Calorimetric and Dielectric Investigations of the Phase

Chem. B , 1997, 101 (49), pp 10191–10197 ... B 101, 49, 10191-10197 .... Journal of Applied Physics 2007 101 (4), 044910 .... 1155 Sixteenth Street ...
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J. Phys. Chem. B 1997, 101, 10191-10197

10191

Calorimetric and Dielectric Investigations of the Phase Transformations and Glass Transition of Triphenyl Phosphite G. P. Johari* and C. Ferrari Department of Materials Science and Engineering, McMaster UniVersity, Hamilton, Ontario, L8S 4L7, Canada ReceiVed: January 6, 1997; In Final Form: May 28, 1997X

The phase transformations and the glass-liquid transition on heating of supercooled liquid triphenyl phosphite (TPP) were studied by differential scanning calorimetry and fixed frequency dielectrometry, and the nature of its various states was discussed. The dielectric behavior of the so-called “glacial” phase shows that the slow rise in its apparent heat capacity on heating is a reflection of its exceptionally broad glass-softening transition, due to a multiplicity of relaxation times, and not its premelting. The static permittivity near its freezing point is 3.6, and the change in both the permittivity and loss shows the temperature range of the supercooled liquid f “glacial” f crystal f liquid phase transformations. These transformations are illustrated by the free energy plots, and calorimetry was done to determine their merits. The heat capacity of the glass is comparable with that of the crystal phase, which indicates that the anharmonic phonon contributions to Cp in the glass and crystal phase are comparable, but that of the glacial phase is more than that of both the glass and crystal phases. In its thermal and dielectric manifestations, the “glacial” phase appears to be similar to an orientationally disordered crystal formed by a first-order transformation of a supercooled metastable liquid such as ethanol, but fails to reveal whether or not that phase is of liquid-crystal type.

Introduction From their comprehensive studies, Kivelson and co-workers1,2 have shown that supercooled liquid triphenyl phosphite (P(OC6H5)3, abbreviated as TPP) undergoes a remarkable phase transformation to a rigid, crystallographically uncharacterized (or apparently amorphous) phase when kept isothermally at a temperature in the 213-225 K range. Differential scanning calorimetry, light scattering, NMR, apparent viscosity, and X-ray diffraction measurements led them to conclude that the new phase, named as the “glacial” phase (it formed unusually slowly and only from the supercooled liquid state), may have defect ordered structures with an unusually large unit cell, akin to that occasionally referred to as the “blue phase” in the liquid-crystal literature. Miltenberg and Blok3 studied the TPP’s behavior by adiabatic calorimetry, provided accurate data for heat capacity, Cp, and relative enthalpy, ∆H, of its various phases as a function of temperature, T, and reported its glass-liquid transition temperature Tg, as 201.8 K and melting point as 297.7 K. Liquid TPP also showed an unusual behavior, in that its (dCp/dT) reached a minimum or zero value in the 203-207 K range. That indicated an apparent transformation in the TPP liquid, which is missed when the liquid is supercooled. Although it is the most accurate of all calorimetric methods, adiabatic calorimetry does not usually yield a satisfactorily interpretable value of Tg, nor does it allow an estimate of the structural relaxation time in a simple manner. The reason is that the thermodynamically determined Tg of a material is defined as the temperature at which its structural relaxation becomes, on heating, fast enough to contribute to its Cp within the time scale of one’s experiment. Thus Tg refers to that temperature at which a plot of the molecular relaxation time against the temperature crosses over the plot for the rate of heating (or cooling) against the temperature. Since the former is a material’s property and the latter an experiment’s feature, the value of Tg depends upon the time scale of one’s experiment. This time scale is readily available for the rate heating X

Abstract published in AdVance ACS Abstracts, November 1, 1997.

