Electrophoresis of spheres with uniform zeta potential in a gel modeled as an effective medium

The effective medium model [H.C. Brinkman, Appl. Sci. Res. A 1 (1947) 27] is used to calculate the electrophoretic mobility of spheres in a gel with uniform zeta potential on their surface. In the absence of a gel support medium or ion relaxation (the distortion of the ion atmosphere from equilibrium due to the presence of an external flow or electric field), our results reduce to those of Henry [D.C. Henry, Proc. R. Soc. London Ser. A 133 (1931) 106]. The relaxation effect can be ignored for weakly charged particles, or for particles with low absolute zeta potential. Using a procedure similar to that employed by O'Brien and White [R.W. O'Brien, L.R. White, J. Chem. Soc. Faraday Trans. 2 74 (1978) 1607], the relaxation effect is accounted for in the present work and results are presented over a wide range of particle sizes, gel concentrations, and zeta potentials in KCl salt solutions. In the limit of no gel, our results reduce to those of earlier investigations. The procedure is then applied to the mobility of Au nanoparticles in agarose gels and model results are compared to recent experiments [D. Zanchet, C.M. Micheel, W.J. Parak, D. Gerion, S.C. Williams, A.P. Alivisatos, J. Phys. Chem. B 106 (2002) 11758; T. Pons, H.T. Uyeda, I.L. Medintz, H. Mattoussi, J. Phys. Chem. B 110 (2006) 20308]. Good agreement with experiment is found for reasonable choices of the model input parameters.

Graphical abstractReduced mobility, ξ, over reduced zeta potential, Y, versus κ   a for a sphere in different gel environments. Ion relaxation is included (salt is KCl) and Y=5Y=5. From the uppermost to lowermost lines, λ/κ=0.0λ/κ=0.0 (open squares and solid line), 0.010 (filled squares and dashed line), 0.027 (open diamonds and dotted line), 0.072 (filled diamonds and solid line), 0.193 (open triangles and dashed line), 0.519 (filled triangles and dotted line), 1.389 (×s and solid line), 3.727 (∗s and dashed line), 10.0 (+s and dotted line).Figure optionsDownload full-size imageDownload as PowerPoint slide