4712
J . Phys. Chem. 1990, 94, 47 12-41 16
of a collection of monomer repeat units on a lattice of close packing. The result of their calculations is that the shape of the complex modulus in the complex plane is similar to that observed for dielectric dispersions, provided the data are first transformed to the complex compliance. Conclusions
The results reported above suggest that the mechanism for the dielectric relaxation processes in simple polar liquids and their mixtures is similar to the dielectric processes observed in polymers except that the temperatures for the liquids are much lower.
Lower temperatures probably imply lower energies. The correlation also suggests that molecular weight is not an important consideration for determining the distribution of relaxation times. The discussion offered in terms of Mansfield's model for dielectric relaxation is a best simple, but its agreement with experiment suggests that a more detailed numerical analysis would warrant the effort. Such analysis would include a three-dimensional lattice, with some built-in disorder such as random displacements of lattice points, and minimization of the dipole interaction terms in such a way that the equilibrium correlation term is satisfied. Registry No. IABR, 107-82-4; ZMEP, 107-83-5.
Vibrational Spectroscopic Studies of the Phase Transitions in Cyclohexane-d,, at High Pressure Julian Haines and Denis F. R. Gilson* Department of Chemistry, McGill University, 801 Sherbrooke St. W.. Montreal, Quebec H3A 2K6, Canada (Received: November 27, 1989)
The infrared spectrum of cyclohexane-d12has been obtained as a function of pressure. The presence of two phase transitions at 5.3 and 7.4 kbar was detected by changes in the C-H stretching region of isotopically dilute C6DllHand by splittings in the internal modes of cyclohexane-d12.The change in the number of isolated C-H stretches and the splitting of the internal modes is consistent with a change in unit cell symmetry from oh to &h at the first transition and then to c2h at the second transition. The C-H stretching region in the highest pressure phase was very similar to that observed at low temperature, indicating these phases are identical.
Introduction
Cyclohexane is known to undergo an order-disorder transition at 186.1 K,] and an X-ray crystallographic studyZindicated that the transition is from a low-temperature, monoclinic structure, space group C2/c (C2t),to a face centered cubic structure, phase I, space group Fm3m (oh'). Cyclohexane has been subject to many variable-temperature vibrational spectroscopic investigations,3-12the majority of which provided results that are consistent with the crystallographic data. Variable-pressure infrared and Raman spectra indicated the presence of two phase transitions at 5.1 and 9.6 kbar at 293 K,13 and the splittings in the spectra were consistent with a change in unit cell symmetry from oh to DZhat the first transition and then to Czhat the second transition. ( I ) Aston, J. G.: Szasz, G. J.; Finke, H. L. J . Am. Chem. Soc. 1943, 65, 1135. (2) Kahn, R.; Fourme, R.: AndrC, D.; Renaud, M. Aero Crystallogr. 1973, B29, 131. (3) Dows, D. A. J. Mol. Spectrosc. 1965, 16, 302. (4) Le Roy, A. C. R. Hebd. Seances Acad. Sci. Paris 1965, 2608,6079, ( 5 ) Ito, M. Specrrochim. Acta 1965, 21, 2063. (6) Obremski, R. J.; Brown, C. W.; Lippincott, E. R. J. Chem. Phys. 1968, 49, 185. (7) Sataty. Y. A.: Ron, A. Chem. Phys. Letr. 1974, 25, 384. (8) Rohrer, U.;Falge, H. J.; Brandmiiller, J J. Ramon Spectrosc. 1978, 7, 15. (9) Zhizhin, G.N.; Krasjukov, Yu.N.; Mukhtarov, E. 1.; Rogovoi, V . N. Zh. Exp. Teor. Fir. Pisma (USSR) 1978, 28, 465. (IO) Mukhtarov, E. 1.; Rogovoi. V. N.; Krasjukov, Yu.N.; Zhizhin, G. N. Opt. Spektrosk. (USSR) 1979, 46, 920. (1 I ) Rogovoi, V . N.; Zhizhin, G. N . Fiz. Toerd. Tela (USSR) 1980, 17, 776
-
I
I.
