Analytic theory of the adsorption-desorption transition of Gaussian polymers interacting with a periodic lattice of adsorbing centers.

Based on the obtained exact analytic solution, we calculate the adsorption-desorption diagram that describes the adsorption of Gaussian polymers onto a rigid surface that bears a periodic array of the adsorbing centers. It is shown that the polymer adsorption onto this substrate is fully governed by a delicate balance between the entropic depletion repulsion of polymers from the rigid surface and their attraction to the adsorbing centers. Magnitudes of these competitive effects are calculated in terms of the reduced overall affinity of the substrate eta(-1) and the reduced separation between the adsorbing centers d. The calculated exact adsorption-desorption diagram eta(d) that describes the equilibrium between the above depletion and adsorption interactions, is shown to obey the scaling law eta approximately d(-1.17).