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J. Phys. Chem. B 2006, 110, 13970-13975
Low-Temperature Heat Capacity of Room-Temperature Ionic Liquid, 1-Hexyl-3-methylimidazolium Bis(trifluoromethylsulfonyl)imide Yoshitaka Shimizu,†,‡ Yoko Ohte,† Yasuhisa Yamamura,‡ Kazuya Saito,*,‡ and Tooru Atake§ National Metrology Institute of Japan, National Institute of AdVanced Industrial Science and Technology, Tsukuba Central 3,1-1-1 Umezono, Tsukuba, Ibaraki 305-8563, Japan, Department of Chemistry, Graduate School of Pure and Applied Sciences, UniVersity of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan, and Structures and Materials Laboratory, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8503, Japan ReceiVed: March 24, 2006; In Final Form: May 22, 2006
Heat capacities of liquid, stable crystal, and liquid-quenched glass of a room-temperature ionic liquid (RTIL), 1-hexyl-3-methylimidazolium bis(trifluromethylsulfonyl)imide were measured between 5 and 310 K by adiabatic calorimetry. Heat capacity of the liquid at 298.15 K was determined for an IUPAC project as (631.6 ( 0.5) J K-1 mol-1. Fusion was observed at Tfus ) 272.10 K for the stable crystalline phase, with enthalpy and entropy of fusion of 28.34 kJ mol-1 and 104.2 J K-1 mol-1, respectively. The purity of the sample was estimated as 99.83 mol % by the fractional melting method. The liquid could be supercooled easily and the glass transition was observed around Tg ≈ 183 K, which was in agreement with the empirical relation, Tg ≈ (2/3) Tfus. The heat capacity of the liquid-quenched glass was larger than that of the crystal as a whole. In the lowest temperature region, however, the difference between the two showed a maximum around 6 K and a minimum around 15 K, at which the heat capacity of the glass was a little smaller than that of crystal.
1. Introduction So-called room-temperature ionic liquid (RTIL) has very low melting temperature compared with ordinary inorganic salts such as NaCl.1,2 Nonvolatility, nonflammability, high ionic and electrical conductivities, and high thermal stability are also characteristics of RTIL. These properties offer a wide range of possible applications. For example, they are expected to be potential synthesizing or catalyzing solvents suitable for substitution of volatile organic solvents3 because of their immiscibility with water and/or some organic solvents. Use as a new nonflammable electrolyte for lithium batteries is also widely pursued.4 Although RTIL is fascinating as a functional liquid, only a few reports5 are found in the literature concerning precise and reliable physical properties. Even a basic mechanism has not been established for their extremely low melting points. Comprehensive studies are, therefore, strongly desired from both application and basic science. To accelerate systematic research in thermodynamics of RTIL, a project was started up as an IUPAC project, which is “No. 2002-005-1-100, Thermodynamics of Ionic Liquids, Ionic Liquid Mixtures, and the Development of Standardized Systems”.6 In this project, some physical properties such as thermodynamic and transport properties of a selected RTIL are to be measured by some independent laboratories. This paper reports the detailed results of precise calorimetry partly involved in the project. Some imidazolium and ammonium salts are known as RTIL.7 1-Hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide * Corresponding author. E-mail:
[email protected]. † National Metrology Institute of Japan, National Institute of Advanced Industrial Science and Technology. ‡ Department of Chemistry, Graduate School of Pure and Applied Sciences, University of Tsukuba. § Structures and Materials Laboratory, Tokyo Institute of Technology.
(abbreviated as [hmim][Tf2N] in this paper), a member of this group, was selected as the first reference compound. The phase behavior of [hmim][Tf2N] was reported on the basis of differential scanning calorimetry in the temperature range from 123 K (-150 °C in the original report) to 353 K (80 °C).8 Although the aim of the IUPAC project was the heat capacity at 298.15 K, our experiment was performed for the whole range of temperatures below room temperature. The present results show the crystal polymorph and formation of liquid-quenched glass (LQG). Glass is known as a nonequilibrium state of matter where some degrees of freedom of molecular motion are frozen in.9 Because LQG still remains in “liquid” state with a prolonged relaxation time for structural relaxation, a comparison of the physical properties with ordinary liquid of electrically neutral molecules is interesting. Recently, Kabo et al.5 reported the formation of an LQG in other RTILs. They indicated that the RTILs have similar properties to those of ordinary molecular liquids. In this paper, the results of precise calorimetry of [hmim][Tf2N] are given for the liquid, stable crystal and LQG. The heat capacity value and its uncertainty of the liquid at 298.15 K are evaluated in accordance with the requirement by the IUPAC project. Comparison is made of thermodynamic and entropic behavior of the LQG of [hmim][Tf2N] and ordinary molecular LQG. 2. Experimental Section The sample of [hmim][Tf2N] (molar mass: 447.417 g mol-1)10 used in this study was distributed by NIST (National Institute of Standards and Technology, U.S.), which is the pilot laboratory of the IUPAC project. It was stated that the purity and water content of the sample were better than 99.5% (on the basis of 1H and 19F NMR) and less than 20 ppm (coulometric Karl Fischer titration), respectively.
