General Theory of Polymer Solutions

Abstract

A general theory of the thermodynamic properties of polymer solutions is given. The theory is intended to be valid for every concentration range. The formalism begins with the assumption of some functional relation between the local free energy density, for an assigned polymer configuration, and the local concentration of segments belonging to various polymer chains. That is, the thermodynamic properties of the segments are presumed known, and the problem is taken to be the determination of changes in the thermodynamic properties which are induced by a joining of the segments into a polymer chain. The local segment concentration is assumed to be close enough to the bulk or average concentration that a Taylor series expansion of the local free energy can be made and cut off at the term containing the square of the fluctuation in local concentration. The resulting free energy of the whole solution can then be cast into a form which includes as one part the free energy of a random distribution of segments, and as a second part the free energy of an imperfect gas with a pairwise additive intermolecular potential, albeit a concentration‐dependent potential. At low concentrations the results are identical to previous treatments based on imperfect gas theory. At high concentrations a previously introduced calculation of the radial distribution function is employed to show that the thermodynamic properties are accurately described as those of a random distribution of segments. The Flory‐Huggins formula is an example of a free‐energy function which can be assumed to hold locally at any concentration, but is then found to hold macroscopically only at high concentrations.