Efficiency Measurements for Chromatography Columns - Using the method of moments provides a better characterization of column effluent curves than the frequently used Gaussian approximation. -
Efficiency Measurements for Chromatography Columns
Using the method of moments provides a better characterization of column effluent curves than the frequently used Gaussian approximation.
 Aug 1, 2005 BioPharm International Volume 18, Issue 8

and the height of a plate, H is:

The vertical scale, corresponding to effluent concentration in our situation, does not affect calculation of H or N.

When time is expressed as in Figure 1, the value of s is independent of both the mass of pulse fed (if the effluent curve is Gaussian) and the column diameter. Moreover the mean residence time equals the time at which the maximum concentration, t max , occurs. The number of plates is expressed in Equation (5).

The Short-cut Method and the Péclet Number

If effluent curves were always Gaussian, then calculating plate numbers and heights would be a simple process. There would, of course, be the nagging problem of determining standard deviations from experimental data, and it has been a common practice to use short-cut methods for this purpose. We discuss a set recommended by the American Society for Testing and Materials.4 Equation (6) from the ASTM is a variant of Equation (5).

If the peak is Gaussian, then the standard deviation is the half-width at 60.7% of peak height and it reduces to Equation (7).

Unfortunately no chromatographic peaks are truly Gaussian, and this is the problem we must deal with next. Figure 2 shows simulated solute concentrations along a column using L as the distance along the column from inlet.5 It makes evident that solute profiles within a column are functions of percolation velocity, adsorbent particle diameters and solute diffusivity as expressed via a dimensionless group known as the Péclet number.

Both peaks are left-skewed, but the magnitude of skewness increases with , or inversely with diffusivity. The primary reason for this is intra-particle diffusional transients, and the degree of skewness depends primarily on a ratio of time constants as in Equation (9).