10.1021/jp0618330 CCC: $33.50 © 2006 American Chemical Society Published on Web 06/27/2006
Room-Temperature Ionic Liquid [hmim][Tf2N] Prior to the present experiments, the sample was dried in a vacuum oven at 50 °C under a vacuum for 14 h. Water content of the dried sample was determined by coulometric Karl Fischer titration as 20 mg g-1. DSC measurements were carried out for comparison with the previous report of phase behavior8 using a DSC822e (Mettler Toledo K.K.) at a cooling and heating rate of 10 K min-1. The sample (7-13 mg) was sealed in an aluminum pan under dry nitrogen atmosphere. The temperature and heat flow were calibrated with mercury (NIST SRM 2225) and indium (NIST SRM 2232) at a heating rate of 10 K min-1. The dried sample was loaded into a gold-plated copper calorimeter vessel (vessel 1) in a glovebox purged by dry helium gas under atmospheric pressure. The amount of the sample put in the calorimeter vessel was 16.6966 g after buoyancy correction. Heat capacity was measured between 79 and 310 K using an adiabatic calorimeter (JTA-2000C, Jecc Torisha Co., Ltd.). The measurements of liquid [hmim][Tf2N] were repeated in the temperature range 240-310 K, including the supercooled liquid state. After the measurements, the water content of the sample was measured to be 29 mg g-1. A part of the sample (5.3619 g) was then transferred into another gold-plated copper calorimeter vessel (vessel 2). The vessel was sealed under the helium atmosphere and set in the same adiabatic calorimeter. The details concerning the preparation of the desired state such as the LQG inside the calorimeter will be described in the Results and Discussion Section. Working thermometers were commercial platinum-resistance thermometers (Tinsley 5187L and Minco S1059 for vessels 1 and 2, respectively). The thermometer attached to vessel 1 was calibrated at the National Physical Laboratory of the UK according to the ITS-90.11 The temperature scale of the thermometer mounted in the vessel 2 was transferred from commercial platinum (above 13.8 K) and germanium (below 13.8 K) resistance thermometers based on the ITS-90.11 Contributions of the sample to the total heat capacity including that of calorimeter vessel 1 were 45, 45, 50, and 60% at 80, 100, 200, and 300 K, respectively. Those for vessel 2 were 75, 40, 35, 40, and 50% at 10, 50, 100, 200, and 300 K, respectively. Time duration needed for thermal equilibration in the calorimeter vessel were 16, 20, 16, and 18 min at 80, 100, 200, and 300 K, respectively, in the measurement using vessel 1. Those of vessel 2 were 5, 30, 40, 30, and 30 min at 10, 50, 100, 200, and 300 K, respectively. 3. Results and Discussion Phase Behavior. Prior to time-consuming adiabatic calorimetry, thermal (phase) behavior of [hmim][Tf2N] was glimpsed by differential scanning calorimetry (DSC). The results are shown in Figure 1, where the heat flow is normalized by the mass of the sample. The solid line is a trace of heating run immediately after cooling to 153 K, with the cooling rate of 10 K min-1 using sample pan 1. The glass transition is observed as a baseline shift around 186 K. On further heating, a broad exothermic hump due to crystallization is observed around 248 K, and then an endothermic peak due to fusion is observed at 265 K. By repeating the experiments, the onset temperature of the fusion could be fixed, but the enthalpy of fusion was distributed from 0.1 to 1.9 kJ mol-1. Tokuda et al.8 reported the DSC experiments, which gave the temperature and enthalpy of fusion as 267 K (-6 °C in the original report) and 4.6 kJ mol-1, respectively. They noted that the crystallization was very slow. Thus it should be considered that the discrepancy of the present results is attributed in part to such a slow rate of crystallization.
