Influence of neutral cyclodextrin concentration on plate numbers in capillary electrophoresis

A quantitative theory of plate number N in capillary electrophoresis was developed for buffers containing neutral cyclodextrins (CDs) capable of forming inclusion complexes. In the theory, N was modeled by longitudinal diffusion, injection extent, width of the detection window, and the detector time constant. The apparent mobility was modeled as a weighted sum of the mobilities of the free-solution analyte and the inclusion complex. The apparent diffusion coefficient was modeled as a similarly weighted sum. Both the apparent mobility and diffusion coefficient were corrected by functions that compensated for increases of buffer temperature caused by Joule heat. The experimental N's and apparent mobilities of neutral thiourea and of the anions, dansyl D- and L-leucine, dansyl D- and L-aspartic acid, benzoate, and 4-nitrophenolate, were determined in buffers containing from 0 to 15 mM beta-CD. The binding constants, and mobilities and diffusion coefficients of the free-solution analyte and inclusion complex, were calculated as regression coefficients by fitting theory to these determinations. The regression coefficients were shown to have physicochemical meaning, as assessed by literature values, independent measurements, and theoretical predictions. The assessment showed the Nernst-Einstein equation does not relate mobilities and diffusion coefficients at the electrolyte concentration used. The interdependence of mobilities, diffusion coefficients, binding constants, and other dispersion sources was interpreted to evaluate the factors affecting the variation of N with CD concentration. From the interpretation, an approximate equation for N in low-concentration CD buffers was derived. The equation depends on free-solution and inclusion-complex mobilities and diffusion coefficients, the binding constant, the potential difference over the effective capillary length, and the number of plates in a CD-free buffer.