Mass and Heat Diffusion in Ternary Polymer Solutions: A Classical Irreversible Thermodynamics Approach

摘要

Governing equations for evolution of concentration and temperature inthree-component systems were derived in the framework of classical irreversiblethermodynamics using Onsager variational principle and were presented forsolvent/solvent/polymer and solvent/polymer/polymer systems. The derivation wasdeveloped from the Gibbs equation of equilibrium thermodynamics using the localequilibrium hypothesis, Onsager reciprocal relations and Prigogine theorem forsystems in mechanical equilibrium. It was shown that the details of mass andheat diffusion phenomena in a ternary system are completely expressed by a 3x3matrix whose entries are mass diffusion coefficients (4 entries), thermaldiffusion coefficients (2 entries) and three entries that describe theevolution of heat in the system. The entries of the diffusion matrix arerelated to the elements of Onsager matrix that are bounded by some constraintsto satisfy the positive definiteness of entropy production in the system. Allthe elements of diffusion matrix were expressed in terms of derivatives ofexchange chemical potentials of the components with respect to concentrationand temperature. The spinodal curves of ternary polymer solutions were derivedfrom the governing equations and their correctness was checked by the Hessianof free energy density. Moreover, it was proved that setting cross-diffusioncoefficients to zero results in a contradiction, and, the governing equationswithout cross-diffusion coefficients do not express the actual phase behaviorof the system.