA at (-)(a287, (----1 223, * * .) 160 and (--) 135 K. (Excitation wavelength =416.7nm = 23 998 cm-'; emission band pass = 6.6nm, slit width = 2.00 nm; sensitivity x 0.75at 135 K.) (b) Influence (-) in EPA at NTCQoftemperature on the fluorescence emission spectrum of 135 (sensitivityx 0.75), (---) 100 (sensitivity x 0.35),(a . .) 80 (sensitivity x 0.35) and (-9 -) 77 K. (Excitation wavelength =420.0 nm = 23 810cK'; emission band pass =6.6nm, slit width = 2.00mm.) FLUORESCENCE QUANTUM YIELDS AND FLUORESCENCE LIFETIMES Table 1 gives the room-temperature fluorescence quantum yields, &M, and corresponding fluorescence lifetimes, rM,of NTCQ for a variety of solvents and temperatures.&M decreases with increasing temperature and with increasing dielectric constant of the solvent. Table 2 shows data at room temperature in glycerol +ethanol mixtures of increasing viscosity. &M and rMincrease with increas- ing viscosity of the solvent. PHOTOPHYSICS OF THE RING-NISOSTERE OF TCQ r 22 20 18 16 14 wavenumber/ 1O3 cm-' FIG. 4.-Fluorescence emission spectra of NTCQ at room temperature in solutions of glycerol in (-) v/v):(YOethanol wavelength = 420.0 nm = 0, (----) 20, (------) 40, (. .... . . .) 60 and (-.---* -a) 80. (Excitation 23 810 cm-'; emission band pass = 6.6 nm, slit width = 2.00 mm; sensitivity not maintained constant.) 20 18 16 14 wavenumber/ 1 O3 cm FIG.5.-Phosphorescence(-) inK77atNTCQofemission spectra EPA (emission band pass = 13.2 nm, slit width=4.00mm) and (---) 10% (v/v) ethyl bromide in EPA (emission band pass= 9.9 rim, slit width = 3.00 mm).Excitation wavelength = 420.0 nm = 23 810 cm-'. POLARIZATION OF FLUORESCENCE OF NCTQ IN EPA AT 77 K Fig. 6(a) shows two corrected polarization of fluorescence excitation spectra emitting at 515.4 and 535.0 nm (19 402 and 18692 cm-I). Fig. 6(b)presents two corrected polarization of fluorescence emission spectra obtained by excitation at 400 and 450 nm (25 000 and 22 222 cm-'). R. B. CUNDALL, D. J. W. GRANT AND N. H. SHULMAN 33 TABLE1.-INFLUENCE OF SOLVENT AND TEMPERATURE, T, ON FLUORESCENCE QUANTUM YIELDS, ~FM,AND FLUORESCENCE LIFETIMES, TM, OF NTCQ solvent Fa T/K 4FM Lic/nmb rM/nsc met hylcyclohexane 2.02 298 0.035 425.5 = 23 502 cm-' -d ethanol 24.6 298 0.016 426.0 = 23 474 cm-' 1.18,1.30 toluene 2.38 298 0.031 426.0 1.91 340 0.024 426.0 1.31 370 0.020 426.0 1.35 d-acetonitrile 37.5 298 0.0 13 426.0 -dchloroform 4.81 298 0.029 426.0 -dcarbon tetrachloride 2.24 298 0.039 426.0 EPA 298 0.019 426.0 1.68 -d160 0.041 426.0 77 0.124 426.0 8.0 ~ ~ ~~ ~~ a Dielectric constant at 20 OC.13 'Excitation wavelength for 4FMmeasurements.Excita-tion wavelength was 380.0 nm ( = 26 316 cm-') for all T~ measurements. Data would not successfully convolute. TABLE 2.-FLUORESCENCE QUANTUM YIELDS, &M, FLUORESCENCE LIFETIMES TM, RELAXATION TIMES, TD, AND CENTRES OF GRAVITY OF FLUORESCENCE, Fcg, OF NTCQ IN GLYCEROL +ETHANOL MIXTURES AT ROOM TEMPERATURE '/o (v/v) mole glycerol fraction [NTCQ]/ in ethanol glycerol Fmol dm-3 4FMaTM/nSb TD/nsc T/mN s m-2d fi,,/cm-le 0 0 3.0 0.016 1.30 0.011 0.1 17 300 20 0.333 5.0 0.018 1.31 0.41 4.1 17 300 40 0.571 5.5 0.022 2.24 1.36 13.6 17500 60 0.750 5.5 0.027 2.67 5.06 50.6 17 5004 80 0.889 3.1 0.042 4.63 19.3 196 18 700 a Excitation wavelength was 426.0 nm (23 474 cm-I).Excitation wavelength was 380.0 nm (26 316 cm-'). 7D = 4'rrqa3/kT. Temperature, 25 "C. Fcg = fiF(V)dV//lF(fi) dV. DISCUSSION ABSORPTION AND FLUORESCENCE EXCITATION SPECTRA The peak at 19 850 cm-' in methylcyclohexane [fig. l(a)] is considered to correspond to the So-o transition, since this overlaps the So-o fluorescence peak at ca.19 560 cm-' [fig. l(b)].For methylcyclohexane ASO-0 = (Eg;:,-E!o-o) is ca. 290cm-'. In view of the fact that there is a blue-shift, accompanied by blurring of vibrational structure, as the dielectric constant of the solvent is increased [fig. l(a), (b) and (c)], the S1 state is considered to be n, T* in nature. The blue-shifts in toluene as compared with methylcyclohexane [fig. l(a) and (b)]probably arise from strong dispersion interactions between the aromatic T-electrons of the solvent and those of the solute. 20 24 28 32 36 wavenumber/ lo3cm-' 100 h5 80 (dc cd cr Y2 60 .I L.l CI cd 0. x 0a 240 e,-0.05. .IU-20 2-0.10 , I, 0 wavenumber/103 cm-' FIG.6.-(a) Polarization of fluorescence excitation spectrum of NTCQ in EPA at 77 K with a band pass of 9.9 nm (slit width = and (-0 -) 535.0 nm = 18692 cm 3.00 nm) and an excitation wavelength of: (-0-) (b)K.Absorption spectrum of NTCQ in EPA at 87 (-) '. 515.4 nm = 19 402 cm-' Polarization of fluorescence emission spectrum of NTCQ in EPA at 77 K with a band pass of 9.9 nm (slit width = 3.00 mm) and an excitation wavelength of: (-0-) 400.0 nm = 25 000 cm-' and (-0-) 450.0 nm = 22 222 cm-'.(-)Fluorescence emission spectrum of NTCQ in EPA at 77 K at an excitation wavelength of 420.0 nm (=23 810crn-') and with an emission band pass of 3.3 nm, (slit width = 1.00 nm). With increasing dielectric constant of the solvent the blue-shifts in the absorption spectrum [fig.l(a)]and slight shifts in the fluorescence spectrum [fig. l(b) and (c)] can be rationalised in terms of the Franck-Condon orientation and solvation energies. If, as is assumed, the S1state is n, T*,then p(So)>p(S1), where p is the dipole moment due to a reduction in localized charge density of the N atom on R. B. CUNDALL, D. J. W. GRANT AND N. H. SHULMAN excitation to a delocalised n* orbital. Values of Ap = [p(So)-p(S1)]can be evalu- ated using the Lippert eq~ation’~ where It is the refractive index of the solvent, E is the dielectric constant of the solvent and a is the Onsager radius, viz. the radius of the spherical cavity occupied by the solute molecule. The value of a for NTCQ was estimated to be 320pm from molecular models and hence Ap =4.02 D for this solute in ethanol and 4.52 D in a~etonitrile.’~ These values, though approximate, are sufficiently large to account for the solvent effects on the spectra.For non-polar solvents dipole- polarization interactions are the main contributions to solvation energy. For polar solvents dipole-dipole forces will be most effective. As the dielectric constant of the solvent increases, the energy difference between the Franck-Condon and the solvent-relaxed states of the SOand S1 states increases. Considerable overlap of the Sz +-So(and possibly S, tSo) and S1 tSotransi-tions in the absorption spectra of NTCQ is indicated by (a)a poor “mirror image relationship” between the absorption and fluorescence spectra [fig.1(a)and (b)], (b) integration of the absorption spectrum in toluene at 298 K [fig. l(a)] between 19400 and 28400cm-’ and insertion into the equation of Birks and Dyson,16 which gives a theoretical value for the fluorescence lifetime of 9.911s which is approximately one-sixth of the experimental value (?M/&M) of 61.6ns (table 2), and (c) the polarisation of fluorescence excitation spectrum in EPA at 77 K [fig. 6(a)] which exhibits a rapid decrease from between 21 000 and 26 000 cm-’. FLUORESCENCE EMISSION The significant decrease in fluorescence emission with increasing solvent polarity [fig. l(b) and (c)]could arise from an increase in non-radiative processes arising from quasi-degeneracy of Sl(n,n*)and S2(n, n*)states of NTCQ in solvents of high dielectric constant, resulting in a pseudo-Jahn-Teller effect.This occurs in other N-heterocyclic molecules, such as quinoline and isoquinoline” in which the S1(n, n*) and Sz(n, n*) states are in close proximity and for which the energy difference AE(S1 -S2)decreases with increasing solvent polarity, thereby increasing the pseudo-Jahn-Teller effect. The broadening of the potential energy surface of the S1 state reduces the barrier width between the S1and Sostates and increases the probability of intersystem crossing. In the case of NTCQ there is an increase in energy of Sl(n,n*)and a decrease in energy of S2(r,n*)as the dielectric constant of the solvent increases. The resulting decrease in energy separation between S1 and S2increases the vibronic coupling between these states.In the limit the potential energy surface of the S1 state effectively broadens thereby reducing the “barrier width” between the potential energy surfaces of the S1and So states. The rate of the non-radiative process from S1 increases and therefore 4FMdecreases with increasing dielectric constant of the solvent (table 1). The loss of vibrational structure of the fluorescence emission with increasing dielective constant of the solvent [fig. l(b) and (c)] can also be explained by vibronic coupling. The broadening of the potential energy surface means that fluorescence occurs over a wider range of nuclear conformations. PHOTOPHYSICS OF THE RING-NISOSTERE OF TCQ Blue-shifts in fluorescence emission as the solvent viscosity increases (fig.4) occur in the absence of solvent shifts in absorption. For the greatest shift [in 80 : 20 (v/v) glycerol : ethanol] the So-opeaks of the absorption and fluorescence spectra overlap indicating that fluorescence emission occurs from the SFc state to the SF state. As the viscosity is reduced emission occurs from an intermediate state between Syc and Sy to an intermediate state between S," and SEq. At low viscosities emission occurs from S? to s:". Solvent relaxation lifetimes TD can be calculated from the Debye equation TD = 4rrqa3/kT where a is the Onsager radius of the molecule, which is assumed to be spherical and q is the solvent viscosity. Despite the fact that calculated TD values are only approximate, it is seen that the blue-shift increases as TD is comparable with or greater than TM( table 2).This is in accord with the above model. Similar blue-shifts in the fluorescence emission spectra of NTCQ in EPA [fig. 3(a)and (b)], together with an associated increase in (bFM and TM (table l), are observed as the temperature is lowered through the glass transition temperature Tg(ca. 150K) of the solvent system. This is attributed to the sudden increase in viscosity as the temperature is lowered through Tg.The considerable solvent shift observed at 80 and 77 K [fig. 3(b)]is probably an experimental artifact arising from the different nature of the solvent matrix. The sample at 80 K had cooled for 12 h whilst that at 77 K was frozen within 30 s.PHOSPHORESCENCE A possible reason for the low &=T yields of NTCQ is that the non-radiative process SotSl is more probable than other processes, particularly inter-system crossing. The relatively long TT value of NTCQ is consistent with a low value of &-. THEORETICAL CONSIDERATIONS All the rr-electron m.0. of NTCQ belong to the A" representation of C,. Hence all rr, rr* states as well as the Sostate belong to the fully symmetric representation, A'. The S1 state is n, rr* and the n-orbital has A' symmetry. The electronic symmetry of the molecule in an n, rr* state is A" and since A" transforms as M,, all the T*trz transitions in NTCQ are symmetry allowed. By assuming that the S2state is rr, rr*, the rapidly decreasing P values in fluorescence excitation [fig.6(a)] within the first 5000 cm-' starting from the So-0 band can be explained by overlap of the vibronic transitions to S1 and Sz, the electric dipole moment, me,of each state having its components positioned perpendicular to each other (i.e.M, for S1 and M,, Myfor S,). The small fluctuations in the polarisation excitation spectrum [fig. 6(a)]at ca. 22 500,23 500 and 24 500 cm-' may be due to a vibronic coupling process between the S1and S2 state through an a" perturbing vibrational mode. Further evidence of such a vibrational coupling is the oscillating nature of the polarisation of the fluorescence emission spectra of NTCQ in EPA at 77 K [fig. 6(b)]. The oscillations probably arise from vibronic transitions from S1uo to asymmetric vibronic a" vibrational modes of So.The energy of the first rr* err transition derived from h.m.0. analysis" is ca. 20000cm-l, which is almost concident with that of the observed So-0 ab-sorption band (rr* tn transition) in non-polar solvents {ca. 19 900 cm-l in R. B. CUNDALL, D. J. W. GRANT AND N. H. SHULMAN 37 methylcyclohexane [fig. l(a)]}. The analysis explains the existence of the postulated strong vibronic coupling between the S1 and S2 states, since such a process is favoured by a close energy proximity between the two states possessing different electronic symmetry properties. In a later paper18 the photophysics of the related compound, TCQ, are discussed and compared with those of NTCQ. We thank Dr.Frank Palmer for advice with the measurement of fluorescent lifetimes, Dr. Hilton Vipond for kindly supplying a sample of NTCQ and the S.R.C. and Mr. I. Sclor of the Isaac Sclor Scholarship Fund for a grant to N.H.S. M. W. Partridge, J. M. Sprake and H. J. Vipond, J. Chem. SOC. C, 1966,497. R. W. Baldwin, G. C. Cunningham and M. W. Partridge, Br. J. Cancer, 1959, 13, 94. R. W. Baldwin, G. C. Cunningham, M. W. Partridge and H. J. Vipond, Br. J. Cancer, 1962, 16, 276. R. T. Parfitt, M. W. Partridge and H. J. Vipond, J. Chem. SOC., 1963, 3062. D. J. Brunswick, M. W. Partridge and H. J. Vipond, J. Chem. SOC. C, 1970, 2641. J. Iball and W. D. S. Motherwall, Acta Crystullogr., Sect B, 1969, 25, 882.'M. L. Bailey, J. P. M. Bailey and C. A. Coulson, Acta Crystallogr., Sect. B, 1970, 26, 1622.C. Nagata, M. Kodoma and A. Imamura, Gann, 1966,57,75. G. G. Hall, G. Gangfield and W. R. Rodwell, Int. J. Quantum. Chem., Symp., 1969, 3, 237. lo G. G. Hall and W. R. Rodwell, J. Theor. Biol., 1975, 50, 107. 11 R. W. Baldwin, H. C. Palmer and M. W. Partridge, Br. J. Cancer, 1962, 16, 740. 12 G. C. Pimintel, J. Am. Chem. SOC.,1957,79, 3323. 13 J. A. Riddick and W. B. Bunger, Organic Solvents (Wiley-Interscience, London, 3rd edn, 1970).14 R. B. Cundall and G. B. Evans, J. Phys. E, 1968,1, 305. 15 see J. B. Birks, Photophysics of Aromatic Molecules (Wiley-Interscience, London, 1970).16 J. B. Birksand D. J. Dyson, Proc. R. SOC.London, Ser. A, 1963 275, 135. 17 R. Li and E. C. Lim, J. Chem. Phys., 1972,57,605.18 R. B. Cundall, D. J. W. Grant and N. S. Shulman, J. Chem. SOC.,Faraday Trans. 2, in press. (PAPER 1/497)

ISSN:0300-9238    

DOI:10.1039/F29827800027

出版商:RSC    

年代:1982

数据来源: RSC

摘要:

