0 - 4 6 2

j. Chem. Thermodynamics 1992, 24, 863-881

Thermodynamic propert ies of deuterated hexamethylbenzene and of its solid solut ions wi th the hydrogenated analog. A large isotope ef fect on the phase transit ion at the temperature 117 K a

T A K A H I R O F U J I W A R A , b A K I R A I N A B A , c T O O R U A T A K E , d and H I D E A K I C H I H A R A e

Department of Chemistry and Microcalorimetry Research Center, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan

(Received 6 September 1991; in finalform 2 December 1991)

The heat capacities of hexamethylbenzene-d18 (HMB-d18) were measured at temperatures T between 4 K and 300 K. The III-to-II transitioq ~ occurs at T = 132.4 K and the molar entropy of transition is 13.1 J ' K ~' mo1-1, which is 1.41 times as large as that of HMB-ha8. The heat capacities of the solid solutions with n(D)/n(H) = 1/9 and n(D)/n(H) = 1 were also measured between T = 14 K and 300 K. Thermodynamic properties of the transition change continuously with the composition. Crystal structures of HMB-h~8 , HMB-da8, and their solid solutions are the same in phase II and phase III. The large isotope effect in the entropy of transition can be attributed to differences in the torsional modes of the methyl groups. Hysteresis phenomena for HMB-da8 and HMB{n(D)/n(H)= 1} and the memory effect for HMB{n(D)/n(H)= 1} in relation to the III-to-II transition were studied. The temperature dependence of the Raman spectrum is also reported.

1. Introduction

H e x a m e t h y l b e n z e n e , h e r e i n a f t e r a b b r e v i a t e d as H M B , e x h i b i t s t w o s o l i d - t o - s o l i d

p h a s e t r a n s i t i o n s a t t h e t e m p e r a t u r e s T = 117 K, (1-3) a n d T = 383 K, (4) b o t h of w h i c h

a r e o f f i rs t o rde r . T h e p h a s e s a re r e f e r r ed to as I, II , a n d I I ! d o w n w a r d s f r o m t h e

m e l t i n g t e m p e r a t u r e : 4 3 8 K . T h e c r y s t a l s t r u c t u r e was f irst d e t e r m i n e d b y

R o b e r t s o n (5) for p h a s e II a t r o o m t e m p e r a t u r e . I t was , in fact , t h e f i rs t o r g a n i c c r y s t a l

" Contribution No. 58 from the Microcalorimetry Research Center. b Present address: Electronics Research Laboratory, Matsushita Electronics Corporation, Takatsuki,

Osaka 569, Japan. c To whom all communications should be addressed. n Present address: Research Laboratory of Engineering Materials, Tokyo Institute of Technology,

Yokohama 227, Japan. e Present address: Japan Association for International Chemical Information, Tokyo 113, Japan.

0021-9614/92/080863 + 19 $02.00/0 O 1992 Academic Press Limited

864 T. FUJIWARA E T AL.

to which the Fourier method was applied successfully. The space group is P i with one molecule in the unit cell. The structure of phase I is highly symmetric (orthorhombic, Fmmm)/6) One of the interesting features of this phase is that it has a large negative expansivity above T = 409 K, ~7) but keeps the same structure. At present, the structure of phase III is not known because of shattering of the single crystal at the transition from phase II to phase III. ~8)

Since the methyl group has a one-dimensional rotational degree of freedom, it is interesting to know the dynamics of methyl rotation as well as the dynamics of the overall molecule in the crystalline state. According to an n.m.r, measurement ¢9) and a neutron-scattering experiment, tl°) the overall molecular librational motion begins at T = 150 K about the hexad axis of the molecule, whereas the torsional motion of methyl groups seems to be taking place even at 2 K. Later neutron-scattering studies ~1t'~2) assigned those two modes; the one at a wavenumber of 60 cm ~ for phases II and III as overall molecular libration, and the other at 137 cm - t for phase III, and at 120 cm ~ for phase II, as torsional motion of the methyl group. Both n.m.r, measurements ~9'13) and the neutron-scattering experiment, (~°) however, suggested that the potential-barrier height which hinders the rotational motion of the methyl group changed only slightly between phases II and IlL For phase III, an n.m.r, technique called field cycling allowed us to identify two rotational tunnelling wavenumbers of methyl groups. ~14) That the one has a large temperature dependence and the other does not was considered to be evidence for the existence of motional coupling between the neighboring methyl groups within a molecule.

We performed heat-capacity measurements for the fully deuterated analog HMB-d18 and the solid solutions: (HMB-h~8 + HMB-d18). X-ray powder-diffraction and Raman-spectroscopic measurements were also made. The results, which will be described below, indicate that there is an extraordinarily large isotope effect on the enthalpy and entropy changes of the III-to-II transition. Hysteresis phenomena and memory effects, similar to those observed for HMB-h~8, ~5) are also presented.

2. Experimental

Ordinary hexamethylbenzene (HMB-h18) and its fully deuterated analog (HMB-d18), whose isotopic purity was 99.3 moles per cent, were obtained from Aldrich Chemical Company, Inc. and Merck, Sharp, and Dohme, Canada Ltd., respectively. They were purified further by fractional sublimation in vacuo. Two samples of solid solution were prepared with a stoichiometric mixture of (HMB-hls+HMB-d~8) from benzene solution.

Heat-capacity measurements were made for samples of HMB-d18 and" with isotopic compositions of n(D)/n(H) = 1/9 and n(D)/n(H) = 1. Two calorimeter vessels, both of which were made of copper plated with gold, were employed; the one (a 6) used for HMB-d18 had a platinum resistance thermometer (Model 8164, Leeds & Northrup Co.) and a germanium resistance thermometer (CryoCal, Inc.) and the other used for n(D)/n(H)= 1/9 and n(D)/n(H)= 1 had a platinum resistance thermometer (Type S1055-1, Minco Products, Inc.) alone. The latter, a new calorimeter vessel, was a beaker-type container with a removal lid fixed at the top

ISOTOPE EFFECT ON PHASE TRANSITION OF HEXAMETHYLBENZENE 865

with an indium seal and six screws. A Karma heater was non-inductively wound around the lower half of the outside wall, while thermometers could be attached to the upper half. The body of the calorimeter vessel was covered (not airtight) by a cylindrical sheath which was cemented to the body at the top and the bottom.

