Calorimetric study of 1,3-diphenyl-1,1,3,3-tetramethyldisiloxane: Emergence of α-, β-, and crystalline-glass transitions

J O U R N A L OF

ELSEVIER

Journal of Non-Crystalline Solids 204 (1996) 38-45

Calorimetric study of 1,3-diphenyl-1,1,3,3-tetramethyldisiloxane: Emergence of et-, 13-, and crystalline-glass transitions H. Fujimori, M. Mizukami, M. Oguni * Department of Chemistry, Faculty of Science, Tokyo Institute of Technology, Ookayama-2, Meguro-ku, Tokyo 152, Japan Received 26 May 1995; revised 28 September 1995

Abstract Heat-capacities of fragile liquid 1,3-diphenyl-l,l,3,3-tetramethyldisiloxane (PMS) were precisely measured in the temperature range between 13 K and 300 K with an adiabatic calorimeter, a- and 13-glass transitions were observed at around 167 K and 69 K, respectively, in the liquid state, and another glass transition at around 150 K in the stable crystalline state. PMS was thus found to be quite a rare substance to show glass transitions both in the liquid and crystalline states in one substance. The interrelation between the transition temperatures is discussed with respect to their modes of molecular motions.

1. Introduction In molecular compounds, the liquid is characterized by the disordered arrangement both in the orientations and positions of molecules. However, some short range-ordered arrangement is expected, based on the enthalpic term in the Gibbs energy, to happen in the liquid as the temperature decreases. The rearrangement of molecules proceeds with surmounting some potential barrier, and therefore the relaxation time, r, for the rearrangement becomes long with the decrease in temperature. A glass transition is a freezing-in phenomenon of the orientational a n d / o r positional rearrangement of molecules due to the elongation of the time compared to the experimental time scale, typically 1 ks [1,2]. In general, only one a-glass transition is observed in one liquid, and thus

* Corresponding author. Tel.: +81-3 5734 2221; fax: +81-3 3724 2222.

the rearrangement has been considered to be a correlated motion of reorientation and diffusion of molecules. The stable crystal was, on the other hand, an ordered arrangement in the positions of molecules and only partial disorder, if any, remains with respect to the orientations. The mutual orientations of molecules become ordered with decreasing temperature, and the reorientation proceeds with surmounting some potential barrier as well. In such a situation, the glass transition potentially takes place also in the stable crystalline state as concerned with the reorientation, rather separated from the diffusional motion, of the molecule (or molecules) [2]. The systematic comparison between the properties of the glass transitions in the different phases in one substance is thus attractive in providing insight into mechanisms of molecular rearrangements in liquids and glasses. It is rare that two or more transitions are observed in one substance. The substances which have been reported to show such glass transitions are

0022-3093/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S 0 0 2 2 - 3 0 9 3 ( 9 6 ) 0 0 1 7 7 - 9

H. Fujimori et al. / Journal of Non-Crystalline Solids 204 (1996) 38-45

39

I

cyclohexene [3], ethanol [4], and 2-bromothiophene [5,6]. In the present study, heat capacities of 1,3-diphenyl-l,l,3,3-tetramethyldisiloxane (PMS, Cl6H22OSi 2, [56-33-7]) were measured with a high-precision adiabatic calorimeter [5]. a- and 13glass transitions were found in the liquid state and another transition in the crystalline state, a-molecular rearrangement process is discussed through the comparison between the transition temperatures.

I

I

~0~ 1

t ,4

/rga

:

I

,iN2- -~V I

I

I

100

200

300

WE Fig. 1. DTA curves of 1,3-diphenyl-l,l,3,3-tetramethyldisiloxane (PMS).

