Efficient Brownian dynamics simulation of particles near walls. II. Sticky walls

In this paper we treat a boundary condition, the "sticky boundary," which appears to be quite useful in mesoscopic models. The sticky boundary is modeled as an infinitely deep, infinitely narrow, potential well adjacent to a reflecting boundary. The free energy corresponding to this boundary is finite. The boundary condition, which can be viewed as an intermediate between the absorbing and reflecting boundary condition, may have many applications, e.g., for the simulation of the partial adsorption of polymer molecules to walls and for the modeling of solvent quality. We will derive an efficient Brownian dynamics algorithm, capable of handling interactions of a diffusing particle with a sticky wall. Our approach avoids the large discretization errors that occur in the simulation of boundary interactions within the "standard" Brownian dynamics approach. The essence of our method was presented before [E. Peters and T. Barenbrug, Phys. Rev. E (to be published)]. The treatment of the wall as proposed here is quite general, and therefore not limited to the use within Brownian dynamics. In other simulation techniques which aim at treating the dynamics of mesoscopic particles near walls, we expect it to be of use as well.