The temperature scale used was based on the IPTS-68 above 13.81 K and the 4He vapor-pressure and gas-thermometric scales below 15 K. ~17) The ITS-90 temperature scale differs from the IPTS-68 by no more than 6 mK at 14 K and gradients differ no more than 0.3 per cent at all the temperatures concerned in the present study. The amount of the sample loaded in the vessel was 49.31 mmol (~8.894 g), 39.35 mmol (~6.456 g), and 20.81 mmol (~3.562 g) for HMB-d18, HMB{n(D)/n(H)= 1/9}, and HMB{n(D)/n(H) = 1}, respectively. The contribution of the sample heat capacity was moderate over the whole temperature range: for HMB-d18, for example, it was 0.61 at T = 10 K, 0.42 at T = 150 K, and 0.47 at T = 300 K.

Hysteresis and memory effects were investigated calorimetrically. For such an investigation, it was necessary to study the thermodynamic properties in the cooling direction. To do that, the adiabatic calorimeter was operated as a conduction calorimeter by maintaining a constant temperature difference (actually a constant electromotive force on the difference thermocouple) between the calorimeter vessel and the surrounding adiabatic shield. The temperature of the calorimeter was measured as a function of time in the cooling direction. This type of measurement is often called total thermal analysis in contrast to more common differential thermal analysis (d.t.a.). The present result of total thermal analysis could be converted to a differential thermogram (figure 6) by numerical differentiation to show thermal anomalies more clearly. Furthermore, it was possible to calculate changes of enthalpy of the specimen relative to the enth~dpy at a selected temperature (122 K in the case of figure 3) because the rate of heat exchange between the calorimeter vessel and the adiabatic shield could be measured. An example of this may be seen in figure 3.

Powder-diffraction diagrams were recorded on a Rigaku model RAD-ROC at the X-ray Diffraction Service of the Department of Chemistry using Cu K~ radiation. Raman spectra were obtained with a JASCO model R800 spectrometer with an argon-ion laser at the excitation wavelength 514.5 nm.

3. Results and discussion

ISOTOPE EFFECT

Primary measured molar heat capacities of HMB-d18 at temperatures between 4 K and 300 K are given in table 1. The thermodynamic quantities derived therefrom are given at round temperatures in table 2. Measured molar heat capacities of HNIB{n(D)/n(H) = 1} and HMB{n(D)/n(H) = 1/9} between T = 14 K and T = 300 K are shown in figure 1 and the primary results are given in tables 3 and 4, respectively. Tables 5 and 6 list the thermodynamic quantities of the solid solutions at round temperatures. The heat capacities of the solid solutions fall between those of the neat components (not shown in figure 1). The transition between phases III and II of the

866 T. F U J I W A R A E T AL.

TABLE 1. Measured molar heat capacities of hexamethylbenzene-dls. M = 1 8 0 . 1 3 g . m o l 1 ; R = 8 . 3 1 4 5 1 0 J - K 1.mol 1

T Cp, m T Cp, m T Cp, m T Cp, m R K R K R K R

Series 1 21.534 2.271 22.409 2.446 23.727 2,717 25.146 3.015 26.383 3.278 27.654 3.555 29.270 3.906 30.917 4.274 32.452 4;622 33.858 4.933 35.249 5.241 36.740 5.574 38.299 5.909 39.921 6.249 41,539 6.594 43.054 6.910 44.521 7.206 46.046 7.506 47.591 7.814 49.182 8.126 50,819 8.437 52.486 8.745 54.186 9.062 55.813 9.345

Series 2 55.575 9.300 57.586 9.659 59.525 9.993 61.245 10.281 62.904 10.562 64.537 10.830 66.208 11.099 67.918 11.372 69.610 11.642 71.566 11.947 73.771 12.286 75,904 12.609 77.976 12.932 79.992 13.235 82.039 13.546 84.115 13.865 86.148 14.179 88.137 14.490 90.083 14.785 92.026 15.082 93.968 15.390 95.871 15.698 97.702 15,981 99.553 16.281

101.468 16.586 103.342 16.898

141.262 22.812 139.883 22.563 143.077 22.799 141.367 22.597 144.925 22.752 142.863 22.656 146.802 22.801 144.505 22.735 148.758 22.838 146.145 22.775 150.705 22.899 Series 5 153.880 23.007 127.948 21.924 156.972 23.075 129.350 22.012 158.871 23.155 130.816 22.119 160.882 23.210 132.273 22.211 162.925 23.306 138.831 22.502 165.064 23.390 145.641 22.746 167.283 23.483 147.604 22.796 169.492 23.587 149.569 22.850 171.689 23.686 151.548 22.913 173.874 23.809 153.574 22.974 176.094 23.924 Series 6 178.446 24.058 125,308 20,814 180.893 24.213 127.266 21.221 183.360 24.344 145,842 22.781 185.838 24.533 147.786 22.812 •88,302 24.680 Series 7 190.775 24.828 126.048 20.966 193,259 24.983 127.730 21.303 195.743 25.172 128.914 21.520 198,245 25.340 129.797 21.745 200,729 25.514 130.670 22.380 203,212 25.702 131.466 32.234 205,728 25.895 132.108 140.088 208,241 26.099 132.650 150.379 210,737 26.296 133.443 58.951 213,225 26.510 134.754 29.599 215,695 26.721 136.400 24.280 218,157 26.938 138.142 23.264 220,629 27.138 139.474 22.896 223,127 27.358 140.384 22.836 225,627 27.570 141.746 22.787 228,113 27.773 143.628 22.761 230.587 28.022 145.573 22.782 233,258 28.319 147.577 22.805 235.916 28.492 149.640 22.855 238,395 28.735 Series 8 240.879 28.992 3.983 0.0129" 243.312 29.180 4.089 0.0242 ~ 245.769 29.481 4.262 0.0251 ~ 248.213 29.659 4.500 0.0326" 250.686 29.904 4.855 0.0410" 253.192 30.141 5.287 0.0523" 255,685 30.394 5.736 0.0672" 258.166 30.621 6.203 0.0843" 260.629 30.900 6.651 0.1045" 263.068 31.119 7.068 0.1230"