2. Experimental PMS ( > 97%), purchased from PCR Inc., was purified by fractional distillation with a home-made rectifier at reduced pressure. The purified sample was loaded into a calorimeter cell (19.696 cm 3 in its volume) under an atmosphere of helium gas at p = 100 kPa and T = 297 K. The mass of the sample used was 16.123 g (_4 56.271 mmol). Heat capacities were measured by the intermittent heating method [7] in the temperature range between 13 K and 300 K with the adiabatic calorimeter described previously [5]. The inaccuracy and imprecision of the heat capacities were estimated previously to be less than +0.3% and _+0.06%, respectively [5]. A platinum resistance thermometer (Minco Products S1059, USA) was used on the temperature scale of ITS-90 [8].

flash depends on pressure of the atmosphere; the present sample was in the Pyrex glass tube with helium gas at about 30 kPa at 77 K. Thus there is the possibility that the flash was out of the range of visible light. Run 2 shows the heating curve at a rate of about 2.5 K min-1 up to 300 K. A baseline shift due to the (x-glass transition was observed at the same temperature, 165 K, as in run 1. The crystallization was not observed by the DTA.

3.2. Heat capacity measurements Experimental molar heat capacities of PMS at constant pressure, Cj,,m, are tabulated in Table 1 and are shown graphically in Fig. 2. The correction for vaporization was not calculated because of lack of data. But the vapor pressure at 438 K is known to be

3. Results 500

3.1. Differential thermal analysis (DTA) 4OO

DTA was carried out as a preliminary study with a home-made apparatus [9]. The results are shown in Fig. 1: Run 1 shows the cooling curve from 300 K to 80 K at a rate of about 3 K min-l. A baseline shift was observed at around 165 K and is attributed to the ~x-glass transition. A sharp exothermic peak following the vitrification of the sample was observed at 127 K. This peak was attributed to the formation of cracks in the sample as in cases of propylene carbonate [9], isopropylbenzene [10], and so on [11], and accompanied with sound but not with a flash of visible light. According to Kishimoto et al. [11], the

T •

T

300

200

d

0 ~

0

100

i/,

i

f

1

rfus i

J

200

300

T/K

Fig. 2. Molar heat capacities of PMS: O, results for glass and liquid; O, results for crystal. Tg,~ and Tf~ denote temperatures of a-glass transition and fusion, respectively.

H. Fujimori et al./ Journal of Non-C~stalline Solids 204 (1996) 38-45

40

Table 1 Molar heat capacities of 1,3-diphenyl-l,l,3,3-tetramethyldisiloxane (PMS); R = 8.31451 J K -t mol-1

Tar

Cp,m

Tar

Cp,m

Tav

Cp,m

Tar

Cp,m

K

R

K

R

K

R

K

R

Crystal 14.01 15.14 16.31 17.55 18.89 20.33 21.83 23.32 24.83 26.41 28.11 29.84 31.62 33.46 35.30 37.12 38.98 40.86 42.71 44.57 46.49 48.49 50.51 52.54 54.55

2.290 2.635 2.991 3.370 3.777 4.209 4.658 5.096 5.527 5.975 6.439 6.904 7.372 7.841 8.302 8.750 9.203 9.655 10.09 10.52 10.99 11.45 11.91 12.37 12.83

56.57 13.25 58.58 13.66 60.59 14.08 62.61 14.50 64.62 14.91 66.64 15.31 68.67 15.72 70.70 16.11 72.74 16.51 74.79 16.90 76.85 17.28 78.91 17.67 80.99 18.05 83.08 18.42 85.18 18.80 87.29 19.17 89.42 19.53 91.56 19.89 93.7l 20.25 95.98 20.61 97.99 20.94 100.02 21.27 102.05 21.59 104.10 21.91 106.15 22.23

108.2l 110.28 112.36 114.45 116.55 118.67 120.79 122.92 125.07 127.23 129.51 132.02 134.54 137.06 139.59 142.12 144.66 147.20 149.75 152.30 154.86 157.42 159.98 162.56 165.14

22.54 167.73 22.86 170.31 23.17 172.64 23.48 174.99 23.79 177.34 24.10 179.70 24.41 182.06 24.72 184.43 25.02 186.80 25.34 189.17 25.66 191.55 26.02 193.93 26.38 196.32 26.73 198.71 27.09 201.10 27.44 203.50 27.80 205.91 28.16 208.31 28.53 210.71 28.92 213.12 29.30 215.51 29.65 217.89 30.00 220.24 30.36 222.81 30.71