(12) Nevsorov, 9. P.; Sechkarev, A. V. fru. Vuzou (Ser. Fir.) (USSR) 1971, 2, 75.
(13) Haines. J.; Gilson, D. F. R. J . Phys. Chem. 1989, 93, 7920. 0 0 2 2 - 3 6 5 4 / 9 0 / 2 0 9 4 - 4 7 12rSO2.50/0
TABLE I: Vibrational Data (cm-,) for Cyclohexane-d,, Dilute in Cvclohexane-d12
Raman 68 K 2918 2915 2910 2893 2882
infrared
240 K 2916 2883
82 K 2917 2914 2908 2893 288 I
205 K
assiant
2913) 2880
vq
1
The presence of many overlapping bands renders the C-H stretching region of the spectrum difficult to interpret. Variable-temperature14 and variable-pressureIs vibrational studies of C-H oscillators of adamantane-d15,dilute in perdeuterated adamantane, have shown the potential of isotopic dilution for studying phase transitions in solids. A similar approach can be taken with C6DIIHdilute in cyclohexane-d,,. Cyclohexane-d,, undergoes a phase transition at 186.0 K and melts at 277.2 K,16 2.6 K below the melting point of cyclohexane. This transition has also been studied by vibrational spectro~copy,'~,'~ including an infrared study of single crystals under pressure.I8 This latter study indicated that the unit cell symmetry of phase I1 was D2h; however, the pressure at which these spectra were recorded was (14) Corn, R. M.; Shannon, V. L.; Snyder, R. G.; Strauss, H. L. J . Chem. Phys. 1984,8/, 5231. 7 7 3( 1 5 ) Salmon, D.; Shannon, V. L.; Strauss, H. L. J. Chem. Phys. 1989,90, 1
I _ .
(16) Mraw, S.C.; Naas-O'Rourke, D. F. J . Chem. Thermodyn. 1980, 12, 691. ( I 7 ) Le Roy, A. C. R. Hebd. Seances Acad. Sei. Paris 1965,2618,4022. (18) Brown, C. W.; Obremski, R. J.; Lippincott, E. R. J. Chem. Phys. 1970. 52, 2253.
0 I 9 9 0 American Chemical Society
High-pressure Cyclohexane-dI2Phase Transitions
The Journal of Physical Chemistry, Vol. 94, No. 1 1 , 1990 4713
I
m
02 K
n
--iS0 bISi I\
2 50
6.1 kbu
w
WAVENUMBER
0
Z a m
a 0
m
m
a
A
r
12.7 kbar
,
v v
2950
2930
2910
2890
2870
WAVENLTMBW
Figure 1. Infrared spectrum (2950-2850 cm-I) (top) of cyclohexane-d,, dilute in cyclohexane-d,, at 205 and 82 K and Raman spectrum (bottom) at 240 and 68 K.
