## Resolution in SFC

Separation in all chromatography and chromato-graphic theory is defined by the resolution, Rs, between two component peaks:

where At is the separation between peak maxima, and w is the mean baseline peak width. Baseline (99.9%) resolution corresponds to Rs = 1.5. The resolution is determined by the number of theoretical plates, N, the capacity factor, k, and the selectivity, a( = k1/k2), by:

For a compound with retention time tR, N is given by:

The column length or height equivalent to a theoretical plate (HETP) is related to average linear mobile phase velocity, u, by:

particle diameter, dp, for a packed column. Cs, the contribution from solute diffusion in the stationary phase, is proportional to dF/Ds where dF is film thickness and Ds, the diffusion coefficient in the stationary phase, is generally negligible for a thin coating.

Differentiation of eqn [13] allows the optimum mobile-phase velocity (i.e. for minimum HETP, Hmin) to be written as:

The A, or multiple-path term, is zero for a capillary column, but, for a packed column:

and:

where dp is column packing particle diameter and X is a constant related to the eddy diffusion coefficient.

The B term defines that portion of H caused by longitudinal diffusion during passage down the column and is given by:

where DM is the diffusion coefficient of the solute in the mobile phase.

Cm arises from the resistance to mass transfer in the mobile phase, and is proportional to d^/DM, where dc is the column diameter for a capillary and the

It follows that Hmin depends only on k and d so that SFC and HPLC on the same column can only be carried out with the same maximum plate number. Similar considerations hold for SFC and GC (Figure 3). However, uopt depends on DM and is much greater in SFC than in HPLC because of the greater diffusivity of solutes in supercritical fluids; it follows that SFC on a packed column is much more rapid than HPLC on the same column (see Figure 3 and below). Because DM is less for a supercritical fluid than a gas, however, speed of analysis in capillary SFC is much reduced in comparison with GC. To offset this effect, capillary column diameters of 50 |im

Velocity (cm s

Figure 3 Efficiency as a function of mobile-phase velocity. Commonly used efficiency velocity ranges are highlighted. Packed column conditions: 5 |im particles, values calculated from the Knox equation with A = 1, B = 2, C = 0.05 (for LC), and C = 0.5 (for SFC). Open tubular column conditions: 50 |im i.d. (SFC), 300 |im i.d. (GC), values calculated from the Golay equation with k= 5. Valuesfor Dm were 10~5 cm2 s~1 for liquid, 2 x 10~4 cm2 s~1 for high density supercritical fluid (100°C), 5 x 10~4cm2 s~1 for low density supercritical fluid (100°C), and 10~1 cm2s~1 for gas.

Velocity (cm s

Figure 3 Efficiency as a function of mobile-phase velocity. Commonly used efficiency velocity ranges are highlighted. Packed column conditions: 5 |im particles, values calculated from the Knox equation with A = 1, B = 2, C = 0.05 (for LC), and C = 0.5 (for SFC). Open tubular column conditions: 50 |im i.d. (SFC), 300 |im i.d. (GC), values calculated from the Golay equation with k= 5. Valuesfor Dm were 10~5 cm2 s~1 for liquid, 2 x 10~4 cm2 s~1 for high density supercritical fluid (100°C), 5 x 10~4cm2 s~1 for low density supercritical fluid (100°C), and 10~1 cm2s~1 for gas.

100 urn

100 urn

Figure 4 Efficiencies for different column diameters.

are the norm in SFC; in fact, capillary SFC is still often comparatively slow and a column diameter of 25 |m would be desirable. The dependence of Cm on d also leads to small preferred column diameters for capillary SFC. Figure 4 illustrates the effect of column diameter on column efficiency.

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