J. Chem. SOC.,Faraday Trans. 2,1982, 78, 39-50 Theoretical Kinetic Analysis of Biphotonic Processes Evidence for the Unusual but Feasible Occurrence of Multi-stationary States and Chemical Oscillations BY JEAN-CLAUDE MICHEAU, STBPHANE BouB" AND EMILEVANDER DONCKT" Collectif de Chimie Organique Physique, UniversitC Libre de Bruxelles, 50, avenue F. D. Roosevelt, B-1050 Bruxelles, Belgium Received 22nd April, 1981 A simple kinetic scheme involving the successive absorption of two photons has been completely analysed and the solutions have been numerically computed within a wide range of parameter values. It is found that, aside from the classical monotonic behaviour described in many textbooks, a system can, under appropriate conditions, respond to photoexcitation in a number of unusual ways.In particular, for a given system and a single set of conditions more than one steady state can be achieved, not all of them being stable, and this results in the existence of critical light intensities around which the system behaves like a chemical amplifier or threshold discriminator. It is also shown by time-dependent analysis that the concentration in some species can be subject to overshoot or to damped oscillations before reaching its stationary value. Although a few experimental cases have been reported, such unusual phenomena have not been widely recognized in photochemistry, and it seems plausible that their possible occurrence in laboratories might have been overlooked or disregarded as being due to artefacts.The aim of this paper is to draw the attention of photochemists to the physical meaning of such unusual observations. The photoionization of many aromatic molecules in glassy solvents (e.g. boric acid or frozen organic solvents) is known1,* to be a biphotonic reaction whose rate is thus proportional to the squared intensity of light under weak irradiation condi- tions. Double excitation in flash photolysi~,~~~ triplet-triplet annihilation5 and photosynthesis whose trigger step involves the successive absorption of two "red" photons6 stand as important examples which pertain to the class of biphotonic events. Such biphotonic processes are also required in efficient solar-energy storage by water splitting into oxygen and hydr~gen.~ The present paper aims at a compre- hensive theoretical re-examination of the major kinetic features which can arise from the successive absorption of two photons.For the sake of simplicity we will restrict our analysis to the following previously described' simple scheme : IS so ---b s1 kfs1 -so ks, S1 T k, So T 2[A++e-] kr [A++e-] --+So where So, S1 and T have their usual meaning. 39 KINETIC ANAL-YSIS OF BIPHOTONIC PROCESSES We will derive the general relationship which correlates the steady-state con- centration of A' with the incoming light intensity (A' and e- are assumed to be trapped within a cage so that recombination appears to be a unimolecular process). Our treatment will rely on the classical expressions (1)-(3): = kSTISl]-kp[T]-IT= gdt d[A'l -IT-k,[A'] = h.(3)dt Is and IT are the rates of light absorption by the ground state So and the triplet state T. For a unit optical pathlength the optical density of the sample is given by C [eqn (4)1: x = ~O(~SOl0-[Sll-[TI-[A+]) +m[TI (4) where E~ and eTare the molar absorption coefficients of So and T, respectively, and [Solo is the ground-state concentration before irradiation. Eqn (5) and (6)are directly derived from Beer's law, with I0 being the total incoming light intensity: RESULTS AND DISCUSSION STEADY-STATE ANALYSIS Under steady-state conditions one has d[S11----d[TI -dCA+l-0-dt dt dt and we now look for an explicit dependence of [A'] on lo,i.e. of eqn (7b) I0=f([A'I>.(7b) Eqn (7c) is straightforward but it contains (uia C)the excited singlet and triplet concentrations which need to be expressed in terms of [A']; this leads (see Appen- dix) to eqn (7d)-(7f): with J-C. MICHEAU, S. BOUE AND E. VANDER DONCKT 41 TABLE 1.-FIXED PARAMETERS' VALUES CORRESPONDING TO THE SIGMOID CURVES A, B AND C (SEE FIG. 1) [Solo= mol dmP3; aSTis the quantum efficiency of intersystem crossing; rs, TT and rA+ are the lifetimes of S1,T and A+,respectively. 0.95 1o5 1o4 10-~ 1 10 A 0.95 1o5 1o5 1 0.1 B 0.50 10' 1o4 10-~ 1 1o3 C and and These equations have been obtained without any restrictive assumption on either I. or the rate constants and concentrations, and they are thus the generalized complete solutions describing the steady states for the scheme being studied.Eqn (76) has been solved numerically for different sets of experimental conditions (see table 1)and the corresponding plots of [A+]against I. are presented in fig. 1. quanta s-' FIG. 1.-Computed sigmoid curves (A, B and C) corresponding to the numerical values given in table 1. KINETIC ANALYSIS OF BIPHOTONIC PROCESSES Let us now discuss the three relevant cases corresponding to the curves shown in fig. 1. In the experimental conditions corresponding to curve A the response of the system to irradiation is quadratic at low light intensities (see table 2), becomes almost linear with an inflexion point at medium intensities and then exhibits progressive saturation corresponding to the ground-state depletion at high intensity.TABLE2.-EVIDENCE FOR THE PARABOLIC FITTING OF CURVE A AT LOW I0 VALUES, SHOWN BY THE QUASI-INVARIABILITY OF THE TERM [A']/[So]oI: EA+I/~Solo(O/O 1 1~/10'~ quanta s-' 1;/10~~(quanta S-~)~ CA+I/[SoloG/(quanta-2 s2) 1 0.57 0.32 3.13 2 0.80 0.64 3.13 3 0.98 0.96 3.14 4 1.13 1.27 3.16 5 1.25 1.56 3.20 10 1.68 2.82 3.55 The case of curve B is the usual and most common one, but even though it describes a truly biphotonic process the parabolic curvature is weak and the function departs only slightly from linearity. The actual concavity, however, shows up when using the Lashish test3 and this case deserves no further comment. The third case (curve C) is a most intriguing one.When the lifetime of the species produced by absorption of the second photon (A' in this scheme) becomes long enough, the slope d[A']/dIo reverses twice and the system can exist in three different stationary states; this implies the possibility of observing non-continuous transitions between states as well as hysteresis phenomena. To our knowledge only one experimental case of bistability has thus far been reported in photochemistry, namelyg the gas-phase photoinduced equilibrium N204 $2N02, but such unusual behaviour has been theoretically predicted for thermochemical systems.lo An interesting consequence of photochemical hysteresis resides in the existence of critical light intensities around which small variations SIodramatically and abruptly affect the response of the system.This is best visualized in fig. 2, which schematically reproduces curve C. The behaviour of the system can be described as follows: if initially [At]=O, a light beam of intensity lo(Cl)-SIo will lead to the stationary state El but a slight increase up to Io(Cl)+610will abruptly drive the system to E2. If I0 is then progressively reduced, [A'] moves along the sigmoid, passing through F1,until it reaches the second critical value lo(C2) whereafter [at Io(C2) -6103 a sudden decay to F2 takes place; resuming the initial intensity Io(C1)-SIo will restore the E1 concentration, the system having thus completed a full hysteresis loop. It is of more than passing interest to note that such a system behaves like an amplifier or threshold discriminator in the sense that a small perturbation SIO strongly affects the stationary composition, and this is strikingly emphasized in fig.3, which describes the time-dependent build-up of A+, obtained by numerical integration of eqn (1)-(3) using the Runge-Kutta procedure. A small relative perturbation SIo/Io==0.002 induces the jump from El to E2, and we found that {[A'](E2) -[A'](E1)}/[At](E1) = 0.7; this corresponds to an amplification ratio (S[A']/[A'])/(Sro/lD> of ca. 350. J-C. MICHEAU, S. BOUE AND E. VANDER DONCKT-€2 t-6 U 0 I, (c, ) FIG. 2.-Schematic amplified presentation of curve C (from fig. 1) displaying two critical intensities lo(C1)and Io(C,) and hysteresis.gO1 h 0 n v)U 1 6 U +-0 3 x 6 x~O-~ time/s FIG. 3.-Time-dependent behaviour of a biophotonic system on either side of the critical light intensity 0.5; T~= s;TT= s; TA+= s; I. =lo(Cl);assumed conditions: e0 = lo4;ET = lo4;as== 1.41x quanta s-'; 61, = 3 x10'~quanta s-'. KINETIC ANALYSIS OF BIPHOTONIC PROCESSES STABILITY OF THE STEADY STATES The recognized occurrence of tristationarity raises the question of the stability of the steady states: do the three states exist as stable systems? This problem has been investigated by linear stability analysis," which basically consists of applying a small perturbation to the steady concentrations of S1,T and A' and seeing if the system thereafter tends to move apart from or return to its initial composition; this procedure being applied to each of the three steady states yields useful information on the stability of the original non-linear system.Since the perturbations S[S,], S[T] and S[A+]whose time-dependence will be studied are kept small, higher-order terms can be neglected and one ends up with the following set of linear differential equations: d dt [-;;J=M where M is the 3 X 3 Jacobian matrix related to the steady-state conditions and explicitly given by cf, g and h have been previously defined by eqn (l), (2)and (3)] ah a[Tl &/ The general solutions to these linear equations are given by eqn (10)-(12) where the subscript 0 indicates the initial perturbation amplitude at time zero: a[&] = 8[Sll0 emf (10) S [TI = S [TIoemf (11) S [A'] = S [A+]0emf.(12) Substituting these values into eqn (8)leads to eqn (13),whose non-trivial solutions require that the secular determinant vanishes: = 0. Expansion of this determinant yields a polynomial equation in o3which has three roots, ol,02 and 03. Depending on the experimental conditions and on the mechanism of the photochemical process, four distinctly different types of behaviour can a priori be encountered. (a)0real and <0: there is a monotonic decay of the initial perturbation and the system gets back to the composition which precedes the perturbation: this is the classical most common case. (b)0real and >O: there J-C. MICHEAU, S. BOUE AND E.VANDER DONCKT is instability; the initial small perturbation spontaneously amplifies itself and drives the system to new different stable conditions. (c) w complex with its real part <O: the concentration oscillates in a damped mode and returns to its stable stationary- state value. (d)w complex with its real part >O: here again there is instability but in this case the system moves and keeps apart from the initial situation and the concentration obeys sustained oscillations. Within the framework of the biphotonic process studied in this paper, only cases (a)-(c)can be encountered, depending on the numerical figures taken for the kinetic parameters. Cases (6) and (c) have been analysed in detail by numerical integration of eqn (1)-(3), and the data presented hereafter show that the condition w real and >O induces bistability, whereas w complex with its real part <O leads to damped oscillations. PHOTOCHEMICAL BISTABILITY IN TRISTATIONARY CONDITIONS The time-dependent variation of [A'] under conditions of photochemical hyster- esis is shown in fig.4 and turns out to depend critically on the starting conditions. (From the experimental viewpoint any desired initial percentage [A']/[S& could be obtained, e.g. by superimposing on I0 a light flash of appropriate intensity and duration.) t timefs FIG.4.-Com uted bistability displayed by the biphotonic process under investigation; assumed condi- Ts=10-7s; 71.=10-'s; 7~+=10-4S; 1,=1.39~1~quanta tions: co=lO{ FT=104; aST=0.5; s-1; the unstable steady state 6' in these conditions lies at [A']/[So] = 0.65.Around 6' the response of the system varies a great deal according to whether [A'] lies just above or below the critical concentration. If initially [A'] = 6' +S[A+] the system will drift towards the stable steady state c', whereas the initial condition [A'] = b'-6[A'] will result in reaching the second stable steady state a'. OCCURRENCE OF CHEMICAL OSCILLATIONS Oscillations are expected to take place whenever the imaginary part of w differs from zero. For the biphotonic scheme studied here only damped oscillations can KINETIC ANALYSIS OF BIPHOTONIC PROCESSES FIG.5.-Photochemically induced damped oscillations of the excited singlet concentration; assumed TT=~x~O-~S; I~=3.6X1O2*conditions: ~g=500;~T=500; @sT=O.99; TS=~O-~S; TA+=~X10-9~; quanta s-'. be anticipated, for the eigenvalues of o always correspond to a negative real part.The oscillating concentration of the excited singlet state shown in fig. 5 arises from the numerical integration of eqn (1)-(3),using appropriate values of the parameters. The physical origin of these oscillations can be understood in the following way; when the light beam is turned on there is a rapid growth of S1 which first parallels the ground-state depletion. Then triplet molecules are generated which compete with So for absorbing light and are meanwhile photoionized into pairs (A++e-); these pairs with a finite lifetime constitute a potential reservoir of So through recombination and induce ground-state feedback.The amplitude of the feedback process decreases with time, leading to damped oscillations. SIDE-EFFECT OF THE TIME-DEPENDENT BEHAVIOUR: THE OVERSHOOT PHENOMENON The biphotonic scheme which we have analysed displays one more interesting feature characterizing the triplet behaviour : the time-dependent numerical integra- J-C. MICHEAU, S. BOUE AND E. VANDER DONCKT tion of eqn (1)-(3) performed with appropriate values of the parameters leads to an overshoot; i.e. once the light is turned on the triplet concentration first reaches a maximum and then monotonically reduces to its equilibrium value (see fig. 6). This illustrates that going across a maximum, as in the case of S1(see fig.S), does not necessarily imply an oscillating response thereafter. 0-I I *I 0.15 1 2 time/ s FIG.6.-Occurrence of a tri let concentration overshoot followed by monotonic deca to ground state. TS= S; TT= S; TA+= lO-'S; Io= 1.9x lo2'assumed conditions: EO= 10 ;ET= lo3;@s~=0.05; quanta s-The appearance of a concentration overshoot is due to a rapid triplet buildup followed by its rather slow subsequent photoionization. Such a phenomenon has been experimentally observed by Joussot-Dubien and Lesclaux2 in the photomag- netic monitoring of the concentration of triplet aromatics in boric-acid glass. In contrast to S1 and T, A' obeys only a classical monotonic growth when light is turned on. As the light beam is turned off all three species (S1,T and A') decay exponentially in the usual way.COMMENTS AND CONCLUSIONS From the detailed kinetic study (steady-state and time-dependent behaviour) of a simple scheme involving the successive absorption of two photons it has been shown that under particular conditions such processes can feature basic but unusual properties such as bistability, critical light intensities, damped oscillations and concentration overshoot. The prerequisite (parameter values) for observing such properties experimentally has been deduced from a theoretical analysis of the kinetic scheme: maps of the parameters' space have been constructed which show that only a very restricted area in that space fulfils the necessary conditions. In particular, long-lived.triplet states and hindered charge recombination will enhance the probability of achieving the appropriate conditions; with respect to this, ordered systems such as the solid (highly viscous) state or micelles12 might offer definite advantages for monitoring kinetics as well as for protecting reactive intermediates from undesirable side-reactions. However, our analysis also points to the fact that even in studies of classical photochemistry and photobiology any unusual observa- tions should first be carefully examined before being rejected as artefacts. KINETIC ANAL-YSIS OF RIPHOTONIC PROCESSES In photochemistry few oscillating systems are known at present and have thus far all been discovered by chance; chemical oscillation shows up during the normal continuous irradiation of the followin sim le s stems: (i) acetone in a~etonitrile,'~ (ii) rhodamine B in dichloroethane, 18(iii) lJ-naphthyridine in cyclohe~ane~~ and (iv) 9,lO-dimethylanthracene in chloroform.l6 Also, a time-dependent colour spatial pattern is observed during the photolysis of a mixture of CC4, KI and starch in a solution of water.17 The mechanisms of these intriguing reactions are still unknown and we thus conclude that any photochemical reaction somehow removed far from equilibrium could a priori feature multistability and oscillations under appropriate (but not necessarily controlled) conditions. The preceding ideas extend beyond the academic framework when considering that photobiological phenomena such as bioenergetics or enzyme kinetics are related to this problem: we particularly allude to the oscillations of the membrane potential in the algae Hydrodictyon Reticulatum l8 during periodic irradiation. It should also be mentioned that, in an attempt to substantiate our model experimentally, the biphotonically induced thermoluminescence of fluorescein in boric-acid glass has been studied.This process, which involves the photoionization of the triplet state under continuous irradiation, is described" by a scheme basically identical to that discussed in this paper, and it has been found2' that this system indeed obeys a switching curve of type A (see fig. 1); furthermore it has been shown2' that the thermoluminescent response of a given sample depends on whether the same average light dose per unit time is delivered with constancy or in a fluctuating manner, and this represents a particular case of bistability.Also per- tinent to the present analysis are the two-photon-generated optical bistabilities recently reported in the field of semiconductors.21 Since the existence of these phenomena does not appear to have been widely reported, it seems worth emphasiz- ing once more their possible occurrence in the photochemist's everyday experiments. APPENDIX STEADY-STATE ANALYSIS The steady-state concentration [TI [eqn (7f)] is directly obtained by equating eqn (2) and (3) to zero; then [TI = (kSTIS1]- kr[A'])/kp. The stationary concentration [S,] is derived from the combination of eqn (5)and (6): wherein substitution of [TI by eqn (7f) yields eqn (15): --._~---1kr[A'] kST[S11- krLA'1 kP which can be written in the equivalent quadratic form: [S,]'-B[S,]-c = 0 where B is a previously defined parameter [see eqn (7e)l and The positive root of eqn (16) corresponds to eqn (74.J-C. MICHEAU, S. BOUE AND E. VANDER DONCKT STEADY-STATE STABILITY In order to predict the time-dependent behaviour of the biphotonic system, the eigen- values of o need to be determined. The coefficients dii of the secular determinant are obtained from the partial derivative of eqn (1)-(3) for steady-state conditions; they are presented explicitly through eqn (18)-(26): ah33 -a[*+l -d31--. 1 7A+ We thank Dr. R. Lefever and Dr. W.Horsthemke for helpful discussions. J-C.M. gratefully acknowledges a scientific and technical grant from the European Communities Committee. K. D. Cadogan and A. C. Albrecht, J. Chem. Phys., 1965,43,2550. J. Joussot-Dubien and R. Lesclaux, J. Chim. Phys., 1964, 61, 1631. U. Lashish, A. Shafferman and G. Stein, J. Chem. Phys., 1976,64, 4205. H. S. Piloff and A. C. Albrecht, J. Chem. Phys., 1968,49,4891. R. E. Merrifield, J. Chem. Phys., 1968, 48, 4318. F. K. Fong, Appl. Phys., 1975, 6, 151. M. Alrngren, Photochem. Photobiol., 1978, 27, 603. A. Charlesby and R. H. Partridge, Proc. R. SOC.London, Ser. A, 1968, 283, 329. C. L. Creel and J. Ross, J. Chem. Phys., 1976, 65, 3779. A. Nitzan and J. Ross, J. Chem. Phys. 1973, 59,241.50 KINETIC ANALYSIS OF BIPHOTONIC PROCESSES 11 G. Nicolis and I. Prigogine, Self Organization in Nonequilibrium Systems (Wiley, New York, 1977), p. 70. 12 S. A. Alkaitis, G. Beck and M. Gratzel, J. Am. Chem. SOC.,1975, 97, 5723. 13 T. L. Nemzeck and J. E. Guillet, J. Am. Chem. SOC.,1976, 98, 1032. 14 R. W. Bigelow, J. Phys. Chem., 1977, 81, 88. 15 I. Yamazaki, M. Fujita and H. Baba, Photochem. Photobiol., 1976,23,69. l6 R. J. Bose, J. Ross and M. S. Wrighton, J. Am. Chem. Soc., 1977, 99, 6119. 17 P. Mockel, Naturwissenschaften, 1977, 64, 224. 18 R. Metlicka and R. Rybova, Biochim. Biophys. Acta, 1967,135, 563. l9 W. Gibbson, G. Porter and M. Savadatti, Nature (London), 1965, 206, 1355. 20 J. C. Micheau, W. Horsthemke and R. Lefever, J. Chem. Phys., to be published. 21 (a) G. P. Agrawal and C. Flytzanis, Phys. Rev. Lett., 1980, 44, 1058; (b)S. W. Koch and H. Haug, Phys. Rev. Lett., 1981, 46, 450. (PAPER 1/647)

ISSN:0300-9238    

DOI:10.1039/F29827800039

出版商:RSC    

年代:1982

数据来源: RSC

摘要:

