Multidimensional systems are primarily used to increase the number of separated compounds, n, which is conveniently characterized as the peak capacity, P, which is defined as the maximum possible number of separated compounds with regularly spaced closely adjacent peaks filling the whole available space in the chromatogram. So-called "orthogonal" systems with different retention mechanisms controlling the selectivity of separation show strong multiplication effects on the peak capacity, which in a two-dimensional (2D) system can be theoretically as high as the product of the peak capacities in the first and second dimension: P_2D = P₁ × P₂

A separation system can be regarded as multidimensional when the mechanism of the separation in each dimension is different.¹ Early 2D separations mainly used the planar mode, including paper chromatography (PC), thin-layer chromatography (TLC), gel electrophoresis (GE) and combinations of these techniques. Later, 2D GC×GC systems became popular. In a 2D column GC×GC or LC×LC separations, the sample is transferred from the first to the second dimension column either off-line or on-line. In the off-line set-up, the fractions from the first column are isolated, preconcentrated and injected onto the second column. On-line multidimensional systems employ manual or automated sample transfer between two or more columns with uninterrupted flow, via one or more switching valves.

The peak capacity under isocratic conditions in a 1D system can be calculated using Equation 1:²

The peak capacity depends primarily on the number of theoretical plates of the column, N, but is strongly affected by the separation selectivity, α, expressed as the relative retention, that is, the ratio of the retention factors of the compounds with adjacent peaks, α = k(_i+1) /k_i, which is constant over the whole chromatogram with n closely adjacent peaks between the elution volume of the first eluted compound, V_R,1, and the elution volume of the last eluted one, V_R,Z (with the resolution R_s = 1).

Figure 1

The peak capacity decreases as the retention factor of the first compound k₁ increases. However, regular spacing of all peaks over the whole chromatogram required for full use of the peak capacity is rarely achieved in practice and the peak capacity required to separate all sample components at a given probability level increases with the second power of the real number of sample components.^3–5

The peak capacity, P_G, is generally higher in gradient elution than in isocratic mode within the same range of elution times or volumes (Figure 1), because of approximately constant and significantly narrower bandwidths w_g in gradient elution:⁶