Statistical properties of surfaces covered by deposited particles

Abstract

The statistical properties of surfaces covered by irreversibly adsorbed colloidal particles are studied as a function of the Péclet number (or equivalently as a function of their rescaled radius R*). More precisely, the radial distribution function g(r) is determined as a function of the coverage θ for five systems corresponding to different values of R*. Also measured is the reduced variance σ2/〈n〉 of the number n of adsorbed particles on surfaces of given area out of the adsorption plane. Finally, the evolution of 〈n〉 with the concentration of particles in solution during the deposition process is determined for the different systems. This allows us to obtain information on the available surface function Φ. All these parameters are compared to their expected behavior according to the random sequential adsorption (RSA) model and to the ballistic model (BM). It is found that the radial distribution function of the system of particles characterized by R*<1 is well predicted by the RSA model whereas for R*≳3 the BM can serve as a good first approximation. On the other hand, one finds surprisingly that the available surface function Φ and the reduced variance σ2/〈n〉 vary with the coverage θ in a similar way for all the systems over the range of value of R* investigated. Their behavior corresponds, in first approximation, to the expectations from the BM. In particular, the reduced variance σ2/〈n〉 exhibits a horizontal tangent at low coverage whereas the RSA model predicts an initial slope of −4. This result is the more intriguing that σ2/〈n〉 is directly related to the radial distribution function g(r), which does vary with R*. Finally, higher order moments of the distribution of the number of particles n adsorbed on our surfaces are also determined as a function of the coverage. They behave, within experimental errors, like those of a Gaussian distribution as predicted by the central limit theorem.