not reported. In the present investigation, the behavior of the isolated C-H oscillators in cyclohexane-d,, with respect to temperature and pressure are reported, in addition to the pressure dependence of the infrared spectrum of cyclohexane-d12. Experimental Section Cyclohexane-dI2 (MSD Isotopes, 99% D) was used for the variable-temperature Raman experiments, and cyclohexane-d,, (MSD Isotopes, 99.5% D) was used for the infrared experiments. Raman spectra were recorded on a Instruments S.A. spectrometer with a Jobin-Yvon Ramanor U-1000 1.0-m double monochromator and a Spectra Physics Model 164, 5-W argon ion laser (514.5-nm line, approximately 200 mW at the sample). The resolution was typically 2 or 4 cm-I. Infrared spectra (1-cm-' resolution) were acquired on a Nicolet 6199 FT-IR spectrometer equipped with a liquid nitrogen cooled mercury cadmium telluride (MCT) detector. The sample temperature was controlled for both infrared and Raman spectra, with a Cryodyne Cryocooler Model 21 cryostat (Cryogenics Technology Inc.) and measured by using a silicon-diode temperature sensor attached to a Cryophysics Model 4025 controller. The Raman spectra were obtained by cooling liquid samples in sealed glass capillary tubes, which were mounted on to the cold finger of the cryostat using indium foil as a conducting junction. The infrared spectra were measured on thin films sprayed on a potassium bromide window at a temperature above the phase transition. For the variable-pressure infrared spectra (2- or 4-cm-' resolution) a 400-pm-thick stainless steel gasket was used with a High Pressure Diamond Optics Inc. (Tucson, AZ) diamond anvil cell (DAC). A layer of 0.14% w/w sodium nitrate in sodium bromide, prepared according to the method of Klug and Whalley,19 and a drop of cyclohexane-d,, were placed into the 400-pm-wide gasket hole. The pressure was calibrated with respect to the frequency shift of the asymmetric stretch of the nitrate ion. The cell was mounted in the sample chamber of the spectrometer on an x-y-z (19) Klug, D. D.; Whalley, E. Rev. Sci. Insfrum. 1983, 54, 1205
2
30
2955
2630 2605 2880 WAVENUMBER
2855
2830
Figure 2. Infrared spectrum (2980-2830 cm-I) of cyclohexane-d,, dilute in cyclohexane-d,, at 3.2, 6.1, and 12.7 kbar.
stage over an optical bench with f4 condensing optics. Results and Discussion Two broad bands were observed in the C-H stretching region of the infrared and Raman spectra of the high-temperature phase of C6DIIHdilute in perdeuterated cyclohexane, Figure I . These spectra are very similar to the spectrum reported for the liquid phase.20 The high-frequency and low-frequency bands in the spectrum of the gas have been assigned as the equatorial and axial C-H stretches, respectively.21 In phase 11, five bands were observed in both the infrared and Raman spectra, three corresponding to equatorial and two to axial C-H stretches, Table I. These bands do not result from the splitting of degenerate modes as C6D,,H has c, symmetry, nor from factor group splitting, as the sample of cyclohexane-d12 is at least 99.5% deuterated, and on the average, there is one C-H oscillator for approximately every eight primitive unit cells, which would eliminate intermolecular coupling between C-H oscillators. The space group of the low-temperature phase of cyclohexane is known to be Ca6with two molecules per primitive unit cell from X-ray crystallography: with the cyclohexane molecules lying on Ci sites. Placing the cyclohexane molecule on a Ci site will cause the twelve C-H stretches to be separated into six sets of two vibrations, of which three correspond to equatorial and three correspond to axial vibrations. The observation of three equatorial and two axial C-H vibrations is consistent with this prediction, based on the structure of phase 11, as the axial and equatorial C-H bonds can each be placed in three.distinct locations in the unit cell. Changes in the number of C-H stretches and their pressure dependences and splittings in the internal modes of cyclohexane-d12 (20) Wong, J. S.; MacPhail, R. A.; Moore, C . B.; Strauss, H. L. J . Phys. Chem. 1982.86, 1478. (21) Caillod, J.; Saw, 0.;Lavalley, J.-C. Specrrochim. Acfcl 1980, 36A, 185.
