Multiple liquid-liquid partition: II. Theory of Martin-Synge distribution (MSD)

Abstract

The theory of Martin-Synge distribution (MSD) was refined, with special attention being focused upon the derivation of the separation functions. The separation function for the fundamental distribution of MSD was obtained in the form v = t2(αk1 + 1)(αk1 + β)[(αk1 + 1)1/2 + (αk1 + β)1/2]2/αk1(β − 1)2, where ν is the number of aliquots vm driven through the apparatus, t the abscissa of the standard normal distribution, α = vm/v8 the phase ratio, β = k1/k2≥ 1 the separation factor, and k1 the partition coefficient of the more rapidly moving component; ν was shown to have minima at given αk1 values. The separation function of the single withdrawal of MSD was presented in the form N = u + 1 = t2(2αk1 + β + 1)2/(β − 1)2+ 1, where N is the number of partition units; N is minimal when αk1 = 0. The elution volumes and standard deviations of the two compounds to be separated were mathematically analyzed in a manner similar to that previously presented when dealing with the theory of counter-current distribution (CCD). As in CCD, the elution volumes in MSD were found to have minima at given αk1 values. However, the standard deviations of the elution curves also have minima in respect to αk1 in MSD, which is a different situation as compared to CCD. The selection of optimal operating conditions was found to be more critical in MSD than in CCD.