Adam–Gibbs model for the supercooled dynamics in the ortho-terphenyl ortho-phenylphenol mixture

Effect of the presence of pinned particles on the structural parameters of a liquid and correlation between structure and dynamics at the local level

Pinning particles at the equilibrium configuration of the liquid is expected not to affect the structure and any property that depends on the structure while slowing down the dynamics. This leads to a breakdown of the structure dynamics correlation. Here, we calculate two structural quantities: the pair excess entropy, S2, and the mean field caging potential, the inverse of which is our structural order parameter (SOP). We show that when the pinned particles are treated the same way as the mobile particles, both S2 and SOP of the mobile particles remain the same as those of the unpinned system, and the structure dynamics correlation decreases with an increase in pinning density, "c." However, when we treat the pinned particles as a different species, even if we consider that the structure does not change, the expression of S2 and SOP changes. The microscopic expressions show that the interaction between a pinned particle and a mobile particle affects S2 and SOP more than the interaction between two mobile particles. We show that a similar effect is also present in the calculation of the excess entropy and is the primary reason for the well-known vanishing of the configurational entropy at high temperatures. We further show that, contrary to the common belief, the pinning process does change the structure. When these two effects are considered, both S2 and SOP decrease with an increase in "c," and the correlation between the structural parameters and the dynamics continues even for higher values of "c."

Dynamics-Entropy Relationship in Metallic Glasses

Establishing a robust quantitative correlation between thermodynamics and dynamics in amorphous matter remains a significant challenge in condensed matter physics. Although the classical Adam-Gibbs relationship represents a pivotal step in this direction and the correlation between relaxation time and configurational entropy has been partially verified in simple liquids, this quantitative link has yet to be tested in realistic glass-forming systems where complex many-body interactions are present. Here we conduct free energy samplings and lattice dynamics analysis to distinguish vibrational entropy from configurational entropy in a realistic Cu-Zr model of a metallic glass. Our calculations unveil a power-law relationship (with a substantial exponent of ∼3) between the logarithmic relaxation time and configurational entropy, surpassing the linear prediction of the original Adam-Gibbs relationship. This nonlinear entropy driven relaxation time variation likely originates from anisotropic nature of atomic many-body interactions, suggesting that factors beyond thermodynamics contribute to the glass transition phenomenon.

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 T_g, whether there is an underlying thermodynamic transition at some finite temperature below T_g, 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.

Thermodynamics and its correlation with dynamics in a mean-field model and pinned systems: A comparative study using two different methods of entropy calculation

A recent study introduced a novel mean-field model system where each particle over and above the interaction with its regular neighbors interacts with k extra pseudo-neighbors. Here, we present an extensive study of thermodynamics and its correlation with the dynamics of this system. We surprisingly find that the well-known thermodynamic integration (TI) method of calculating the entropy provides unphysical results. It predicts vanishing of the configurational entropy at temperatures close to the onset temperature of the system and negative values of the configurational entropy at lower temperatures. Interestingly, well below the temperature at which the configurational entropy vanishes, both the collective and the single-particle dynamics of the system show complete relaxation. Negative values of the configurational entropy are unphysical, and complete relaxation when the configurational entropy is zero violates the prediction of the random first-order transition theory (RFOT). However, the entropy calculated using the two-phase thermodynamics (2PT) method remains positive at all temperatures for which we can equilibrate the system, and its values are consistent with RFOT predictions. We find that with an increase in k, the difference in the entropy computed using the two methods increases. A similar effect is also observed for a system where a randomly selected fraction of the particles are pinned in their positions in the equilibrated liquid. We show that the difference in entropy calculated via the 2PT and TI methods increases with pinning density.

Activation volume in superpressed glass-formers

In pressurized glass-forming systems, the apparent (changeable) activation volume Va(P) is the key property governing the previtreous behavior of the structural relaxation time (τ) or viscosity (η), following the Super-Barus behavior: [Formula: see text], T = const. It is usually assumed that Va(P) = V#(P), where [Formula: see text] or [Formula: see text]. This report shows that Va(P) ≪ V#(P) for P → Pg, where Pg denotes the glass pressure, and the magnitude V#(P) is coupled to the pressure steepness index (the apparent fragility). V#(P) and Va(P) coincides only for the basic Barus dynamics, where Va(P) = Va = const in the given pressure domain, or for P → 0. The simple and non-biased way of determining Va(P) and the relation for its parameterization are proposed. The derived relation resembles Murnaghan - O'Connel equation, applied in deep Earth studies. It also offers a possibility of estimating the pressure and volume at the absolute stability limit. The application of the methodology is shown for diisobutyl phthalate (DIIP, low-molecular-weight liquid), isooctyloxycyanobiphenyl (8*OCB, liquid crystal) and bisphenol A/epichlorohydrin (EPON 828, epoxy resin), respectively.