4714
The Journal of Physical Chemistry, Vol. 94, No. 1 I, 1990
Haines and Gilson
TABLE 11: Infrared Data for Cyclohexane-dll Dilute in Cyclohexane-dI2 phase 111 (6.1 kbar) phase I (3.2 kbar) V. duldp, d In uldp, Y, duldp, d In uldp, cm-' cm-'/kbar kbar-I cm-I cm-llkbar kbar-I 2918 2887
I .23 I .62
0.00042
2923
0.84
0.000 3 3
2898
I .29
0.00044
2887
0.69
0.000 24
0.000 56
indicated the presence of two high-pressure transitions at 5.3 and 7.4 kbar, respectively. In comparison, the two transitions were observed at 5.1 and 9.6 kbar in cyclohexane itself. The intermediate phase, phase 111 (since the low-temperature phase at ambient pressure is commonly labeled phase 11, the intermediate phase at high pressure is labeled phase III), in cyclohexane-d12 is stable over a significantly narrower pressure range, 2.1 kbar, as compared with 4.5 kbar for cyclohexane. A C-D bond is shorter than a C-H bond, and therefore, replacing the hydrogen atoms in cyclohexane by deuterium will have an effect similar to an increase in pressure or, in the case of a variable-pressure experiment, a reduction in temperature. According to the phase diagram constructed by Wiirflinger?, a reduction in temperature will reduce the temperature range of stability of the intermediate phase. The higher pressure transition in cyclohexane-d,, is shifted relative to that in cyclohexane; however, the lower pressure transition occurs at essentially the same pressure in both compounds. This results from the shift in the triple point to higher pressure and temperature in the deuterated compound. Six C-H stretches were observed in the infrared spectrum of phase 11, the highest pressure phase, Figure 2. This is consistent with a C , structure with the molecules located on Cisites, thereby confirming that this phase is the same as phase I1 obtained at low temperature. Below the phase transition at 7 . 4 kbar, three C-H stretches were observed, one equatorial and two axial. If the molecules are located on C, sites in a Du unit cell, as was proposed for phase 111 in cy~lohexane,'~ then the twelve C-H stretches would be separated into two sets of four stretching vibrations located on general positions and two sets of two for those lying on the mirror plane, yielding one set of two and one set of four equatorial and one set of two and one set of four axial stretches. The resulting spectrum would, therefore, contain four bands, which is not inconsistent with the spectrum observed, as it is possible that two bands could overlap. The equatorial band appeared to have a shoulder at 7.3 kbar, which is further evidence for the D2h unit cell. It should be noted that all possible site groups for the cyclohexane molecule, which has D3d symmetry, would yield a spectrum containing an even number of bands. The only other site groups that would yield four spectral bands are C3and C3", which would not, however, be consistent with the splitting of the internal modes in cyclohexane-d,2 into up to three components. I n phase I, below 5.3 kbar, two broad bands were observed, corresponding to the set of six equatorial and the set of six axial C-H stretches of the molecules located on 0,sites in the disordered crystal. This spectrum was very similar to that observed for the high-temperature phase, except that the bands were shifted to higher wavenumber. The number of C-H stretches present in each phase is further evidence that the phase transitions involve a change in site symmetry from oh to c2h to Ci and a change in unit cell symmetry from o h to Dzl to C2h. Ab initio calculationsz3have predicted that the axial C-H bond is longer than the equatorial bond. Thus it should be a weaker bond with a lower force constant. It is expected, therefore, that the axial stretch will occur at a lower frequency, which is observed, and also that it should exhibit a ggreater relative shift with increasing pressure. The pressure coefficients, duldp, and the logarithmic pressure derivatives, d In u/dp, of the C-H stretching frequencies are given in Table 11, and those of other selected modes (22) Wlirflinger, A. Eer. Bunsen-Ges. Phys. Chem. 1975, 79, 1195. (23) Chiu. N . S.: Ewbank,J . D.: Shafer, L. J . Mol. Struct. 1982, 86, 397.
u,
cm-I 2947 294 i 2935 2919 2910 290 I
phase I1 (12.7 kbar) duldp, d In uldp, cm-'/kbar kbar-I 1.83 0.000 63 1 1.42 0.73 0.00048 0.000 25 0.54 0.000 19 2.03 0.000 70 1.09 0.000 38
assignt
1
uq
L
2950
c
2940
-
2930
Y'
I
I
I
2920
c
/
r
2910
-
"*
2900 L
,I
2890 2880
r1 ' 0
"
"
5
"
"
g
"
-A
10
15
20
PRESSURE/KBAR Figure 3. Pressure dependence of the C-H stretching region of cyclohexane-d, I dilute in cyclohexane-d12.
a Figure 4. Structure of phase I1 of cyclohexane.
of cyclohexane-d,, are given in Table 111. In the disordered phase, the axial C-H stretch is indeed more sensitive to pressure, Figure 3, but in phases I11 and I1 a range of du/dp values was observed. It was also apparent in both temperature and pressure studies that the frequencies of the axial stretches showed a greater spread than those of the equatorial. Phases 111 and I1 will, as a result of lower symmetry, have different compressibilities along each crystal axis, and a given C-H stretch will exhibit a different pressure dependence depending on its location in the unit cell and the molecular stacking.
