A Second Glass Transition in Pressure Collapsed Type II Clathrate

Article pubs.acs.org/JPCB

Cite This: J. Phys. Chem. B XXXX, XXX, XXX−XXX

A Second Glass Transition in Pressure Collapsed Type II Clathrate Hydrates Ove Andersson*,† and Ulrich Haü ssermann‡ †

Department of Physics, Umeå University, 901 87 Umeå, Sweden Department of Materials and Environmental Chemistry, Stockholm University,106 91 Stockholm, Sweden

‡

ABSTRACT: Type II clathrate hydrates (CHs) M·17 H2O, with M = tetrahydrofuran (THF) or 1,3-dioxolane, are known to collapse, or amorphize, on pressurization to ∼1.3 GPa in the temperature range 77− 140 K. On heating at 1 GPa, these pressure-amorphized CH states show a weak, stretched sigmoid-shaped, heat-capacity increase because of a glass transition. Here we use thermal conductivity and heat capacity measurements to show that also type II CH with M = cyclobutanone (CB) collapses on isothermal pressurization and undergoes a similar, weak, glass transition upon heating at 1 GPa. Furthermore, we reveal for both THF CH and CB CH a second, much more pronounced, glass transition at temperatures above the thermally weak glass transition on heating in the 0.2−0.7 GPa range. This result suggests the general occurrence of two glass transitions in water-rich (94 mol %) pressure-collapsed CHs. Because of a large increase in dielectric permittivity concurrently as the weak heat capacity increase, the first glass transition must be due to kinetic unfreezing of water molecules. The thermal features of the second glass transition, measured on isobaric temperature cycling, are typical of a glass−liquid−glass transition, which suggests that pressureamorphized CHs transform reversibly to liquids.

■

INTRODUCTION Glasses are generally known to be nonequilibrium solid states in which the positions of atoms, ions, or molecules lack longrange translational periodicity. Glasses are typically produced by cooling or, occasionally, pressurizing liquids, which causes molecular motions to become progressively slower and, in the liquid to glass transition range, kinetically freeze on the time scale of an experimental observation. The reverse transition on heating, i.e., the kinetic unfreezing of molecular motions or the glass to liquid transition, is observed as an abrupt decrease in the viscosity and increase in the heat capacity and thermal expansion coefficient, and these glass transition features shift to higher temperatures with increasing heating rate. If the system is temperature cycled in the glass−liquid−glass transition range, then thermodynamic properties such as volume, enthalpy, thermal expansion, and heat capacity show hysteresis and time dependence. The glass transition temperature, Tg, is commonly defined as the temperature where the heat capacity rises abruptly on heating at ∼10 K min−1 rate or, in results of dynamic measurements, the temperature where the relaxation time is 102 s.1 The concept of glassy states can be extended beyond glassified liquids to include other types of kinetically frozen states, in particular those of orientationally disordered crystals (ODICs) such as proton-disordered ices and clathrate hydrates.2 In ODICs, the molecules show orientational degrees of freedom but translational periodicity of their center of mass. On cooling of ODICs, rotational molecular motions become progressively slower and, like in the case of liquids, if the rate is sufficiently high to circumvent an ordering transition, then © XXXX American Chemical Society

these motions eventually freeze on the time scale of the study. This phenomenon, and the reverse on heating, shows similar characteristics in thermodynamic properties as a normal liquid−glass−liquid transition, e.g., thermal hysteresis and time dependence. However, this orientational glass transition differs from that of a normal glass transition because only molecular reorientation is unfrozen, in contrast to unfreezing of both reorientation and translational motions at glass to liquid transitions. Besides freezing of liquids by rapid cooling or pressurization, it may also be possible to form glasses by pressure collapse of crystals or pressure-induced amorphization (PIA). Mishima and co-workers established that hexagonal ice collapses to an amorphous state on pressurization to 1.5 GPa at 77 K, so-called high-density amorphous ice (HDA),3 which transforms to another distinct amorphous state, low-density amorphous ice (LDA), on depressurization at temperatures in the 125−140 K range.4 If HDA is instead heated at pressures near 1 GPa, it gradually densifies and the ultimately densified state is named very HDA (VHDA).5 (Annealing of HDA near 0.2 GPa and 125 K instead produces a state named “expanded” HDA, or eHDA.6) The findings of HDA and LDA of Mishima and coworkers have been used to suggest that water can form two (or more) glassy states which transform to distinct liquids through glass to liquid transitions on heating.7 Although such transitions Received: February 5, 2018 Revised: March 26, 2018 Published: March 27, 2018 A

DOI: 10.1021/acs.jpcb.8b01269 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B

and the type II structure of THF CH remains stable up to ∼1 GPa at 130 K16 and 1.3 GPa at 77 K,8 where it collapses to an amorphous state. The transformation behavior of type II M·17 H2O CHs is similar to that of hexagonal ice, which amorphizes on pressurization in the same temperature range but at slightly lower pressures.8 Here we use thermal and dielectric measurements to explore the transition properties of two different CHs: THF CH and CB CH at low temperatures and high pressures.

have been reported, the existence of several liquid states of water remains disputed.7 In addition to pure ice, PIA has also been reported for several different type II clathrate hydrates (CHs)8,9 and a type I clathrate hydrate.10 CHs are inclusion compounds in which the ice lattice forms various types of Archimedes polyhedral cages through hydrogen bonds.11,12 These cages can accommodate guest species M of varying size, from neon and hydrogen to large-sized, weakly polar, molecules, such as tetrahydrofuran (THF), 1,3-dioxolane, and cyclobutanone (CB). The latter CHs normally crystallize in the type II structure (Fd3̅m). In type II CHs, the hydrogen-bonded H2O network combines to form two types of cagespentagonal dodecahedron (D) and hexakaidecahedral (H)which are shown in the inset of Figure 1. The type II unit cell is ∼17 Å and consists of 16 D-cages and

