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A unified equation to evaluate elution profiles of reversible as well as irreversible (pseudo-) first-order reactions in dynamic chromatography and on-column reaction chromatography has been derived. Rate constants k1 and k(-1) and Gibbs activation energies are directly obtained from the chromatographic parameters (retention times tR(A) and tR(B) of the interconverting or reacting species A and B, the peak widths at half-height wA and wB, and the relative plateau height h(p)), the initial amounts A0 and B0 of the reacting species, and the equilibrium constant K(A/B). The calculation of rate constants requires only a few iterative steps without the need of performing a computationally extensive simulation of elution profiles. The unified equation was validated by comparison with a data set of 125,000 simulated elution profiles to confirm the quality of this equation by statistical means and to predict the minimal experimental requirements. Surprisingly, the recovery rate from a defined data set is on average 35% higher using the unified equation compared to the evaluation by iterative computer simulation.

Dynamic capillary electrophoresis (DCE) and direct calculation of the rate constants of isomerization has been applied to determine the cis-trans isomerization barriers of the angiotensin-converting enzyme inhibitor captopril. The separation of the rotational cis-trans isomeric drug has been performed in an aqueous 50 mM borate buffer at pH 9.3. Interconversion profiles featuring plateau formation, peak-broadening, and peak coalescence were observed. To determine the rate constants of the forward and backward reaction (k(cis-->trans) and k(trans-->cis)) of the isomerization process in dynamic capillary electrophoresis, a novel straightforward calculation method using the experimental parameters plateau height, h(plateau), peak width at half height w(h), the total migration times of the cis-trans isomers t(R) and the electroosmotic break-through time t(0) as well as the peak ratio of the cis-trans isomers is presented for the first time. From temperature dependent measurements the rate constants k(cis-->trans) and k(trans-->cis) and the kinetic activation parameters DeltaG( not equal), DeltaH( not equal), and DeltaS( not equal) of the cis-trans isomerization of captopril were obtained. From the activation parameters the isomerization barriers of captopril at 37 degrees C under basic conditions were calculated to be DeltaG( not equal) (cis-->trans) = 90.3 kJ.mol(-1)and DeltaG( not equal) (trans-->cis) = 90.0 kJ.mol(-1*).

Enantioselective chromatographic methods, representing the most commonly used techniques for the determination of enantiomeric ratios, can also be used for the evaluation of stereochemical integrity. In the present study, dynamic capillary electrokinetic chromatography (DEKC) was employed to determine the enantiomerization barrier of thalidomide. In the presence of the chiral mobile phase additive carboxymethyl-beta-cyclodextrin, the interconverting enantiomers of thalidomide produced characteristic elution profiles exhibiting plateaus and/or peak broadening between 25 and 55 degrees C at pH 8. To obtain the enantiomerization barrier of thalidomide from experimental data, the fast and efficient simulation program ChromWin was used to simulate the experimental interconversion profiles and to obtain the apparent rate constants k1app(T). Additionally, these values were compared with the novel approximation function for the direct calculation of enantiomerization barriers from chromatographic parameters of elution profiles. From the rate constants k1app(T) of temperature-dependent measurements the kinetic activation parameters deltaG(T)#,deltaH#, and deltaS# of the enantiomerization of thalidomide were obtained. At 25 degrees C, the enantiomerization barrier deltaG# was determined to be 102 +/- 1 kJ/mol at pH 8 in the dynamic electrokinetic chromatographic experiment.

An approximation function for enantioselective dynamic chromatography of racemic mixtures of interconverting enantiomers has been derived that allows the direct calculation of enantiomerization rate constants (k1 and k(-1)) and Gibbs activation energies of enantiomerization, deltaG++ , from chromatographic parameters, i.e., retention times of the enantiomers A and B ((t(A)R and t(B)R), peak widths at half height (WA and wB) and the relative plateau height (hplateau), without computer simulation. The reaction rate constants of enantiomerization, k(-1), obtained with this approximation function, have been validated by comparison with a simulated dataset of 15,625 chromatograms. The mean, standard deviation and confidence interval show a high correlation between the approximated and simulated rate constants. The average deviation from the Gibbs activation enthalpy of enantiomerization, deltaG++, has been estimated to be as small as about +/- 0.11 RT.

Dynamic electrokinetic chromatography (DEKC) and computer simulation have been used to determine the enantiomerization barrier of the drug chlorthalidone, which is commonly employed as a diuretic. The separation of enantiomers was performed in an aqueous 100 mM citric acid/phosphate buffer system at pH 5 containing 12.5 mg/mL carboxymethyl-beta-cyclodextrin and dimethyl-beta-cyclodextrin each as a dual chiral recognition system. The enantiomerization that occurred during separation resulted in a peak distortion, i.e., plateau formation and peak broadening. The interconversion profiles were simulated with ChromWin software, which is based on the theoretical plate as well as on the stochastic model using the experimental data plateau height, hplateau; peak width at half height, Wh, and total retention time, tR. Peak form analysis yielded the rate constants, k1 and k(-1) as well as the kinetic activation parameters, deltaG++, deltaH++, and deltaS++ of the enantiomerization reaction of chlorthalidone 1. At 37.5 degrees C, the enantiomerization barrier, deltaG++, was determined to be 100.6 +/- 0.4 kJ/mol(-1); the activation parameters by temperature-dependent measurement, deltaH++ = 69.2 +/- 0.2 kJ/mol , deltaS++ = -101 +/- 6 J K(-1) mol(-1) and the half-life, tau, was found to be approximately 2.5 hr.