The phase behaviour of a suspension of colloids near a soft interface is investigated. Particular emphasis is given to entropic interactions mediated by membrane fluctuations and their consequences on the local (re)organization of the suspension. In a generalized van der Waals description, the suspension undergoes a first-order phase transition where a dense phase of colloids coexists with a dilute one. We predict a decrease of the critical volume fraction compared to the value in the absence of fluctuation-induced interactions. These results highlight potential applications of entropic forces to control the thermodynamic state of a colloidal suspension.

Adsorption of polymers is a phenomenon of great importance in a number of areas of our daily life. However, understanding this phenomenon is essential. This work focuses on the theoretical study of the polyethylene glycol (PEG) adsorption phenomenon on thenatural clay-layer surface. Clay is considered as a matrix. Different adsorption regimes have been presented. The expressions of the surface coverage ratio as a function of the volume fraction of monomer for each regime were calculated. A strong adsorption was noted for the first two regimes (dilute surface, and bidimensional semi-dilute surface) confirmed by the exponential term. When the surface becomes saturated, we are in the plateau regime for which the adsorption varies logarithmically, due to the occupation of most of the sites available on the clay-layer surface. Finally, we presented the variation of the volume fraction as a function of 𝑧(axis perpendicular to the surface), we have shown that a layer of polyethylene glycol (PEG) adsorbed on a natural clay-layer surface is composed of three zones (proximal, central and distal) with different volume fractions.