Sedimentation equilibrium in nonideal heterogeneous systems. I. Fundamental equations for heterogeneous solute systems and some preliminary results

Abstract

AbstractThe sedimentation‐equilibrium method is extended to treat nonideal solutions of heterogeneous macromolecules. The solute is assumed to be heterogeneous not only in molecular weight but also in other quantities such as partial specific volume, second virial coefficient and specific refractive increment. General expressions for various observable molecular weights, especially for weight‐average, z‐average, and number‐average molecular weights, are derived. Their dependences on sedimentation parameter and solute concentration are discussed in detail. For the extrapolation of observable molecular weights, giving a type of weight‐average, and z‐average, to infinite dilution to estimate the molecular weight and the second virial coefficient, average concentration is superior as a concentration variable to original concentration. The plots of observable molecular weight versus average concentration are usually less influenced by the choice of the sedimentation parameter, especially of rotor speed. The general expressions are applied to a few special cases; monodisperse polymer, polydisperse homologous polymer, and polymer blend. The results are compared with experiments on a monodisperse, polystyrene, a polydisperse poly(methyl methacrylate), and a mixture of the two polymers, all in 2‐butanone at 25°C. The agreement between the theory and experiments is satisfactory.