Ideal Polymers near Scale-Free Surfaces

Abstract

The number of allowed configurations of a polymer is reduced by the presence of a repulsive surface resulting in an entropic force between them. We develop a method to calculate the entropic force, and detailed pressure distribution, for long ideal polymers near a scale-free repulsive surface. For infinite polymers the monomer density is related to the electrostatic potential near a conducting surface of a charge placed at the point where the polymer end is held. Pressure of the polymer on the surface is then related to the charge density distribution in the electrostatic problem. We derive explicit expressions for pressure distributions and monomer densities for ideal polymers near a two- or three-dimensional wedge, and for a circular cone in three dimensions. Pressure of the polymer diverges near sharp corners in a manner resembling (but not identical to) the electric field divergence near conducting surfaces. We provide formalism for calculation of all components of the total force in situations without axial symmetry.

13 pages, 6 figures

References in corpus (4)

• Polymer-mediated entropic forces between scale-free objects
• Entropic force of polymers on a cone tip
• Kinetics of First Passage in a Cone
• Pressure exerted by a grafted polymer on the limiting line of a semi-infinite square lattice

Cited by in corpus (10)

• Anomalous Dimension in a Two-Species Reaction-Diffusion System
• Diffusion in the Presence of Scale-Free Absorbing Boundaries
• Calculation of a fluctuating entropic force by phase space sampling
• Long Polymers Near Wedges and Cones
• Cross-link induced shrinkage of grafted Gaussian chains
• Quantum particle in a spherical well confined by a cone
• Attractive and repulsive polymer-mediated forces between scale-free surfaces
• Pinning and unbinding of (ideal) polymers from a wedge corner
• Localization of random walks to competing manifolds of distinct dimensions
• Entropic pressure in lattice models for polymers