Moment Theory of Chromatography for the Analysis of Reaction Kinetics of Intermolecular Interactions

Moment theory was applied to the kinetic study of intermolecular interactions. The association equilibrium constant (K_A) and association (k_a) and dissociation (k_d) rate constants of chemical reactions were analytically determined on the basis of the moment theory from elution peak profiles measured by high-performance liquid chromatography (HPLC). The HPLC data were measured under the conditions that neither immobilization nor fluorescence labeling of solute and ligand molecules is required. These are the advantages of the moment analysis method for determining accurate values of K_A, k_a, and k_d. Moment equations were developed on the basis of the Einstein equation for diffusion, the random walk model, and the general rate model of chromatography. The moment analysis method was applied to the inclusion complex formation system between dibenzo-18-crown-6 or dibenzo-15-crown-5 and alkali metal cations. It was demonstrated that the values of K_A, k_a, and k_d can be determined on the assumption that the stoichiometry between crown ethers and cations is 1:1 or 2:1. The influence of the difference in the size between the inner cavity of crown ethers and cations on the association and dissociation of the inclusion complex was considered. The moment analysis method using HPLC is effective for analyzing intermolecular interactions from various perspectives because it is based on the separation technique and has different characteristics from other methods such as spectroscopy. The results of this study contribute to the dissemination of an opportunity for studying intermolecular interactions from equilibrium and kinetic points of view to many researchers because HPLC is widespread.