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The Thermal Conductivity of Triphenyl Phosphite’s Liquid, Glassy and Glacial States Alexander I Krivchikov, and Ove Andersson J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b00271 • Publication Date (Web): 25 Feb 2016 Downloaded from http://pubs.acs.org on March 4, 2016

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The Journal of Physical Chemistry

The Thermal Conductivity of Triphenyl Phosphite’s Liquid, Glassy and Glacial States Alexander I. Krivchikov† and Ove Andersson∗,‡ B. Verkin Institute for Low Temperature Physics and Engineering of NAS Ukraine, 47 Lenin Ave., Kharkov 61103, Ukraine, and Department of Physics, Umeå University, 901 87 Umeå, Sweden E-mail: [email protected] Phone: +46 90 7865034. Fax: +46 90 7866673

∗

To whom correspondence should be addressed ILT ‡ Umeå University †

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Abstract The thermal conductivity κ and heat capacity per unit volume ρCp of triphenyl phosphite (TPP) were measured under different pressure and temperature conditions, and with time during the sluggish liquid to glacial state transformation at temperatures about 15 K above the glass transition temperature. As the transformation slowly proceeds during several hours, ρCp decreases monotonically from that of the liquid state to a value close to that of the vitrified state. Concurrently, κ increases non-monotonically with intermediate local maximum followed by a minimum, before the final rise to a higher κ. The properties of the ultimately formed glacial state depend on the thermal history, which implies that the state formed under these conditions is a heterogeneous mixture of nanocrystals and mainly amorphous-like solid, and that the relative amount and microstructure depend on the conditions of the transformation. The non-monotonic changes in phonon propagation during the liquid to glacial transformation suggest microstructural changes which are consistent with a liquid- liquid transformation and sluggish growth of nanocrystals within amorphous-like solid domains. The isobaric thermal conductivity of the as-formed glacial state shows a reversible step increase, just prior to crystallization on heating, which deviates from the typical behaviour of glasses, liquids and crystals. An increase in pressure shifts the step to higher temperatures and suppresses crystallization, which reveals another reversible rise in κ and Cp . These results show that increased molecular mobility in the glacial state increases and suggest reduced thermal resistance at boundaries or that the motions carry heat.

Introduction The structure of matter has generally a profound impact on the properties. A typical molecular substance can crystallize in a few different modifications under normal conditions, but it is commonly also possible to circumvent crystallization to obtain an amorphous or glassy state. A polyamorphous transition, i.e. when a state transforms from an amorphous state to another one via a distinct transition is, however, a rare phenomenon. The most famous 2 ACS Paragon Plus Environment

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example is water, a strong associated liquid, which displays at least two distinct amorphous solid states: low-density and high-density amorphous ices. 1 The finding of these different amorphous ices has ultimately led to the suggestion that water can exist in two distinctly different liquid forms: high-density and low-density liquid water, and that the transformation between these occurs at a first-order liquid-liquid transition LLT. 2 This conjectured phenomenon provides the fundament for the most discussed models of supercooled water’s unusual properties, e.g. the density decrease and heat capacity increase observed on cooling. More recently, LLTs have also been suggested for two other pure molecular associated liquids: triphenyl phosphite 3–6 and n-butanol, 7 and a homogeneous mixture of glycerol and water. 8 Other remarkable examples include the elements phosphorus, 9 silicon, 10 carbon, 11 and cerium. 12 But because of the difficulties to distinguish a homogeneous liquid phase from a liquid with nanocrystals, and the often severe conditions of simultaneous high pressure and high temperatures by which these states are observed, LLTs are in several cases disputed, including the system studied here: triphenyl phosphite, TPP. Upon cooling liquid TPP (liquid 1) to a temperature slightly above the glass transition temperature Tg = (200 ± 2 K at 1 atm), 13 it transforms sluggishly into another, "apparently amorphous", state referred to as a "glacial state", which has several properties typical of an amorphous state. The state was initially tentatively described as a defect-ordered crystal, 3 which forms as neighboring molecules group in locally preferred structures. As the temperature is lowered, the structures become energetically more favorable but cannot grow due to geometric frustration, leading to frustration limited domains. This microscopic model has since been scrutinized in numerous studies, but the nature of the glacial state is still disputed; the most frequently discussed possibilities include: (i) a second glassy state (vitrified liquid 2) with or without nanocrystals, (ii) a mixture of small crystallites in a very viscous liquid and (iii) a liquid-crystal or plastic-crystal phase. 14,15 In case (i), the transformation is described as an irreversible phase transition associated with local-ordering of neighbouring molecules forming (frustrated) molecular clusters, or a new amorphous, possibly glassy, state



