A method for determination of thermodynamics and solubility parameters of polymers in dilute solutions from critical volume fractions

An equation using the critical volume fraction and segment number of polymer was proposed for the partial molar entropy change of a polymer for mixing in dilute solution. The partial molar enthalpy change of polymer for mixing was determined from the thermodynamic equilibrium property of two polymer phases at the critical temperature. The solubility or cohesion parameter of a polymer fraction at the critical temperature was calculated by using the partial molar enthalpy change and repeat unit volume of the polymer. The solubility parameter of high molar mass polymer at the theta temperature was determined by extrapolating solubility parameter values of the polymer fractions to high molar mass by using the solubility parameter-segment number relation of polymer fraction. This relation gives good straight line. The solubility parameter of the polymer at the theta temperature and the exchange energy parameter for polymer–solvent pair were obtained directly from the intercept and the slope of this line, respectively. These equations were applied to the critical point data of polystyrene (PS) in methylcyclohexane (MCH) and in cyclohexane (CH) solutions. The results obtained in this study coincide with the literature values for the solubility parameter of PS and exchange energy parameter for PS in CH solution. It was also found that the partial molar entropy change of a polymer for mixing at theta temperatures has about a constant value.