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LC Method Scaling, Part II: Gradient Separations
 Mar 1, 2014 LCGC Europe Volume 27, Issue 1, pp. 138  143

If scaling isocratic separations is so simple, why is gradient scaling so confusing?

In last month's "LC Troubleshooting" instalment (1), we looked at how to scale isocratic separations when the column size or packing particle size is changed. The process is quite simple. First, find a column with approximately the same plate number, then adjust the flow rate to give an acceptable pressure. The most common problems that result from mistakes in this scaling process give somewhat lower resolution than is expected or higher pressures. With gradients, unexpected consequences may occur from the changes that may be relatively unimportant in isocratic methods. In this month's discussion, we turn our attention to the proper scaling of gradient methods.

Resolution and Plate Number

Last month (1) we looked at the fundamental resolution equation for isocratic conditions:

where R s is resolution, N is the column plate number, α is the separation factor, and k is the retention factor. A similar equation can be stated for gradient separations:

where N* is the effective plate number under gradient conditions, α* is the gradient separation factor, and k* is the gradient retention factor. As with isocratic conditions, we must be careful to keep from changing the chemistry of the system by keeping the same brand and series of column packing, the same mobile phase, and the same column temperature. We'll see below that we have some additional factors to be careful of with gradients. If we keep these things constant, k* and α* (the ratio of k* values for two adjacent peaks) should remain constant. If α* is unchanged, we will obtain the same resolution if we keep the same column plate number.

The column plate number cannot be measured easily under gradient conditions, so we measure it under isocratic conditions. Because the plate number is a characteristic of the column, the use of isocratic conditions is not a problem. We use the same approach we used with isocratic conditions to select a column with an equivalent plate number so that we maintain the same resolution with the scaled method. We saw that we could obtain approximately the same plate number if we kept the column length-to-particle-diameter ratio constant within a range of +50% to –25%. Thus, we can determine the desired column length from:

where L 1 and L 2 are the column lengths, and d p1 and d p2 are the particle diameters of the original and new column, respectively. So far, nothing is different between the isocratic and gradient scaling process.

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