Can One Measure Rate Constants Using Chromatographic Methods?

Thermodynamic and Kinetic Characterization of Polycyclic Aromatic Hydrocarbons in Reversed-Phase Liquid Chromatography

The retention of six polycyclic aromatic hydrocarbons (PAHs) was characterized by reversed-phase liquid chromatography. The PAHs were detected by laser-induced fluorescence at four points along an optically transparent capillary column. The profiles were characterized in space and time using an exponentially modified Gaussian equation. The resulting parameters were used to calculate the retention factors, as well as the concomitant changes in molar enthalpy and molar volume, for each PAH on monomeric (2.7 micromol/m2) and polymeric (5.4 micromol/m2) octadecylsilica. The changes in molar enthalpy become more exothermic as ring number increases and as annelation structure becomes less condensed. The changes in molar volume become more negative as ring number increases for the planar PAHs, but are positive for the nonplanar solutes. In addition, the rate constants, as well as the concomitant activation enthalpy and activation volume, are calculated for the first time. The kinetic data demonstrate that many of the PAHs exhibit very fast transitions between the mobile and stationary phases. The transition state is very high in energy, and the activation enthalpies and volumes become greater as ring number increases and as annelation structure becomes less condensed. The changes in thermodynamic and kinetic behavior are much more pronounced for the polymeric phase than for the monomeric phase.

Thermodynamics and kinetics of solute transfer in reversed-phase liquid chromatography

In this study, the thermodynamic and kinetic behavior of a homologous series of fatty acids is examined using a polymeric octadecylsilica stationary phase and a methanol mobile phase. The zone profiles are evaluated as the temperature is varied from 20 to 60 degrees C and the average pressure from 400 to 4570 p.s.i. (1 p.s.i.=6894.76 Pa). The rate constant for solute transfer from mobile to stationary phase (k(ms)) appears to be relatively constant with carbon number. In contrast, the rate constant from stationary to mobile phase (k(sm)) decreases logarithmically with increasing carbon number. This suggests that the mass transport processes become progressively slower, owing to the smaller diffusion coefficients of the larger solutes in the stationary phase. The activation energy decreases slightly in the mobile phase and increases slightly in the stationary phase with increasing carbon number. The activation energy in the stationary phase ranges from 41.6 to 55.9 kcal/mol, while the thermodynamic change in internal energy ranges from -9.8 to -29.0 kcal/mol for C10 to C22, respectively (1 cal=4.184 J). The activation volume increases with increasing carbon number in both the mobile and stationary phase. The activation volume in the stationary phase ranges from 31.7 to 211 cm3/mol, while the thermodynamic change in molar volume ranges from -27.1 to -104 cm3/mol for C10 to C22, respectively. These large changes in activation energy and volume suggest that the solutes do not enter and leave the stationary phase in a single step, but in a stepwise or progressive manner.

Monte Carlo model of nonlinear chromatography: correspondence between the microscopic stochastic model and the macroscopic Thomas kinetic model

The Monte Carlo model of chromatography is a description of the chromatographic process from a molecular (microscopic) point of view and it is intrinsically based on the stochastic theory of chromatography originally proposed by Giddings and Eyring. The program was previously validated at infinite dilution (i.e., in linear conditions) by some of the authors of the present paper. In this work, it has been further validated under nonlinear conditions. The correspondence between the Monte Carlo model and the well-known Thomas kinetic model (macroscopic model), for which closed-form solutions are available, is demonstrated by comparing Monte Carlo simulations, performed at different loading factors, with the numerical solutions of the Thomas model calculated under the same conditions. In all the cases investigated, the agreement between Monte Carlo simulations and Thomas model results is very satisfactory. Additionally, the exact correspondence between the Thomas kinetic model and Giddings model, when near-infinite dilution conditions are approached, has been demonstrated by calculating the limit of the Thomas model when the loading factor goes to zero. The model was also validated under limit conditions, corresponding to cases of very slow adsorption-desorption kinetics or very short columns. Different hypotheses about the statistical distributions of the random variables "residence time spent by the molecule in mobile and stationary phase' are investigated with the aim to explain their effect on the peak shape and on the efficiency of the separation.

Experimental and theoretical studies of rate constant evaluation for the solute-matrix interaction in affinity chromatography

In an investigation of the problem of determining kinetic parameters for the interaction of a solute with immobilized ligand sites on an affinity matrix, a combination of experimental studies and numerical simulations of frontal chromatography of methyl orange on Sephadex G-25 has yielded a simpler method than existing procedures for characterizing solute-matrix kinetics. A significant change in approach has entailed the direct evaluation of the kinetic contribution to boundary spreading from the flow-rate dependence of boundary variance under conditions of concentration-independent chromatographic migration (linear kinetics). This kinetic contribution is then interpreted in terms of an experimentally more appropriate form of a quantitative relationship for diffusion-free chromatographic migration (H. W. Hethcote and C. DeLisi, 1982, J. Chromatogr. 240, 269-281). Finally, the results of numerical simulations of concentration-dependent chromatographic migration (Langmuir kinetics) have indicated that rate constants should also be determinable under these conditions by extrapolation of their apparent values obtained by the above procedure to infinite dilution.

Affinity diffusion. I. Method for measuring dissociation constants of precipitating antibodies

Dissociation constant (Kd) of antigen-antibody reactions can be obtained from the rates (measured by the progression of the precipitate vs. time) with which antigens diffuse into antibody-containing gels, as a function of antibody-concentration. A bovine serum albumin vs. rabbit anti-bovine serum albumin system was studied with whole antiserum and with its purified IgG fraction. A value was found for Kd of approximately 1.0 x 10-5 moles per liter. It is note- worthy that in monodimensional single diffusion gel precipitation systems of this type, the rate of progression of the precipitate front is significantly faster than the molecular diffusion coefficient of the antigen.