Thermodynamic Expressions Relating Different Types of Preferential Interaction Coefficients in Solutions Containing Two Solute Components

In aqueous solutions that contain a macromolecular solute (charged or uncharged) and molecules or ions of a smaller solute, differences between solute−macromolecule and water−macromolecule interactions have solute-concentration-dependent thermodynamic effects that are characterized quantitatively by “preferential interaction” coefficients. Of primary interest in this paper are Γμ1 and Γμ3, defined as partial derivatives that specify the dependence of the molality of the smaller solute on the macromolecular molality at fixed temperature and pressure and the chemical potential indicated by the subscript (μ1 for water and μ3 for the smaller solute). Coefficients of the type Γμ3 (but not Γμ1) are direct gauges of thermodynamic effects due to the preferential interactions of a small solute with a macromolecule. Although individual values of Γμ3 cannot generally be obtained directly by any experimental method, corresponding values of Γμ1 are directly measurable for involatile solutes (0.01 ≲ m3 ≲ 3 m) by an acc...