Correspondence between chromatography, single-molecule dynamics, and equilibrium: a stochastic approach

We report a detailed study concerning the correspondence between separations by chromatography, dynamic quantities coming from single-molecule measurements at the interfaces and phase partition equilibrium by using the unifying approach of the stochastic description. The fundamental hypotheses allowing establishing the proper links between the three experimental techinques are discussed, and the full correspondence between the different quantities is determined from basic principles. The expressions of the errors on the retention factor which are intrinsically linked to the separation process, and which arise form peak splitting, peak tailing, stochastic bias, injection step, and number of the anlyte molecules are derived under general conditions and discussed in detail. Reference is made to the growing area of microsystems or anaosystems and chip technology, with numerical examples. How to determine the impact of single-molecule dynamics observations on the chromatographic peak shape of the experimentally observed sorption time distribution and, in general, of the behaviour of the species at the stationary phase (surface, interfaces) is pointed out.