Apex Exponents for Polymer--Probe Interactions

TL;DR

This paper analytically and numerically investigates how the configuration entropy of self-avoiding polymers attached to probe tips varies with probe geometry, revealing continuous scaling exponents and entropic barriers.

Contribution

It introduces analytical calculations and simulations of apex exponents for polymer-probe interactions, highlighting how these exponents depend on probe angle and attachment point.

Findings

Apex exponents vary continuously with probe tip angle.

Polymers tend to slide to an end when able to move through the attachment point.

Apex exponents quantify the entropic barrier to threading through the probe eye.

Abstract

We consider self-avoiding polymers attached to the tip of an impenetrable probe. The scaling exponents $\gamma_1$ and $\gamma_2$, characterizing the number of configurations for the attachment of the polymer by one end, or at its midpoint, vary continuously with the tip's angle. These apex exponents are calculated analytically by $\epsilon$-expansion, and numerically by simulations in three dimensions. We find that when the polymer can move through the attachment point, it typically slides to one end; the apex exponents quantify the entropic barrier to threading the eye of the probe.