Fragile vs strong liquids: a saddles ruled scenario

– 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 τintra and τinter are well separated, that is τinter ≫ τintra: 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Goldstein in [1] to define and estimate a crossover temperature Tx, above which this hopping-relaxation description is no longer valid, since τintra and τinter are not well separated. Below Tx, on the other hand, crossing of potential energy barriers by thermal activation becomes the primary mechanism of diffusion. The Goldstein temperature Tx is in general higher than the glass transition temperature Tg: in the interval Tg < T < Tx 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 Tx as the temperature below which the ideal Mode Coupling Theory (MCT) [5] breaks down. This is because MCT is considered