Thickness of the particle-free layer near charged interfaces in suspensions of like-charged nanoparticles

When a suspension of charged nanoparticles is in contact with a like-charged water–solid interface, next to this interface a particle-free layer is formed. The present study provides reliable measurements of the thickness of this particle-free layer with three different techniques, namely optical reflectivity, quartz crystal microbalance (QCM), and direct force measurements with atomic force microscopy (AFM). Suspensions of negatively charged nanoparticles of different size and type are investigated. When the measured layer thickness is normalized to the particle size, one finds that this normalized thickness shows universal inverse square root dependence on the particle volume fraction. This universal dependence can be also derived from Poisson–Boltzmann theory for highly asymmetric electrolytes, whereby one has to assume that the nanoparticles represent the multivalent coions.