1602
J. Phys. Chem. 1995, 99, 1602-1607
Calorimetric Study on Structural Relaxation of 1-Pentene in Vapor-Deposited and Liquid-Quenched Glassy States? -
Kiyoshi Takeda? Osamu Yamamuro,* and Hiroshi Suga* Department of Chemistry and Microcalorimetry Research Center, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan Received: November IO, 1994@
A calorimetric study was made of the three condensed states (glass, liquid, and crystal) of 1-pentene in the temperature range 13-300 K. The glassy states were formed by two different methods, vapor deposition (VQ) and liquid quenching (LQ). Each glass was prepared in situ in each sample cell of two adiabatic calorimeters designed for general purpose and for VQ samples. The glass transition temperatures (Tg= 70 K) and heat capacities of the two glasses were essentially the same. Much larger exothermic effect due to the structural relaxation was observed below Tgfor the VQ glass than that for the LQ glass. The enthalpy relaxation process was analyzed in terms of the Adam-Gibbs (AG) equation. The relaxation processes for the VQ sample exhibited linear relations in log z vs (TSJ' plot (z, enthalpy relaxation time; S,, configurational entropy) at all of the observed time and temperature ranges. Taking the effect of relaxed entropy into account, the residual entropy of the VQ and LQ samples was estimated to be 31.69 and 19.66 J K-I mol-', respectively.
Introduction
* To whom correspondence should be addressed.
the structural relaxation in which the molecular motions are quite cooperative and the clusterlike structure may be important.' It is also a merit of this method that the structural relaxation can be observed for the nonequilibrium state far from the equilibrium one that can be realized by such as the vapor-quenched or hypercooled methods. Simple organic molecules like 1-pentene are suitable for the calorimetric experiment because their intramolecular configurations involve large excess enthalpy to be relaxed. Wietze16 and Gibson and Giauque7revealed that glassy states do not satisfy the third law of thermodynamics and possess a definite amount of residual entropy at 0 K. Since the residual entropy results from the configurational disorder of the glass, it provides the information for not only the thermodynamic property but also the structure of the glass. Both the glass transition and residual entropy can be accepted as a manifestation of the nonergodic nature of the frozen-in disordered system from the viewpoint of statistical mechanics. In the present work, a calorimetric study was carried out for glassy 1-pentene (CH2=CHCH2CH2CH3), prepared by two different methods, vapor deposition (VQ) and liquid quenching (LQ). The heat capacity and the residual entropy data were obtained for both samples. The residual entropies of the glassy samples considering the effect of relaxed entropy were evaluated for the first time. Based on these quantities, the structural (configurational) disorder was compared between the VQ and LQ glasses. Enthalpy relaxation process was observed over a long period below the glass transition temperature. These relaxation processes were analyzed in terms of the Adam-Gibbs equation and the dependence of the preparation technique on the kinetic parameters was discussed semiquantitatively. The calorimetric study of the VQ glass of butyronitrile was made by Hikawa et aL4 in 1988. One of the purposes of the present study is therefore to compare our results with theirs and to find out some universal features of the VQ glass.
*
Experimental Section
From the viewpoint of thermodynamics, the glassy state is characterized by its metastability and nonequilibrium nature.' The former is related to the crystallization which is a phase transformation from the supercooled liquid to the stable crystal. The latter causes the structural relaxation and the residual entropy associated with the frozen-in disorder. The structural relaxation, which is the main interest of this study, is a recovery phenomenon of a nonequilibrium liquid into an equilibrium liquid at given external conditions. During this process, the liquid passes through a number of transient structures with significant intra- and intermolecular correlation depending on the structure and interaction energy of the constituent molecules. The relaxation path itself and the various physical properties are dominated by these drifting structures, and so the relaxation processes are substantially nonlinear and nonexponential.2 This intrinsic complexity of the relaxational nature requires simple substances in molecular structure and interaction energy as the subjects of the experimental studies. So far, however, most of studies have been done for relatively complex systems such as polymers and two- or three-component metals. From this viewpoint, our group have performed the calorimetric study for simple molecular organic substance^.^-^ Although the organic molecules have intramolecular degress of freedom, the van der Waals interaction between the constituent atoms is quite simple in the sense that it is nearly isotropic and short range in nature. The adiabatic calorimetry employed in this study can observe the structural relaxation through its enthalpy aspect in the timedomain temperature measurement. The relaxation is usually observed as an exothermic effect of the calorimeter cell below the glass transition where the relaxation time of the liquid is in the range of 100-100 000 s. In this region, we can investigate
' Contribution No. 84 from the Microcalorimetry Research Center.
