Influence of ignored and well-known zone distortions on the separation performance of proteins in capillary free zone electrophoresis with special reference to analysis in polyacrylamide-coated fused silica capillaries in various buffers. I. Theoretical studies.

Distortion of the starting zone upon its electrophoretic migration toward the detection window gives rise to both symmetrical zones caused by diffusion, sedimentation in the horizontal section of the capillary and the curvature of the capillary, and asymmetrical zones having their origin in Joule heating, sedimentation in the vertical section of the capillary, pH and conductivity differences between the sample zone and the surrounding buffer, solute adsorption onto the capillary wall, and association-dissociation of complexes between the analyte and a buffer constituent or between analytes. Interestingly and importantly a theoretical study shows that moderate pH and conductivity differences as well as adsorption and all of the above interactions when they are characterized by a fast on/off kinetics do not increase the zone broadening (or only slightly), because the sharpening of one boundary of the zone is about the same as the broadening of the other boundary. In addition the peak symmetry caused by a conductivity difference is in most experiments counteracted by a pH difference. The experimentally determined plate numbers in the absence of electroosmosis exceeded one million per meter in some experiments (Part II). These plate numbers are among the highest reported [Z. Zhao, A. Malik, M.L. Lee, Anal. Chem. 65 (1993) 2747; M. Gilges, K. Kleemiss, G. Schomburg, Anal. Chem. 66 (1994) 2038; H. Wan, M. Ohman, L.G. Blomberg, J. Chromatogr. A 924 (2001) 591 (plate numbers determined in the presence of electroosmosis may be higher, although the width of the zone in the capillary may be larger) [p. 680 in S. Hjertén, Electrophoresis 11 (1990) 665]). Capillary free zone electrophoresis is perhaps the only separation method, which, under optimum conditions, gives a plate number not far from the theoretical limit. A prerequisite for this high performance is that the polyacrylamide-coated capillary is washed with 2 M HCl between the runs and stored in water over night (Part II). The difference between the experimentally determined total variance and the sum of the calculated variances originating from the width of the starting zone, longitudinal diffusion, Joule heating, sedimentation in the vertical section of the capillary, curvature of the capillary (i.e., the sum of all other variances) was in our most successful experiments about 28% of the variance of diffusion. The zone broadening, 2sigma, caused by diffusion was estimated at 0.77 mm. The total zone width (2sigma) calculated from the experimentally determined plate number was as small as 1 mm when the migration distance was 40 cm. Accordingly, the only efficient way to reduce drastically the total zone width is to decrease the analysis time and, thereby, the diffusional broadening. An important finding was that the variance originating from the loops of the capillary is not always negligible in high-performance runs. Therefore, one should employ straight capillaries and avoid CE apparatus with cartridges that require a strong curvature of the capillary, common in most commercial instruments. Mathematical formulas have been derived for the sedimentation of the solute zone, the enrichment factor, and the migration time in experiments where the solute is dissolved in a dilute running buffer. This zone sharpening method gave very narrow starting zones (0.04-0.4 mm). However, upon high dilution of the buffer the enrichment becomes so strong that part of the sample zone probably sediments out of the capillary; the almost inevitable change in pH may decrease the mobility of the proteins and, thus, cause the enrichment factor to become still lower than expected. Diffusion of the protein in the very narrow starting zone (located close to the tip of the capillary) and sometimes the thermal expansion of the buffer in the capillary contributes to additional loss of protein in the enrichment step. In some buffers, the interaction between the protein and the buffer constituents is so slow that the peaks become broad. Therefore, different types of buffers should be tested when high resolution is required. The relation sigma2 (the variance of the interaction between a protein and the buffer constituents) = constant x u (the mobility) seems to be valid for all proteins in the applied sample, at least when they have similar molecular masses. To facilitate the understanding of the progress of a free zone electrophoresis experiment, we have discussed in simple terms how the concentrations of the background electrolytes become rearranged during a run and why the difference between the mobilities of the proteins and the mobilities of the background electrolyte determines whether a peak exhibits fronting or tailing. A theoretical analysis of zone broadening in capillary zone electrophoresis, chromatography, and electrochromatography indicates that electrochromatography in homogeneous gels might be the only chromatographic technique which can compete in performance with free electrophoresis. Using an equation, valid not only for electrophoresis, but also for chromatography and centrifugation, the mobility of a concentration boundary has been calculated for the first time and was, as expected, low. Equations based on the Kohlrausch regulating function do not permit such calculations. Another regulating function (the H function) and some of its characteristics are briefly discussed. The theoretical discussions in this paper and the experimental studies in Part II show that high-performance electrophoresis deserves its prefix when the runs are designed to give minimum zone broadening. Some guidelines are given to facilitate this optimization. The plate numbers are so high that the resolution cannot be increased by more than 30% even if they approach the theoretically maximum values.