10.118 0.3516" 10.928 0.4341"

Series 11 7.568 0.1490" 8.029 0.1785" 8.504 0.2118" 9.018 0.2508" 9.583 0.3010"

10.222 0.3655 a 10.994 0.4430" 11.908 0.5514 a 12.932 0.6776 ~ 14.064 0.8501"

Series 12 9,862 0.3276"

10.575 0,3921" 11.439 0.5638 ~

Series 13 10.652 0.4072" 11.878 0.5489 a 13.360 0.7421"

Series 14 10.715 0.4164" 11.756 0.5352 ~ 12.882 0.8009 12.943 0.6825 ~ 14.325 1.0144 14.372 0.9115"

Series 15 15,798 1.2484 15.835 1.1404" 17.194 1.4765 17.221 1.3772 a 18.558 1.7145 18.573 1.6481" 19,919 1.9645 t9.925 1.9314 a 21.417 2.249 21.417 2.246" 22.959 2.558 22.960 2.550"

Series 16 13.764 0.8520 13.831 ° 0.8165" 15.372 1.1743 15.412 1.0631" 16.805 1.4084 16.837 1.3018"

Series 17 4.100 0.0225 a 4.250 0.0297" 4.605 0.0366 a

ISOTOPE EFFECT ON PHASE TRANSITION OF HEXAMETHYLBENZENE

TABLE 1--continued

867

T Cp, m T Cp, m T Cp, m T Cp, m R K R K R K R

105.244 17.223 107.237 17.568 109.300 17.922 111.383 18.290 113.435 18.649 115.457 19.005

Series 3 114.434 18.808 116.437 19.175 118.416 19.537 120.417 19.904 122.433 20.280 124,373 20.607 126.244 20.977 128.185 21.357 130.186 22.018 131.677 72.756 132.448 143.025 133.153 77.821 134.762 33.717 137.302 24.293 139.532 23.071

265.503 31.352 7.479 0.1465 a 5.422 0.0581 a 267.973 31.609 7.878 0.1701 a 6,468 0.0972" 270.456 31.883 Series 9 7.497 0.1485 ° 272.915 32.117 3.968 0.0192" 8 ,415 0.2077 a 275.357 32.369 4 .171 0.0247" 9.253 0.2727" 277.882 32.637 4.462 0.0327 a Series 18 280.468 32.910 4.885 0.0419 ~ 11,290 0.6340 283.013 33.176 Series 10 11,377 0.4897" 285.543 33.440 3.981 0.0216" 12,550 0.7445 288.057 33.734 4.187 0.0263 a 12,607 0.6359 a 290.555 33.976 4.515 0.0337 a Series 19 293.035 34.211 4.926 0.0425 ~ 10.583 0.5133 295.505 34.587 5.339 0.0547" 10.654 0.4072" 297.960 34.738 5,774 0.0682 ~ 11.615 0.6486 300.472 34.971 6 .241 0.0860 a 11.687 0.5234 a

Series 4 6.713 0.1081 ~ 12.897 0.8123 130.759 22.108 7.165 0.1254" 12.959 0.6853 ~ 132.245 22.196 7.597 0.1527 a Series 20 133.809 22.284 8.025 0.1786 ~ 9.545 0.4099 135.353 22.369 8.474 0.2113 a 9.626 0.3061 a 136.877 22.436 8.907 0.2448" 10.973 0.4419 138.386 22.487 9.430 0.2870"

" "Instantaneous" heat capacity.

TABLE 2. Thermodynamic quantities of hexamethylbenzene-dls. M = 180.13 g 'mol -1 ; R = 8.314510J.K - l . m o l 1

T Cp, m AroKH ° AToKS~ T Cp, m AToKH~ A]oKS~ R R . K R K R R , K R

10 15 20 25 30 40 50 60 70 80 90

100 110 120

Phase III 0.453 0 0 150 1.122 3 .813 0.3542 160 1.976 11.486 0.7357 170 2.985 23.838 1.283 180 4.069 41.446 1.922 190 6.271 93.271 3.398 200 8.282 166.22 5.017 210

10.08 258.22 6.688 220 11.70 367.19 8.365 230 13.24 491.91 10.028 240 14.77 631.91 11.676 250 16.36 787.54 13.314 260 18.05 959.41 14.951 270 19.82 1148.7 16.598 280

290 300

Phase II 22.88 2004.3 22.967 23.19 2234.5 24.452 23.61 2468.5 25.870 24.15 2707.2 27.234 24.78 2951.7 28.556 25.46 3203.0 29.845 26.24 3461.4 31.106 27.09 3729.7 32.346 27.96 4005.1 33.569 28.89 4289.3 34.779 29.84 4582.8 35.977 30.81 4886.0 37.166 31.82 5199.2 38.347 32.86 5522.5 39.524 33.92 5856.4 40.695 34.94 6200.7 41.862

868 T. FUJIWARA E T AL.

TABLE 3. Measured molar heat capacities of hexamethylbenzene {n(D)/n(H) = 1}, M = 171.21 g. mol- 1; R = 8.314510 J, K - 1. mol- 1