Present address: Department of Chemistry, Naruto University of Education, Naruto, Tokushima 772, Japan. 5 Present address: Research Institute for Science and Technology, Kinki University, Kowakae, Higashi-Osaka 577, Japan. @Abstractpublished in Advance ACS Abstracts, January 1, 1995.
0022-365419512099-1602$09.00/0
Preparation of Samples. A commercial material of 1-pentene, whose purity was claimed to be more than 99.8 mol % by 0 1995 American Chemical Society
Structural Relaxation of 1-Pentene gas chromatography (GC), was purchased from Tokyo Kasei Kogyo Inc. The sample was purified by a vacuum distillation prior to the calorimetric measurement. For the LQ sample, the purified sample of 6.9115 g corresponding to 0.097 15 mol (M = 71.142 g mol-’, which was calculated based on IUPAC Atomic Weights reference’) was distilled through a capillary tube into a calorimeter cell of 17.46 cm3 capacity. Helium gas (about 500 Pa at 78 K) was then introduced into the cell to enhance the thermal equilibration between the sample and the cell, and the transfer tube was finally pinched off with soldering at the tip. For the VQ sample, the purified sample was stored in a sample container made of Pyrex glass and fitted on the vapordeposition line of the adiabatic calorimeter of vapor-condensation type? The sample vapor was deposited through a transfer tube onto the inner wall of calorimetric cell controlled at temperatures between 38 and 47 K. The amount of the sample deposited for 50 h was 1.0401 g (0.014 62 mol), which was determined from the molar heat capacity data in the range 110- 120 K, so as to agree with those of the LQ sample. The surface area inside the cell was about 80 cm2 and so the sample was accumulated as a film with a thickness of about 100 ium. The purity of sample was determined by a fractional melting method to be 99.2 and 99.1 mol % for the VQ and LQ samples, respectively. These values were poorer than those on purchasing. It is supposed that the used samples contained some kind of impurity which cannot be detected by GC, because any trace of impurity could not be detected also by our GC analysis after the calorimetric measurement. Calorimetric Measurements. In the present study, the calorimetric measurements of the VQ and LQ samples were done by two different adiabatic calorimeters. The VQ sample was measured by means of a calorimeter of vapor-condensation type.4 On the other hand, the LQ sample was measured by means of a traditional adiabatic calorimeter designed for bulk sample^.^ The imprecision of the heat capacity was within 1 and 0.1 % for the VQ and LQ samples, respectively. The heat capacity measurement was carried out in the temperature range 12-120 K for the VQ sample and 12-300 K for the LQ sample. In both calorimeters, temperature measurement was performed by using Rh-Fe resistance thermometers calibrated based on the temperature scale E F T 6 (T < 30 K) and IPTS68 (T > 30 K). The heat capacity difference caused by the conversion to the new temperature scale ITS9010was estimated to be smaller than 0.05% over the temperature range 12-300 K. The LQ glass was prepared by cooling the supercooled liquid of 1-pentene at the rate of about 3 K min-’ from 78 K. The crystalline phase was obtained by annealing the LQ sample at several temperatures between the glass transition (Tg = 70 K) and the fusion (Tf,, = 107.8 K) temperatures. For the VQ glass, exothermic effect due to the enthalpy relaxation was observed for about 100 000 s at 53, 58, 62, and 69 K in the course of the heat capacity measurement. The enthalpy relaxation of the LQ glass was also observed at 68.5 K to compare with the data of the VQ glass at 69 K. The relaxation was observed after heating the LQ sample from 20 to 68.5 K at the rate of about 2 K min-I.
