Serially coupled capillary columns Window diagram Optimization CompressibilityIn two recent publications, Jennings and his collaborators [1,2]
41,to the operation of serially connected pairs of gas chromatographic columns. In both publications they conclude that the method provides only a first approximation which has to be followed by empirical adjustment for best results. This view, as we will show elsewhere [5], is entirely incorrect and reflects major errors in their approach. The first, in the theoretical extension offered by lngraham, Shoemaker, and Jennings [l], is an algebraic errorwhich leads to a totally incorrect equation forthe calculation of column lengths. The second, is that these authors, as also did Jakeoka, Richard, Mehran, and Jennings [2], totally ignored the effect of carrier gas compressibility in their theory. It is with this latter point that we deal here.The very earliest publication in elution gas chromatography [6] established that retention volume is influenced by the inletloutlet pressure ratio. We had assumed that, in the light of the work of Hildebrand and Reilley in 1964 [7] and, more recently of Buys and Smuts [8], it has been widely appreciated that in serial columns of differing composition, so too is relative retention. Thus, in operating a two column serial system, say A and B, the relative retention of any pair of solutes depends upon whether A or B is at the inlet end. In both the publications referred to [1,2] such variation of relative retention was observed and led these authors to propose the rather remarkable explanation that: "Because the carrier gas velocity is lower than the average at the inlet end, and higher than the average at the outlet end, solutes encounter (per unit length of column) more solubility sites at the inlet end, and fewer solubility sites at the outlet end, than would be expected". If this were true, the concepts of both compressibility corrected and specific retention volume for single substrate columns would obviously be meaningless. Although the basic theory for coupled columns of equal gas permeability and porosity has been presented earlier [7,8] we present here a new version because it is both simpler and free of earlier assumptions.We designate the column at the inlet end of the pair F, and that at theoutlet end B,with Foperatingoverthepressuredroppi topand B over the drop p to po. The James-Martin compressibility corrections are jF over F and j B over B.The total dead time t d (unretained solute) is, in termsof the column lengths, LF and LB, given by L No ---where u is the velocity at p and j is the compressibility correction from pi to po which should be the same whicheverway around the column system is operated.The retention time of a retained solute, t R is, correspondingly, given by LB (1 + ke') whence, the fully corrected retention time, t'R, is given by