Glass transition in chlorobenzene–decalin under pressure

Temperature Dependence of Structural Relaxation in Glass-Forming Liquids and Polymers

Understanding the microscopic mechanism of the transition of glass remains one of the most challenging topics in Condensed Matter Physics. What controls the sharp slowing down of molecular motion upon approaching the glass transition temperature Tg, whether there is an underlying thermodynamic transition at some finite temperature below Tg, what the role of cooperativity and heterogeneity are, and many other questions continue to be topics of active discussions. This review focuses on the mechanisms that control the steepness of the temperature dependence of structural relaxation (fragility) in glass-forming liquids. We present a brief overview of the basic theoretical models and their experimental tests, analyzing their predictions for fragility and emphasizing the successes and failures of the models. Special attention is focused on the connection of fast dynamics on picosecond time scales to the behavior of structural relaxation on much longer time scales. A separate section discusses the specific case of polymeric glass-forming liquids, which usually have extremely high fragility. We emphasize the apparent difference between the glass transitions in polymers and small molecules. We also discuss the possible role of quantum effects in the glass transition of light molecules and highlight the recent discovery of the unusually low fragility of water. At the end, we formulate the major challenges and questions remaining in this field.

Dynamics of linear molecules in water: Translation-rotation coupling in jump motion driven diffusion

We study by computer simulations, and by theory, the coupled rotational and translational dynamics of three important linear diatomic molecules, namely, carbon monoxide (CO), nitric oxide (NO), and cyanide ion (CN^-) in water. Translational diffusion of these molecules is found to be strongly coupled to their own rotational dynamics which, in turn, are coupled to similar motions of the surrounding water. In particular, we find that coupled orientational jump motions play an important role in all three cases. While CO and NO show similar features, CN^- exhibits certain differences. Our results agree well with the known experimental values of the diffusion coefficient. We examined the validity of hydrodynamic predictions and found them to be inadequate, particularly for rotational diffusion. A mode coupling theory approach is developed and applied to understand the complexity of translation-rotation coupling.

Distinguishing different classes of secondary relaxations from vapour deposited ultrastable glasses

Secondary relaxations persistent in the glassy state after structural arrest are especially relevant for the properties of the glass. A major thrust in research in dynamics of glass-forming liquids is to identify what secondary relaxations exhibit a connection to the structural relaxation and are hence more relevant. Via the Coupling Model, secondary relaxations having such connection have been identified by properties similar to the primitive relaxation of the Coupling Model and are called the Johari-Goldstein (JG) β-relaxations. They involve the motion of the entire molecule and act as the precursor of the structural α-relaxation. The change in dynamics of the secondary relaxation by aging an ordinary glass is one way to understand the connection between the two relaxations, but the results are often equivocal. Ultrastable glasses, formed by physical vapour deposition, exhibit density and enthalpy levels comparable to ordinary glasses aged for thousands of years, as well as some particular molecular arrangement. Thus, ultrastable glasses enable the monitoring of the evolution of secondary processes in case aging does not provide any definitive information. Here, we study the secondary relaxation of several ultrastable glasses to identify different types of secondary relaxations from their different relationship with the structural relaxation. We show the existence of two clearly differentiated groups of relaxations: those becoming slower in the ultrastable state and those becoming faster, with respect to the ordinary unaged glass. We propose ultrastability as a way to distinguish between secondary processes arising from the particular microstructure of the system and those connected in properties to and acting as the precursor of the structural relaxation in the sense of the Coupling Model.

New experimental evidence about secondary processes in phenylphthalein-dimethylether and 1,1'-bis(p-methoxyphenyl)cyclohexane

The slow secondary (beta) process of 1,1'-bis (4-methoxyphenyl) cyclohexane and phenolphthalein dimethylether has been investigated by dielectric spectroscopy. New experimental results about the pressure dependence of the two processes are reported, as well as new data about the dependence of the characteristic relaxation frequency on the cooling rate used to vitrify the system in isobaric conditions. Previous investigations on these systems suggested that the first one is not a true Johari-Goldstein relaxation and both processes should originate from the flip flop motion of the phenyl ring. The results herein reported evidence that the characteristic frequency of the beta process of phenolphthalein dimethylether is more sensitive to pressure variation and to the vitrification procedure than that of 1,1'-bis (4-methoxyphenyl) cyclohexane. Such results suggest an intermolecular origin for the secondary process in phenolphthalein dimethylether and an intramolecular origin for the other one, which do not completely agree with the previous interpretation. We evidence that the microscopic mechanism at the basis of these two processes is still an open question, which should be debated on the basis of new experimental investigations.

