Random sequential adsorption of charged segments on a line.

Abstract

We analytically investigate a one-dimensional random sequential adsorption (RSA) model in which deposition probabilities are nonuniform and depend on the polarization state of the available intervals. Adsorbed segments behave as dipoles with two possible orientations, leading to orientation-dependent placement rules that combine stochastic selection with deterministic relaxation to energetically favorable positions. By generalizing the standard RSA integral equation to include polarization-dependent boundary conditions, we derive and solve uncoupled functional recurrences for the mean coverage, obtaining exact results for both deterministic and stochastic regimes. Furthermore, we compute the variance using the law of total variance, identifying distinct intracase and intercase contributions to the fluctuations. The model exhibits a continuous transition between steplike coverage profiles as the orientation probability varies, providing a tractable framework for studying interaction-driven nonuniform adsorption processes.