T Cp, m T Cp, m T Cp, m T Cp, m R g R K R K R

Series 1 138.404 21.631 301.747 32.707 144.989 21.679 14,056 0,7761 140.688 21.603 Series 2 147.522 21.748 14.806 0.9016 143.122 21,633 118.009 18.576 149.998 21.816 16,094 1 .1042 145.710 21.695 120.576 19.105 152.476 21.859 17.660 1.3597 148.245 21,739 122.585 19.532 155.006 21.936 19.244 1.6058 150.723 21.825 130.316 32.799 157.578 22.006 20.950 1.9051 153.201 21.889 138.478 21.553 160.153 22.100 22.781 2.263 155.679 21.959 t40.890 21.565 Series 5 24.615 2.579 158.157 22.051 143.369 21.637 116.461 18.297 26.515 2.947 160.636 22.108 145.849 21.678 116.802 18.574 28.442 3.319 163.113 22.209 148.324 21.756 117.163 18.339 30.369 3.676 165.592 22.339 Series 3 117.543 18.443 32.320 4.060 168.073 22.397 121.399 20.319 117.922 18.569 34.294 4.460 170.549 22.505 123.050 20.560 118.300 18.672 36.222 4.841 173.027 22.628 124.859 21.002 118.677 18.618 38.118 5.213 175.506 22.729 126.842 20.957 119.052 18.660 40.047 5.581 177.982 22.841 128.829 21.030 119.430 18.877 41,994 5.946 180.456 22.986 130.960 21.173 119.810 18.850 43.958 6.295 182.930 23.086 133.335 21.270 120.188 18.997 45.963 6.649 185.406 23.182 135.812 21.362 120.567 18.972 48.031 7.025 187.885 23.359 138.294 21.431 120.943 19.171 50.118 7.401 190.359 23.500 140.773 21.515 121.321 19,233 52.206 7.814 192.830 23.694 143.255 21,578 121.701 19,492 54.197 8.157 195.301 23,844 145.830 21.678 122.081 19,479 56.086 8.486 197.774 23.953 148,508 21.742 122.459 19,586 57.990 8.806 200.250 24.149 151.189 21.814 122.836 19.720 59.896 9,117 202.727 24.296 Series 4 123.214 19.904 61.807 9.424 205.198 24.394 79,463 12.187 123.592 20.363 63.723 9.756 207.666 24.632 81.198 12.459 123.965 21.400 65.643 10.057 210.135 24.914 83,387 12.797 124.334 23.311 67.567 10.356 212.606 25.006 85.589 13.149 124.692 29.501 69.493 10.660 215.077 25.126 87.776 13.492 125.000 48.372 71.421 10.949 217.544 25.332 89.905 13.818 125.246 80.204 73.354 11.254 220.011 25,557 91.926 14.128 125.445 86,062 75.291 11.548 222.478 25,814 93.882 14.425 125.719 28.589 77.232 11.852 224.945 25,928 95.845 14.756 126.040 39.827 79.176 12.169 227.410 26,064 97.806 15.065 126.243 160.442 81.121 12.443 229.874 26,297 99.766 15.383 126.336 160.310 83.070 12.751 232.334 26.475 101.824 15.728 126.451 132.130 85.022 13.051 234.791 26.804 104.067 16.102 126.635 89.240 86.972 13.374 237.258 27.017 106.312 16.486 126.884 61.464 88.925 13.693 239.728 27.064 108.469 16.838 127.185 45.219 90,882 13.991 242,197 27.213 110.631 17.248 127.518 37~56 92,839 14.287 244.666 27.503 112.795 17.620 127.874 33.545 94,796 14,597 247.132 27.723 114.953 18.020 128.277 27.414 96.755 14.928 249.601 27.898 117.115 18.426 128,719 25.166 98,717 15.220 252.073 28.152 119.223 18.803 129.177 24.404

100.678 15.533 254.552 28.379 120.984 19.165 129.642 23.255 102.800 15.912 257.042 28.528 122.461 19.569 130.110 22.551 105.005 16.280 259.533 28.746 123.940 20.500 130,576 22.267 107,198 16.665 262.021 28.983 124.982 23.534 131.110 22.036 109.403 17.052 264.506 29.319 125.544 38.826 131.857 21.863

ISOTOPE EFFECT ON PHASE TRANSITION OF HEXAMETHYLBENZENE

TABLE 3--continued

869

T Cp, m T Cp, m T Cp, m T Cp,m R K R K R K R

111.556 17.396 266.992 29.527 125.917 143.677 132.908 21.673 113.720 17.803 269.481 29.708 126.193 178.363 134.261 21.547 115.789 18.183 271.968 29.925 126.646 82.728 135.904 21.519 117.864 18.558 274.451 30.161 127.206 43.662 137.846 21.495 120.050 18.993 276.936 30.412 127.779 32.810 140.136 21.517 122.247 19.402 279.418 30.627 128.408 27.044 142.619 21.596 124.399 20.864 281.900 30.929 129.227 24.582 145.226 21.672 126.073 68.063 284.385 31.041 130.311 22.962 147.955 21.760 127.255 71.488 286.865 31.316 131.580 21.993 150.709 21.850 128.634 36.138 289.346 31.550 133.107 21.684 153.488 21.894 130.356 26.098 291.825 31.772 134.954 21.521 156.266 21.960 132.270 23.156 294.305 32.016 137.239 21.478 159.040 22.031 134.273 22.325 296.784 32 .452~ 1 3 9 . 8 1 9 21.550 136.263 21.852 299.267 32.531 142.404 21.596

30

20

10

T/K

50 100 150 200 250 300 I I I I

oOO °°

e o

/ /

I I 50 100

I 10

T/K

capacites

%

o A

a

o 4

Q2

°

o

o

Q

I I 20 30 40

FIGURE 1. Measured molar heat of ~ , HMB{n(D)/n(H) = 1/9}. t , A, The molar heat capacities of undercooled phase II.

4

0

(D, HMB{n(D)/n(H)= 1}; and

870 T. FUJIWARA E T AL.

TABLE 4. Measured molar heat capacities of hexamethylbenzene {n(D)/n(H) = 1/9}. M=164 .06g .mo l 1 ;R=8.314510J .K - l 'mo1-1

T Cp, m T Cp, m T Cp, m T Cp, m

K R K R K R K R

Series 1 156.647 21,161 159.179 21.253 161.721 21.311 164.325 21.406 166.869 21.477 169.346 21.573 171.825 21.671 174.305 21.740 176.784 21.885 179.328 22.010 181.870 22.116 184.351 -22.220 186.831 22.360 189.313 22.463 191.791 22.583 194.271 22.733 196,753 22.908 199.174 22.996 201.596 23.140 204.083 23.295 206.566 23.458 209.051 23.594 211.534 23.789 214.019 23.940 216.507 24.115 218.998 24.293 221.484 24.428 223.967 24.705 226.456 24.801 228.944 24.954 231.431 25.114 233.916 25.261 236.397 25.486 238.879 25.685 241.359 25.831 243.835 26.012 246.314 26.145 248.786 26.374 251.259 26.603 253.734 26.811 256,209 26.959 258.686 27.185 261.160 27.394 263.634 27.535 266.105 27.759 268.575 28.020 271.046 28.251 273.516 28.430 275.979 28.785 278.447 28.847 280.914 28.988

