A statistical mechanical non-lattice coordination theory to describe the solution thermodynamics of polymer mixtures.

Abstract

A theoretical model has been developed to advance the study of the thermodynamics of highly concentrated binary polymer solutions. This statistical mechanical theory was developed to allow the modeling of the molar Gibbs and Helmholtz free energies of mixing as well as the standard derived functions, such as the solvent and solute activities, and the molar enthalpies and entropies of mixing. Three major results have been generated from this work: (1) The polymer/solvent interactions can be partitioned into a coordination term, which leads to a configurational entropy, and an interaction energy of mixing term, which leads to the standard enthalpy of mixing; (2) The temperature dependence of the enthalpy of mixing yields an interaction energy of mixing which incorporates an additional entropy of mixing which is present for all types of systems, even athermal mixtures; and (3) The theory enables the use of experimentally obtained enthalpies of mixing to be used directly in the prediction of solvent activities, and experimentally determined solvent activities to be used as a predictor of the enthalpies of mixing without differentiating the experimental data. The theory was tested on fifteen binary systems. These systems had a range of physical property characteristics, from mixtures which can be considered almost ideal, to highly non-ideal athermal polymer solutions, to aqueous polymer solutions. The studied systems were; benzene/cyclopentane, benzene/cyclohexane, benzene/biphenyl, benzene/diphenylmethane, benzene/1,2-diphenylethane, cyclohexane/bicyclohexyl, n-hexane/n-hexadecane, toluene/polystyrene, chloroform/polystyrene, methylethylketone/polystyrene, cyclohexane/polystyrene, benzene/polypropylene glycol, benzene/polyethylene glycol, water/glucose, and water/polyethylene glycol. Parameters for each of these systems and components are tabulated. The experimental solvent activity data are graphed with the regression lines, and the experimental enthalpy of mixing data are graphed with the curves predicted from the solvent activity parameters. The average relative error of fit for the regression of the solvent activity data up to a polymer volume fraction of about 0.85 is less than ±0.0035, while for the entire solvent activity data set it is ±0.025. The average relative error of fit for the molar enthalpy of mixing predictions (excluding the water/PEG data) is less than ±0.005.