Theory of relaxation dynamics in glass-forming hydrogen-bonded liquids

Using fit functions in computational dielectric spectroscopy

This work deals with the development of an appropriate set of fit functions for describing dielectric spectra based on simulated raw data. All these fit functions are of exponential character with properly chosen cofunctions. The type of the cofunctions is different for translation, rotation and their coupling. As an alternative to multiexponential fits we also discuss Kohlrausch-Williams-Watts functions. Since the corresponding Fourier-Laplace series for these stretched exponentials has severe convergence problems, we represent their Fourier-Laplace spectrum as a Havriliak-Negami expression with properly chosen parameters. A general relation between the parameter of the Kohlrausch-Williams-Watts and the Havriliak-Negami parameters is given. The set of fit functions is applied to the concrete simulation of the hydrated ionic liquid 1-ethyl-3-methyl-imidazolium triflate with H(2)O. The systematic variation of the water mole fraction permits to study the gradual transition from a neutral molecular liquid to molecular ionic liquids.

Quantitative theory of a time-correlation function in a one-component glass-forming liquid with anisotropic potential

The Shintani-Tanaka model is a glass-forming system whose constituents interact via an anisotropic potential depending on the angle of a unit vector carried by each particle. The decay of time-correlation functions of the unit vectors exhibits the characteristics of generic relaxation functions during glass transitions. In particular it exhibits a stretched exponential form, with the stretching index beta depending strongly on the temperature. We construct a quantitative theory of this correlation function by analyzing all the physical processes that contribute to it, separating a rotational from a translational decay channel. These channels exhibit different relaxation times, each with its own temperature dependence. Interestingly, the separate decay function of each of these processes is a temperature-independent function, and is shown to scale (exhibit data collapse) at different temperatures. Taken together with temperature-dependent weights determined a priori by statistical mechanics this allows one to generate the observed correlation function in quantitative agreement with simulations at different temperatures. This underlines the danger of concluding anything about glassy relaxation functions without detailed physical scrutiny.

Theory of specific heat in glass-forming systems

Experimental measurements of the specific heat in glass-forming systems are obtained from the linear response to either slow cooling (or heating) or to oscillatory perturbations with a given frequency about a constant temperature. The latter method gives rise to a complex specific heat with the constraint that the zero frequency limit of the real part should be identified with thermodynamic measurements. Such measurements reveal anomalies in the temperature dependence of the specific heat, including the so called "specific heat peak" in the vicinity of the glass transition. The aim of this paper is to provide theoretical explanations of these anomalies in general and a quantitative theory in the case of a simple model of glass formation. We first present interesting simulation results for the specific heat in a classical model of a binary mixture glass former. We show that in addition to the formerly observed specific heat peak there is a second peak at lower temperatures which was not observable in earlier simulations. Second, we present a general relation between the specific heat, a caloric quantity, and the bulk modulus of the material, a mechanical quantity, and thus offer a smooth connection between the liquid and amorphous solid states. The central result of this paper is a connection between the micromelting of clusters in the system and the appearance of specific heat peaks; we explain the appearance of two peaks by the micromelting of two types of clusters. We relate the two peaks to changes in the bulk and shear moduli. We propose that the phenomenon of glass formation is accompanied by a fast change in the bulk and the shear moduli, but these fast changes occur in different ranges of the temperature. Last, we demonstrate how to construct a theory of the frequency dependent complex specific heat, expected from heterogeneous clustering in the liquid state of glass formers. A specific example is provided in the context of our model for the dynamics of glycerol. We show that the frequency dependence is determined by the same alpha -relaxation mechanism that operates when measuring the viscosity or the dielectric relaxation spectrum. The theoretical frequency dependent specific heat agrees well with experimental measurements on glycerol. We conclude the paper by stating that there is nothing universal about the temperature dependence of the specific heat in glass formers-unfortunately, one needs to understand each case by itself.

Quantitative theory of a relaxation function in a glass-forming system

We present a quantitative theory for a relaxation function in a simple glass-forming model (binary mixture of particles with different interaction parameters). It is shown that the slowing down is caused by the competition between locally favored regions (clusters) that are long-lived but each of which relaxes as a simple function of time. Without the clusters, the relaxation of the background is simply determined by one typical length, which we deduce from an elementary statistical mechanical argument. The total relaxation function (which depends on time in a nontrivial manner) is quantitatively determined as a weighted sum over the clusters and the background. The "fragility" in this system can be understood quantitatively since it is determined by the temperature dependence of the number fractions of the locally favored regions.

Aging and relaxation in glass-forming systems

We propose that there exists a generic class of glass-forming systems that have competing states (of crystalline order or not) which are locally close in energy to the ground state (which is typically unique). Upon cooling, such systems exhibit patches (or clusters) of these competing states which become locally stable in the sense of having a relatively high local shear modulus. It is in between these clusters where aging, relaxation, and plasticity under strain can take place. We demonstrate explicitly that relaxation events that lead to aging occur where the local shear modulus is low (even negative) and result in an increase in the size of local patches of relative order. We examine the aging events closely from two points of view. On the one hand we show that they are very localized in real space, taking place outside the patches of relative order, and from the other point of view we show that they represent transitions from one local minimum in the potential surface to another. This picture offers a direct relation between structure and dynamics, ascribing the slowing down in glass-forming systems to the reduction in relative volume of the amorphous material which is liquidlike. While we agree with the well-known Adam-Gibbs proposition that the slowing down is due to an entropic squeeze (a dramatic decrease in the number of available configurations), we do not agree with the Adam-Gibbs (or the Volger-Fulcher) formulas that predict an infinite relaxation time at a finite temperature. Rather, we propose that generically there should be no singular crisis at any finite temperature: the relaxation time and the associated correlation length (average cluster size) increase at most superexponentially when the temperature is lowered.