S1089-5647(97)00084-9 CCC: $14.00

experiment, but not for adiabatic measurements. For that reason and for reinvestigating the characteristics of the structural relaxation of its glacial phase, its glass-liquid transition, and its various phase transitions, TPP’s various phases were studied by differential scanning calorimetry (DSC), and dielectric measurements. These studies and their implications for our current understanding of the TPP’s behavior are reported. Experimental Methods Triphenyl phosphite (99% purity) was purchased from Acros Chimica. A 50 mL sample was cooled in a sealed container and allowed to heat, until it crystallized. The crystallized sample was heated further to 296 K, and the impurity-rich liquid present with the crystal phase at 296 K was poured out. The liquid studied here was obtained by melting the remaining crystals. This is expected to have improved the sample’s purity. A differential scanning calorimeter, Model DSC 4 (Perkin Elmer Corp.), was used. The data acquisition and analysis software had been written originally for earlier studies by Sartor et al.4 Both sealed stainless steel and open aluminum pans were used to contain the samples, and helium was used as purge gas. During the DSC scan of the sample, a baseline recorded previously was subtracted from the calorimetric signal, i.e., (dH/ dt)q, where H is the heat output/input in joules, t is the time in seconds, and q is the heating rate. This eliminated the effects of (a) the instrument’s imperfect balance setting, (b) the temperature-dependent heat flow background, and (c) the difference between the DSC pans’ thermal capacities. The samples were cooled, heated, and annealed at a predetermined temperature while kept in the instrument. The samples were cooled at 150 K/min and heated at 30 K/min, except when mentioned otherwise. From our earlier calibrations, the thermal lag of the instrument was 2.1 K for a heating rate of 30 K/min. This rather high heating rate was chosen so that the effects of the competing rates of crystallization and of other phase transformations could be reduced over the temperature range of interest. DSC curves are corrected for the thermal lag. The mass of the samples used was in the 6-32 mg range, which © 1997 American Chemical Society

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was determined with an accuracy of 0.5%. All DSC curves have been normalized by the sample’s mass, so that the DSC signal is in watts per gram of the sample with 0.5% accuracy. The relative permittivity, ′, and loss, ′′, were measured by means of a General Radio 1689 Digibridge, which was interfaced with a computer for automatic data collection after zeroing the assembly. The dielectric cell was a 12 parallel plate miniature capacitor of 16.3 pF capacitance in air and free from stray capacitance. The accuracy is 0.1% for ′ and 1% for ′′. The temperature was measured to (0.1 K by means of a copperconstantan thermocouple immersed in the bubble-free liquid already containing the capacitor inside a 10 mm diameter glass vial. The development of opacity, and mixed opaque clusters in an initially clear liquid, was observed at different temperatures. These observations agreed with Cohen et al’s.2 Results A total of 43 DSC scans were made with the sample contained in Al and stainless steel pans. One set from these is shown in Figure 1, where curve 1 is part of the first scan which was obtained for a sample cooled from 323 to 163 K at 30 K/min and scanned on heating to 323 K at 30 K/min. The curve shows a glass-liquid transition endotherm beginning at 211.5 K and ending at 218 K. The sample was then cooled from 323 to 163 K at 150 K/min and heated to 323 K at 30 K/min. This scan is shown by curve 2. The endotherm in curve 2 is similar to that of curve 1, but with a less prominent overshoot. This overshoot is characteristic of the Tg endotherms and is a reflection of the recovery of the enthalpy and entropy lost by the glassy state on its irreversible, time/temperature-dependent structural relaxation during the course of heating. On further heating, an exothermic minimum appears at 272 ( 1 K, with an onset at 262 K. This is followed by a near horizontal curve over a 20 K range, and then the melting endotherm appears. The endotherm remained incomplete up to 323 K, and its peak could not be measured, because the magnitude of (dH/dT)q reached values beyond the limits (-80.2/+80.2 mJ/s) we had set for the calorimeter. To investigate the features of structural relaxation of the supercooled liquid phase by an analysis of its Tg endotherm, a sample was cooled from 323 to 165 K at 150 K/min, heated to 208 K (Ta), annealed for 15 min (ta), cooled to 163 K at 150 K/min, and reheated, during which its scan was obtained. The Tg endotherm in the scan thus obtained is shown as curve 3 in Figure 1. Another Tg endotherm obtained without annealing the sample (after all experiments with this sample were completed) is shown as curve 4 in Figure 1. The overshoot in curve 3 has become more prominent, as more enthalpy and entropy were lost on structural relaxation of the glass during annealing at 208 K. The formation of the “glacial” phase and the effects of annealing of the supercooled liquid phase were then studied by increasing both Ta and ta of the supercooled liquid, so that the increased self-diffusion rate and the longer annealing time could allow substantial nucleation and growth of the “glacial” phase. With that aim, the sample was cooled from 323 to 163 K at 150 K/min, heated to 235 K, annealed for 5 min at 235 K, cooled to 163 K at 150 K/min, and finally scanned during heating to 323 K at 30 K/min. This scan is shown as curve 5 in Figure 1. The Tg endotherm appears at the same temperature, but the crystallization onset temperature decreases. The same sample was then annealed for 15 min at 230 K by following the same procedure as above and then scanned. The scan is shown as curve 6. The crystallization onset temperature decreases still further, but the exothermic minimum remains at 272 K. These

