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## Finite-Thickness and Charge Relaxation in Double-Layer Interactions

### Abstract

We extend the classical Gouy-Chapman model of two planar parallel\ud interacting double-layers, which is used as a first approximation to\ud describe the force between colloidal particles, by considering the finitethickness\ud of the colloids. The formation of two additional double layers\ud due to this finite thickness, modifies the interaction force compared\ud to the Gouy-Chapman case, in which the colloids are semi-infinite objects.\ud In this paper we calculate this interaction force and some other\ud size-dependent properties using a mean field level of description, based on\ud the Poisson-Boltzmann (PB) equation. We show that in the case of finitesize\ud colloids, this equation can be set in a closed form depending on the\ud geometrical parameters and on their surface charge. The corresponding\ud linear (Debye-H¨uckel) theory and the well-known results for semi-infinite\ud colloids are recovered from this formal solution after taking appropriate\ud limits. We use a density functional corresponding to the PB level of description\ud to show how in the case when the total colloidal charge is fixed,\ud it redistribute itself on their surfaces to minimize the energy of the system\ud depending on the afore mentioned parameters. We study how this charge\ud relaxation affects the colloidal interactions

Topics: Natuur- en Sterrenkunde
Year: 2006
OAI identifier: oai:dspace.library.uu.nl:1874/19192