Glass and liquid 14.30 2.494 74.61 17.14 15.56 2.859 76.47 17.50 16.86 3.238 78.33 17.85 18.18 3.621 80.20 18.19 19.54 4.017 82.07 18.53 20.97 4.432 83,95 18.87 22.44 4.857 85.83 19.21 23.98 5.295 87.72 19.54 25.66 5.765 89.62 19.87 27.43 6.256 91.52 20.20 29.23 6.746 93.43 20.52 31.06 7.234 95.36 20.84 32.91 7.720 97.29 21.17 34,77 8.198 99.23 21.48 36.63 8.669 101.18 21.79 38.50 9.141 103.1422.11 40.39 9.611 105.1222.42 42.29 10.09 107.10 22.73 44.20 10.55 109.09 23.04 46.15 11.02 111.10 23.35 48.14 11.50 113.12 23.65 50.14 11.97 115.1423.96

143.61 146.00 148.41 150.84 153.30 155.79 158.3l 160.85 163.40 165.93 168.06 170.15 172.27 174.58 177.07 179.55 182.04 184.54 187.03 189.53 192.03 194.53

28.10 28.43 28.77 29.12 29.47 29.82 30.21 30.60 31.40 33.87 46.07 48.07 48.15 48.23 48.31 48.39 48.48 48.59 48.69 48.80 48.91 49.01

31.05 31.40 31.71 32.02 32.33 32.65 32.98 33.32 33.65 33.99 34.33 34.68 35.02 35,37 35.72 36.11 36.50 36.92 37.40 37.97 38.69 39.72 41.46 46.92

223.49 50.61 225.62 50.77 228.93 50.95 231.10 51.13 233.63 51.32 236.16 51.45 238.69 51.61 241.22 51.78 243.76 51.97 246.29 52.13 248.83 52.30 251.36 52.48 253.90 52.66 256.44 52.85 258.98 53.05 261.53 53.24 264.07 53.44 266.61 53.65 269.16 53.83 271.70 54.04 274.25 54.23 276.80 54.42

Table 1 (continued)

Tav K

Cp,m Tar R

K

Glass and liquid 52.10 12.43 117.18 54.03 12.86 119.24 55.95 13.29 121.31 57.84 13.71 123.40 59.73 14.11 125.53 61.61 14.51 127.69 63.47 14.90 129.88 65.34 15.29 132.10 67.19 15.67 134.35 69.05 16.04 136.62 70.90 16.41 138.93 72.76 16.78 141.26

Cp,m Tar R

24.27 24.57 24.88 25.19 25.50 25.82 26.13 26.44 26.77 27.10 27.43 27.76

K

197.04 199.61 201.87 204.05 206.23 208.40 210.57 212.74 214.90 217.05 219.20 221.35

Cp,m Ta, R

49.14 49.26 49.37 49.49 49.61 49.72 49.83 49.95 50.08 50.21 50.34 50.47

K

279.34 281.89 284.44 286.99 289.53 292.08 294.63 297.18 299.73 302.28

Cp,m R

54.62 54.82 55.03 55.25 55.46 55.66 55.85 56.08 56.29 56.55

2.3 k P a [12], o n l y 1 / 6 c o m p a r e d w i t h that o f p r o p y lene c a r b o n a t e , w h i l e t h e v o l u m e o f the v a c a n t s p a c e w i t h i n the c a l o r i m e t e r cell w a s f o u n d to b e 3.182 c m 3 n e a r l y e q u a l to 2 . 7 1 0 c m 3 in the c a s e o f p r o p y lene c a r b o n a t e [9]. C o n s i d e r i n g that the c o r r e c t i o n for v a p o r i z a t i o n in p r o p y l e n e c a r b o n a t e at 300 K w a s less t h a n 0 . 0 2 % , the c o r r e c t i o n in P M S w a s neglected. T h e h e a t c a p a c i t i e s in the glassy state, s h o w n in Fig. 2 a n d t a b u l a t e d in T a b l e 1, are t h o s e for the s a m p l e c o o l e d at 6 0 m K r a i n - ~ a n d 2.5 K m i n - ~ in the t e m p e r a t u r e r a n g e s b e t w e e n 120 K a n d 170 K a n d b e t w e e n 5 0 K a n d 9 0 K, r e s p e c t i v e l y . T h e liquid s a m p l e w a s c r y s t a l l i z e d b y k e e p i n g its t e m p e r a t u r e at a b o u t 2 2 0 K for 2 days. T h e h e a t c a p a c i t i e s in the c r y s t a l l i n e state w e r e m e a s u r e d f r o m 14 K to 223 K, a n d the results for the s a m p l e , c o o l e d at 50 m K r a i n - ~ b e t w e e n 120 K a n d 160 K, are t a b u l a t e d in T a b l e 1.

