Article pubs.acs.org/JPCB
Vivid Manifestation of Nonergodicity in Glassy Propylene Carbonate at High Pressures Igor V. Danilov,†,‡ Elena L. Gromnitskaya,† and Vadim V. Brazhkin*,† †
Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk, Moscow 142190, Russia Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region 141700, Russia
‡
ABSTRACT: As glasses are nonergodic systems, their properties should depend not only on external macroparameters, such as P and T, but also on the time of observation and thermobaric history. In this work, comparative ultrasonic studies of two groups of molecular propylene carbonate glasses obtained by quenching from a liquid at pressures of 0.1 and 1 GPa have been performed. Although the difference in the densities of the different groups of glasses is small (3−5%), they have significantly different elastic properties: the difference in the respective bulk moduli is 10−20%, and the difference in the respective shear moduli is 35−40% (!). This is due to the “closure of nanopores” in the glass obtained at 1 GPa. The pressure and temperature derivatives of the elastic moduli for these groups of glasses are also noticeably different. The glass-transition temperatures of glasses from different groups differ by 3−4 K. The character of absorption of ultrasound waves near the glass-transition temperature also differs for different groups of glasses. The differences in the behaviors of these groups of glasses disappear gradually above the glass-transition temperature, in the region of a liquid phase. Glasses with a wide diversity of physical properties can be obtained using various paths on the (T,P) diagram.
■
in temperature and pressure, several fictive temperatures corresponding to the “freezing” of certain contributions to relaxation, as well as several order parameters, are introduced.4,5 As glass is a nonergodic system, the properties of glasses should depend not only on external macroparameters, such as P and T, but also on the thermobaric history.6,7 The structure and physical characteristics of glasses depend on the path and time of obtaining glasses in the (T,P) coordinates. In particular, glasses obtained from liquids at different cooling rates have different fictive temperatures,8 which affect the microstructure, local density, and relaxation time of the glasses.9,10 The baric processing history also affects the structure and hardness of glasses,11,12 as well as their glass-transition temperature, Tg.13,14 Glass transition is sometimes considered an analogue of second-order phase transition. The Erenfest relation for usual second-order phase transitions provides the condition
INTRODUCTION Simple liquids and gases are ergodic systems; that is, their average characteristics over time are equivalent to their average characteristics over phase, and their properties at times of measurement that are not too small are certainly determined by external parameters. A nonequilibrium metastable state of liquids and gases can exist for only very short times. Crystals are conditionally ergodic systems; that is, relaxation within a given crystal lattice occurs very rapidly, but there are additional minima in the configuration space that correspond to other metastable crystal lattices and are separated by very high energy barriers. In some cases, a metastable crystalline state can exist without relaxation for a very long time, for example, a diamond under normal conditions. Many molecular materials and all organic compounds are also conditionally ergodic systems; that is, their properties are reversible at available times and vary unambiguously only in a certain range of temperatures and pressures.1,2 Glasses and amorphous solids are good examples of metastable nonergodic systems. Glasses are fundamentally not in an equilibrium state, and the properties of glasses can vary with time at fixed external parameters (annealing or aging of glasses).3 In contrast to metastable crystal phases, in which only several possible energy minima exist in the configuration space, glasses have a continuum of such minima and, correspondingly, a continuous spectrum of relaxation times. The broad spectrum of relaxation times in glasses is due to a broad distribution of short- and medium-range order parameters in glasses. To approximately describe the behaviors of glasses with variations © XXXX American Chemical Society
Π=
ΔCpΔκT TgVg(Δα)2
=1
where ΔCp, ΔκT, and Δα are the changes in the heat capacity, compressibility, and thermal expansion coefficient during transition and Tg and Vg are the transition temperature and specific volume, respectively. This condition is valid when only one order parameter, together with pressure and temperature, is sufficient for the description of a system.5 In the case of a Received: May 23, 2016 Revised: July 11, 2016
A