■

EXPERIMENTAL SECTION Cyclobutanone (99%) and tetrahydrofuran (puriss. p.a., 99.9%, less than 0.005% water) were purchased from Sigma-Aldrich Chemicals. Their solutions in pure water, Milli-Q Ultrapure WaterSystems, were prepared by weighing in concentrations of about M·16.5 H2O, where M is the guest molecule. (The exact compositions were THF·16.4 H2O and THF·16.5 H2O for thermal conductivity and dielectric measurements, respectively, and CB·16.4 H2O.) This concentration, which is slightly deficient of water compared with a clathrate hydrate of ideal stoichiometry (M·17 H2O), reduces the risk of ice in the samples. The transient hot-wire method was used for measuring the thermal conductivity κ and heat capacity per unit volume c.17,18 The hot-wire probe was a thin Ni-wire, 0.1 or 0.3 mm in diameter, placed horizontally in custom-made Teflon cells of 39 mm internal diameter and 13 mm internal height. The cells made for CB−water solutions were designed for small sample sizes of about 7 mL (filled by half with Teflon), whereas the THF−water cells were of normal size, requiring ca. 15 mL of sample. The cell also contained a calibrated chromel−alumel thermocouple with an estimated temperature inaccuracy of ±0.5 K.17 (See ref 18 for a schematic view of the cell.) The cell was filled with one of the solutions, sealed with a Teflon lid, and mounted into a 45 mm internal diameter piston cylinder. The whole pressure cylinder device was thereafter placed in a vacuum chamber with a built-in helium cryostat equipped with a heater.19 Pressure was determined from the ratio, load/area, and it was corrected for the friction. This correction was determined during increasing pressure in a separate, in situ experiment using the pressure dependence of the resistance of a manganin wire. Values for κ and c were obtained simultaneously from the results of the Ni-wire temperature rise of ∼3.5 K during a 1.4 s heat pulse of about constant power. During the pulse, the Niwire resistance was measured versus time, which enabled the temperature rise of the wire to be determined. (Because of the low thermal diffusivity of CHs and the short measurement time of only 1.4 s, the heat wave reflected against the Teflon cell wall does not interfere with the measurements.) The analytical solution for the temperature rise was fitted to the data points, thereby yielding data with estimated uncertainties of ±2 and ±5% in κ and c, respectively. The hot-wire method is well-suited to establish the glass transition behavior under pressure as the quantity c shows the typical sigmoid-shaped increase of the specific heat capacity. Moreover, due to the transient nature of the method, both κ and c show method-specific features at a pronounced glass transition. These (artificial) features are known to be the consequence of time dependence in the heat capacity.20,21 It causes a peak in κ and dip in c because κ and c are treated as adjustable, time-independent, parameters in the fitting of the analytical solution for the temperature rise of the hot-wire. This has been previously analyzed in detail (ref 21), and it was found

Figure 1. (a) Heat capacity per unit volume and (b) thermal conductivity measured on pressurization: THF CH (circles) at 133 K and CB CH (squares) at 130 K. The increase in both properties near 1 GPa is due to the amorphization process during which the structures collapse. The inset shows the oxygen positions in the two types of cages of type II structures: (left) pentagonal dodecahedron (D, with 12 pentagonal faces - 512) with a cage radius of ∼3.9 Å and (right) hexakaidecahedral (H, 51264) with a cage radius of ∼4.7 Å. Only the latter type of cage is occupied in M·17 H2O.

8 H-cages (136 water molecules) with average cage radii of, respectively, 3.91 and 4.73 Å.12 In the cases of CB CH and THF CH, only the eight H-cages are occupied, which results in an ideal molar composition of M·17 H2O (8/136). The oxygen coordination in CHs is close to tetrahedral; i.e., the firstneighbor environment of each water molecule is similar to that in hexagonal and cubic ice. CH systems are interesting for a number of reasons, but here we focus on one, namely, their pressure-instability at low temperatures, which produces amorphous states via pressure collapse or PIA.8,9 At high temperatures, type II THF CHs decompose in gradual steps, initially into ice and type I clathrate, THF·7 H2O, at 0.23 GPa.13−15 However, below about 140 K, crystal−crystal transformations are kinetically inhibited B


Article

The Journal of Physical Chemistry B that the κ peak maximum and increase in c occur at a relaxation time of about 0.3 s. In the glass transition ranges, the heating and cooling rates were ∼0.3 K/min. In separate experiments, using the same high-pressure equipment, vacuum chamber, and cryostat, the capacitance and conductance of a capacitor filled with THF CH were measured in the 102 Hz−1 MHz frequency range by means of a Solartron 1260 impedance analyzer. In the range 100 mHz− 100 Hz, a HP33120 function generator was instead used to provide a sinusoidally varying signal to the sample capacitor and a reference capacitor placed in series. (A few tests using a dielectric interface, 1296A, in combination with a Solartron 1260 impedance analyzer gave identical results.) The voltages over the capacitors (100 points) were measured simultaneously by two HP3457A voltmeters during at least one period, and the capacitance and conductance of the sample were determined for each frequency. The capacitor was a cylindrically shaped (concentrical) brass capacitor with an air capacitance of about 17 pF with spacers made of Teflon, which contributes with about 3 pF. Thus, assuming that the dimensions of the capacitor do not change, the relative permittivity, ε, can be roughly estimated from ε = (C′ − 3 pF)/14 pF, where C′ is the measured capacitance of the capacitor filled with sample. An older version of the custom-made electronics for the dielectric measurements has been previously described in more detail.22

■

RESULTS The CHs were formed by freezing the solutions in Teflon sample cells kept at 0.1 MPa and thereafter temperature cycling the samples slightly below the freezing point of 277.4 K for THF CH23 and 273.2 K24 for CB CH for more than 1 h while simultaneously measuring the properties. (As shown by Bauer et al.,25 crystallization of THF CH, THF·16.65 H2O, is fast and does not require annealing.) The results for κ on isobaric cooling the ultimately formed CHs at about 0.05 GPa agreed to within better than 2% with previous results measured at 0.1 GPa.26 Both CHs show a weakly positive, or “glass-like”, temperature dependence of κ above 100 K (not shown here in a figure), i.e., in the temperature range where normally phonon−phonon scattering prevails, causing the typically observed κ ∼ T−1 dependence of crystals. The unusual glasslike κ behavior of CHs has been reported before for CB and THF26 but also for other type II CHs, e.g., 1,3-dioxolane, as well as type I CHs, e.g., methane27 and Xe;28 the reason for the glass-like κ dependence seems still to be unresolved. The CHs were cooled to low temperature at 0.05 GPa and thereafter pressurized isothermally at ∼130 K to study their known collapse to an amorphous state.8,9 As shown in Figure 1, both κ and c increase weakly on pressurization up to 0.9 GPa at 130 K. On further pressurization, κ of THF CH starts to decrease at 0.93 GPa, before a pronounced increase commences at 1.05 GPa. In CB CH, only the latter is detected and it starts at 1 GPa. Concurrently, c of the two CHs increases abruptly with start at 0.87 and 0.93 GPa for CB CH and THF CH, respectively. All of these features are due to collapse of the CHs.8,9 The abrupt changes in the properties level off and appear complete above 1.2 GPa. After pressurization to 1.3 GPa, the CHs were depressurized to 1 GPa and temperature cycled (Figure 2). This procedure is known to increase the thermal stability of the collapsed states which makes it possible to avoid reversion to the crystalline CH on pressure decrease to ambient pressure.9,25 It is also known that collapsed THF and 1,3-dioxolane (DXL) CHs display a glass transition, here