3.3. Fusion and calorimetric determination o f purity T h e f u s i n g t e m p e r a t u r e a n d purity o f the s a m p l e were determined by a fractional-melting experiment. T h e large e n d o t h e r m i c t e m p e r a t u r e drift a p p e a r e d in e a c h t e m p e r a t u r e - r a t i n g p e r i o d d u r i n g fusion, a n d w a s f o l l o w e d for 6 0 m i n after e a c h e n e r g y input. T h e e q u i l i b r i u m t e m p e r a t u r e d u r i n g the f u s i o n w a s thus e s t i m a t e d b y e x t r a p o l a t i n g the drift to i n f i n i t e t i m e in t e r m s o f a n e x p o n e n t i a l f u n c t i o n . T h e o b t a i n e d characteristic t i m e o f the drift c u r v e w a s a r o u n d 25 min.

H. Fujimori et al. / Journal of Non-C~stalline Solids 204 (1996) 38-45 Table 2 Fraction of melt ( f ) and equilibrium temperature (T(f)) f

T(f)/K

0.1813 0.3111 0.4447 0.5795 0.7149 0.8502

226.872 227.021 227.083 227.117 227.139 227.163

7fu ~ = 227.23 + 0.02 x = 0.0022+_.0.0001 a

a Mole fraction of impurity species.

The equilibrium temperatures derived as a function of the fraction melted are summarized in Table 2, and were fitted with the van't Hoff equation [13]. The fusing point was determined to be 227.23 _+ 0.03 K and the mole-fraction purity of the sample to be 0.9978 +_ 0.0001. The molar enthalpy and molar entropy of fusion were evaluated to be 14.65 + 0.04 kJ mol- t and 64.5 + 0.2 J K- t mol- t, respectively.

3.4. ce-, 13-, and crystalline-glass transitions 3.4.1. or-glass transition Fig. 3 shows the temperature dependences of spontaneous temperature drift rates in two series of heat-capacity measurements by the intermittent heating method in the a-glass transition region. Open and closed circles represent the results for rapidly precooled (9 K rnin- l ) and slowly precooled (60 mK

min - l ) samples, respectively. The rates were evaluated at 6 min after each heating in the series of measurements. The dependence of the drift rate versus temperature curves on the precooling rates and the heat capacity jump associated with the anomalous drifts are characteristic phenomena of the glass transition [2]. The glass transition temperature, Tg, at which the relaxation time became 1 ks, was estimated according to the following empirical relation [9,14]: When the sample was precooled rapidly at the rate of = 10 K rain -t, the spontaneous temperature drift showed a change-over from exotherrnic to endothermic one at around the Tg. When the sample was precooled slowly at the rate of = 10 mK rain -t, on the other hand, the endothermic drift showed its maximum rate at around the Tg. The a-glass transition temperature, Tg, and the associated molar heat capacity jump at the Tg were thus found to be 1 6 7 + 1 K and 1 3 7 . 3 + 0 . 5 J K -~ tool - l , respectively.

3.4.2. r-glass transition Spontaneous heat evolution and subsequent absorption effects depending on the precooling rate of the sample were found in the glass below the a-glass transition temperature. Fig. 4 shows the temperature dependences of the spontaneous temperature drift rates observed in series of heat-capacity measureI A

I

I

I

0.1

I

approx, coolingrate /

T I

41

\

ooo

2.5 t(. min -1

. . .

