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arXiv · hep-lat/9410023

Polymer-Chain Adsorption Transition at a Cylindrical Boundary

S. Boettcher
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Abstract

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.

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S. Boettcher. 1995-01-24. Polymer-Chain Adsorption Transition at a Cylindrical Boundary. https://doi.org/10.1103/physreve.51.3862

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