On the theory of polymer adsorption at an interface

Exact results are given for the grand partition function of a single model chain adsorbed at an interface. The model chosen corresponds to a walk on a 5‐choice, instead of a 6‐choice, simple cubic lattice by disallowing step reversals. The flexibility of this model is rendered variable by assigning different weights to consecutive steps made in the same direction. The obtained results are compared to those of a previous model for Gaussian chains. Satisfactory agreement between the models allows the previously undetermined flexibility parameter to be determined. The segment density in the vicinity of the interface is obtained as a function of this parameter. Correspondence with polymer chains is established through this parameter. We conjecture that the volume fraction of segments in the diffuse layer resulting from the loops does not exceed 0.1, even when the volume fraction in the interface is unity.