Fragility and thermodynamics in nonpolymeric glass-forming liquids

For nonpolymeric supercooled liquids, the empirical correlation m = 56Tg DeltaCp(Tg)/DeltaHm provides a reliable means of correlating dynamic and thermodynamic variables. The dynamics are characterized by the fragility or steepness index m and the glass transition temperature Tg, while thermodynamics enter in terms of the heat capacity step DeltaCp at Tg and the melting enthalpy DeltaHm. The combination of the above correlation with the 23 rule for the Tg/Tm ratio yields an expression, m = 40DeltaCp(Tg)/DeltaSm, which was rationalized as the correlation of the thermodynamic and kinetic fragilities. Defining a thermodynamic fragility via DeltaCp(Tg)/DeltaSm also reveals that the slopes in Kauzmann's original DeltaS(T)/DeltaSm versus T/Tm plot reflect the fragility concept [Chem. Rev. 43, 219 (1948)], so long as Tm/Tg = 1.5. For the many liquids whose excess heat capacity is a hyperbolic function of temperature, we deduce that the fragility cannot exceed m = 170, unless the Tg/Tm = 2/3 rule breaks down.

Correlation of primary relaxations and high-frequency modes in supercooled liquids. I. Theoretical background of a nuclear magnetic resonance experiment

The question regarding a possible correlation of the time scales of primary and secondary relaxations in supercooled liquids is formulated quantitatively. It is shown how this question can be answered using spin-lattice relaxation weighted stimulated-echo experiments, which are presented in an accompanying paper [A. Nowaczyk, B. Geil, G. Hinze, and R. Böhmer, Phys. Rev. E 74, 041505 (2006)]. General theoretical expressions relevant for the description of such experiments in the presence of correlation effects are derived. These expressions are analyzed by Monte Carlo integration for various correlation scenarios also including exchange processes, which are the hallmark of dynamical heterogeneity. The results of these numerical simulations provide clear signatures that allow one to distinguish uncorrelated from differently correlated cases. Since modified spin-lattice relaxation effects occur in the presence of nonexponential magnetization recovery, it is shown how to correct for them to a good approximation.

Correlation of primary relaxations and high-frequency modes in supercooled liquids. II. Evidence from spin-lattice relaxation weighted stimulated-echo spectroscopy

Using spin-lattice relaxation weighted stimulated-echo spectroscopy, we report evidence for a correlation of the primary and secondary relaxation times. The experiments are performed using deuteron nuclear magnetic resonance somewhat above the calorimetric glass-transition of ortho-terphenyl, D-sorbitol, and cresolphthalein-dimethylether. The data analysis is based on the procedure outlined in the accompanying theoretical paper [B. Geil, G. Diezemann, and R. Böhmer, Phys. Rev. E 74, 041504 (2006)]. Direct experimental evidence for a modified spin-lattice relaxation is obtained from measurements on a methyl deuterated acetyl salicylic acid glass. The limitations of the present experimental method are discussed.