Figure 2. (a) Real C′ (dots) and imaginary C″ (circle) parts of the capacitance for pressure collapsed THF CH measured at 0.5 Hz on second heating cycle at 1 GPa. The capacitance in the unfrozen state above 140 K corresponds to a relative permittivity of about 100. (b) Heat capacity per unit volume measured on first heating and (c) thermal conductivity measured on temperature cycling at 1 GPa: collapsed THF CH (circles) and collapsed CB CH (squares). Arrows show the sequence of cycling, and the dashed line for c of THF CH shows a linear extrapolation of that for its glassy state.28 The vertical line indicates the temperature onset of a weak sigmoid-shaped rise of c.

denoted as glass transition 1 (GT1), at a temperature Tg1 just below 140 K at 1 GPa.29 It should be noted that Tg1 is associated with a relaxation time τ of only 0.3 s due to the transient heating of the probe (see ref 21 and the Experimental Section) as opposed to the much longer τ of ∼102 s in, e.g., differential scanning calorimetry using typical heating rates of ∼10 K min−1. Figure 2a shows the change in the capacitance measured at constant frequency f of 0.5 Hz on second heating of collapsed THF CH, i.e., after the sample had been temperature cycled once to about 160 K at 1 GPa. The capacitance increases strongly in the 130−150 K range, and the loss has a maximum at 138 K. The maximum can be used to calculate an average dielectric relaxation time τdie = (2πf max)−1, which gives τdie = 0.3 s at 138 K. Moreover, as shown in Figure 2b and c, both c and κ of collapsed THF CH and CB CH show weak features slightly below 140 K; these are similar to those reported before for DXL and THF CHs.29 The heat capacity shows a sigmoidshaped weak increase and κ changes slope, at least on cooling and second heating run. It has already been concluded that this behavior is due to a glass transition and arises when the (heat capacity) relaxation time is 0.3 s in good correspondence with the dielectric data.29 The thermal conductivity also shows an irreversible change during first heating, and becomes a few percent higher during subsequent cooling and second heating, for which the data coincide. This behavior is repeatable and a C


Article


recording the results shown in the figure. The sample had thus been conditioned (relaxed) at 0.4 GPa at a temperature well above 132 K. The sample studied at 0.5 GPa had instead been pressurized from 0.05 to 0.5 GPa at 132 K, before it was cooled and reheated at 0.5 GPa. The weak slope change in κ is hardly detected on heating at 0.5 GPa, but it is better resolved on subsequent cooling (red solid line in Figure 3c). Further up in temperature, both c and κ display more pronounced features; e.g., κ increases relatively abruptly at a temperature slightly above 150 K at 0.5 GPa and then shows a maximum at a temperature just before the sample was cooled. On cooling, the behavior reversed but with a slight shift in temperature. The 0.4 GPa sample, which was not cooled after the maximum, shows that κ decreases to a level below that prior to the peak, and then κ and temperature change suddenly at 163 K due to crystallization. Concurrently, as the peak shows up in κ, c increases abruptly. As argued in the Discussion section, these features in κ and c suggest a second glass transition (GT2 at Tg2) in collapsed CB CH, just before crystallization. Figure 4 shows corresponding results for collapsed THF CH, which are similar to those of collapsed CB CH. That is, first a sigmoid-shaped weak increase in c with a simultaneous weak change in the slope of κ at about 130 K on heating at 0.35 GPa,

consequence of densification during first heating of collapsed CHs to about 160 K at 1 GPa.29 To explore the pressure change of the weak glass transition features observed at 1 GPa, the samples were depressurized and studied at lower pressures using various pretreatments. The properties as well as the temperature of the sample were measured continuously during all changes in pressure and temperature to detect transitions. Crystallization transitions in the metastable collapsed state are exothermic and observed also as discontinuous changes in the properties, but no such features were detected prior to the results shown in Figure 3. Figure 3

Figure 3. (a) Excess sample temperature ΔT plotted against temperature during heating of collapsed CB CH at 0.4 GPa. (ΔT was calculated by subtracting a third-order polynomial function fitted to sample temperature versus time data in the 105−160 K range from the corresponding data in the full range.) (b) Heat capacity per unit volume and (c) thermal conductivity of collapsed CB CH measured on heating at the pressures indicated. The results for κ on subsequent cooling are also shown for the 0.5 GPa sample (red solid line). The vertical arrows indicate glass transition features at GT1 and GT2 (see the Discussion section). The dashed dark yellow and blue vertical lines demark the crystallization ranges at 0.4 and 0.7 GPa.

shows the properties for collapsed CB CH on heating in the 0.4−0.7 GPa range, and similar results were obtained down to 0.2 GPa. The excess temperature of the sample, defined here as the sample temperature minus that of the near surroundings, shows that the collapsed CB CH recrystallized at 163 K on heating at 0.4 GPa (Figure 3a). Moreover, the results of c show a weak sigmoid-shaped increase concurrently as those of κ show a change of slope at about 132 K. The slight upturn in c is made more obvious in Figure 3b by a dashed line that extrapolates the low-temperature data. However, the features here are even less pronounced than the ones at 1 GPa (Figure 2), and results for samples with different thermal history indicate that the possibility to observe these depends on the history. The 0.4 GPa sample in Figure 3 had been pressurized from 0.05 to 0.4 GPa at 145 K before cooling to 100 K and reheating while

Figure 4. (a) Natural logarithm of the dielectric relaxation time τdie of collapsed THF CH at 0.4 GPa. τdie was calculated from the frequency of maximum dielectric loss, f max, where τdie = 1/(2πf max): results of frequency spectra (filled symbols) and measurement at constant frequency (open symbols). The vertical dashed line shows the temperature of τdie = 0.3 s. (b) Heat capacity per unit volume and (c) thermal conductivity of collapsed THF CH measured on heating at the pressures indicated; the sample was thereafter cooled before reaching the crystallization temperature. Results on cooling are shown only at 0.35 GPa (blue line). The vertical dashed line indicates the temperature onset of the sigmoid-shaped weak rise of c and change of slope of κ(T). D


