A fast algorithm for treating dielectric discontinuities in charged spherical colloids
Electrostatic interactions between multiple colloids in ionic fluids are attracting much attention in studies of biological and soft matter systems. The evaluation of the polarization surface charges due to the spherical dielectric discontinuities poses a challenging problem to highly efficient computer simulations. In this paper, we propose a new method for fast calculating the electric field of spaced spheres using the multiple reflection expansion. The method uses a technique of recursive reflections among the spherical interfaces based on a formula of the multiple image representation, resulting in a simple, accurate and close-form expression of the surface polarization charges. Numerical calculations of the electric potential energies of charged spheres demonstrate the method is highly accurate with small number of reflections, and thus attractive for the use in practical simulations of related problems such as colloid suspension and macromolecular interactions.
Key wordselectrostatic polarization method of images Green’s functions colloidal suspensions dielectric spheres
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- French, R.H., Parsegian, V.A., Podgornik, R., Rajter, R.F., Jagota, A., Luo, J., Asthagiri, D., Chaudhury, M.K., Chiang, Y., Granick, S., Kalinin, S., Kardar, M., Kjellander, R., Langreth, D.C., Lewis, J., Lustig, S., Wesolowski, D., Wettlaufer, J.S., Ching, W.Y., Finnis, M., Houlihan, F., von Lilienfeld, O.A., van Oss, C.J., Zemb, T. 2010. Long range interactions in nanoscale science. Rev Mod Phys 82, 1887–1944.CrossRefGoogle Scholar
- Frenkel, D., Smit, B. 2002. Understanding Molecular Simulation: From Algorithms to Applications. Academic Press, New York.Google Scholar
- Greengard, L. 1987. The Rapid Evaluation of Potential Fields in Particle Systems. MIT, Cambridge.Google Scholar
- Jackson, J.D. 2001. Classical Electrodynamics, 3rd Edition. John Wiley & Sons, New York.Google Scholar
- Lindell, I.V. 1993. Application of the image concept in electromagnetism. In: Stone, W.R. (ed), The Review of Radio Science 1990–1992. Oxford University Press, Oxford, Pages 107–126.Google Scholar
- Qiao, Z., Li, Z., Tang, T. 2006. A finite difference scheme for solving the nonlinear Poisson-Boltzmann equation modeling charged spheres. J Comput Math 24, 252–264.Google Scholar
- Xu, Z., Cai, W., Cheng, X. 2011. Image charge method for reaction fields in a hybrid ion-channel model. Commun Comput Phys 9, 1056–1070.Google Scholar