Combining colloidal-probe experiments and computer simulations, we analyze the solvation forces F of charged silica colloids confined in films of various thicknesses h. We show that the oscillations characterizing F(h), for sufficiently large h, are determined by the dominant wavelength of the bulk radial distribution function. As a consequence, both quantities display the same power-law density dependence. This is the first direct evidence, in a system treatable both by experiment and by simulation, that the structural wavelength in bulk and confinement coincide, in agreement with predictions from density functional theory. Moreover, theoretical and experimental data are in excellent quantitative agreement.

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 l, which is related to the average particle distance, and the decay length x, which measures how far particle correlates to obtain periodic oscillations, are in good agreement with the mean particle distance 2p/q max and the correlation length 2/Dq 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 r À1/3 with the particle number density r irrespective of the particle size and the ionic strength and shows a pure volume effect. Upon comparing with literature results, the l ¼ r À1/3 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 l ¼ 2(R + k À1 ), which only approaches the value of average particle distance under specific conditions. The decay length x is controlled both by the particle size and the ionic strength of the suspensions, and x ¼ R + k À1 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-VerweyOverbeek (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.

We present theoretical, computer simulation and experimental results for the structural length scales characterizing bulk and confined charged colloidal suspensions. The target quantities are the bulk pair correlation functions on the one hand, and the oscillatory solvation forces of the colloids in films of various thicknesses on the other. Recently we have shown, for a system with very low salt concentration, that these quantities are characterized by the same wavelength in the asymptotic limit, in agreement with predictions from density functional theory. Here we consider systems with larger ionic strengths of added salt. Our results indicate that the wavelength remains essentially unaffected, whereas the correlation length and the amplitude depend significantly on the amount of added salt. Indeed, already at ionic salt strengths as low as 10 −3 mol l −1 the force oscillations essentially disappear.

Combining computer simulations and experiments we address the impact of charged surfaces on the solvation forces of a confined, charged colloidal suspension (slit-pore geometry). Investigations based on the colloidal-probe atomic-force-microscope technique indicate that an increase in surface charges markedly enhances the oscillations of the force in terms of their amplitude. To understand this effect on a theoretical level we perform grand-canonical Monte-Carlo simulations (GCMC) of a coarse-grained model system. It turns out that various established approaches of the interaction between a charged colloid and a charged wall, such as linearized Poisson-Boltzmann (PB) theory involving the bulk screening length, do not reproduce the experimental observations. We thus introduce a modified PB potential with a space-dependent screening parameter. The latter takes into account, in an approximate way, the fact that the charged walls release additional (wall) counterions which accumulate in a thin layer at the surface(s). The resulting, still purely repulsive fluid-wall potential displays a nonmonotonic behavior as function of the surface potential with respect to the strength and range of repulsion. GCMC simulations based on this potential reproduce the experimentally observed charge-induced enhancement in the force oscillations. We also show, both by experiment and by simulations, that the asymptotic wave- and decay length of the oscillating force do not change with the wall charge, in agreement with predictions from density functional theory.

Micellar solutions of nonionic surfactants Brij 35 and Tween 20 are confined between two surfaces in a colloidal-probe atomic-force microscope (CP-AFM). The experimentally detected oscillatory forces due to the layer-by-layer expulsion of the micelles agree very well with the theoretical predictions for hard-sphere fluids. While the experiment gives parts of the stable branches of the force curve, the theoretical model allows reconstruction of the full oscillatory curve. Therewith, the strength and range of the ordering could be determined. The resulting aggregation number from the fits of the force curves for Brij 35 is close to 70 and exhibits a slight tendency to increase with the surfactant concentration. The last layer of micelles cannot be pressed out. The measured force-vs-distance curve has nonequilibrium portions, which represent "jumps" from one to another branch of the respective equilibrium oscillatory curve. In the case of Brij 35, at concentrations <150 mM spherical micelles are present and the oscillation period is close to the micelle diameter, slightly decreasing with the rise of concentration. For elongated micelles (at concentration 200 mM), no harmonic oscillations are observed anymore; instead, the period increases with the decrease of film thickness. In the case of Tween 20, the force oscillations are almost suppressed, which implies that the micelles of this surfactant are labile and are demolished by the hydrodynamic shear stresses due to the colloidal-probe motion. The comparison of the results for the two surfactants demonstrates that in some cases the micelles can be destroyed by the CP-AFM, but in other cases they can be stable and behave as rigid particles. This behavior correlates with the characteristic times of the slow micellar relaxation process for these surfactants.