Polymer-mediated entropic forces between scale-free objects

TL;DR

This paper investigates the universal entropic forces exerted by polymers near scale-invariant objects, deriving their form and amplitude through analytical and numerical methods, with implications for nanoscale interactions.

Contribution

It introduces a universal form for entropic forces between polymers and scale-free objects, relating force amplitudes to polymer correlation exponents and computing these exponents for various configurations.

Findings

Entropic forces scale as F=AkT/h with a universal amplitude A.

Computed exponents or different polymer-obstacle configurations.

Estimated forces of about 0.1 pN at 0.1 micron for single polymers.

Abstract

The number of configurations of a polymer is reduced in the presence of a barrier or an obstacle. The resulting loss of entropy adds a repulsive component to other forces generated by interaction potentials. When the obstructions are scale invariant shapes (such as cones, wedges, lines or planes) the only relevant length scales are the polymer size R_0 and characteristic separations, severely constraining the functional form of entropic forces. Specifically, we consider a polymer (single strand or star) attached to the tip of a cone, at a separation h from a surface (or another cone). At close proximity, such that h<<R_0, separation is the only remaining relevant scale and the entropic force must take the form F=AkT/h. The amplitude A is universal, and can be related to exponents \eta governing the anomalous scaling of polymer correlations in the presence of obstacles. We use analytical, numerical and epsilon-expansion techniques to compute the exponent \eta for a polymer attached to the tip of the cone (with or without an additional plate or cone) for ideal and self-avoiding polymers. The entropic force is of the order of 0.1 pN at 0.1 micron for a single polymer, and can be increased for a star polymer.