(71f) On Estimate of Change in Change in Entropy of Mixing at Glass Transition of Partially Miscible Blends

A mathematical framework was developed by Sharma (1998) to account for multiple glass transition temperatures observed using Differential Scanning Calorimeters in partially miscible blends. A thermodynamically miscible blend of more than one polymer posses one unique glass transition temperature. Immiscible blends have been found to have the same glass transition temperatures as the constituents. The partially miscible blends have been observed to have two or more glass transition temperatures different or shifted from the blend constituent values. The quadratic expression can be written as;

ATg^2 + BTg + C = 0

when beta is 0 the case of immiscible blends result and when beta is infinity the case of miscible blends result. The partially miscible blends are somewhere inbetween. In industrial practice, systems such as PVC/SAN, PC/SAN over certain AN compositions, PET/PHB have been found to be partially miscible. Estimates of entropy change of blend can be expressed in terms of delta P of the blends. The combined first two laws of thermodynamics can be written as;

Äh = TgÄS + VÄP For the simple case of isothermal and isochoric blending process;

ÄÄS = -V/Tg(ÄÄP)

Modifying the Couchman equation (1978)including the dissimilair of entropy of mixing effects a cubic equation results for the blend glass transition temperature. The Taylor approximation was used to render the equation from trancedental to algebraic with closed form direct solution. The cubic equation can be solved for by use of Vieta's substitution or by reducing it to a quadratic once one root is known. The cubic equation assumes the form;

az^3 + bz^2 - cz - d = 0

where a, b, c and d are expressed in terms of change in heat capacity, change in pressure, volume of blend anf composition of blend. The implications of this expression are discussed.