I

100 o

°

o

•

..o

50

¢0

£

--. "~ 73

~. 3

0

/

I

-0.1

- 5 0 ~-

i

3 -s oo K

approx, cooling rate o o o 9K-rain-l • * • 60 mK.min-1

d 50

60

70 Y/K

80

90

Fig. 4. The rates of spontaneous temperature drifts in the /3-glass

-150 -

i

J

120

140

i 160 F/K

180

Fig. 3. Spontaneous temperature-drift rates in the a-glass transition region after each energy input: O, sample precooled at 9 K rain- 1; O , sample precooled at 60 m K r a i n - t

transition region in the two different series repeated in the temperature range between 50 sample precooled at 2.5 K m i n - t ; O , sample m K r a i n - i. The temperature drift was followed temperature rating period after the intermittent the drift rate was calculated at 6 min.

of measurements K a n d 9 0 K: O , precooled at 2 0 0

for 7 min in each energy input and

H. Fujimori et al. / Journal of Non-C~stalline Solids 204 (1996) 38-45

42 t

I

I

!

1 .0 /

I

q~

I

I

2.5 p

E

7

2.0'

f

q~

1.0 - -

I

50

~0

I 70 F/K

I 80

~- appr. . . . . . ling rate, 1 ooo 4K'min-1 " ' " 50mK'min-1 -1 0 __F 1

90

Fig. 5. Excess molar heat capacities of liquid glass as referred to the smoothed molar heat capacity curve of the crystal. The upper and lower broken lines were drawn so as to assess the molar heat capacity curves in the equilibrium and frozen-in states, respectively, with respect to a certain molecular rearrangement motion relevant to the 13-glass transition.

ments for the glasses precooled at rates of 2.5 K rain-~ ( Q ) and 200 mK min-l ( 0 ) , respectively, in the relevant temperature range between 50 K and 80 K. Fig. 5 shows the excess molar heat capacities after subtracting the smoothed heat capacity values of the crystal from the experimental results of the rapidly cooled glass. A very small heat capacity jump was found in the region of 65 to 70 K. Both phenomena are understood to originate from freezing-in or -out of some rearrangement motion of molecules as a 13-glass transition as found in propylene carbonate [9], isopropylbenzene [10], and so on [ 15,16]. The calorimetric 13-glass transition temperature, Ts~, was estimated to be about 69 + 2 K by using the same empirical relation as described above for the a-glass transition. The molar heat capacity jump associated with the 6-glass transition was estimated to be 0.10+_0.03 J K -t mol -~ at 69 K. The value corresponds to 0.08% of the total heat capacity of the glass and 0.06% of the jump associated with the ~x-glass transition.

3.4.3. Crystalline-glass transition Anomalous spontaneous heat evolution and absorption effects depending on the cooling rate were found in the temperature range between 130 K and 160 K in the crystalline state. Fig. 6 shows the temperature dependences of spontaneous temperature drift rates at 6 min after each energy input for the

1

120

130

"!"

140

I

I

150

160

_.-.-J 170

F/K

Fig. 6. The rates of spontaneous temperature drifts in the crystalline-glass transition region in the two different series of measurements repeated in the temperature range between 125 K and 165 K: O, sample precooled at 4 K m i n - I ; O, sample precooled at 50 m K rain- t. The temperature drift was followed for 7 min in each temperature rating period after the intermittent energy input and the drift rate was calculated at 6 rain.

samples cooled at rates of 4 K min -l ( O ) and 50 mK min -1 ( 0 ) , in the relevant temperature range between 120 K and 160 K. Fig. 7 shows the excess molar heat capacities obtained by subtracting the smoothed molar heat capacities of glass from the experimental values, for the purpose of displaying clearly the jump associated with the anomalous drifts. -

2

T

~

--

\

6 I q oo

q 5o 7-/K

J 2oo

Fig. 7. Excess molar heat capacities of crystal as referred to the smoothed molar heat capacity curve of glass; the heat capacity curve of glass above the cx-glass transition temperature region was estimated by the extrapolation of the curve at lower temperatures. The upper and lower broken lines were drawn so as to assess the molar heat capacity curves in the equilibrium and frozen-in states, respectively, with respect to a certain molecular rearrangement motion relevant to the glass transition in the crystalline state.