Figure 1. Measured DSC data for TPP are shown by continuous curves and simulated data by dots. For curve 1 the sample was cooled at 30 K/min and heated at the same rate. For all experiments (curves 2-9) the sample was cooled from 323 to 163 K at 150 K/min and heated at 30 K/min. Curve 2 was obtained during heating as for the samples of curve 1. Curve 3 was obtained after annealing the sample for 15 min at 208 K. Curve 4 was obtained for another sample, but unannealed, as for curve 1. Curve 5 is for a sample annealed for 5 min at 235 K. Curve 6 is for that annealed for 15 min at 230 K. Curve 7 is for that annealed for 15 min at 233 K. Curve 8 is for a sample annealed also for 15 min at 233 K, and curve 9 is for a sample annealed identically. A comparison between curves 7 and 9 shows lack of reproducibility of the behavior of the samples of identical thermal history. For annealing, the sample was cooled from 323 to 163 K at 150 K/min, kept for 5 min at 163 K, heated to the annealing temperature at 150 K/min, annealed for a predetermined period, cooled to 163 K at 150 K/min, and finally reheated to 323 K at 30 K/min, during which the scan was obtained. Curve 10 is for a sample cooled at 150 K/min and heated at 10 K/min, without annealing. The circles shown on curve 1 are the data calculated from the equations and the method given in refs 22-25. The parameters used for calculations are ln A )- -244.2, x ) 0.34, β ) 0.58, and ∆h ) 431 kJ/mol, as fitted to curves 1, 2, and 3. These are included here for a future intercomparison with the parameters obtained for other materials.

changes are attributed to partial crystallization of the sample during the annealing when crystal nuclei are likely to have formed and grown enough that, after annealing at a higher temperature and/or for a longer time, the sample’s crystallization onset temperature decreased. The sample was heated to 323 K, cooled to 163 K at 150 K/min, and annealed for 15 min at 233 K, and a DSC scan obtained for its annealed state. This is shown as curve 7 in Figure 1. The Tg endotherm decreases to nearly one-fifth of its original height, and (dH/dT)q increases slowly on heating beyond 210 K. A second broad exotherm appears before the prominent endotherm due to crystallization with the onset temperature of 236 K and a plateaulike feature at 246 K. The latter is due to the compensation of the rising part of the DSC signal of the first exotherm and the decreasing part of the signal of the second exotherm. The first, shallow and incomplete exotherm that terminates at the plateaulike feature indicates liquid f “glacial” transformation. This would occur only if the “glacial” phase nucleated to a certain extent during annealing at 233 K. It is followed by a deeper exotherm, with an onset at 252 K and a minimum at 255.5 K, which is

Phase Transformations of TPP attributed to the “glacial” f crystal transformation. The exothermic features appear at a lower temperature than those of the liquid f crystal transformation. Attempts were further made to obtain the “glacial” phase by annealing at 233 K. One sample was annealed at this temperature for 15 min, and its scan is shown as curve 8. Another sample, which was annealed identically, showed a qualitatively different behavior, as seen in curve 9 in Figure 1. The exothermic minimum in these curves also appears near 255 K, but the total area is less than for curve 7 and the minimum is less sharp. The lower onset and minima temperatures than those observed for the liquid f crystal transformation indicate that most of the liquid had transformed ultimately to the crystal phase during the annealing and only a small amount of the glacial phase remained to crystallize. (The absence of the second endotherm confirms that no liquid phase existed after annealing and scanning to 260 K.) Attempts were also made to obtain a larger amount of “glacial” phase by first annealing at 233 K for 10-15 min the samples that had been rapidly cooled initially from 323 to 163 K, heating the annealed sample at 30 K/min to various selected temperatures in the range 243-253 K, cooling, and then finally scanning to 323 K. None of the scans showed a prominent exotherm to indicate the “glacial” f crystal phase transformation. The onset temperatures of 236 K for the liquid f “glacial” transformation and ∼248 K for the “glacial” f crystal transformation are ∼10 K higher than (227 and 237 K, respectively2) determined by heating at 1 K/min and ∼20 K higher than those (217 and 227 K, respectively) determined by adiabatic calorimetry.3 As the phase transformations occurred in the metastable state of the liquid, these temperatures are expected to vary from one study to another of the same sample, depending upon whether crystal nuclei were present or not, their concentration in the glassy state, the impurity of the sample, the measurement method, and the latter’s sensitivity to thermal effects. The average value for the heat evolved Qirrev, on the supercooled liquid’s crystallization, determined from the 23 DSC scans, is 23.1 ( 0.1 kJ/mol. This is lower than ∆Hm, the heating of melting, of 25.09 kJ/mol at Tm of 297.7 K,3 because in a DSC scan the heat is released over a temperature range in which ∆Hexc of the liquid over the crystal phase is lower than ∆Hm and approaches ∆Hm at Tm. Thus Qirrev is the sum of the increasing ∆Hexc weighted by the decreasing fraction of the untransformed sample as the temperature is increased during scanning, and its value of 23.1 kJ/mol corresponds to an average ∆Hexc of the supercooled liquid below Tm. Dielectric permittivity, ′, and loss, ′′, of two samples of TPP were measured for 1 kHz fixed frequency at different temperatures over the 77-373 K range, and measurements for each sample were repeated. The values are plotted against the temperature in Figure 2. Each frame contains two sets of curves for two different samples and three experimental runs. ′ and ′′ of the supercooled liquid could be measured only in the 218295 K range in one series of measurements when TPP did not crystallize during cooling to 218 K at 1 K/min. Curve 2 in the upper frame has been shifted up by adding 0.3 to the measured ′ and that in the lower frame by multiplying the measured ′′ by 10, as indicated. When TPP did not crystallize on cooling, its ′ increased from 3.27 at 375 K to 3.81 at 229 K and then decreased to 3.45 at 218 K. Below 218 K, ′ and ′′ decreased too rapidly with time to allow dielectric measurements at T < 218 K. This was due to the crystallization of the supercooled liquid. The increase in ′ on cooling is the effect of the temperature alone, where ′