Molecular dynamics study of the thermal and the density effects on the local and the large-scale motion of polymer melts: scaling properties and dielectric relaxation

Results from a molecular dynamics simulation of a melt of unentangled polymers are presented. The translational motion, the large-scale and the local reorientation processes of the chains, as well as their relations with the so-called "normal" and "segmental" dielectric relaxation modes are thoroughly investigated in wide temperature and pressure ranges. The thermodynamic states are well fitted by the phenomenological Tait equation of state. A global time-temperature-pressure superposition principle of both the translational and the rotational dynamics is evidenced. The scaling is more robust than the usual Rouse model. The latter provides insight but accurate comparison with the simulation calls for modifications to account for both the local chain stiffness and the nonexponential relaxation. The study addresses the issue whether the temperature or the density is a dominant control parameter of the dynamics or the two quantities give rise to comparable effects. By examining the ratio /alphatau//alphaP between the isochronic and isobaric expansivities, one finds that the temperature is dominant when the dynamics is fast. If the relaxation slows down, the fluctuations of the free volume increase their role and become comparable to those of the thermal energy. Detectable cross-correlation between the "normal-mode" and the "segmental" dielectric relaxations is found and contrasted with the usual assumption of independent modes.

Two secondary modes in decahydroisoquinoline: Which one is the true Johari Goldstein process?

Broadband dielectric measurements were carried out at isobaric and isothermal conditions up to 1.75 GPa for reconsidering the relaxation dynamics of decahydroisoquinoline, previously investigated by Richert et al. [R. Richert, K. Duvvuri, and L.-T. Duong, J. Chem. Phys. 118, 1828 (2003)] at atmospheric pressure. The relaxation time of the intense secondary relaxation tau(beta) seems to be insensitive to applied pressure, contrary to the alpha-relaxation times tau(alpha). Moreover, the separation of the alpha- and beta-relaxation times lacks correlation between shapes of the alpha-process and beta-relaxation times, predicted by the coupling model [see for example, K. L. Ngai, J. Phys.: Condens. Matter 15, S1107 (2003)], suggesting that the beta process is not a true Johari-Goldstein (JG) relaxation. From the other side, by performing measurements under favorable conditions, we are able to reveal a new secondary relaxation process, otherwise suppressed by the intense beta process, and to determine the temperature dependence of its relaxation times, which is in agreement with that of the JG relaxation.

Effect of chemical structure on the isobaric and isochoric fragility in polychlorinated biphenyls

Pressure-volume-temperature data, along with dielectric relaxation measurements, are reported for a series of polychlorinated biphenyls (PCB), differing in the number of chlorine atoms on their phenyl rings. Analysis of the results reveals that with increasing chlorine content, the relaxation times of the PCB become governed to a greater degree by density rho relative to the effect of temperature T. This result is consistent with the respective magnitudes of the scaling exponent gamma yielding superpositioning of the relaxation times measured at various temperatures and pressures, when plotted versus rho(gamma)/T. While at constant (atmospheric) pressure, fragilities for the various PCB are equivalent, the fragility at constant volume varies inversely with chlorine content. Evidently, the presence of bulkier chlorine atoms on the phenyl rings magnifies the effect which the density has on the relaxation dynamics.

Emergence of a new feature in the high pressure-high temperature relaxation spectrum of tri-propylene glycol

We investigated dielectric relaxation of a tri-propylene glycol system under high compression. By increasing temperature and pressure we observed that a new relaxation process emerges from the low frequency tail of the structural peak. This new peak starts to be visible at about 0.5 GPa and becomes clearly evident at 1.7 GPa. However, this additional peak merges again with the structural one as the glass transition is approached, since it has a weaker temperature dependence. This finding enriches the relaxation scenario of molecular glass formers confirming that the application of very high hydrostatic pressure can favor the detection of new relaxation or otherwise unresolved processes in supercooled liquid systems.

