Adhesion between a charged particle in an electrolyte solution and a charged substrate: Electrostatic and van der Waals interactions

The equilibrium separation between a charged particle in an electrolyte solution and a substrate with an initially uniform surface charge density is obtained using the classical Derjaguin–Landau–Verwey–Overbeek theory. The electrostatic free energy is obtained by coupling the electric response of the substrate with the electric potential obtained from the solution of the Debye–Hückel equation. The van der Waals free energy is calculated by integrating the 6–12 Lennard-Jones potential. Metallic, dielectric, and semiconducting substrates are considered in turn. At low ionic strength, our results demonstrate a distinct response to the charged particle in each case. For example, in the case of a metallic substrate, the attached state (corresponding to equilibrium separation at short range) is always close to the van der Waals energy minimum. In addition, the application of a surface charge of sign opposite to that of the particle facilitates the transition from the detached state (corresponding to large separation at which the interaction between the particle and the substrate is negligible) to the attached state but scarcely changes the equilibrium separation. In the case of a dielectric substrate, the attached state is located at a distance of around two orders of magnitude larger than that for a metallic substrate and this equilibrium separation decreases as the (opposing) surface charge increases. A semiconducting substrate can behave either like a metal or like a dielectric, depending on the ratio of its Debye length to that of the electrolyte solution.

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