43

H. F u j i m o r i et al. / J o u r n a l o f N o n - C ~ s t a l l i n e Solids 204 (1996) 3 8 - 4 5

Table 3 Standard molar thermodynamic functions of PMS; R = 8.31451

Table 3 (continued) T

C o

j . K -I .tool -I T

C p,m °

7" o AoHm

7" o A°Sm

n

R/K

R

o a qOn~

R

Crystal 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 227.23

0 1.272 4.111 6.945 9.450 11.79 13.97 15.98 17.86 19.63 21.27 22.81 24.30 25.73 27.14 28.58 30.01 31.36 32.70 34.11 35.53 36.94 38.35 39.37

0 5.078 31.30 86.92 169.1 275.4 404,4 554.2 723.5 911.1 1116 1336 1572 1822 2086 2365 2658 2965 3285 3619 3967 4330 4706 4987

0 0.922 2.626 4.842 7.189 9.552 11.90 14.20 16.46 18.67 20.82 22.92 24.97 26.97 28.93 30.85 32.74 34,60 36,43 38.24 40.03 41.79 43.54 44.80

875.4 902.6 958.3 1041 1148 1279 1431 1603 1794 2002 2226 2465 2719 2988 3271 3568 3929 4411 4897 5387 5883 6384 6891 7405

3.808 5.577 7.798 10.15 12.54 14.92 17.26 19.55 21.80 23.99 26.12 28.20 30.23 32.23 34.18 36.09 38.27 41.03 43.66 46.17 48.59 50.92 53.18 55.36

0 0.415 1.061 1.945 2.962 4.044 5.158 6.286 7.417 8.545 9.665 10.78 11.87 12.96 14.03 15.09 16.13 17.16 18.18 19.19 20.19 21.18 22.15 22.85

Glass and liquid l0 20 30 40 50 60 70 80 90 100 I10 120 130 140 150 160 170 180 190 200 210 220 230 240

1.379 4.151 6.952 9.517 11.94 14.17 16.23 18.16 19.94 21.61 23.18 24.69 26.15 27.58 29.00 30.46 48.08 48.41 48.81 49.28 49.81 50.40 51.03 5[.70

-

83.73 39.55 24.14 15.87 10.42 - 6.398 - 3.185 -0.485 1.867 3.969 5.886 7.660 9.318 10.88 12.37 13.79 15.16 16.53 17.88 19.24 20.58 21.90 23.21 24.51

-K

p,m

T o AoHm

T o A0Srn

R

R/K

R

~n~o a

R

Glass andliquid 250 260 270 280 290 298.15 300

52.40 53.14 53.89 54.67 55.49 56.17 56.33

7925 8453 8988 9531 10081 10536 10640

57.49 59.56 61.58 63.55 65.48 67.03 67.38

25.79 27.04 28.29 29.51 30.72 31.69 31.9t

~ Cbn~/ R = ( A oT S m o -- A To H mo / T ) / R .

The dashed lines were drawn as guides for eyes. From the systematic dependence of the spontaneous temperature drift rates on the thermal pretreatments of the sample and the appearance of the heat capacity jump, it was concluded that the glass transition occurred also in the stable crystalline state of PMS. The crystalline-glass transition temperature, Tgc, and the jump were estimated to be 150 + 1 K and 0.84 _+ 0 . 0 8 J K - 1 m o l - ~ , respectively.

3.5. Standard thermodynamic functions Standard thermodynamic functions of PMS were derived from the heat capacity data for crystal, slowly cooled glass, and liquid samples, and are tabulated in Table 3. Heat capacity values below 13 K were then estimated by extrapolating the data below 25 K in terms of odd-order polynomial functions as follows:

Cp,m//(J K - t

mol-~)

= 0 . 6 0 6 9 ( T / K ) + 5.271 × 1 0 - 3 ( T / K ) 3

- 8.122 × 1 0 - 6 ( T / K ) 5 + 4.622 × 1 0 - 9 ( T / K ) 7

(1)

for the crystal, and

Cp.ml(J K -l

tool-l)

= 0 . 7 2 0 2 ( T / K ) + 5.060 × 1 0 - 3 ( T / K ) 3 - 8.479 × 1 0 - 6 ( T / K ) 5 + 5.314 × 1 0 - 9 ( T / K ) 7

(2)

