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

Abstract

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 highperformance 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.

Moment Analysis Method for Measurement of Reaction Equilibrium and Rate Constants by Using High-Performance Liquid Chromatography

“…Figure (A) indicates that DB18C6 does not react easily with Mg 2+ . A similar result was also observed for Li + . The low reactivity of DB18C6 with Mg 2+ and Li + probably stems from the low size compatibility between DB18C6 and the metal cation.…”

“…It is possible to form (DB15C5) 2 -K + . In the previous study, 21 chromatographic data were also analyzed on the assumption that (DB18C6) 2 -Rb + , (DB18C6) 2 -Cs + , and (DB15C5) 2 -K + are formed. It seems that the formation of an inclusion complex between crown ether and the metal cation with a stoichiometry of 2:1 is also correlated with d M /d CE .…”

“…Both S and L are in the free state in the mobile phase and are not chemically modified. In the previous study, 21 to demonstrate the effectiveness of the moment analysis method, it was applied to the inclusion complex formation systems, as an example, between crown ethers, i.e., dibenzo-18-crown-6 (DB18C6) and dibenzo-15crown-5 (DB15C5), and alkali metal cations, i.e., Li + , Na + , K + , Rb + , and Cs + . The validity of the moment analysis method was demonstrated by determining the values of K A , k a , and k d for the formation of the inclusion complexes between them.…”

“…In the previous study, it was implied that the degree of consistency in the size between the inner cavity of crown ether and metal cation provides an influence on the inclusion complex formation. It seemed that the values of K A , k a , and k d are correlated with the ratio of the diameter of the metal cation ( d M ) to that of the inner cavity of the crown ethers ( d CE ).…”

“…In this study, the moment analysis method was applied to other inclusion complex formation systems between DB18C6 and alkaline earth metal cations, i.e., Mg 2+ , Ca 2+ , and Sr 2+ . In addition, the inclusion complex formation between DB18C6 and two kinds of alkali metal cations, i.e., Na + and Cs + , was reanalyzed because experimental data were scattered in the previous study . Some items of information about experimental data and analytical results concerning the formation of inclusion complexes between DB18C6 and the two kinds of alkali metal cation were explained in the Supporting Information.…”