The Kauzmann paradox interpreted via the theory of frustration- limited-domains

Glass transition as a topological phase transition

The glass transition is described as a phase transition in the system of topologically protected excitations in matter structure. The critical behavior of the system is considered in both static and dynamic cases. It is shown that the proposed model reproduces most of the characteristic thermodynamic and kinetic properties of glass transition: the Vogel-Fulcher-Tammann law, the behavior of susceptibility and nonlinear susceptibilities, and heat capacity behavior as well as the appearance of a boson peak in the frequency dependence of the dynamic structure factor near the glass transition temperature.

Configurational entropy of glass-forming liquids

The configurational entropy is one of the most important thermodynamic quantities characterizing supercooled liquids approaching the glass transition. Despite decades of experimental, theoretical, and computational investigation, a widely accepted definition of the configurational entropy is missing, its quantitative characterization remains fraught with difficulties, misconceptions, and paradoxes, and its physical relevance is vividly debated. Motivated by recent computational progress, we offer a pedagogical perspective on the configurational entropy in glass-forming liquids. We first explain why the configurational entropy has become a key quantity to describe glassy materials, from early empirical observations to modern theoretical treatments. We explain why practical measurements necessarily require approximations that make its physical interpretation delicate. We then demonstrate that computer simulations have become an invaluable tool to obtain precise, nonambiguous, and experimentally relevant measurements of the configurational entropy. We describe a panel of available computational tools, offering for each method a critical discussion. This perspective should be useful to both experimentalists and theoreticians interested in glassy materials and complex systems.

Zero-temperature glass transition in two dimensions

Liquids cooled towards the glass transition temperature transform into amorphous solids that have a wide range of applications. While the nature of this transformation is understood rigorously in the mean-field limit of infinite spatial dimensions, the problem remains wide open in physical dimensions. Nontrivial finite-dimensional fluctuations are hard to control analytically, and experiments fail to provide conclusive evidence regarding the nature of the glass transition. Here, we develop Monte Carlo methods for two-dimensional glass-forming liquids that allow us to access equilibrium states at sufficiently low temperatures to directly probe the glass transition in a regime inaccessible to experiments. We find that the liquid state terminates at a thermodynamic glass transition which occurs at zero temperature and is associated with an entropy crisis and a diverging static correlation length. Our results thus demonstrate that a thermodynamic glass transition can occur in finite dimensional glass-formers.

Thermodynamic nature of vitrification in a 1D model of a structural glass former

We propose a new spin-glass model with no positional quenched disorder which is regarded as a coarse-grained model of a structural glass-former. The model is analyzed in the 1D case when the number N of states of a primary cell is large. For N → ∞, the model exhibits a sharp freezing transition of the thermodynamic origin. It is shown both analytically and numerically that the glass transition is accompanied by a significant growth of a static length scale ξ pointing to the structural (equilibrium) nature of dynamical slowdown effects in supercooled liquids.

Molecular dynamics study of one-component soft-core system: thermodynamic properties in the supercooled liquid and glassy states

Molecular dynamics simulations were performed to study the thermal properties of a supercooled liquid near the glass transition regime and of glasses in a one-component soft-core system with the pair potential φn(r) = ɛ(σ/r)(n), in which n = 12. The results are examined along a phase diagram, in which the compressibility factor defined by [Formula: see text] is plotted against the reduced density ρ* = ρ(ɛ/kBT)(3/n) (or the reduced temperature T* = ρ*(-n/3)). Similarly, a time-dependent dynamical compressibility factor can be plotted against the time-dependent reduced density [Formula: see text] (or the reduced time-dependent temperature). Analytical expressions of the specific heats CV and CP and of the entropy, S, were obtained as a function of [Formula: see text] or of the scaled potential U*. Even for a rapid cooling process, the CV values are found to be affected by non-equilibrium relaxations in the [Formula: see text] region, where [Formula: see text] is the given initial value of [Formula: see text]. The problem of the Kauzmann paradox is discussed using these expressions. The fluctuation of the time-dependent temperature, Tt*, which determines CV, is characterized by the spectra that are obtained by multitaper methods. The thermal fluctuation along the non-equilibrium relaxation under NVE conditions was also examined.

On the mechanism of reorientational and structural relaxation in supercooled liquids: the role of border dynamics and cooperativity

Molecular dynamics simulation and analysis based upon the many-body potential energy landscape (PEL) are employed to characterize single molecule reorientation and structural relaxation, and their interrelation, in deeply supercooled liquid CS(2). The rotational mechanism changes from small-step Debye diffusion to sudden large angle reorientation (SLAR) as the temperature falls below the mode-coupling temperature T(c). The onset of SLAR is explained in terms of the PEL; it is an essential feature of low-T rotational dynamics, along with the related phenomena of dynamic heterogeneity and the bifurcation of slow and fast relaxation processes. A long trajectory in which the system is initially trapped in a low energy local minimum, and eventually escapes, is followed in detail, both on the PEL and in real space. During the trapped period, "return" dynamics occurs, always leading back to the trap. Structural relaxation is identified with irreversible escape to a new trap. These processes lead to weak and strong SLAR, respectively; strong SLAR is a clear signal of structural relaxation. Return dynamics involves small groups of two to four molecules, while a string-like structure composed of all the active groups participates in the escape. It is proposed that, rather than simple, nearly instantaneous, one-dimensional barrier crossings, relaxation involves activation of the system to the complex, multidimensional region on the borders of the basins of attraction of the minima for an extended period.

