Bridging the gap between two different scaling laws for structuring of liquids under geometrical confinement

Structural forces are a phenomena obtained in liquids of one-component (e.g. for organic solvents) and two-components (colloidal dispersions), alike. So far, those two systems were discussed separately, using two different scaling laws. In this review article, an attempt is made to bridge the gap between both scaling laws by defining the scaling limit for two-component systems. Colloidal probe atomic force microscopy (CP-AFM) is used to measure structural forces in suspensions of silica nanoparticles (NPs) of three different sizes. In these two-component systems (solid NPs suspended in water), oscillatory behaviour can be obtained in the force vs. separation profiles. The wavelength λ is larger than the actual particle diameter d and rather depends on the particles' volume fraction ϕ following the inverse cubic root law λ∝ϕ^-13. It is shown that the real particle diameter d can be determined by a gedankenexperiment by extrapolating the fitted wavelength λ from the structural force measurements at a specific particle concentration to a particle volume fraction ϕ of 52% - the packing factor for simple cubic packing - using the well-known inverse cubic root scaling law. This extrapolation can be interpreted as a transition from a two-component system towards a one-component-like problem. In this case, particles are in contact and the wavelength λ is equal to the particle diameter d, λ = d as for one-component systems. The determined diameters d of the different silica nanoparticles agree well with independent measurements using transmission electron microscopy (TEM), validating the used approach. The proposed method can be extended to numerous dispersions of spherical nano-sized objects, for which structural forces can be measured.