Analysis of self-associations from partition isotherms

Self-associations can be studied from the measurements of the partition of the self-associating solute between two immiscible liquids. The apparent partition coefficient, Kapp, is proportional to the ratio of the apparent weight fraction of monomer, fa, in each phase. If one assumes that the Adams-Fujita convention for the activity coefficients of the self-associating species applies, then fa is related to Mna and Mwa, the apparent values of the number and weight average molecular weights, respectively; and one can use previously developed methods to analyze the self-association. In order to use the method, one must make an independent study at the same temperature of one of the phases by an appropriate thermodynamic method, such as vapor pressure osmometry or sedimentation equilibrium. Then one can test the other phase for the type of self-association present and evaluate the equilibrium constant or constants (ki) and the nonideal term (BM1) from the partition data. One can also evaluate the partition coefficient (Kpar). From these measurements, one can obtain the free energy (delta G0) for the association in each phase and for the transfer between phases. Temperature-dependence studies will provide the enthalpy (delta H0) or entropy (delta S0) of self-association or transfer. This method should be quite useful for studying small molecules of biological importance.