J. Chem. SOC.,Faraday Trans. 2,1982, 78, 51-71 Collisional Quenching of Electronically Excited Carbon Atoms, C[2p2('So)] BY DAVIDHUSAIN"AND DAVIDP. NEWTON The Department of Physical Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EP Received 13th May, 1981 Electronically excited carbon atoms in the 2p2('S0)state, 2.684 eV above the ground state, have been monitored in the time-resolved mode by resonance line absorption at A = 247.9 nm [3s('Py)c2p2('So)]following the irradiation of CC14 in the gas phase. The experimental arrangement, including low-energy repetitive pulsing on a flow system kinetically equivalent to a static system, pre-trigger photomultiplier gating, signal averaging and computerised analysis of the photoelectric decay signals, has been employed to study the removal of this optically metastable species by a range of added gases.Absolute rate data for the collisional quenching of C(2'S0) are reported for the species He, Xe, N2,Clz, CO, C02, H20, CH4, CC14,C2H2 and C3H6. The resulting second-order rate constants obtained by this technique are compared with those reported hitherto, principally from "single-shot" mode high-energy photolysis pulse experiments. Rate data for all the atomic states of carbon in the 2p2 configuration (3PJ,'Dz,'So)are discussed, where appropriate, within the context of the symmetry of the potential surfaces involved in collision on the basis of the weak spin-orbit cou ling approximation. The rate data for C[2p2('So)] are also compared with the analogous data for Si[3p 4('So)].A number of direct, kinetic investigations of the electronic states of atomic carbon arising from the overall 2p2 ground-state configuration have been reported, yielding absolute second-order rate data for the collisional removal of CQ3PJ), C(2102)176-8 and C(21S0)1'9-11 by added gases. The experimental limitations for most earlier rate measurements on the hi her 1 in of the two optically metastable 5 yg = 2.684 eV,12 XAnm=namely C[2p2(1So)] {E[2p ('SO)-~P~(~Po)] 0.645 s-' 13} have been stressed in the most recent of the studies on this state by Husain and Norris' ' who employed time-resolved resonance line absorption on C(2'SO), generated by low-energy repetitive pulsing, rather than "single-shot" mode measurements coupled with high-energy photolysis.1*9 The present paper extends the previous work of Husain and Norris," which dealt with a limited number of collision partners, to the removal of C(2'SO) by a wider range of added gases. The fundamental basis of this investigation remains the relationship between the electronic structure of atoms and their reactivity. Ideally, these atom-molecule collisional processes are best considered in terms of potential energy surface calculations coupled with reaction dynamics on the surface, as has been des- cribed, for example, for the reaction between C(23PJ) +02(X 'Xi) by Kinnersley and Murrell,14 yielding an absolute reaction rate constant essentially in agreement with experiment4 However, the large range and complexity of the processes studied experimentally to date for atomic carbon clearly requires the use of a simplified approach in terms of the symmetries of the potential energy surfaces involved.The rate data for C(2'S0) obtained in this investigation are therefore compared, where appropriate, with data for C(2lSO) derived reviously from "single-shot" measure-ments together with rate constants for C(2GJ) and C(2lD2) and discussed in terms of correlations for species mainly at infinite separati~n.'~-'' This approach, at least in the weak spin-orbit coupling approximation, is now being adopted in biblio- graphic compilations of rate data for some light atom collisions.'* 51 COLLISIONAL QUENCHING OF c[2p2(1so)] EXPERIMENTAL The experimental arrangement described by Husain and Norris" for the earlier studies on C(2lSO) was essentially that employed in the present investigation.A fully detailed account of this type of system, originally designed for time-resolved resonance line absorption in the vaccuum ultraviolet and incorporating "pre-trigger" photomultiplier gating (E.M.I. 9816 QB), has been described hitherto." The modifications that were made to the earlier system'' for use in the ultraviolet region employing air optics and including a system of short focus lenses2' essentially results in the present experimental arrangement. In brief, C(2'S0) was generated by the repetitive pulsing (E= 125 J, 0.2 Hz) generally of a CC14 +He mixture ([He] :[CCl,] = 5 x lo4:1) through the Spectrosil wall (A > 165 nm) of the coaxial lamp and vessel assembly using a flow system that is kinetically equivalent to a static system.20 The excited atom was then monitored by resonance line absorption at A = 247.9 nm [3s('Py) t2p2('S0),12gA = 1.9x lo9s-l 21] using the above p.m.tube, mounted on the exit slit of a Czerny-Turner 0.3 m grating monochromator (McPherson Corporation, U.S.A.). The resulting photoelectric signals were amplified without distortion2' and then captured, digitised and stored in a fast response transient recorder (Data Laboratories DL 920) used in the "A/," mode." The transient recorder was interfaced to a signal averager (Data Laboratories DL 4000), the contents of which, generally representing the results of 32 individual experiments on a given flowing reactant mixture, were transferred to a paper-tape punch (Data Dynamics punch 1183) in ASCII code for direct input into the University of Cambridge IBM 370 computer.As hitherto,:: all data were subjected to the numerical data smoothing procedure of Savitsky and Golay. The signals at A = 247.9 nm were analysed using the standard Beer-Lambert law [Itr= I,exp(-ecl)] as hitherto" rather than using a modified law of the type Itr= I, exp [-(~cl)~].~~Calibration of y for the A = 247.9 nm transition in this experimental arrangement, which necessarily involves an assumption concerning the relationship between the initial photochemical yield of [C(2lS0)] and [CCl,] (initial), could not be readily estab- lished in view of the complex relationship between [C(21So)],=o and the light intensity from the ph~toflash,'*~*'~ and also the complex low-wavelength photochemistry of cc14.25-28 The factor y would, of course, directly affect the absolute rate data for C(2'S0) reported in this paper and those presented hitherto." All materials (He, Xe, N2,Clz,CO, C02, H20, CH4, CC14, C2H2and C,H6) were prepared for use essentially as described previously.3*7,8,20929-33 RESULTS AND DISCUSSION Previous investigations of the low-wavelength photolysis of CC425-27 have not been primarily concerned with a quantitative description of the production of C(2lSO). To the best of our knowledge, the only analogous studies involving direct monitoring of this atomic state in such a context have been reported for C302as the photochemical precursor in a flash-photolysis investigation.For that molecule, Braun et al.' have reported a complex relationship between [C(2'S0)] and the flash intensity. Husain and Kirsch' reported a Stern-Volmer type of relationship between [C(2lS0)]and the concentration of quenching gas, consistent with the secondary photochemical production of C(2lSO)from a primary product of the photolysis of C302,most probably C20. In the present circumstances, we note the low yield of C(2lSO)resulting from the photochemical precursor, CCI4,which was employed in the majority of the rate measurements here on this atomic state and the critical dependence for obtaining a measurable yield of the C(2'S0) atom on the low- wavelength transmission of the high-purity quartz (Spectrosil) of the common wall of the reactor and also on the flash energy, particularly on the use of high voltages.These limitations give rise to scatter in the resulting rate data for C(2lSO)as indicated in earlier measurements. Decay curves for resonance absorption due to C(2lSO) resulting from the photolysis of CC14+He mixtures have been displayed hitherto'' D. HUSAIN AND D. P. NEWTON and such decays, modified by the addition of gases for collisional quenching, constitute the basis of the present investigation. For the study of the quenching of C(2lSO)by C2H2, it was found that this particular gas itself gave rise to significant yields of the excited atomic state on photolysis (as did CO) in the presence of He and therefore decays for this precursor are presented here as examples, noting that the remaining quenching studies of C(21S0) employed CC14 as the source.Fig. l(a) shows a typical computerised output of an experiment in this investiga-tion, indicating the variation in the transmitted radiation at A =247.9 nm {C[3s('P?) +2p2('S0)]}resulting from the decay of C(2lSO)following the photolysis of a C2H2+He mixture. Fig. l(b) shows the smoothed data derived from the raw data given in fig. l(a)following the numerical data smoothing procedure of Savitsky and G01ay.~~Fig. 2 gives an example of the first-order kinetic plot for the decay of C(2'SO)using the smoothed data in fig. l(b). 0.28 ...ai... *. * * : ....-:.I..I .. ... ......... ..:I0 -26 .. ........::::I............... .... ............ ... ..... .......... h ... .... ...... ...v) ...... .... .................dC .. .... .................. .... .......c ............................ .... ............... ..... ............... . ..5j '0.24 ... ........ ... . . .. .............. ............................... ... v ........> ...................... -= ... 0.22 ....... ..... -0.20 0.25 0.24 hvl C.w E: 0.23 0.21 0.20 200 300 400 500 600 700 time/ps FIG. 1.-Digitised time-variation of the transmitted liFht intensity at A =247.9 nm [3s('P:)+2p2(lS0)] indicating the decay of resonance absorption by C(2 So) following the pulsed irradiation of acetylene. [C2H2]=2.8 x 1013molecules cmP3,[He] =7.0 x lo" atoms ~m-~;E =125 J (10 kV,2.5 pF);repetition rate =0.2 Hz; gate duration =130 ps; microwave power for spectroscopic source =100 W; flow lamp conditions 1% COinHe.ptotaI=133 N m-2;p.m.voltage =1.6 kV;no. of experimentsfor averaging =32. (a)Raw data. (b)Smoothed data. COLLISIONAL QUENCHING OF c[2p2('so)] -1.5 -2.0 .......................................................................... ..................................... _. ..............-2.5 ........................cr-................................................................... ....... ..-............. -3.5 -1-4.0 -I FIG.2.-Pseudo-first-order plot for the decay of C(2'S0) obtained by monitoring the absorption of resonance radiation at A =247.9 nm [3s('Py) t2p2$'So)] following the pulsed irradiation of acetylene. [C2H2]=2.8 x lOI3 molecules ~m-~, [He] =7.0 x 10' atoms cmV3; E = 125 J (10 kV,2.5 pF); repetition rate =0.2 Hz; gate duration = 130 ps; microwave power for spectroscopic source = 100 W; flow lamp conditions 1% CO in He. ptotal= 133 N m-2; p.m. voltage = 1.6 kV;no. of experiments for averaging= 32. Smoothed data. The slopes of the first-order plots of the type given in fig. 2, namely, In [In (Io/Itr)ltagainst time, are given by -k' where this quantity is the overall first-order decay coefficient in a given experiment.In a series of experiments with an added quenching gas, Q, k' can be expressed in the form k'= K +kcCi4[CC4] +ko[Q], when CC14 is the photochemical precursor. kCCI4 and ko represent absolute second-order rate constants for the collisional removal of C(2lSO) by CC14 and Q, respectively. K is taken to be a constant in such a series of kinetic runs and includes the small first-order contributions due to weak spontaneous emission* and to diffusion. Whilst the assumption of a low degree of photolysis at the relatively low flash energies employed here (125 J) compared with the higher energies in the "single- shot mode" experiments with C302 (E= 1125 J)9 is sensible, some scatter in the data will result due to the removal of C(2'SO) by photolysis products.This should be relatively small in view of the competing, efficient removal of C(2'SO) by the precursor, CC14. The resulting plot of k' against [CC14] was found to be similar to that reported in the previous investigation'' and yielded a quenching rate constant of kcc14 =3.3 f0.4 x lo-'' cm3 molecule-' s-' (300 K), in agreement with the earlier measurement of Husain and Norris" [(2.7 f0.5) x lo-" cm3 molecule-' s-l, table 1, see later]. Values of the quantity K indicated above obtained from these experiments may be used to derive a crude estimate of the upper limit for the quenching rate constant of C(2'SO) by the helium buffer gas (table 1).Of course, with an added quenching gas, [CC14] is held constant and we may write k'= K +ko[Q] in order to obtain values of ko. Fig, 3, constructed from data of the type shown in fig.1 and 2, shows the variation of k' with [C2H2], yielding = D. HUSAIN AND D. P. NEWTON TABLE RA RATE DATA FOR THE COLLISIONAL REMOVAL OF C(Z3PJ, 2'02, 2'So) BY VARIOUS GASES (Second-order rate constants, cm3 molecule-' s-' ;third-order rate constants, cm6 s-'; T = 300 K) gas c(23pJ) C(2'D2) (1.263 eV) C(2'S0) (2.684 eV) He <3 x (7) Ne (1.1*0.4) X (7) Ar G 10-1~(7) Kr (9.4f 1.6)x 10-1~(7) (7f1)x 10-l2 (*)Xe (1.1~0.3)~10-'~(7) (11)H2 (6.9* 1.2) x (M = He) (4)" (2.6f0.3) x lo-'' (6). <5 x 10-1~ (7.1f2.5) x lop3' (M = He) (2,3)" 4.15 x lo-'' (1) ~4 x 10-l4 (9) <7 x (5) <5 x (1)2 x 10-1~(10) N2 (3.1f1.5)x (M = Ar) (3)" (4.1f1.2) x (6) (3.2k0.2)x (*) -2.5 X (1) ~3 x (9) O2 (2.6f0.3) x lo-'' (4) 2.6 x lo-" (8) (9.9f 1.8)~ (11) (10)(3.5f1.5)x lo-'' (2,3) <5 x 10-l2(1) -5 x 10-1~ -3.3 x lo-" (1) 2.5 x (5) NO (4.8f0.8)X lo-'' (4) (4.7k 1.3) x lo-'' (8) (4.8k0.5) x lo-'' (11) (7.3f2.2) x lo-'' (2,3) 9.2 x lo-" (1) 1.1x 10-'O (1) Clz (7.6k0.7)x lo-'' (*) (*)CO (6.3f2.7) x (M= He) (3)" (1.6f0.6)x lo-'' (8) <4.6 x 10-1~ s6 x (9) s3.5 x (10)co2 (4) (3.7f1.7) x lo-'' (8) -3 x (*) (2,3) sl.0 x 10-l6(10) N20 (1.3k0.3)X lo-'' (4) (1.4f0.5) x lo-"' (8) s5 x (11) ' (2.5f1.6)x lo-'' (2, 3) H20 (4) -1.7 X lo-'' (8) -1.6X lo-'' (*) ~3.6 (2,3)x 10-1~ CH, <2.5 X lo-'' (3) (2.1f0.5) x lo-'' (8) <10-12 (*) <5 x (1) 3.2x lo-" (1) <lo-" (9) <6 x (5) -3.0 x 10-1~(10) C2H2 <6 X lo-'' (5) (5.4* 1.2)x lo-" (*) C2H4 <6 x (5) 3.7 x lo-'' (8) (9.0+1.6)x lo-" (11) C3H6 (1k0.5)x lo-"' (*) CCl, (3.3f0.4) x lo-'' (*) (2.7f0.5) x lo-'' (1 1) C302 (1.8f0.2) x 10-"(4) 1x lo-'" (9) Errors, lu.References are given in parentheses; *, this work. " Third order. (5.4* 1.2)x cm3 molecule-' s-l (table 1). The magnitude of this quenching constant will be discussed later. Table 1 gives the values of the second-order quenching rate constants for C(2lSO) obtained in this investigation together with the absolute rate data reported hitherto both for the C(2lSO)state and for the Z3PJ and 21D2states. C 0I, L I S I0 N A L QUENCH IN G OF c[2p2('so)] 01 I I I0 1 2 3 4 [C2H2]/1013molecules ~rn-~ FIG.3.-Plot of pseudo-first-order rate coefficients (k')forthe decay of C(2lSO)in the presence of C2H2.C(2lSO) +Xe, He Despite the large scatter in the experimental data for the plot of k' against [Xe], the results indicate (table 1) that C(2'SO) is quenched with relatively high efficiency by this gas (ca. 1 in 100,collisions), particularly when compared with deactivation by He (table l), and the resulting value of ko for Xe is clearly a number of fundamental interest. The relatively efficient transfer of the large quantity of electronic energy of the lower lying C(2'Dz) (1.263 eV) to Xe and Kr, corresponding to ca. 1 in 2 and 200 collisions, respectively, has been discussed previously by analogy with more detailed considerations of data for O(21D2).7 A detailed discussion of the quenching data for C(2'SO) and C(2'D2) would be facilitated by knowledge of the appropriate potential energy curves for the C-noble- gas transient diatomic molecules.Unfortunately, no detailed spectroscopic data for Xe-C, for example, have yet been reported. Earlier spectroscopic measure- ment~~on an Xe-soot discharge did yield a band with a head close to the frequency of the transition C(2'SO-2'D2) at 11454 cm-' but this could be attributed to a molecular system involving xenon only. The analogy with the quenching of 0(2'D2) and 0(2lSO) by the noble gases remains the most convenient general vehicle for discussion in the present context. Quenching of O(2'SO) is inefficient for all the noble whereas, for 0(2'D2),deactivation in the presence of Xe, Kr and Ar proceeds at ca.1 in 3, 14 and 320 collisions, respectively.37938 This large difference in the collisional behaviour of the 'So and 'D2 states was accounted for .~~by Donovan et ~1 in terms of a semi-quantitative potential energy diagram for XeO derived, in part, from the limited available spectroscopic data for Xe0.40 More recently, this curve-crossing mechanism39 had been given quantitative expression by Kinnersley and M~rrell,~' who have employed the ab initio calculated potential energy curves of the noble-gas oxides reported by Dunning and Hay42 and have calculated the collisional quenching rates of O(2'02) by the noble gases. D. HUSAIN AND D. P. NEWTON Naturally, we would hope that the collisional quenching rates for C(2lSO) and C(2lD2) by the noble gases (table 1) will stimulate similar calculations on the potential energy curves for the noble-gas-C molecules42 and calculations of the quenching C(2lSO)+ N2 The relatively efficient collisional quenching of C(2lSO) by N2 observed in this investigation (table 1) is not in accord with the results of the previous high-energy "single-shot" measurements reported by Husain and Kirsch.' The considerably improved quality of the rate data obtained in this investigation, particularly when seen in terms of the plot of k' against [N2] [fig.4(a)] and the advantages of the low-energy repetitive pulsing system, leads to confidence in the qualitative difference obtained for this gas.Donovan and Husain16 have given a correlation diagram connecting the states of C+N2 and those of CN+N using C,symmetry in the collision complex and employing the weak spin-orbit coupling approximation. That diagram may be marginally modified by correlating through NCN(X 3Xg),44 arbitrarily placed exothermically in energy on this diagram relative to the species N + CN (or C + N2). The lowest excited state listed by Her~berg~~ is NCN(A 311,) (T,= 30 383.7 ~m-l).~'This particular triatomic molecule may not contain the ideal geometry for considering the nature of the collision complex in this instance but is the only one available whose electronic state is assigned. Certainly for the third-order kinetic removal of CQ~P,) by N2 (table l), Braun et al.' reported transient absorption due to CNN following the matrix isolation infrared measure- ments of Milligan and J~cox.~~ Detailed consideration of the collisional quenching of C(2'SO) by N2, simply using the electronic states of NCN as an initial measure of the interaction on collision, would require an extensive knowledge of the state manifold.Whatever the first singlet state of NCN, one of the 5 singlet surfaces correlating with C(21D2) +N,(X 'Xi)(3lA'+ 2lA") will correlate with it and, indeed, it is the result of surface crossing between this singlet surface and one of those arising from C(z3P,) + N2(X 'Xi)(3A'+ 23A"), presumably facilitated by statistical considerations of the type described for C20 (see later) and N20,47-49 that gives rise to the overall efficient physical quenching of C(2lD2) by N2 (table 1).6 However, the large number of singlet surfaces arising from C(21D2) +N2(X 'Xi), in turn, means that C(21S0) +N2 will then only correlate with, at the lowest energy, the fourth singlet electronic state of NCN, whose potential minimum is presumably not exothermically accessible to those of these initial reactants.Physical quenching will involve non-adiabatic transitions from the 'A' surface derived from C(2lSO) + N2 to one of the above singlet surfaces; chemical reaction to CN(X 2X+) + N(24S) ('A" + 3A"),which is exothermic (AH= -0.685 eV l2>'O), would clearly involve a spin change. The sum of these two overall routes is seen to be relatively efficient (table 1).C(2lSO)+ c12 There is no previous measurement with which we may compare the rapid rate for the collisional removal of C(2'S0) by C12 observed as a result of this investigation [fig. 4(b), table 13. The only analogous comparison that may be made is that for the removal of Si(3lS0) by C12 (table 2, see later) which is seen to be comparably rapid {k[Si(3'S) +C12] = (7.3f0.1)x cm3 molecule-' s-' (T= 300 K)}.31 Reaction of C(21SO) with C12 is presumed to be exothermic according to + C12 -+ CCl+ C1, AH = -1.363 eV.'2,50*51C(2*SO) 58 CO LLI S I ON A L QUENCHING OF c[2p2('so)] 2.5 2.0 3 'v) m2> 1.5 , 1.o 0 1 2 3 4 [N2]/ 1014molecules cmP3 3.5 3.0 4 'v) m 0 d> -Y 2.5 1 2 .o, I I I I 0.5 1.0 1.5 2 .o 2 5 [CIJ/ 10l3 molecules cmP3 FIG.4.-Plots of pseudo-first-order rate coefficients (k')for the decay of C(2'SO)in the presence of (a)N2 and (b)Clz.The thermochemistry is based on the value of D(C-Cl) =3.8*0.5 eV given by Gaydon.'l The spectroscopy of this molecule is not included in the recent compila- tion of Huber and Herzberg." We assume a *rI ground state for this molecule analogous to that of CF." On this basis, C(21So)+Cl&X '2;) (lA') does not correlate with the ground-state products CCl(X 211)+Cl(3 PJ).The relatively high D. HUSAIN AND D. P. NEWTON collisional quenching efficiency could clearly arise from non-adiabatic transitions between the 'A' surface arising from the reactants and the singlet surfaces correlat- ing with C(2'D2) +C12(X'Xi) (3'A' +2lA").There are no rate data available at present for the removal of C(23PJ) and C(2lDZ) by Clz for further consideration within the context of the potential surfaces available for collisional removal. C(2lSO)+co The collisional removal of the 3PJ,'DZand, in particular, the 'Sostates of atomic carbon by carbon monoxide may be considered in more detail than hitherto. In purely experimental terms, we have seen that the quality of the computerised photoelectric decay traces obtained for C(21S0) in this investigation, including those derived from the photolysis of CO itself, are superior to those obtained hitherto from single-shot measurement^.^ Fig. 5(a)shows the variation of k' with [CO], the line presented corresponding to the least squares slope + 1g to yield the resulting upper limit (table 1).Detailed consideration of the surfaces involved in collision has not been presented in the earlier studies for the removal of the three states of [c0)/10~~molecules ~rn-~ [CO~]/IO'~molecules cmW3 FIG. 5.-Plots of pseudo-first-order rate coefficients (k')for the decay of C(2lSO)in the presence of (a)CO and (b)COz. CO LLI SI0N AL QUENCH IN G OF c[2p2(lS,)] atomic carbon by this reactant A convenient basis for discussion is a correlation diagram constructed using the weak spin-orbit coupling approximation” and employing such crude data on C20 as are conveniently The result is shown in fig. 6. Apart from the use of standard spectroscopic data for the atoms and diatomic molecules in~olved,’~’~~ the inclusion of C20 in the diagram is based on (a)an estimate of the heat of formation of C20from its atoms following Harteck et al.” of -300 kcal (-13 eV) which, in turn, would yield, with Do(CO)= 11.092 eV,” a value of D(C-CO) =1.9 eV and (b)the energies of the low lying ‘Anand ‘Z+ states of C20 ayproximately 0.5 and 0.8 eV above the X ’2-ground state, re~pectively.’~ Bayes’ employed an approximate semi-empirical molecular- orbital calculation using data for the analogous molecule CO;’ and we therefore employ the resulting electronic energies reported for these excited states of C20 with some caution.The role of C20 in the photolysis of C3O2 both as indicated from the results of product analyses on static photochemical sy~terns~~*’~-~~ and, more pertinent to + + + + c2o(x3C3 FIG.6.