Results and Discussion Heat Capacity and Standard Thermodynamic Functions. The heat capacity was measured by standard intermittent heating mode, Le., repetition of equilibration period and energizing period. Exothermic effect due to the enthalpy relaxation was
J. Phys. Chem., Vol. 99, No. 5, 1995 1603
50
60
70
I 80
T / K Figure 1. Temperature dependence of the enthalpy relaxation rate of glassy 1-pentene observed in the course of the heat capacity measure-
ments for the VQ (closed circles) and the LQ (open circles) samples. observed during the heat capacity measurement for the VQ and LQ samples below and around T,. The observed enthalpy relaxation rate -dHJdf was plotted against temperature in Figure 1. For the LQ glass, exothermic followed by endothermic temperature drifts were observed as usual glass transitions.” The relaxation rate gradually increased with the temperature and had a maximum just below Tg.For the VQ glass, on the other hand, the exothermic effect started just above the deposition temperature and was accelerated rapidly by heating. The broken lines drawn for the VQ sample represent the slowing down of the enthalpy relaxation rate caused by an annealing of the sample for about 100 OOO s. Further heating caused the large exothermic effect again. This cycle of exothermic effect was repeated four times between 47 and 70 K. This strange exothermic effect is quite similar to that observed for butyronitriie.43 Since the exothermic relaxation rate was nearly constant within an equilibration period of temperature measurement after each energy input, the “instantaneous” or “isocodigurational” heat capacity was evaluated by regarding this effect as a part of heat leakage from the surroundings. Therefore, the heat capacities of the VQ and LQ samples below T, correspond to the contribution only due to the vibrational degrees of freedom which attain the thermal equilibrium instantaneously. On the other hand, endothermic effects observed just above T, were included into the determination of heat capacity, since the effects ceased within the period of temperature measurement (about 30 min). Accordingly, the heat capacity obtained above Tgis composed of sum of the vibrational and configurational contributions. In the high-temperature region (T > 250 K), the slight heat capacity contribution due to the enthalpy of vaporization inside the calorimeter cell was not negligible because of rather high vapor pressure of the sample. By subtracting this effect from the apparent value, the heat capacity under the saturated vapor pressure, C,, was obtained. The correction for the enthalpy of vaporization was about 0.3% of the total heat capacity at around 300 K. The molar heat capacities under saturated vapor pressure for the VQ, LQ and crystalline (CR) samples are tabulated in Table 1 and also plotted in Figure 2. For both VQ and LQ samples, a glass transition was observed at essentially the same temperature around 70 K. This result is consistent with the observation by the differential thermal analysis already reported.12 The crystalline sample fused at 107.8 K. The enthalpy and entropy of fusion were 5.846 kJ
1604 J. Phys. Chem., Vol. 99,No. 5, 1995
Takeda et al.
TABLE 1: Molar Heat Cauacities of lhentene under Saturated Vauor Pressure (M = 71.142 e mol-') T/K
CJJ K-' mol-'