J. Phys. Chem. B, Vol. 101, No. 49, 1997 10193

Figure 2. Dielectric permittivity (A) and loss (B) measured for 1 kHz frequency plotted against the temperature in different temperature ranges. The results of two sets of experiments with different samples are shown by curves labeled 1 and 2.

) s, and the decrease that follows is the effect of the structural relaxation for 1 kHz frequency (ω ) 2πf, f ) 1 kHz), when the dielectric relaxation time, τ, has increased such that ω2τ2 becomes significantly more than zero, and ′ < s.5 In a separate experiment, the sample was cooled from 308 to 133 K and its ′ and ′′ were measured on heating at 1 K/min. The values measured at 218 K agreed with those measured during cooling, but the crystallization of the sample caused ′ and ′′ to decrease at 220 K and above too rapidly to allow measurements of the supercooled liquid on heating. Discussion a. Calorimetry and Phase Transformations. The variation of Cp with temperature of the liquid TPP shows that its (dCp/ dT) reaches a low, almost zero value in the 300-307 K range (Figure 4 in ref 3). This discontinuity in the slope3 was interpreted as a narrowly avoided thermodynamic transition point, which implies that the temperature Tm,glac, at which glacial and liquid phases of TPP coexist, is above the Tm of 297.7 K, or that at a T slightly above Tm, the liquid phase may be metastable. Hence, TPP had apparently supercooled through both its glacial f liquid and liquid f crystal transformations in our experiments. Such an occurrence is not unusual, for high cooling rates are known to vitrify the isotropic as well as the nematic, cholesteric, or smectic phases of the same material. If that also occurred here, there would be a region between Tm,glac and Tm over which the Gibbs free energy of the “glacial” phase would be lower than that of the liquid phase. So, annealing of the latter in the 300-307 K range would produce the “glacial” phase. The “glacial” phase may then be rapidly supercooled, and its calorimetric behavior may be studied on heating. Figure 3A is an illustration of the manner in which the free energy of the various phases is expected to change accordingly.

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Figure 4. DSC data (scans) obtained to investigate the “glacial” phase formation and its crystallization under different thermal conditions. The curves are identified in Table 1.

TABLE 1: Thermal History and Calorimetric Parameters of Triphenyl Phosphite Figure 3. Illustration of the Gibbs free energy plots against temperature. The “glacial” phase is assumed to form at Tm,glac > Tm in the illustration part A, and at Tm,glac < Tm in the illustration in part B. Tg of the “glacial” phase is assumed to be higher than Tg of the supercooled liquid phase in both illustrations. Note that in the range between Tm,glac and Tm in part A, the glacial phase is more stable than any other phase. In the region where the “glacial” phase forms from the supercooled liquid, the transformation is expected to occur from supercooled liquid to “glacial” phase, and from “glacial” phase to crystalline phase.