Article


amorphous ice (VHDA) on heating at 1 GPa.31 The c increase for VHDA (and collapsed CHs) is larger but of similar order as that found previously for the glass−liquid transition of hyperquenched glassy water (HGW)32 and amorphous solid water (ASW)33 at 0.1 MPa or vacuum pressure, which suggests that GT1 is a glass−liquid transition associated with H2O. On the other hand, the apparently sluggish change in volume on heating at 1 GPa, which occurs on a significantly longer time scale than the dielectric relaxation, seems inconsistent with fluidity on the same time scale as the dielectric relaxation. The weak thermal features at Tg1 make it difficult to determine the pressure-induced change of Tg1. The features cannot with definite certainty be identified in the results for κ and c at all pressures in the 0.35−0.7 GPa range, shown in Figures 3 and 4. The reason for the diminished glass transition signatures is, at least partly, associated with the decrease in density. The heat capacity per unit volume c is the specific heat times density. Thus, the density acts as an amplifying factor when the specific heat capacity increase at Tg is pressure independent. The increase of c, in excess of that for the kinetically frozen state of collapsed THF CH at 1 GPa (indicated by a dashed line in Figure 2), is 0.24 MJ m−3 K−1 for a 18 K range above Tg1. With an estimated density of ∼1.4 g cm−3 for the collapsed and densified THF CH at 1 GPa, this corresponds to 3.8 J H2O-mol−1 K−1. (If the density of the collapsed CHs would be 7−8% higher than the collapsed and ultimately densified ice,34 as the difference between the crystalline phases at 0.1 MPa, then the density is 1.44 g cm−3 at 1 GPa.) The corresponding excess c at 0.35 GPa is 0.20 MJ m−3 K−1 or 17% less than that at 1 GPa. The density difference accounts partly for the difference, but also the vicinity of the second glass transition may affect the broad GT1 feature in c, making it harder to identify. However, the large increase of dielectric permittivity at GT1 corroborates the identification of Tg1 in Figure 4. The agreement between the temperature of τdie = 0.3 s at 0.4 GPa and the weak rise in c at 0.35 GPa is within 1.5 K. Combining the results for Tg1 at 0.35 and 0.4 GPa with those at 1 GPa yields ΔTg1/Δp = 13 and 12 K/GPa for collapsed THF CH and CB CH, respectively. Glass Transition 2 (GT2). GT1 has been reported in several previous studies of CHs, and it is well-established from the complementary glass transition features shown in c, κ, and complex capacitance. However, GT2 is new and shows features, e.g., the rise in κ on heating of collapsed CB CH in the 165− 173 K range at 0.7 GPa (Figure 4), that can be mistaken for crystallization. This type of continuous increase is typical at sluggish crystallization processes, and the discontinuous change following the increase is certainly due to exothermic crystallization. However, pronounced glass transitions also give rise to an increase in κ in results of transient hot-wire and hot-strip methods.20,21 When the heat capacity step at Tg is large and occurs in a narrow temperature range, two method-specific (artificial) features arise in κ and c.20,21 The former shows a peak and the latter a dip due to time dependence in c. Since measurements on subsequent cooling at 0.5 GPa (red solid line in Figure 3c) show that the increase in κ is (quasi) reversible, the rise in κ on heating is not due to (irreversible) crystallization or other irreversible transformations. Crystallization can also be excluded for the cases when κ shows a maximum followed by a decrease on heating, e.g., at 0.4 GPa in Figure 4b. Crystallization is here instead detected as a simultaneous discontinuous change in κ and temperature; the

which is indicated by the vertical dashed line in Figure 4b and c. On further heating, this is followed by more pronounced features in both c and κ at higher temperatures. As in the case of CB CH, these are quasi-reversible and observed also on cooling (blue line in Figure 4c). To establish the (dielectric) relaxation time, collapsed THF CH was also studied by dielectric spectroscopy at 0.4 GPa, both by isochronal measurements on isobaric heating at 0.3 K/min rate and by measuring the spectra while the temperature was kept constant. The results showed only one dielectric relaxation process similar to that in Figure 2a. Figure 4a shows a plot of ln τdie against temperature, calculated from both sets of data. The vertical dashed line in Figure 4a shows the temperature of τdie = 0.3 s at 0.4 GPa, which is only slightly higher than that of the accelerated rise in c at 0.35 GPa.

■

DISCUSSION Clathrate Hydrate Formation and Their Subsequent Pressure Collapse. Both CB and THF solutions crystallized abruptly after slight supercooling at a pressure near ambient pressure. THF CH appears to form rapidly, but the sample was still temperature cycled and annealed for more than 1 h near the melting point of 277.4 K.23 Since CB CH initially showed nonrepeatable results on temperature cycling above 250 K, with discrepancies significantly larger than the imprecision of ∼0.2%, it was temperature cycled two times between its melting point of 273.2 K24 and 100 K, before repeatable results were recorded on cooling. These latter results agree within 2% of previous results measured at 0.1 GPa;26 the reason for the initial measurement problem remains uncertain. The behavior of κ and c of CB CH on pressurization at 130 K, which is similar to that of THF CH, confirms that also this type II CH pressure collapses. The structural collapse of CHs is associated with both strong densification and an order to disorder change. Generally, these two effects change κ in opposite directions; densification raises κ, whereas increasing disorder lowers κ. The major collapse is thus detected as an increase in both c and κ due to densification. Just prior to the collapse, κ of THF CH shows an additional feature, a weak decrease, which is likely due to the effect of increasing disorder. Therefore, the initial weak decrease of κ of THF CH suggests that the transformation starts with an order−disorder process such as distortion of the cages, and presumably the empty ones. This effect is less obvious in CB CH due to its already low κ. Glass Transition 1 (GT1). The results for κ and c on heating of collapsed CB CH at 1 GPa (Figure 2) show the same features as previously observed for collapsed DXL and THF CHs,29 i.e., a weak but clearly detectable sigmoid-shaped increase in c and a concurrent change in the slope of κ. Moreover, the increase in capacitance on heating the collapsed THF CH measured at 0.5 Hz frequency (Figure 2a) shows that this is the temperature range of kinetic unfreezing of dipolar motions on the same time scale as that of the thermal measurements. A rough estimate of the relative permittivity, ε, in the unfrozen, high-temperature, state using the initial (empty) capacitance of the capacitor yields ε ≈ 100. Because of the weak dielectric contribution from THF in THF CH (Δε is about 2.5 or less),30 the large change, of slightly less than Δε = 100, shows that the process is associated with water. This suggests that the weak features in c and κ are due to a glass transition associated with the kinetic unfreezing of water molecules in the collapsed CHs. The same behavior and size of c increase are indeed found also for very high density E


