# Attractive and repulsive polymer-mediated forces between scale-free surfaces

## TL;DR

This paper investigates universal polymer-mediated forces between scale-free surfaces, revealing conditions under which these forces are attractive, repulsive, or null, depending on geometry and adsorption properties, with a focus on ideal polymers.

## Contribution

It derives a universal form for polymer-mediated forces between scale-free objects, including conditions where the force vanishes at the adsorption transition.

## Key findings

- Force magnitude scales as 1/h with a universal amplitude
- Amplitude depends on geometry and polymer universality class
- Force vanishes at the adsorption transition point for ideal polymers

## Abstract

We consider forces acting on objects immersed in, or attached to, long fluctuating polymers. The confinement of the polymer by the obstacles results in polymer-mediated forces that can be repulsive (due to loss of entropy) or attractive (if some or all surfaces are covered by adsorbing layers). The strength and sign of the force in general depends on the detailed shape and adsorption properties of the obstacles, but assumes simple universal forms if characteristic length scales associated with the objects are large. This occurs for scale-free shapes (such as a flat plate, straight wire, or cone), when the polymer is repelled by the obstacles, or is marginally attracted to it (close to the depinning transition where the absorption length is infinite). In such cases, the separation $h$ between obstacles is the only relevant macroscopic length scale, and the polymer mediated force equals ${\cal A} \, k_{B}T/h$, where $T$ is temperature. The amplitude ${\cal A}$ is akin to a critical exponent, depending only on geometry and universality of the polymer system. The value of ${\cal A}$, which we compute for simple geometries and ideal polymers, can be positive or negative. Remarkably, we find ${\cal A}=0$ for ideal polymers at the adsorption transition point, irrespective of shapes of the obstacles, i.e. at this special point there is no polymer-mediated force between obstacles (scale-free or not).