The Journal of Physical Chemistry, Vol. 94, No. 1 1 , 1990 4715
High-pressure Cyclohexane-d12Phase Transitions
TABLE 111: Infrared Data for Cyclohexane-d12(1200-600 em-') phase 111 (5.7 kbar) phase I (4.8kbar) cm-'
duldp, cm-' / kbar
I I62 m
0.34
d In u/dp, kbar-I 0.00029
1084 s
0.04
0.00004
1068 m
0.07
988 m 917 s
11,
722 m 687 m LI
Y,
duldp,
d In uldp,
u,
cm-'
cm-'/kbar
kbar-I
cm-'
1162 m 1092 s 1083 s
0.15 0.14 -0.27
0.00013 0.00013 -0.00025
0.00007
1067 s 1065 sh
0.53
0.00050
0.39
0.00040
995 m 990 m 982 m
0.18 0.15 -0.52
0.00018 0.00015 -0.0005 3
0.42
0.00046
917 s
0.36
0.00039
1162 m 1093 m 1082 m 1070 s 1068 s 1065 sh 1062 s 1002 sh 997 m 986 m 980 m 921 m 918 sh 885 w 875 w 799 w 783 w 729 sh 726 s 688 s 684 s
0.58 0.09
0.0008 1 0.00013
721 s 683 s
0.30 0.29
0.00042 0.00043
phase I1 (17.6kbar) duldp, d In uldp, cm-' /kbar kbar-' 0.25 0.23 0.05
assianta
0.0002 1 O.Oo0 21 0.00005
1
0.0
0.31 0.13
0.0003 1 0.00013
0.28 0.00030
0.09 0.66 0.12 0.27
1
0.0001 1
1 0.000391 0.00017 0.00092
Following ref I8
An attempt was made to assign the six distinct C-H stretching vibrations in phase I1 on the basis of their pressure coefficients. Lattice energy calculations were performed by using a Buckingham pairwise potential of the form V=
+ B exp(-Cr)
(1)
Williams' (1972) parameter set for hydrocarbons was used for the coefficients A, B, and CSz4The calculations were performed with the use of the structural data for cyclohexane,2 Figure 4. It should be noted that the experimental pressure coefficients were obtained for C6DI,H in cyclohexane-dlz and the interatomic distances would be shorter than those used in the calculations. The calculations should still, however, give an indication as to the relative dependence of the potential energy of the different hydrogens on interatomic distance for C6Dl in cy~lohexane-d,~. The energy contribution for each distance, rij, was summed for all atom pairs within 1 nm, and the contributions to the total energy of the three carbons and six hydrogens of the asymmetric unit were obtained. The distances rij were reduced by steps up to a maximum of 10% and the energy contributions were recalculated. This permitted the dependence of the potential energy for each of the six C-H groups to be determined as a function of the reduction in distance. Hal (0.1963,0.5042, -0.1271) was found to have the greatest energy dependence on distance, followed by He, (0.1831, 0.5879, 0.0488) and then Ha, (0.3755, 0.2462, -0.1 144). Hc2 (0.3985, 0.5254, 0.0803), He3 (0.4682, 0.1776, 0.0690), and Ha, (0.3550, 0.381 3, 0.2083) were found to have the lowest dependences. The labeling of the hydrogens follows the crystal coordinates given by Kahn and co-workers.2 Thus, the axial vibration at 2910 cm-' can be assigned to Hal,as it has the largest pressure coefficient. Similarly, the bands at 2947,2901, 2941, 2935, and 2919 cm-l can be assigned to Hcl, Ha3, He2,He3, and Ha2,respectively. The observed pressure dependence of Hcz is, however, greater than that of Ha3. The discrepancies between the observed pressure dependences and the calculated energy dependence on distance could result from an isotropic reduction in the interatomic distances. The distance along each crystal axis should be reduced by a different amount, as the space group of cyclohexane phase 11 is monoclinic, and therefore, the compressibilities along the crystal axes a, 6, and c are not equal. The anisotropy of the compressibility is not known and, in addition, i ~ not ~ extend to the the pVT data of Wiirflinger and W i s o t ~ kdo (24)Williams, D. E.Acta Crystallogr. 1972, A28, 84. (25)Wisotzki. K.D.:Wiirflinger, A. J . Phys. Chem. Solids 1982,43, 13.