Fluctuation Effects in the Adam-Gibbs Model of Cooperative Relaxation

A generalization of the Adam-Gibbs model of relaxation in glass-forming liquids is formulated that takes into account fluctuation in the number of molecules inside the cooperative region. The configurational fraction links the excess entropy with kinetic properties described in the Adam-Gibbs model. We express the configurational fraction at the glass-transition temperature in terms of the width of the distribution of relaxation times, the nonlinearity parameter that demarcates the variations of the relaxation time with structure and temperature, the steepness index that is proportional to the slope of the logarithm of the relaxation time with respect to temperature, the excess heat capacity under constant pressure, and the number of correlated molecules or structural units. The configurational fraction in the absence of fluctuation effects is also determined for several glass-forming liquids at the glass-transition temperature.

The Adam-Gibbs relation and the TIP4P/2005 model of water

We report a numerical test of the Adam-Gibbs relation for the TIP4P/2005 model of water. The configurational entropy is here evaluated as the logarithm of the number of different basins in the potential energy landscape sampled in equilibrium conditions. Despite the non-monotonic behaviour which characterise the density dependence of the diffusion coefficient, the Adam-Gibbs relation is satisfied within the numerical precision in a wide range of densities and temperatures. We also show that expressions based on the excess entropy (the logarithm of the number of sampled microstates in phase space) fail in the region of densities where a tetrahedral hydrogen bond network develops.

Length-Scale Dependence of the Stokes-Einstein and Adam-Gibbs Relations in Model Glass Formers

The Adam-Gibbs (AG) relation connects the dynamics of a glass-forming liquid to its thermodynamics via the configurational entropy and is of fundamental importance in descriptions of glassy behavior. The breakdown of the Stokes-Einstein relation (SEB) between the diffusion coefficient and the viscosity (or structural relaxation times) in glass formers raises the question as to which dynamical quantity the AG relation describes. By performing molecular dynamics simulations, we show that the AG relation is valid over the widest temperature range for the diffusion coefficient and not for the viscosity or relaxation times. Studying relaxation times defined at a given wavelength, we find that SEB and the deviation from the AG relation occur below a temperature at which the correlation length of dynamical heterogeneity equals the wavelength probed.

Relaxation and physical aging in network glasses: a review

Recent progress in the description of glassy relaxation and aging are reviewed for the wide class of network-forming materials such as GeO2, Ge x Se1-x , silicates (SiO2-Na2O) or borates (B2O3-Li2O), all of which have an important usefulness in domestic, geological or optoelectronic applications. A brief introduction of the glass transition phenomenology is given, together with the salient features that are revealed both from theory and experiments. Standard experimental methods used for the characterization of the slowing down of the dynamics are reviewed. We then discuss the important role played by aspects of network topology and rigidity for the understanding of the relaxation of the glass transition, while also permitting analytical predictions of glass properties from simple and insightful models based on the network structure. We also emphasize the great utility of computer simulations which probe the dynamics at the molecular level, and permit the calculation of various structure-related functions in connection with glassy relaxation and the physics of aging which reveal the non-equilibrium nature of glasses. We discuss the notion of spatial variations of structure which leads to the concept of 'dynamic heterogeneities', and recent results in relation to this important topic for network glasses are also reviewed.

Adam-Gibbs model in the density scaling regime and its implications for the configurational entropy scaling

To solve a long-standing problem of condensed matter physics with determining a proper description of the thermodynamic evolution of the time scale of molecular dynamics near the glass transition, we have extended the well-known Adam-Gibbs model to describe the temperature-volume dependence of structural relaxation times, τ_α(T, V). We also employ the thermodynamic scaling idea reflected in the density scaling power law, τ_α = f(T⁻¹V^−γ), recently acknowledged as a valid unifying concept in the glass transition physics, to differentiate between physically relevant and irrelevant attempts at formulating the temperature-volume representations of the Adam-Gibbs model. As a consequence, we determine a straightforward relation between the structural relaxation time τ_α and the configurational entropy S_C, giving evidence that also S_C(T, V) = g(T⁻¹V^−γ) with the exponent γ that enables to scale τ_α(T, V). This important findings have meaningful implications for the connection between thermodynamics and molecular dynamics near the glass transition, because it implies that τ_α can be scaled with S_C.