DOI: 10.1021/acs.jpcb.6b05188 J. Phys. Chem. B XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry B liquid−glass transition, it is necessary to use several order parameters, and the Davies−Jones inequality, Π > 1, is satisfied.15 The condition Π > 1 means that the state of the glass is ambiguously determined by the pressure and temperature and that the structure and properties of the glass can change significantly after a closed cycle on the (T,P) plane. This is most clearly manifested when a part of this cycle passes through the region of a liquid phase. Configuration changes in a glassy state are “suppressed” and the pressure-induced changes in the structure are insignificant, whereas configuration changes are possible in a liquid state and the response of the structure to the applied pressure can be significant. As a result, glasses obtained by high-pressure cooling of liquids should have a higher density and, correspondingly, a different structure of medium-range order as compared to glasses compressed at the same pressure at low temperatures. There are only a few comparative studies of the properties of glasses obtained through different paths on the (T,P) diagram. A surprisingly large effect was detected in glassy polystyrene.16 The rate of the pressure-induced increase in the glass-transition temperature for glassy polystyrene obtained at atmospheric pressure appeared to be dTg/dP = 74.2 K/kbar, which is more than two times that for glass obtained from a liquid at a high pressure, dTg/dP = 31.6 K/kbar . However, the temperature and pressure dependences of the specific volume presented in this work indicate quite a sharp structural transformation in a polystyrene melt at a pressure of 0.05−0.2 GPa, and the change in the slope of the glass-transition curve is not directly associated with nonergodicity effects. It has recently been shown12 that glasses with the same chemical composition and density but different thermal and pressure histories have different short- and medium-range structures and macroscopic properties. Experiments and computer simulations show that quenching pressure has a larger effect on the medium-range structure (and, correspondingly, on the density), whereas annealing time has a larger effect on the short-range structure (and, correspondingly, on the hardness, which is determined by the network rigidity in the short-length scales). The elastic moduli of glasses are very sensitive to changes in their densities and the structures of short- and medium-range orders.17 It is of interest to compare the pressure and temperature dependences of the elastic properties of glasses obtained through different paths on the (T,P) diagram. As far as we know, such studies have not yet been performed. In this work, we perform a comparative ultrasonic study of the elastic properties of glassy propylene carbonate obtained through various (T,P) paths. Propylene carbonate is a wellknown molecular glass former (Tg = 158 K) studied previously.18,19 Because of its simple structure, compactness, and simple van der Waals intermolecular interactions and the absence of hydrogen bonds, propylene carbonate is a convenient model material. We studied liquid and glassy propylene carbonate by dielectric spectroscopy (up to 4.2 GPa) and the ultrasonic method (up to 1.7 GPa).20 The experimental results implied that many relaxation and elastic properties of propylene carbonate could be qualitatively described on the basis of the Lennard-Jones potential. However, a large Poisson coefficient of glassy propylene carbonate indicates a noticeable contribution from noncentral forces to intermolecular interactions. Relaxation in supercooled liquid propylene carbonate has a simple form up to the highest pressure, and the glasstransition temperature increases almost linearly with pressure.20
It is obvious that structures of short-range order in liquid propylene carbonate do not change at pressures of up to 4 GPa, and the liquid is densified owing to the “closure of nanopores” and “degradation” of medium-range order. Glassy propylene carbonate is a very convenient material for studying nonergodicity effects. In this work, glassy propylene carbonate was obtained by two methods. In the first method, glasses were obtained by the quenching of a liquid from room temperature to 78 K at 0.1 GPa (low-pressure glass (LPG)). The second method of obtaining glasses involves compression of a liquid at room temperature up to 1 GPa, quenching of the liquid to 78 K at 1 GPa, and subsequent decompression to 0.1 GPa (highpressure glass (HPG)). Then, a comparative analysis of the pressure and temperature dependences of the elastic properties of these glasses was performed.
■
EXPERIMENTAL METHODS Measurements were carried out with a low-temperature ultrasonic piezometer in the pressure range up to 1.1 GPa and temperature interval of 78−295 K using the method described in previous works.21,22 The investigated sample was placed in a thin-walled Teflon cylinder whose ends were closed with two copper caps (D ∼ 18 mm, h ∼ 7−8 mm). The sample was abruptly cooled to the temperature of liquid nitrogen at a rate of 15−20 K/min. Ultrasonic measurements were carried out on an original setup based on the PXI platform (National Instruments). To generate and detect ultrasonic waves, we used lithium niobate (LiNbO3) piezoceramic plates of the y and x cuts, with resonance frequencies of 5−10 MHz. The accuracy of measurement of the transit time of an ultrasonic signal was ∼1 ns. A change in the length of the sample was determined with an accuracy of up to 0.001 mm using a dial-type micrometers remote from a low-temperature area. The density of the compressed sample was determined from a change in the length of the sample in reference to the initial total length of the sample and its initial density. The accuracy of the ultrasound measurements of density and velocity was naturally limited by the accuracy of measurement of the initial total length of the sample. Measurements and errors have been described in detail earlier;20 here, we emphasize that the accuracy of our relative measurements with experimental statistics was much higher.
