Polymer-mediated forces between scale-free objects

**Mohammad Maghrebi**

Yacov Kantor, Mehran Kardar

**Outline**

**I.** Entropic force on polymers: Universal amplitude related to polymer exponents

The exponent

ηdepends on surface absorbtivity (D or N) and its shape, as well as state of the polymer (self-avoiding, phantom, ...)

**II.** Phantom polymers: Exact results from solutions of the diffusion equation

, 0.1 pico-Newton at 0.1 micron

The amplitude is exactly zero at depinning transition for identical surfaces. Is this more generally true?

**III.** Self-avoiding polymers: Numerical results, and ε-expansions

Is the exponent for the singular dependence on angle ?

**IV.** Many polymers: Results from star polymers

Similar force expressions should exist for any combination of

self-similar shapes, scale-invariant boundaries, and ambient scale-invariant field.

Exact results can be obtained in two dimensions using methods of conformal field theory

G. Bimonte, T. Emig, and M. Kardar, Euro. Phys. Lett.

104, 21001 (2013)