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.

Using Monte Carlo simulations in the grand canonical and isobaric ensembles we investigate freezing phenomena in a charged colloidal suspension confined to narrow slit pores. Our model involves only the macroions which interact via a Derjaguin-Landau-Verwey-Overbeek (DLVO) potential supplemented by a soft-sphere potential. We focus on DLVO parameters typical for moderately charged silica particles (with charges Z approximately 35) in solvents of low ionic strengths. The corresponding DLVO interactions are too weak to drive a (bulk) freezing transition. Nevertheless, for sufficiently small surface separations L(z) the confined systems display not only layering but also significant in-plane crystalline order at chemical potentials where the bulk system is a globally stable fluid (capillary freezing). At confinement conditions related to two-layer systems the observed in-plane structures are consistent with those detected in ground state calculations for perfect Yukawa bilayers [R. Messina and H. Lowen, Phys. Rev. Lett. 91, 146101 (2003)]. Here we additionally observe (at fixed L(z)) a compression-induced first-order phase transition from a two-layer to a three-layer system with different in-plane structure, in agreement with previous findings for pure hard spheres.

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