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that nucleates and grows in the matrix of the highly fragile liquid. 5,6,16–21 This deduction differ from that of Hedoux and co-workers, 22–28 who instead find results consistent with a nano or microcrystalline mixture. More specifically, they explain the transformation in terms of classical nucleation theory suggesting that the glacial state is a mixture of untransformed liquid 1 and a certain amount of a crystalline fraction of a stable crystal phase (crystal 1). But Mei and co-workers 29,30 deduced that the glacial state is not a simple two-component mixture of nanocrystalline and supercooled liquid phases. The microstructural evolution during the transformation is apparently complex and may not be described in simple models. Different frustration models 31,32 and reverse Monte Carlo (RMC) modeling 30 have been employed to interpret and understand the structural changes during the transformation. Specifically, Mei and co-workers 29,30 used RMC simulations to analyse neutron and high-energy X-ray diffraction results of glacial samples, and concluded that "the glacial state forms unusually weak intermolecular hydrogen bonds between an oxygen atom connected to a phenyl ring and an adjacent phenyl ring aligned in an approximately antiparallel configuration." The process is associated with cooperative molecular rearrangements and low temperature conformational changes. 33 Further, Schwickert et al. 34 used small angle neutron scattering to study the transformation and required a four-step sequence to describe the results: (I) cluster formation, (II) rapid nucleation, (III) agglomeration, and finally (IV) saturation. Recently, Baran et al. 35 reported polymorphism in TPP and also that the glacial state likely contain crystalline nuclei. A similar result of a second crystal phase of TPP, but obtained by crystallization from an ionic liquid solution, was reported by Golovanov et al. 36 The stable crystal phase of TPP at 1 atm has trigonal symmetry, with a rhombohedral lattice, space group R¯3¯3, whereas the new phase reported by Golovanov et al. 36 is monoclinic, space group P 21 /n. 37 There is a consensus that the ultimately formed glacial state typically contains nanocrystals, but the key issue is whether or not the nucleation and growth is preceded or accompanied by an LLT. The latter is advocated by the recent results of Mosses et al. 16 and Kobayashi et al. 38 Mosses et al. 16 find results consistent with a microstructure of small clusters with


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a locally preferred structure of higher polarity coexisting with liquid 1 during the transformation. The authors describe the two different coexisting liquid phases as "polyamorphic ’echoes’ of the crystal polymorphs" of TPP. In the LLT scenario of TPP, it is thus argued that the liquid to glacial transformation is distinct from a classical nucleation process. The transformation may instead consist of a two-step transition sequence: first a transition from liquid 1 to an intermediate metastable state (liquid 2, or rather the glassy state of liquid 2), through spinodal decomposition (SD) at low temperatures (near Tg ) and nucleation and growth (NG) at higher temperatures, and then a subsequent crystallization of the metastable state into a mixed state of liquid and nanocrystals, or else that these two distinct, but associated, processes proceeds almost concomitantly. 38 Kobayashi et al. 38 have also provided arguments against the possibility (ii) but do not, however, exclude an unknown, exotic, process. These more elaborate ideas of (almost) concurrent LLT and crystallization can explain the diverging conclusions and provide a unified picture of the transformation in TPP, but the issue will likely remain disputed. In this study, we have followed the change in phonon propagation during the transformation from the liquid to glacial state, and established the thermal properties of the liquid, glassy and glacial states. Moreover, we have applied high pressure to obtain the glacial state under significantly different conditions to compare the properties of differently formed glacial states. The results imply that the ultimately formed glacial state is a heterogeneous mixture of a crystal phase and an amorphous-like solid, and that the relative amount and microstructure depends on the temperature-pressure-time conditions of the transformation. Further, a non-monotonic change in phonon propagation during the liquid to glacial state transformation is consistent with an LLT proceeding or concurrently occurring with the growth of nanocrystals, with the latter growing in a solid environment.



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Experimental The material, triphenyl phosphite (TPP) of better than 99 % purity, was supplied by Fisher Scientific and used without further purification. The transient hot-wire method was used to measure the thermal conductivity κ and the heat capacity per unit volume ρCp , or density times specific heat capacity, of TPP with estimated inaccuracies of ±2 % and ±5 % in κ and ρCp , respectively, under normal conditions. 39,40 The hot-wire probe was a semi-circular Niwire which was inserted in a custom-made 17 mm deep and 37 mm internal diameter Teflon sample cell. The cell was filled with the sample (TPP) and sealed with a tightly fitting Teflon lid before inserted in a piston-cylinder type apparatus of 45 mm internal diameter. The whole assembly was thereafter transferred to a hydraulic press, which supplied the load. For measurements above room temperature, the cylinder was heated via an external electric heater, and for low temperature measurements, the cylinder was cooled by spraying liquid nitrogen on the cylinder. This gave a maximum cooling rate of about 2 K min−1 , whereas the heating rate was kept below 0.5 K min−1 . Results on heating and cooling differ slightly due to reversal of frictional forces and changes in thermal gradients. Due to the relatively fast cooling employed here, these effects caused differences of about 1-2 % between results on cooling and heating. Pressure was determined from the load/area with correction for friction. This correction was determined in a separate in situ experiment using the pressure dependence of the resistance of a manganin wire.The temperature was measured by a chromel-alumel thermocouple, which had been calibrated to within ±0.2 K against a commercially available silicon diode thermometer. During each measurements of a value for κ and ρCp , the hot-wire was heated 3-4 K above the surrounding temperature by a 1.4 s long pulse of nominally constant power (i.e. an average heating rate of about 150 K min−1 ), and its electrical resistance was measured as a function of time. The wire acted as both the heater and the sensor for the temperature rise, which was calculated by using the relation between its resistance and temperature. The 6 ACS Paragon Plus Environment