-Correlation diagram connecting the states of C+CO with those of C2+0uia those of C20 using C,symmetry in the collision complex. D. HUSAIN AND D. P. NEWTON the present investigation, on the observed yield of C(2lSO) in flash-photolysis experiment^,^ has been recognised in earlier work. Indeed, one factor that led Husain and Kirschg to restrict their reported quenching rate constant of C(2'S0) by CO to an upper limit in their measurements using C302 as the photochemical precursor was the possible role of the secondary photolysis of C20 which resulted from the initial irradiation of C302.It was envisa ed that C(2lSO) resulted from the secondary photolysis of either or both C20( A) and C2O(lX).Whilst it is considered that C20 will play a fundamental role in the collisional removal processes for C(23P,, 21D2, 2lSO) with CO and, indeed, may partly account for the lack of linearity in the first-order plots for the removal of C(2lSO) at the long time delays in the presence of CO in these experiments, the effect of secondary photolysis of C20 in terms of its yield on atomic carbon will clearly be small in this investigation. By contrast with the magnitude of an expected primary photochemical yield of C20 from C302, a collisional yield arising from C + CO will be very low. Dealing first with C(23PJ)+CO(X 'Xi), we see from fig.6 that these pair of states correlate with C20(X3X-).Husain and Kirsch3 demonstrated overall third- order kinetics for C(23P,) + CO + He. The resulting third-order rate constant3 (table 1)indicates a relatively short lifetime for the energised C20(X 'X-) (T= s)resulting from the initial recombination process. The data for the removal of C(21D2) by CO (table 1) have been reported as a second-order rate constant resulting from measurements carried out at a single total pressure @He= 6.65 kN m-2).8 The relatively high overall quenching efficiency, corresponding to ca. 1 in 10 collisions, is entirely consistent with the effect of many trajectories within the region of surface crossing associated with a long-lived complex. This type of effect is well established for the highly efficient quenching of O(2lD2) by N2 61,62,47-49 as noted hitherto.We would presume that similar considerations would apply to C(21D2) + CO(X 'X+) which correlates with both C2O(lA) and C2O(lX) (fig. 6). For overall physical quenching of C(2lD2) to C(z3P,), it is envisa ed that 8this results from the curve crossing between surfaces arising from C20( A, 'X+), on the one hand, and that from C20(X 3X'), on the other. The state manifold of C20 is clearly not understood sufficiently to permit discussion of the physical quenching of C(2lSO) by CO via a surface correlating with a defined electronic state of this triatomic molecule. The inefficient quenching rate for C(2lSO), noting both the unfavourable thermochemistry and the spin-forbidden nature of the chemical reaction to ground-state products C(2lSO)+ CO(X 'Z+) -+C2(X1Xi)+ O(z3P,), AH = +2.198 eV 12*50 must arise from non-adiabatic transitions following surface crossings, facilitated by the well depth of an energetically- and symmetry-favoured state of C20.C(2'SO) + c02 The absolute rate constant describing the collisional removal of C(2lSO) by C02 observed in this investigation (table 1) is greater than the estimate obtained by Husain and Kirschg from the pulse-radiolysis measurements of Meaburn and Perner." It has been stressed generally and particularly recently by Husain and Norris," that Meaburn and Perner" restricted their description of the rate data for C(2lSO) to half-life measurements of this atomic state under the extreme conditions of pulse radiolysis.The translation of these half -lives into absolute rate constants involved the assumption by the later workers' of first-order kinetics for C(21S0). The present measurement therefore comprises the first photochemical COLLIS I0 N A L Q UENCHING OF c[2p2(’so)] investigation of this particular collisional process. The absence of a “blank” on the plot of k’ against C02[fig. 5(b)]arises from the experimental scatter in that quantity relative to the clear variation of the decay coefficient with the added reactant gas. For this reason, no error is quoted in the resulting quenching rate constant (table 1). However, notwithstanding this limitation, the magnitude of ko is clear. From the thermochemical viewpoint, oxygen-atom abstraction c+c02 +co+co is exothermic for the all three low-lying states [AH(eV):C(23PJ), -5.639;C(2’&), -6.903; C(2’S0), -8.323 12*44950].A correlation diagram connecting the states of C +COz with those of CO +CO using C,symmetry in the collisional complex which is not, of course, the least symmetrical complex,15 is shown in fig. 7. Furthermore, CO(X’C+) t CO(X’C+) + CO(X’C+) + CO(X’Z+ 1 + CO(X’C+) + co(d3A) / CO(X’C+) + CO(U’~C+)C(ZID,) + I‘ eV FIG. 7.-Correlation diagram connecting the states of C+C02 with those of CO+CO assuming C, symmetry in the collision complex. the diagram is constructed using the lowest excited state for CO2(A1Al) calculated by England and coworker^.^^-^^ We have stressed the need hitherto” for the use of low-lying calculated states in correlation diagrams involving C02, despite the existence of an extensive spectroscopy of this which often yields broad envelopes for vibronic transitions in accord with the Franck-Condon principle for transitions between linear and bent states. The rate data for C(23PJ) and 63D.HUSAIN AND D. P. NEWTON C(2'D2)+C02are in accord (table 1)with the resulting diagram (fig. 7): C(23PJ)+ C02only correlate via the 3A'+3A"surfaces with endothermically placed products [CO(X 'Z+)+CO(a 'TIr)] and chemical reaction to two ground-state CO molecules would involve surface crossing with the lowest 'A'surface followed by non-adiabatic transitions; C(2'D2)+C02(X'Xi) correlate via the 'A' surface with ground-state products and hence the observed rapid removal rate for the 'D2state (table 1)2is in accord with this.Alternatively, physical relaxation of C(2'D2)to C(z3P,)involves, at least initially, the attractive part of this 'A' surface followed by surface crossing and non-adiabatic transitions with the triplet surfaces correlating with C(z3PJ)+ C02. C(2lSO) +C02do not correlate with thermochemically accessible products (fig. 7) and the relatively efficient removal of C(2'SO)whether by chemical reaction or physical relaxation must involve surface crossing and non-adiabatic transitions. As usual, we must note the limitations of the use of correlation diagrams in this context as they do not contain the detail that one obtains from the combination of full potential surface calculations nor, of course, from molecular dynamic calcula- tions on such surfaces.In particular, energy barriers and the regions of surface crossing are absent from such diagrams. This is of particular importance when dealing with molecules such as C02 and N20 as we have stressed in various publications and in various reviews hithert~.'~*'~,~~~~~ These are 18-electron, linear, closed-shell structures and even highly exothermic oxygen-atom abstraction reac- tions for a wide range of atomic states often involve large energy barriers on this account. C(2lSO)+H20 To the best of our knowledge, the absolute rate constant, albeit of limited accuracy, for the collisional removal of C(2'So)by H20 in the gas phase obtained in this investigation (table 1)constitutes the first measurement of this fundamental property, despite extensive experimental interest in reactions of atomic carbon with water in various laboratories concerned with nuclear recoil and radiation ~hemistry.~~It was not determined from previous time-resolved resonance line absorption measurements on the 'So state following pulsed irradiati~n"~' nor by plate photometry.' The present measurement in which the low photochemical yield of C(2'SO)is monitored following photolysis through Spectrosil quartz (A > ca.165 nm) will clearly be particularly prone to interference from the products of the low-wavelength (A <ca. 190 nm) photolysis of H20 itself.27 This effect has, of course, been recognised in rate measurements for the removal of both C(23PJ)3*4 and C(21D2)8by this molecule and, in view of the possible role of exothermic reaction between species such as C(Z3P,)+OH(X 211),3rate measurements have been expressed as upper limits (table 1).By contrast, the larger rate constant reported for reaction between C(2'D2)and HzO (table 1)8may be more confidently ascribed to these particular reactants alone as removal of C(21D2)by OH, for example, would imply a rate constant for reaction between these two transient species considerably greater than the collision number for sensible photochemically generated particle densities of OH. Low concentrations of H20had to be employed in this investigation to obtain an estimate for the quenching rate constant of C(2'SO), limiting the removal of this atomic state by products of photolysis.Notwithstanding the scatter in the decay traces for the present measurements on C(2'SO)in general, and for the plot of k' against [H20] in particular, an estimate of kHzOcan be extracted from the data (table 1).Direct comparison of rates of reaction of C+H20 in the gas phase obtained by the present general type of inve~tigation,~'~''' including C0L L I S I0 N A L Q U EN C HI N G 0F c[2p2(‘so)] this work, cannot be readil Y made with previous investigations for atomic carbon. Maddock and have observed formaldehyde (and also species such as CH3CH0, CH30H, HCOOH and CH3COCH3) when carbon atoms are directed onto an ice surface.However, not only is the reaction phase different, including the effects of a wide range of secondary free radicals in the solid matrix, but the initial reactant is the ionic species 14C+, with translational energies up to 67 eV,” resulting from the use of ion-beam techniques, which is subsequently neutralised on collision. A correlation diagram connecting the states of C+H20 with those of both CO +H2 and CH +OH is shown in fig. 8. This is constructed on the basis of the 1 eVI c 0(X’Ct)+ FIG. 8.-Correlation diagram connecting the states of C+H20 with those of CO+H, and CH+OH assuming C, symmetry in the collision complex. weak spin-orbit coupling approximation and assuming C,symmetry in the collision complex. In principle, such a diagram could include a state manifold of CH2044.72 as an intermediate but this would then necessitate further speculation on various processes of insertion, bond formation and bond fission to obtain the normal formaldehyde molecule from the initial reaction of C+H20.Some limited and D. HUSAIN AND D. P. NEWTON certainly incomplete discussion has been given hitherto for the removal of C(2'D2)+ H20 in terms of potential energy surfaces leading to the reaction products CO+ H2 but not including CH+OH in the product state manifold. Further, no detailed discussion of the potential surfaces involved in the reaction between CQ~P,)+ H20 has been given3 other than to note the high reaction exothermicity to yield ground- state products: C(23PJ)+H,O(X 'Al) --+ CO(X 'X+)+H2(X'Xi), AH = -6.0465 eV 4430 [CO(X'C+)+ H2(X 'Xi) are displaced in fig.81, the close-to-thermoneutral nature of reaction leading to the s in and orbitally allowed products, CO(a3n,)+H2(X'Xi) (AH = -0.0097 eV ?4,50) and the possible role of non-adiabatic transi- tions following surface crossing between the 'A' surface leading to CO(X 'C')+H2(X'Xi), and the 3A'+3A"surfaces correlating with C(23P,)+H20(X1A1). Fig. 8 indicates that the exothermic process C(2'So)+H20(X'A1)% CO(D'A) +H2(X 'Xi), AH = -0.5517 eV 44950 is symmetry-allowed and presumably accounts for the removal of this electronically excited atom in this instance (table 1). Any emission from the resulting CO(DIA) to the X 'Z+ ground state would be very weak.73 Spin-allowed collisional relaxation to the CO(A'n) state, where the energy to be transferred is relatively small (0.1106 eV), would be expected to be reasonably efficient for a number of quenching gases and hence detection of the resulting CO(A'n) state may be considered for future experiments concerned with the decay of atomic carbon generated in the pulsed mode.Whilst the suggestion of the difficult procedure of monitoring product electronic states other than the ground state may easily be made for systems of such complexity, the construction of experiments for the study of atomic carbon in the presence of oxygen-containing molecules, with monitoring designed to detect the strong CO(A 'TI-X 'X+) emission in the vacuum ultraviolet (T,= 65 075.77cm-' 'O), would, in fact, be of general use as it would constitute, a spectroscopic marker.This can be seen by reference to the short radiative lifetime [T~(O,0) = 10.7 f0.3 n~]'~for the transition. This strong emission from CO(A'n-X 'C+)could therefore be used to monitor, in "real time", the decay of the relatively long-lived species, C(2'S0)in this instance, or other atomic states of carbon in others from which the CO(A'n) state is collisionally derived. Indeed, Hancock et al.7J776have observed CO(A 'II-X 'X+) emission following the production of C2(a311u)from the multi-photon dissociation of acrylonitrile, C2H3CN,by a TEA C02laser. The emission is attributed to the effect of either the direct reaction C2(a3TI,) +02(X'Xi) --+ CO(AIll) + CO('Z+) or the pair of processes c2(a3~u)+ 02(x + CO~(X5,')+ ~(2's~) C(2'SO)+ 02(X'Xi) -+ CO(A'II) + O(23PJ).However, whilst the time-dependence of the CO(A 'n-X 'X+) emission was in accord with the recent measurement for the quenching rate constant of C(2'SO)+ 02 obtained by the present method reported by Husain and Norris," C(2'SO)+ 02(X'Xi), in fact, correlate with CO(d3A)+O(23PJ)[see fig. 6 in ref. (ll)]. On the other hand, the emission observed in Hancock's sy~tem~~,'~ may result from C 0L LI S I0 N A L QU EN CH IN G 0F c[2p2('so)] products following non-adiabatic transitions and certainly the possibility of using CO(A 'n) as a spectroscopic marker for C(2'S0) remains. C(2lSO)+CH4, cc14 The absolute quenching rate data obtained in this investigation for C(2lSO) by the polyatomic molecules CH4 and CC4 are given in table 1.Clearly these rate constants are not amenable to the fundamental consideration of the type afforded to diatomic reactant gases. Abstraction reactions by C(2lSO) would appear to be thermochemically favourable in both cases: The principal doubt in the thermochemistry concerns CC14. The molecule CCl is not included in the recent, detailed spectroscopic compilation of Huber and Herz- bergSo other than incorporating a suggested value of Do(C-Cl) = 3.34 eV by reference to flame chemistry. Ga don" suggests D(C-Cl) =3.8*0.5 eV. In any Yevent, C1-atom abstraction by the So atom would clearly be exothermic and efficient quenching by chemical reation is suggested. CH4 shows negligible reactivity towards C(2lSO) (table 1) whereas removal of C(2lD2) by this molecule is considerably more efficient (table 1).8 The present measurements only yield total atomic removal rates and do not separate the contributions from chemical reaction and energy transfer.The present results may be compared with the conclusions of Skell and Enge17' who have reacted the products of a carbon arc deposited on a solid matrix at 77 K, in this case, containing alkanes of choice. By employing different time domains for warming the matrix, these authors attribute products to specific elec- tronic states of atomic carbon and, in this instance, conclude that of the three states arising from the 2p2 configuration, only C(2lSO) is chemically reactive towards the alkanes.Certainly, H-atom abstraction by C(23P,) would be endothermic (AH = +1.015 f0.09 eV and the slow rate observed from the present type of investi-gation for the removal of CQ~P,) by CH4 (table 1)3is in accord with this. However, the observed removal of C(21D2) by CH4 with effectively unit collisional efficiency (table 1)and with no contribution by chemical reaction, which would be exothermic for this atomic state (AH = -0.249 eV 1230777), is surprising. Whilst it is stretching a coq arison, C(21D2)+H2(X 'Xi) correlate through both CH2(G1AI) and YCH2(b B1) via deygotential wells" to exothermic products CH(X 211)+H(l2S1,2) (AH= -0.251 eV ). On the other hand, notwithstanding the exothermicity for chemical reaction between C(21S2) and CH4, it would only require an energy barrier of ca.0.12 eV €or chemical reaction to contribute 1% to the total removal rate of the 'D2 state at room temperature. The removal of C(2lSO) by C2H2 (table 1)proceeds at a relatively rapid rate, corresponding to ca. 1 in 20 collisions. The computerised photoelectric decay traces for the resonance transition at A = 247.9 nm (fig. 1and 2) were of relatively good quality for this particular quenching gas, yielding degrees of light absorption of up to ca. 10% but also indicating departures from linearity at long-time delays D. HUSAIN AND D. P. NEWTON for the excited atom. This latter aspect was not investigated further in view of the complexities of the phot~chemistry~~ and the limitations from restricting direct monitoring to C(2'SO).Even though the data for k' against [C2H2] demonstrate scatter (fig. 3), the resulting high collisional removal rate, derived from the slope of this plot, enables secondary reactions by the products of photolysis of C2H2 itself27 with C(2lSO) to be sensibly neglected. To the best of our knowledge, we are unable to compare the absolute second-order quenching rate constant for the reaction of C(2lSO) with C2H2 obtained in this investigation with a comparable measurement derived by any other technique. Unlike the study of "C, generated by nuclear recoil production, with C2H4, as investigated by Wolfgang and co- worker~,~~no similar study of "C with acetylene appears to have been reported.Skell and coworkers have carried out a number of investigations of reactions of species derived from a carbon arc which, in turn, are deposited onto a solid matrix. Reactions under suitable conditions have been attributed to those of C(2'SO) with olefins, including C2H4.80-82 However, no similar study ascribed to C(2'SO) +C2H2 appears to have been reported. The rapid removal rate of C(2'SO) by q;opylene (table 1) is comparable with that obtained previously for C(2lSO) +C2H4. Skell and coworkers80-82 have postu- lated the role of an insertion reaction of C(2lSO) [or C(2'D2)] of the type: C(2'So) +CH,-CH=CH, +CH*=C=CH-CH3 to account for the production of buta-1,2-diene following the reaction of the products of a low-intensity carbon arc with gaseous propylene.Such a reaction would clearly facilitate rapid removal of the excited atomic state. Perhaps the most convenient vehicle for fundamental discussion of the reactivity of atomic carbon with C2H2 and C3H6 at this stage is that of analogy with the crude but relatively detailed consideration given to the removal of C(z3P,, 2'D2,2'SPl with C2H4 as presented by Husain and Norris." In essence, Husain and Norris constructed a crude potential energy diagram for a collision of atomic carbon along the perpendicular bisector (z-direction) of the C-C bond in C2H4 in the L,ML,S,M.basis, using the standard Clebsch-Gordon coefficient^.^^ The P, orbital occupancy was then taken as an approximate measure of the initial interaction with the v-bonding system of the olefin.By contrast with the present reaction with C2H2, not only were there data for reaction of the three atomic states of carbon arising from the 2p2 configuration for comparison (table 1)5,891'but part of the diagram could be placed, albeit roughly, on an absolute energy basis using the results of CNDO calculations for the lowest singlet and triplet states of C CH2/\-CH2 given by Field.84 Further, in the case of "C+C2H4, Wolfgang et al.79 had, indeed, demonstrated that reaction proceeded in this geometrical manner from the detection of "C centre-labelled allene. We presume that similar considerations to those given above for C(2'S0) +C2H4, and which account for the efficient removal of the 'S atom," will also apply to C(2'So) +C2H2 and C3H6.~(23,)AND si(3ls0), A GENERAL COMPARISON The most general and convenient comparison that can be made for collisional rate data for the specific electronic states of atomiccarbon in the C(z3P,, 21D2,21S0) levels in the context of Group IV atoms is clearly with those of the next light atom in the Group, namely atomic silicon. There is now a relatively large body of COLLISIONAL QUENCHING OF c[2p2('so)] absolute rate constants for all the low-lying states of atomic silicon arising from the 3p2 configuration [Si(33PJ), Si(3'D2) (0.781 eV), Si(3lS0) (1.909eV)],12 most of which has been obtained by time-resolved resonance line absorption following pulsed irradiati~n,~'~~ 1785186including the kinetic study of atomic silicon in specific spin-orbit levels of the 3p2(3PJ) ground state2' (J=O,0; J = 1,16 cm-'; J= 2,43 cm-l).12 A limited number of rate constants for reactions for Si(33PJ) have been reported following resonance line absorption measurements on atomic silicon in a flow discharge Clearly, this now large body of collisional rate data for the two sets of atomic states for C(2p2)and Si(3p2) can be given detailed consideration within the overall structure of the appropriate potential energy surfaces discussed earlier in this paper.17 We restrict our consideration to a general comparison of the reactivity of C(2lSO) and Si(3lS0).Whilst the order of both sets of states in the np2configuration is the same, and some similarities in the collisional behaviour of atomic carbon and silicon might be expected on this simple basis, the electronic states of the reactants including those of added gases might well be TABLE2.-COMPARISON OF RATE DATA FOR THE COLLISIONAL QUENCHING OF c[2P2('s0)] (2.684 ev)AND si[3p2('so)]BY VARIOUS GASES (k,cm3 molecule-' s-'; T = 300 K) He 40-l~(*) s1.3x (86) Xe 40-l~(11) <2 x 10-l~(9)(7* 1)x 10-l2 (*) H2 <5 x 10-lS(11) ~4 x 10-1~(9) s5 x 10-l2 (1) -2 x 10-1~(10) N2 02 ~3 x 10-l~(9) -5 x 10-l~ (3.2f0.2) x (9.9f 1.8)~ (*) (11) (1.5k0.2)~lo-" (86) NO c12 co <4.6 x 10-l4(*) (4.8f0.5) x lo-" (7.6* 0.7) x lo-" s6 x (9) (11) (*) (1.2k0.05)x (7.31t0.1)x lo-" ~10-l~(31) (31) (31) s3.5 x 10- l6 (10) -3 x 10-l2 (*) (1.7*0.3)x lo-" (31) s1.ox (10) s5 x 10-l2(11) (4.3*0.4) x lo-" (86) -1.6 x lo-" (*) <10-12 (*) (9.4* 1.2)~ lo-" (31) <lo-" (9) -3.0 x 10-1~(10) (5.2* 1.2) x lo-" (*) (l.l*O.l)x 10--'"(31) (9.0f 1.6)~ lo-" (11) (2.5 *0.3) x lo-'' (31) C3H6 (1.0*0.5)x lo-"(*)cc1, (3.3f0.4) x lo-" (*) (2.7f0.5)x lo-'* (11) 1x 10-l0 (9) References are given in parentheses; *, this work. D.HUSAIN AND D. P. NEWTON differently ordered within the energy manifold in some cases if the reactant gas has low-lying electronic states. Of course, product states for the chemistry of atomic carbon and silicon with a given reactant gas may be very different in terms of both energy and electronic type, including the states of intermediates.Notwithstanding these general limitations which would correctly imply that, at the minimum, a comparison should be restricted to each reactant gas in terms of correlation diagrams, it is striking how similar the overall quenching rate constants for C(21SO) and Si(3lS0) are found to be for the reactant gases investigated (table 2). We follow the procedure employed hitherta,31 in this case, for a general presentation of the collisional rate data for both C(2lSO) and Si(3lS0) taken from table 2with ionisation potential (fig. 9). The ionisation potentials are taken from corn pi la ti on^^^*^^ with 0 0 0 ;o 0 0 0 + a 0 m 3 0 0 0 00 9 11 13 15 17 19 21 23 25 i.p/eV FIG. 9.-Correlation between the rate constants (k~)for the collisional quenching of C(2lSO) and Si(3lS0) and the ionisation potential of the quenching species. 0,C(2lSO) and 0,Si(3'So).the exception of that for C302which is taken from Baker and Turner (i.p.= 10.6 eV).91 For both 'SOstates, there is a reasonable correlation (in the classical sense) between the overall quenching rate constant and the ionisation potential which is, of course, only an indication of an attractive interaction on collision. We thank the S.R.C. for support and for a Post Doctoral appointment held by one of us (D.P.N.) during the tenure of which this work was carried out. W. Braun, A. M. Bass, D. D. Davis and J. D. Simmons, Proc. R. SOC. London, Ser. A, 1969, 312,412. D. Husain and L. J. Kirsch, Chem. Phys.Lett., 1971, 8, 543. D. Husain and L. J. Kirsch, Trans. 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ISSN:0300-9238    