On the Breakdown of the Stokes−Einstein Law in Supercooled Liquids

The wavevector-dependent shear viscosity, eta(k), is evaluated for a range of temperatures in a supercooled binary Lennard-Jones liquid. The mode coupling theory of Keyes and Oppenheim (Phys. Rev. A 1973, 8, 937) expresses the self-diffusion constant, D, in terms of eta(k). Replacing eta(k) with the usual viscosity, eta identical with eta(k = 0), yields the Stokes-Einstein law. It is found that the breakdown of the SE law in this system is well described by keeping the simulated k-dependence. Simply put, bath processes on all length scales (wavevectors) contribute to D, the system is much less viscous at finite k, and thus D exceeds the SE estimate based upon eta. The functional form of eta(k) allows for the estimation of a correlation length that grows with decreasing T.

Are defect models consistent with the entropy and specific heat of glass formers?

We show that pointlike defect model of glasses cannot explain the thermodynamic properties of glass formers, as for example, the excess specific heat close to the glass transition, contrary to the claim of Garrahan and Chandler [Proc. Natl. Acad. Sci. U.S.A. 100, 9710 (2003)]. More general models and approaches in terms of extended defects are also discussed.

Configurational entropy and its crisis in metastable states: ideal glass transition in a dimer model as a paragidm of a molecular glass

We discuss the need for discretization to evaluate the configurational entropy in a general model. We also discuss the prescription using restricted partition function formalism to study the stationary limit of metastable states where a more stable equilibrium state exists. We introduce a lattice model of dimers as a paradigm of molecular fluid and study stationary metastability in it to investigate the root cause of glassy behavior. We demonstrate the existence of entropy crisis in metastable states, from which it follows that the entropy crisis is the root cause underlying the ideal glass transition in systems with particles of all sizes. The orientational interactions in the model control the nature of the liquid-liquid transition observed in recent years in molecular glasses.

Competition between short-ranged attraction and short-ranged repulsion in crowded configurational space: aA lattice model description

We describe a simple nearest-neighbor Ising model that is capable of supporting a gas, liquid, and crystal, in characteristic relationship to each other. As the parameters of the model are varied, one obtains characteristic patterns of phase behavior reminiscent of continuum systems where the range of the interaction is varied. The model also possesses dynamical arrest, and although we have not studied it in detail, these "transitions" appear to have a reasonable relationship to the phases and their transitions.

Neutral polymer slow mode may signify an incipient growth-frustrated domain-forming glass

Kivelson, et al. [J. Chem. Phys. 101, 2391 (1994)] propose a model for glass-forming liquids based on the potential existence of frustration-limited structures. Frustration-limited structures are equilibrium supramolecular assemblages. The maximum size of an assemblage is limited by geometric constraints. Here I propose that the "slow mode" found in the quasielastic light scattering spectra of some but not all neutral polymer solutions corresponds to the presence of an incipient growth-frustrated domain-forming glass in these solutions. A physical picture is proposed for the origin of frustration in polymer solutions.

Significance of the free volume for metastability, spinodals, and the glassy state: an exact calculation in polymers

A lattice model of semiflexible linear chains (with equilibrium polydispersity) containing free volume is solved exactly on a Husimi cactus. A metastable liquid (ML) is discovered to exist only at low temperatures and is distinct (and may be disjoint) from the supercooled liquid (SCL) that exists only at high temperatures. The free volume plays a significant role in that the spinodals of the ML and SCL merge and then disappear as the free volume is reduced. The Kauzmann temperature T(K) occurs in the ML without any singularity. At T(MC)>T(K), the ML specific heat has a peak. For infinitely long polymers, the peak height diverges and the free volume vanishes at T(MC), resulting in a continuous liquid-liquid transition. Contrary to the conventional wisdom, both T(K) and T(MC) occur in the ML and not in the SCL.

Importance of interactions for free-volume and end-group effects in polymers: an equilibrium lattice investigation

We consider a lattice model of a polymer system in which we distinguish between the end (E) and the middle (M) groups. The free volume is represented as a "hole" or "void" (0), which constitutes a separate species in addition to the two "species" M and E. There are three different exchange interaction energies, and correspondingly three Boltzmann weights w(ij), i not equal j=0,E,M between different species. We define the free volume associated with the species j=M or E, as the average number of voids next to j. Using a recently developed equilibrium lattice theory, we calculate the free volume v(E) and v(M) associated with an end group and a middle group, respectively, and investigate the effects of interactions among them. Our calculations show that v(E) and v(M) are intricate functions of w(ij), the pressure and the molecular weight, and that their difference can change sign under certain conditions. These conditions are elucidated. We demonstrate that when the end group is chemically dissimilar from the middle group, the middle group may have more free volume than the end group. We find that the conditions that favor a middle group having more free volume over an end group are w(E0)<1, w(M0)<1, and w(ME)>1. The effect of pressure and molecular weight can be of either type and appears to be dependent on the interactions.

Supercooled liquids and the glass transition

Glasses are disordered materials that lack the periodicity of crystals but behave mechanically like solids. The most common way of making a glass is by cooling a viscous liquid fast enough to avoid crystallization. Although this route to the vitreous state-supercooling-has been known for millennia, the molecular processes by which liquids acquire amorphous rigidity upon cooling are not fully understood. Here we discuss current theoretical knowledge of the manner in which intermolecular forces give rise to complex behaviour in supercooled liquids and glasses. An intriguing aspect of this behaviour is the apparent connection between dynamics and thermodynamics. The multidimensional potential energy surface as a function of particle coordinates (the energy landscape) offers a convenient viewpoint for the analysis and interpretation of supercooling and glass-formation phenomena. That much of this analysis is at present largely qualitative reflects the fact that precise computations of how viscous liquids sample their landscape have become possible only recently.