Sub-Tg relaxations due to dipolar solutes in nonpolar glass-forming solvents

It is well known that rigid dipolar solutes (in smaller quantity) dispersed in a nonpolar glassy matrix exhibit a sub-T(g) (or beta(s)) relaxation due to the solute often designated as Johari-Goldstein (JG) relaxation, which is intermolecular in nature. In this article, we report the results of our study of such a sub-T(g) process in a wide variety of dipolar solutes in different glassy systems using dielectric spectroscopy over a frequency range of 20-10(6) Hz down to a temperature of 77 K. The T(g) of these solutions are determined using differential scanning calorimetry. The solvents used in this study are o-terphenyl (OTP), isopropylbenzene (IPB), and methylcyclohexane. In the case of rigid molecular solutes, like mono-halogen benzenes, the activation energy (DeltaE(beta)) of the beta(s) process is found to increase with decreasing T(g) of the solvent, with a corresponding decrease in the magnitude of the beta(s) process. In the case of more symmetrical molecular solute, for example, tert-butylchloride, the change in DeltaE(beta) is not very appreciable. These results emphasize the importance of the size of the cage of the host matrix in the relaxation of the solute molecules. We have also studied the sub-T(g) relaxation(s) due to some flexible molecular solutes, viz., 1butylbromide, 1hexylbromide, 1butylacetate, and benzylacetate. These solutes in IPB matrix exhibit only one relaxation, whereas in OTP matrix they exhibit an additional sub-T(g) process, which may be identified with a JG type of relaxation. These observations lead us to the conclusion that the beta process observed in the glassy states of these pure solutes is predominantly intramolecular in nature.

Effect of pressure on the secondary relaxation in a simple glass former

We have studied dielectric spectra of the glass-forming liquid metafluoroaniline under hydrostatic pressure up to 700 MPa. Its glass transition pressure p(g) increases approximately linearly with temperature. Above p(g)(T), a well pronounced secondary relaxation, the Johari beta peak, is observed showing activated behavior. The activation energy rises proportionally to pressure and, consequently, proportionally to the glass transition temperature T(g)(p). The activation volume is independent of temperature but exhibits different values for pressures higher and lower than the pressure where the liquid left the ergodic regime. The activation volumes are about 1/10 and 1/6 of the molecular volume of fluoroaniline, respectively, suggesting that there are two different species of clusters.

Classification of secondary relaxation in glass-formers based on dynamic properties

Dynamic properties, derived from dielectric relaxation spectra of glass-formers at variable temperature and pressure, are used to characterize and classify any resolved or unresolved secondary relaxation based on their different behaviors. The dynamic properties of the secondary relaxation used include: (1) the pressure and temperature dependences; (2) the separation between its relaxation time taubeta and the primary relaxation time taualpha at any chosen taualpha; (3) whether taubeta is approximately equal to the independent (primitive) relaxation time tau0 of the coupling model; (4) whether both taubeta and tau0 have the same pressure and temperature dependences; (5) whether it is responsible for the "excess wing" of the primary relaxation observed in some glass-formers; (6) how the excess wing changes on aging, blending with another miscible glass-former, or increasing the molecular weight of the glass-former; (7) the change of temperature dependence of its dielectric strength Deltaepsilonbeta and taubeta across the glass transition temperature Tg; (8) the changes of Deltaepsilonbeta and taubeta with aging below Tg; (9) whether it arises in a glass-former composed of totally rigid molecules without any internal degree of freedom; (10) whether only a part of the molecule is involved; and (11) whether it tends to merge with the alpha-relaxation at temperatures above Tg. After the secondary relaxations in many glass-formers have been characterized and classified, we identify the class of secondary relaxations that bears a strong connection or correlation to the primary relaxation in all the dynamic properties. Secondary relaxations found in rigid molecular glass-formers belong to this class. The secondary relaxations in this class play the important role as a precursor or local step of the primary relaxation, and we propose that only they should be called the Johari-Goldstein beta-relaxation.

Minimal model for Beta relaxation in viscous liquids

Contrasts between beta relaxation in equilibrium viscous liquids and glasses are rationalized in terms of a double-well potential model with structure-dependent asymmetry, assuming structure is described by a single order parameter. The model is tested for tripropylene glycol where it accounts for the hysteresis of the dielectric beta loss peak frequency and magnitude during cooling and reheating through the glass transition.

