Retention corrected volume, function

If the mobile phase is a liquid, and can be considered incompressible, then the volume of the mobile phase eluted from the column, between the injection and the peak maximum, can be easily obtained from the product of the flow rate and the retention time. For more precise measurements, the volume of eluent can be directly measured volumetrically by means of a burette or other suitable volume measuring vessel that is placed at the end of the column. If the mobile phase is compressible, however, the volume of mobile phase that passes through the column, measured at the exit, will no longer represent the true retention volume, as the volume flow will increase continuously along the column as the pressure falls. This problem was solved by James and Martin [3], who derived a correction factor that allowed the actual retention volume to be calculated from the retention volume measured at the column outlet at atmospheric pressure, and a function of the inlet/outlet pressure ratio. This correction factor can be derived as follows. 

Tung (55) has shown that the normalized observed SEC chromatogram, F(v), at retention volume v is related to the normalized SEC chromatogram corrected for instrument broadening, W(y), by means of the shape function G(v,y) through the relation... 

Figure 4,14. Diagram of the thermodynamic cycle used to explain retention in reversed-phase chromatography by solvophobic theory. Na = Avogadro number, AA = reduction of hydrophobic surface area due to the adsorption of the analyte onto the bonded ligand, y = surface tension, = energy correction parameter for the curvature of the cavity, V = molar volume, R = gas constant, T = temperature (K), Pq = atmospheric pressure, AGydw.s.i a complex function of the ionization potential and the Clausius-Moscotti functions of the solute and mobile phase. Subscripts i = ith component (solute or solvent), S = solute, L = bonded phase ligand, SL = solute-ligand complex, R = transfer of analyte from the mobile to the stationary phase (retention), CAV = cavity formation, VDW = van der Waals interactions, ES = electrostatic interactions.

Both 12r and I m depend on the average pressure within the column - a quantity that lies intermediate between the inlet pressure F, and the outlet pressure F (atmospheric pressure). The pressure drop correciitm factor j. also known as the compressihiUty factor, ac-counls for the pressure within the column being a nonlinear function of the F,/F ratio. Corrected retention volumes 1 r and 12, which correspond lo volumes at the average column pressure, arc obtained from the relationships... 

Kg, is the volume of mobile phase that has entered the column at time t, k is the value for the band at that time, and the corrected retention volume V equids — to]. It is necessary to know isocratic values of k as some function of 0. 

If accurate efficiency data are required, the variance of the injection profile should be measured as a function of the flow rate, with a correction applied by subtracting the first moment of the injection profile from the peak retention time and the variance of the injection profile from the band variance. In actual analytical practice it is often sufficient to minimize this contribution by making sure that the volume of the injection device is much smaller than the volume of the column, that the device is properly swept by the mobile phase, and that actual injection is rapid. The use of a bypass at the column inlet permits a higher flow rate through the injection device than through the column, effectively reducing the band-broadening contribution of the injection system. 

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