We investigate the equilibrium properties of a colloidal solution in contact with a soft interface. As a result of symmetry breaking, surface effects are generally prevailing in confined colloidal systems. In this Letter, particular emphasis is given to surface fluctuations and their consequences on the local (re)organization of the suspension. It is shown that particles experience a significant effective interaction in the vicinity of the interface. This potential of mean force is always attractive, with range controlled by the surface correlation length. We suggest that, under some circumstances, surface-induced attraction may have a strong influence on the local particle distribution. Colloidal suspensions are solutions of fairly large objects, with typical size ranging from 1 nm to 1 µm. The primary question of their stability and phase behaviour is the foundation of many technological applications [1]. Formally, the statistical description of a colloidal dispersion involves colloid-colloid, colloid-solvent and solventsolvent interactions. However, such detailed and complex information is usually not required to understand essential features, and it has been found more appropriate to develop effective descriptions where the colloids interact through a potential of mean force [2]. The individual forces acting between particles then depend explicitly on the temperature and on the chemical potential of the solvent. Examples of such effective potentials include dispersion forces, DLVO theory for charged systems, or depletion interactions in polydispersed solutions.On the other hand, it has been recognized long ago that surface effects are prevailing in confined colloidal systems [3,4]. The mutual influence of bulk and surface properties on each other is a challenging problem, that conversely may lead to unusual behaviours. For instance, when a bidispersed hard-sphere suspension is brought in contact with a flat substrate, excluded-volume effects are known to push the larger beads toward the wall of the sample [5]. Recent experiments done with curved or corrugated surfaces have shown that geometric features of the surface can also create and modulate entropic force fields [6]. These depletion forces can be used to grow oriented colloidal crystal, with numerous potential applications such as the fabrication of photonic bandgap crystals [7].In this Letter, we present some new findings regarding the static organization of nanoparticles near a fluctuating surface. Adsorption of colloidal particles on a flexible interface is an essential step in many biological processes, and the underlying physics of this mecha-

We re-examine here the theoretical study of the phase separation between phospholipids and grafted long polymer chains onto a fluid membrane. The polymer chains are assumed to be anchored to the membrane by one extremity (anchor). The anchors are big amphiphile lipid molecules. The anchors and phospholipids forming the bilayer phase separate under the variation of a suitable parameter (temperature, pressure, membrane environment, ...). To investigate the demixtion transition, we elaborate a new approach that takes into account the membrane undulations. We show that these undulations have the tendency to induce additional attractive forces between anchors, and consequently, the separation transition is accentuated and occurs at high temperature. Quantitatively, we show that the membrane undulations contribute with an extra positive segregation parameter chi m > 0 , which scales as chi m approximately kappa(-2) , where kappa is the bending rigidity constant. Therefore, the attraction phenomenon between species of the same kind is significant only for those membranes of small bending rigidity constant. Finally, the study is extended to the case where the lengths of the anchored polymer chains are randomly distributed. To achieve calculations, we choose a length distribution of fractal form. The essential conclusion is that the polydispersity increases the size of domains alternatively rich in phospholipids and anchors.

Surface effects are generally prevailing in confined colloidal systems. Here we report on dispersed nanoparticles close to a fluid membrane. Exact results regarding the static organization are derived for a dilute solution of nonadhesive colloids. It is shown that thermal fluctuations of the membrane broaden the density profile, but on average colloids are neither accumulated nor depleted near the surface. The radial correlation function is also evaluated, from which we obtain the effective pair potential between colloids. This entropically driven interaction shares many similarities with the familiar depletion interaction. It is shown to be always attractive with range controlled by the membrane correlation length. The depth of the potential well is comparable to the thermal energy, but depends only indirectly upon membrane rigidity. Consequences for the stability of the suspension are also discussed.

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We consider a crosslinked polymer blend made of two polymers of different chemical nature. We suppose that such a system incorporates small colloidal particles, which prefer to be attracted by one polymer, close to the spinodal temperature. This is the so-called critical adsorption. As assumption, the particle diameter, d 0 , is considered to be small enough in comparison with the size of microdomains (mesh size) ξ * ∼ an 1/2 , with a -the monomer size and n -the number of monomers between consecutive crosslinks. The critical fluctuations of the crosslinked polymer mixture induce a pair-potential between particles located in the non-preferred phase. The purpose is the determination of the Casimir pair-potential, U2(r), as a function of the interparticle distance r. To achieve calculations, use is made of an extended de Gennes field theory that takes into account the colloid-polymer interactions. Within the framework of this theory, we first show that the pair-particle is attractive. Second, we find for this potential the exact form:, with the known universal amplitudes AH > 0 and BH > 0 (the Hamaker constants). This expression clearly shows that the pair-potential differs from its homologue with no crosslinks only by the two exponential factors exp(−r/ξ * ) and exp(−2r/ξ * ). The main conclusion is that the presence of reticulations reduces substantially the Casimir effect in crosslinked polymer blends.