Crystal 15.01 5.306 15.46 5.709 16.08 6.291 16.80 7.009 17.69 7.918 18.69 8.967 19.72 10.11 20.75 11.28 21.82 12.49 22.89 13.71 23.93 14.89 24.97 16.06 26.02 17.22 27.04 18.38 28.04 19.57 29.02 20.87 30.03 21.94 31.10 23.04 32.15 24.22 33.20 25.37 34.23 26.49 35.26 27.61 36.30 28.74 37.34 29.76 38.40 30.82 39.45 31.88 40.52 32.91 41.59 33.91 42.66 34.93 43.73 35.95 44.81 36.93 45.89 37.88 46.97 38.85 48.06 39.78 49.15 40.69 50.23 41.63 51.33 42.53
T/K
CJJK-' mol-'
52.42 53.52 54.61 55.71 56.82 57.92 59.03 60.15 61.26 62.38 63.50 64.63 65.76 66.89 68.03 69.17 70.32 71.47 72.62 73.78 74.98 76.25 77.54 78.84 80.16 81.49 81.90 82.96 84.03 85.09 86.15 87.21 88.26 89.32 90.37 91.42 92.46 93.52 94.57 95.62
43.42 44.31 45.14 45.99 46.85 47.63 48.48 49.29 50.02 50.84 51.58 52.35 53.13 53.85 54.64 55.35 56.12 56.88 57.64 58.46 59.12 59.94 60.67 61.40 62.13 62.90 62.84 63.35 63.91 64.46 64.98 65.52 66.05 66.56 67.19 67.90 68.59 69.61 7 1.02 72.94
TK
CJJK-' mol-'
96.68 97.74 98.80 99.85 100.90 101.92 102.90 103.82 104.62 105.68 106.71
74.48 76.08 78.11 81.09 86.04 95.02 105.5 143.8 169.5 254.0 642.8
T/K
CJJK-' mol-'
35.17 31.37 36.21 32.72 37.31 33.72 38.46 34.75 39.57 36.04 40.69 37.04 41.80 38.03 42.92 39.16 44.03 40.46 45.16 41.07 46.30 42.63 49.58 46.10 Fusion at 107.85 K 50.67 46.62 51.78 48.08 54.84 51.17 VQ sample 55.88 52.23 59.96 52.85 12.58 6.679 59.30 56.02 13.29 7.234 60.37 57.37 14.15 8.328 61.47 58.83 15.08 9.178 63.22 62.00 15.94 9.897 64.30 64.16 16.81 10.78 65.39 64.86 17.73 11.73 66.49 68.27 18.64 12.64 67.61 66.47 19.54 12.90 70.12 120.3 20.48 14.76 72.11 136.0 21.47 15.90 74.10 133.6 22.48 17.13 75.16 133.0 23.52 18.31 76.22 132.9 24.60 19.58 77.29 133.0 25.68 20.71 78.35 133.5 26.76 21.80 79.43 132.7 27.84 23.00 80.51 132.2 28.89 24.06 8 1.59 134.4 29.93 26.19 30.98 26.68 32.02 27.81 LQ sample 33.05 29.05 34.09 30.25 12.34 5.284
mol-' and 54.48 J K-' mol-', respectively. The enthalpy value was 0.7% larger than the literature value 5.807 kJ It is considered that the previous author measured the heat capacity of a mixture of the liquid and crystal because 1-pentene was found to be difficult to crystallize completely. Standard thermodynamic functions were calculated numerically from the experimentalheat capacity data of the LQ sample and tabulated at round temperatures in Table 2. The third-law entropy S(r)-S(O,cr) is graphically shown in Figure 3. The zeropoint entropy (residual entropy) of the glassy samples was 17.75 J K-' mol-'. Since the heat capacities of the LQ and VQ samples essentially agreed, the third law entropies evaluated from these data should coincide with each other. However, this residual entropy is an apparent value since the configurational entropy decrease during the exothermic enthalpy relaxation has not been taken into account in the present calculation. The effect of the relaxed entropy on the residual entropy will be discussed later. Enthalpy Relaxation in Glassy Samples. The configurational enthalpy relaxed in the glass transition region can be evaluated from the exothermic temperature drift rate by means of the usual method." In Figure 4,the configurationalenthalpy traced during the measurement is shown as a function of temperature for both the VQ and LQ samples. The total enthalpy of the VQ glass relaxed below Tgwas more than 1 kJ mol-', while that of the LQ glass was about 0.15 kJ mol-'. It was elucidated that the VQ glass possesses much more unstable
TK
CJJK-' mol-I
TK
12.78 13.25 13.77 14.33 14.95 15.61 16.42 17.40 18.41 19.39 20.21 2 1.07 21.94 22.85 23.80 24.76 25.74 26.72 27.72 28.77 33.18 34.12 35.05 36.03 37.05 38.07 39.09 40.10 41.10 42.11 43.11 44.11 45.11 46.10 47.09 48.08 49.07 50.06 5 1.05 52.03