Article


same Tg2 of collapsed THF CH and collapsed CB CH does not support that GT2 is due to unfreezing of guest mobility. Moreover, in a phase-separated sample, and heated at the low rate of 0.3 K min−1 as done here, water should crystallize more than 15 K below the crystallization of the collapsed CHs at 0.4 GPa (163 K).46 Another possibility for two different glass transitions is unfreezing of proton and oxygen (H2O) mobility at Tg1 and Tg2, respectively. Such a transition sequence would not require a heterogeneous sample. Proton mobility has been long discussed as a possibility for Tg detected for solid amorphous water at atmospheric pressure47 and more recently by Shepard and Salzman.48 The large increase in dielectric constant at Tg1 provides firm evidence of, at least, proton (or H2O reorientational) mobility, but it cannot, with certainty, establish fluidity. Although the dielectric relaxation time of the main relaxation process, τdie = 102 s, provides a fair estimate of glass−liquid transition temperatures of many glass formers,49,50 there are several known deviations such as monoalcohols.50 However, for monoalcohols, the relaxation time of the prominent (Debye) dielectric relaxation process suggests higher glass−liquid transition temperature than the correct one determined through calorimetric measurements. This is apparently not the case for CHs for which the dielectric data either show the same glass−liquid temperature as the calorimetric data (Tg1) or show mobility at temperatures below the glass−liquid temperature (Tg2). Thus, GT1 can be due to unfreezing of orientational H2O motions, or proton mobility, and GT2 the subsequent glass−liquid transition of the solid water solution. Also, this scenario is consistent with GT2 being more or less dielectrically featureless. However, such a transition sequence, an orientational glass transition (GT1) followed by a clearly distinguishable glass−liquid transition (GT2), is unusual and perhaps unique. To show the striking similarities between the shape and size of features in κ and c of GT2 and those at a glass−liquid transition of an archetypal glass former, we have included such results in Figure 5. The black squares in Figure 5c and d show results of the well-established glass−liquid transition of glycerol−water solution (20 wt % or 56 mol % water) measured on heating at atmospheric pressure; the dark yellow dots show corresponding results of GT2 of collapsed CB CH measured on heating at 0.4 GPa. The sizes of the features are similar, whereas those at the orientational Tg of typical plastic crystal phases, e.g., those of cyclohexanol45 and cyclooctanol,51 are less pronounced, roughly half the size or less, which is due to the smaller heat capacity rise at Tg. Although it is not possible to firmly establish the nature of the two glass transitions in collapsed CHs, the results suggest that the collapsed CHs are in a liquid state above Tg2, which implies that the pressure-collapsed CHs states are reversibly linked to a liquid state, and thus true glasses. Finally, it should be noted that, because of the size of the c increase and value of Tg2, GT2 in collapsed CHs most likely does not relate to any of the two glass transitions reported for low-density and highdensity amorphous ices.52 Method-Specific Glass Transition Features. By analyzing the artificial peak in κ, it is possible to estimate the activation energy and substantiate the size of the heat capacity increase at GT2, which is partly obscured by crystallization. The glass transition temperature is commonly determined at constant heating or cooling rates using methods such as differential scanning calorimetry (DSC). However, the

latter is caused by the exothermic crystallization at about 163 K. Thus, at 0.4 GPa, crystallization occurs just after the appearance of a (second) glass transition in collapsed CB CH. Crystallization cannot be excluded as a reason for the rise at 0.7 GPa, but it is reasonable to assume that the rise observed here is also due to GT2. On further pressurization, it was not possible to detect Tg2, and the κ peak and c dip associated with Tg2 seem to gradually become broader and diminish with increasing pressure. There is also a tendency that the Tg increase with increasing pressure accelerates, which is an atypical behavior. Possibly this could be related to the gradual densification of HDA into VHDA observed by Loerting et al.35 and Nelmes et al.6 on pressurization. Nature of the Glass Transitions. It is not unusual to find double glass transitions in a heterogeneous multicomponent system such as water−alcohol mixtures,36,37 hydrogels,38 and for water in confinement.39−41 However, in the case of collapsed CHs, the components, THF or CB and H2O, become perfectly homogeneously mixed as the samples crystallize upon cooling. This homogeneous distribution should remain after pressure collapse, but the necessary procedure to stabilize the collapsed state by heating to high temperatures at 1 GPa introduces an uncertainty in the homogeneity. Previous finding of HDA−LDA type of transitions in such pretreated samples may be due to water-rich sample domains caused by sluggish phase separation on heating to above 170 K at high pressure.42 Moreover, to avoid pure ice, the samples were made with slight excess of solute with respect to the ideal composition of 17 mol of H2O for each mole of the guest. Therefore, one cannot exclude that the sample consists of some amount of guest-rich and guest-poor domains that undergo separate glass transitions. On the basis of this and previous interpretations of glass transitions in amorphous ices, we can outline two scenarios that explain the occurrence of a second glass transition in pressure collapsed CH samples; one of these requires a heterogeneous sample. Below, we discuss the supporting and contradicting evidence for the two cases. The nature of GT2 with a large heat capacity increase is typical of that for a glass−liquid transition in amorphous solids and, to some extent, orientational glass transitions in so-called plastic crystal phases such as one phase of cyclohexanol,43−45 which is a special case of ODICs. The amorphous structure of collapsed CHs thus implies that GT2 is a glass−liquid transition, or else an unusual, perhaps unique, orientational glass transition in an amorphous solid. The concurrent weak, or nonexistent, features in the dielectric data are consistent with increased mobility of the, only weakly polar, guests. This indicates that GT1 is associated with H2O and GT2 with the guests, either in guest-rich domains, i.e., it requires a phaseseparated sample, or as a pure orientational motion inside the collapsed cages. However, pure THF and CB have different van der Waals radii of 2.95 Å (THF) and 3.25 Å (CB)11 and also significantly different melting temperatures of, respectively, 165 and 222 K. The former seems to exclude that guest motion would start at identical temperatures in amorphous ice, and the latter suggests that CB and THF liquids show different glasstransition temperatures. Unfortunately, their glass−liquid transition temperatures seem experimentally undetermined. The relatively common finding of vitrification at 2/3 of the melting temperatures indicates glass−liquid transitions near 110 and 148 K for pure THF and CB, respectively. Although the glass−liquid temperatures of THF and CB can be differently affected by the presence of water, the virtually F