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analytical solution for the temperature rise with time was fitted to the data points for the hot-wire temperature rise with κ and ρCp as fitting parameters. The method is well-suited to establish the glass transition behaviour under pressure as Cp shows the typical sigmoid-shaped increase of the heat capacity ρCp and the temperature dependence of κ often changes due to the increase in the thermal expansion coefficient at a glass transition. In addition, when the heat capacity increase is abrupt and large, two artificial features may arise in the form of a peak in and a dip in ρCp , which occur when the relaxation time of a relaxation process, e.g. the α-relaxation, is of order of the probe time, i.e. about 1 s. 41 The artificial peak in κ and dip in ρCp arise due to a time dependence in Cp during the heating event, which is not accounted for since κ and ρCp are adjustable, time-independent, parameters in the fitting of the analytical solution for the temperature rise of the hot-wire. As a consequence of the short time-scale of the hot-wire method of about 1 s, these features occur at a higher temperature than the glass transition temperature determined by e.g. more commonly used differential scanning calorimetry. The artificial peak and dip are superimposed on the real changes in the properties and a detailed analysis (Ref. 41) shows that the relaxation time is 0.3 s at the maximum in κ and minimum in ρCp .

Results and Discussion To obtain the glassy state of the sample, the temperature was decreased at a rate exceeding 1.3 K min−1 at nominally isobaric conditions while κ and ρCp were recorded (Figure 1). The results, at 0.10 and 0.48 GPa, show the typical sigmoid - shaped heat capacity changes at a glass transition. These measurements were done on cooling the pressure vessel at rates in the range 1.3 K min−1 to 2 K min−1 , and on subsequent heating at rates 0.1 K min−1 to 0.4 K min−1 . But since each value was recorded by rapidly heating the hot-wire probe ( 150 K min−1 ), all data were recorded on heating the sample, independent of the relatively slow cooling or heating of the vessel. The transient heating of the probe also determines



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the time-scale of the measurements. That is, all results pertain to heating of the sample and correspond to a relaxation time of about 1 s (see experimental section). From the data measured on cooling, we obtain Tg of 218 and 276 K at, respectively, 0.1 and 0.48 GPa. The results differ between heating and cooling of the vessel mainly due to the different direction of frictional forces. The results show several glass features in addition to the sigmoid-shaped jump of ρCp . Besides real effects of the glass transition, two artificial effects arise: a peak in κ and a dip in ρCp , which are associated with the method. 41 The pressure induced densification of the sample shifts Tg , or rather the temperature at which the relaxation time of the α relaxation is about 1 s, to higher temperatures with the pressure rate of ∂Tg /∂p ≈165 K GPa−1 . (The corresponding value for the glacial state is 150 K GPa−1 .) This gives an extrapolated value for Tg at 1 atm, which is in fair agreement with literature values considering the differences in experimental conditions. 14,21,25,42,43 Moreover, κ of the glassy state of TPP shows a linear pressure dependence: (∂κ/∂p)T =0.108 W m−1 K−1 GPa−1 , which is the same as that for the supercooled liquid sample. Values of ρCp decrease slightly with increasing p. The general temperature behavior of κ(T) below and above Tg is typical for glasses and liquids, respectively. The thermal conductivity of glasses is normally small with only a weakly positive temperature dependence, and that of liquids is equally small but temperature independent, or with a weakly negative temperature dependence. 44,45 This temperatureindependent, or amorphous-like, κ is in sharp contrast to the strong negative temperature dependence, κ ∼ T −1 , typically observed for polycrystalline material at corresponding temperatures. As shown in Figure 1, κ(T ) is almost temperature independent and the behavior remains virtually unchanged at the 0.1 and 0.48 GPa isobars. This is in accord with Einstein’s theory based on heat transport by localized excitations, 46 which sets a lower limit for κ and leads to the concept of minimum thermal conductivity. 47 In the glassy state, ρCp shows a linear dependence, (∂ρCp /∂T )p ≈ 4000 Jm−3 K−2 , whereas it is almost independent of temperature in the supercooled liquid state. The latter shows that the density of the


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Figure 1: (Color online) (a) Heat capacity per unit volume and (b) thermal conductivity for the liquid, supercooled liquid (SCL) and glassy states of TPP plotted against temperature at: 0.10 GPa (stars) and 0.48 GPa (triangles). Data were measured under nominally isobaric conditions during cooling (open symbols) and subsequent heating (gray symbols). The solid curves represent data smoothed using spline interpolation.