J. Phys. Chem. B, Vol. 110, No. 28, 2006 13971
Figure 1. DSC chart of heating run of [hmim][Tf2N]: solid line, after cooling to 153 K with the sample pan 1; dotted line, after cooling from 267 K that is in the course of fusion with sample pan 2; dashed line, the same as dotted line with sample pan 1.
The dotted line is the result of the heating run measured with sample pan 2 after cooled from 267 K, that is, in the course of fusion around 265 K. Two peaks are observed around 265 and 271 K. The peak at a lower temperature is the same as that of the simple heating run after cooling to 153 K from room temperature described above. The higher temperature peak should be also attributed to fusion of another solid phase. The onset temperature of this peak is 271 K. The broken line is the result of the heating run with sample pan 1 obtained by the same procedure as the dotted line. In this case, a single peak is observed with the onset temperature of 271 K and the enthalpy of fusion is 27 kJ mol-1. From the present results, it can be concluded that the peak at 271 K should be the fusion of the stable crystalline phase, and the peak reported by Tokuda et al.,8 the fusion of a metastable phase. A smaller value of the enthalpy of the peak at 265 K is consistent with this consideration. The magnitude of the enthalpy of fusion obtained in this experiments should be used for a comparison with that obtained by adiabatic calorimetry. Heat Capacity of Liquid. In conjunction with the IUPAC project, the heat capacity of the liquid was measured 11 times, including the supercooled state. The heat capacity at 298.15 K was calculated by least-squares fitting, assuming a quadratic polynomial of temperature for each run. Their arithmetic average (631.5 J K-1 mol-1) is adopted for the report of the IUPAC project. The evaluation of uncertainty was made for the heat capacity as summarized in Table 1. The details can be found in Supporting Information. The combined standard uncertainty of Cp at 298.15 K is 0.24 J K-1 mol-1. The expanded uncertainty was obtained using the combined standard uncertainty and coverage factor k ) 2, which corresponds to the 95% of confidence level. The final value of Cp at 298.15 K for the IUPAC project is thus (631.6 ( 0.5) J K-1 mol-1. Cryoscopy. Purity of the sample of [hmim][Tf2N] was determined by the fractional melting method.12 It is the method
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TABLE 1: Uncertainty Budget for Cp at 298.15 K source of uncertainty
u(xi)
c(xi)
-1
-1
c(xi)u(xi)/J K-1 mol-1
heat capacity regression measurement dispersion temperature scale
0.035 J K mol 0.034 J K-1 mol-1 0.007 J K-1 mol-1 0.001 J K-1 mol-1
1 1 1 1
0.035 0.034 0.007 0.001
heating energy voltage drop across the heater voltage drop across the standard resistor standard resistance heating duration integration
0.003 J 5.76 × 10-5 V 5.81 × 10-5 V 0.00018 ohm 0.003 s 5.78 × 10-5 J
13.5 416 406 10 0.9 13
0.035 0.024 0.024 0.002 0.003 0.001
enthalpy change in vessel fitting temperature scale
0.0168 J 0.0168 J 1.81 × 10-5 J
13.5 13 13
0.228 0.227 0.001
temperature increase regression
8.20 × 10-5 K 8.20 × 10-5 K
317 317
0.026 0.026
sample amount weighing molar mass
8.11 × 10-7 mol 0.0002 g 0.0081 g mol-1
1.7 × 104 38 1.4
0.015 0.008 0.012
for purity assay based on melting point depression. Melting point depression is evaluated from the relation between the equilibrium temperatures during fusion and the fraction melted, which is determined from the energy supplied as a latent heat after complete crystallization into the stable phase by suitable treatment described later. Figure 2 shows a van’t Hoff plot. If there are no impurities that form solid solution with the main component, the equilibrium temperature should show a linear dependence on the inverse of the fraction melted as
T ) T0 -
R‚T02 1 ‚x ‚ ∆fusH ip f
(1)
where T, T0, R, xip, and f are equilibrium temperature, melting point of a pure sample, gas constant, total concentration of impurities, and fraction melted, respectively. In fact, the plot is slightly concave upward, indicating the formation of solid solution. A modified equation was proposed for systems forming solid solution by Masterangelo and Dornte13 as
T ) T0 -
R‚T02 1 ‚x ‚ ∆fusH ip k f+ 1-k
(
)
