Effect of temperature and volume on structural relaxation time: Interpretation in terms of decrease of configurational entropy

We describe a model for the thermodynamics and dynamics of glass-forming liquids in terms of excitations from an ideal glass state to a Gaussian manifold of configurationally excited states. The quantitative fit of this three parameter model to the experimental data on excess entropy and heat capacity shows that "fragile" behavior, indicated by a sharply rising excess heat capacity as the glass transition is approached from above, occurs in anticipation of a first-order transition--usually hidden below the glass transition--to a "strong" liquid state of low excess entropy. The distinction between fragile and strong behavior of glass formers is traced back to an order of magnitude difference in the Gaussian width of their excitation energies. Simple relations connect the excess heat capacity to the Gaussian width parameter, and the liquid-liquid transition temperature, and strong, testable, predictions concerning the distinct properties of energy landscape for fragile liquids are made. The dynamic model relates relaxation to a hierarchical sequence of excitation events each involving the probability of accumulating sufficient kinetic energy on a separate excitable unit. Super-Arrhenius behavior of the relaxation rates, and the known correlation of kinetic with thermodynamic fragility, both follow from the way the rugged landscape induces fluctuations in the partitioning of energy between vibrational and configurational manifolds. A relation is derived in which the configurational heat capacity, rather than the configurational entropy of the Adam-Gibbs equation, controls the temperature dependence of the relaxation times, and this gives a comparable account of the experimental observations without postulating a divergent length scale. The familiar coincidence of zero mobility and Kauzmann temperatures is obtained as an approximate extrapolation of the theoretical equations. The comparison of the fits to excess thermodynamic properties of laboratory glass formers, and to configurational thermodynamics from simulations, reveals that the major portion of the excitation entropy responsible for fragile behavior resides in the low-frequency vibrational density of states. The thermodynamic transition predicted for fragile liquids emerges from beneath the glass transition in case of laboratory water and the unusual heat capacity behavior observed for this much studied liquid can be closely reproduced by the model.

Atactic polystyrene, as reported in a recent contribution by our group, displays a marked change in glass transition when exposed to toluene vapor due to plasticization associated with vapor sorption within the polymer. The dependence of the glass transition temperature of the polymer-penetrant mixture on the pressure of toluene vapor is characterized by the so-called "retrograde vitrification" phenomenon, in that, at a constant pressure, a rubber to glass transition occurs by increasing the temperature. In this contribution, we have used a theoretical approach, based on the nonrandom lattice fluid thermodynamic model for the polymer-toluene mixture, to predict the state of this system, i.e., rubbery or glassy, as a function of fluid pressure and system temperature. The experimentally detectable glass transition is assumed to be a kinetically affected evidence of an underlying II order thermodynamic transition of the polymer mixture. On the basis of this hypothesis, the Gibbs-Di Marzio criterion, stating that equilibrium configurational entropy is zeroed at the glass transition, has been applied to locate the transition. The working set of equations consists of the expression of configurational entropy obtained from the adopted lattice fluid model equated to zero, coupled with the equation expressing the phase equilibrium between the polymer phase and the pure toluene vapor phase in contact and with the equations of state for the two phases. Theoretical predictions are in good qualitative and quantitative agreement with the experimental results previously obtained gravimetrically performing "dynamic" sorption experiments, which represent a neat example of the occurrence of so-called "type IV" glass transition temperature vs pressure behavior. The peculiar retrograde vitrification phenomenon and the glass transition temperature vs pressure envelope determined experimentally are well described by the proposed theoretical approach.

The binary molecular glass former 2-picoline in tri-styrene is investigated by means of broadband dielectric spectroscopy with the aim of understanding the role of secondary relaxation processes that emerge during the glass transition. It is shown that the "high frequency wing," which is seen in neat picoline, becomes a separate process in the mixture and exhibits all the features of a Johari-Goldstein relaxation. In particular, the previously found relation between activation energy and Tg is recovered. In addition, below Tg the width parameter of this secondary relaxation is shown to be governed by a common temperature dependence, and the time scale is characterized by an isokinetic point. Above Tg pronounced deviations from an Arrhenius behavior are observed.

