Plate Theory and Extensions - Chromatographic Dead Volumes > Page 34
The expression for the thermodynamic dead volume is more complex than that for the kinetic dead volume and will depend on the size of the solute molecule. In common with the kinetic dead volume, it contains the volume of moving phase VI(m). However,it also includes that portion of the interstitial volume that is size dependent (Y), together with the pore volume available to the solute (also size dependent (W). Equation (39) shows the major retention factor, (xK3VS(A)), is also molecular size dependent ((x) is not unity), thus, unless the values for (Y), (W) and (x) are available or can be determined, it is not possible to determine the retention volume difference between two solutes accurately. This is particularly true for LC, when porous stationary phases (supported on silica) are used and if the solute molecules differ significantly in size. The experimental determination of (Y), (W) and (x) is difficult, although theoretically possible, and can be lengthy and tedious. Equation (39) has important implications in the measurement of the capacity factor (k'). Using equation (39) the equation for (k') can be seen to be
which simplifies to
Equation (40) shows that the same errors are involved in the measurement of (k') as those in the measurement of the thermodynamic dead volume. If the solute is well retained, i.e.,
WK2Vp(2) + xK3VS(A) >> VI(m) + YVI(S) + WVp(1)
then the corrected retention volume can be used for thermodynamic calculations with greater confidence.