String model for the dynamics of glass-forming liquids

We test the applicability of a living polymerization theory to describe cooperative string-like particle rearrangement clusters (strings) observed in simulations of a coarse-grained polymer melt. The theory quantitatively describes the interrelation between the average string length L, configurational entropy Sconf, and the order parameter for string assembly Φ without free parameters. Combining this theory with the Adam-Gibbs model allows us to predict the relaxation time τ in a lower temperature T range than accessible by current simulations. In particular, the combined theories suggest a return to Arrhenius behavior near Tg and a low T residual entropy, thus avoiding a Kauzmann "entropy crisis."

The relationship of dynamical heterogeneity to the Adam-Gibbs and random first-order transition theories of glass formation

We carefully examine common measures of dynamical heterogeneity for a model polymer melt and test how these scales compare with those hypothesized by the Adam and Gibbs (AG) and random first-order transition (RFOT) theories of relaxation in glass-forming liquids. To this end, we first analyze clusters of highly mobile particles, the string-like collective motion of these mobile particles, and clusters of relative low mobility. We show that the time scale of the high-mobility clusters and strings is associated with a diffusive time scale, while the low-mobility particles' time scale relates to a structural relaxation time. The difference of the characteristic times for the high- and low-mobility particles naturally explains the well-known decoupling of diffusion and structural relaxation time scales. Despite the inherent difference of dynamics between high- and low-mobility particles, we find a high degree of similarity in the geometrical structure of these particle clusters. In particular, we show that the fractal dimensions of these clusters are consistent with those of swollen branched polymers or branched polymers with screened excluded-volume interactions, corresponding to lattice animals and percolation clusters, respectively. In contrast, the fractal dimension of the strings crosses over from that of self-avoiding walks for small strings, to simple random walks for longer, more strongly interacting, strings, corresponding to flexible polymers with screened excluded-volume interactions. We examine the appropriateness of identifying the size scales of either mobile particle clusters or strings with the size of cooperatively rearranging regions (CRR) in the AG and RFOT theories. We find that the string size appears to be the most consistent measure of CRR for both the AG and RFOT models. Identifying strings or clusters with the "mosaic" length of the RFOT model relaxes the conventional assumption that the "entropic droplets" are compact. We also confirm the validity of the entropy formulation of the AG theory, constraining the exponent values of the RFOT theory. This constraint, together with the analysis of size scales, enables us to estimate the characteristic exponents of RFOT.

Adam-Gibbs relation for glass-forming liquids in two, three, and four dimensions

The Adam-Gibbs relation between relaxation times and the configurational entropy has been tested extensively for glass formers using experimental data and computer simulation results. Although the form of the relation contains no dependence on the spatial dimensionality in the original formulation, subsequent derivations of the Adam-Gibbs relation allow for such a possibility. We test the Adam-Gibbs relation in two, three, and four spatial dimensions using computer simulations of model glass formers. We find that the relation is valid in three and four dimensions. But in two dimensions, the relation does not hold, and interestingly, no single alternate relation describes the results for the different model systems we study.

Two factors governing fragility: stretching exponent and configurational entropy

We derive an analytical expression showing that the fragility of a supercooled liquid is a result of (i) a thermodynamic term depending on change in configurational entropy and (ii) a kinetic term depending on change in the nonexponentiality or "stretching" of the relaxation function, as quantified by the exponent beta of the Kohlrausch-Williams-Watts (KWW) relaxation function. Our expression indicates that there is not a direct correlation between the non-Arrhenius scaling of liquid viscosity and the nonexponential nature of glassy relaxation. Rather, the temperature dependence of the stretching exponent beta provides a lower limit for fragility, which can be increased through changes in the configurational entropy. Our result explains the apparent contradiction between those researchers showing a correlation between beta and fragility and those who question such a correlation due to the spread of the data.

Idealized glass transitions under pressure: dynamics versus thermodynamics

The interplay of slow dynamics and thermodynamic features of dense liquids is studied by examining how the glass transition changes depending on the presence or absence of Lennard-Jones-like attractions. Quite different thermodynamic behavior leaves the dynamics unchanged, with important consequences for high-pressure experiments on glassy liquids. Numerical results are obtained within mode-coupling theory (MCT), but the qualitative features are argued to hold more generally. A simple square-well model can be used to explain generic features found in experiment.

