Polymer-chain adsorption transition at a cylindrical boundary.

In a recent letter, a simple method was proposed to generate solvable models that predict the critical properties of statistical systems in hyperspherical geometries. To that end, it was shown how to reduce a random walk in D dimensions to an anisotropic one-dimensional random walk on concentric hyperspheres. Here, I construct such a random walk to model the adsorption-desorption transition of polymer chains growing near an attractive cylindrical boundary such as that of a cell membrane. I find that the fraction of adsorbed monomers on the boundary vanishes exponentially when the adsorption energy decreases towards its critical value. When the adsorption energy rises beyond a certain value above the critical point whose scale is set by the radius of the cell, the adsorption fraction exhibits a crossover to a linear increase characteristic to polymers growing near planar boundaries. PACS numbers: 05.20.-y, 05.40.+j, 05.50.+q