A phenomenological analysis of the ortho-positronium (o-Ps) annihilation from positron annihilation lifetime spectroscopy (PALS) and the dynamics from broadband dielectric spectroscopy (BDS) are reported on a small molecular glass former of intermediate H-bonding and fragility: salol. The dielectric spectra extend over a very broad frequency range of about 2 × 10(-2)-3.5 × 10(11) Hz, providing information on the α-relaxation, the secondary relaxation giving rise to the excess wing, and the shallow high-frequency minimum in the micro- to milli-meter wave range. A number of empirical correlations between the o-Ps lifetime, τ(3)(T), and the various spectral and relaxation features have been observed. Thus, the phenomenological evaluation of the τ(3)(T) dependence of the PALS response of the amorphous sample reveals three characteristic PALS temperatures: T(g)(PALS), T(b1)(L) = 1.15T(g)(PALS) and T(b2)(L) = 1.25T(g)(PALS), which are discussed in relation to similar findings for some typical small molecular vdW- and H-bonded glass formers. A slighter change of the slope at T(b1)(L) appears to be related to the transition from excess wing to the primary α-process-dominated behavior, with the secondary process dominating in the deeply supercooled liquid state below T(b1)(L). The high-temperature plateau effect in the τ (3)(T) plot occurs at T(b2)(L) and agrees with the characteristic Stickel temperature, T(B)(ST), marking a qualitative change of the primary α process, but it does not follow the relation T(b2)(L) < T(α) [τ(3)(T(b2)) < τ(α)]. Both effects at T(b1)(L) and T(b2)(L) correlate with two crossovers in the spectral shape and related non-exponentiality parameter of the structural relaxation, β (KWW). Finally, the application of the two-order parameter (TOP) model to the structural relaxation as represented by the primary α relaxation times from BDS leads to the characteristic TOP temperature, T(m)(c), close to T(b1) from PALS. Within this model the phenomenological interpretation is offered based on changes in the probability of occurrence of solid-like and liquid-like domains to explain the dynamic as well as PALS responses. In summary, all the empirical correlations support further very close connections between the PALS response and the dielectric relaxation behavior in small molecule glass formers.

Glass and gel formers exhibit unusual mechanical characteristics and amorphous phases which are highly dependent on their thermal history. We introduce a lattice model with T-shaped molecules that exhibits glassy and gel-like states without introducing artificial frustration. This system has a large number of degenerate energy minima separated by small barriers leading to a broad, kinetically-explored landscape. It particularly replicates valence-limited materials, which can form self-assembled materials with highly controlled physical properties. Despite its remarkable simplicity, this model reveals some of the fundamental kinetic and thermodynamic properties of the glass transition and of gel formation. A dearth of low temperature experimental and simulation measurements has inhibited investigation in this field. We overcome this difficulty by using a modified Metropolis Monte Carlo method to quickly provide equilibrium samples. Then kinetic Monte Carlo techniques are used to explore the properties of the equilibrium system, providing a touchstone for the non-equilibrium glassy states. Fully-dense simulation samples reveal a fragile-to-strong crossover (FSC) near the mean-field (MF) spinodal. At the FSC, the relaxation time returns to Arrhenius behavior with cooling. There is an inflection point in the configurational entropy. This behavior resolves the Kauzmann Paradox which is a result of extrapolation from above the inflection point. In contrast, we find that the configurational entropy remains finite as the temperature goes to zero. We also observe different kinetics as the system is quenched below the FSC, resulting in non-equilibrium, amorphous states with high potential energy persisting for long periods of time. Simulation samples remain at non-equilibrium conditions for observation times exceeding those permitting complete equilibration slightly above the FSC. This suggests the FSC would often be identified as the glass transition without indication that there is true arrest or a diverging length scale. Indeed, our simulations show these samples do equilibrate if sufficient time is allowed. To elucidate the complex, interdependent relation time and length scales at the FSC will require careful consideration of the spatial-dynamic heterogeneity. Dynamic mean-field simulations at high density and in the solvated regime reveal a rich range of morphological features. They are consistent with simulated and experimental results in colloidal systems. Stability limits of decreasing length scales beneath the phase separation bimodal coincide into a single curve, which terminates at the fully-dense MF spinodal, suggesting that gelation and vitrification are the same phenomena. Our work indicates that gelation is, therefore, a result of phase separation arrested by a glass transition.

Thermodynamic aspects of the glass transition of silicates

Studies of the Gaussian core model (GCM) have shown that it behaves like a mean-field model and the properties are quite different from standard glass former. In this work, we investigate the entropies, namely, the excess entropy (Sex) and the configurational entropy (Sc) and their different components to address these anomalies. Our study corroborates most of the earlier observations and also sheds new light on the high and low temperature dynamics. We find that unlike in standard glass former where high temperature dynamics is dominated by two-body correlation and low temperature by many-body correlations, in the GCM both high and low temperature dynamics are dominated by many-body correlations. We also find that the many-body entropy which is usually positive at low temperatures and is associated with activated dynamics is negative in the GCM suggesting suppression of activation. Interestingly despite the suppression of activation, the Adam-Gibbs (AG) relation that describes activated dynamics holds in the GCM, thus suggesting a non-activated contribution in AG relation. We also find an overlap between the AG relation and mode coupling power law regime leading to a power law behavior of Sc. From our analysis of this power law behavior, we predict that in the GCM the high temperature dynamics will disappear at dynamical transition temperature and below that there will be a transition to the activated regime. Our study further reveals that the activated regime in the GCM is quite narrow.