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liquid increases to about the same extent as Cp decreases on cooling. Values of Cp of the liquid and glassy state in the temperature range 300 to 150 K, assuming pressure independent ρCp and calculated using the density data of Ferrer et al., 48 agree to within 5 % with previous calorimetric results done at the equilibrium vapor pressure. 13,49 With the same assumption and density data of Demirjian et al., 15 the results of the glacial state in the 200 to 150 K range agree to within 5 % with literature data. 13,49 The irreversible transformation from the supercooled liquid state to the glacial state of TPP was studied at 0.1, 0.48 and 0.5 GPa isobars. The metastable glacial state was produced by the commonly used protocol, i.e. the sample was first cooled rapidly to below Tg and thereafter heated to a temperature above Tg where it was kept until the transformation was complete. Accordingly, the thermal properties was measured during isothermal aging of the sample after it had been heated with a rate ≈0.3 K min−1 from below Tg to a temperature about 15 K higher than Tg . The results for the changes of ρCp and κ are plotted against time in Figure 2. The changes as a function of time: ∆κ(t) = κ(t) − κSCL and ∆(ρCp )(t) = (ρCp )(t) − (ρCp )SCL , are the differences between measured values, κ(t) and ρCp (t), of the sample and the (initial) values for the supercooled liquid state: κSCL and (ρCp )SCL . The thermal property data reveal three time-intervals with different behavior during the annealing experiment. The first interval shows an aging process in which the results reflect the time-independent thermal properties of the supercooled liquid. The intermediate interval shows the transformation, and the final part establishes the stationary thermal properties of the metastable glacial state. As shown in Figure 2, the results at the three pressures are qualitatively similar with an initial dwell time of about 1 h at 0.1 GPa, 16 h at 0.48 GPa and 50 h at 0.5 GPa, without detectable changes. Thereafter, ρCp starts to decrease, and the decrease continues during several hours until the change levels off, which apparently marks the completion of the transformation. The change in ρCp is almost monotonic but the curve shows a weak


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bend at about half the transformation range. The change in κ is more complex with an initial increase. After a while, the κ increase ceases and changes to a decrease, which is most clearly seen in the data measured at the two highest pressures (Figure 2). Finally, κ(t) again increases and levels off at a higher value than the initial one. The minimum of κ(t) is correlated with the weak bend in the data of ρCp . (Heating to, or annealing at, higher temperatures induces an abrupt increase in κ , without an intermediate minimum, which is likely due to direct crystallization to a semicrystalline state.) The formation of the new state from the supercooled liquid leads ultimately to an increase in κ and a decrease in Cp . These changes are both consistent with the known growth of nanocrystals, but the non-monotonic change in κ suggests a more complex time-evolution of the microstructure than simply nucleation and growth of crystals, which would lead to monotonic increase of κ. That is, the results, which show an intermediate minimum in κ, require a kinetic model which includes, at least, two microscopically distinct processes. The current understanding of the microstructure in the glacial state of TPP also requires that the effect of "locally favored structures" or, in Kivelson and co-workers’ terminology, "preferred local structure" 3,50 is taken into account in such kinetic model. It has been suggested that locally favored structures nucleate and grow (NG) during the transformation at our conditions (well above Tg ), and that the growth eventually ceases due to geometrical constraints and the associated built-up of strain. It has also been deduced that the ultimate cluster size of a few nanometers depends on temperature, 13,34 and therefore it likely also depends on pressure, which is another variable in our experiments. In a recent model, 16,38 it is inferred that the LLT and growth of nanocrystals occur concurrently, or almost concurrently, and that crystals grow inside liquid 2. The growth of crystals inside an amorphous-like solid, or an extremely viscous liquid, may explain the unusual results of κ(t). We have illustrated the model schematically in the images depicted in Figure 2. This time-evolution of the microstructure is consistent with the results for κ. The initial increase in κ is due to the growth of amorphous-like solid domains with locally favoured structures and nanocrystals, i.e. visu-