Effect of chain length on fragility and thermodynamic scaling of the local segmental dynamics in poly(methylmethacrylate)

Local segmental relaxation properties of poly(methylmethacrylate) (PMMA) of varying molecular weight are measured by dielectric spectroscopy and analyzed in combination with the equation of state obtained from PVT measurements. Significant variations of glass transition temperature and fragility with molecular weight are observed. In accord with the general properties of glass-forming materials, single molecular weight dependent scaling exponent gamma is sufficient to define the mean segmental relaxation time taualpha and its distribution. This exponent can be connected to the Gruneisen parameter and related thermodynamic quantities, thus demonstrating the interrelationship between dynamics and thermodynamics in PMMA. Changes in the relaxation properties ("dynamic crossover") are observed as a function of both temperature and pressure, with taualpha serving as the control parameter for the crossover. At longer taualpha another change in the dynamics is apparent, associated with a decoupling of the local segmental process from ionic conductivity.

What Can We Learn by Squeezing a Liquid?

Relaxation times tau(T,upsilon) for different temperatures, T, and specific volumes, upsilon, collapse to a master curve vs Tupsilon(gamma), with gamma a material constant. The isochoric fragility, mV, is also a material constant, inversely correlated with gamma. From these experimental facts, we obtain a three-parameter function that accurately fits tau(T,upsilon) data for several glass-formers over the supercooled regime, without any divergence of tau below Tg. Although the values of the three parameters depend on the material, only gamma significantly varies; thus, by normalizing material-specific quantities related to gamma, a universal power law for the dynamics is obtained.

Pressure effects on the α and α′ relaxations in polymethylphenylsiloxane

In some polymers, in addition to the usual structural alpha relaxation, a slower alpha' relaxation is observed with a non-Arrhenius temperature dependence. In order to understand better the molecular origin of this alpha' relaxation in poly(methylphenylsiloxane) (PMPS) we have studied, for the first time, the pressure dependence of its relaxation time, together with the usual temperature dependence, by means of dynamic light scattering (DLS). For the same material the alpha relaxation was also studied by means of DLS and dielectric spectroscopy (DS) in broad temperature and pressure ranges. We find that the temperature dependence of both alpha and alpha' relaxation times, at all pressures studied, can be described by a double Vogel-Fulcher-Tammann (VFT) law. The pressure dependence of the characteristic temperatures Tg (glass transition temperature) and T0 (Vogel temperature) as well as the activation volumes for both alpha and alpha' processes are very similar, indicating, that both relaxation processes originate from similar local molecular dynamics. Additionally, for both alpha and alpha' relaxations the combined temperature and pressure dependences of the relaxation times can be described using a parameter Gamma=rhon/T with the same value of the exponent n.

Entropy theory of polymer glass formation revisited. I. General formulation

A generalized entropy theory of glass formation is developed by merging the lattice cluster theory for the thermodynamics of semiflexible polymer melts at constant pressure with the Adam-Gibbs relation between the structural relaxation time and the configurational entropy. Since experimental studies have suggested that the relative rigidity of the chain backbone and the side groups is an essential parameter governing the nature of glass formation in polymers, we incorporate this rigidity disparity parameter, along with monomer structure, into our new theoretical description of the polymer fluid thermodynamics. Our entropy theory is compared with alternative theories that describe the rate of structural relaxation in glass-forming liquids in terms of an activated rate process.

Thermodynamical scaling of the low frequency relaxation time in liquid crystalline phases

The low frequency relaxation times tau//, which characterize the flip-flop molecular motions in liquid crystalline phases, recently determined in high-pressure experiments for eight liquid crystalline substances, were reanalyzed considering a relation proposed for the glass-forming liquids [C. Dreyfus, Phys. Rev. E 68, 011204 (2003); R. Casalini and C. M. Roland, Phys. Rev. E 69, 062501 (2004)]. The data, measured at constant pressure, constant temperature, and constant molar volume, could be rescaled onto a master line in the ln tau// vs 1/(T V(gamma)m) plot, with gamma as an adjustable parameter (Vm=1/rho is the specific volume). The obtained gamma values are in good agreement with other estimations; here, the value of gamma parameter was determined for the crystal-like smectic- E phase.

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.

Temperature and volume effects on the change of dynamics in propylene carbonate

Dielectric relaxation and PVT measurements were carried out on propylene carbonate. From these, we show that thermal energy exerts a stronger influence than volume on the temperature dependence of the dynamic properties. Data obtained at all temperatures and pressures superimpose, when expressed as a function of T-1 V-3.7 . The scaling exponent is consistent with more thermally governed dynamics, and can be interpreted as a reflection of the soft nature of the potential. The change of dynamics observed in the conductivity and relaxation data transpires at a fixed value of either quantity, independent of temperature and pressure.