Generating function methods for macromolecules at surfaces. I. One molecule at a plane surface

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Abstract
The problem of a macromolecule adsorbed on a single surface is treated by means of a generating function technique. The basic method has the virtues of simplicity and flexibility. The statistical weights that appear in the generating functions for tails, trains, and loops can be calculated with use of a variety of models. The essential physics of the adsorption process, and the occurrence of a critical point, are transparent in this treatment. Illustrative calculations are done for the simplest case, in which tails have unit weight, trains have binding energies proportional to their lengths, and loops are weighted by lattice walk statistics. Methods for treating more realistic models for chains, and for handling their interactions when there is multiple chain adsorption, are discussed.