It is also of course possible that Tm,glac is below Tm and that the latter can be obtained only from the metastable liquid TPP, as Kivelson et al.1 have concluded. In the slow heating and cooling experiments,3 the “glacial” phase was not formed on supercooling to 245 K, and even at 245 K only the crystalline phase formed. That implies that the free energy curve for the glacial phase meets the free energy curve for the supercooled liquid phase at a temperature below 245 K, i.e, Tm,glac < 245 K, as illustrated in Figure 3B. The “glacial” f (metastable) liquid phase transformation may be observable only on heating the “glacial” phase toward Tm rapidly enough to prevent its crystallization. The endothermic transformation at Tm,glac would be observable only when a sufficient amount of the “glacial” phase is present. To examine the merits of the two above-given free energy illustrations for the phase transformation of TPP, two sets of experiments were performed. For those of Figure 3A, a sample of TPP inside the DSC instrument was heated to 313 K, brought to a temperature Ta of 308 K, annealed for a period ta of 2 min, cooled to 163 K at 150 K/min, equilibrated, and heated to 313 K at 30 K/min, during which its DSC scan was obtained. The experiment was repeated with the same sample and conditions, except for the Ta, which was chosen as 303, 302, 301, 298, 293, and 291 K in each experiment. The DSC scans obtained are shown as curves 1-7 in Figure 4 and identified in Table 1. For determining the merit of the illustration in Figure 3B, the sample was cooled from 313 K to a temperature, Ta, of 248 K, kept at Ta for a period, ta, of 10 min, cooled thereafter to

curve

t a , Ta

Tmin [K]

∆Cp [J/(mol/K)]

Qirrev [kJ/mol]

Tonset [K]

1 2 3 4 5 6 7 8 9 10 11

2 min, 308 K 2 min, 303 K 2 min, 302 K 2 min, 301 K 2 min, 298 K 2 min, 293 K 2 min, 291 K 10 min, 248 K 10 min, 238 K 10 min, 233 K 10 min, 218 K

271.3 273.1 270.0 271.8 271.4 273.3 271.8 271.5 271.5 269.7 257.4

179.0 181.6 178.4 179.0 181.6 178.8 177.7 176.4 176.4 176.4 176.4

23.4 23.4 23.1 22.8 23.6 23.4 23.4 23.1 22.0 22.0 15.0

264.3 265.5 261.6 262.6 262.5 265.6 262.5 263.0 262.5 260.5 252.8

163 K at 150 K/min, thermally equilibrated, and finally heated to 313 K at 30 K/min, during which its DSC scan was obtained. This is shown as curve 8 in Figure 4. The experiment was repeated but with Ta chosen as 238, 233, and 218 K. The DSC scans are shown by curves 9-11 in Figure 4 and identified in Table 1. ∆Cp determined from the height of the Tg endotherm Qirrev determined from the area of the crystallization exotherm, Tonset, the onset temperature of the exotherm, and Tmin, the temperature of the minimum of the exotherm, are listed in Table 1. Within the measurement errors, ∆Cp, Qirrev, Tonset, and Tmin remain unchanged for the various thermal treatments of the sample shown by curves 1-7 and listed in Table 1, which shows that the “glacial” phase did not form on annealing for 2 min in the 291-302 K range. Therefore, the curve for TPP’s “glacial” phase in Figure 3A is not an acceptable illustration for its free energy variation. Qirrev, Tonset, and Tmin of the sample annealed for 10 min at 218 K (curve 11), as listed in Table 1, are quite different from the values for curves 1-7. Qirrev decreases by 35%, Tonset by 12 K, and Tmin by 15 K. Thus 10 min annealing at a lower temperature is more effective in producing the “glacial” phase from the metastable liquid than annealing at a temperature above Tm. Its evidence is already seen from curve 7 in Figure 1, where

