Thermodynamic Nonideality in Macromolecular Solutions: Interpretation of Virial Coefficients

Consideration is given to the interpretation of virial coefficients reflecting thermodynamic nonideality in incompressible solutions of a single macromolecular species for which there is no volume change on mixing. Expressions are presented for the concentration dependence of thermodynamic activity under conditions where either the chemical potential of solvent or the pressure is fixed, these two conditions being mutually exclusive. For the former situation, which applies to partition equilibrium procedures, the thermodynamic activity is most conveniently defined on the molar scale because the coefficients in polynomial expansions for the osmotic pressure and the activity coefficient in terms of molarity are then related to each other without the inclusion of partial molar volume terms. Under conditions of constant pressure a similar situation prevails provided that the osmotic pressure and the corresponding activity coefficient are expanded in powers of molality. In either case conversion of the virial expansions to the other concentration scale is possible, but requires the introduction of partial molar volume terms into the virial coefficients. The implications of these findings are discussed in relation to results obtained by osmometry, isopiestic measurements, equilibrium dialysis, gel chromatography, and sedimentation equilibrium.