Zone broadening in electrophoresis with special reference to high‐performance electrophoresis in capillaries: An interplay between theory and practice
Authors: Hjertén Stellan 
Published: May 2005

Approximate equations have been derived for the total (final) zone width (plate height, plate number and resolution) as a function of the width of the starting zone and of the zone broadening caused by diffusion, Joule heat, adsorption and the difference in conductivity (δk) between a solute zone and the surrounding buffer. Two cases are treated: (A) the conductivity differences eliminate entirely or (B) partially, the diffusional broadening at one boundary of a zone. When adsorption is negligilbe one can derive from these equations the field strength – and for case A also the electrical conductivity – that gives the minimum zone broadening (plate height). Interestingly, at this minimum, contributions to the zone broadening from diffusion, Joule heat and conductivity differences have the ratio 4:1:1 in case A. In case B the ratio between the broadening caused by diffusion (including that caused by conductivity and pH differences) and broadening due to Joule heat is 4:1. The total zone width, plate height and optimal field strength calculated from the derived equations agree satisfactorily with experimental values. A simple method to estimate the variance of the zone broadening caused by the Joule heat led to a formula similar to that calculated mathematically. An appropriate width of the starting zone can be calculated rapidly by means of a simple formula. Following a run the true width can be estimated graphically from measurements of plate heights or zone widths at low field strengths. For high resolution the width of the starting zone usually should not exceed 0.5 mm. A new principle for the design of multi‐buffer systems which generate sufficiently narrow starting zones has been developed for carrier‐free zone electrophoresis. This zone sharpening method permits application of wide zones of concentrations below the detection limit of the monitor. The diffusion coefficient (D) and the universal parameter D/u (u = mobility) appear in many of the equations derived and are often the only variables which are not easily accessible. Simple methods have therefore been developed by which they can be determined with sufficient accuracy. Fortunately, they are raised to the power of 1/5 in many formulas and therefore only a rough estimation is required. True plate numbers (calculated in the absence of electroendosmosis) often differ considerably from apparent plate numbers (calculated in the presence of electroendosmosis). A mathematical relationship between the true and apparent plate numbers has been derived. An equation covering different types of electrophoresis (ideal zone electrophoresis, nonideal zone electrophoresis, and displacement electrophoresis) is presented (indirect detection is described by the same equation). Since an equation can be formulated which is valid for electrophoresis, chromatography and centrifugation the analogy among these methods is obvious. This analogy should be utilized to create novel methods and to increase the resolution in existing ones (examples are discussed). New principles are presented for the application of sample and flushing the electrophoresis tube with fresh buffer, both of which facilitate automation.