Phase Transformations of TPP ∆Cp decreased to one-fifth of the original value after annealing for 15 min at 233 K and where the scan showed two exotherms, the first at the supercooled liquid f “glacial” phase transformation and the second at the “glacial” f crystal phase transformation. A comparison between the features of curves 8, 9, and 10 in Table 1 shows that ∆Cp and Qirrev do not change beyond the experimental errors with change in the annealing temperature. So, the extent of this transformation in 10 min is negligible, if any, in the 233-248 K range. The “glacial” phase seems to form from the supercooled liquid and not on annealing the liquid at 298 < T < 308 K. We conclude that its formation is not the reappearance of a mesomorphic transition at T > Tm missed during the supercooling of TPP; the metastable liquid and “glacial” phase can be in thermodynamic equilibrium only at T < Tm, as illustrated by Tm in Figure 3B. b. Static Permittivity, Phase Transformation, and Dielectric Relaxation. The magnitude of TPP’s permittivity is relatively low. Since the viscosity of TPP at 298 K is on the order of several poise, its dielectric relaxation time would be on the order of several nanoseconds, and hence the permittivity of TPP at 298 K is equal to its static permittivity, s. This value is 3.58 and decreases on heating in the 295-373 K range. The low value and its further decrease mean that the dipole moment of TPP is exceptionally low, as for o-terphenyl,6 in which case the data are consistent with the Debye theory for noninteracting dipoles. The low s value cannot be attributed to an antiparallel dipolar alignment of the TPP molecules with a large dipole moment, because in that case s would increase with the temperature.7 That increase is not observed here. We now discuss how the phase transformations of TPP is indicated by the ′ and ′′ data measured for 1 kHz frequency during heating at 1 K/min. The increase in ′ from 2.9 at 205 K to 3.8 at 220 K indicates the recovery of molecular motions in the supercooled state or the glass f liquid transition.5 Thereafter, over a 5 min period heating by 5 K, ′ in curve 1 in Figure 2A decreases from 3.8 at 220 K to 2.95 at 225 K. This is attributed to the supercooled liquid f “glacial” phase transformation. On further heating to 241 K, at 1 K/min, ′ of the “glacial” phase increases to 3.0 (curve 1), as is expected when the dielectric relaxation time decreases on heating, and ′ increases toward s, as observed on heating a dipolar material through its Tg or glasslike transition range.5 On further heating to 246 K, ′ decreases to 2.8 and remains near this value until 272 K. The decrease from 3.0 to 2.8 is attributed to the “glacial” f crystal phase transformation. Further heating causes ′ of the crystal phase to first increase from 2.8 at 270 K to 3.63 at 297.7 K, the melting point.3 The increase over the 27 K range is due to the melting of the crystals. The broad temperature range may be partly due to the presence of impurities, which lower the melting point, and partly due to the intergranular melting.8-10 On heating above 298 K, ′ finally decreases to 3.27 at 375 K, where the values agree with those measured during cooling. To summarize, the ′ data first show the glass-liquid transition as a rapid rise in the value over a narrow temperature range and thereafter a rapid decrease at the liquid f “glacial”, another decrease at the “glacial” f crystal, and finally an increase at the crystal f liquid transformation. Corresponding changes also occur in ′′, where it shows a peak at 136.4 K in the glassy state and another at 218.7 K in the supercooled liquid state. The ∂′′/∂T on the high-temperature side of the 218.7 K peak in curves 1 and 2 in Figure 2B itself decreases on the liquid f “glacial” transformation at 225 K and then slightly increases as the decrease is overcompensated by an increase in ′′ toward a peak value in the 225-245 K range. On further heating, ′′ decreases rapidly up to 248 K,

J. Phys. Chem. B, Vol. 101, No. 49, 1997 10195 as the “glacial” transforms to the crystal phase. It increases monotonically on heating thereafter, as the amount of liquid TPP phase at the grain junction of the microcrystals formed on crystallization increases. The liquid phase contained in the grain junctions remains in thermodynamic equilibrium with the crystals8-10 and leaches out gradually with time the impurities dissolved in the crystals. But when the temperature increases, as here, the amount of liquid also increases, diluting the impurity content of the liquid. As the major fraction of ionic purities are now present in the liquid phase, where their mobility is high and becomes even higher on heating, the dc conductivity increases. The increase in ′′ observed above 296 K is therefore primarily due to an increase in the dc conductivity due to an increase in the ionic mobility with temperature. Figure 2B shows that the ′′ peak due to R-relaxation appears at 218.7 K (′′peak ) 0.251) in the supercooled liquid state and that due to the localized molecular motions or the JohariGoldstein relaxation (this term is used to avoid confusion between this relaxation and β-relaxation of the mode-coupling theory, as in recent reviews11-13) appears at 136.4 K (′′peak ) 0.0062) in the glassy state. The dielectric relaxation time of TPP is 159 µs at 218.7 K for the long-range motions, as deduced from the positions of the ′′ peaks in Figure 2B and at 136.4 K for the localized motions in the glassy state. The “glacial” phase of TPP formed on heating from 77 to 254 K was cooled to 130 K, and its ′ and ′′ were measured again as a function of temperature, but its ′ was found to be already so low that its sub-Tg relaxation peak could not be discerned. Thus although the occurrence of the phase transformations is evident in the dielectric studies, the magnitude of the changes in ′ and ′′ is too small, and it transforms to crystal phase too rapidly to allow its characterization in these experiments. Also, s of liquid TPP is small even at high temperatures. Since TPP contains at least 1% impurity, which is likely to be H3PO3 formed by hydrolysis due to moisture absorption, it is possible that part of the contributions to ′ and ′′ are due to the H3PO3 dipoles in the sample. That makes the interpretation of the dielectric relaxation data somewhat more subjective, but not the dielectric indication of the phase transformations. The “glacial” phase does show dielectric characteristics of a transition from a glasslike to a liquidlike phase, but whether the “glacial” phase is an orientationally disordered crystal or a mesomorphic liquid phase (liquid crystal) remains to be investigated. Nevertheless, the results of this study do not disagree with Kivelson et al’s1,2 suggestion of a “blue-phase”like cholesteric liquid crystal structure for the “glacial” phase of TPP. Optical spectroscopy can determine that. c. Structural Relaxation of the Glacial Phase. The glass or glasslike transition of the “glacial” phase on heating could not be observed here. Nevertheless, the slowly increasing slope in the 220-245 K range of the DSC scans 8 and 9 in Figure 1 indicates an increase in the heat absorption, which is consistent with the observation3 that (∂Cp/∂T) rises relatively slowly on heating the “glacial” phase from 290 K (Figure 2 in ref 3). Such an increase usually occurs when the glass transition is exceptionally broad as a consequence of a broad distribution of structural relaxation times,4,14,15 but it also occurs when part of the heat is used up in the melting of the high-energy, highentropy phase present at the grain junction of the low-energy, low-entropy phase,8-10 the latter being the metastable liquid here. (This causes the melting and phase transformation to smear out in temperature.) So, it is not certain whether the increase in (∂Cp/∂T) is a reflection of the glasslike transition of the “glacial” phase or the smeared-out endotherm due to the melting at its crystal-grain junctions, before its crystallization

