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 η depends 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)

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