Fragilities of liquids predicted from the random first order transition theory of glasses

Abstract

A microscopically motivated theory of glassy dynamics based on an underlying random first order transition is developed to explain the magnitude of free energy barriers for glassy relaxation. A variety of empirical correlations embodied in the concept of liquid "fragility" are shown to be quantitatively explained by such a model. The near universality of a Lindemann ratio characterizing the maximal amplitude of thermal vibrations within an amorphous minimum explains the variation of fragility with a liquid's configurational heat capacity density. Furthermore, the numerical prefactor of this correlation is well approximated by the microscopic calculation. The size of heterogeneous reconfiguring regions in a viscous liquid is inferred and the correlation of nonexponentiality of relaxation with fragility is qualitatively explained. Thus the wide variety of kinetic behavior in liquids of quite disparate chemical nature reflects quantitative rather than qualitative differences in their energy landscapes.I t is believed that all classical fluids could form glasses if cooled sufficiently fast so as to avoid crystallization. Central to glass formation is a dramatic slowing of molecular motions on cooling the liquid. The existence of a universal description of glass transitions is suggested by empirical observations connecting deviations from the Arrhenius law for the slowing of rates, nonexponential relaxations in the super cooled liquid state, and the behavior of thermodynamic properties on cooling (1). Quantitative differences in behavior of different substances sometimes obscure this universality. This has led to a classification of liquids into "fragile" ones like o-terphenyl, having the most dramatic deviations from the Arrhenius law, and into "strong" ones like pure SiO 2 where the Arrhenius equation works well (1). In this paper, we show how the fragile versus strong behavior of liquids can be understood within a microscopically motivated theory based on the idea that glassy dynamics is caused by an underlying thermodynamic, ideal "random first order" transition (2-7).The notion that a random first order transition lies at the heart of glass formation received its early theoretical support from the remarkable confluence of approximate microscopic theories of the liquid glass transition (8-10) and the behavior of a large class of exactly solvable statistical mechanical models of spin glasses with quenched disorder (11). Two closely connected theories of the liquid glass transition suggest features similar to first order transitions. One of these, the so-called mode-mode coupling theory (8, 12), focuses on the feedback between the slow fluctuations of fluid density in a molecule's environment on the motion of that molecule. This theory predicts a sharp transition in the dynamics as well as a characteristic behavior of the time correlation functions near the predicted transition. Mössbauer effect (13) and neutron scattering (14) are roughly consistent with these precursor phenomena. At temperatures below the transit...

Intermolecular Forces and the Glass Transition

“…The universal features of the dynamics of supercooled liquids and glasses are explained by the random first order transition theory 1,25,37,38 . At the mean field theory level the underlying microscopic framework provides a description of several characteristic transition temperatures that are expected in glassy systems.…”

Universal scaling between structural relaxation and vibrational dynamics in glass-forming liquids and polymers

“…2 offers the opportunity to find the DW factor u 2 g at the glass transition of the model polymer system. At the glass transition τ α = τ α g ≡ 10 2 s in laboratory units 1 24 (f ∼ = 0.1). Our data yield f ∼ 0.12-0.13 (d is taken from the monomer radial distribution function), which is close to f = 0.129 for the melting of a hard-sphere face-centred cubic solid 22 .…”

Route to calculate the length scale for the glass transition in polymers

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