Fragile vs . strong liquids: A saddles-ruled scenario

Abstract

PACS. 61.20.Gy -Theory and models of liquid structure. PACS. 64.70.Pf -Glass transitions.Abstract. -In the context of the energy landscape description of supercooled liquids, we propose an explanation for the different behaviour of fragile and strong liquids. Above Goldstein's temperature Tx, diffusion is interpreted as a motion in the phase space among saddles of the potential energy. Two mechanisms of diffusion then arise: mechanism A takes place when the system overcomes potential energy barriers along stable uphill directions, while mechanism B consists in finding unstable downhill directions out of a saddle. Depending on the mutual efficiency of A and B, the usual classification of liquids in fragile and strong is recovered. Moreover, this scenario naturally predicts the possibility of a fragile-to-strong crossover when lowering the temperature.After the seminal paper by Goldstein in 1969 [1], it has become customary to think of the dynamical evolution of supercooled liquids in terms of motion of the state point of the system upon its rugged potential energy surface [2]. More precisely, at low temperatures, but above the glass transition, the diffusion of a system at equilibrium can be interpreted as the result of two different processes: the thermal relaxation into basins defined by the many minima of the potential energy (intra-basin relaxation) and the hopping from basin to basin by crossing potential energy barriers (inter-basin relaxation) [1].Crucial condition for this description to be correct is that the two relaxation times τ intra and τ inter are well separated, that is τ inter ≫ τ intra : if these time scales are of the same order, it is not sensible to discriminate between the thermalization inside a minimum and the hopping among different minima. Indeed, the very requirement of the separation between these two time scales led Goldstein in [1] to define and estimate a crossover temperature T x , above which this hopping-relaxation description is no longer valid, since τ intra and τ inter are not well separated. Below T x , on the other hand, crossing of potential energy barriers by thermal activation becomes the primary mechanism of diffusion. The Goldstein temperature T x is in general higher than the glass transition temperature T g : in the interval T g < T < T x a supercooled liquid is still in equilibrium on experimental times and can be described in terms of relaxation into basins and thermally activated hopping among them.Some authors [3,4] have subsequently interpreted T x as the temperature below which the ideal Mode Coupling Theory (MCT) [5] breaks down. This is because MCT is considered c EDP Sciences

Spin glasses and fragile glasses: Statics, dynamics, and complexity

“…The physical interpretation of this transition is rather simple: above the phase transition the system is near a saddle point of the Hamiltonian, whereas below it the system is near a local minimum of the Hamiltonian (63)(64)(65)(66)(67). This picture is very interesting, also because it gives a clear explanation of the origin and of the properties of the celebrated boson peak (68).…”

Real space origin of temperature crossovers in supercooled liquids

“…[30], in analogy with what happens in mean field models [31,32]: the vanishing as T approaches T c of the mean intensive number of negative directions (intensive index) of stationary points of the potential energy, n s (T ). Numerical simulations [33,34,35,36,37,38] found that n s (T ) decreases with decreasing T , and fits were performed to show that n s (T c ) = 0 [33,34,35].…”

Understanding fragility in supercooled Lennard-Jones mixtures. II. Potential energy surface

“…17,18,19,20,21,22,23 High-order stationary points could offer a simple explanation of the fragile behavior of glass-formers, in terms of an increase of average energy barriers. 24 This feature is encoded, in an effective way, in a number of models of energy landscapes developed in the last years, 25,26,27,28 and has sometimes been addressed in numerical simulations. 29 Statistical properties of high-order stationary points of the PES have been investigated recently for a variety of monoatomic and binary systems, both in the liquid 30,31 and supercooled regime.…”