■
EXPERIMENTAL RESULTS AND DISCUSSION The transit time of longitudinal and shear ultrasonic waves, as well as the length of the sample, was measured with an increase and decrease in pressure. The velocities of the ultrasonic waves and the density of the sample were calculated from these data. Figure 1 shows the pressure dependences of compression, the adiabatic bulk modulus, the shear modulus, and the Poisson coefficient of low- and high-pressure propylene carbonate glasses, calculated from the experimental dependences of the velocities of ultrasound waves at T = 78 K. The equation of state, V = V0(P), was obtained by integrating the experimental pressure dependence of the inverse bulk modulus. The density of HPG at a temperature of 78 K and at atmospheric pressure (1.37 g/cm3) is 5% higher than the density of LPG (1.3 g/ cm3); the difference between these densities at a pressure of 1 GPa is 3%. The pressure dependences of the elastic characteristics and compression of propylene carbonate are almost linear except for the Poisson coefficient of HPG. The pressure dependences B
DOI: 10.1021/acs.jpcb.6b05188 J. Phys. Chem. B XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry B
Figure 2. Temperature dependences of the (a) longitudinal, vl, and (b) transverse, vt, ultrasonic wave velocities under isobaric heating at 0.1 and 1 GPa. The dashed line corresponds to a significant drop in ultrasonic transmission at the glass−liquid transition.
the transverse velocities, vt, of the shear ultrasonic wave in LPG and HPG at low temperatures are significantly different (≈11%), in agreement with a noticeable difference between shear moduli G. Above the glass-transition temperature (167 K) in a viscous-liquid region, the velocities of shear waves begin to approach each other. The behavior at a high pressure of P = 1 GPa is similar, but a significant difference in both the velocities, vl and vt, holds at all temperatures because the glasstransition temperature at a pressure of 1 GPa is high (233 K) and melts are in a viscous state up to room temperature. The adiabatic bulk modulus, Bs, and shear modulus, G, of polypropylene carbonate subjected to isobaric heating were calculated from experimental data on the ultrasonic velocities (Figure 3). It is seen that both moduli for different groups of glasses become identical in a liquid-phase region. Kinks on the experimental dependences of the shear modulus correspond to kinks on the temperature dependences of the transverse wave and are associated with the glass−liquid transition. The softening temperatures, Tg, of glasses at high pressures differ by 3−4 K; these temperatures are higher for LPGs. The obvious reason for this relation is that the stable phase above the glass-transition temperature is a high-pressure liquid, and the LPG having a medium-range order structure different from the structure of this liquid can be metastably overheated above the equilibrium glass-transition temperature. As already mentioned, propylene carbonate has very simple behavior under compression: The glass-transition temperature increases linearly with pressure up to 4 GPa and the spectrum consists of only α-relaxation.20 It means that the short-range order structure of liquid propylene carbonate is not changed at 1 GPa. Thus, one can suggest that only an intermediate-range order structure (first sharp prepeak, etc.) significantly changes with pressure. In addition to the velocities of ultrasound waves, we studied the attenuation of both longitudinal and shear ultrasonic waves. Figure 4 shows the transmission (a quantity inverse to
Figure 1. Pressure dependences of (a) the equation of state, (b) adiabatic bulk modulus BS, (c) shear modulus G, and (d) Poisson’s ratio for glassy propylene carbonate at 78 K. The closed blue and open red squares correspond to HPG and LPG, respectively.
