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under conditions of no overload If the excessive sample volume (which now also acts as part of the eluting mooile phase) is of such a value that it just allows the peaks to touch at the base, the peak separation in ml of mobile phase passed through the column will be equivalent to the sample volume (Vi) plus half the base width of both peaks shown in figure 7.
(a -l)nKaAs = Vj +2^(vrn + ÊàÀç) + 2^/n” (vm + Ag)
where (n) is the column efficiency and is assumed to be the same for both peaks,
(Ka and Êü) are the distribution coefficients of the two solutes (a) and( b), and (a) is the separation ratio of solutes (a) and (b).
Figure 7 Two Solutes Eluted Under Conditions of No Volume Overload
Vj = (a -1 )nKaAs -2Vn((vm +KaAs) + (vm + Kb A$))
Noting that Vo = nvm and
. V . V . . .
nKaAs=Va nKbAs=Vb ^ = ka — = kb and kb = a«a
Vi = V0
(«-1)ka-^|2 + ka(a+0|
Noting also that (n) is large, and thus, to the first approximation,
Vi í V0(a-l)ka ............................................................. (15)
It is seen from equation (15) that the maximum overload volume is linearly related to the (k'i value of the first eluted solute of the critical pair, the function (a-1) and the column dead volume. Consequently, the larger the column, either in length and/ or radius, the larger the sample volume can be. This assumes that the column is of such a size, that it can be efficiently packed with practical techniques and that the particle size of the packing is chosen such that the pump pressure available can provide the necessary mobile phase flow-rate.
In the authors opinion volume overload employing a solution of the material in the mobile phase at a level of about 5% w/v is the recommended method of sampling for preparative columns if the system is not optimized. However, as will be seen later a combination of volume overload and mass over load has also been suggested as an alternative procedure. An example of progressive volume overload is given in figure 8.
Sample Mass Overload
Band dispersion from sample mass overload is a direct result of the chromatographic process proceeding under conditions, where the adsorption isotherm of the solute on the stationary phase, is no longer linear. The development of an equation that describes the extent of band spreading as a function of mass of sample placed on the column, Is complex. This problem has been elegantly approached by Gulochon and his co-workers (15-18) from the basis of the adsorption isotherm of the solute on the stationary phase.
The form of the isotherm need not be Langmuir in nature, but in any event, must, be experimentally determined in order to identify the true profile of the overloaded peak. In practice, the determination of the adsorption isotherm of each compound to be separated by a preparative chromatographic procedure can be arduous and time consuming. A better alternative might be to design the fully optimized column from basic principles in the manner previously described.
Progressive Volume Over Load of an LC Column
FLOW RATE Iml/nwi SAMPLE VOLUME Þ ul
SOLUTES A ANlSOLE
â BENZYL ACETATE Ñ ACETOPHENONE
Knox and Pyper (14) assumed that the majority of the adsorption isotherms were, indeed, Langmuir in form and then postulated that all the peaks that were overloaded would be approximately triangular in shape As a consequence, Knox and Pyper assumed that mass overload could be treated in a similar manner to volume overload. Whether all solute/stationary phase Isotherms are Langmuir in type, is a moot point, and the assumpt’on should be taken with some caution. Knox and Pyper then suggested that the best compromise was to utilize about half the maximum sample volume as defined by equation (15) which would then reduce the distance between the peaks by half. They then recommended that the concentration of the solute was increased until dispersion due to mass overload just caused the two peaks to touch. Knox summarized his recommendations in the following way (19),
1/ Develop an analytical separation which gives the best possible resolution between the critical solutes.
2/ Determine the difference between the retention volumes of the two solutes (AV) (equation (15)).
3/ Employ sample volumes of about 0.4AV containing increasing
concentrations of solute until the gap between the critical pair is just filled.
Unfortunately, this procedure assumes that the critical pair can be well resolved and column overload is a practical solution to tne problem. More often, due to the complex nature of the mixture values for (a) of 1.1, 1.2, or even less, are the best that can achieved. Under such circumstances, the optimum column must be designed which, in the design procedure, will automatically be given a radius that will accommodate the load that is required.
(1) E.Katz, KL.Ogan and R.P.W.Scott, J. Chromatogr, 289( 1984)65.
(2) R.P.W. Scott, J Chromatogr., 468( 1989)99.
(3) J.H.Purnell, Nature, Ho 4704 , Dec.9,( 1959)2009.