Download (direct link):
Conversely, difficult separations snould be carried out on long, narrow columns, packed with relatively large particles and operated at very low flow rates.
The Minimum Solvent Consumption
The minimum solvent consumption will be obtained from the product of the optimum flow-rate and the analysis time,
Vsol = Qopttrnin
Substituting for (trnjn) from equation (21) and for (Qopi) from equation (30),
(l+6k'+| ik'2)' 2Ä.+ ó--2
y(l+6k'+11k'2 j ,05
jf'Kl+k')^ Ë 2k*
Ak'(a-1)j <pP 3(l+k')2
The above equation reduces to a surprisingly simple function.
It is seen that for a fully optimized column, the solvent consumption required to complete an analysis is independent of the inlet pressure, viscosity of the mobile phase and even the diffusivity of the solute in the mobile phase. Equation (31) again emphasizes the importance of the extra column dispersion in the control of the solvent consumption and consequentially, the economy of the analysis. The need to adjust the phase system to ensure that, not only is the separation achieved, but that the last peak is not eluted at too high a value of (ê'ã) is also demonstrated by equation (31) .Employing equation (31), a graph was constructed showing the relationship between solvent consumption and the function (a-1) and is shown in figure (6). It is seen form figure (6) that the solvent consumption for an LC analysis need not be large if a fully optimized column system is employed. In fact for most analyses the consumption should lie between i and 5 ml per analysis. Even for very difficult analyses, due to the optimum columns having small radii, the solvent consumption is still restricted to about 7.5 ml
Graph of Solvent Consumption against Separation Ratio
Figure (6) allows the solvent consumption of any analysis to be compared with which would be obtained from a fully optimized column. The data used is obtained from the reduced chromatogram and the extra column dispersion of the respective apparatus. It should be bourne in mind that the extra column dispersion assumed in the above calculations was equivalent to a standard deviation of 2.5 microlitres. This value for (oe) could be expected from a well designed chromatographic system.
The Peak Capacity of the Optimized Column
The peak capacity of a given column system is given by equation (15) in chapter (5) on page (69) and is reiterated here,
Substituting for (n) from equation (I) and simplifying,
k9(l + k')
2k’(a — l) V
2 + k‘ + k'a
2 + 3k '-k'a
2 + k' + k'a j
Equation (32) shows that the peak capacity of the optimized column is only dependent on the separation ratio of the critical pair (a) and the magnitudes of (k') for the first eluted peak of the pair and for that of (k'2), the last eluted peak. A graph of peak capacity against separation ratio, calculated from equation (32) is shown in figure (7)
Figure 7 Graph of Peak Capacity against Separation Ratio
it is seen from figure (7) that the peak capacity of the chromatographic system increases very rapidly as the separation becomes more difficult. For simple separations, where (a) ranges from 1.06 to 1.12, the capacity lies between about 21 and 42. However, between (a) values of 1.05 to 1.01 the
peak capacity changes from 50 to about 125 it should be remembered, however, the peak capacity as calculated, is a optimistic figure, as it assumes that all the components are equally spaced. Giddings has pointed out (5), the actual effective peak capacity for real samples may be less than half the values calculated from the above theory.
Maximum Sample Volume
The maximum permissible charge that can be placed on an LC column was discussed in chapter 5 on page (54) and is given by the following equation,
Vsamp = 1........................................ (33)
Now (Vr) is equal to the total solvent used to elute the first peak of the critical pair and is given by equation (31), by substituting (1 +k') for (1 +k'2). Thus substituting for (Vr) from equation (31) and for (n) from equation (1) in equation (33),
Vsamp = 3.42oe .................................................. (34)
It is seen from equation (34) that for a fully optimized column the maximum sample volume depends solely on the extra column dispersion (oe). This again emphasizes the importance of not only using equipment with low extra column dispersion but, also, knowing the value of (oe) for the particular chromatograph being used.
The Optimum Capacity Ratio
Throughout the optimization procedure, the role played by the capacity ratio has not been examined, and (k > has been treated as a constant in the equations. As a consequence, the effect of the magnitude of (k‘) on chromatographic performance has not been considered. This is because, in choosing the phase system to provide the maximum separation ratio for the critical pair, the value for (k') is automatically defined by the phase system