Measured heat capacities were smoothed out and integrated appropriately to yield standard thermodynamic quantities for the stable phase sequence. Resultant standard thermodynamic quantities at round temperatures are tabulated in Table 3. Thermodynamic Properties of LQG. The usual cooling procedure (ca. -1.6 K min-1) brought the sample into the liquidquenched glass (LQG). The heat capacity of the LQG was measured from 5 K. In the course of the measurement, a glass transition was encountered around 180 K, with a large step in heat capacity, as seen in Figure 3. The temperature drift during equilibration periods plotted in Figure 4 shows characteristic temperature dependence due to the so-called enthalpy relaxation around a glass transition: below the glass transition temperature, an exothermic effect is observed, with a maximum around 180 K. The temperature drift turns into negative around 183 K. The glass transition temperature (Tg) is therefore determined as 183
(2)
where k is the ratio of concentrations of impurities in solid and liquid phases. The plot assuming this equation is linear, implying the validity of the treatment. The purity (mole fraction) of [hmim][Tf2N] used for the calorimetry is estimated as 99.83%. The melting point of the pure [hmim][Tf2N] (T0) and the calorimetric sample are determined as 272.13 and 272.10 K, respectively. Heat Capacity of Solids and Standard Thermodynamic Functions. Because a usual cooling procedure may result in incomplete crystallization of the liquid as suggested by the results of DSC, the stable phase was prepared by holding the sample for a few days around 215 K, where the exothermic phenomenon was started. The exothermic effect ceased after three days. The measured heat capacities are shown in Figure 3. Fusion of the stable phase was observed at 272.10 K. Enthalpy and entropy of fusion were determined as 28.34 kJ mol-1 and 104.2 J K-1 mol-1, respectively, for the stable phase. These are summarized in Table 2. The heat capacity of metastable phase detected by DSC could not be measured.
Figure 2. van’t Hoff plots of [hmim][Tf2N]: circle, according to the method by Mastrangel and Dornte; cross, according to a simple theory assuming crystallization of the pure solid.
Room-Temperature Ionic Liquid [hmim][Tf2N]
J. Phys. Chem. B, Vol. 110, No. 28, 2006 13973 TABLE 3: Thermodynamic Quantities of Crystal and Liquid of [hmim][Tf2N] T/K
Figure 3. Heat capacities of liquid and solid states of [hmim][Tf2N]: triangle, immediately after quenching from liquid state; circle, after holding at 215 K for three days before the measurement; square, after holding at 180 K for four days.
TABLE 2: Thermodynamic Quantities of Fusion and Glass Transition phase
thermodynamic quantities Crystal Tfus ) 272.10 K ∆fusH ) 28.34 kJ mol-1 ∆fusS ) 104.2 J K-1 mol-1
fusion
Liquid Tg ) 183 K (TK ) 154 K)
glass transition
K. Above the glass transition temperature, an exothermic effect due to crystallization appears from 215 K. Annealing at 180 K until the heat evolution ceased (four days) changed drastically the temperature dependence of the temperature drift, as shown in Figure 4. An exothermic effect is absent, whereas an endothermic effect is largely enhanced. This is a typical consequence of the enthalpy relaxation. The annealing also affected the magnitude of heat capacity. The annealed LQG showed slightly smaller heat capacity than the quenched LQG. The relation between Tg and Tfus of the RTIL [hmim][Tf2N] satisfies the empirical relation Tg ≈ (2/3)Tfus of glasses formed by quenching molecular liquids and polymers.14 A similar trend was reported for [bmim][PF6].5 The heat capacity jump, ∆glCp(Tg), and its ratio against Cp of LQG, ∆glCp(Tg)/ Cp(glass, Tg), at Tg are 181 J K-1 mol-1 and 0.46, respectively, for the present compound. The latter is much larger than that of [bmim][PF6] and similar to those of some molecular liquids.5 This implies [hmim][Tf2N] has a property as a fragile liquid. A parameter D, calculated with eq 3, is often used to characterize the fragility of liquid,15
D)
(Tg/TK) - 1 0.0255
(3)
Cp [H(T) - H(0)] S(T) - S(0) -[G(T) - H(0)] /J K-1 mol-1 /T/J K-1 mol-1 /J K-1 mol-1 /T/J K-1 mol-1
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 272.1
16.58 35.73 54.88 73.00 89.65 105.03 119.14 132.28 144.53 156.00 166.80 177.03 186.78 196.16 205.1 221.9 237.6 252.7 267.4 281.9 296.3 310.7 325.3 340.0 355.0 370.3 385.8 401.3 416.7 432.0 447.5 463.8 481.1 499.8 504.0
Crystal 4.47 11.68 20.11 28.89 37.65 46.21 54.45 62.38 69.99 77.29 84.31 91.05 97.54 103.80 109.86 121.39 132.23 142.50 152.30 161.71 170.80 179.65 188.30 196.79 205.2 213.4 221.7 229.9 238.0 246.1 254.2 262.2 270.3 278.5 280.2