44

H. Fujimori et al. / Journal of Non-Crystalline Solids 204 (1996) 38-45

energy can be calculated from each glass transition temperature by the following equation; 1 Ae a log ~"= log z 0 + 2.303 RT '

2 ~

4@0

Tfus \

200

22-g30[ o

t

j_

1 oo

200

3oo

T/K

Fig. 8. Molar entropies of PMS: O, results for glass and liquid; O, results for crystal. Tg,~, TfuS, and TK denote a-glass transition temperature, fusing temperature, and Kauzmann temperature, respectively.

for the glass. The residual entropy should exist in the crystal at 0 K, because the molecular orientations are frozen-in at the crystalline-glass transition temperature. But the value could not be estimated since the absolute entropy had not been derived spectroscopically. Therefore the standard thermodynamic functions were calculated on the assumption that there existed no residual entropy in crystal at 0 K. Fig. 8 shows the molar entropy of PMS as a function of temperature. The molar entropy at 298.15 K was evaluated to be 557.3 +__ 1.5 J K-1 mol-~, and the residual molar entropy of the glass to be 22.93 + 0.06 J K - l m o l - i ( = R In 15.8). The Kauzmann temperature, T K, [17] was evaluated to be 1 3 7 _ 1 K by extrapolating the entropy of equilibrium liquid to intersect the curve for the crystal as shown with a broken line in the figure.

4. Discussion

It is noted that the glass transitions were found both in the liquid and stable crystalline states in one substance of PMS. The transition temperatures were determined to be Tg~ = 167 K, Tg~ = 69 K, and Tgc = 150 K. Since the relaxation process associated with the glass transition is assumed to be due to the classical thermal activation, in general, the activation

(3)

w h e r e z 0 = 10 -13 to 10 -16 s as discussed previously [18], and T=Tg at z = 1 ks [1,2]. The activation energies for the respective relaxation processes are then evaluated to be A e ~ = 56 _+ 5 kJ mol -~, A ~'al3 = 23 + 2 kJ m o l - l, and A eac = 50 + 4 kJ m o l - I. Here it is interesting that the Tgc is near the Tg~ (rather than Tg~). Same observations have been reported in cyclohexene (Tg~ (phase I ) = 81 K, Tg~ (phase II) = 83 K and Tg~ = 78 K) [3], ethanol (Tgc = 97 K and Tg~ = 97 K [4]), and in 2bromothiophene (Tgc -- 120 K [5] and Tg~ = 130 K [6]). We have previously interpreted the c~- and 13-glass transitions in liquids as connected to the presence of the short-range-ordered region, namely structured cluster, and as due to the freezing-in of the rearrangements of molecules within the cluster and in the gap between the clusters, respectively [18]. The glass transition in the crystalline state, on the other hand, takes place under the completely ordered arrangement of molecules with respect to their positions. Thus the c~- and crystalline-glass transitions have a common character that the molecular rearrangements relevant to the transitions proceed within the ordered regions of molecules apart from the difference in the structures of ordered arrangements. It is easy to imagine that the progress of ordering and generally the progress of close packing of molecules increase the potential barrier for the relevant rearrangement. The rearrangement process in the liquid state is, as stated above, considered to be a correlated motion of reorientation and diffusion of molecules, while that in the crystalline state to be a rather pure reorientation of a molecule (or molecules). The above observations that Tgc and Tg~, and therefore A eac and A e,~, are rather close to each other in one substance might suggest a possibility that the cx-process in liquid is essentially connected with the reorientation of a molecule (or molecules) as in the crystalline state: This process would be interpreted as implying that the molecules within the closely-

H. Fujimori et al. / Journal of Non-Crystalline Solids 204 (1996) 38-45

packed ordered region in liquid can change their mutual configuration primarily through the reorientation and that the reorientation is a c c o m p a n i e d by a displacement of a small distance compared to the separation b e t w e e n the centers of neighboring molecules. The diffusion of molecules would then be realized through repetition of such processes at such low temperatures.

Acknowledgements This work was partly supported by G r a n t s - i n - A i d for Scientific Research, the Ministry of Education, Science, Sports and Culture of Japan (Grant No. 06453017 and 07240211).

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