Article


experimental results and a model for the time dependence in the glass transition range c(t ) = c∞ + (c0 − c∞)e−(t / τ)

β

(1)

where c0 and c∞ represent the short and long time values associated with the glass and kinetically unfrozen states, respectively, τ is the calorimetric relaxation time, β is an exponent between 0 and 1, and here we used β = 0.5. That is, c∞ − c0 = Δc is the total increase in c due to kinetic unfreezing of a process. The calculations yield the temperature increase of the wire probe versus time for a given relaxation time. To study GT1, values for κ and Δc were taken directly from the experimental results for collapsed THF CH at 1 GPa: κ = 0.5 W m−1 K−1 and Δc = 0.24 MJ m−3 K−1. For GT2, the parameters were kept the same except for Δc, which was estimated from the experimental data to be about 5 times larger; exact determination of Δc is not possible due to crystallization in the range. The power supplied to the hot-wire probe was chosen so that the heating of the wire was the same as that in the experiments (∼3.5 K). After the temperature rise of the wire probe had been calculated, the analytical solution was fitted with c and κ as adjustable, time-independent, parameters, just as done in the experiments. The results for the two sets of calculations are shown in panels a and b of Figure 5. In the approximate τ-range, 10−3− 103 s, the time dependence of c affects the results and causes an artificial maximum in κ at τ = 0.3 s. The real c increase is observed at about the same τ. The artificial dip in c occurs at slightly longer τ of ∼2 s for GT2, whereas it can hardly be detected at GT1. To directly compare calculated and measured data, we transformed values for τ to temperatures assuming τ = τdie. The dielectric results54 were described by an Arrhenius function

Figure 5. Method-specific features in the glass transition range. (a) Results calculated for thermal conductivity and (b) heat capacity per unit volume plotted against relaxation time for two cases: GT1 with Δc1 = 0.24 MJ m−3 K−1 (red symbols) and GT2 with Δc2 = 1.2 MJ m−3 K−1 (blue symbols), corresponding to the experimentally determined value and estimated value at Tg1 and Tg2, respectively. (c, d) Comparison with experimental results for collapsed THF CH (GT1, open circles) and collapsed CB CH (GT2, dark yellow dots) by transforming the relaxation times to temperatures using an Arrhenius function fitted to dielectric data at GT1 (see text). For GT2, the transformation was done with 4 times as large activation energy as that for GT1. Linear functions (baselines) were added to the calculated data to account for the temperature dependence of the properties (dashed lines). (The experimental data at GT2 has been shifted in temperature for the comparison and vertically for clarity.) Black squares in panels c and d show experimental results for a glycerol− water solution (20 wt % water) at atmospheric pressure. The results for κ have been shifted vertically by 0.1 W m−1 K−1.

τdie = Ae EA / RT

(2)

where A and the activation energy EA are fitting parameters and R is the gas constant. The function was fitted to experimental results for τdie of collapsed THF CH in the range 130−170 K at 1 GPa,54 where τdie was calculated from the maximum of dielectric loss, f max, τdie = 1/(2πf max). The fit yielded ln A = −33.70 and EA = 37.57 kJ mol−1. The equation was used to convert τ to temperatures in the range 90−170 K for GT1, i.e., also outside the fitting range. A similar function was used for GT2, but 4 times larger activation energy was required to obtain agreement with the experimental results. Since the calculations do not account for any temperature dependence in c and κ, other than that in c due to τ(T), linear functions were added to all data sets to obtain fair agreement with the experimental results well outside the glass transition range. These functions are illustrated as dashed lines in panels c and d of Figure 5. These calculations clarify the reasons for the distinct differences in κ and c behaviors in the transition ranges of GT1 and GT2. The former is associated with a very small heat capacity rise of 0.24 MJ m−3 K−1 as well as a small Arrhenius activation energy of 38 kJ mol−1, which makes it hard to detect the typical artificial glass transition features of the hot-wire method. Still, the calculations indicate that there is a small superimposed (artificial) peak in κ near 140 K. GT2, however, is associated with roughly 5 times larger heat capacity increase and 4 times larger activation energy, where the latter result

molecular motions, which kinetically freeze on cooling and unfreeze on heating, can also be investigated with transient methods such as that used here or, more commonly, modulated DSC.53 In our case, it introduces a second time scale, that of the transient heating pulse of the probe, in addition to the slow cooling or heating rates of the surroundings. The latter is here due to the slow temperature change of the pressure vessel, which determines the vitrification temperature on cooling. However, the much shorter time scale of the transient heating of the probe shifts the kinetic freezing seen in the measured c to higher temperatures. Moreover, when the (heat capacity) relaxation time of the sample is about the same as the time of the pulse, c varies during the heating pulse and, thus, becomes time-dependent. The latter introduces two auxiliary (nonreal) glass transition features in the measured c and κ. These features can be calculated from the values for c of the kinetically frozen and unfrozen states assuming a function for the time dependence of c (eq 1).21 This was done here to show the different characteristics of the two glass transitions, and to roughly estimate the activation energy and heat capacity increase at Tg2. The temperature rise of the wire probe was calculated by finite element analysis using κ determined from the G


