Physical parameters that characterize macromolecular or colloidal systems often depend on the properties of different molecular species in equilibrium with one another , Typical examples are encountered in experiments that use spectroscopic or electrochemical probes to characterize surfactant aggregates or protein solutions and in studies of the influence of salt on the solubility of proteins in solution. The general theory of linked functions or thermodynamic linkage theory, developed in the early 1960s by Wyman , provides a molecular and thermodynamic basis to analyze data from such systems.
The thermodynamic linkage approach can be used to relate an observed property (fohs) to the properties of the individual components of the system that are linked together in coupled equilibria. For example, if Pj is the property we wish to investigate, and f is the fraction of the y'th component in the system, a three-component system is represented by
In general, for a system with k + 1 contributing components,
Equations such as (6.1) and (6.2) can be used as models for nonlinear regression after the fractions fi are expressed in terms of the relevant equilibria and equilibrium constants of the system . In this chapter, we set out the general theory needed for obtaining the fractions fi and discuss a number of examples of its use.
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