Sequential addition of particles: Integral equations

Abstract

We present an integral-equation solution of the structure of systems built through the sequential quenching of particles. The theory is based on the Replica Ornstein–Zernike equations that describe the structure of equilibrium fluids within random porous matrices. The quenched particles are treated as a polydisperse system, each of them labeled by the total density at the time of its arrival. The diagrammatic expansions of the correlation functions lead to the development of the liquid-theory closures appropriate for the present case. Numerical solutions for the deposition of hard disks show excellent agreement with simulation. We also discuss a binary-mixture treatment, which is shown to provide a very good approximation to the polydisperse approach.

Sequential deposition of polydisperse particles with double layer interactions: An integral-equation theory

“…In this approximation the instantaneous Replica Ornstein-Zernike (ROZ) system [3,12] reduces to a single equation determining the equilibrium configuration of the annealed molecules prior to quenching. The effect of polydispersity is included into the equation as shown in Eq.…”

“…[3] for sequential quenching is based on the multicomponent treatment, in which particles depositing on a surface at different times are regarded as different species. Its application to the RSA of the polydisperse particles was recently investigated [11].…”

“…The applications are widespread including polymer science, biomaterials, pulp and paper industry, and food chemistry. For the situations where there are no attractive interactions among particles but there are strong interactions between particles and the surface, the deposition of particles will grow a monolayer film, the structure of which can be obtained by methods based on statistical thermodynamics and the adsorption may be reasonably considered as an irreversible process [3]. This is often modeled by the random sequential adsorption (RSA), in which no surface diffusion and desorption occur.…”

“…RSA gives rise to the configurations which are different from their equilibrium counterparts. Previously, we proposed a model called sequential quenching (SQ) [3], in which the added particle diffuses on a surface after its arrival onto the surface. After a particle gets equilibrated with other previously quenched ones, the particle itself is quenched in place and the new addition begins in the same fashion.…”

Sequential quenching of square-well particles

“…Our preliminary work 23 showed that it is actually necessary to treat the system as a mixture of an infinite number of species. The c(r) in the above equations are the direct correlation functions, i.e., the sume of all virial coefficients ͑''diagrams'' or ''cluster integrals''͒ in the corresponding total correlation functions h(r) which are free from nodal points.…”