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Figure 2: (Color online) Temporal change of the heat capacity per unit volume (a) and the thermal conductivity (b) of TPP for pressures of: 0.10 GPa (red), 0.48 GPa (blue) and 0.50 GPa (dark yellow) plotted against annealing time during the irreversible transformation of the supercooled liquid to the glacial state at fixed temperatures of 237 K, 294 K and 295.3 K, respectively. The arrows show the final changes. The dot lines indicate the time of the anomalous minimum in . The images on the right are tentative visualizations of the microstructure during the different times indicated by the numbers: light blue - supercooled liquid, gold- amorphous-like solid with low molecular mobility, green-nanocrystals and whiteinterfaces or strained domains, which can kinetically freeze and unfreeze on temperature cycling providing slightly higher thermal boundary resistance in the frozen state. 12 ACS Paragon Plus Environment

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alization (1) in Figure 2, but as these reach close to their initially limiting sizes, the ordering process gradually ceases (2). The growing strain at the boundaries between amorphous-like solid domains and nanocrystals causes increased thermal resistance and, thus, a decrease of κ, which reaches a minimum at maximum strain (3). But as nanocrystals and the locally favored structures apparently slowly agglomerate to their ultimate sizes through a second, subsequent, process, κ increases and finally levels off at a higher level (4). This kinetic model with a second process in which locally favored structures and, perhaps, nanocrystals agglomerate into slightly larger entities agrees well with the kinetic model suggested by Mizukami et al. 13 and Schwickert et al.. 34 But since the heat capacity decreases by almost the same amount during this latter process, it shows that the liquid to solid transformation proceeds further with about the same amount of liquid transforming into amorphous-like solid of locally favoured structures, with internal growth of nanocrystals. The kinetics and slightly higher temperature of the process observed in our experiment at 0.1 GPa are in good agreement with previous results at atmospheric pressure. For example, Ha et al. 3 wrote that "If a liquid sample of TPP is quick-quenched (in a matter of minutes) to a temperature in the range 225-213 K and held at that temperature, the sample gradually becomes turbid, then nearly opaque (in a matter of hours), and then clear again (in a time about twice the time to maximum opacity)." It is reasonable to associate the onset of turbidity with the start of the transformation. The opacity indicates an intermediate state, which is inhomogeneous. Although it is not certain, it may very well be associated also with strong phonon scattering and, thus, the minimum in κ. Finally, as the inhomogeneities gradually diminish as amorphous-like solid domains and nanocrystals aggregates into larger entities, κ increases and levels off at a slightly higher value. This model accounts well for the unusual changes in κ during the transformation. We cannot, however, completely exclude that the local maximum in κ is, at least partly, due to an increase in the relaxation time of the α-relaxation during the transformation. This would gradually push the artificial peak in κ to higher temperatures and eventually into



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the temperature range of our annealing experiment. This possibility of an artificial peak in κ versus time was discussed by Venkateshan and Johari, 51 who reported a similar nonmonotonic behavior of κ(t) of a polymerizing liquid. Negative evidence for assigning the local maximum in κ of TPP versus time entirely to the artificial peak is that we do not observe an increased error in our fitting routine, which normally accompanies the artificial features. Moreover, the artificial part of κ is always positive, and the subsequent minimum value of κ is in one case lower than the initial value for the supercooled liquid (Figure 2), which indicate that the decrease from (2) to (3) in Figure 2, is not fully explained by the decreasing size of the artificial peak as the transformation proceeds. We also find the final microstructural glacial state of Schwickert at al. 34 and Mosses et al. 16 of amorphous-like solid (with nanocrystals) separated by interfacial liquid consistent with our results for κ (T) of the glacial state. As the glacial state is heated (Figures 3 and 4), κ(T) shows a reversible (Figure 4), step change in κ. We note that this is a new characteristic feature of the glacial state, which is distinct from the known behavior of κ on heating liquids and glasses as well as crystals. If we account for the higher pressure,then the broad step in κ agrees well in temperature with the equally broad step increase in capacitance observed on heating the glacial state at 1 atm (Figure 7 in Ref. 13). Moreover, as shown in Figures 3 and 4, the data for ρCp show a broad step increase characteristic of a (broad) glass transition. These results show the kinetic unfreezing of a process in the glacial state. Mizukami et al. 13 attributed the process to an α-relaxation process, with a cluster-size dependent relaxation time. We surmise that the process is due to the inter-cluster liquid suggested in the microscopic model by Schwickert at al., 34 with a broad relaxation time distribution due to interfacial effects caused by amorphous-like solid domains and nanocrystals. At the end of the liquid to glacial transformation, the relative amount of the interfacial liquid, with longer relaxation time due to the interfacial effects, increases simultaneously as the amount of bulk liquid diminishes. This accounts for the broad glass transition range and small heat capacity increase, and the temperature upshift of about 10 K (Figures 3 and 4). The changes are


