Configurations of polymers attached to probes

Abstract

We study polymers attached to spherical (circular) or paraboloidal (parabolic) probes in three (two) dimensions. Both self-avoiding and random walks are examined numerically. The behavior of a polymer of size $R_0$ attached to the tip of a probe with radius of curvature $R$, differs qualitatively for large and small values of the ratio $s=R_0/R$. We demonstrate that the scaled compliance (inverse force constant) $S/R_0^2$, and scaled mean position of the polymer end-point $<x_{\perp }>/R$ can be expressed as a function of $s$. Scaled compliance is anisotropic, and quite large in the direction parallel to the surface when $R_0\sim R$. The exponent $\gamma$, characterizing the number of polymer configurations, crosses over from a value of ${\gamma }_1$ - characteristic of a planar boundary - at small $s$ to one reflecting the overall shape of the probe at large $s$. For a spherical probe the crossover is to an unencumbered polymer, while for a parabolic probe we cannot rule out a new exponent.

LaTeX, 6 pages, 4 figures

References in corpus (3)

• Simulations of grafted polymers in a good solvent
• The persistence length of two dimensional self avoiding random walks
• Apex Exponents for Polymer--Probe Interactions

Cited by in corpus (6)

• Polymer-mediated entropic forces between scale-free objects
• Entropic force of polymers on a cone tip
• Hidden multiple bond effects in dynamic force spectroscopy
• Ideal Polymers near Scale-Free Surfaces
• Diffusion in the Presence of Scale-Free Absorbing Boundaries
• Entropic forces exerted on a rough wall by a grafted semiflexible polymer