Liquid–liquid phase separation in multicomponent polymer solutions. IX. Concentration‐dependent pair interaction parameter from critical miscibility data on the system polystyrene–cyclohexane

Abstract

Critical miscibility data obtained from measurements of phase‐volume ratios have been used to calculate the concentration dependence of the pair interaction parameter for the system polystyrene–cyclohexane. The measured temperature and concentration ranges are 11–30°C and 4–18% polymer by weight, respectively. With the Gibbs free energy of mixing expressed in polymer segment mole fractions, x^*, the pair interaction parameter is g(x^*, T) = 0.4961 + 71.92/T + 0.2312x^* + 0.0750x^*2. In a polymer volume fraction formulation the parameter is g(φ, T) = 0.4099 + 90.65/T + 0.2064 φ + 0.0518 φ², which approximates to χ(φ, T) = 0.2035 + 90.65/T + 0.3092 φ + 0.1554 φ². Comparison of the temperature and concentration dependence with that obtained by other authors shows very good agreement, even when extensive extrapolations in temperature and concentration are applied. The present function is believed to be the most accurate. Solutions of mixtures of two narrow‐distribution polystyrenes in cyclohexane show separation into three liquid phases under the exact conditions predicted by theoretical calculation with the present pair‐interaction function.