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reminiscent of those for glass transitions of cross-linked polymers in which the artificial peak in κ diminishes, becomes broader, and moves to higher temperatures with increasing degree of cross-linking. 52 This suggests that interfacial effects, or something equivalent, induce a similar restraining effect as a high degree of cross-links in polymers, which causes the artificial peak in κ to vanish as here at Tg of the glacial state. The step in the heat capacity at the glass transition of the glacial state prior to crystallization at 0.1 GPa and 0.5 GPa isobars is about 13% and 40% of that for the supercooled liquid (1) at Tg , suggesting that fair amount of the interfacial liquid still remains after the liquid to glacial state transformation, or else that also clusters take some part in the glass transition prior to crystallization. Because of suppressed crystallization tendency at high pressures, it is possible to follow the glacial state to higher temperatures above Tg at 0.5 GPa, which reveals an even larger reversible increase in κ and ρCp . The behavior is smeared for a glacial state formed at 0.1 GPa, and subsequently pressurized from 0.1 GPa to at 0.5 GPa, whereas the glacial state formed at 0.5 GPa show a more distinct two-step increase in κ on heating, which can be attributed to kinetic unfreezing of untransformed (interfacial) liquid and amorphous-like solid, respectively. On further heating above 330 K, the samples crystallized irreversibly (not shown in the figure). The weak transition in the glacial state is obviously a glass transition, but at a normal glass to liquid transition there is typically no increase in κ on heating. The step increase in κ of the glacial state is small but significant and reversible, as shown by the results on temperature cycling (Figure 4). On the basis of the microstructural model, we conclude that the kinetic unfreezing of interfacial liquid and, at higher temperatures, amorphous-like solid domains of locally favoured structures reduces strain, and therefore also phonon-boundary scattering. The boundary resistance thus changes reversibly as the interfacial liquid (and clusters) freezes and unfreezes on temperature cycling. Another possibility is that the lowtemperature step of the two-step increase in κ, is due to the kinetic unfreezing of an internal process in the amorphous-like solid, e.g. a molecular rotation, with a relaxation time which is cluster-size dependent, as suggested by Mizukami et al. 13 In that case, the additional high



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0.18

0.16

0.14 150

200

250

300

T(K)

Figure 3: (Color online)(a) Heat capacity per unit volume and (b) thermal conductivity of the glacial state of TPP plotted against temperature at: 0.10 GPa (red), 0.48 GPa (blue) and 0.50 GPa (black). Data were measured on cooling and subsequent heating under nominally isobaric conditions. Grey arrow indicates the change measured on isothermal pressurization at 237 K of the glacial sample formed at 0.1 GPa and 237 K. The black line represents the subsequently measured data on heating of the glacial sample at 0.5 GPa, after it had been first cooled to low temperatures. The boxes indicate transformation ranges of the glacial state.


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temperature step observed on heating at 0.5 GPa must be due to some other, unknown, process. It should be noted that the difference in temperatures for the increase in ρCp and κ, where the latter observed at a about 18 K lower temperature (see Figure 4), is consistent with our understanding of the features. The increase in ρCp is observed when the relaxation time of the process is sufficiently short to (almost) attain thermal equilibrium despite the rapid temperature rise of the probe (150 K min−1 , see experimental), i.e. when the relaxation time is 0.3 s or less. 41 The increase in κ is, however, due to the decrease of elastic strain and the concomitant decrease in phonon scattering as the glassy liquid kinetically unfreeze on the time-scale of the heating rate of the surrounding (about 0.3 K min−1 ), i.e. when the relaxation time is about 102 s or less. The 103 -times longer time-scale associated with the increase in κ is therefore consistent with its occurrence at lower temperature than the increase in Cp . If instead the process contributed directly to heat transport, like a phonon mode, then the increase in κ would be observed at the same temperature as the increase in Cp . The results for the kinetics of the transformation (Figure 2) show that the overall process slows down with an increase in pressure. Moreover, the ultimate change in κ, ∆κ(t = ∞), is independent on pressure, and the value, ∆κ=0.0085±0.005 W m−1 K−1 , is ten times less than that for the similar process reported for n-butanol at 120 K (∆κ=0.081±0.01 W m−1 K−1 ). 45 Furthermore, the value for ∆(ρCp )(∞) of TPP is about the same as the heat capacity step at Tg . That is, the heat capacity of the glacial state is comparable to that of the glassy state. We also note that the reduced crystallization tendency upon densification of liquid TPP corroborates Mierzwa et al’s 19 similar finding in their dielectric high-pressure studies of TPP. The subsequently measured κ and ρCp of the glacial state are plotted against temperature in Figure 3. The isobaric behavior provides information about the microstructure, and the lack of large glass transition features in the data for the glacial state at 0.1 GPa shows



1.8

1.6

-3

-1

C (MJ m K )

(a)

p

1.4

1.2

1.0

-1

)

0.210

(b)

0.205

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(W m K

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0.200

0.195

0.190

0.185 200

250

300

350

T(K)

Figure 4: (Color online) Heat capacity per unit volume and (b) thermal conductivity plotted against temperature for the glacial state on temperature cycling at 0.5 GPa. The increase of ρCp and κ on heating, indicated by the vertical arrows, show the kinetic unfreezing and freezing of processes in the glacial state. On further heating above 320 K, the sample crystallizes.