W
u 2
U
m U 0 m m
a
17.6kbu
1
Figure 5. Infrared spectrum (1200-600 cm-I) of cyclohexane-d12 at 4.8, 5.7, and 17.6kbar.
temperature region of the X-ray study. Even considering these sources of error, the bands at 2910 and 2947 cm-I can still be assigned to Hal and HcI, respectively. The C-H vibrations, both in C6Dl,Hand in C6HIZ,show higher du/dp and d In u/dp values than most of the other internal modes, Tables I1 and 111, since vibrations on the "outside" of the molecule are more susceptible to the decreases in intermolecular distances as the pressure increases. Profound changes were observed in the internal modes of cyclohexane-d12at the two phase transitions, Figure 5. The spectra of phase I contained broad bands, characteristic of a disordered structure. In both phases 111 and 11, many of the internal modes were affected in the same way as the corresponding modes of and cyclocy~lohexane.'~ In phase Ill of both cy~lohexane-d,~ hexane, u29, a CD2 and a CH2 twist, respectively, was split, al-
J . Phys. Chem. 1990, 94,47 16-4723
4716
though this splitting was more prominent in cyclohexane-d12. Degenerate modes such as u28. 129, 130, and 131 split in phase I1 of both compounds, as did the nondegenerate modes, uI4 and u15. In phase 111, the observed splitting of the nondegenerate a,, modes (such as u I 4 ) and the degenerate e, modes (such as 129) into two and three components, respectively, Table 111, is consistent with the proposed DZhunit cell symmetry. Further splitting was observed in phase 11. In particular, I 2 8 and ~29,both of e, symmetry, split into at least three components, and four weak bands appeared in the 900-750-~m-~ region of the spectrum, including the overtone, 2uI6,and the al, mode, us. The latter mode is forbidden in the free molecule but becomes allowed in the crystal, as the molecule is located on a site of lower symmetry. The spectrum of this phase resembles that reported for a single crystal of phase I1 under pressure in a DAC."' The splittings observed for phases 111 and I1 are further evidence for the proposed unit cell symmetries as, although the predicted number of components were not always observed, no band split into more bands than predicted. The pressure dependences and logarithmic pressure derivatives of selected internal mode frequencies of cyclohexane-d,, are listed in Table 111. For several bands, the d In u/dp values are lower in phase 111 than the other two phases; however, there are several exceptions. This trend is not as pronounced as that observed in cyclohexane. In most cases, the d In u/dp values for the modes in all three phases are lower than those calculated for the corresponding modes in cyclohexane. As the C-D bond is shorter than the C-H bond, cyclohexane-d12is more dense than cyclohexane and, therefore, less compressible, which leads to smaller shifts in frequency with increasing pressure. The vibrations, u15,~ 2 9 and . ~30,which correspond to a mixture of a CD, rock and a CCC bend, a CD, twist, and a ring stretch,%s7
respectively, are among those with the highest d In u/dp values. These vibrations were also among those that exhibited the highest d In u/dp values in cyclohexane. In particular, the ring stretch, u30 (which is 131 in cyclohexane due to the relative positions of the CH2 and CD2 rocks as a result of the isotope effect), is the internal mode with the highest d In u/dp value in both compounds, excluding the C-H stretches. This is in agreement with the trend reported by Ferraro28that stretching vibrations are more pressure sensitive than bending or twisting vibrations. For all the bands that split in phases 111 and 11, the higher frequency component was found to have a higher d In u/dp value than the low-frequency component. This is a result of the increase in factor group splitting due to the increased intermolecular interaction at higher pressure. In most cases, the d In u/dp value for the high-frequency component is much larger than that of the lower frequency component, indicating that the factor group splitting increases significantly due to the reduction in intermolecular distances. In phase 111, in particular, negative values are observed for the lowest frequency components of several split bands, indicating that the increase in factor group splitting makes a significant contribution to the pressure shift. Acknowledgment. This research was supported by grants from the Natural Sciences and Engineering Research Council of Canada. J.H. acknowledges the award of a scholarship from NSERC. (26) Snyder, R. G.; Schachtschneider, J. H. Specrrochim. Acra 1%5,21, 169. (27) Forel, M. T.; Garrigou-Lagrange, C. Ann. Chim. Paris 1973,8,207. (28) Ferraro, J. R. Vibrational Specrroscopy at High Exfernal Pressures: The Diamond Anvil Cell; Academic Press: Orlando, FL. 1984.