10196 J. Phys. Chem. B, Vol. 101, No. 49, 1997 occurs. The anneal-and-scan technique developed to resolve such occurrences4,14,15 could not be used here because of the narrow temperature range of the existence of the “glacial” phase. This issue is resolved by the dielectric data available here. In Figure 2A, ′ of the “glacial” phase increases on heating from 225 to 241 K in curve 1. If this increase were due to an increase in the intergranular liquid on premelting of the “glacial” phase, ′′ would increase rapidly, as it does during the premelting of the crystal phase near 276 K. Instead, ′′ remains constant and then decreases, as seen in curve 1 in Figure 2B. We conclude that the increase in ′ and a decrease in ′′ show that the observed effects are relaxational and not caused by intergranular melting. d. Excess Cp of Glass, Glacial, and Crystal Phases. Because of the 3-fold symmetry of the TPP molecule and the steric hindrance to intramolecular motions, it is instructive to examine how the Cp of its glass, crystal, and “glacial” phase differ. This is appropriately done in terms of the excess Cp of glass16,17 over the crystal phase and over the “glacial” phase. The magnitude of Cp,exc ()Cp,glass - Cp,crystal) of TPP read from Figure 2 in ref 3 is remarkably small; that is, Cp,glass and Cp,crystal are very similar even near Tg, and this is quite different from the observations on most other glasses.16,17 A comparison with other materials may be done only in terms of the ratio Cp,exc/ Cp,crystal at a temperature far below the adiabatic calorimetric Tg, so that any errors from contributions from the onset of molecular motions near Tg can be avoided. We chose a temperature of 0.75Tg. This ratio is 0.039 for TPP at 150 K, as calculated from the data in ref 3, is 0.064 for H2SO4‚3H2O at 113 K,18 and 0.081 for C2H5OH at 72.8 K.19 The small values of Cp,exc mean that the anharmonic phonon contribution to Cp in the glassy state of TPP is remarkably similar to that in the crystal phase and/or that there is little contribution to Cp from the sub-Tg relaxations and from the unfrozen kinetic modes of long-range diffusion in the glassy phase, modes that are expected to persist when molecular dynamics involves, as is often the case, a broad distribution of relaxation times. Alternatively, it may mean that there is a large contribution from molecular motions in the crystal phase that raises its Cp. Since no glasslike transition was observed in crystalline TPP on heating it from 110 to 296 K, this alternative seems unlikely. The dielectric relaxation data have already shown that there is a sub-Tg relaxation in the glassy state of TPP, and the analysis of the Tg endotherm (see caption for Figure 1) shows that the distribution of configurational or structural relaxation time near 202 K is relatively broad, because β is found to be 0.58 from an analysis of the DSC scan (see caption for Figure 1). Thus we are left with the conclusion that the phonon contributions to Cp of glass is comparable to that in the crystal phase of TPP. This is unusual among glasses.16,17 An opposite situation is found for Cpexc of the supercooled liquid over the “glacial” phase, because as the data in Figure 2 of ref 3 show at T < 196 K, Cp of the “glacial” phase is higher than that of both the glass and the crystal phase, which implies that the phonon contribution in the glacial phase is more than that in the other two phases. Alternatively, its glasslike transition is smeared out over a much broader temperature range than is the glass transition of the liquid phase, and so its Cp has contributions from the persisting molecular degrees of freedom. There is a considerable, albeit slow, increase in the slope of the DSC scan in both curves 8 and 9 in Figure 1 in the 230245 K range, which indicates a broad Cp endotherm interrupted by the onset of crystallization. This is characteristic of a variety of materials, particularly those in which the distribution of

