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Equation of state of surface-adsorbing colloids

We have developed a simulation model to describe particle adsorption to and desorption from liquid interfaces. Using this model we formulate a closed interfacial equation of state for repulsive elastic spheres. The effect of a long-range attractive interaction is introduced by perturbation theory, and the effect a short-range attraction is studied using direct simulation. Based on our model predictions we conclude that for polymeric particles the surface pressure cannot be modelled directly by inert particles that interact via some effective potential. Internal degrees of freedom within gel particles are all-important. Consequently, the surface pressure of a fully packed layer is not proportional to kT/d^2, where d is the particle diameter; but proportional to kT/dm^2, where dm is the size of the molecular units that make up the particle. This increases the surface pressure and modulus by some four orders of magnitude. For short range interaction we study the dynamic behaviour, and find fractal-like structures at low concentrations. At intermediate coverage an irregular structure is formed that resembles a spinodal system. This system freezes, which arrests the spinodal structure. At high surface coverage the simulations show poly-crystalline domains. For dilute systems, the strength of the surface layers is determined by simulated compression and expansion. We find a power law for the surface pressure (Pi ~ Gamma^10+/-0.5), which is related to the (fractal) structure of the adsorbed network. The power law is consistent with surface percolation.