300.758 30.857 114.882 17.545 149,030 20.969 303.272 31.045 116.993 18.529 151.012 21.025 305.783 31,207 118.509 21.122 152,997 21.066

Series 2 119.309 35.532 154,980 21.107 14.789 0.8129 119.892 57.917 156,960 21.164 16.592 1.0570 120.336 67.251 158.941 21.217 17.78l 1.2211 120.787 58.642 160.922 21.277 18.620 1.3725 1 2 1 . 3 1 8 47,626 Series 4 19.708 1.5266 121.924 38.868 79,115 11.511 21.019 1.7433 1 2 2 . 6 3 9 30.927 80.831 11.765 22.327 1.9539 123.436 25.748 82.651 12.055 23.664 2.158 124.279 23,775 84.600 12.362 25.003 2.384 125.167 22.424 86.550 12,661 26.334 2.611 126.086 21,877 88.502 12.971 27.729 2.838 127.036 21.404 90,457 13.284 29.164 3.086 127.995 20.924 92.412 13.596 30.629 3.345 129.223 20.977 94,476 13.932 32.144 3,612 130.716 20.748 96.542 14.267 33.588 3.864 132.212 20.617 98.575 14,599 35.096 4.141 133.959 20.568 100.610 14.925 36.752 4,452 135.945 20,610 102.571 15,257 38.628 4.794 137.932 20.659 104.606 15.622 40.599 5.144 139.916 20.738 106.646 15.963 42.461 5.470 141.902 20,814 108.785 16.343 44.414 5,812 143.892 20.840 123.878 24.142 46.447 6,154 145.880 20.860 138.816 20.646 48.502 6,508 147.865 20.924 140.958 20.723 50.577 6,886 149.852 20.981 143.235 20.819 52.671 7,248 151.840 21.066 145.514 20.860 54.788 7,614 153.828 21,099 147.793 20.908 56.932 7,972 155.814 21.151 150.070 20.977 59.075 8,326 157.801 21.181 152.347 21.063 61.210 8,681 159,789 21.248 154.626 21.099 63.370 9.030 161.776 21.303 Series 5 65.415 9.351 163.762 21.363 251.005 26.651 67.334 9.659 165.745 21.453 253.355 26.767 69.258 9.971 167.729 21.537 255.365 26.856 71,186 10.266 169.712 21.562 257.442 27.082 73.119 10.559 Series 3 259.927 27.287 75.054 10.866 116.484 1 8 . 9 6 8 262.407 27.418 77.062 11.178 117.886 19,149 264.884 27.683 79.071 11.489 119.326 19.312 267.368 27.930 81.014 11.789 120,811 19.489 269.848 28.121 82.959 12.096 122.294 19.633 272,326 ~8.325 84.905 t2.394 123.779 19.776 274.803 28,525 86.855 12.698 125.268 19.930 277.284 28.686 88.805 13.022 126.757 20.085 279.768 28.934 90.757 13.333 128.245 20.156 282.251 29.143 92.821 13.657 129.732 20,263 284.728 29.409 94.886 13.980 131.220 20.348 287.210 29.635 96.844 14.294 132.707 20.414 289.691 29.837 98.803 14.624 134.197 20.445 292.170 30.091

ISOTOPE EFFECT ON PHASE TRANSITION OF HEXAMETHYLBENZENE

TABLE 4--continued

871

T Cp, m T C p , m T Cp, m T C p , m

R K R K R K R

283.376 29.171 100.763 14.952 135.833 20.536 294.654 30.239 285.834 29.374 102.800 15.290 137.620 20.597 297.130 30.493 288.288 29.653 104.835 15.639 139.408 20.672 299.606 30.675 290.744 29.886 106.795 15.975 141.193 20.754 302.080 30.899 293.201 30.090 108.758 16.321 143.074 20.805 304.554 31.069 295.660 30.330 110.720 16.697 145.060 20.856 298.177 30.595 112.762 17.075 147.048 20.891

solid so lu t ions is first o r d e r in the s a m e w a y as in the nea t c o m p o n e n t s , a n d h e a t

capac i t i es o f u n d e r c o o l e d phase I I a re s h o w n by filled s y m b o l s in the t r a n s i t i o n

region.

F o r HMB{n(D)/n(H) = 1}, s low t e m p e r a t u r e drif t was o b s e r v e d be low T = 20 K

after r a p i d dr i f t w h e n the c a l o r i m e t e r h e a t e r h a d b e e n t u r n e d off as in the case o f

H M B - d l s .t18) The re fo r e , on ly the r a p i d dr i f t was t a k e n in to a c c o u n t in d e t e r m i n i n g

the h e a t c a p a c i t y b e t w e e n T = 14 K a n d T = 20 K; it wil l be ca l led " i n s t a n t a n e o u s "

hea t capac i ty . I n the case o f HMB{n(D)/n(H) = 1/9}, h o w e v e r , such a s low effect was

no t o b s e r v e d d o w n to T = 1 4 K . H M B - h 1 8 also s h o w s a s low a p p r o a c h to

equ i l ib r ium, b u t it o c c u r r e d on ly b e l o w T = 6 K. 118)

T h e r m o d y n a m i c p r o p e r t i e s for the fou r m a t e r i a l s a re s u m m a r i z e d in tab le 7, a n d

their c o m p o s i t i o n d e p e n d e n c e s for the I I I - t o - I I t r a n s i t i o n are s h o w n in f igure 2. T h e

TABLE 5. Thermodynamic quantities of hexamethylbenzene {n(D)/n(H)= 1}. R=8.314510J.K-l .mo1-1

. A20KHm T Cp m T o AToKSm T Cp m A~oKH~ A~oKS~ K R R . K R K R R - K R

Phase Ill 20 1.742 0 0 30 3.608 26.664 1.055 40 5.575 72.620 2.363 50 7.396 137.45 3.803 60 9.137 220.30 5.309 70 10.73 319.78 6.839 80 12.28 434.88 8.373 90 13.86 565.47 9.910