Johari and Ferrari intermolecular barriers is very broad. On that basis, we infer that the glasslike transition endotherm of the “glacial” phase is much broader than its liquid’s glass transition endotherm. In its higher Cp of the “glacial” phase over the glass and the crystalline phases, TPP is similar to C2H5OH, whose orientationally disordered crystal phase has a higher Cp than its glass and ordered crystal phase at T < 97 K,19 although the glasslike transition temperature of the former is the same as Tg ()97 K) of its liquid phase.17a,19 Concluding Remarks One of the crystal phases of TPP is undoubtedly an ordinary crystalline phase whose space group seems to be unknown. A brief interpretation of its powder pattern indicated that isotropic rotation of the TPP molecule occurs in the crystal phase,20 and thus this is a plastic phase. If that rotation was about the dipolar, 3-fold axis of the molecule, it would have no dielectric consequences. The low value of 2.8 for s of this phase and the lack of a significant ′′ on cooling to 77 K show that this phase is effectively nondipolar and that if it were indeed a plastic phase, the rotation of the TPP molecules in it involves no change in the dipole vector. The second phase may be either one of the several liquid crystal phases or an orientationally disordered crystal phase. It is noteworthy that, although a reversible, isotropic to anisotropic liquid-liquid transition, as in the formation of liquid crystal phases, leads to an increase in the viscosity (non-Newtonian in the liquid crystals), such transitions are not found to occur between two isotropic liquid phases. (A recent conjecture for such a transition in liquid water has been refuted by experiments.21) Further, a first-order phase transformation from the supercooled liquid to an apparently rigid, orientationally disordered crystal is not unusual, and several cases of such occurrences are known, although the crystal structure data for these crystals are not available. Thermally activated rotational diffusion does occur in such crystals; they show a glasslike transition, and they are known to mimic liquids in their thermodynamic, dielectric, and NMR properties (see p 117 in ref 17a), although that has not been observed for the “glacial” phase of TPP. They also show a macroscopic phase transition that leads to various degrees of opalescence in the sample when the solid phase slowly separates from the liquid or from another solid. Ethanol is an example of this latter type of behavior. Its liquid supercools (below its Tm of 159 K) and vitrifies at 97 K, its Tg. Its Cp,exc/Cp,crystal is 0.038 at 72.7 K (0.75 Tg).17b,19 On heating the glass above Tg, its supercooled liquid crystallizes by a first-order transformation to a phase named crystal II (phenomenologically similar to the “glacial" phase). Crystal II forms also on keeping the glassy sample for several days at 77-78 K,19 by heating to 120 K at 2 K/min,19 and by annealing for several minutes at 105 K (our unpublished results). Cp of this phase is higher than Cp of the glassy ethanol at temperatures approaching Tg, as is found to be the case also for the “glacial” and glassy states of TPP at 180 K < T < 201.8 K (Miltenburg, private communication, and Figure 2 in ref 3). Thus like ethanol, TPP vitrifies on supercooling the liquid. Its glassy state transforms to crystal II (“glacial” phase for TPP) on heating to T > Tg. Crystal II supercools to 77 K to a disorder frozen-in state. On heating from 77 K, that state shows a glass-to-liquidlike transition with an onset at ∼97 K, with lesser increase in Cp, and an endotherm broader than for the glass-liquid transition. On further heating, it melts at 127 K, and the melt transforms immediately to crystal I, the high-temperature, most stable monoclinic phase of ethanol. Like TPP, the most stable

Phase Transformations of TPP crystal phase of ethanol is also obtained by slowly supercooling the liquid 10-15 K below its Tm. The plots of free energy against temperature for ethanol are similar to the ones used as an illustration for TPP in Figure 3B. Whether the “glacial” phase of TPP is an orientationally disordered new phase with a larger space group, an anisotropic liquid crystal, or a “blue phase” of the type suggested by Cohen et al.1,2 remains to be ascertained by other methods, particularly optical spectroscopy using polarized light. Although the dielectric data here provide little information on its structure, the thermodynamic analogy of its behavior with that of ethanol suggests that occurrence of the type is not unusual. The “glacial” phase does show a much broader distribution of structural relaxation times, as its glasslike transition endotherm is exceptionally broad. The (∂Cp/∂T) minimum of near zero magnitude observed for TPP near 304 K (Figure 2 in ref 3) seems to have no dielectric or phase-structuring consequences. Acknowledgment. C.F. is grateful for partial support for his travel from Istituto Fisica Atomica e Molecolare del CNR, Pisa, Italy. This research was supported by a grant from Natural Sciences and Engineering Council of Canada. C.F. is grateful to D. A. Wasylyshyn of the group for his courteous help and hospitality. References and Notes (1) Ha, A.; Cohen, I.; Zhao, X.-L.; Lee, M.; Kivelson, D. J. Phys. Chem. 1196, 100, 1.

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