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that the state does not consist of appreciable amount of liquid 1. That is, the glacial state cannot be a state composed of nanocrystals embedded in a matrix of mainly non-transformed supercooled liquid. The weak temperature dependence of κ indicates that it could be a fully amorphous solid but, as argued in more detail above and below, the results for the glacial state as a function of both temperature and pressure suggest that it is a mixture of an amorphous-like solid and nanocrystallites with some amount of interfacial liquid. The thermal conductivity behavior of the glacial state κgl (T ) is similar to that of the glassy state κg (T ) but the magnitude is slightly larger: ∆κgl (T ) = κgl (T ) − κg (T ) = 0.008 ± 0.002 W m−1 K−1 . From isothermal data (not shown), we deduce that κ of the glacial state varies linearly with pressure: (∂κ/∂p)T = 0.114 W m−1 K−1 GPa−1 , which is only slightly larger than that of the glassy state. Thus, according to these results, κgl (T ) is only weakly dependent of temperature and pressure within the pressure range up to 0.5 GPa and for temperatures down to 100 K. However, the value and behavior of κ and ρCp of the glacial state do not seem to be independent of the thermal history. In the case when the state formed at 0.1 GPa was pressurized up to 0.5 GPa, ρCp increased weakly with increasing pressure. But if we instead compare values of the state formed by annealing at 0.1 GPa, with those for the state formed by annealing at 0.48 GPa, then ρCp appears to decrease with increasing pressure. Although, data for ρCp of this method must be evaluated with care keeping in mind the relatively high uncertainty and its sensitivity to poor thermal contact, this is an odd occurrence. Moreover, the same comparison using the data for κ shows that the glacial state formed at 0.48 GPa has significantly higher κ than that of the glacial state, which was formed at 0.1 GPa and thereafter pressurized up to 0.5 GPa (Figure 3). As discussed quantitatively below, this difference is well outside the imprecision of the method, which shows that the states formed at different pressures are not identical. Unlike an ordinary glass, which is typically formed by cooling or pressurizing through a glass transition, the glacial state is the result of a transition from a liquid into a solid at constant temperature and pressure. The lack of a significant glass transition on subsequent



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cooling implies that the glacial state is not simply a supercooled liquid, which spontaneously transforms into a crystalline state when it is heated to higher temperatures. At crystallization, the heat capacity did not change, whereas the thermal conductivity increased abruptly by the amount ∆κcr (T ) = κcr (T ) − κgl (T ) = (0.036 ± 0.002) W m−1 K−1 . Since the crystallization transition occurs just above the transformation between the supercooled liquid state and the glacial state, these transformations could be related. Indeed, it has been suggested that the glacial transformation is due to nucleation of the crystalline phase. 22–28 As mentioned above, it now seems generally accepted that the ultimately formed glacial state is a two-component state consisting of mainly an amorphous-like solid with small embedded crystalline domains. 16,45,53 We therefore consider if a two-component state, in which the amount of the components varies with the conditions of the transformation, is consistent with the thermal properties. Assuming that heat is conducted along parallel paths, κ of components in a medium is additive. It follows that a two-component medium consisting of glassy (amorphous-like solid domains) and nano-crystalline material can be approximated as a weighted sum of the thermal conductivities of the glass κg (T, p) and the crystalline phase κcr (T, p) according to the following expression: 54

κgl (T, p) = (1 − xcr )κg (T, p) − xcr κcr (T, p),

(1)

where xcr is the volume concentration of the crystalline phase. According to eq. 1, xcr can be calculated from the values of thermal conductivity jumps κgl and κcr at the transformations to the glacial state and crystal phase, respectively.

xcr = ∆κgl /(∆κgl + ∆κcr )

(2)

Using experimental data of ∆κgl and ∆κcr in eq. 2, we find xcr =17% ± 5% at 0.1 GPa and 0.48 GPa, which is in good agreement with literature data for xcr . 25,27,28 As mentioned above, we did one experiment where the glacial state was pressurized isothermally from


