Capillary electrophoretic separation of uncharged polymers using polyelectrolyte engines. Theoretical model

We recently demonstrated that the molecular mass distribution of an uncharged polymer sample can be analyzed using free-solution capillary electrophoresis of DNA-polymer conjugates. In these conjugates, the DNA is providing the electromotive force while the uncharged polydisperse polymer chains of the sample retard the DNA engine with different amounts of hydrodynamic drag. Here we present a theoretical model of this new analytical method. We show that for the most favourable, diffusion-limited electrophoresis conditions, there is actually an optimal DNA size to achieve the separation of a given polymer sample. Moreover, we demonstrate that the effective friction coefficient of the polymer chains is related to the stiffness of the two polymers of the conjugate, thus offering a method to estimate the persistence length of the uncharged polymer through mobility measurements. Finally, we compare some of our predictions with available experimental results.