Adsorption of a Chain Polymer between Two Plates

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Abstract
A lattice model of adsorption of an isolated chain polymer between two plates is investigated using a matrix formalism and a grand canonical ensemble (GCE) formalism. The matrix formalism is particularly convenient for calculating the polymer segment density as a function of the distance from one of the plates for different fixed plate separations. The GCE formalism can be used to calculate the fraction of loops (sequences of polymer segments whose ends are in contact with one plate and whose intermediate segments lie between the two plates), bridges (sequences of polymer segments whose ends are in contact with different plates and whose intermediate segments lie between the two plates), and trains (sequences of polymer segments which are wholly in contact with one plate or the other). All of the foregoing quantities have been calculated in the limit of infinite molecular weight as a function of the distance of separation between the plates and the energy of adsorption of a polymer segment on a plate. The self‐excluded volume of the polymer chain is ignored. In addition the average sizes of loops, bridges, and trains, and the effective force of attraction between the plates is calculated.