Spin-Lattice Relaxation of the Solltonic Defect in Isotopically Substituted trans-Polyacetylene Robert St. Denis,+Eric J. Hustedt,' Colin Mailer,$ and Bruce H. Robinson*.+ Department of Chemistry. University of Washington, Seattle, Washington 98195, and Department of Physics, University of New Brunswick, New Brunswick, Canada E3B 5A3 (Received: October 9, 1989)
We have measured the spin-lattice relaxation rates, R , , for the spin of the electron defect in pristine trans-polyacetylene (t-PA) as a function of temperature for the isotopic forms (CD),, ("CD),, (CH), and ("CH),. The data have been compared with the soliton-phonon-based dynamics model of Maki and the localized metal-phonon based dynamics model of Robinson et at. We concluded that the latter model is preferred; it exactly explains the R I data for (CD), and (I3CD), t-PA. We find that the R1 data of the proton-containing forms of t-PA, (CH), and ("CH),, are complicated by the presence of spin 1/ 2 nuclei, which are strongly coupled to each other, and which provide an additional dynamic path for defectspin relaxation. We show how the dynamic models may be modified to include this additional spin relaxation mechanism. The result suggests that the nature of nuclear relaxation in proton-containing &PA may be more complex than assumed in previous treatments.
Introduction trans-Polyacetylene (t-PA) is the prototypical low-dimensional organic semiconductor. The experimental evidence for the structure of t-PA has been extensively summarized.' The nature of conductance is believed to be related to the ability of t-PA to sustain a defect which acts as a boundary between two domains which show bond alternation of opposite phase. Figure 1 shows the defect delocalized over a few carbons. The defect is thought to be self-localizing: that is, the spin defect will extend over a maximum number of carbons, beyond which bond alteration will start. The spin defect will have very low probability of being in the regions of bond alternation. The early work of Salem and 'University of Washington. *University of New Brunswick.
Longuet-Higgin~~*~ using Huckel theory showed that "the configuration with equal bond lengths is unstable with respect to bond alternationn2when the length of the polymer chain exceeds 55 carbons. The authors then speculate that this number is the maximum range of delocalization of the defect in a region of uniform carbon-carbon bonds. Experimental evidence indicates that the defect is in fact delocalized nearly up to this maximum distance.28 This estimation was based on Huckel theory and on assumptions about the dependence of the so-called Hiickel @ parameter on the bond length. (1) Chien, J. C. W. Polycefylene; Academic Press: New York, 1984. (2) Salem, L. The Molecular Orbital Theory of Conjugated Sysrems; Benjamin: Reading, MA, 1974; p 517. ( 3 ) Longuet-Higgins, H.C.; Salem, L.Proc. R. Soc. (London) 1959, A251, 172.
0022-3654/90/2094-47 16$02.50/0 0 1990 American Chemical Society