5.84 16.17 29.09 43.30 58.11 73.11 88.07 102.87 117.45 131.77 145.81 159.57 173.05 186.26 199.21 224.3 248.6 271.9 294.5 316.5 337.9 358.9 379.4 399.5 419.4 439.0 458.4 477.6 496.6 515.5 534.2 552.8 571.3 589.8 593.7
1.37 4.49 8.98 14.41 20.46 26.90 33.62 40.49 47.46 54.48 61.50 68.52 75.51 82.46 89.35 102.9 116.4 129.4 142.2 154.8 167.1 179.2 191.1 202.7 214.2 225.6 236.7 247.7 258.6 269.4 280.0 290.6 301.0 311.3 313.5
272.1 280 290 298.15 300 310
615.0 620.0 626.3 631.6 632.9 639.5
Liquid 384.3 390.9 398.9 405.2 406.6 414.0
697.8 715.5 737.4 754.8 758.7 779.6
313.5 324.6 338.5 349.6 352.1 365.6
where TK is the Kauzmann temperature, at which extrapolated entropy of supercooled liquid is equal to that of an ordered crystal. The comparison of entropy between the stable crystal and the LQG is shown in Figure 5 in terms of the configurational entropy,
Sc(T) ) ∆fusS -
∫TT
fus
Cp(glass) - Cp(crystal) dT T
(4)
where the difference in vibrational contribution was neglected. By smooth extrapolation shown by a dotted line in Figure 5, TK is estimated as 154 K. This results in D ) 7.4, which is smaller than that of [bmim][PF6] (D ) 14.8).5 The present magnitude of the D parameter also supports that [hmim][Tf2N] is a fragile liquid. The residual entropy of the LQG of [hmim][Tf2N] at 0 K was calculated to be 23 J K-1 mol-1 while assuming that the stable phase obeys the third law of thermodynamics. In Adam-Gibbs theory of glass transition,16 a coordination of glass-forming molecules is expected. The size (Z) of the cooperatively rearranging region (CRR) can be estimated from the ratio of configurational entropies at high-temperature limit and at the glass transition temperature. At the glass transition temperature, the configurational entropy is ca. 40 J K-1 mol-1,
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Figure 4. Temperature drifts around a glass transition of [hmim][Tf2N]: triangle, immediately after quenching from liquid state; square, after holding at 180 K for 4 days before the measurements.
Figure 5. Experimental configurational entropy of [hmim][Tf2N]. Dotted line shows its smooth extrapolation, which leads to Kauzmann temperature of 154 K.
as seen in Figure 5. The configurational entropy at hightemperature limit is estimated as 161 J K-1 mol-1 assuming17
Sc(T) ) Sc∞ -
A T2
Figure 6. Heat capacity difference between the stable crystal and the liquid quenched glass of [hmim][Tf2N] below 30 K.
dependence, respectively. The size of CRR at Tg is therefore estimated as Z (Tg) ≈ 4. Reported Z (Tg) for LQG of simple molecular compounds is within 4-8.17,18 The present Z (Tg) implies that the coordination of [hmim][Tf2N] at the glass transition temperature is similar to LQG of molecular liquids. It is noted that no information is attainable concerning coordination mode from the present analysis. The heat capacity of LQG of [hmim][Tf2N] is compared with that of the stable crystal; as a whole, the former is larger than the latter, as seen in Figure 6. This comparison suggests that molecular packing in the LQG is looser than that of the crystal. This can be seen energetically in terms of excess enthalpy of 12.1 kJ mol-1 of the LQG with respect to the stable crystal at 0 K. However, the excess heat capacity of the LQG shows a minimum around 15 K, where the heat capacity of the glass is smaller than that of the crystal. Some reports18,19 have been published for such interesting phenomena. In the case of [hmim][Tf2N], further studies are needed to clarify the heat capacity difference in terms of molecular structure and/or intermolecular interaction. In the lowest temperature region, it is widely known that amorphous solids show another common property owing to highly disordered structure. The so-called boson peak or lowenergy excitation belongs to such common properties.20,21 In Figure 6, a peak is clearly seen around 6 K in the curve of excess heat capacity, which should be a symptom of such a contribution of low-frequency vibrations in the glass. This implies that the physical properties of the glassy state of [hmim][Tf2N] are similar to other glass formers. 4. Conclusion
(5)
where Sc∞ and A are configurational entropy at the hightemperature limit and a coefficient describing its temperature
The heat capacities of liquid, stable crystal, and LQG of [hmim][Tf2N] were measured in the temperature range 5-310 K by adiabatic calorimetry. Some standard thermodynamic functions were established for the equilibrium phase sequence.
