Extended random sequential adsorption model of irreversible deposition processes: From simulations to experiments

Abstract

An experimental study of the irreversible deposition of colloidal particles of various radii R on a solid surface is presented over a wide range of the Péclet number, Pe, or reduced radius R* (Pe ‫؍‬ R* 4 ). The experimental data are analyzed by means of a new generalized random sequential adsorption model that takes explicitly the diffusion of the particles during the deposition into account. It allows description of the continuous transition from a random sequential adsorption-like to a ballistic-like deposition behavior. It depends on three parameters: d s , related to the diffusion of the particles before adhesion; n s , related to the number of allowed adhesion trials of a particle; and R e , representing the effective particle radius. The model allows accounting for all of the experimental observations relative to the radial distribution functions and the number density f luctuations over the whole coverage range and all investigated values of R*. In addition, it is found that d s ͞R is proportional to R* ؊2 as expected for a diffusional process. Moreover, the parameters d s and n s appear to be connected through the empirical relation (d s ͞ R)n s 2͞3 ‫؍‬ C, where C is found to be of the order of 50. This unique statistical model allows an accurate description of the irreversible deposition process, whatever the inf luence of gravity with respect to diffusion.The structure of an assembly of particles deposited or adsorbed on a solid surface depends on the ability of the particles to diffuse along the surface: when they can diffuse on the surface, the laws of statistical mechanics predict the properties of the system. In the case of irreversible deposition processes in which, once adsorbed, the particles can neither move along the surface nor desorb from it, the structure depends on the particle interactions and on a parameter R*, related to the Péclet number by Pe ϭ R* 4 , which characterizes the relative importance of the gravitational field with respect to the Brownian motion of the particles during the deposition process (1). Large values of R* (R* Ͼ 3) correspond to deposition processes in which gravity plays a dominant role, whereas small values of R* (R* Ͻ 1) characterize purely diffusional deposition processes.Over the last few years, our understanding of these irreversible deposition processes has evolved from both the experimental and the theoretical point of view, and a great effort toward modeling has been undertaken. For the case of large R*, the ballistic-deposition (BD) model has been developed (2, 3). It has been shown experimentally that this model describes accurately such deposition processes (4). For the case of small R*, the random sequential adsorption (RSA) model has been introduced (5). Its validity for describing adsorption processes is less clear. Although it seems to predict quite accurately the radial distribution function, g(r), of the assembly of the adsorbed particles (6, 7), it leads to contradictory results as far as the density fluctuations of adsorbed particles is...

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