Irreversible adsorption/deposition kinetics: A generalized approach

A generalized random sequential adsorption (RSA) approach is developed by t aking into account diffusion, particle/wall hydrodynamic interactions as we ll as external forces (e.g., gravity). In analogy to the previous concept o f Pagonabarraga and Rubi' [Physica A 188, 553 (1992)] the position dependen t available surface function <(Phi)over bar>(z, theta) is introduced. Using this definition, constitutive expressions for the adsorption flux are form ulated which represent the generalization of previous models, including the widely used Langmuirian kinetic approach. It is shown that the overall ava ilable surface function Phi(Delta, theta) plays the crucial role in these e xpressions. It represents the net probability of transferring a particle fr om the arbitrary distance Delta to the interface for a given surface covera ge. Explicit expressions in the form of definite integrals are formulated w hich enable one to calculate the <(Phi)over bar>(Delta, theta) function in terms of the Phi(z, theta). In the case of hard spheres, Phi(z, theta) is c alculated up to the second order of the surface coverage theta using geomet rical arguments. The effect of an external force gravity is characterized b y the dimensionless radius of particles R*, where R* --> -infinity correspo nds to the purely ballistic case, R* --> -infinity to the diffusion RSA, an d R* --> -infinity reflects the case of infinite gravity acting outwards fr om the surface. Using these expressions, the overall <(Phi)over bar>(Delta, theta) function is also calculated. It is found that the RSA available sur face function is not recovered for R* = 0 as expected, but for R* --> -infi nity. The transition from the R* = 0 to the ballistic case (R* = infinity) is analyzed. Unexpectedly, it is found that for R* = 1 the second order ter minal the coverage expansion of <(Phi)over bar>(Delta, theta) appears negat ive which seems an entirely new result. It is also deduced that in the case of an energy barrier, whose extension is much smaller than the particle di mension, the adsorption process can well be characterized for R* = 0 in ter ms of the classical RSA model. This can be explained by the fact that for a high energy barrier the adsorbing particles could randomize over the depos ition plane before crossing the barrier and adsorbing irreversibly. (C) 199 9 American Institute of Physics. [S0021-9606(99)71106-2].