Room-Temperature Ionic Liquid [hmim][Tf2N] The heat capacity at 298.15 K was determined as (631.6 ( 0.5) J K-1 mol-1 after detailed consideration of possible uncertainties. Thermodynamic behavior of the LQG of [hmim][Tf2N] was compared with LQG of another ionic liquid. The ratio between the temperatures of the glass transition and fusion satisfies the empirical relation Tg ≈ (2/3) Tfus. The jump of heat capacity at Tg and the magnitude of the D parameter suggest that the present compound should be classified as a fragile liquid. The size of the cooperatively rearranging region in the framework of Adam-Gibbs theory is estimated as about 4. The heat capacity difference between the LQG and the stable crystal shows a socalled boson peak around 6 K. All of these findings are normal as molecular LQG and no remarkable difference was observed from conventional LQG for the LQG of [hmim][Tf2N]. Supporting Information Available: The detail is given of uncertainty estimation for the heat capacity of the liquid state at 298.15 K. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) John, S. W.; Michael, J. Z. J. Chem. Soc., Chem. Commun. 1992, 965. (2) Pierre, B.; Ana-Paula, D.; Nicholas, P.; Kuppuswamy, K.; Michael, G. Inorg. Chem. 1996 35, 1168.
J. Phys. Chem. B, Vol. 110, No. 28, 2006 13975 (3) Wassersheid, P.; Keim, W. Angew. Chem., Int. Ed. 2000, 39, 3772. (4) Sakaebe, H.; Matsumoto, H. Electrochem. Commun. 2003, 5, 594. (5) Kabo, G. J.; Blokhin, B. V.; Paulechka, Y. U.; Kabo, A. G.; Shymanovich, M. P.; Magee, J. W. J. Chem. Eng. Data 2004, 49, 453 (6) Magee, J. W.; Kabo, G. J.; Frenkel, M. ACS Symp. Ser. 2005, 901, 160. (7) Dzyuba, S. V.; Bartsch, R. A. Chemphyschem. 2002, 3, 161. (8) Tokuda, H.; Hayamizu, K.; Ishii, K.; Susan, M. A. B. H.; Watanabe, M. J. Phys. Chem. B 2005, 109, 6103. (9) Suga, H.; Seki, S. J. Non-Cryst. Solids 1974, 16, 171. (10) Loss, R. D. Pure Appl. Chem. 2003, 75, 1107. (11) Preston-Thomas, H. Metrologia 1990, 27, 3. (12) Tunnicliff, D. D.; Stone, H. Anal. Chem. 1955, 27, 73. (13) Masterangelo, S. V. R.; Dornte, R. W. J. Am. Chem. Soc. 1955, 77, 6200. (14) Sakka, S.; Mackenzie, J. D. J. Non-Cryst. Solids 1971, 6, 145. (15) Angell, A. C. J. Non-Cryst. Solids 1991, 131-133, 13. (16) Adam, G.; Gibbs, J. H., J. Chem. Phys. 1965 43, 139. (17) Yamamuro, O.; Tsukushi, I.; Lindquvist, A.; Takahara, S.; Ishikawa, M.; Matsuo, T. J. Phys. Chem. B 1998, 102, 1605. (18) Atake, T.; Abe, R.: Honda, K.; Kawaji, H.; Johnsen, H.-B.; Stolen, S. J. Phys. Chem. Solids 2000, 61, 1373. (19) Saito, K.; Massalska-Arodz, M.; Ikeuchi, S.; Maekawa, M.; Sciesinski, J.; Sciesinska, E.; Mayer, J.; Wasiutynski, T.; Sorai, M. J. Phys. Chem. B 2004, 108, 5785. (20) Yamamuro, O.; Takeda, K.; Tsukushi, I.; Matsuo, T. Physica B 2002, 311, 84. (21) Saito, K.; Kobayashi, H.; Miyazaki, Y.; Sorai, M. Sold State Commun. 2001, 118, 611.
