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For a deeply supercooled liquid near its glass transition temperature, wesuggest a possible way to connect the temperature dependence of its molarexcess entropy to that of its viscosity by constructing a macroscopic model,where the deeply supercooled liquid is assumed to be a mixture of solid-likeand liquid-like micro regions. In this model, we assume that the mole fractionx of the liquid-like micro regions tends to zero as the temperature T of theliquid is decreased and extrapolated to a temperature Tg*, which we assume tobe below but close to the lowest glass transition temperature Tg attainablewith the slowest possible cooling rate for the liquid. Without referring to anyspecific microscopic nature of the solid-like and liquid-like micro regions, wealso assume that near Tg, the molar enthalpy of the solid-like micro regions islower than that of the liquid-like micro regions. We then show that thetemperature dependence of x is directly related to that of the molar excessentropy. Close to Tg, we assume that an activated motion of the solid-likemicro regions controls the viscosity and that this activated motion is acollective motion involving practically all of the solid-like micro-regions sothat the molar activation free energy for the activated motion is proportionalto the mole fraction, 1-x, of the solid-like micro regions. The temperaturedependence of the viscosity is thus connected to that of the molar excessentropy through the temperature dependence of the mole fraction x. As anexample, we apply our model to a class of glass formers for which the molarexcess entropy at temperatures near Tg is proportional to 1-T/TK with TK < Tg\sim Tg* and find their viscosities to be well approximated by theVogel-Fulcher-Tamman equation for temperatures very close to Tg. We estimatethe values of three parameters in our model for three glass formers in thisclass.

A macroscopic model that connects the molar excess entropy of a deeply supercooled liquid near its glass transition temperature to its viscosity