924 (2001) 43–52 Journal of Chromatography A, www.elsevier.com / locate / chroma Capillary electrophoretic separation of uncharged polymers using polyelectrolyte engines Theoretical model a a, b c c * L.C. McCormick , G.W. Slater , A.E. Karger ,W.N. Vreeland , A.E. Barron , d d C. Desruisseaux , G. Drouin a Department of Physics, University of Ottawa, 150 Louis-Pasteur, Ottawa, Ontario K1N 6N5, Canada b Applied Biosystems, Foster City, CA, USA c Department of Chemical Engineering, Northwestern University, Evanston, IL, USA d Department of Biology, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada Abstract 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.  2001 Elsevier Science B.V. All rights reserved. Keywords: Mathematical modelling; Capillary electrophoresis; Polymers; DNA 1. Introduction an unbiased way to all the polymer chains of the sample, one can in fact use free-solution capillary The polydispersity of a polymer solution is not electrophoresis (CE) to study the distribution of easily determined using conventional methods such polymer sizes. Indeed, the uncharged polymer then as gel permeation chromatography [1] and mass acts like a parachute, or ‘‘drag’’, and the retardation spectrometry [2]. Recently, we proposed and tested a due to the drag molecule is directly proportional to new method to characterize the distribution of the its contour length. We called this method free varying degrees of polymerization of a water-solu- solution conjugate electrophoresis (FSCE). ble, uncharged polymer species [3]. The method is In our original paper [3], we showed the sepa- based on the idea that if a set of ‘‘engines’’ of ration of each of 3400, 5000 and 20 000 nominal uniform size and charge distribution is conjugated in molecular mass poly(ethylene glycol) (PEG) samples using conjugated oligomeric DNA engines 20 and 35 bases long. Excellent quantitative results were ob- *Corresponding author. E-mail address: gslater@science.uottawa.ca (G.W. Slater). tained and compared with matrix-assisted laser de- 0021-9673 / 01 / $ – see front matter  2001 Elsevier Science B.V. All rights reserved. PII: S0021-9673(01)00990-6