Article


(5) Loerting, T.; Salzmann, C.; Kohl, I.; Mayer, E.; Hallbrucker, A. A second distinct structural “state” of high-density amorphous ice at 77 K and 1 bar. Phys. Chem. Chem. Phys. 2001, 3, 5355−5357. (6) Nelmes, R. J.; Loveday, J. S.; Strässle, T.; Bull, C. L.; Guthrie, M.; Hamel, G.; Klotz, S. Annealed high-density amorphous ice under pressure. Nat. Phys. 2006, 2, 414−418. (7) Amann-Winkel, K.; Böhmer, R.; Fujara, F.; Gainaru, C.; Geil, B.; Loerting, T. Colloquium: Water’s controversial glass transitions. Rev. Mod. Phys. 2016, 88, 011002. (8) Handa, Y. P.; Tse, J. S.; Klug, D. D.; Whalley, E. Pressure-induced phase transitions in clathrate hydrates. J. Chem. Phys. 1991, 94, 623− 627. (9) Suzuki, Y. Evidence of pressure-induced amorphization of tetrahydrofuran clathrate hydrate. Phys. Rev. B: Condens. Matter Mater. Phys. 2004, 70, 172108. (10) Tulk, C. A.; Klug, D. D.; Molaison, J. J.; dos Santos, A. M.; Pradhan, N. Structure and stability of an amorphous water−methane mixture produced by cold compression of methane hydrate. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 86, 054110. (11) Davidson, D. W. Clathrate Hydrates. In Water  A Comprehensive Treatise; Franks, F., Ed.; Plenum: New York, 1973; Vol. 2, Chapter 3. (12) Sloan, E. D. Clathrate Hydrates of Natural Gas, 2nd ed.; Dekker: New York, 1998. (13) Manakov, A. Yu; Goryainov, S. V.; Likhacheva, A. Yu.; Fursenko, B. A.; Dyadina, Y. A.; Kurnosov, A. V. High-pressure boundary of hydrate formation in the tetrahydrofuran−water system. Mendeleev Commun. 2000, 10, 80−81. (14) Dyadin, Yu. A.; Bondaryuk, I. V.; Zhurko, F. V. Clathrate Hydrates at High Pressures. In Inclusion Compounds, Inorganic and Physical Aspects of Inclusion; Atwood, J. L., Davies, J. E. D., MacNicol, D. D., Eds.; Oxford University Press: Oxford, U.K., 1991; Vol 5, pp 213−275. (15) Dyadin, Yu. A.; Kuznetsov, P. N.; Yakovlev, I. I.; Pyrinova, A. V. The system water-tetrahydrofuran in the crystallization region at pressures of up to 9 kbar. Dokl. Chem. 1973, 208, 9−12. (16) Andersson, O.; Johari, G. P. Collapse of an ice clathrate under pressure observed via thermal conductivity measurements. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 78, 174201. (17) Håkansson, B.; Andersson, P.; Bäckström, G. Improved hot-wire procedure for thermophysical measurements under pressure. Rev. Sci. Instrum. 1988, 59, 2269−2275. (18) Andersson, O.; Inaba, A. Thermal conductivity of crystalline and amorphous ices and its implications on amorphization and glassy water. Phys. Chem. Chem. Phys. 2005, 7, 1441−1449. (19) Andersson, O.; Sundqvist, B.; Bäckström, G. A low-temperature high-pressure apparatus with a temperature control system. High Pressure Res. 1992, 10, 599−606. (20) Birge, N. O.; Nagel, S. R. Specific-heat spectroscopy of the glass transition. Phys. Rev. Lett. 1985, 54, 2674−2677. (21) Andersson, O. Simulation of a glass transition in a hot-wire experiment using time-dependent heat capacity. Int. J. Thermophys. 1997, 18, 195−208. (22) Forsman, H. Application of the many-body theory of Dissado and Hill to the complex permittivity of 1,2,4-butanetriol at pressures to 1 GPa. J. Phys. D: Appl. Phys. 1989, 22, 1528−1536. (23) Yamamuro, O.; Oguni, M.; Matsuo, T.; Suga, H. Calorimetric study of pure and KOH-doped tetrahydrofuran clathrate hydrate. J. Phys. Chem. Solids 1988, 49, 425−434. (24) Morris, B.; Davidson, D. W. A clathrate hydrate of cyclobutanone: dielectric relaxation of the host and guest molecules. Can. J. Chem. 1971, 49, 1243−1251. (25) Bauer, M.; Többens, D. M.; Mayer, E.; Loerting, T. Pressureamorphized cubic structure II clathrate hydrate: Crystallization in slow motion. Phys. Chem. Chem. Phys. 2011, 13, 2167−2171. (26) Andersson, P.; Ross, R. G. Effect of guest molecule size on the thermal conductivity and heat capacity of clathrate hydrates. J. Phys. C: Solid State Phys. 1983, 16, 1423−1432.

pertains to the narrow temperature range of the artificial peak in κ, i.e., ∼140−150 K range at 0.4 GPa.

■

CONCLUSIONS Type II CHs of composition M·17 H2O, where M is the encaged guest, show common behavior on pressurization at temperatures below 140 K. CB CH collapses to an amorphous state in a similar manner as shown before for 1,3-dioxolane and THF CHs. The collapsed states can be stabilized by heating at high pressure, e.g., from 130 to 160 K at 1 GPa, a range in which all collapsed CHs show a thermally weak but dielectrically strong glass transition. The latter shows that the glass transition is due to kinetic unfreezing of water molecules. If the stabilized states are thereafter depressurized to a pressure in the range 0.2−0.7 GPa and isobarically heated from low temperatures, results for κ and c show two glass transitions on heating, first the weak one detected also at high pressure and then a more pronounced glass transition, just prior to crystallization. The thermal features of the latter are typical of a glass−liquid transition. At least two different scenarios explain these results: (i) an orientational or glass−liquid transition in water followed by an orientational glass transition of the guests or a glass−liquid transition associated with solute-rich sample domains and (ii) an orientational glass transition in water followed by a glass−liquid transition associated with the water solution. The case of two glass−liquid transitions (case i) can only occur if the sample is heterogeneous with water-rich and water-deficient parts relative to the ideal CH composition. Scenario ii offers one explanation as to why property changes observed at Tg of pure water can be significantly different from those observed at Tg of water mixtures. A glass−liquid−glass transition in collapsed CHs, as indicated by the results reported here on temperature cycling at constant pressure, implies that the collapsed state of a CH is reversibly linked to a liquid state.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +46 90 7865034. Fax: +46 90 7866673. ORCID

Ove Andersson: 0000-0003-1748-9175 Ulrich Häussermann: 0000-0003-2001-4410 Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS We acknowledge financial support for equipment from Carl Trygger Foundation and Magnus Bergvalls foundation. REFERENCES

(1) Donth, E. The Glass Transition: Relaxation Dynamics in Liquids and Disordered Materials; Springer Series in Materials Science, Vol. 48; Springer: Berlin, 2001. (2) Suga, H. Thermodynamic aspects of glassy crystals. Ann. N. Y. Acad. Sci. 1986, 484, 248−263. (3) Mishima, O.; Calvert, L. D.; Whalley, E. ‘Melting ice’ I at 77 K and 10 kbar: A new method of making amorphous solids. Nature 1984, 310, 393−395. (4) Mishima, O.; Calvert, L. D.; Whalley, E. An apparently first-order transition between two amorphous phases of ice induced by pressure. Nature 1985, 314, 76−78. H


