Glass-forming liquids: one or more ‘order’ parameters?

Abstract

We first summarize the classical arguments that the vast majority of glass-forming liquidsrequire more than one ‘order’ parameter for their description. Critiques against thisconventional wisdom are then presented, and it is argued that the matter deserves to bereconsidered in the light of recent experimental developments. Out of the eight basicthermoviscoelastic frequency-dependent response functions, there are generally threeindependent functions. For stochastic dynamics we show that there are only twoindependent response functions; for this case it is shown how analytic continuation may beutilized to express the third response functions in terms of two others. Operationalcriteria are presented for the linear thermoviscoelasticity being described by a single‘order’ parameter, in which case there is just one independent thermoviscoelasticresponse function. It is shown that a description with a single ‘order’ parameterapplies to a good approximation whenever thermal equilibrium fluctuations offundamental variables like energy and pressure are strongly correlated. Resultsfrom computer simulations showing that this is the case for a number of simpleglass-forming liquids, as well as a few exceptions, are briefly presented. Finally,we briefly discuss a new conjecture according to which experiments at varyingtemperature and pressure follow the density scaling expression for the relaxation time,τ = F(ρx/T) (ρ and T are density and temperature), if and only if the liquid is ‘strongly correlating’, i.e., to agood approximation is described by a single ‘order’ parameter.