5.669 6.137 6.681 7.291 7.946 8.650 9.553 10.68 11.84 13.04 13.97 15.01 16.07 17.15 18.17 19.36 20.45 21.58 22.82 24.14 29.06 30.11 31.11 32.18 33.25 34.30 35.35 36.37 37.39 38.34 39.31 40.27 41.21 42.15 43.09 44.03 44.93 45.85 46.78 47.70
53.02 54.00 54.99 55.98 56.96 57.95 58.94 59.94 60.94 61.94 62.85 63.98 65.02 66.07 67.14 68.21 69.03 69.58 70.10 70.57 7 1.02 71.53 72.22 73.13 74.14 75.37 76.39 72.02 73.02 74.04 75.08 76.13 77.19 78.27 79.36 80.46 81.57 82.69 83.83 84.98
CJJK-' mol-'
T/K
48.85 89.19 49.64 90.39 50.5 1 9 1.57 51.47 92.55 52.44 97.61 53.41 98.82 54.45 100.05 55.49 101.28 56.59 102.51 57.77 103.76 59.25 105.00 60.41 106.26 62.04 108.78 63.95 110.06 66.38 111.34 69.88 112.62 72.50 113.91 77.10 115.21 84.73 116.51 97.87 117.82 119.1 119.14 131.9 120.46 134.6 123.13 134.9 124.70 135.0 126.06 134.5 127.43 134.3 128.80 135.4 130.18 135.2 131.56 134.8 132.95 134.7 134.35 134.3 135.76 134.1 137.16 133.9 138.58 133.6 140.00 133.3 141.43 142.87 133.0 132.8 144.31 132.6 145.76 132.4 141.24
CJJK-' mol-' 132.1 131.6 131.6 131.4 130.3 130.2 130.1 130.2 130.0 129.8 129.8 129.7 129.6 129.3 128.9 129.1 129.0 129.0 129.1 128.9 128.9 128.8 128.5 128.8 128.4 128.4 128.6 128.5 128.5 128.5 128.6 128.3 128.4 128.5 128.3 128.4 128.3 128.7 128.6 128.5
T/K
CJJK-' mo1-I
143.83 146.45 149.09 151.76 154.46 157.17 159.91 162.69 165.46 168.28 171.11 173.97 176.86 179.76 182.69 185.65 188.62 191.62 194.64 197.68 203.77 209.88 216.01 222.17 228.35 234.56 340.79 247.04 253.31 259.59 265.78 272.15 278.42 284.68 290.94 297.20 303.45
128.6 128.6 128.8 128.9 129.1 129.1 129.4 129.4 129.7 129.9 130.1 130.4 130.6 131.0 131.2 131.6 132.0 132.2 132.7 133.2 134.0 134.8 135.9 137.0 138.2 139.6 140.7 142.2 143.5 145.1 146.7 148.5 150.0 151.9 153.5 155.4 157.1
and strained structure than the LQ glass as revealed by the enthalpy. This result is similar to that of the butyronitrile studied beforee4 The relaxation processes of the VQ and LQ samples were compared at similar temperature (69 K). Figure 5 shows the plots of the configurational enthalpy against time for the VQ and LQ samples. The origin of abscissa was taken to be 600 s after an appropriate energy input, and that of ordinate was the equilibrium enthalpy. The experimental curves were fitted to the Kohlrausch-Williams-Watts (KWW) functiont4
where z is the relaxation time and /3 is the nonexponential parameter. Obviously eq 1 is reduced to a simple exponential form for #I = 1. The best fit curves by the KWW function are shown by solid curves in Figure 5. Both values of #I (0.84 for the VQ and 0.45 for the LQ samples) are clearly smaller than unity and they are definitely different from each other. The deviation from unity indicates the nonexponentiality of the relaxation function, which is one of the universal properties of the structural relaxation phenomena in liquids. The significant difference of #I between the LQ and VQ samples was revealed for the first time by the present study. Estimation of Codgurational Entropy and Residual Entropies of Glassy Samples. In this section, we will estimate the configurationalentropy of the glassy samples which relaxed
J. Phys. Chem., Vol. 99, No. 5, 1995 1605
Structural Relaxation of 1-Pentene 200
VQsample
150 4
L
8
o
0
0
LQsample
A
A
A
CRsample
io0 h \
G 50
0
0
T I K Figure 2. Molar heat capacities of 1-pentene under the saturated vapor pressure. TABLE 2: Thermodynamic Functions of Crystalline, Liquid, and Glassy 1-Pentene at Rounded Temperatures (M = 71.142 g mol-', R = 8.314 51 J K-l mol-') H - H(O,cr)/ SG - G(O,cr)/ TK