DOI:10.1039/F29827800051

出版商:RSC    

年代:1982

数据来源: RSC

摘要:

J. Chem. Soc., Fclraday Trans. 2,1982, 78, 73-80 A Resolvent Approach towards the Electronic Structure of Systems Constructed of Chain Fragments Branched Polyenes BY PETERKARADAKOV Faculty of Chemistry of the Sofia State University, A. Ivanov Boul. 1, Sofia 1126, Bulgaria AND OBISCASTARO” Institute of Organic Chemistry, Bulgarian Academy of Sciences, Sofia 1113, Bulgaria Received 15th May, 1981 A resolvent approach (in the HMO approximation) towards the electronic spectra and wavefunctions of systems consisting of chain fragments has been proposed. As an application, branched polyene chains with/without bond alternation have been considered. It is shown that the branching of an infinite polyene leads to the appearance of local states, whose energies and wavefunctions have been studied extensively.The interest taken in the electronic structure of periodic systems is accompanied by an equal interest towards the effect of interruptions in the periodicity on the electronic spectra of such systems. The treatment of systems with interrupted periodicity is complicated by the loss of translational symmetry, so that one can obtain some qualitative insight into their electronic structure only for simple models by simple methods. Such studies have up to now been mainly carried out within the framework of the Huckel molecular orbital (HMO) approximation. In ref. (1) and (2) the effect of Coulomb (a)or resonance (p) integral perturbations on the electronic spectra of polyenes was considered, and ref. (3) and (4) have extended these investigations to (AB)N chains.It has been shown that such local perturbations can cause the appearance of local states, and analytical formulae have been derived for the energies of these states in some boundary cases of infinite chains. Discrete electronic states have been demonstrated to exist in a variety of polymers with complicated elementary units’ and chains with complicated end substitutents.6 In this paper we centre our attention on one particular interruption in periodicity: chain branching in polyenes. Although in principle the HMO treatment of systems constructed of chain fragments can be performed through the method of finite difference^,^ the transfer matrix method’ or the polynomial matrix method,’ we shall show an alternative resolvent approach to be advantageous.In the treatment proposed in this paper, the resonance integrals, which “sew together” the chain fragments, are considered as a perturbation of the direct sum of the HMO matrices of all fragments. The application of the method to branched polyenes with/without bond alternation readily yields expressions for the HMO energy levels and wavef unctions. The possibility of local-state appearance has been considered and analytical expressions for the energies (and wavefunctions, when bond alternation is absent) of such states are reported for the case of infinite branched polyenes. 73 ELECTRONIC STRUCTURE OF BRANCHED POLYENES METHOD Let us consider a system consisting of two chain fragments (the extension of the treatment to systems including more chain fragments is straightforward).The HMO eigenvalue/eigenvector problem for this system can be represented as (H+V)c =0 (1) where H’ and H” are the Huckel matrices of the two chains, W describes the interaction between the chains (we shall express the elements of H’, H” and W in units of p, a resonance integral corresponding to a chain without bond alternation), and c’ and c” are column vectors for coefficients of the atoms of the corresponding chains in the HMO. If the resolvent matrix (Green’s-function matrix) is defined as GH=I (2) eqn (1)can be transformed into (I +GV)c =0 (3) [see ref. (lo]. We should emphasize that eqn (3) is an exact equation, as is eqn (1).The block form of H ensures that G is also a block matrix: where G’ and G’are defined as G’H’=I, G“H”=1. Now eqn (3)can be expanded as c’+ G‘Wc‘’=0 GfWC‘+C‘’ = 0 For the elements of the matrices G’ and G”there exist analytical formulae valid for chains of arbitrary length,4 and therefore eqn (4) provide a basis for the analysis of the HMO energy levels and wavefurictions of the system being discussed. The analysis of eqn (4) is complicated when W is a matrix of high rank, but for the case of branched polyenes it is a first-rank matrix, which makes the use of eqn (4) expedient. BRANCHED POLYENES WITHOUT BOND ALTERNATION We shall consider two cases [fig. l(a) and (b)]. In fact, fig. l(b) is a particular case of fig.l(a) when M = 1. The elements of the interaction matrix W are Wr,= &KSM~ (5) P. KARADAKOV AND 0. CASTARO (b) L' ! FIG. 1.-Branched polyenes without bond alternation. The expansion of eqn (4a)and (46)by the elements of W defined by eqn (5) leads to Setting r = K in eqn (6a)and s = M in eqn (66)one obtains CX+ G&cL = 0 (7a1 GLMc~+cL=O. (7b1 The condition for the existence of a non-zero solution of eqn (7)is 1-G&GLM = 0. (8) The general formula for the matrix elements of the resolvent matrix in the case of a J-atom chain fragment without bond alternation is4 G,, = Gqp= (-l)'-'sin po sin (J+ 1-q)w/[sin o sin (J+ l)o] (qsp) (9) where w is introduced as x = P-'(a -E) = 2 cos 0. (10) Eqn (9) is not defined at x = *2, but as will be seen later this does not affect the present discussion.The case when 0 <1x1 <2 is described by real values of w, and for )xI >2 one employs complex w : w = it + d(-x). (11) 8(y)is the unit function 1: y*o 8(y)=Io: y (0. The combination of eqn (8) and (9)yields an equation for o of the form 1-sin KO sin (t-K + 1)osin Mo sin (N-M + l)o/ [sin2o sin (L+ 1)o sin (N+ 1)o]=o (12) which, together with eqn (lo), determines the energy spectrum of the branched system. ELECTRONIC STRUCTURE OF BRANCHED POLYENES If we set ck=A from eqn (6), (7) and (9) one can obtain the coefficients of the atomic orbitals in the HMO: c: ={ (-l)‘-KAsin rwlsin KO, (-l)r-KAsin (L+ 1-r)w/sin (L+ 1 -K)o, 1 G r G K K sr <L (13) c: =( (---I)’-~Bsin su/sin MU, (-I)’-~Bsin (N+ 1-s)o/sin (N+ 1-~)w, 1ss s M M ss sN (14) A can be determined through a normalization of the wavefunction.The search for a complex root of eqn (12)in the form of eqn (11) leads to 1 -sinh Ks sinh (L-K + 1)t sinh sinh (N-M + 1)(/ [sinh2 6 sinh (L+ 1)t sinh (N+ 1)5]= 0. (16) This equation has a non-zero solution if KM(L-K + 1)(N-A4+ 1)(L+ l)-I(N+ l)-I> 1. (17) Eqn (17)is easily fulfilled for the interesting cases of branching; e.g.even for K = 1, L =M = 2, a non-zero solution of eqn (16) exists for N >7. When eqn (16) has a non-zero solution, there exist in the spectrum two states with energy 1x1>2 [see eqn (10) and (ll)],given by XI= k2cash 6. (18) The wavefunctions of these states are localized about the place of branching.For arbitrary K,L,M,N satisfying eqn (17)this statement can be proved numerically with the use of eqn (13)-(15). For some boundary cases an analytical proof is possible, and the values of XI and the coefficients of the corresponding HMO can be calculated exactly. (a) K,L,M,N +00 (branching equivalent to a bridge-bond between two infinite chains). The real solutions of eqn (12) cover continuously the interval (0, T),and the corresponding values of x form the zone of the bulk states Ixl<2. The asymptotic form of eqn (16) is 1 -(4 sinh2()-I = 0 and sinh = 1/2; ,$ == 0.481. For xI from eqn (18) one obtains XI= f51’2 =*2.236. The coefficients in the wavefunctions corresponding to eqn (18) are obtained as c, = A exp (-n[) P.KARADAKOV AND 0.CASTANO (because the system is alternant, we show only the coefficients of the bonding state), where the number n is introduced as follows: the atoms participating in the bridging bond are assigned n = 0, their four nearest neighbours n = 1, and so on. We have used the fact that eqn (15) transforms into B = A/(2 sinh 6)=A (for the bonding state). Obviously the squares of the coefficients decrease exponentially as the distance of the atom from the bridging bond increases, and consequently the states in eqn (18) are localized on this bond. For the normalization constant A one obtains A = (tanh 6/2)1/2=0.473. (b) M = 1; K, L, N + 00 (branching of an infinite chain at an atom).In this case a zone of bulk states Ix I <2 is also formed. The asymptotic form of eqn (16) is 1 -[exp (25)-1]-l= o and exp (6)= 21/2; 6 == 0.346. The energies of the corresponding states [eqn (IS)] are XI = *(2ll2+ 2-1/2)== *2.12 1. For the HMO coefficients of eqn (19)one obtains cn = 2-1-n/2 (we show again only the bonding-state coefficients). The atom at which the branching takes place is assigned n = 0, its three first neighbours n = 1, and so on. In this case, we have used the fact that eqn (15) transforms into B = A exp (-6) (for the bonding state) and A = [exp (26)-1l1l2[exp (26)+ 21-l’~= $. The expression for the coefficients shows that the states in eqn (19)are localized on the atom at which the chain branches.BRANCHED POLYENES WITH BOND ALTERNATION Let us investigate the cases shown in fig. 2(a) and (b). The elements of the interaction matrix W are now Wrs = aar,2K-la2M-l,s (20) (we introduce a = Pa/@< b = Pb/@).The supposition that in the bonding between the chains occurs for odd-numbered atoms does not lead to a loss in generality, because we shall be concerned mainly with the boundary cases when the chains are of infinite length. The equations equivalent to eqn (6) and (8) in this case are =C: QG;,~K-~c;M-~0, r= 1,. . . ,2L (214 +c,” = 0, s = 1, . . . ,2N (21b)aG:2~-1ci~-~ ELECTRONIC STRUCTURE OF BRANCHED POLYENES FIG. 2.-Branched polyenes with bond alternation. and 1-a2G~~-i,2~-iG2"~-i,z~-i (22)=0 respectively. The elements of the resolvent matrix for a 2J-atom chain fragment exhibiting bond alternation are4 (G is a symmetric matrix) G2p-1,2q-1 = C-l(w)x[bsin po +a sin (p-1)o]sin (J-q + l)w (qap) (23a) G2p,2q= C-'(w)x sin po[bsin (J-q + 1)o+a sin (J-q)o] (q2p) (23b) G2p-1,2q= -C-'(w)[b sin po +a sin (p-l)o] x[bsin(J-q+l)o+a sin(J-q)o] (qsp) (234 G2p,2q--1 = -C-'(w)x2 sin po sin (J-q + 1)o (qap + 1) (234 where C(o)= ab sin o[bsin (J+ l)w +a sin Jo].In eqn (23)o is introduced as 22 x -a -b2=2abcoso. (24) The resolvent matrix with elements given by eqn (23)is not defined at x2= (afb)2. The case when a -6 * <x2<(a+6)2is described by real values of o. Values1'of x for x2>(a+b) are described by complex w o =it (254 and the case x2<(a-b)2by w =it+v.The formulae (21)-(24) allow the calculation of the energy spectrum and wavefunctions for arbitrary K,L, M, N, but exact solutions can again be found only for the boundary cases. (a) K, L, M, N +co (a bridging bond between two infinite alternating chains). The energy values corresponding to real solutions form in this case two zones of bulk states: -(a +b)<x <a -b; -(a -b)<x <a +b,separated by a gap of 2(b-a). P. KARADAKOV AND 0. CASTANO The asymptotic form of the equation for 6, obtained by combining eqn (22), (23a), (24)and (25), is 1-(a2+ b2f2ab cosh 6)/(4b2sinh26)= 0. (26) [The upper sign refers to eqn (25a)and the lower to eqn (25b).] The solution of eqn (26)is cosh 6 = [(5~*+20b~)~’~*a]/(4b). The introduction of eqn (27) into (24)leads to xf = a2+ b2f2-lU[(5u2+20b2)1’2fa]. (28) The states given by eqn (28) can be proved to be localized about the bond connecting the chains, as in the case of polyenes without bond alternation.The upper signs in eqn (28)correspond to “outer” states (w =‘it) and the lower signs to “inner” states (w = it +T),situated in the forbidden zone. (b) M = 1; K, L, N -* 00 (branching of an infinite alternating chain). In this case 6 is determined from the asymptotic equation 1 -[bexp (-6) fa]/(2bsinh 6)= 0. (29) (The upper sign corresponds to “outer” states and the lower to “inner” states.) Solving eqn (29)with respect to exp (4)one obtains exp (5)= [(~~+8b’)~’~*a]/(2b). (30) The combination of eqn (24)and (30)determines the energies of the local states.The common quantum-chemical parameterization for b and a is b =exp (T), a = exp (--7) (31) where T = ~-‘K(R~-Ra), Rb and R, are the lengths of the corresponding bonds and K is an empirical parameter. Using eqn (31), fig. 3 shows the influence of bond alternation on the electronic spectra of branched infinite polyene chains. 7 FIG. 3.-Influence of bond alternation on the electronic spectra of branched polyene chains (xl in units of p). The dashed lines correspond to the boundaries of the upper zone of the bulk states. Note the change in scale in the upper part of the figure. For further explanations, see text. 80 ELECTRONIC STRUCTURE OF BRANCHED POLYENES Curves a’ and a’’ are for the “outer” and “inner” states, respectively, in the case of a bridging bond between two infinite chains and curves b’ and b” show the behaviour of “outer” and “inner” states for a chain branched at an atom.Only the positive part of the spectrum is shown because of its symmetry about the abscissa. CONCLUSIONS The method developed in this paper has enabled us to study the effect of chain branching on the electronic spectra of infinite polyenes. It has been shown that the branching of a non-alternating infinite chain is connected with the presence of two local states in the spectrum, whose energies and wavefunctions have been calculated exactly. The branching of an infinite alternating chain leads to the appearance of four local states, two “outer” and two “inner” states, whose energies depend markedly on bond alternation.In this respect the branching of the chain leads to an effective “broadening” of the bands in comparison with unbranched chains and to a decrease of the width of the gap in the case of alternating chains. G. F. Kventzel, Teor. Eksp. Khim., 1968,4, 291; 1969, 5, 26; G. F. Kventzel and Y. Kruglyak, Theor. Chim. Acta (Berlin), 1968, 12,1. 0.Castaiio and P. Karadakov, 2.Phys. Chem. N.F.,in press; report made at the IVth Symposium of Quantum Theory of Adsorption and Catalysis, Moscow, 1981. G. F. Kventzel, Teor. Eksp. Khim., 1969, 5, 435. P. Karadakov and 0.Castaiio, J. Mol. Srruct. Theochem., submitted for publication. I. V. Stankevich and 0.B. Tomilin, Zh. Strukt. Khim., 1974, 15,1004. 1. V.Stankevich and 0.B. Tomilin, Zh. Strukt. Khim., 1980, 21,15.’T. K. Rebane, in VoprosiKvantovoi Khimii, ed. M. G. Veselov (in Russian) (Leningrad University, Leningrad, 1963), p. 15.-’Y. Jido, T. Inagaki and H. Fukutome, Progr. Theor. Phys., 1972,48, 808. M. V. Kaulgud and V. H. Chitgopkar, J. Chem. SOC.,Faraday Trans. 2, 1977, 73, 1385. 10 T. Kato, Perturbation Theory for Linear Operators (Springer, Berlin, 1966), chap. IV, 0 6. (PAPER 1/783)

ISSN:0300-9238    

DOI:10.1039/F29827800073

出版商:RSC    

年代:1982

数据来源: RSC

摘要:

