Kanji Miyabe

Moment equations for chromatography based on Langmuir type reaction kinetics

Moment equations were derived for chromatography, in which the reaction kinetics between solute molecules and functional ligands on the stationary phase was represented by the Langmuir type rate equation. A set of basic equations of the general rate model of chromatography representing the mass balance, mass transfer rate, and reaction kinetics in the column were analytically solved in the Laplace domain. The moment equations for the first absolute moment and the second central moment in the real time domain were derived from the analytical solution in the Laplace domain. The moment equations were used for predicting the chromatographic behavior under hypothetical HPLC conditions. The influence of the parameters relating to the adsorption equilibrium and to the reaction kinetics on the chromatographic behavior was quantitatively evaluated. It is expected that the moment equations are effective for a detailed analysis of the influence of the mass transfer rates and of the Langmuir type reaction kinetics on the column efficiency.

Kinetic Study of Interaction between Solute Molecule and Surfactant Micelle

We developed moment analysis of affinity kinetics by chromatographic capillary electrophoresis (MKCCE) method for the kinetic study of intermolecular interactions. Association and dissociation rate constants of the interaction in a micellar electrokinetic chromatography (MEKC) system between thymol and sodium dodecylsulfate micelle were determined by the MKCCE method. It is a method based on the moment theory for the kinetic study of intermolecular interactions under the conditions that neither immobilization nor chemical modification of molecules is required. In CCE mode, experimental conditions are controlled so that the migration of solute-micelle complex is stopped and only solute molecules migrate in a capillary. Mass transfer behavior of solute molecules in the CCE system is analogous to that in a chromatographic system. However, because it was difficult in practice to really perform CE experiments under the CCE conditions, CE data were measured with changing experimental conditions, i.e., applied pressure, under the conditions that the migration velocity of solute-micelle complex was around zero. The rate constants could be analytically determined from the CE data. In the MKCCE method, it is not necessary to fit elution curves numerically calculated to those experimentally measured for the determination of the rate constants. Regarding the interaction between thymol and SDS micelles, association equilibrium constant and association and dissociation rate constants were determined as 6.35 × 10(3) dm(3) mol(-1), 5.6 × 10(4) dm(3) mol(-1) s(-1), and 8.7 s(-1), respectively. It was demonstrated that the MKCCE method was effective for the kinetic study of intermolecular interactions.

Moment Analysis of Mass Transfer Kinetics in Micellar Electrokinetic Chromatography Systems

Moment equations were developed for quantitatively studying the separation characteristics of micellar electrokinetic chromatography (MEKC). They explain how the first absolute and second central moments of elution peaks are correlated with some fundamental parameters of the partition equilibrium and mass transfer kinetics in MEKC systems. In order to discuss the influence of the mass transfer kinetics on peak broadening, the moment equations were used to analyze the separation behavior in MEKC systems. Separation conditions were chosen on the basis of practical MEKC experiments previously conducted. It was quantitatively clarified that both the solute permeation at the interfacial boundary of surfactant micelles and axial diffusion of solute molecules in a capillary had a predominant contribution to the spreading of the elution peaks in MEKC systems. This is a preliminary study for the analytical determination of rate constants concerning solute permeation at the interface of surfactant micelles from elution peak profiles measured by MEKC. In addition, it was also indicated that the experimental conditions of MEKC systems could be controlled so that the interfacial solute permeation would have a predominant role for the band broadening. For example, the contribution of the interfacial permeation was about 33 times larger than that of the axial diffusion of solute molecules under the MEKC conditions in a previous study. This means that the rate constants could appropriately be determined for the interfacial solute permeation.

Numerical correction for asymmetrical peak profiles for moment analysis of chromatographic behavior

A numerical correction method is proposed for the moment analysis of some properties of chromatographic columns, even when the profiles of their elution peaks exhibit some asymmetry. Information on the retention equilibrium and the mass transfer kinetics of a C18-silica gel packing material is derived by the moment analysis from the experimental data obtained under three different sets of conditions: (1) the tailing peaks eluted from the column used; they are not corrected by the numerical method; (2) the same peaks are corrected by the numerical method, which provides the information on the column radial heterogeneity and on the efficiency at its center; and (3) symmetrical peaks having nearly Gaussian profiles eluted from another column packed with the same material; these peaks are not corrected by the numerical method. The analytical results obtained under the three different conditions are compared. The results demonstrate that the numerical correction method allows the determination of the information on the chromatographic behavior of columns from asymmetrical peak profiles, i.e., column efficiency at radial center, order of the polynomial functions for representing the radial distributions of mobile phase flow velocity and column efficiency, ratio of the flow velocity near the wall to that at the column center, and ratio of the column efficiency near the wall to that at the column center.

Moment analysis for reaction kinetics of intermolecular interactions

Moment equations were developed on the basis of the principle of relativity for analyzing elution peak profiles measured by ACE to analytically determine the association (ka) and dissociation (kd) rate constants of intermolecular interactions. Basic equations representing the mass balance, mass transfer rate, and reaction kinetics in ACE system in a Galilean coordinate system S were transformed to those in another coordinate system S′, which imaginarily moved with respect to S. Moment equations for ACE peaks in S′ in the time domain were derived from the analytical solution of the modified basic equations in the Laplace domain. Moment equations for ACE peaks in S were derived from those in S’ by the inverse Galilean transformation. The moment equations were used for analyzing some ACE data previously published to determine ka and kd values. It was demonstrated that the moment equations were effective for extracting the information about affinity kinetics of intermolecular interactions from the elution peak profiles measured by ACE. The moment equations were also used to discuss the influence of mass transfer and reaction kinetics on ACE peak profiles. Some results of the numerical calculations are also indicated in Supporting Information.

Kinetic Study of Chiral Intermolecular Interactions by Moment Analysis Based on Affinity Capillary Electrophoresis

Capillary electrophoresis is a method for analyzing intermolecular interactions that does not require immobilization of molecules to a solid surface or introduction of a luminescent moiety. Recently, an advanced method, moment analysis based on affinity capillary electrophoresis (MA-ACE), was developed. This method can determine not only the equilibrium constant but also the rate constants of an intermolecular interaction. Through MA-ACE, it became possible to theoretically predict an increase in the variance of an observed peak caused by intermolecular interaction. In this study, we confirm the prediction and determine the kinetic constants by using MA-ACE to analyze an intermolecular interaction between cyclodextrin and phenoxypropionic acid. A numerical calculation is performed to confirm that the derived rate constants by MA-ACE are appropriate.