100 15.43 711.85 11.451 110 17.15 874.69 13.001 120 18.98 1055.1 14.570

Phase II 130 21.12 1423.9 17.496 140 21.49 1637.0 19.076 150 21.79 1853.5 20.569 160 22.11 2072.9 21.985 170 22.49 2295.9 23.336 180 22.95 2522.9 24.634 190 23.49 2754.9 25.889 200 24.11 2993.0 27.109 210 24.81 3237.5 28.302 220 25.56 3489.3 29.474 230 26.33 3748.6 30.626 240 27.12 4015.9 31.764 250 27.95 4291.3 32.887 260 28.84 4575.1 34.001 270 29.76 4868.1 35.106 280 30.69 5170.4 36.205 290 31.62 5481.9 37.299 300 32.56 5802.6 38.386

872 T. F U J I W A R A E T AL.

TABLE 6. Thermodynamic quantities of hexamethylbenzene {n(D)/n(H) = 1/9}. R = 8.314510 j . K - l . m o l 1

A2O KSm A20 KSm T C e, m AT0 KH ~ r o T Cp, m AT0 KH ~ r o

R R - K R K R R ' K R

Phase III 20 1.573 0 0 30 3.240 23.910 0.9467 40 5.021 65.187 2.122 50 6.791 124.29 3.434 60 8.478 200.71 4.822 70 10.08 293.56 6.251 80 11.63 402.13 7.697 90 13.21 526.27 9.157

100 14.82 666.33 10.632 I10 16.55 823.07 12.125

Phase lI 120 19.41 1137.9 14.805 130 20.27 1336.7 16.397 140 20.70 1541.8 17.916 150 20.99 1750.2 19.354 160 21.26 1961.5 20.717 170 21.59 2175.7 22.016 180 22.01 2393.7 23.262 190 22.50 2616.2 24.465 200 23.07 2843.9 25.632 210 23.68 3077.8 26.773 220 24.34 3317.8 27.890 230 25.03 3564.6 28.987 240 25.75 3818.4 30.068 250 26.50 4079.6 31.134 260 27.29 4348.4 32.187 270 28.11 4625.4 33.232 280 28.96 4910.8 34.270 290 29.84 5204.8 35.302 300 30.72 5507.6 36.328

"reverse" temperature, i.e. the temperature at which the sample cooling was stopped and the measurements of heat capacity started upwards, was 78 K, 78.3 K, 93.8 K, and 99.3K for HMB-hla, HMB{n(D)/n(H)=I/9}, HMB{n(D)/n(H)=I}, and HMB-d18, respectively. These temperatures lie outside the hysteresis loop, shown in figure 1 of reference 15 and figure 3 of this paper, and therefore the values of AtrsH ~ in table 7 represent true equilibrium properties.

AtrsS~(HMB-d18 ) is 1.41"AtrsSm(HMB-hls); that is a surprisingly large isotope effect if one considers the closeness of the temperatures of transition. The reason why we studied the solid solutions was two-fold; firstly, to make certain that the isotope effect was not due to instrumental errors but was of a genuine nature, and secondly, to see whether there was a discontinuous change in thermodynamic behavior on

TABLE 7. Transition and melting temperatures and molar enthalpy and entropy of transition of hexamethylbenzene

Tt~(III = II) Atr~H ~ ArraS:, Ttr~(IIl = I) Tfus ~' K kJ. too l - 1 J. K - 1. m o l - 1 K K

HMB-h18 117.5_+ 0.1 1.10 a 9.3" 382 b 439 b n(D)/n(H) = 1/9 120.4+0.2 1.21 10.0 n(D)/n(H) = 1 126.5-t-0.1 1.46 11.5 HMB-dl 8 132.4_+0.1 1.73 ___0.05 13.1 _+0.5 381 b 437 b

" From reference 3. b Determined by d.s.c, measurement.

ISOTOPE EFFECT ON PHASE TRANSITION OF HEXAMETHYLBENZENE 873

1.6

°~ 1.4

1.2 (c)

.---.

-

1.5

o~

(b)

1

130 -

12o (a) -

I 0 0.5

x

FIGURE 2. Composition dependences of (a), III-to-II transition temperature; (b), molar transition enthalpy; and (c), molar transition entropy; x is the mole fraction of HMB-dla.

going from HMB-h18 to HMB-d18. As is evident from figure 2, AtrsS ~ shows a continuous change as the mole ratio n(D)/n(H) is changed, which assures us that the large isotope effect is real. There remains a possibility that deuterium substitution may lead to a small gradual change in the crystal structure either in phase II or in phase I I I in such a way that the AtrsS~n curve appears continuous.

X-ray powder-diffraction experiments were then conducted on HMB-d18 and HMB{n(D)/n(H) = 1/9} to compare with the diffraction of HMB-has. The results, presented in the Appendix, showed that deuterium substitution did not change the cr~istal structure except for a small change in the size of the unit cell. Therefore, the isotope effect in AtrsS ° is not of structural origin.

Raman-spectral measurements were undertaken to determine whether there was a large difference in the molecular or submolecular motions. The results described in the Appendix show that the difference in the molecular libration between HMB-h18

874 T. FUJIWARA ET AL.

4

O

I I I

t"

t /

110 120 130

~K

FIGURE 3. Hysteresis effect observed in the molar enthalpy change AHr, of HMB{n(D)/n(H) ~ 1}. Each series of measurements in the heating direction had a different reverse temperature: @, T~ov = 120.5 K; A, T~ev = 118.1 K; A, T~ev = 115.0 K; (D, T~ev = 78.8 K. mR, The molar enthalpy change obtained by total thermal analysis in the cooling direction.

and HMB-d18 is not large enough to account for the difference in AtrsSm, but the wavenumber of methyl torsion undergoes considerable change upon deuter ium substitution.

Al though the unusually large difference in the entropy of the I I I - to - I I t ransit ion of H M B - d , a and HMB-h18 p rompted us to do this research, the results were no t very startling because all the properties investigated changed cont inuously as the isotopic composi t ion changed. Thus, the largest contr ibut ion to the isotope effect must come from the difference in the torsional modes of methyl groups.

