Fluctuation Effects in the Adam-Gibbs Model of Cooperative Relaxation.

A generalization of the Adam-Gibbs model of relaxation in glass-forming liquids is formulated that takes into account fluctuation in the number of molecules inside the cooperative region. The configurational fraction links the excess entropy with kinetic properties described in the Adam-Gibbs model. We express the configurational fraction at the glass-transition temperature in terms of the width of the distribution of relaxation times, the nonlinearity parameter that demarcates the variations of the relaxation time with structure and temperature, the steepness index that is proportional to the slope of the logarithm of the relaxation time with respect to temperature, the excess heat capacity under constant pressure, and the number of correlated molecules or structural units. The configurational fraction in the absence of fluctuation effects is also determined for several glass-forming liquids at the glass-transition temperature.