J. Chem. SOC.,Faraday Trans. 2, 1982,78, 81-93 Examination of the Dielectric Susceptibility of Poly(y-Benzyl-L-glutamate) BY LEONARDA. DISSADOAND ROBERTM. HILL* Chelsea College, University of London, Pulton Place, London SW6 5PR Received 20th May, 1981 The published literature on the dielectric susceptibility of poly( y-benzyl-L-glutamate), in both solid form and in solutions of differing association, has been examined in terms of a many-body, cooperative theory of dielectric response. It is shown that the shape of the susceptibility as a function of frequency is, in a limited manner, sensitive to the degree of association of the a-helical molecule. Of the two types of dipolar tunnelling transitions that can occur between the molecules only the synchronous flip-flop mechanism is sensitive to the association, the single dipolar flip process remaining unperturbed.The examination of a d.c. bias field experiment shows that neither mechanism is sensitive to d.c. fields, but that both the frequency of the maximum dielectric loss and the amplitude of the susceptibility vary in accordance with the predictions of the many-body theory. Poly( y-benzyl-L-glutamate) is a synthetic polypeptide possessing the optically active a-helical molecular structure. It can therefore be treated as an archetype for more sophisticated biomolecules such as DNA and RNA. Dielectric measure- ments have been proposed' as a means of probing the connection between the dynamic electric properties and the structure of these materials. For this reason the frequency-dependent susceptibility, ~(w),of poly( y-benzyl-L-glutamate) (PBLG) has been measured in the solid form and as a function of its degree of association for solutions, in which it has been dissolved, over ranges of appropriate variables such as temperature, concentration and d.c.bias Extensive examination has been made of the change of the dielectric increment and the loss-peak frequency as functions of these variables. The full interpretation of these results is clearly of importance in understanding the dynamics of a-helix structures. Since the shape function of the dielectric susceptibility, for varying frequency, has not been characterised in these assessments, a full understanding of the available information has not been possible.The d.c. bias experiments' have been examined in terms of Brownian motion'' and lead to non-linear terms in the rate equation and in the susceptibility function, which both become field-dependent. Experimentally there is no evidence for a change in the shape function with applied field, and in particular no evidence for the characteristic Debye shape at zero field which was obtained. Recently we have presented a new approach to the theory of dielectric suscepti- bility12*13which, for the first time, does describe accurately both the shape function and the temperature dependences of the amplitude of the susceptibility and the characteristic frequency of the relaxation process. In particular, for materials in a class which is characterised by an alignment transition of their permanent dipoles at a critical temperature T,,a relationship between the characteristic maximum loss frequency and the amplitude was predicted and has been observed experi- mentally.'4'15 In view of this support for the general theory, the published experi- mental results on PBLG have been re-analysed in terms of the new model, and it will be shown that they confirm a simple and illuminating interpretation. 81 82 DIELECTRIC SUSCEPTIBILITY OF POLY(y-BENZYL-L-GLUTAMATE) THEORY It has been shownI2 that dielectric relaxation in solids and liquids, or in gases under sufficient pressure, is a cooperative, many-body process. When these systems possess re-orientable dipoles with two alternative local equilibrium positions the theory predicts a linear susceptibility of the form x(w>= d2(wp/l)n~'(~>cos (n,r/2)~(w/w,) (1) with the normalised shape function, F(w/op)given by 1-n F(w/w,) = wp+iw ZF1(1 -n, 1-m;2- n ;-wp+iw in which w is the frequency and upthe frequency of maximum loss. 2F1( , ; ; ) is the gaussian hypergeometric function16 and m and n, which both lie in the range from zero to unity, are correlation indices for specific dipole transitions.In order to comprehend their nature it is necessary to realise that although relaxation measurements are concerned de fact0 with disorder, such disorder will exist on more than one le~e1.l~ For example we may define a structural matrix of individual molecules in terms of relative orientations of their axes and translations from site to site which, if perfect, form a crystal matrix exhibiting space-group symmetry operations.It is insufficient to use a correlation length to describe partial ordering of such a matrix, since that measure eliminates the effect of short-range ordering. The short-range ordering itself requires an index to describe its regularity. Liquids differ from solids only in having a shorter correlation length and a more irregular structure. When the molecules are dipolar a second level of disorder exists, that of dipolar orientation. It is this disorder that is directly coupled to an electric-field probe and which produces changes in the nett polarisation. The presence of partial local order, however, means that orientation relaxations cannot be regarded as being individual dipole re-orientations (flips).The motions of any molecule along a coordinate, and in particular along the relaxation coordinate, will couple to other molecules because of the partially regular local structure. The fraction of molecules within the correlated region which are coupled in such a manner is the correlation index n. We therefore find the general result that n = 0, no local structure, no correlation, individual molecules n = 1, full crystalline structure, complete correlation 0 <n <1, partial local structure, partial correlation. In developing these concepts it has been considered that a partially ordered region once created does not change.This is an unjustifiable assumption: obviously there is molecular transport in liquids and even in solids structural re-adjustments can take place when there is structural disorder present. As long as these motions, which exchange molecules between different regions of partial order, do not lead to irreversible changes they can be regarded as time-dependent fluctuations. In a dipolar system they will leave the total polarisation unchanged and can be considered as dipole-exchange fluctuations (flip-flops) whose behaviour can be described in terms of the correlation index m. Such fluctuations will be strongly correlated in liquids for which molecular transport may form a hydrodynamic motion" involving the whole liquid. In solids the correlation will be reduced because the presence of free volume allows such fluctuations to occur without affecting so many other L.A. DISSADO AND R. M. HILL 83 correlated regions. In perfect crystals this form of fluctuation cannot occur. Hence we have m = 1, liquids with perfect hydrodynamic motion m = 0, perfect crystalline structure, no fluctuations 0 < m < 1, viscous fluids or plastics subject to creep. In this picture the relaxation rate upmust be referred to the relaxation of the partially correlated groups and the magnitude of the susceptibility increment, x'(O),depends on the coupling of the dipoles within the group to the electric field. The shape function, defined in eqn (2),indicates that the dielectric susceptibility can be normalised with respect to up.The dielectric loss, given by the imaginary part of the complex susceptibility, ~"(o),has the asymptotic behaviour O<W, in accordance with experimentally observed behaviour in a wide range of dielectric materials.l9 The real part of the susceptibility, ~'(o),as determined from relationship (2) has the forms x'(0)K &(l-n) O>O, (4a) and X'(o)K~'(O)-aw" 0<wp (46) in agreement with the Kramers-Kronig transformation of x"(w). Note that the observed exponent m may be equal to unity either for a perfect synchronous exchange correlation or when the measuring frequency w is too high for these orientation exchanges to respond. The limiting frequency for solids has been estimated, from calculations based on amorphous glasses, as in the range 108-10'o Hz2' and has been observed in butyl stearate in the range of lo9Hz,'~,~~ in good agreement with the predicted value.In small-molecule liquids the limiting frequency will be orders of magnitude higher, approaching that 6f a phonon, i.e. ca. 10l2Hz. Large polymer-chain molecules have yet another level of order beyond those already discussed; in this level the re,gularity of the monomer units or polymer segments is defined. Only when this molecular structure possesses the perfect regularity of a crystalline lattice can the polymer be regarded as a single molecular entity. The PBLG molecule in its a-helix molecular configuration is such a polymer, and can be regarded as cylindrical in shape with a large dipole moment parallel to the cylindrical long axis.In all the cases considered here PBLG is present as an a-helix with, at most, a small degree of association. At room temperature the PBLG-solution phase diagram22 shows that for volume fractions -6%the solution exists as the isotropic phase of a liquid crystal. Room temperature is, however, close to an isotropic-order-liquid-crystal transition tem- perature (TJ,and an increase in concentration drives the system closer to the transition. It is in regions close to phase transitions, such as here, that critical behaviour can be observed.23 We have previously discussed the isotropic-nematic liquid-crystal transition as a function of temperature in terms of a ferroelectric mean-field mode1;15 the effect of a d.c.bias can be directly introduced into this 84 D I EL E CTR I c suscE PTI B I LITY oF POL Y (7-B EN ZY L -L -G LUTA M AT E ) -FIG. 1.-Schematic representation of the potential energy of a double potential minima system of interacting dipoles. The double lined arrow indicates the orientations of the macroscopic dipole. The symbols are defined in the text. model as a modification to the internal mean field, thus allowing the field dependence at a fixed temperature to be discussed. The cooperative nature of the many-body system requires the normalised occupation number difference between the two alternative dipole orientations, designated 1 and 2 in fig. 1, to be a function of itself under thermal equilibrium conditions.'2713 If N1 and N2 are the occupation numbers then the equilibrium- normalised number difference is given by for the dipole alignment system discussed Here B is the average internal-field-splitting energy of the minima in the potential-energy diagram, fig.1, T,is the intermolecular interaction term expressed for convenience as a temperat~re,~~and Me is proportional to the mean field and hence to the polarisa- tion. For this type of system the characteristic frequency has been shown to be12 B+kTcMe up= ua cosh ( kT with the frequency ua having the activated form Va = YO exp (-A/kT) (7) where A is the average potential barrier height. For the particular case considered here, that of macromolecules in solution, uo can be expressed in terms of the viscosity of the solvent, q,by replacing the molecule by an equivalent sphere of radius a as kT uo =-(8)4.rra3q by considering Brownian motion of the sphere.Thus upcontains the effect of other PBLG dipoles as a correlative factor2' as well as the relaxation rate of the molecules as individuals. We note that the complete quantum states of the local potential surface, fig. 1,of the dipole describes a spinning dipole.26 The states below the maximum have discrete orientations with respect L. A. DISSADO AND R. M. HILL FIG. 2.-(a) Coordinate system for the spinning dipole. Angles 0 and 9 correspond to quantised cooperative modes but angle @ is free. Cooperative translations occur in the z axis only, and cooperative librations about the x and y axes.(b)Diagrammatic representation of two adjoining planar liquid-crystal clusters in the smectic-like phase. Association of the molecules destroys the planar regularity and forms the nematic phase. to the axis of spin, those above form a continuum with only a small component along the spin axis, fig. 2(a).No significant difference is introduced by altering the potential surface to a sinusoidal form. Rotational Brownian motion2’ only allows small angle changes within the continuum above the maximum, hence the presence of the activation energy in vq,eqn (7). The extra feature of eqn (6) is the presence of large, discrete angle tilting which cannot be included within the Brownian motion framework but which is equivalent to a mixing in of flipped dipoles.This is necessitated by the presence of an environment of identical large dipolar mole5ules generating an ordered structure in which there are energetic differences between orientations separated by a rotation of 7~ rad and produces the correlative factor in up. The deviation, M’(O),of M from the equilibrium value Meunder the application of unit observation field is given by M’(O)=(l-MS)(kT)-’(l-(l-MZ)-)Tc -1 T * (9) The other parameters in eqn (1)are the average dipole moment of the local system, d, and 5, which can be considered as the maximum reorientation frequency between local configurations of dipole orientation^^^'^^ within the partially ordered group of molecules, and is generally of the order of 10l2Hz.The temperature and field behaviour given above is based on the Weiss theory of order-disorder transitions. This approach has been used as it is most illustrative of the particular features under discussion. More sophisticated expressions, based on scaling theories,23 can be used without altering the form of the dynamics as expressed in eqn (1) and (2). However, the extent of the available experimental data is insufficient to justify such an approach at the present time. In the absence of the rn and n processes the predicted frequency behaviour for the solutions would be of the Debye form x(u)cc(1+iu/u,,-* (10) 86 D I E L E CTR I c suscE PTI B I L ITY OF PO LY (y-B EN ZY L -L -G LUTA M ATE) and the observed non-Debye behaviour is commonly ascribed to a suitable distribu- tion of relaxation times, (up)-', owing to a range of molecular weights.In practice the range of molecular weights is finite and there is a well-defined average value. Hence the range of upexpected from eqn (8) will be limited. The resultant effect would be to produce non-Debye behaviour over a frequency band in the neighbour- hood of the mean value, but to leave the wings of the frequency characteristic in the Debye form. In the experimental results examined here no evidence of Debye behaviour was observed, whereas the power-law behaviour contained in eqn (2 was general, a result consistent with cooperative behaviour near a transition point. 32 EXPERIMENTAL SHAPE FUNCTION Dielectric measurements have been made on a wide range of forms of PBLG.2-'o The published data have been examined and observed to obey the power laws form predicted in eqn (2)-(4). The characteristic shape parameters m and n have been determined for these and are listed in table 1, together with details of the TABLE1.-SUSCEPTIBILITY SHAPE FUNCTION PARAMETERS FOR PBLG frequency molecular sample m n range/Hz weight ref.solid, orientationally ordered film 0.31 0.87 10-lo6 -2 solid, prepared by Leuchs method 0.42 0.81 3 x 10-'-106 1.2~10~ 3 solution in benzene with E -caprolactam 0.78 0.50 5x 10-lo6 6.9~10~ 4 solution in trans -1,2-dichloroethylene containing NN-formidemethylamide 1.0 0.50 lo2-lo4 4.6~10' 5 solution in purified ethylene dichloride 0.78 0.49 7x10-2x104 3x103-4x104 6 solution in ethylene dichloride 0.61 0.49 2x102-2x104 1.5~10~ 7 solution in ethylene dichloride 0.54 0.52 102-104 -8 solution in dioxan -0.44 7x10-2x104 6x105-2x106 6 solution in dioxan with DMF 0.76 0.51 7 X 10-2 X lo4 1o5 9 solution in dioxan 0.81 0.54 3x10-2x104 1.5~10~ 10 samples and the conditions of measurement, where these are available.Where possible the normalisation technique" has been used to increase the significance of the values of these parameters. From inspection of table 1 it is apparent that the solid form is essentially different from that in solution, as the exponent m is less and the exponent n is greater. From the magnitudes of m and n it can be concluded that the lattice structure governing polymer-dipole motion in the solid is of a much more regular nature than in solution, although the value of n observed is by no means as large as that for many near-perfect crystalline system^.^' The fluctuations are also still considerable, as appropriate to the plastic polymeric state in which the measurements were made.More interesting, however, is the behaviour of PBLG in a number of solutions of differing association. The values of n observed vary only over a limited range and the average is well defined at 0.505,independent of the nature of the solvent, which clearly indicates that in solution the dipolar single-flip processes are charac- teristically correlated and independent of the form of interaction between the solution and the helical molecule.This is not the case for the synchronous flip-flop process, characterised by the exponent m,in which the variation is large, extending L. A. DISSADO AND R. M. HILL from complete correlation in trans-1,2-dichloroethylene containing NN-form- idemethylamide as a de-aggregant to ca. 0.6 in ethylene dichloride. The results for the latter solvent are variable and suggest that the exact value of the parameter m was sensitive to impurities. In dioxan solution the average value of m appears to be ca. 0.8, as it is in benzene containing E-caprolactam. Within the experimental ranges investigated there was no evidence for change in the characteristic exponents for any one sample under varying experimental conditions.The effects of solvents on the structure of PBLG have been and there is general agreement that the configuration of the solute is dependent on the hydrogen-bonding ability of the solvent, i.e. on the association. Ethylene dichloride gives a weak association and leaves the molecules as linear, rod-like helices with a dipole moment proportional to the molecular weight.6 In contrast dioxan gives a stronger association and forms long, non-linear the association taking place through hydrogen bonding at the ends of the initially individual helical molecules. As the exponent rn is sensitive to the degree of association we are led to the conclusion that these particular hydrogen-bonding sites decrease the correla- tion of synchronous flip-flops between the elongated molecules, compared with the individual, non-associated molecule.The longer the associated molecule the smaller the value of m. In table 1 clear evidence is shown that such a change is indeed taking place. Perfect flip-flop correlation occurs for a solute which contains de-aggregant, and the frequency range that has been investigated is orders of magnitude less than the expected limiting frequency for this process. Furthermore, the lowest value of correlation occurs in the solid material in which the association must be large. The solvent independence of n reveals that the structure whose regularity n measures is that of the regions of liquid-crystal ordering, which is determined by inter-helix steric interactions, van der Waals’ forces and dipolar interactions.It may be speculated that a value of n equal to one-half indicates that the regularity occurs in three of the six molecular degrees of freedom consistent with a smectic- like liquid-crystal phase in which one translation and two end over tail rotations will be cooperative motions, fig. 2(a) and (b). That the value of m is unity for the unassociated perfectly formed a-helical molecule indicates perfectly correlated dipole exchange and hence a perfect flow. This refers to perfectly correlated hydrodynamic motion within the smectic-like planes, i.e. free molecular transport in a plane perpendicular to that axis which has near-crystalline regularity. The effect of association is to extend molecules so that they either cross into another plane or, less likely, fold within the same plane.In either case the correlation of the exchange (transport) is reduced. To obtain perfect (m= 1)correlation molecular transport would have to be correlated from plane to plane and would not be possible in a liquid under isotropic pressure conditions. D.C. BIAS MEASUREMENTS The normalisation technique has also been applied to the d.c. bias field measure- ments on PBLG in solution made by Block and Hayes.’ The normalising parameter in this case is the electric field. The resultant plot, fig. 3, shows a well-defined susceptibility plot with the exponent rn being unity and the exponent n one-half, as reported in the previous section and in table 1. Fig. 3 also contains the trace of the datum pointlg at each value of the field.The straight line through these points indicates that a single relationship between the amplitude of the susceptibility and the characteristic frequency, as a function of the magnitude of the bias field, 88 DIELECTRIC SUSCEPTIBILITY OF POLY(Y-BENZYL-L-GLUTAMATE) , I I I exists. Fig. 4 shows the separate electric-field dependences of both the characteristic frequency and the amplitude. All the information regarding the interaction of the d.c. bias field with the helical molecule in a de-aggregated form is contained in these two plots. /8 1.0 1 I I I I I Ill 1o5 lo6 bias field/V m-' FIG.4.-The field dependences of both the frequency of maximum loss, up,and the amplitude of the susceptibility, A(x).The data are taken from the field-shift points shown in fig.3. L. A. DISSADO AND R. M. HILL From eqn (l),(6) and (9) two relationships between the amplitude of the susceptibility and the characteristic peak-loss frequency can be derived. These have been determined A(X)QJ," (11) and A(x)oc where A(x) is the amplitude of the susceptibility function. The former is applicable when the activation term, eqn (7), dominates the cooperative term [1-(1-M: )T,/TI,i.e.when the temperature is outside the transition region which lies in the neighbourhood of the temperature T,. The proportionality (12) holds in the alternate case when T is close to T,. Inspection of the locus of the field-shift points in fig.3 shows that the equivalent experimental inter-relationship is of the form A(x)cc WPO.~ (13) which clearly indicates that the temperature at which the measurements were made, 20°C, is in the cooperative transition region. Furthermore the magnitude of the exponent in relationship (13) is totally consistent with the value of n of 0.5 determined from the shape analysis using eqn (3a) and (4a). Relationships (11) and (12) have been predi~ted'~"' and ob~ervedl~"~ with temperature as the external vhriable, but this is the first time that a characterisation in terms of electric field has been established. The effect of a doc. bias field, of magnitude ED, can be included in the scaling expressions given earlier by adding a term EDd to the internal field term B; hence, with d as the dipole moment &=B+E,d.(14) Eqn (5) has been solved iteratively" to give Me for a range of values of the normalised variable B/(kT,)and the solutions are shown in diagrammatic form in fig. 5. The effect of the field is contained in this diagram by changing the magnitude ___----p.01 .__---/ / c----0*51-1.0-0 1.0 2 .o 3.O Tc/ T FIG. 5.-Plot of the solutions of eqn (5) for a range of values of the parameter B/(RT,). The arrows indicate the direction of shift of the effective value of B/(kTc)on the application of an external d.c. bias electric field for increasing alignment as discussed in the text. 90 D I E I_ E CT R I C S LJ S C E PT 1 B I L I TY 0F P 0I, Y (7-B EN Z Y L--L -G LUTA M ATE) 1 oz FIG.6.-Plot of the effect of d.c. bias field on both the peak-loss frequency, wp,and the amplitude of the susceptibility, A(x). (-) B/(kTc)=O.O1, T/Tc=1.25; (---) R/(kTc)=O.l, T/Tc=0.8; (---) B/(kTc)=0.3,T/Tc=1.25. of B as indicated by eqn (14). When EDis in the same direction as Me the effective value of Me is increased. Such an increase in Me in the critical region around T = T,results in an increase in upfrom eqn (6). The results of a detailed calculation for a specific set of parameters is given in fig. 6 and can be compared with the equivalent experimentally determined field dependence of fig. 4. In this region of behaviour it can be shown that up=Const. x Mz cosh (BD+,","Me) * Agreement with the experimental results is good.The equivalent relationship for the amplitude of the susceptibility is automatically ensured as relationship (12) is obeyed. The underlying physics of relationship (12) lies in the existence of partially correlated molecular clusters in the critical region. Above T, these give a nett polarisation against a non-polar background; below T, they represent a decrement from a perfectly polar system. In either case their fluctuations (m)and regularity (n)are determined by the same forces and, in the case under consideration here, are unchanged. The effect of temperature is to change the correlation length of the clusters; above T, there is an increase with decreasing temperature and below T,a decrease with decreasing temperature. In the latter case the unaligned clusters form a polarisation decrement. The effect of a d.c.bias field is to convert clusters, at any temperature, into decremental clusters. A comparison of the field-dependent values of M for T> T, in fig. 5 reveals that the behaviour followed is similar to that of the temperature dependence for T< T, and B =0. As the field increases the correlation length of the decremental clusters decreases (Me+1)and the number of dipoles within the correlation length decreases. This has the two-fold effect that L. A. DISSADO AND R. M. HILL there are less cluster dipoles to respond to the a.c. probe field, thus decreasing the amplitude A(x)and increasing the relaxation rate up,which involves the readjust- ment of fewer molecules.The index n measures the fraction of those cluster dipoles whose motions are correlated at any one time. The scaling relationship (12)shows that only the fraction of dipoles whose motion is not correlated with the group, 1-n, are free at any one time to respond to the a.c. field probe giving A(x)=: [NG(E)]'-" (164 where NG(E)is the number of dipoles in the cluster for d.c. bias E. For times longer than 5-l the disturbance is distributed over the whole of the cluster, and the relaxation rate upwill be determined by all molecules within the cluster wp=: [NG(I?)]-' (166) which together give eqn (12). CONCLUSIONS In the examination of the dielectric behaviour of solutions, as in the case of solids and liquids, the information about the system appears in three forms: as changes in the magnitudes of a characteristic frequency and of the amplitude.of the susceptibility, and in the shape of the susceptibility as a function of frequency.All of these changes can be driven by the action of an external variable. Byneglecting the information contained in the shape function only an incomplete understanding of the nature of the response of the system can be achieved. It has been shown here that the susceptibility shape function does contain useful informa- tion which is in addition to that which can be obtained by investigation of the other parameters. The approach that has been developed here does not replace the more conventional approach, but strengthens it in specific aspects, particularly in the correlation of dipolar effects between the macromolecules in solution.It has been shown that the effect of varying the association of solvents for PBLG is to change the pre-peak exponent rn in the dielectric loss curve, and hence in the real part of the susceptibility. Previous work had concentrated on the change in amplitude, the dielectric increment and the peak-loss frequency. The results reported here are in agreement with the previous conclusions, but give more detail of the effects of molecular association in that the parameter rn is the correlation of dipolar exchange and is weakened as the degree of association increases. Hence the bonding between individual helical molecules interferes with molecular trans- port.This is not reflected in the response of individual dipolar flips, which are unaffected by molecular association, and hence correlated not along the length of the molecule but in planes perpendicular to the length. It has also been shown that the susceptibility/frequency shape characteristic is invariant under d.c. field conditions, as it is under varying temperature and weak solution concentrations. However, the magnitude of the susceptibility and the frequency of the peak loss, which together determine a specific point on the general susceptibility characteristic, can be normalised with respect to the field, indicating that the field is a parameter in the dynamic equation of state describing the system. The development of the equation of state to include this term has been given.The susceptibility shape function has been completely described by the theory of dynamic cooperative systems recently presented by us. 12,13,15 Comparison with the experimental results show that for PBLG molecules in solution the degree of correlation of single dipole re-orientations is exactly one-half, independent of the 92 D I ELECT R I c s US cE PT I B I L I T Y oF POL Y (Y-B EN zY L -I, -G LUT AM ATE) association of the solvent. Only for the solid form has a different value for this correlation been observed, as expected from consideration of the changes of the lattice structure. It has been clearly established that the degree of correlation of synchronous exchange dipole orientations is affected by the degree of association or aggregation of the molecules.A relationship between the amplitude of the susceptibility and the frequency of maximum loss, as a function of the magnitude of the bias field, has been observed and is consistent with the general theory. The observation of the particular power law indicates that the temperature used in the experimental observations, ca. 20 "C, was close to the critical region in which a dipole alignment transition can be expected. N.m.r. investigations have shown a significant decrease of both linewidth and second moment in the same temperature region,34 which is further evidence of a critical temperature. It is known that this temperature is greater than, but close to, the isotropic/ordered liquid-crystal transition.22 A detailed examination of the characteristic frequency as a function of the applied field under d.c.bias conditions has shown non-linear behaviour which, in the experimental arrangement used, has been applied in such a sense as to further align the dipoles in their originally preferred direction. Although this analysis is perforce rudimentary it is nevertheless comprehensive in terms of the experimental information assessed. As the first of its kind it clearly indicates what further experimental information is required for a full investigation of this interesting system. Further detailed experiments of the field dependence as functions of the direction of the field applied and of the temperature would allow the exact relationships between the structure of the a-helix molecule and its dipolar dynamics in solution to be determined. At present it is certain that the PBLG molecules are correlated in terms of individual dipolar re-orientations and of synchronous exchange processes.The authors acknowledge the tenure of an S.R.C. Research Assistantship by L.A.D. during part of the time in which this work was carried out, and very helpful discussions with Dr. H. Block. G. P. South and E. H. Grant, Biopolymers, 1975,13, 1777. A. Tanaka and Y. Ishida, J.Polym. Sci., 1973, 11, 1117. K. Hikichi, K. Saito, M. Kaneko and J. Furuichi, J. Phys. SOC.Jpn, 1964, 19, 577. H. Block, E. F. Hayes and A. M. North, Trans. Faraday SOC.,1970, 66, 1095. H. Block and E. F.Hayes, Trans. Furuday Soc., 1970,66, 2512. A. Wada, Bull. Chem. SOC.Jpn, 1960, 33, 822. A. Wada, J. Chem. Phys., 1959,31, 328. A. Wada, J. Chrm. Phys., 1959,31,495. A. Wada, J.Polym. Sci., 1960, 45, 145. 10 A. Wada, J. Chem. Phys., 1958, 29, 674. I1 A. Morita, J. Phys. D, 1978, 11, 1357. 12 L. A. Dissado and R. M. Hill, Nature (London), 1979,279, 685. 13 L. A. Dissado and R. M. Hill, Nature (London), 1979, 281, 286. 14 M. E. Brown, J. Mater. Sci., 1981, 16, 1410. 15 L. A. Dissado and R. M. Hill, Philos. Mag., 1980, 41, 625. 16 L. C. Slater, Generalised Hypergeometric Functions (Cambridge University Press, Cambridge, 1966).17 A. K. Jonscher, L. A. Dissado and R. M. Hill, Phys. Status Solidi (b),1980, 102, 351. 18 L. D.Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon Press, London, 1959).19 R. M. Hill, Nature (London), 1978, 275, 96. 2o J. Joffrin and A. Levelut, J. Phys. (Paris), 1975, 36, 811. 21 J. S. Dryden, J. Chem. Phys., 1957, 26, 604. L. A. DISSADO AND R. M. HILL 93 22 W. G. Miller, C. C. Wu, E. L. Wee, G. L. Santee, J. H. Rai and K. G. Goebel, Pure Appf. Chem., 1974,18?, 37. 23 P. C. Hohenberi, and B. I. Halperin, Rev. Mod. Phys., 1977, 49,435. 24 R. L. Melcher, Phys. Acoust., 1976,12, 1. 25 M. G. Brereton and G. R. Davies, Polymer, 1977, 18,764. 26 K. J. Kobayashi, J. Phys. SOC.Jpn, 1968, 24,497. 27 R. T. Cox, Rev. Mod. Phys., 1952, 24, 312. 28 P. W. Anderson, B. I. Halperin and C. Varma, Philos. Mug., 1972, 25, 1. 29 W. A. Phillips, J. Low Temp. Phys., 1972, 7, 351. 30 B. I. Halperin, P. C. Hohenberg and S. K. Ma, Phys. Rev. Lett., 1972, 29, 1548. 31 R. M. Hill, J. Muter. Sci.,1981, 16, 118. 32 P. Doty, J. H. Bradbury and A. M. Holitzer, J. Am. Chem. SOC.,1956,78, 947. 33 A. K. Gupta, C. Dufour and E. Marchal, Biopolymers, 1974, 13, 1293. 34 J. A. E. Kail, J. A. Sauer and A. E. Woodward, J. Phys. Chem., 66, 1292. (PAPER 1/815)

ISSN:0300-9238    

DOI:10.1039/F29827800081

出版商:RSC    

年代:1982

数据来源: RSC

摘要:

