Calculation of the osmotic pressure and theta temperature of polymer solutions through cubic equations of state and the McMillan-Mayer solution theory framework

摘要

The osmotic compressibility factor of several polymer solutions was correlated with the polymer concentration and temperature through different cubic equations of state, with particular focus on the McMillan-Mayer solution theory. The equations of state employed were those of van der Waals, Redlich-Kwong, Peng-Robinson, and SoaveRedlich-Kwong. All of these equations present two parameters that take into account the attractive and repulsive interactions between the solute molecules in a given solvent, with these parameters being dependent on the nature of the system (solute and solvent) and on the temperature. As the attractive and repulsive interactions are well defined in the parameters of the cubic equations of state, the theta temperature for each polymer system studied may be calculated by a simple and efficient procedure. For the purposes of comparison, the virial equation truncated at the third term was also included in this study. It was confirmed that the attractive parameter has a linear dependence on the temperature, while the repulsive parameter varies according to a quadratic profile. Accordingly, the model to be minimized presents five adjustable parameters that depend only on the nature of the polymer system. The agreement between the experimental and calculated values is within the experimental error.