for both groups of glasses are completely reversible. Although the difference in the densities is rather small, the glasses have significantly different elastic properties: the bulk and shear moduli for HPG are larger than those for LPG by 10−20 and 35−40% (!), respectively. One can propose that such a significant increase in elastic moduli is associated with the closure of nanopores in the liquid at 1 GPa and a corresponding change in the HPG structure. “Nanopores” in liquids are often associated with the so-called first sharp prepeak in the structure factor. Even several volume percents of “soft” nanoregions in a liquid or glass can significantly affect the elastic moduli. The pressure derivatives of the moduli are also larger for HPG: (dBS/dP)HPG,P=0 = 8.5, (dBS/dP)LPG,P=0 = 6, (dG/dP)HPG,P=0 = 1.4; (dG/dP)LPG,P = 0 = 1. The pressure derivatives of the bulk modulus and the Poisson coefficient for HPG indicate that the interactions in glasses obtained by highpressure quenching are almost central of a Lennard-Jones type, in contrast to those in LPGs. Comparative studies of two types of glasses were also performed, with isobaric heating of LPG and HPG at a low pressure of 0.1 GPa and high pressure of 1 GPa. Figure 2 shows the experimental isobaric temperature dependences of the velocities of longitudinal, vl, and transverse, vt, ultrasonic waves. All dependences exhibit a characteristic kink, corresponding to the glass-transition (softening) temperature of a given glass. The temperature dependences are reversible up to the glasstransition temperatures. It is noteworthy that the initial values of vl for LPG and HPG during the process of heating at a low pressure of 0.1 GPa are insignificantly different (≈4%), and differences disappear altogether at T > 120 K. These velocities obviously coincide in a relaxed liquid state. At the same time, C
DOI: 10.1021/acs.jpcb.6b05188 J. Phys. Chem. B XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry B
MHz for longitudinal and shear waves, respectively). Shear waves with frequencies ω > 1/τ (where τ is the relaxation time in the liquid) can still propagate. In a nonviscous liquid state, in which ω < 1/τ, only longitudinal ultrasonic vibrations are observed. It is interesting that the amplitude of the signal increases strongly before the softening of LPG (acoustic translucence). This effect is apparently due to the relaxation of stresses and “healing of defects”.20 This effect is not observed in HPG, likely because of the denser structure of this glass. To summarize, the elastic and relaxation properties of glassy propylene carbonate depend strongly on the thermobaric prehistory. In contrast to those of metastable crystals, the characteristics of glasses can be continuously varied over a wide range. Pressures of about 1 GPa are actively used in industry. Consequently, the properties of many molecular glasses can be purposefully changed by varying the parameters of their fabrication. In the future, it would be interesting and important to study the structure of liquid propylene carbonate under high pressure. Such a study is rather challenging as the substance is molecular low-Z compound; however, it is possible using powerful synchrotron sources.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected].
Figure 3. Temperature dependences of (a) shear modulus G and (b) adiabatic bulk modulus BS under isobaric heating at 0.1 and 1 GPa. Dashed lines are guides to the eyes.
Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS We are grateful to S.M. Stishov, M.V. Kondrin, and A.G. Lyapin for discussion of the results. This work was supported by the Russian Science Foundation (project no. 14-22-00093).
■
REFERENCES
(1) Brazhkin, V. V. Metastable Phases, Phase Transformations, and Phase Diagrams in Physics and Chemistry. Phys.-Usp. 2006, 49, 719− 724. (2) Brazhkin, V. V. Metastable Phases and ‘Metastable’ Phase Diagrams. J. Phys.: Condens. Matter 2006, 18, 9643−9650. (3) Feltz, A. Amorphe und Glasartige Anorganische Festkörper; Akademie-Verlag: Berlin, 1983. (4) Tool, A. Q. Relation between Inelastic Deformability and Thermal Expansion of Glass in Its Annealing Range. J. Am. Ceram. Soc. 1946, 29, 240−253. (5) Prigogine, I.; Defay, R. Chemical Thermodynamics; Wiley, 1954. (6) Gupta, P. K.; Mauro, J. C. The Laboratory Glass Transition. J. Chem. Phys. 2007, 126, No. 224504. (7) Mauro, J. C.; Loucks, R. J.; Gupta, P. K. Fictive Temperature and the Glassy State. J. Am. Ceram. Soc. 2009, 92, 75−86. (8) Angeli, F.; Villain, O.; Schuller, S.; Charpentier, T.; de Ligny, D.; Bressel, L.; Wondraczek, L. Effect of Temperature and Thermal History on Borosilicate Glass Structure. Phys. Rev. B 2012, 85, No. 054110. (9) Levelut, C.; Le Parc, R.; Faivre, A.; Champagnon, B. Influence of Thermal History on the Structure and Properties of Silicate Glasses. J. Non-Cryst. Solids 2006, 352, 4495−4499. (10) Ruta, B.; Baldi, G.; Chushkin, Y.; Rufflé, B.; Cristofolini, L.; Fontana, A.; Zanatta, M.; Nazzani, F. Revealing the Fast Atomic Motion of Network Glasses. Nat. Commun. 2014, 5, No. 3939. (11) Smedskjaer, M. M.; Youngman, R. E.; Striepe, S.; Potuzak, M.; Bauer, U.; Deubener, J.; Behrens, H.; Mauro, J. C.; Yue, Y. Irreversibility of Pressure Induced Boron Speciation Change in Glass. Sci. Rep. 2014, 4, No. 3770. (12) Smedskjaer, M. M.; Bauchy, M.; Mauro, J. C.; Rzoska, S. J.; Bockowski, M. Unique Effects of Thermal and Pressure Histories on
Figure 4. Temperature dependences of the transmission coefficients of (a) longitudinal and (b) transverse ultrasonic waves measured at different pressures. The solid blue and open red squares correspond to HPG and LPG, respectively.