CJR
J mol-'
S(0,cr)lR
J mol-'
Crystal 0 0 10 0.21 84 20 1.254 40 3.895 60 5.913 80 7.452 100 9.836 Fusion (Tf., = 107.85 K)
0 10 20 40 60 Glass transition 80 100 120 140 160 180 200 220 240 260 280 300
0 0 0 -1.594 4.697 0.0757 0.4996 -22.63 60.45 2.201 -238.0 494.0 -768.8 1319 4.184 6.105 -1626 2434 -2793 3804 7.867 Afu&, = 5.846 kJ mol-' A&,, = 54.48 J K-' mol-'
Glass and Liquid 3055 0 0.3687 3063 3 144 1.654 3650 4.367 4591 6.682 (Tgzz 70K) 16.05 6504 15.67 9138 15.48 11730 15.46 14300 15.55 16880 15.75 19480 16.05 22 120 16.43 24820 16.90 27590 17.44 30450 18.06 33390 18.73 36460
2.135 2.263 2.890 4.889 7.094 10.35 13.89 16.73 19.11 21.18 23.02 24.70 26.24 27.69 29.07 30.38 31.64
3055 2875 2664 2024 1036 -383.1 -2411 -4964 -7942 -11290 -14970 -18940 -23180 -27670 -32390 -37330 -42460
below the glass transition temperature to some extents. The residual entropy calculated in the previous section did not account for this quantity. The calculation follows the method used for b~tyronitrile.~ This method was based on the concept of the fictive temperature Tfic proposed by To01.*9'~ He characterized the glassy states by assuming that each glassy state at a temperature T exhibits the same structure as that of the equilibrium liquid at a fictive temperature Tfi,. Consequently, the
T / K Figure 3. Third law entropy of the glass and liquid (open circles) and crystalline (closed circles) 1-pentene. The closed marks on the vertical axis denote the estimated residual entropy of the LQ and VQ glasses initially prepared.
faster the cooling rate of liquid, the higher the fictive temperature of the resulting glass. Generally T < Tfi, when T < Tgand T = Tfi, when T = Tg. Since the same structure is considered to have the same configurational enthalpy, the time dependence of Tficis derived by the equation
HC@>= H",4(Tfic(t>>
(2)
where qq( T) denotes the configurational enthalpy of equilibrium liquid at temperature T. The configurational entropy S, is then estimated by means of the equation S, = L;[C,(r)/Tl d T
(3)
Here, TK is the Kauzmann temperature at which the configurational entropy van is he^'^^'^ and C,(r) is the configurational part of heat capacity defined by
1606 J. Phys. Chem., Vol. 99, No. 5, 1995 1200
Takeda et al.
u
to be 31.7 and 19.7 J K-' mol-1, respectively. These quantities are graphically shown on the vertical axis in Figure 3. It is obvious that the residual entropy should depend on the preparation method by which a particular nonequilibrium state was realized. As far as we know, this is the first time the difference between the residual entropies of the VQ and LQ glasses is quantified. The residual entropy of the LQ glass does not differ much from that obtained from the heat capacity data (=17.75 J K-' mol-I). This means that the effect of relaxed part on the residual entropy was minor for the LQ glass. On the other hand, the residual entropy for the VQ glass is much larger than that of the LQ glass. This result reflects an extremely large-scale disorder in the molecular arrangement and conformation of the VQ glass. Application of the Adam-Gibbs Equation. Adam and GibbsI8derived a relationship, known as the Adam-Gibbs (AG) equation, between the relaxation time z and the configurational entropy Sc for the glass-forming liquid.
I
-300
I
40
I
I
50
60
i
I
z = z, exp(A,us~lk,TS,) 4
,
70
80
or its logarithmic form
T J K Figure 4. Configurational enthalpy versus temperature diagram for the VQ and LQ glasses.
