Polymer-Chain Adsorption Transition at a Cylindrical Boundary

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.

latex, 12 pages, 3 ps-figures, uuencoded

References in corpus (3)

• Random Walks in Noninteger Dimension
• Spherically-Symmetric Random Walks in Noninteger Dimension
• Statistical Models on Spherical Geometries

Cited by in corpus (5)

• Universality in Random Walk Models with Birth and Death
• SPHERICALLY SYMMETRIC RANDOM WALKS I. REPRESENTATION IN TERMS OF ORTHOGONAL POLYNOMIALS
• SPHERICALLY SYMMETRIC RANDOM WALKS II. DIMENSIONALLY DEPENDENT CRITICAL BEHAVIOR
• SPHERICALLY SYMMETRIC RANDOM WALKS III. POLYMER ADSORPTION AT A HYPERSPHERICAL BOUNDARY
• Quantum Ultra-Walks: Walks on a Line with Hierarchical Spatial Heterogeneity