Investigations of the role of spatial dimensionality and interparticle interactions in model glass-formers

Abstract

Liquids and solids are low temperature phases of matter and are ubiqui- tous in nature. When a liquid is cooled to temperature below the freezing temperature, under equilibrium condition, it undergoes a first order phase transition to a crystalline solid. However a finite amount of time is required for the development (“nucleation”) of crystalline order (“nucleation time” τnucleation). Similarly, a finite amount of time (“relaxation time” τrelaxation) is required for the liquid to reach equilibrium at a given temperature T. The typical temperature dependence of τnucleation and τrelaxation are schematically shown in Fig. 1.1(a) (the red and the blue lines respectively). Typically, as a liquid is cooled, τnucleation goes through a minimum (because it is deter- mined by the competition between (i) a free energy barrier-crossing prob- ability which increases monotonically and (ii) the mobility which decreases monotonically as T decreases) and τrelaxation increases monotonically. Fur- ther τnucleation > τrelaxation at any given T so that the two curves do not intersect each other. Thus there is the following interesting possibility : if a liquid is cooled with a cooling rate such that the amount of time spent at a given temperature is more than τrelaxation but less than τnucleation then it can avoid crystallization and can remain in the liquid phase even below its freezing point. This is the window between the red (non-monotonic) line and the blue (monotonic) line at any given temperature in Fig. 1.1(a).