Dependence of cooperative relaxation of amorphous polymers on diluent concentration

The Adam–Gibbs molecular theory, which describes the temperature dependence of relaxation phenomena in the main transition region in terms of the configurational entropy of a system, has been extended to include the effect of concentration of a low‐molecular‐weight compound on the viscoelastic behavior of concentrated polymer solutions. The concentration dependence of relaxation times in the polymer–diluent mixture leads to an expression of the concentration dependence both of the shift factor in the Williams–Landel–Ferry (WLF) equation and of the glass transition temperature Tg of the mixture. The constants of the WLF equation and the concentration dependence of Tg are given in terms of a difference between the specific heats of the liquid and glass ΔCp of the equilibrium temperature T2 of the second‐order transition, and of the parameter Δμs /k, which includes the chemical potential Δμ and the configurational entropy s of the smallest cooperatively rearranging region. The resulting relationships also predict the temperature dependence of the constants of the concentration WLF equation. Good agreement was found between theory and the viscoelastic and Tg data on the systems poly(vinyl acetate) + diethyl phthalate, poly(methyl methacrylate) + diethyl phthalate and polystyrene + dibutyl phthalate. This finding indicates that the configurational entropy, at least in the first approximation, is responsible for the concentration dependence of relaxation phenomena in concentrated polymer solutions.