J. Chem. SOC.,Faraday Trans. 2,1982,78,95-102 Ultrasonic Relaxation Studies of Poly(methylpheny1-siloxane) and its Solutions in Toluene ALASTAIRM. NORTHAND RICHARDBYANDREWR. EASTWOOD,T A. PETHRICK* Department of Pure and Applied Chemistry, University of Strathclyde, Glasgow G1 1XL Received 21st May, 1981 Ultrasonic attenuation measurements, covering the frequency range 5-100 MHz and the temperature range 253-298 K, made on two samples of poly(methylphenylsi1oxane) of nominal molecular weight 4x lo3 (MS 550) and 4.6 x lo5 (MS 350) and on their solutions in toluene are reported. The acoustic attenuation has been compared with the amplitude predicted for a viscoelastic relaxation process. In the case of the MS 550 polymer a good correspondence between experiment and Navier-Stokes theory was observed.In contrast, the MS 350 polymer exhibited a poor correspondence between experiment and theory. This is found to arise from the presence of a significant amount of unreacted cyclic material which exhibits a conformational relaxation. Ultrasonic attenuation in poly(dimethylsi1oxane) has been investigated as a function of molecular weight' and concentration.2 For low molecular weight materials there is a close correspondence between the predictions of a modified Navier-Stokes equation and the amplitude of the observed acoustic attenuation at lower frequencies. Higher molecular weight materials exhibit an additional contri- bution to the relaxation spectrum which is associated with interchain entanglement. Conformational relaxation in these polymers occurs in the high-megahertz frequency range and does not shift significantly with temperature.To date these are the only polymers in which normal-mode processes of viscoelastic character are clearly resolved from apparently localised conformational processes, and it is desirable to confirm this analysis with polymers expected to have a different separation of the two types of relaxation. Poly(methylphenylsi1oxane)should have sterically more hindered substituents on the backbone, and so be such a polymer. In addition, the conformational process in poly(dimethylsi1oxane) was thought to involve a low activation barrier, and so could not be rationalised in terms of simple activated rate process theory. For this reason, too, it is desirable to study a chain in which the behaviour of more normal thermally activated conformational rotation can be compared with viscoelastic relaxation processes.Finally, there is some difficulty in rationalising the high-frequency relaxation (studied3 by dynamic Kerr effect and dielectric relaxation) of poly(methylpheny1- siloxane) with lower-frequency viscoelastic relaxation4 and with expectations pre- dicted from the studies of poly(dimethylsi1oxane). Consequently it was decided to study this polymer in order to confirm the nature of the high-frequency conforma- tional relaxation and the general applicability of the overall analysis.'.* t Present address: Department of Mechanical and Civil Engineering, Glasgow College of Technology, Glasgow G4 OBA.95 RELAXATION IN POLY(METHY LPHENYLSILOXANE) EXPERIMENTAL MATERIALS The poly(methylphenylsi1oxane)(PMPS) samples used in this study were kindly supplied by Professor J. Lamb and Professor A. J. Barlow of the Department of Electrical Engineering, University of Glasgow. They were identical with those used in the earlier viscoelastic4 and dielectric3 studies. The polymers correspond to dimethylsiloxanes having 25 '/o of their methyl groups replaced by phenyl groups. They are designated MS 350 (a material with shear viscosity of 15600 cSt) and MS 550 (a material with viscosity 130 cSt). The samples were originally obtained from Midland Silicones Company (MS 350) and Hopkin and Williams Ltd (MS 550).The polymers had been characterised by the Polymer Supply and Characterization Centre, and the gel permeation chromatographic data reported by Kim.4 These data were rechecked in these laboratories using a Waters chromatograph equipped with both refractive index and ultraviolet detectors. Because of the significance of the findings complete traces are presented in fig. 1. The high molecular weight polymer (MS 350) contains a significant low molecular weight component not apparent in the data published previously. The use of dual detectors eliminates the possibility that this is due to solvent (which confusion may have arisen in the earlier analysis). The solvent peak is marked in fig. 1. The analysis of the FIG. 1 .-G.p.c. traces of the poly(methylphenylsi1oxane)samples studied in this paper.The upper pair of traces were obtained using a U.V. detector and the lower pair of traces were obtained using a refractive index detector. (a)MS 550; (b)MS350. major peaks is in agreement with that of Kim, the nominal weight average molecul_ar we_ights of the polymer (in the peaks) being 4x lo3 and 4.6 x lo5, the former having Mw/MNof 1.56 and the latter 26.9. The molecular weight of the lower peak in the distribution of the MS 350 polymer corresponds closely to that of cyclic trimer, which would have been used in the synthesis. The zero shear viscosity data were found to agree closely with those of A. R. EASTWOOD, A. M. NORTH AND R. A. PETHRICK Kim, indicating that the low molecular weight impurity did not arise by degradation on storage.PHYSICAL MEASUREMENTS Densities of the pure polymers and the solutions were measured using specific gravity bottles. Viscosity data were obtained according to the procedure outlined in BS188, the temperature of the thermostat being controlled to better than kO.1 K yielding a precision of measurement of better than 0.5%. ULTRASONIC MEASUREMENTS Attenuation (a/f2)data were obtained over the frequency range 5-100MHz using a conventional pulse technique (15-100 MHz) and an acoustic resonator (5-10 MHz). The precision of measurement was typically better than k2% over the entire frequency range. Velocity (u) measurements were performed using the beat method, and the precision of these measurements is estimated to be *3%.RESULTS AND DATA ANALYSIS The acoustic attenuation data for the polymers MS 350 and MS 550 are pre- sented in fig. 2 and 3. Their general shape of the curves resembles those for PDMS reported previously. CALCULATION OF VISCOELASTIC CONTRIBUTION, BULK POLYMERS In order to calculate the normal-mode viscoelastic contribution from the frequency-dependent shear viscosity it is necessary to interpolate the viscoelastic data reported by Kim4 to the temperatures and frequencies used in this study. a/f2 depends on the real part of the complex viscosity and its calculation requires a knowledge of the imaginary part XLof the complex shear impedance as wellAas the real part RL reported by Kim.4 In principle it is possible to obtain both RL and XLfrom the relaxation spectrum.The method employed here is that proposed by Ferry’ and involves an iterative fitting of a calculated relaxation spectrum to the experimental data. First, the relaxation spectrum H(T)is related to the real part, GI,of the complex rigidity modulus dln G’H(T)=AG’~ dlnw where u-l= T,G’= (R;-X’,)/p and p is the density. The computed relaxation spectra exhibited maxima well displaced from the ideal Maxwell relaxation time, that for MS 550 being three decades below the ideal value. In addition, the spectrum of MS 550 was broader than that for MS 350. In the case of the PMPS polymers the values of XLare very small, and G’ is computed by neglecting XL.This procedure has been discussed by Barlow and Lamb6 and tends to give a value of RLwhich is high.The initial predictions were based on a calculation with A = 1. Subsequent variation of A between 1.O and 0.9 indicated that agreement between theory and experiment was always better than 5%. RLwas then calculated from 03 RL/p*/2= [I-,H(r)w2T2/(1+ In RELAXATION IN POLY(METHYLPHENYLSIL0XANE) 0 10 30 100 0 10 50 100 7 800loooi 400 t 0 10 30 100 0 10 30 100 0.5 252 K 0.4 -(f) 269 K 264K 400 0.2 280 K 0 10 30 100 0 10 30 100 log (frequency/MHz) FIG. 2.-Ultrasonic attenuation curves [(a)-(e)]and calculated shear viscosity curves (f)for MS 550 as a function of temperature. (a)252, (6) 269, (c) 264, (d)280 and (e) 311 K. Solid lines in the attenuation curves refer to the observed attenuation data, the dashed lines the calculated shear contribution.The best fit of the relaxation spectrum to the experimental data and analytic function presented by Kim, and a test of the derivative function, indicated that a value of A in the region of 1to 0.9 was appropriate The function was found to be insensitive to the precise value of A in this range. Next, using the relaxation spectrum H(r),the real shear viscosity p: was calculated using the relation co 1+w2r2)sIn r. (3) A. R. EASTWOOD, A. M. NORTH AND R. A. PETHRICK 99 1000I 1 1000* 800-(b) 600-400 --Jbx -----x-x-x----zoo ----_ I I 0 10 30 100 loool 7 600E W ”0 10 30 100 0 10 30 100 10001 1 Oe5I 800 600 400 -200 ---------I-----pz KT-k -0 10 30 100 log (frequency/Mhz) FIG.3.-Ultrasonic attenuation curves [(a)-(e)]and calculated bulk viscosity curves (f)for MS 350 as a function of temperature. (a)252, (6)269, (c) 277, (d)287 and (e)321 K.Solid lines in the attenuation curves refer to the observed attenuation data, the dashed lines the calculated shear contribution. Substitution in the Navier-Stokes equation yields a f2-87r2p1/3pv3 (4) as the contribution from shear viscosity, with z, the velocity of sound at the appropriate frequency. However, the total acoustic attenuation from viscous processes in organic liquids includes both a pure shear component as described above, and also a volume viscosity.Thus the total viscous attenuation is obtained by multiplying the shear RELAXATION IN POLY(METHYLPHENYLSIL0XANE) contribution of eqn (4) by a factor K K = 1+p,fj/pi (5) where pfj is the volume or bulk viscosity of the liquid. The values of (a/f2)shearcalculated for MS 550 are presented in fig. 2 together with the experimental data. The calculated values lie well below the experimental observations, indicating that K has a finite value in these experiments. CONFORMATIONAL CONTRIBUTION TO BULK VISCOSITY Calculation of the values of pfj for MS550, fig. 2, indicates that this parameter is independent of frequency, varying only with temperature. This implies that the bulk viscosity is associated with a relaxation process occurring at higher frequency. This is consistent with the hypothesis in the case of PDMS that an increase in the parameter K at high frequency is associated with a change of the relaxation from one dominated by normal-*mode motion to one reflecting the conformational changes.In this case, although the amplitude factor reflected in K is independent of temperature, the ratio of the shear to bulk viscosity drops from 6.5 to 2.7 over the experimental temperature range. Such behaviour is usual in the case of confor- mational changes in organic liquids and implies that rotational isomerism of the polymer backbones occurs in the high-megahertz region at room temperature. This proposition is consistent with dielectric studies of Baird and Sengupta7 and Beevers et Because the relaxation frequency could not be determined, the activation barrier to conformational change likewise was unobtainable.However, the temperature dependence of the amplitude of the process can be analysed in terms of the energy difference between rotational isomeric states, yielding a value of 2.6 kJ mol-' for MS 550. In contrast, MS350 exhibits attenuation curves which do not provide such a clear cut analysis of the data, fig.3. For this polymer the bulk viscosity, and the parameter K, are frequency dependent. The increase in the bulk viscosity at high frequencies on lowering the temperature indicates that the observed relaxation spectrum is composed of an overlap of the 'normal-mode' process [reflected in the shear viscosity, eqn (4)] and a relaxing conformational contribution.This shift of the internal rotational isomerism to lower frequency implies a higher activation energy. Alternatively, some other conformational change is present. Support for this latter hypothesis comes from the analysis of the chromatographic traces, fig. 1, indicating the presence of cyclic trimer. Conformational changes associated with a cyclic structure would be slower than those of the less constrained linear chain and therefore would occur at lower frequency. Further support for this interpretation comes from studie's3 of the Kerr effect in this sample. It was observed that the anisotropy decay corresponded to two distinct relaxation processes. The occurrence of the trimer would also explain the apparent breadth of the relaxation in this work as well as in the earlier ACOUSTIC ABSORPTION IN TOLUENE SOLUTIONS Solutions of the polymers in toluene were also investigated, fig.4. As in the case of PDMS, there is a marked decrease in the attenuation as the concentration A. R. EASTWOOD, A. M. NORTH AND R. A. PETHRICK i-I Elilv,IA 0.5 0.6 0-7 0.8 0.9 1.0 0.5 0.6 0.7 0.8 0.9 1.0 concentration (wt%) concentration (wto/o) FIG.4.-Ultrasonic attenuation for (a) MS 550 and (b)MS 350 as a function of concentration. The solid lines are the computed viscoelastic contribution, with no allowance for chain entanglement. is decreased. The theoretical normal-mode and bulk viscosity contribution, shown as full lines in fig.4,was predicted using the equation a/fzolution (0)(rc~s/rc~B)c= (a/f:olymer)(a) +a/f:oluene (1-C> (6) where c is the concentration of polymer. In this equation the second term reflects the concentration dependence of the contribution from the solvent. The details of the calculation have been discussed previously.* At high concentrations there is a significant difference between the predictions based on eqn (6) and experimental observations. This difference is ascribed to polymer-polymer interactions, and again there is a correspondence between the concentration at which this deviation occurs and that at which polymer chain entanglement can be seen in flow viscosity. CONCLUSIONS Poly(methylphenylsi1oxane) exhibits similar behaviour to that observed in the more flexible PDMS.The low-megahertz relaxation is predominantly ‘normal- mode’ in character, and internal rotation occurs at higher frequencies at room temperature. An additional relaxation occurs in the case of the MS 350 polymer, and this may be associated with conformational changes involving ring inversion of a cyclic trimer. The more concentrated solutions in toluene give further evidence of chain entanglement. It would therefore appear that these facets of polymer motion in solution and in liquid polymer are not unique to poly(dimethylsi1oxane). One of us (A.R.E.) thanks the S.R.C. for a postdoctoral research fellowship. The help and assistance of the technical staff in the Department of Electrical Engineering, University of Glasgow and the collaboration of Professor J.Lamb are gratefully acknowledged. W. Bell, A. M. North, R. A. Pethrick and B. T. Poh, J. Chem. Soc., Faruday Trans. 2, 1979,75, 1115. W. Bell, J. Daly, A. M. North, R. A. Pethrick and B. T. Poh, J. Chem. SOC.,Furaday Trans 2, 1979,75, 1452. RE LA X A T I0 N I N P 0L Y (M ETHYL P H E N Y J,S I LO X AN E ) M. S. Beevers, D. A. Elliott and G. Williams, Polymer, 1980, 21, 279. M. G. Kim, J. Chem. SOC.,Faraday Trans. 2, 1975,71, 426. ’ J. D. Ferry, Viscoelastic Properties of Polymers (Wiley, Chichester, 1970), p. 259. A. J. Barlow and J. Lamb, Proc. R. SOC.London, Ser. A, 1959,253, 52. M. E. Baird and C. R. Sengupta, J. Chem. SOC.,Faraday Trans. 2,1974, 70, 1741 (PAPER 1/822)

ISSN:0300-9238    

DOI:10.1039/F29827800095

出版商:RSC    

年代:1982

数据来源: RSC

摘要:

J. Chem. Soc., Faradcly Trans. 2, 1982, 78.103-112 Electronic and Vibrational Spectra of [Me4NI2UO2Br4 BY COLIN D. FLINTAND PETER A. TANNER Department of Chemistry, Birkbeck College, University of London, Malet Street, London WClE 7HX Received 25 th May, 1981 Raman and polarized infrared, electronic absorption and luminescence spectra have been recorded for [Me4NI2UO2Br4 at temperatures down to 6 K. In contrast to a previous study the spectra are interpreted in an analogous manner to those of the corresponding tetrachloro complex. Eight electronic origins have been located in the low-energy region of the absorption spectrum. The static and vibronic intensity mechanisms are discussed under the model of Denning. The detailed interpretation of the polarized absorption spectrum of Cs2U02C14 has enabled a model of the electronic structure of the uranyl ion to be formulated.2 It is desirable to test this model against the electronic spectra of a variety of uranyl compounds in order to determine its range of applicability and the likely values of the parameters employed.In this paper we report a detailed study of the electronic absorption, luminescence and vibrational spectra of single crystals of [Me4NI2UO2Br4 and compare the energies and symmetries of the eight lowest excited states of the U02Br;- ion with those of the UO2Cl;- ion. DiSipio et al.3 have reported the absorption spectrum of this compound and assigned eleven electronic origins, nine being degenerate in the idealized D4h anion point group. There is little correlation between the results of DiSipio et al.and the Denning model. Our measurements were carried out on thicker crystals at higher sensitivity and resolution but were limited to the lower-energy part of the spectrum. Whilst there was some resemblance between our spectra and those of DiSipio et al., we note that the polarization directions differ. We also derived different selection rules4 and as a result our interpretation of the spectrum is quite different, but consistent with the work of Denning and our previous studies on salts of the UO2Clz- anion. Wong et al.’ have carried through a detailed study of the luminescence spectrum of Cs2U02Br. However, at low temperatures the intrinsic luminescence was masked by intense emission from exciton traps.No polarization studies were performed and the symmetries of the luminescent states could therefore not be derived. The absorption spectrum of this compound has also been briefly described.6 We are unaware of any previous investigation of the luminescence spectrum of [Me4NI2UO2Br4, although the ground-state vibrational data have been reported.’ EXPERIMENTAL [Me4NI2UO2Br4 was prepared by mixing the solution obtained by dissolving hydrated uranium trioxide in concentrated hydrobromic acid, with a slight excess of Me4NBr in 4 mol dmP3 aqueous hydrobromic acid. The crystalline solid was recrystallised three times from 4moldm-3 aqueous hydrobromic acid and large crystals were grown by the slow evaporation of this solution in the absence of light.Spectral measurements were made as previously 103 ELECTRONIC SPECTRA OF [Me4NI2UO2Br4 RESULTS AND DISCUSSION STRUCTURAL AND VIBRATIONAL DATA [Me4NI2U02Br4 crystallises" in the space group P42/mnm (0:;)with two formula units per Bravais cell, and is isostructural with the corresponding chloride" for which the selection rules have already been given.4 The U02Br2- ion occupies a D2,,site with C2axes along the Br-U-Br bonds. The U-0 bond distance is 176(2)pm and the two U-Br distances are 278.3(6)and 282.8(4)pm. Firm vibrational assignments for the U02Br;- ion in Cs2U02Br4 have recently been given" and the internal U02Br;- modes in [Me4NI2UO2Br4 are analogously assigned. Fig. 1 compares the mull and single-crystal infrared spectra of 4000 3000 2000 1500 1000 500 wavenumber/cm--' FIG.1.-Infrared spectra of [Me4NI2UO2Br4.(a)85 K mull infrared spectrum from 4000 to 400 cm-' (400-200cm-' at 300K). (b) 85 K axial single-crystal spectrum from 4000 to 1550cm-' (note the discontinuity at 2000 cm-I). (c) 300 K single crystal spectrum from 1400 to 400 cm-' (note the change of scale at 2000 cm-'). [Me4NI2UO2Br4 and the assignments for the internal modes of the U02Br;- ion based on these and the Raman spectra are listed in table 1. The behaviour of the single-crystal infrared spectrum of this compound is very similar to that of [Me4N]2U02C14.4 In the bromide salt, the bands at 3610, 3538 and 1609cm-' lose intensity on heating the crystal at 373-383 K.However, it was not possible to completely remove these bands from the spectrum by heating the crystal for several days at 373 K. In the corresponding chloride these features have been associated with water absorbed into the crystal interstices. It was shown that this introduces a non-centrosymmetric perturbation to the uranyl ion and that several non-equivalent uranyl sites are produced by this process. A similar phenomenon occurs in the bromide and we label the unperturbed majority site A and most important minority site B. On heating crystals of [Me4NI2UO2Br4at 373 K, the observation of the V~(~~OU"O) band at 800 cm-I becomes clearer and the weak band at 834 cm-' assigned to Y~(U'~O~), loses intensity. LUMINESCENCE sPECTRUM OF [Me4NI2UO2Br4 a, T and u polarized spectra at 85 and 100K were recorded from 490 to 700 nm, and unpolarised single-crystal spectra from 498 to 610 nm at temperatures C.D. FLINT AND P. A. TANNER TABLE 1.-WAVENUMBERS/cm-' OF INTERNAL U02Bri-MODES FROM THE VIBRATIONAL SPECTRA OF [Me4NI2UO2Br4" single -crys tal mull infrared infrared Raman assignment 1740vw v2+ Vl 1108s v2 + v11 1080m vl+ v3 1072w v2 + v4 1008w v1+ v6 minority site mvw 839w v2; vl at minority site majority site 914s 834w 800w 833s 804vw v2; v1 at majority site v 1 (l60u*O) 770w v1-lattice mode 742mw V2- V4; V1- V9 721m v2 -v11 577w v1-v3 453s v3+ v1 and cation mode 250s v3 194m v11 17s' v6 162s v4 142vw v5 96' v9 80s v7 a Underlined bands were measured at 85 K, others at 300 K; the notation for labelling the normal modes is that of ref.(1); 'ref. (7). down to 6K. Fig.2 shows the first group of bands in the 100K spectra. The +Ag(n7a)(IA)and +A,(a)(IIA)electronic origins are readily identified by their polarisations, at 19 957 and 19 982 cm-', respectively. The v1 and v2 frequencies based on IA and IIA (table 2) correspond to the ground-state vibrational frequencies determined for the majority site (A)in table 1. In the 85 and 100K luminescence spectra, weak structure associated with another site (B) is observed. Fig. 3 clearly shows the enhanced intensity of site B bands at lower temperatures due to excitation transfer from site A.IB and IIB are at 49 cm-' to lower energy than IA and IIA, respectively. At 6 K almost TABLE~.-WAVENUMBERS/C~-~OF INTERNAL U02Br:-MODES IN THE LUMINES-CENCE OF [Me4NI2UO2Br4 mode site A site B Vl 833 841 v2 914 922 v3 263 261 v6 183 185 vt 164 v10 65 63 a From progressions on vibronic structure; the vll progressions on vlo, v3 and v2 are coincident with other structure. ELECTRON I c sPECTRA oF [Me4N]2U02Br4 I I I I 1 19.0 19.4 19.0 20.2 wavenumber/ 103cm-' FIG. 2.-100 K polarized luminescence spectra of [Me4NI2UOZBr4 between 492 and 527 nm. complete depopulation of site A occurs and since IB and IIB are in thermal equilibrium most of the spectral features may be assigned to vibronic structure based on IB. This aids interpretation of the higher-temperature spectra, where different vibronic structure on IA, IIA and IB, IIB overlap.The polarizations of corresponding features in the spectra of sites A and B are similar and the ul and u2 vibrational frequencies at site B are 841 and 922 cm-l, in agreement with the vibrational data (table 1). There is evidence from both the absorption and emission spectra of [Me4NI2 U02Br4for the presence of other non-equivalent uranyl sites. Weak shoulders are observed at ca. 6 cm-' to lower energy of IA, IIA, IB, IIB and associated vibronic structure and correspond to sites C and D. Similar bands may be associated with other origins in the absorption spectrum. A feature at 11cm-' to high energy of origin I is also observed in both emission and absorption, and is assigned as an origin of a further site.Structure based upon this origin is clearly visible in the 107C. D. FLINT AND P. A. TANNER I 19.8 Zd.0 wavenumber/ 103cm-' FIG. 3.-Temperature dependence of the first group of bands in the luminescence spectrum of [Me4N]2U02Br4. low-temperature absorption spectra.. The origin itself is coincident with IB + vl0 in the T absorption spectrum, so that the polarization of this band is uncertain. The presence of these multiple-site origins and the associated vibronic structure mask weak features of the intrinsic luminescence. For site A, the v3 and v6 vibronic origins (a and cr polarized) are located at 263 and 183 cm-', respectively, below the origins IA and IIA.These magnitudes are both ca. 10 cm-' higher than those observed in the 300 K infrared spectra. As in the case of the U02C12- ion, the intensity of the v6[vas(u-x)] mode coupled to the Eg(D4h)state is very weak. The vloS(Br-U-Br) vibronic origins are identified by their polarizations at 65 cm-' below I and 11. Wong et a1.' did not report corresponding features in the luminescence of Cs2U02Br4 because of intense bands in this region due to excition traps. The observation of the anti-Stokes v10 bands and the Y~~(UO~CI:-)/ Y~~(UO~B~:-)frequency ratio of 1.60 in [Me4N]2U02X4 confirm the assignments. The broad 100K shoulder in fig. 2 at ca. 109cm-' below IA corresponds to v10 based on IB. The other shoulder in this region (at ca.90cm-' below IA) is too intense to be assigned to IIB+vlo. In the 13 K spectrum, fig. 3, frequencies of 90f2 cm-' may be identified with origins IA and IB. Raman bands are observed at 87 f1cm-' for [Me4NI2UO2X4 (X = C1, Br) so that the corresponding lumines- cence frequency may be associated with a tetramethylammonium ion model. Other- wise, the frequency is close to the 96 cm-' far-infrared band reported by Newberry.' The internal U02B1-2- v11 progressions on vibronic origins are mostly coincident with other structure based on IA and IIA, but the first members of progressions in v4 on IA +nvl + v2 are observed very weakly in the 7~ spectrum. Most of the 85 K features between 330 and 750 cm-' below IA are assigned to internal cation modes or to hot bands. At lower temperatures the hot bands disappear and new features are observed which correspond to the internal cation modes based on origin IB.Progressions on the above features were followed up to 5Vl at 85 K and to 3Vl at 18 K. For site A, the intensities of bands in the nv1 progression are greatest at ELECTRONIC SPECTRA OF [Me4N]2U02Br4 TABLE 3.-wAVENUMBERS/Cm-' OF INTERNAL CATION MODES IN THE LUMINES-CENCE SPECTRUM OF [Me4NI2UO2Br4 luminescence infrared Raman 338" 370 367 457" 453 454 (495)754" 754 956 954,957 948,955 1176 1170 1175 1294 1295 1291 (1314) (1336) 1419 1415 1419 1442 1448 1440,1453 (1467) 1457 1459 1484 1482 1476 2959 2955 2955 3015 3020 3022 3040 3036 3032 a Indicates a coincidence with another structure.n = 0, and the calculated U-0 bond length increase in the Egstate is 6.7 f0.3 pm. The different v1 progression frequencies at sites A and B aid the assignment of bands, but the low-energy region is complicated by the appearance of further internal cation modes which overlap the nvl progressions on other vibronic origins. The derived wavenumbers of internal cation modes are given in table 3 and are similar to those observed in the luminescence of [Me4NI2UO2Cl4. The frequencies of the v(C-H) stretching modes are the same (within experimental error) at sites A and B. The strongest v(C-H) mode (at 304 cm-') has a similar relative intensity to the corresponding band in [Me4NI2UO2Cl4, and 3040+ nvl(n 23) are the strongest spectral features to low energy of 690 nm.A B soR PTI ON SPECTRUM OF [Me4N]2U02Br4 85 K a,n and u spectra were recorded from 504 to 449 nm, and the crystal thicknesses employed gave total absorption to higher energy. 10K n and u spectra were recorded at a resolution of 2.5 cm-' from 502 to 460 nm. A thinner crystal, with the (001) face developed, was used for the 1OK a spectrum from 502 to 406 nm. The first two groups of bands in the 10 K polarized spectra are traced in fig. 4. The spectra are interpreted analogously to the absorption spectra of [Me4N]2U02C14.4 The IA and IIA electronic origins are identified in fig. 4 as the first strong features in the a, n and cr spectra, respectively. As in luminescence, other weaker bands in the region of the electronic origins may be identified with multiple sites, and these features are not referred to in the following analysis.Vibronic structure based on I and I1 is observed at 61cm-' (vlo),248 cm-' (v3) and 750*2 cm-'(v2) to high energy and the band polarizations confirm the assign- ments. The 1/6 vibronic origin may be associated with a very weak feature at 178cm-' above I. Progressions in the v1 mode on the above features are observed C. D. FLINT AND P. A. TANNER to several members, the first two quanta having magnitudes of 722 and 718.5 cm-' (except for v2,where x12is ca.8 cm-l). A very weak 7r polarized band at 909 cm-' may be associated with the first member of the u4 progression on the intense v2 vibronic origin, but further members of the vl progression on this band were obscured.Intense v3 and v6 vibronic origins in the a,7r and u spectra, together with vl0 (a,CT) and v8 (a,T,u)vibronic origins, confirm the assignment of origin IIIA at 20 283 cm-' as The derived frequencies of v3, v6 and v8 are 246, 170 and ca. 80-96 cm-', respectively, from the 85 K spectra, and that of vl0 is the same as in the A,(D2h) ground state. Structure based on I11 exhibits a different 85 to 10K wavenumber shift than structure based on I and 11, and the low-frequency vibrational modes give rise to fairly intense 85 K anti-Stokes features. The vl progression frequency for structure based on I11 is 721 cm-'. The relative intensity of origin I11 increases from 85 to 10K and this feature exhibits total absorption in the 7r spectrum (fig.4). In [Me4NI2UO2Cl4 the intensity of I11 is enhanced by the non-centrosymmetric perturbation associated with the introduction of water molecules into the crystal. The polarization of bands becomes less distinct as the temperature is reduced from 85 to 10K, and the bands are more I I 1 I I 1 20.6 20.6 20.4 20.2 20.0 wavenumber/ lo3cm-' FIG. 4.(~) ELECTRONIC SPECTRA OF [Me4N]2U02Br4 1 I I I wavenumber/103 cm-' FIG. 4.-(a) 10 K polarized absorption spectra of [Me4NI2UO2Br4 between 502 and 479 nm. (Note that the scale in the Q spectrum is slightly different.) (6) lOK polarized absorption spectra of [Me4NI2UO2Br4 between 485 and 461 nm. diffuse as the quantity of water absorbed by the crystal increases.These latter two effects are not apparent in the absorption spectrum of [Me4NI2U02Br4. A new LY and CT polarized intense feature at 1070cm-' above I does not correspond to the v2vibronic origin based on I11 because it does not display the expected anharmonicity in the nvl progression. This band is assigned to origin IV B1, (D2h),so that the tetragonal field splitting of 111and IV (ca.755 cm-') is smaller than in [Me4NI2UO2Cl4 (ca. 1000 cm-'). Vibronic structure based on IV is rather weaker than structure based on 111. A medium intensity v3vibronic origin is located at 239-257 cm-' above IV in LY, T and c,and some of the structure at 70,96 and 109 cm-' is associated wtih vg. Much weaker bands are located at 180 and 190 cm-' which presumbly correspond to Vg.Successive v1 quanta for structure based on IV are 716 and 712 cm-'. A new intense feature at ca. 187 cm-' above I has successive v1 quanta of 726 and 720 cm-' and must be assigned to a v3vibronic origin based on a non-degenerate electronic origin V. Other, much weaker bands could correspond to v8 and v6,and V is tentatively associated with a new very weak band at 1616 cm-' above I in the LY spectrum. C. D. FLINT AND P. A. TANNER TABLE 4.-cOMPARISON OF ORIGIN POSITIONS IN cs2UO2cl4AND (Me4N)2U02Br4a - Cs2U02C14 at 4 Kb (Me4N)2U02Br4 at 10 K label wavenumber/cm-' D~~ D~,,Dcoh D~,, D2h wavenumber/cm-l label I 20 095.7 19 968 I I1 20 097.3 19 993 I1 I11 20 406.5 20 283 I11 IV 21 310 21 038 IV V 22 026.1 22 150 VI VI 22 076 22 150 VII VII 22 410 21 584 V VIII 22 750 22 431 VIII a The transformation properties from D4,,to DZhsymmetry differ in these compounds since the two-fold symmetry axes are dihedral in Cs2U02Cl4 and along the bond directions in [Me4NI2UO2Br4; ref.(2). The location of the 85 K VIII-vl0anti-Stokes band in CY aids the assignment of VI and VII, and B3,(D2h)at 218 cm-' above I at 10 K. These origins appear in both CY and upolarizations, indicating that the orthorhombic distortion does not lead to any observable splitting. The v3 vibronic origin is intense, at 234 cm-' above the origins, and a very weak vf,vibronic origin is also located. The initial v1quantum has a wavenumber of 729 cm-' for structure based on VI and YII.Origin VIII A,(D2h)is assigned to a very weak band in CY at 2463 cm-above I at lOK (the other polarizations were not recorded in this region). Structure is located on VIII at similar vibrational frequencies to that on I11 and the v3 vibronic origin exhibits total absorption. This spectral region is complex and some' further new features are apparent. Firm assignments cannot however be made because of the overlapping of bands and the absence of 7~ and uspectra. However, all features up to the transmission limit at ca. 400 nm may be associated with vibronic structure built upon g tg electronic transitions. If it is assumed that origin V corresponds to B1,(D2h) symmetry (since no v2 or vl0vibronic origins are located) then the tetragonal field splitting of V and VIII is 747 cm-'.This splitting is almost identical to, and in the opposite sense to that of I11 and IV. Under the model of Denning, the baricentres of the cylindrical field states have energies 3A, (19 981 cm-ll,, 20 661cm-'Ag, 22 150 cm-'@,)t and 'Ag (21 958 cm-'). The ordering of states differs slightly from those in the spectra of the U02Clz- ion (table 4). SUMMARY AND CONCLUSIONS As in the spectra of the corresponding ~hloride,~ the presence of multiple non-equivalent uranyl sites limits the information available from the spectra of [Me4N]2U02Br4. However, polarization studies confirm that the luminescence is t Denning uses the labels II, A and @ to indicate R values of 1, 2 and 3.Each of these spin-orbit corn onents of the 3A, has A = 2 and it would be more consistent to refer to these states as 3Alg, 3A2g and I:A3,. 112 ELECTRON I c s P E CTR A OF [Me4NI2UO2Br4 due to a magnetik dipole allowed E, -+A1,(Dqh)pure electronic transition. The electronic origins I and II are at very slightly lower energy (by ca. 70 cm-') than in the [Me4NI2UO2Cl4 spectrum. Four vibronic origins due to ungerade internal UO2Br;-modes have been located, the vibronic intensity mechanisms being analogous to those cited for CS~UO~C~~.~Very weak progressions in the u4us(U-Br) mode based upon vibronic origins are detected, but in luminescence the expected progressions in the vll mode are coincident with other structure.As in the luminescence spectrum of [Me4NI2UO2Cl4, the low-energy region is domi- nated by the presence of internal cation mode vibronic origins, and nul progressions thereupon. Polarized studies of the electronic absorption spectrum of [Me4NI2U02Br4 enable the location of eight electronic origins and associated vibronic structure in the low-energy region. The tetragonal field splittings of the A, (I11 and IV, and V and VIII) states are opposite in sign, as expected, and have the magnitudes of 755 and 847 cm-', respectively. The assignments differ from those given by Snellgrove6 for the fourth and higher excited states in Cs2U02Br4 and are totally different from those of DiSipio et al.' The intensity introduced into electronic origins by the non-centrosymmetric perturbation by water molecules in crystal interstices is greater for origins I11 and IV than I and 11.Assuming a C2uperturbation of the UO2Br:- ion, then the polarizations of the origins in the absorption spectrum can only be accounted for by water molecules situated along the U-Cl(X) bond axis [so that this axis becomes C2(z) in C2". A water molecule could occupy, for example, a Wyckoff site el. Under this model, the 7r and a polarizations of I11 and IV, respectively, may be accounted for since the intensity source lIIu(crucrZ)Al,B2(C2u)is coupled to 'A,(cr,S,) under C2usymmetry, and the latter state is mixed with 3A,(a,S,) by spin-orbit coupling. The situation is analogous to the perpendicular spectrum2 of CSUO~(NO~)~except that whereas in the latter case a route also exists to 311,(cruS,), this is not so in [Me4NI2U02Br4.In the a,cr spectrum of [Me4N)2U02Br4, the 'Z~(cr,a~) intensity source BI(C~~) is coupled to lng((T~7r:)B3,(D2h), B1(C2u)but the coupling is via the 7rE oxygen orbital, and the perturbation is much weaker than that of the 8, orbital, since the latter orbital has a much greater equatorial spatial extension. We thank the S.R.C. and the University of London Central Research Fund for financial support. We are most grateful to a referee for pointing out some discrepan- cies in the original manuscript. These have been corrected. R. Denning, T. Snellgrove and D. Woodwark, Mol. Phys., 1976, 32,419. R. Denning, T.Snellgrove and D. Woodwark, Mol. Phys., 1979, 37, 1109. L. DiSipio, E. Tondello, G. de Michelis, G. Pelizzi, G. Ingletto and A. Montenero, Inorg. Chim. Acra, 1979, 37, 149. C. Flint and P. Tanner, J. Chem. SOC.,Faraday Trans. 2, 1981, 77, 1865. D. Wong, A. Wong and E. Wong, J. Chem. Phys., 1972,56,2838. T. Snellgrove, D. Phil. Thesis (Oxford University, 1974).'J. Newberry, Spectrochim. Acta, Part A, 1969, 25, 1699. C. Flint and P. Tanner, J. Chem. SOC.,Faraday Trans. 2, 1978, 74, 2210. C. Flint and P. Tanner, J. Chem. SOC.,Furuday Trans. 2, 1979, 75, 1168. 10 L. DiSipio, E. Tondello, G. Pelizzi, G. Ingletto and A. Montenero, Cryst. Struct. Cornrnun., 1974, 3, 297. 11 C. Flint and P. Tanner, J. Chem. SOC.,Faraday Trans. 2, 1981,77,2339. (PAPER 1/873)