HYSTERESIS AND MEMORY EFFECTS

In accordance with the order of the I I I - to - I I transition, a hysteresis effect was observed in the transit ion region as shown in figure 3 for H M B { n ( D ) / n ( H ) = 1}.

ISOTOPE E F F E C T ON PHASE T R A N S I T I O N OF H E X A M E T H Y L B E N Z E N E 875

E

150

100

50

[ [

0 I I 120 130 140

T/K

F I G U R E 4. Molar heat capacity of HMB{n(D)/n(H) = 1 } obtained in the heating direction showing the memory effect: the "halt" temperature was 126.1 K; T~ov = 115.9 K.

Similar results were obtained also for HMB-d18 (not shown in the figure). In the transition region, a period ~3 h was needed to attain apparent equilibrium, otherwise about 0.5 h was required. A reference temperature Tref, where the relative enthalpy values were normalized, was chosen to be 150 K where the specimen is completely in phase II. The reverse temperature T~, v of each series is indicated in the figure caption. Trev was varied to obtain the overall picture of the hysteresis effect.

The nature of the hysteresis effect was essentially the same as for HMB-hI8. t~ 5,19) Therefore, a brief description of the materials of the present study will be given. As seen in figure 3, the enthalpy of transition is larger when Trev is lower. A simple interpretation is that the transition from phase II to phase III is not complete unless the specimen is cooled to a sufficiently low temperature; otherwise the specimen at Trey is a mixture of phase II and phase III; the amount of phase III depends on T~e v

876 T. FUJIWARA E T AL.

4

o

0 ~ 110 120 130

T/K FIGURE 5. Molar enthalpy change AH m of HMB{n(D)/n(H) = 1} obtained: O, in the cooling direction

showing the memory effect. The "halt" temperature was 117.1 K and T, ev= 125.5 K. O, The molar enthalpy change obtained in the heating direction for comparison: T~ev = 116 K. The hysteresis loop is also indicated.

and is manifested in the magni tude of the enthalpy of transit ion measured in the heating direction.

The cooling curve for HMB{n(D)/n(H)= 1} was also examined by performing a total thermal analysis, and is shown by filled squares in figure 3. This curve was drawn so that the enthalpy value at T = 122 K coincided with the calorimetric results; 122 K is the temperature at which the total thermal analysis was started downward. This curve completes the hysteresis loop. "

Just as was reported for HMB-h18, ~15' 19) evidence has been obtained to show that in HMB{n(D)/n(H)= 1}, each crystallite of a powdered specimen has a specific (and different) transition temperature or, in other words, each crystallite has a built-in memory as to where it should begin phase transition. Results are given in figure 4 where the I I I - to - I I transit ion shows two split heat-capacity anomalies. In this example, the specimen was first cooled to T = 78 K, where it was almost completely

ISOTOPE E F F E C T ON PHASE T R A N S I T I O N OF H E X A M E T H Y L B E N Z E N E 877

450 -

400

350

300

250

I I I I

• 0•• ~ 0 0 • • B i

ODO

I I I I 0 1 2 3 4

10 3.t/s

F I G U R E 6. Reciprocal of the time derivative of the cooling curve (O of figure 5) obtained for HMB{n(D)/n(H) = 1}, which is equivalent to the molar heat capacity and shows a min imum at the "halt" temperature.

converted to phase III. It was then heated to T = 126.1 K (the "halt" temperature), an intermediate temperature within the transition region, and then cooled again to T = 115.9 K (T~,v, which lies outside the transition region in this particular run but inside the hysteresis loop), where the usual heat-capacity run was begun in the heating direction. About 3 h was allowed for equilibrium after each heat input in the transition region: T = 124 K to 132 K. In figure 4, the minimum of the heat capacity at T = 126.1 K between the two peaks coincides with the halt temperature. This result can be interpreted by our memory-model as follows.

Suppose that each crystallite in the specimen has its own transition temperature. Only such crystallites (called Group A) which have Ttr s below 126.1 K (the halt temperature) were transformed into phase II during the first heating. When the specimen was subsequently cooled, a small fraction of A persisted in phase II even at T = 115.9 K, but a majority of A was transformed back to phase III. Now, when the heat capacity was measured from T = 115.9 K upwards, Group A gave the first peak in figure 4 and the fraction of the specimen that has Ttr s higher than 126.1 K gives rise to the second peak. This result is quite reproducible, and if one changes the halt temperature, the position of the minimum in the heat capacity moves accordingly.

Similar results were also observed in the cooling direction by the total thermal analysis method (figure 5). In this case, the specimen was first brought to phase II

878 T. FUJIWARA E T AL.

g-

(c)

I I I

(b)

lO I

20

(a)

30 40 50 60

360. O/Tr

FIGURE 7. X-ray powder diffraction patterns of HMB-h18 (a), at the temperature 296 K and (b), at the temperature 4.2 K; and (c), of HMB-d18 at the temperature 26 K.

by heating it to T = 160 K, cooling it to T = 117.1 K, where part of phase II was converted to phase III, and then heating it again to T - - 125.5 K. The cooling curve was then recorded; the numerical differentiation of the cooling curve shows tyro split peaks, as seen in figure 6, with a minimum at T = 117.1 K, the halt temperature in this run.

The memory effect does not seem to be a kinetics-related phenomenon. During the heat-capacity measurements, no unusual thermal drift was observed after each heat input and, therefore, there was at least an apparent equilibrium at each temperature. Mnyukh ~2°) once suggested a similar idea for ammonium chloride. It is very tempting to speculate how the memory of the transition temperature is coded in each

7

ISOTOPE EFFECT ON PHASE TRANSITION OF HEXAMETHYLBENZENE 879

150

100

5O

I

°%°--- 1

(a) ~_,

I I I

13 0

0 D

0 0

~x A

(b)

1

i

(c)

~rs

I I I I 100 200 300 400

T/K

FIGURE 8. Q, Temperature dependence of the R~man wavenumber shifts obtained for HMB-h18 in the heating direction. The results reported earlier: O, reference 24; A, reference 25; ff], reference 26.

crystallite. Study of such a mechanism will itself constitute an interesting research topic. At present, we can only infer that the surface energy might play a significant role in determining the overall Gibbs energy of a particular crystallite. Preparing powder specimens of uniform crystallite size and measuring the enthalpy of solution for various crystallite sizes will give us a clue to the mechanism.

