usual dispersion processes that take place in the column to provide a value for the ultimate peak variance. Consequently, if the column efficiency is not to be seriously reduced the maximum volume of sample that can be placed on the column must be limited. Consider a volume (Vi) of sample, injected onto a column. This sample volume will constitute a rectangular distribution on the front of the column. Now, (as discussed in Dispersion in Chromatography Columns of this series) the variance of the peak eluted from the column will be the sum of the variances of the injected sample plus the normal variance of the eluted peak. Thus:                                  where  s2  is the variance of the eluted peak, si2 is the variance of the eluted sample,          and sc2 is the variance due to column dispersion. The maximum increase in band width that can be accepted due to any (and all) extraneous

The Effect of Temperature and Solvent Composition on the Minimum Variance/Unit  Column Length (Hmin) Taking the values for the capacity ratios and separation ratios derived from equations (47), (48) and (49) in equation (40) the manner in which (Hmin) changes with temperature and solvent composition can be identified. The minimum variance per unit length of the column is solely a function of the capacity factor of the solute, the particle diameter and the packing factors (see Book 9). Thus, the influence of temperature and solvent composition on (Hmin

column efficiency and the analysis time. It is also seen that the contribution to dispersion from longitudinal diffusion is the same for both columns and so the striking difference between the performance of the two columns depends solely on the effect of the column radius on the resistance to mass transfer terms. This is clearly illustrated by the large difference in slopes of the two linear curves for the resistance to mass transfer shown in figure 17.   The Optimum Velocity and Minimum Variance per Unit Length   Equation (4) can be put in the simple form,   (5)   where B = 2Dm   and C=   In order to determine the optimum velocity where (H) is a minimum and thus the maximum efficiency is obtained, equation (5) must be differentiated and equated to zero.   That is,   solving for (uopt

The Minimum Variance/Unit Length of the Column   The minimum value of (H) is given by equation (9) and it is seen that it is directly proportional to the column radius and a function of the capacity ratio of the solute but, unlike the optimum velocity (H(min.)) is independent of the solute diffusivity. A graph relating the function of the capacity ratio (k') that controls the magnitude of (H(min.)) to the actual value of (k') is shown in figure 19.   (H(min.)) increases as the capacity ratio

that can be placed on the column and thus, the ultimate sensitivity of the analysis. Now, summing the variances         where () is the overall variance of the eluted peak,            () is the variance of the sample volume,     and () is the variance due to column dispersion. It has been established that the variance of a rectangular distribution of sample volume (Vi) will be . It can again be assumed that the peak variance can be increased by 10% as a result of extra column dispersion without seriously denigrating column performance. Unfortunately, all the permitted extra column dispersion can not be assigned to the effect of a finite sample volume as some must be allocated to other dispersion sources. As an arbitrary judgment half of the permissible extension of peak width will be allotted to the effect of the sample volume (i.e., the variance can be increased by 5 %). This is a variable proportion as it

To develop an HETP equation it is necessary to first identify the dispersion processes that occur in a column and then determine  the variance that will result from each process per unit length of column. The sum of all these variances will be (H), the Height of the Theoretical Plate, or the total variance per unit column length. There are a number of methods used to arrive at an expression for the variance resulting from each dispersion process and these can be obtained from the various references provided. However, as an example, the Random-Walk Model introduced by Giddings (3) will be employed here to illustrate the