A Dynamic Model for the Attachment of a Brownian Particle Mediated by Discrete Macromolecular Bonds

A model is presented for the attachment of a Brownian particle to a surface mediated by both the conservative colloidal forces and the formation of macromolecular bonds. By considering Brownian motion and bond formation as coupled stochastic processes, the model derives a governing equation for the time-dependent probability density of having a given number of bonds and separation distance from the surface. The model predicts the deposition rate of particles to a surface as a function of the physicochemical parameters of the binding molecules, including the density, interaction length, stiffness, and formation and dissociation kinetic rate constants. Furthermore, two limiting simplifications of the full model are explored which correspond to particle attachment rate limited by the rate of Brownian motion or by the rate of bond formation.