We are grateful to Dr S. Takeda for helpful discussion. This work was supported by a Grant-in-Aid for Scientific Research administered by the Ministry of Education, Science and Culture of Japan.

Appendix

~-RAY P O W D E R D I F F R A C T I O N

The powder pattern of HMB-h18 measured at room temperature in the range of 20 from n/18 to n/3 is shown in figure 7(a). Patterns of HMB{n(D)/n(H)= 1/9} and HMB-d18 were the same as that of HMB-h18. All the diffraction peaks could be

880 T. FUJIWARA E T AL.

150 --

100 ---

7

50 -

I I i

(a) 1 i

O O

I • ~ o ~ o o o o~ o O . . . ~ , ~ . , e

(b)

~ o ~ A - - m

(c)

--i

Lrs

0 I i l 0 100 200 300

T/K

FIGURE 9. O, Temperature dependence of the Raman wavenumber shifts obtained for HMB-dx8 in the heating direction. The results reported earlier: ©, reference 24; /k, reference 25.

indexed by the lattice parameters of phase II determined by Brockway and Robertson. 15)

Patterns of HMB-h18 and HMB-d18 at T=4.2 K and T = 26 K are shown in figures 7(b) and 7(c), respectively. The pattern of HMB{n(D)/n(H)= 1/9} is very similar to that of HMB-d~8, both in phase III. It is surprising that the diffraction pattern for phase III may be indexed on the basis of a pseudo-cubic unit~cell, which has been confirmed by our recent studies (2x'22) of high-resolution neutron powder diffraction for HMB-d~8.

The pattern of HMB-h~8 at T = 4.2 K is a mixture of that of HMB-d18 in phase III and that of HMB-ht8 in phase II. This means that in HMB-h~8 a portion of phase II failed to change to phase III even at T = 4 K, although annealing was not attempted. Thus, all HMBs have the same crystal structure in phase II. They also have the same structure in phase III.

ISOTOPE EFFECT ON PHASE TRANSITION OF HEXAMETHYLBENZENE 881

It should be noted that when HMB-d18 was rapidly cooled from r o o m temperature to 4 K, the same pattern as that of phase I I was obtained, whereas slow cooling, especially in the transition region, gave a completely different and much simpler pat tern as shown in figure 7(c). This is not the case with HMB-h18 and complete freezing of phase II was not observed even on rapid cooling.

RAMAN SPECTRA

The temperature dependence of Raman shifts is given in figure 8 for HMB-h18 and in figure 9 for HMB-d18. At T = 88 K, there is a weak band at a wavenumber of about 60 cm 1 for HMB-h18, which is due to residual phase II, as noted also by Prasad et

a/. ~23) Because of hysteresis effects, the appearance of the Raman spectra is complicated, but we were able to identify four major bands: (a), (b), (c), and (d).

In the wavenumber region below 250 cm 1, methyl torsion and librational motions of the entire molecule are possible. With the help of measurements of the mole ratio dependence and the assignments proposed by previous authors, we conclude that the band (a) at T = 88 K is due to methyl torsion, and bands (b), (c), and (d) are due to l ibrational modes.

REFERENCES

1. Huffman, H. M.; Parks, G. S.; Daniels, A. C. J. Am. Chem. Soc. 1930, 52, 1547. 2. Frankosky, M.; Aston, J. G. J. Phys. Chem. 1965, 69, 3126. 3. Atake, T.; Gyoten, H.; Chihara, H. J. Chem. Phys. 1982, 76, 5535. 4. Spaght, M. E.; Thomas, S. B.; Parks, G. S. J. Phys. Chem. 1932, 36, 882. 5. Brockway, L. O.; Robertson, J. M. J. Chem. Soe. 1939, 1324. 6. Watanabe, T.; Saito, Y.; Chihara, H. Sei. Papbrs Osaka Univ. 1949, 2, 9. 7. Chihara, H.; Seki,, S. Nature 1948, 162, 773. 8. Cellotti, G.; Bertinelli, F.; Stremmenos, C. Acta Crystallogr. A 1975, 31,582. 9. Allen, P. S.; Cowking, A. J. Chem. Phys. 1967, 47, 4286.

10. Rush, J. J.; Taylor, T. I. J. Phys. Chem. 1964, 68, 2534. 11. Rush, J. J. J. Chem. Phys. 1967, 47, 3936. 12. Rush, J. J.; Taylor, T. I. J. Chem. Phys. 1966, 44, 2749. 13. Bernard, H. W.; Tanner, J. E.; Aston, J. G. J. Chem. Phys. 1969, 50, 5016. 14. Takeda, S.; Soda, G.; Chihara, H. Solid State Commun. 1980, 36, 445. 15. Yoshimoto, Y.; Fujiwara, T.; Atake, T.; Chihara, H. Chem. Lett. 1985, 1347. 16. Saito, K.; Atake, T.; Chihara, H. J. Chem. Thermodynamics 1987, 19, 633. 17. Atake, T.; Chihara, H. Bull. Chem. Soe. Jpn. 1974, 47, 2126. 18. Atake, T.; Fujiwara, T.; Chihara, H. J. Chem. Thermodynamics 1984, 16, 281. 19. Yoshirnoto, Y. Doctoral Dissertation, Osaka Univ. 1983. - 20. Mnyukh, Yu. V. Mol. Cryst. Liq. Cryst. 1979, 52, 163. 21. Inaba, A.; Fujiwara, T.; Chihara, H.; Goto, Y.; Kamiyama, T.; Asano, H. unpublished results. 22. David, W. I. F.; Ibberson, R. M., Inaba, A. to be published. 23. Prasad, P. N.; Woodruff, S. D.; Kopelman, R. Chem. Phys. 1973, l, 173. 24. Bougeard, D. Von; Bleckmann, P.; Schrader, B. Ber. Bunsenges. Phys. Chem. 1973, 77, 1059. 25. Suzuki, M. J. Raman Spectrosc. 1973, 1,371. 26. Gerard, M.; Dumas, G.; Vovelle, M. F. Spectrochim. Acta 1977, 33, 169.