Study of isocratic separations by extended statistical theories of overlap

A problem first proposed by Giddings in 1983 is investigated here using theory based on extended statistical models of overlap. This problem addressed the applicability of simple statistical theory, as it existed in 1983, to one type of isocratic chromatographic separation. In this separation, the plate number is constant, the bandwidths of single-component peaks increase with elution time, and single-component peaks are distributed uniformly along an axis defined by the difference between standard-state chemical potentials of analytes in the mobile and stationary phases. By use of extended statistical theory, one can show that Giddings' basic insight is correct and even better than he envisioned. The extended theory is needed, however, to account quantitatively for the effects of single-component-peak amplitudes on peak overlap, especially when the plate number is small.