Effect of particle size and Debye length on order parameters of colloidal silica suspensions under confinement

Abstract

Using atomic force microscopy (AFM) and small angle X-ray scattering (SAXS), we show a full comparison between structuring of nanoparticles in confinement and in bulk in order to explain the effect of confinement on characteristic lengths and the scaling law of the characteristic lengths. Three different-sized particle suspensions are used to check the generalization and the correlation between the characteristic lengths and the system parameters, like particle diameter and Debye length. The two characteristic lengths obtained from AFM force curves, the oscillatory wavelength λ, which is related to the average particle distance, and the decay length ξ, which measures how far particle correlates to obtain periodic oscillations, are in good agreement with the mean particle distance 2π/q_max and the correlation length 2/Δq in bulk, respectively, obtained from the structure peaks of SAXS diagrams. Although confinement causes layering of nanoparticles parallel to the confining surfaces, the characteristic lengths in the direction perpendicular to the confining surfaces follow the bulk behavior. The wavelength scales as ρ^−1/3 with the particle number density ρ irrespective of the particle size and the ionic strength and shows a pure volume effect. Upon comparing with literature results, the λ = ρ^−1/3 scaling law can be applied more generally for charged particles, as long as the repulsive interaction is sufficiently long-ranged, than the previous expression of λ = 2(R + κ⁻¹), which only approaches the value of average particle distance under specific conditions. The decay length ξ is controlled both by the particle size and the ionic strength of the suspensions, and ξ = R + κ⁻¹ is proposed in the paper. In addition, the interaction strength, the force amplitude and maximum scattering intensity, increases linearly with particle concentration. On the other hand, the Monte Carlo (MC) simulations and approximate hypernetted chain (HNC) closure calculation based on Derjaguin-Landau-Verwey-Overbeek (DLVO) potential are employed to study the characteristic lengths from the theoretical point of view. The experimental wavelengths are in good agreement with the theoretical counterparts and the experimental decay lengths show the same qualitative behavior as theoretical ones on the particle size and ionic strength.