Theory of zone separation in isotachophoresis: a diffusional approach

The qualitative characteristics of isotachophoresis differ substantially from "classical" separation methods such as chromatography or zone electrophoresis. Self-sharpening zone boundaries and step-like concentration profiles are the most specific features of this method, which does not allow the description of the isotachophoretic separation in usual "chromatographic" terms, such as resolution or number of theoretical plates. A theory is presented in this paper, combining the usual isotachophoretic separation characteristics with the theory of isotachoporetic zone boundary, which is the only element of the isotachophoretic system with dispersional properties. This allows us to consider situations near the limits of the isotachophoretic method as far as both selectivity and sample amount (i.e., zone size) are concerned. Based on a simplified expression of the concentration profiles across the isotachophoretic zone boundary, separation and separation limits are described and discussed in terms of resolution, selectivity and zone capacity. Equations are derived showing the relationships between resolution, boundary width, selectivity, sample amount, and column and electrolyte conditions. A simple phenomenological equation is presented, expressing isotachophoretic resolution as a function of only sample amount (or sample zone length) and boundary width. A thermodynamic form of this equation is derived, which is shown to be similar to such an expression for resolution in zone electrophoresis. In both cases resolution is a function of sample selectivity, electric field strength and column length. A simple theoretical model for zone capacity is presented, making it possible to estimate the separation performance of isotachophoretic systems. Based on the presented theory, parallels between isotachophoresis and zone electrophoresis are discussed and both methods are compared.