Electrokinetic transport of rigid macroions in the thin double layer limit: A boundary element approach

Abstract

A boundary element (BE) procedure is developed to numerically calculate the electrophoretic mobility of highly charged, rigid model macroions in the thin double layer regime based on the continuum primitive model. The procedure is based on that of O'Brien (R.W. O'Brien, J. Colloid Interface Sci. 92 (1983) 204). The advantage of the present procedure over existing BE methodologies that are applicable to rigid model macroions in general (S. Allison, Macromolecules 29 (1996) 7391) is that computationally time consuming integrations over a large number of volume elements that surround the model particle are completely avoided. The procedure is tested by comparing the mobilities derived from it with independent theory of the mobility of spheres of radius a in a salt solution with Debye–Hückel screening parameter, κ. The procedure is shown to yield accurate mobilities provided κa exceeds approximately 50. The methodology is most relevant to model macroions of mean linear dimension, L, with 1000 > κ L > 100 and reduced absolute zeta potential ( q | ζ | / k B T ) greater than 1.0. The procedure is then applied to the compact form of high molecular weight, duplex DNA that is formed in the presence of the trivalent counterion, spermidine, under low salt conditions. For T4 DNA (166,000 base pairs), the compact form is modeled as a sphere (diameter = 600 nm) and as a toroid (largest linear dimension = 600 nm). In order to reconcile experimental and model mobilities, approximately 95% of the DNA phosphates must be neutralized by bound counterions. This interpretation, based on electrokinetics, is consistent with independent studies.