Communication: Towards first principles theory of relaxation in supercooled liquids formulated in terms of cooperative motion

Abstract

A general theory of the long time, low temperature dynamics of glass-forming fluids remains elusive despite the almost 20 years since the famous pronouncement by the Nobel Laureate P. W. Anderson, "The deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition" [Science 267, 1615 (1995)]. While recent work indicates that Adam-Gibbs theory (AGT) provides a framework for computing the structural relaxation time of supercooled fluids and for analyzing the properties of the cooperatively rearranging dynamical strings observed in low temperature molecular dynamics simulations, the heuristic nature of AGT has impeded general acceptance due to the lack of a first principles derivation [G. Adam and J. H. Gibbs, J. Chem. Phys. 43, 139 (1965)]. This deficiency is rectified here by a statistical mechanical derivation of AGT that uses transition state theory and the assumption that the transition state is composed of elementary excitations of a string-like form. The strings are assumed to form in equilibrium with the mobile particles in the fluid. Hence, transition state theory requires the strings to be in mutual equilibrium and thus to have the size distribution of a self-assembling system, in accord with the simulations and analyses of Douglas and co-workers. The average relaxation rate is computed as a grand canonical ensemble average over all string sizes, and use of the previously determined relation between configurational entropy and the average cluster size in several model equilibrium self-associating systems produces the AGT expression in a manner enabling further extensions and more fundamental tests of the assumptions. © 2014 AIP Publishing LLC. [http://dx

Quantitative relations between cooperative motion, emergent elasticity, and free volume in model glass-forming polymer materials

“…The approach of AG is further advanced by recognition that the strings can be analytically described as a kind of equilibrium polymerization, enabling a functional form for string length L that can be extended to the glass transition (21). Recently, Freed (22) provided an analytic extension of transition state theory that accounts for string-like cooperative barrier crossing events, providing a theoretical basis for the string model extension of the AG description (21). Our analysis of data starts from this fully developed "string model" of relaxation, a quantitative descendant of the AG model that preserves the original AG conception of the physical nature of glass formation.…”

“…The venerable Adam-Gibbs (AG) theory of glass formation (18), and the more recent random first-order transition theory (19), emphasize the temperature dependence of the configurational entropy in cooled liquids and its relation to collective motion, although these theories do not explicitly define the form of the "cooperatively rearranging regions" (CRRs). This approach can be extended by identifying these CRRs with string-like clusters of cooperative particle exchange motion (20)(21)(22) and analytic calculation of the configurational entropy (23). In addition to these approaches to glass formation, the mode-coupling theory (24), and dynamic facilitation models (25) postulate a "dynamical" glass transition that is unrelated to any underlying thermodynamic transition.…”

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

“…These results strongly suggest that the time scale described by the AG relation is proportional to D A and not to τ α,A (or η). Theoretical investigations along the lines of [23][24][25]52] therefore offer a promising way of investigating further and rationalising our results.…”

“…Recent works have proposed cooperatively moving highly mobile particles, called "strings", as candidates for CRR [23,25,50,51], in that the string length is found to be inversely proportional to the configurational entropy as envisaged in the AG theory. The string life time is found to be proportional to t * , the time when the non-Gaussian parameter α 2 is maximum [23].…”

“…Its rationalization is considered fundamental to understanding the glass transition problem [20][21][22][23][24][25][26][27][28][29][30]. The AG relation can be written as X(T ) = X 0 exp A X T Sc(T ) , where X is an appropriate measure of dynamics i.e.…”