,
300 h
-E
200
I\
(6)
1
where k~ is the Boltzmann constant, Ap the activation free energy per mole, and sf the configurational entropy of the subsystem (cluster) which is able to change its configuration cooperatively. This relationship asserts that the relaxation time becomes longer with decreasing Sc. The slowing down of the exothermic enthalpy-relaxation rate in each pseudoisothermal experiment can be qualitatively explained in terms of the AG equation. The exothermic relaxation of the VQ sample of 1-pentene was analyzed in terms of the AG equation. The relaxation time at each instance was assumed to be identical with the effective relaxation time proposed by Kovacs.Ig The effective relaxation time Zeff is defined by
3 20
40
f
60
80
1 ks
Figure 5. Configurational enthalpy versus time plot for the VQ and LQ glasses observed around 69 K. The solid lines indicate the best fit curves calculated by using the KWW relaxation function. (4) where denotes the equilibrium heat capacity of liquid and Gib the vibrational part of the heat capacity of liquid. Equation 3 is rewritten as
where AfJ represents the entropy of fusion. The entropy of fusion is not exactly identical with the configurational entropy at ThSbecause there is a slight difference in vibrational entropy between the liquid and the crystal. This difference can be calculated from the heat capacity difference between the glass and the liquid as shown in eq 5 . In the present case, it was estimated to be 9.3 J K-' mol-'. The fictive temperatures of the VQ and LQ glasses at the initial frozen states were estimated by use of eq 2 to be 85.2 and 71.4 K, respectively. By using these values and eq 5, the corrected residual entropies of the VQ and LQ glasses referred to the initial states were calculated
Plots of log z vs ( T S J I , which is named the Adam-Gibbs plot hereafter, were displayed in Figure 6 for several temperatures at which the long-time annealing of the VQ sample was carried out. The numerator of the right-hand side of eq 7 is practically constant in each process,I8 and so the plot should give a nearly straight line if the AG equation is valid for the observed relaxation. As shown in Figure 6, the experimental data were well reproduced by the AG equation for all of the observed temperature and relaxation time regions. Similar results were obtained also in the case of b~tyronitrile.~ The slope of the AG plot is proportional to the two parameters sf and Ap, both being related to the microscopic structure of liquid. The quantity sa would be rather insensitive to the changes in the size of the cooperative unit (cluster) and the extemal parameters (e.g. temperature) because the numbers of intercluster and intracluster configurations are essentially unchanged; the former depends on the cluster shape and the latter the molecular shape. On the other hand, the quantity Ap, the molar activation free energy of the cooperative rearrangement, may be influenced by local structure of the liquid and the extemal parameters. @ is decomposed into the following form:
A p = A U i - p A V - TAS
(9)
The slight decrease of the slope with increasing temperature in
Structural Relaxation of 1-Pentene
J. Phys. Chem., Vol. 99, No. 5, 1995 1607
VQ sample is smaller than that of the LQ sample. According to the above argument, the effect of the difference in the extemal parameters p and T on the activation free energy is not significant in this case. As described in the preceding sections, the VQ glass has larger configurationalenthalpy and larger local strain in the molecular conformation and probably smaller density than the LQ glass. Although the magnitude of a total thermodynamic quantity does not always influence the corresponding activation value, it is likely that the VQ glass has larger activation enthalpy and volume than the LQ glass.
5.4
5 n
m \
2
4.6
W
bo
Conclusions
0
3
4.2 0
69K
0
D 0 0
3.8 I
I
0.48
( S, T )
I
I
0.49
0.51
0.5
-'/
( H mol-')
(
-'
Figure 6. Adam-Gibbs plots for enthalpy relaxation processes of the VQ glasses at several temperatures. 4.8
4.5
References and Notes
n
CA \
3 4.2
k
W
.
MI
0
M
0
3.9
3.6
The difference in the thermodynamic properties and enthalpy relaxation processes between the VQ and LQ glasses was quantitatively investigated with the two adiabatic calorimeters. It was found that the VQ glass exhibits much larger configurational enthalpy and residual entropy than those of the LQ glass. This indicates that the VQ glass possesses much locally-strained and disordered structure compared with the LQ glass. The enthalpy relaxation process was well reproduced by the AdamGibbs equation for all of the relaxation-time and temperature regions. The difference in parameters of the AG equation between the VQ and LQ glasses was consistent with the difference in their thermodynamic parameters and resulting local structures. Taking the similar results on b~tyronitrile~ into account, the properties of the VQ glass described above are considered to be universal for all of the VQ glasses of simple molecular substances.
.. I
I
0.5
0.52
( S, T )
-'/
( kJ mol-')
-'
0
Figure 7. Adam-Gibbs plots of the enthalpy relaxation processes observed for the VQ and LQ glasses at around 69 K.
FIgure 6 can be explained by the decrease of Ap due to the third term of eq 8 since AS should be positive in the activation processes. Figure 7 gives a comparison of the AG plots between the VQ and LQ glasses observed in the similar temperature region (corresponding to Figure 5). Both of the data can be well reproduced by straight lines. It was found that the slope of the
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