Free volume, excess entropy and mechanical behavior of polymeric glasses

Abstract

AbstractFree volume fraction of the Williams‐Landel‐Ferry(WLF)‐Doolittle type has been applied to the analysis of the nonequilibrium state for the glassy polymers. The free volume fraction is a two parameter variable since it depends on the free volume and the occupied volume. The excess entropy is derived from the mixing of vacant and occupied sites, and for polymers a factor is added which corresponds to disordering the molecular segments. A relationship between the excess entropy and enthalpy is derived. For a given level of fractional free volume, there is a unique rate constant associated with changing that level of the fractional free volume. The reciprocal of this rate constant, which depends on the exponential order of the fractional free volume, can be considered as a time constant for changing the molecular conformational probability, and its value is in the order of the average dielectric relaxation time in the corresponding state. When mechanical deformation is. imposed with a rate which is too fast as compared to this time constant, the deformation without a change in the conformational probability, i.e., the reversible elastic deformation, will ensue. In contrast, a sufficiently slow deformation will be accompanied by a change in fractional free volume and the excess entropy, and the above‐mentioned time constant will change with deformation. Since dilation will tend to shorten this time constant, tensile deformation will result in reducing the modulus accompanied by the increase in entropy. Shear deformation is considered as a mixture of compression and tension, where only tension contributes to a change in entropy, and the net result is the strain softening which can be predicted from the tensile behavior. Uniaxial compression is controlled by the shear behavior, and the excess entropy and the fractional free volume increase, while the occupied volume decreases with strain. A constitutive relationship has been proposed which accounts for the effects of temperature, pressure, strain rates and thermal history on nonlinear viscoelastic behavior of polymeric glass.