attenuation) of an ultrasonic signal in the isobaric heating regime at pressures of 0.1 and 1 GPa. The amplitude of the signal in the glassy state depends weakly on the temperature; it decreases sharply at T > Tg and is not detected at 190−235 K (dashed lines in Figures 2 and 3). The maximum attenuation of the signal is observed when the α-relaxation peak of propylene carbonate passes through our experimental frequency (10 and 5 D
DOI: 10.1021/acs.jpcb.6b05188 J. Phys. Chem. B XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry B Glass Hardness: Structural and Topological Origin. J. Chem. Phys. 2015, 143, No. 164505. (13) Wondraczek, L.; Sen, S.; Behrens, H.; Youngman, R. E. Structure-Energy Map of Alkali Borosilicate Glasses: Effects of Pressure and Temperature. Phys. Rev. B 2007, 76, No. 014202. (14) Wondraczek, L.; Behrens, H.; Yue, Y.; Deubener, J.; Scherer, G. W. Relaxation and Glass Transition in an Isostatically Compressed Diopside Glass. J. Am. Ceram. Soc. 2007, 90, 1556−1561. (15) Davies, R. D.; Jones, G. O. Thermodynamic and Kinetic Properties of Glasses. Adv. Phys. 1953, 2, 370−410. (16) Quach, A.; Simha, R. Pressure-Volume-Temperature Properties and Transitions of Amorphous Polymers; Polystyrene and Poly (orthomethylstyrene). J. Appl. Phys. 1971, 42, 4592−4606. (17) Deschamps, T.; Margueritat, J.; Martinet, C.; Mermet, A.; Champagnon, B. Elastic Moduli of Permanently Densified Silica Glasses. Sci. Rep. 2014, 4, No. 7193. (18) Schneider, U.; Lunkenheimer, P.; Brand, R.; Loidl, A. Broadband Dielectric Spectroscopy on Glass-forming Propylene Carbonate. Phys. Rev. E 1999, 59, 6924−6936. (19) Wang, L.-M.; Velikov, V.; Angell, C. A. Direct Determination of Kinetic Fragility in Dices of Glassforming Liquids by Differential Scanning Calorimetry: Kinetic Versus Thermodynamic Fragilities. J. Chem. Phys. 2002, 117, 10184−10192. (20) Kondrin, M. V.; Gromnitskaya, E. L.; Pronin, A. A.; Lyapin, A. G.; Brazhkin, V. V.; Volkov, A. A. Dielectric Spectroscopy and Ultrasonic Study of Propylene Carbonate under Ultra-high Pressures. J. Chem. Phys. 2012, 137, No. 084502. (21) Stal’gorova, O. V.; Gromnitskaya, E. L.; Dmitriev, D. R.; Voronov, F. F. Ultrasonic Piezometer for the 0−2.0 GPa Pressure and 77−300 K Temperature Range. Instrum. Exp. Tech. 1996, 39, 880− 883. (22) Gromnitskaya, E. L.; Yagafarov, O. F.; Stalgorova, O. V.; Brazhkin, V. V.; Lyapin, A. G. Pressure-Driven “Molecular Metal” to “Atomic Metal” Transition in Crystalline Ga. Phys. Rev. Lett. 2007, 98, No. 165503.
E
DOI: 10.1021/acs.jpcb.6b05188 J. Phys. Chem. B XXXX, XXX, XXX−XXX
