Polymer-mediated forces between scale-free objects
Yacov Kantor, Mehran Kardar
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)