Article

The Journal of Physical Chemistry B (27) Krivchikov, A. I.; Korolyuk, O. A.; Romantsova, O. O. Heat transfer in crystalline clathrate hydrates at low temperatures. Low Temp. Phys. 2007, 33, 612−616. (28) Krivchikov, A. I.; Gorodilov, B. Ya.; Korolyuk, O. A.; Manzhelii, V. G.; Romantsova, O. O.; Conrad, H.; Press, W.; Tse, J. S.; Klug, D. D. Thermal conductivity of Xe clathrate hydrate at low temperatures. Phys. Rev. B: Condens. Matter Mater. Phys. 2006, 73, 064203. (29) Andersson, O.; Inaba, A. Glass transitions in pressure-collapsed ice clathrates and implications for cold water. J. Phys. Chem. Lett. 2012, 3, 1951−1955. (30) Gough, S. R.; Hawkins, R. E.; Morris, B.; Davidson, D. W. Dielectric properties of some clathrate hydrates of structure II. J. Phys. Chem. 1973, 77, 2969−2976. (31) Andersson, O. Glass−liquid transition of water at high pressure. Proc. Natl. Acad. Sci. U. S. A. 2011, 108, 11013−11016. (32) Johari, G. P.; Hallbrucker, A.; Mayer, E. The glass−liquid transition of hyperquenched water. Nature 1987, 330, 552−553. (33) Hallbrucker, A.; Mayer, E.; Johari, G. P. Glass−liquid transition and the enthalpy of devitrification of annealed vapor-deposited amorphous solid water. A comparison with hyperquenched glassy water. J. Phys. Chem. 1989, 93, 4986−4990. (34) Loerting, T.; Salzmann, C. G.; Winkel, K.; Mayer, E. The relation between high-density and very-high-density amorphous ice. Phys. Chem. Chem. Phys. 2006, 8, 2810−2818. (35) Loerting, T.; Schustereder, W.; Winkel, K.; Salzmann, C. G.; Kohl, I.; Mayer, E. Amorphous ice: Stepwise formation of very-highdensity amorphous ice from low-density amorphous ice at 125 K. Phys. Rev. Lett. 2006, 96, 025702. (36) Elamin, K.; Sjöström, J.; Johansson, H.; Swenson, J. Calorimetric and relaxation properties of xylitol-water mixtures. J. Chem. Phys. 2012, 136, 104508. (37) Inaba, A.; Andersson, O. Multiple glass transitions and two step crystallization for the binary system of water and glycerol. Thermochim. Acta 2007, 461, 44−49. (38) Hofer, K.; Mayer, E.; Johari, G. P. Glass-liquid transition of water and ethylene glycol solution in poly(2-hydroxyethyl methacrylate) hydrogel. J. Phys. Chem. 1990, 94, 2689−2696. (39) Oguni, M.; Maruyama, S.; Wakabayashi, K.; Nagoe, A. Glass transitions of ordinary and heavy water within silica-gel nanopores. Chem. - Asian J. 2007, 2, 514−520. (40) Oguni, M.; Kanke, Y.; Nagoe, A.; Namba, S. Calorimetric study of water’s glass transition in nanoscale confinement, suggesting a value of 210 K for bulk water. J. Phys. Chem. B 2011, 115, 14023−14029. (41) Cerveny, S.; Mallamace, F.; Swenson, J.; Vogel, M.; Xu, L. Confined water as model of supercooled water. Chem. Rev. 2016, 116, 7608−7625. (42) Andersson, O.; Nakazawa, Y. Transitions in pressure collapsed clathrate hydrates. J. Phys. Chem. B 2015, 119, 3846−3453. (43) Sherwood, J. N. The Plastically Crystalline State; Wiley: Chichester, U.K., 1979. (44) Adachi, K.; Suga, H.; Seki, S. Phase changes in crystalline and glassy-crystalline cyclohexanol. Bull. Chem. Soc. Jpn. 1968, 41, 1073− 1087. (45) Andersson, O.; Ross, R. G.; Bäckstrom, G. Thermal conductivity of crystalline and glassy crystal cyclohexanol under pressure. Mol. Phys. 1989, 66, 619−635. (46) Salzmann, C. G.; Mayer, E.; Hallbrucker, A. Effect of heating rate and pressure on the crystallization kinetics of high-density amorphous ice on isobaric heating between 0.2 and 1.9 GPa. Phys. Chem. Chem. Phys. 2004, 6, 5156−5165. (47) Fisher, M.; Devlin, J. P. Defect activity in amorphous ice from isotopic exchange data: insight into the glass transition. J. Phys. Chem. 1995, 99, 11584−11590. (48) Shephard, J. J.; Salzmann, C. G. Molecular reorientation dynamics govern the glass transitions of the amorphous ices. J. Phys. Chem. Lett. 2016, 7, 2281−2285. (49) Hecksher, T.; Nielsen, A. I.; Olsen, N. B.; Dyre, J. C. Little evidence for dynamic divergences in ultraviscous molecular liquids. Nat. Phys. 2008, 4, 737−741.

(50) Huth, H.; Wang, L.-M.; Schick, C.; Richert, R. Comparing calorimetric and dielectric polarization modes in viscous 2-ethyl-1hexanol. J. Chem. Phys. 2007, 126, 104503−104504. (51) Andersson, O.; Ross, R. G. Thermal conductivity, heat capacity and phase diagram of cyclooctanol in liquid, solid and glassy crystal states under high pressure. Mol. Phys. 1990, 71, 523−539. (52) Amann-Winkel, K.; Gainaru, C.; Handle, P. H.; Seidl, M.; Nelson, H.; Böhmer, R.; Loerting, T. Water’s second glass transition. Proc. Natl. Acad. Sci. U. S. A. 2013, 110, 17720−17725. (53) Simon, S. L. Temperature-modulated differential scanning calorimetry: theory and application. Thermochim. Acta 2001, 374, 55− 71. (54) Andersson, O.; Johari, G. P. Nature of the pressure-induced collapse of an ice clathrate by dielectric spectroscopy. J. Chem. Phys. 2008, 129, 234505.

I


A Second Glass Transition in Pressure Collapsed Type II Clathrate

Recommend Documents