On relaxation nature of glass transition in amorphous materials

We investigated a possible correlation between molecular mobility and physical stability in glassy celecoxib and indomethacin and identified the specific mobility mode responsible for physical instability (crystallization). In the glassy state, because the structural relaxation times are very long, the measurement was enabled by time domain dielectric spectroscopy. However, the local motions in the glassy state were characterized by frequency domain dielectric spectroscopy. Isothermal crystallization was monitored by powder X-ray diffractometry using either a laboratory source (supercooled state) or synchrotron source (glassy state). Structural (α) relaxation time correlated well with characteristic crystallization time in the supercooled state. On the other hand, a stronger correlation was observed between the Johari-Goldstein (β) relaxation time and physical instability in the glassy state but not with structural relaxation time. These results suggest that Johari-Goldstein relaxation is a potential predictor of physical instability in the glassy state of these model systems.

Factors determining glass transition temperature and relaxation time of poly(vinyl chloride)

One of the greatest challenges in contemporary condensed matter physics is to ascertain whether the formation of glasses from liquids is fundamentally thermodynamic or dynamic in origin. Although the thermodynamic paradigm has dominated theoretical research for decades, the purely kinetic perspective of the dynamical facilitation (DF) theory has attained prominence in recent times. In particular, recent experiments and simulations have highlighted the importance of facilitation using simple model systems composed of spherical particles. However, an overwhelming majority of liquids possess anisotropy in particle shape and interactions, and it is therefore imperative to examine facilitation in complex glass formers. Here, we apply the DF theory to systems with orientational degrees of freedom as well as anisotropic attractive interactions. By analyzing data from experiments on colloidal ellipsoids, we show that facilitation plays a pivotal role in translational as well as orientational relaxation. Furthermore, we demonstrate that the introduction of attractive interactions leads to spatial decoupling of translational and rotational facilitation, which subsequently results in the decoupling of dynamical heterogeneities. Most strikingly, the DF theory can predict the existence of reentrant glass transitions based on the statistics of localized dynamical events, called excitations, whose duration is substantially smaller than the structural relaxation time. Our findings pave the way for systematically testing the DF approach in complex glass formers and also establish the significance of facilitation in governing structural relaxation in supercooled liquids.

Relation between the dispersion of α-relaxation and the time scale of β-relaxation at the glass transition

In this Reply we show that contrary to the statements of Goldstein, the empirical function we proposed [D. Prevosto, M. Lucchesi, S. Capaccioli, R. Casalini, and P. A. Rolla, Phys. Rev. B 67, 174202 (2003)] for the pressure and temperature dependencies of the configurational entropy is mathematically and physically valid. Specifically we demonstrate that the condition of equal second derivatives, necessary for the configurational entropy to be a function of state, has physically reasonable solutions without the necessity of imposing implausible constraints.

We use thermodynamics of lattice vacancies to test the merits of the view that (i) statistical entropy, k(B) ln Omega, vanishes on vitrification of a liquid and hence there is no residual entropy and (ii) k(B) ln Omega of a nonergodic state would increase with time t as its structure relaxes. We argue that this view conflicts with the precepts of the configurational entropy of a crystal, -R[x ln x+(1-x)ln(1-x)], where x is the fractional population of vacancies, and with the observed decrease in x with t on structural relaxation. The issue of whether the entropy of a kinetically arrested crystal state is equal to k(B) ln Omega or equal to -R[x ln x+(1-x)ln(1-x)] can be resolved by measuring the vapor pressure, the emf of an electrolytic cell, and by scanning calorimetry. We also consider how the energy landscapes of a crystal and liquid differ, and point out that since crystals are in a nonequilibrium state, their thermodynamic data are inappropriate for testing the validity of the third law.

The rotational dynamics of the spin probe 2,2,6,6-tetramethyl-piperidin-l-oxyl (TEMPO) dissolved in the molecular glass former phenyl salicylate (Salol) have been investigated via electron spin resonance spectroscopy, in a temperature interval ranging from the supercooled to the glassy state of Salol. The comparison of experimental data with predictions of both diffusive and jump reorientational models has been made. It has been proved that in both the supercooled and the glassy state, the TEMPO spin probe rotates according to a jump process. In the investigated temperature range, the angular jump size Φ has been found to be constant and holds 75°. Moreover, the temperature dependence of the reorientational correlation times, which is well described by a double Arrhenius law, has been studied. The crossing temperature from the first to the second Arrhenius regime is found to be near to the glass transition temperature. Comparison with the results of a previous study on the reorientational dynamics of a TEMPO probe in o-terphenyl, has shown that rotational motion happens in structural cages with comparable free volumes.