On chemisorption of polymers to solid surfaces

The irreversible adsorption of polymers to a two-dimensional solid surface is studied. An operator formalism is introduced for chemisorption from a polydisperse solution of polymers which transforms the analysis of the adsorption process to a set of combinatorial problems on a two-dimensional lattice. The time evolution of the number of polymers attached and the surface area covered are calculated via a series expansion. The dependence of the final coverage on the parameters of the model (i.e. the parameters of the distribution of polymer lengths in the solution) is studied. Various methods for accelerating the convergence of the resulting infinite series are considered. To demonstrate the accuracy of the truncated series approach, the series expansion results are compared with the results of stochastic simulation.