Changes in dynamic crossover with temperature and pressure in glass-forming diethyl phthalate

Dielectric relaxation measurements have been used to study the crossover in dynamics with temperature and pressure, onset of breakdown of the Debye-Stokes-Einstein law, and the relation between the alpha and the beta relaxations in diethyl phthalate. The measurements made over 10 decades in frequency and a broad range of temperature and pressure enable the dc conductivity and the alpha- and the beta-relaxations to be studied altogether. The isobaric data show that the alpha-relaxation time tau(alpha) has temperature dependence that crosses over from one Vogel-Fulcher-Tammann-Hesse form to another at T(B) approximately 227 K and tau(alpha) approximately 10(-2) s. The dc conductivity sigma exhibits similar crossover at the same T(B). At temperatures above T(B), tau(alpha) and sigma have the same temperature dependence, but below T(B) they become different and the Debye-Stokes-Einstein law breaks down. The breadth of the alpha relaxation is nearly constant for T<T(B), but decreases with increasing temperature for T>T(B). The time dependence of tau(beta) is Arrhenius, which when extrapolated to higher temperatures intersects tau(alpha) at T(beta) nearly coincident with T(B). Isothermal measurements at various applied pressures when compared with isobaric data show that the shape of the alpha-relaxation depends only on tau(alpha), and not on the T and P combinations. At a constant temperature, while tau(alpha) increases rapidly with pressure, the beta-relaxation time tau(beta) is insensitive to applied pressure. This behavior is exactly the same as found in 1,1(')-bis (p-methoxyphenyl) cyclohexane. The findings are discussed in the framework of the coupling model.

Pressure evolution of the excess wing in a type-B glass former

Glass formers are defined as "type B" when they exhibit a distinct Johari-Goldstein (JG) relaxation, but lack an excess loss ("excess wing," EW) in their structural relaxation peak. By studying the dielectric spectra of a well-known type-B glass former under high pressure, we unequivocally show the existence of an EW, simultaneously with the JG relaxation. Moreover, at very high pressures (0.6 GPa), the EW becomes a distinct relaxation peak, although correlated with the structural relaxation. The implication is that the EW, rather than the higher frequency relaxation ascribed to the JG process, is perhaps a universal feature of glass formers, albeit not always discernible at ambient pressure. Our findings may reconcile all opposing points of view present in the literature, as well as indicate that the type-A or type-B classification of glass formers should be modified or even discontinued.

Influence of molecular structure on the dynamics of supercooled van der Waals liquids

Dielectric spectroscopy was carried out on the van der Waals liquid, 1,1(')-di(4-methoxy-5-methylphenyl)cyclohexane (BMMPC) in the supercooled state at pressures up to 218 MPa. The excess wing in this type-A glass former exhibits a response to pressure and temperature changes that is identical to that of the primary structural relaxation peak, indicating that the two processes reflect correlated molecular motions. Under no conditions was a distinct secondary peak observed in BMMPC, unlike the structurally very similar BMPC [1,1(')-bis(p-methoxyphenyl)cyclohexane]. However, the pressure dependences of both the glass temperature and fragility for the two materials are very close. The fragility is a decreasing function of pressure, although there is no concomitant narrowing of the relaxation peak. The pressure dependence of the relaxation times could be described as a simple volume-activated process, with the activation volume at the glass transition having the same magnitude as the molar volume.

Correlation between nonexponential relaxation and non-Arrhenius behavior under conditions of high compression

Photon correlation spectroscopy was used to investigate the behavior of the dynamical properties of 1,1'-di(4-methoxy-5-methyl-phenyl)cyclohexane (BMMPC) at elevated pressures. The fragility of BMMPC measured by the steepness index m(T) is decreasing and the nonexponentiality parameter beta(KWW) is increasing with increasing pressure. This result strongly suggests that the phenomenological correlation between the steepness index and nonexponentionality is also preserved under high compression. The pressure dependence of the structural relaxation times is well characterized by a simple activation volume form. The activation volume continuously increases with decreasing temperature, which is probably due to the increase of cooperativity of the structural relaxation process. Moreover, we found that the glass-transition temperature exhibits a significant dependence on pressure.

Effect of pressure on the dynamics of glass formers

A description of the pressure dependence of the structural relaxation time has been derived from the Adam-Gibbs theory by writing the configurational entropy in terms of the excess heat capacity and the molar thermal expansion. This new equation was tested successfully on dielectric relaxation data for an epoxy compound over a wide range of temperature and pressure.