Exothermodynamic relationships in liquid chromatography

Exothermodynamic relationships in reversed-phase and hydrophobic interaction chromatography, with the temperature, organic modifier or salt concentration, and carbon number of the eluite and of the stationary phase ligate as the operating variables, are classified and the links between various linear free energy relationships established. Starting from Martin's relationship based on group additivity, we arrive at two linear free energy relationships: one between the logarithmic retention factors, kappa, obtained on two different columns with eluites of close structural similarity and the other between kappa and the logarithmic octanol-water partition coefficient. Molecular interpretation of classical enthalpy-entropy compensation is offered by the combination of van't Hoff's relationship with linear exothermodynamic relationships between thermodynamic quantities on one hand and properties of the eluite, the eluent, or the stationary phase on the other. Thus, the compensation temperature is expressed by the enthalpy and entropy changes per unit of the above properties. Furthermore, the criterion for the invariance of the compensation temperature is set within the framework of dual compensation. A generalized compensation model is developed to extend the concept of enthalpy-entropy compensation to phenomena involving compensation by any two chromatographic variables by drawing analogies between the dependence of kappa on the reciprocal temperature and on other operating variables, such as the organic modifier concentration in the eluent. The existence of 12 different compensation parameters is revealed, each marking the common intersection point of linear plots of free energy versus variables of the retention process. The compensation model leads to 12 three-parameter equations, each describing the retention behavior in reversed-phase chromatography as a function of two chromatographic variables. The family of exothermodynamic relationships encompasses most characteristic features of chromatographic retention and is expected to facilitate the organization, interpretation, and prediction of retention data.