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0.10 GPa to 0.50 GPa at T = (236.6 ± 1.0) K. The subsequently measured κ and ρCp of the glacial state are plotted against temperature in Figure 3. During the compression, ρCp remained almost constant, but κgl increased by 20%, which gives a relatively small pressure dependence of (∂κ/∂p)T = 0.078 W m−1 K−1 GPa−1 . This result deviates from the isobaric data, which suggest a significantly larger value of 0.114 W m−1 K−1 GPa−1 . As a consequence of this difference, κgl of the compressed sample was lower at 0.5 GPa and 237 K than κgl of the state produced by first annealing at 0.48 GPa and 294 K and then cooling to 237 K. The accelerated increase of κ with increasing temperature at T >274 K suggests densification and improved interfacial contact between nanocrystals. Still, a difference remained up to temperatures above 295 K, the annealing temperature for glacial state produced at 0.48 GPa, which shows that the states differed in microstructure. A reverse experiment, i.e. a glacial state formed at 0.5 GPa and room temperature, and thereafter depressurized to 0.1 GPa at about 237 K, showed about 5% higher κ than the glacial state formed at 0.1 GPa. The higher κ of the state formed near 0.5 GPa than that formed at lower pressures, indicates a somewhat higher density, slightly more clusters/crystals and/or that these have larger sizes. The results for the pressurized glacial state can be explained in terms of a heterogeneous glacial state. More specifically, a two-component mixture in which the relative amount and microstructure depends on the conditions of the transformation from the supercooled liquid, or changes upon pressurization. As discussed here, it can consist of a major fraction of an amorphous-like solid and a minor fraction of a crystalline phase. This hypothesis is consistent with the similar conjecture that the ultimately formed glacial state of n-butanol is a mixture of two different coexisting states, a crystal phase embedded in a disordered, glassy state. As a consequence, two glacial states of TPP obtained by different pressure-temperature-time conditions are not identical, but differ because of slightly different degree of crystallinity and microstructure, e.g. because crystals and clusters do not grow to the same sizes. Finally, we briefly compare the results with those of other purported LLTs or amorphousamorphous transitions. Only two of these have been studied through κ measurements, viz.,



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(i) n-butanol and (ii) the amorphous ices: high-density and low-density amorphous ices (HDA and LDA), which are produced under high pressure conditions. At the HDA to LDA transition, κ increases as it does here for the liquid to glacial transformation of TPP. But the growth of nanocrystals during the transformation in TPP precludes definite determination of κ for the conjectured liquid 2 of TPP. It is, however, highly unlikely that liquid 2 would have higher κ than that of the glacial state because of the normal increase of κ with increase in crystallinity. It implies that the thermal conductivities, as well as the densities, of the liquid states of TPP are not widely different from each other, which is distinct from the case of ice. At the HDA to LDA transition, the density decreases abruptly by about 20 % 55 concurrently as κ increases, ∆κ=0.57±0.02 W m−1 K−1 near 1 bar. 56 This is a much larger increase than that found for both TPP, ∆κ=0.0085±0.005 W m−1 K−1 at 237 K and 0.1 GPa, and nbutanol, ∆κ=0.081±0.01 W m−1 K−1 at 120 K and 1 atm. 45 Moreover, the transition in ice is reversible in the sense that pressure cycling in the 0 to 0.5 GPa range at 130 K, produces the LDA state below 0.05 GPa on depressurization and the HDA state above 0.4 GPa on repressurization. The transformations are likely driven by the density difference between the two states as the change in Gibbs energy G of a phase is given by (∂G/∂p)T = V , where V is the volume. Thus, if the density of the conjectured liquid 2 of TPP is lower than that of liquid 1, then pressurization would energetically favor a reverse transformation. However, we found no indication of a reverse transformation on pressurization of the glacial state of TPP. We can conclude that if these transformations are indeed LLTs or amorphous-amorphous transitions, the results suggests that κ increases in all cases, but that the increase and the nature of the transition differ significantly between the case of ice and TPP.

Conclusions The unusual behaviors of the thermal conductivity during the liquid to glacial state transformation, and on subsequent temperature cycling of the glacial state are consistent with


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the microstructural models recently discussed by Shimizu et al. 6 and Mosses et al. 16 In particular, the results for κ during the transformation suggest two different microstructural processes, which ultimately lead to an increase in κ. From the model we identify the initial process as concurrent growth of amorphous-like solid domains and nanocrystals, and the second as agglomeration and further growth of these into larger entities. An intermediate minimum in κ arises when crystals grow only in amorphous-like solid domains, which causes a limit in growth and a gradually increasing strain at the boundaries. Subsequent agglomeration and growth into larger entities reduces the boundaries leading to an ultimate increase of κ. Temperature cycling of the glacial state shows a reversible step decrease and increase in κ, which are associated with kinetic freezing and unfreezing, respectively, of a relaxation process in the glacial state. We surmise that this process is due to a glass transition of interfacial liquid, which reduces the thermal boundary resistance as it transforms into the liquid state. The step increase in κ at the kinetic unfreezing of the glacial state distinguishes the state from normal glasses for which κ typically remains constant, or decreases slightly, on heating through the glass transition.

Acknowledgement This work was supported by the Swedish Research Council, grant no. 621-2012-3336. We acknowledge financial support for equipment from Carl Trygger Foundation and Magnus Bergvalls foundation.

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