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# Determining dwell volume of gradient HPLC systems

 Reference Number: AA-00407 Created: 04/11/2012 08:51 PM Last Updated: 07/23/2016 04:48 PM

1. Theory

The major application of HPLC using gradient conditions is for reversed-phase (RP-HPLC) systems1, however the general conclusions are also applicable to other HPLC modes (normal-phase, aqueous normal phase, ion-exchange, etc.). For RP-HPLC separations, the solute retention factor k can be approximately related to the volume-fraction of organic modifier (B) in a mobile phase as: where kw is the (extrapolated) value of k for water as the mobile phase ( =0), and S is a constant characteristic for each solute in the sample. Retention time in a linear-gradient separation can be expressed as: Here, t0 is the column dead-time, k0 is the value of k at the start of the gradient, and b is a gradient steepness parameter given by equation 3 below: where  is the change in the volume-fraction of organic modifier (B) during the gradient ( =0.01%B), Vm is the column dead-volume, and F is the flow-rate. The quantity td is the equipment hold-up or ‘dwell' time, equal to the hold-up or ‘dwell' volume VD divided by flow-rate. The equipment dwell volume is often wrongly assumed to be negligible (VD=0), which leads to the problems. Relative retention tR/t0 can be defined, and from Eq. 2 (assuming td=0): If column dimensions or flow-rate are changed, t0=Vm/F will change. However, as long as Q is held constant (by varying tG), b and tR/t0 remain constant for each solute, and relative retention will not change. Eq. 2 and Eq. 4 are actually only approximations when VD>0, but it is still possible to calculate exact values of tR as a function of k0, t0, b and VD. Resolution in gradient elution can be expressed in terms that are similar to isocratic separation: where k* (the average retention factor k during gradient elution) is given as: For peaks that elute later in the gradient, and for which k0>1.15b, 2. Dwell-volume effects

According to Eq. 4 above, relative retention should remain unchanged as long as b (and Q) are constant, assumes that VD=0. When there is a significant dwell volume VD in the instrument, this situation changes. As mentioned in the opening paragraph gradient conditions are delayed by a dwell time tD=VD/F. As a result analytes is under isocratic conditions (for a time tD) with k=k0. As a result the value of b, the gradient steepness parameter (b=0 for isocratic elution) is smaller than given by 3 for the gradient elution. The composite value of b (b'; i.e. effective gradient steepness) for a separation of a sample undergoing isocratic elution at the start is therefore smaller. The effective gradient steepness b' is therefore a combination of initial elution with b = 0 and elution with b calculated by equation 3. As a result solutes which are weakly retained (elute early) will undergo the most migration during isocratic part of the run and as a consequence for these compounds b' will be greatest. For later eluting compounds b'/b will approach 1 and become smaller as tR becomes smaller. This combined gradient steepness parameter b' will depend both on k0 and the ratio of dwell volume to column volume (VD/Vm). To assure there are minimal changes in relative retention of the compounds if a gradient HPLC method is transferred from one instrument to another, one should keep both Q and (VD/Vm) constant. If VD/Vm is held constant while changing column dimensions, relative retention (tR/t0) should remain unchanged.

1 J. W. Dolan and L. R. Snyder; “Maintaining fixed band spacing when changing column dimensions in gradient elution” J. Chromatogr. A, Vol. 799, 13 March 1998, Pages 21-34.  Ask a Question 