ISSN:0300-9238    

DOI:10.1039/F29827800103

出版商:RSC    

年代:1982

数据来源: RSC

摘要:

J. Chem. SOC.,Faraday Trans. 2,1982, 78, 113-121 Dynamics of Highly Entangled Rod-like Molecules BY S. F. EDWARDS*AND K. E. EVANS? Cavendish Laboratory, Madingley Road, Cambridge CB3 OHE Received 2nd June, 1981 The diffusion of rod-like molecules is studied in the case of high density. It is argued that when one goes to densities higher than those permitting rotational freedom for the rods, the diffusion of one rod will depend critically upon the cooperation of the others. A calculation of this effect using mean-field theory yields a transition to immobility at a certain density, and this is offered as a simple model akin to a glass transition. 1. INTRODUCTION Experimentally, all glasses are found to behave in a very similar way around their glass-transition temperature (see, for example Johari and Goldstein’’2 on organic glasses).In polymeric systems in particular it is easy to visualize how a transition to immobility (except for local oscillations) can occur when the system is very highly entangled. However, the standard analytical model for a polymer, that of a Gaussian chain, cannot be used as the basis for a model of a glass, given its assumption of infinite flexibility. The addition of some form of stiffening to the chain model might produce a model of the glass-transition phenomenon but would also introduce considerabie analytical difficulties. For this reason we go to the other extreme and consider infinitely stiff, rod-like polymers for which a simple model can be constructed.It will be argued that when one goes to densities higher than those permitting rotational freedom for the rods, the diffusion of one rod will depend critically on the cooperation of the others. The rod is like a particle trying to diffuse along a line but meeting gates (other rods) which open and close through thermal fluctu- ations. This process will continue until at a critical density (well below the maximum permissible packing density) there is a complete cessation of mobility owing to the cooperative effect of the rods on each other. The important point to make is that although we are using the specific case of rod molecules, in a rather simple model (because it is accessible analytically), it is the fact of cooperative motion that is important.Similar cooperative mechanisms may be the basis for a greater under- standing of glass-transition processes generally. The properties of rod-like molecules were first studied in the dilute solution case by Kirkwood and Riseman3 and Kirkwood and A~er.~ By dilute solution we mean c s l/L3, where c is the number of rods per unit volume and L the length of the rod, i.e. there are assumed to be no inter-rod interactions, only hydrodynamic interactions with the solvent. As the concentration is increased rod-rod interactions will begin to occur and drastically reduce the rotational freedom of the rods. (It is assumed, at this stage, that the rods are Ion and thin so that their axial translational diffusion is unaffected.) Doi and Edwards” have examined the concentration region l/L3<< c << l/dL2, t Present address: I.C.I. Corporate Laboratory, The Heath, Runcorn, Cheshire WA7 4QE.113 DYNAMICS OF ROD-LIKE MOLECULES where d is the rod diameter (see section 2). As one approaches the upper limit, solutions of rod-like molecules, initially randomly ordered, become increasingly locally ordered until at concentrations c = 10/L2da phase transition (the so-called isotropic-nematic liquid-crystal phase transition) occurs. For a review of this transition and the properties of a liquid crystals see, for example, de Gennes' and Chandrasekhar.8 The ordered (nematic) phase is characterised by order in the orientation of the molecules, while translationally they are still completely disordered.Experimentally, this transition has only been observed using fairly flexible rod-like molecules. Whether it could actually be seen in a system of hard rods of finite thickness, with no other interactions, is open to conjecture. Onsager's original theoretical examination of this transition' using hard rods requires that the volume fraction 4, defined by 4 = crLd2/4, is much smaller than unity and that L >> d. Using these assumptions Onsager predicted a transition to an ordered phase at c -4/L2d. Flory" looked at this transition using a lattice model. Although this model can cope with higher volume fractions than Onsager's it really assumes an ordered phase as a starting point. Also it suffers from the inevitable problem of lattice models that rotations can only occur in finite jumps.Theoretically, then, for hard rods we have the prediction of a phase transition at c r= 5/dL2provided that the axial ratio L/d 310. Having said this one could visualize a situation where c -l/dL2but the rods are still randomly ordered, both translationally and orientationally. Ideally, this could be done simply by maintaining the system at a sufficiently high temperature that as the concentration of rods is increased the system still remains randomly ordered. In practice this may involve temperatures high enough to cause chemical breakdown of the rod molecules. (Using a molecule with a low axial ratio, L/d =r 5, e.g. a polyphenyl of the form might allow this regime to be reached.) Alternatively, one might consider raising the concentration to a lower level, at a suitable, but lower, temperature and then rapidly quench the system.The system should remain randomly ordered if quenched rapidly enough and the behaviour to be described below would then occur. Mathematically we can avoid these difficulties by including nothing but repulsive forces, whereupon the problem ceases to involve temperature, and by ignoring the possibility of an ordered phase. It may turn out therefore that the present study is too idealised to be applicable to real system. Nevertheless it is perhaps the simplest model to study, and may be valuable starting point for more realistic systems. 2. A TUBE MODEL FOR RODS Doi and Edwardssy6 have shown that, in the regime l/L3< c << l/dL2,where the rods are orientationally disordered, the effects of steric constraints between the rods will dramatically reduce the rotational diffusion constant, D,, of the rods from the dilute solution value DrO (see fig.1).(Kirkwood has previously to D,=r Dr0/c2L6 calculated DrO to be DrO= (l~7'/3777&~)In (L/3d) S. F. EDWARDS AND K. E. EVANS where qsis the viscosity of the solvent.) This is then shown to lead to a viscosity 7= qs[l + (cL’)~],as opposed to the dilute solution viscosity qo= qs(l+ cL3).The translational diffusion is assumed to be unaffected at these concentrations. If now we increase the concentration towards c = l/dL2 rotational freedom will be so reduced that translational motion along a rod axis will be hampered by the presence of other rods in its path, because there is inadequate freedom to sidstep the obstacles.The motion of a rod will then be like a particle diffusing along a line but meeting gates which open and close randomly through thermal fluctuations. Doi and Edwards’ have shown that in a random configuration the mean number of rods penetrating a cylinder of radius b and length L, N(b),is given by N(b)= cbL2. (1) We are studying the regime where b = d and N(b)= 1,[more accurately b == 2d and N(b)= 2-31, in which case c = l/dL2,as was originally postulated. / much reduced rotational freed om FIG. 1.-Highly entangled rod with much reduced rotational freedom. In this regime, then, we can envisage our test rod diffusing along a tube with a free translational diffusion constant Do.The presence of other rods will modify this constant. (Note that over long distances the rods will still execute random motion: it is only on the scale =L that they have no rotational freedom.) We may treat these obstacle rods as perfectly reflecting barriers opening and closing along the path of the test rod. Let x be the coordinate of the test rod down the tube. Then, if no barriers were present, it would obey the simple diffusion equation where P(x,t) is the probability of finding the rod at x at time t. This has the solution a3 Go(x, x’; t, t’)Po(x‘,t’)dx’ (3) DYNAMICS OF ROD-LIKE MOLECULES where Po(x’,t’)is the initial probability of finding the particle at (x‘, t’) and Suppose, now, a reflecting barrier is placed at position R at time tR and removed at time to.Then the solution, using the method of images to find the Green function applicable while the barrier is on, is 03 P(x,t)= GO(&XI;t, ~Q)Q’(XI, x2; to,t~) x Go(~2,x’; tR, t’)Po(x’,t’)dx‘ dxl d~2 where where 0, x<R O,(x-R)={0,” x>Rx<R}. The two halves of Q’ represent the solution for each side of the barrier. Symboli- cally, we have P= GoQ’GoPoI where Q’= Or( Go + dJOr+ el(Go + do)81. This may be rewritten as P = (GO+ GoQGo)Po (7)I Suppose, now, that there are many barriers appearing and disappearing along the path of the rod. This can be represented by (;~-D~s-xa a‘ V,)G(x,x’,t, t’)=tI(x-x’)S(t-t’) (9) S.F. EDWARDS AND K. E. EVANS where C, V, is the sum of the effect of all the barriers, each labelled by a suffix a and occurring at different positions along the tube for different periods. To identify V we expand eqn (9) and compare it with eqn (7)and (8). Expanding eqn (9)we have Neglecting correlations between barriers we may average, giving (G)=Go+NGo(V)Go+* (11)*a where N is the total number of barriers. Comparison with eqn (7) gives (V)= Q to first order. Equivalently, we have G = Go+ GoQGo for one gate. Sofor many non-interacting barriers we have G =n(Go+ GoQ"'Go) 1 -giving (G)= Go+NGo(Q)Go+. -. The evaluation of this term is to be found in Appendix I. It is found that, to first order in V,Dois modified by the presence of barriers, to give where r is the average period a barrier is on and pB is the number of barriers per unit time.3. SELF-CONSISTENCY ARGUMENT FOR THE TUBE MODEL Eqn (12) represents the first two terms of an equation D =f(Do).If the full functional form off were known as self-consistent, the mean-field argument could be applied, i.e. that D =f(D).The phase transition, if any, could then be examined, along the lines of the Curie-Weiss model for ferromagnetism. A simple argument will now be given for the form of f(Do). Consider a rod of length L diffusing with free diffusion constant Do along a tube. Let a be the average distance between barriers, each of which remains on for an average time r.Let T be the time for the rod would take to diffuse a distance a if no barriers were present. Then Do= a2/2T. (13) Now, if barriers are applied, the rod will take a time T'>T to traverse this distance. The average delay will be approximately rtla, since the amount of delay is proportional to the likelihood of the rod being in contact with the barrier. The shorter the distance between barriers, the greater the delay to the rod. Hence T' = T -k grL/a (14) where g is a numerical constant. so D=-=aL DO 2T' l+grL/Ta' 118 DYNAMICS OF ROD-LIKE MOLECULES But, by definition, pB = 1/Ta,so D = DO(1+ gPBLT)-'. (16) Let us suppose the barriers are themselves freely moving rods (the level of the model used in the Green function approach).Then L2Do=-27 since the rod barriers must diffuse a distance of approximately L = J27D0.Using this in eqn (16)gives D = Do[1+ JZ~PB(DO~)''~TI-' and D = Do-c(DOT)~/~PB+ -.* This is exactly the same form as that found previously [eqn (12)]. Let us now apply a self-consistency argument and say that the barrier rods are also delayed by the effect of other rods. Then eqn (17)becomes D = L2/27. (20) Putting this in the original eqn (15) and using eqn (13) gives DOD= (l+g*)a3D and therefore D = Do(l-gL3/a3). (22) Using the value of g from the Green function expansion we have D = ~~(1-1.2~~~-~). (23) So, as the concentration increases the effective translational diffusion constant of the rods decreases until a =r 1.lL when D goes to zero and motion ceases, a freezing-in process due to entanglements having occurred. From the previous discussion we know that c == l/a2d (since L = a in this regime).So D = Do[l- C(C~L~)~/~] (24) where C is a numerical constant =:1. 4. CONCLUSIONS Strictly speaking, in the self -consistency argument we have assumed the barriers are moving perpendicular to the test rod. Obviously, in reality they will be at all possible angles, in which case L should be replaced by an effective length L calculated from an average over all orientations. Experimentally, the viscosity of rods in concentrated solutions (the regime of l/L3<< c << 1/L2d)has been shown to have a greater dependence on concentration than that predicted by Doi and Edwards in their consideration of rotational diffusion (see Berry et a/.").This may possibly be due to a decrease in the translational S. F. EDWARDS AND K. E. EVANS diffusion via the process described above. Unfortunately a first-principles calcula- tion of the viscosity of a rod system with c.=l/dL2seems to be prohibitively difficult. Doi and Edwards were able to calculate the viscosity of their model by assuming that an affine deformation would occur for small deformations. This assumption may be valid for c << l/dL2but it certainly is not for c =l/dL2.In the latter regime bending must occur if the centres of the rods are to move affinely, and this must be allowed for in the calculation of the viscosity from the stress tensor.Obviously this is a very simple model, and suffers from the usual defect of statistical mechanical arguments not leading to an exact solution, i.e. an intuitive picture translated into mathematics produces a realisation of the intuition but no proof of its correctness: higher-order terms in our expansions could upset the answers, almost certainly by introducing critical indices, but quite possibly by negating the whole picture. However, it does illustrate the possibility of a coopera- tive entanglement effect producing a cessation of mobility, which may be of direct relevance to an understanding of the dynamics of the glass transition. K.E.E. acknowledges an S.R.C. CASE award, partially supported by I.C.I. Plastics Division. Mr.W. Reddish is thanked for several helpful discussions. APPENDIX I EVALUATION OF NGo(Q)Go FOR THE ROD MODEL From eqn (11) and (8)we have 1/2 dR T/2 a3 NGo(Q)Go= lim iV[ dtk drl dr2Go(x,rl, t, t, + 7/2)1 I I-CO -[/2 1 -T/2 T --m T+-m dE dF I= dt, exp [iE(t -t, -7/2)exp [iF(t,-7/2-tl)]][ -G(E)G(F)T(T)(2d2 = 1=27~8(E -F) exp [iE(t-~/2)]exp [iF(-~/2- t1)]G(E)G(F)T(7)(2d2 DYNAMICS OF ROD-LIKE MOLECULES Doing the spatial average gives dR Go(x-y~-R)GO(y2+R dk-x’)=I Gexp -ik(x-x’) exp -ik(y2-y1)G2(k). Combining the two averages and defining as the number of rods per unit length per unit time gives and then S. F. EDWARDS AND K. E. EVANS so Referring back to eqn (A.l) we have, symbolically, GOTGO.If we are to have first-order changes in Do we should expect the first term in the expansion of T to be of order k2, which by inspection of eqn (A.2) is indeed the case.Evaluating eqn (A.2) to first order (i.e. to order k2)gives Hence (bearing in mind that k2 = --S2/Sx2) we have that first-order change in Do is ’ G. P. Johari and M. Goldstein, J. Chem. Phys., 1970, 53, 2372.’ G. P. Johari and M. Goldstein, J. Chem. Ph\gy., 1971, 55, 4245. J. Riseman and J. G. Kirkwood, J. Chem. Phys., 1950,18, 512. J. G. Kirkwood and P. L. Auer, J. Chem. Phys., 1951, 19, 281. M. Doi and S. F. Edwards, J. Chem. SOC.,Faraday Trans. 2, 1978, 74, 560. M. Doi and S. F. Edwards, J. Chem. SOC.,Faraday Trans. 2, 1978, 74, 918.’ P. G. de Gennes, The Physics of Liquid Crystals (Clarendon Press, Oxford, 1974). S. Chandrasekkar, Liquid Crystals (Cambridge University Press, Cambridge, 1977). L. Ansager Ann. N.Y. Acad. Sci., 1949, 51, 627, 10 P. J. Flory, Proc. R. SOC.London, Ser. A, 1956, 234, 73. 11 G. C. Berry, P. Metzger and S. G. Chu, U.S.-China Bilaterial Symposium on Chemistry and Physics of Polymers, 1979, to be published. (PAPER 1/890)

ISSN:0300-9238    

DOI:10.1039/F29827800113

出版商:RSC    

年代:1982

数据来源: RSC