Scaling of layer spacing of charged particles under slit-pore confinement: an effect of concentration or of effective particle diameter?

Abstract

This paper tests the generality of the scaling law for layer spacing of charged particles under confinement and resolves the established contradictions in the literature. The present determined layer spacings λ, also called the wavelength of oscillatory force, by colloidal probe atomic force microscopy are compared to previously obtained ones, Δh, also called step size, by using a thin film pressure balance. For charged particles, e.g. silica nanoparticles and micelles of anionic surfactant, the layer spacing under confinement is found to depend solely on the particle number density ρ in the relation λ (or Δh) =ρ−1/3. The previous description for the layer spacing using the effective particle diameter 2(R + κ−1) is not general and only applicable at specific conditions of particle volume fraction and ionic strength. We claim that when particles are dominated by electrostatic repulsion and in a low pressure reservoir, ρ−1/3 is a general scaling law for layer spacing of particles, which indicates that particles under confinement are still randomly distributed in a fluid-like manner as they are in bulk. As a side-effect an equation to obtain the ionic strength I of colloidal suspension from measured conductivity is established. Ionic strength I is needed to determine the values for Debye length κ−1, which are in very good agreement with the theoretical ones.