Entropic force of polymers on a cone tip

Mohammad F. Maghrebi^1a, Yacov Kantor² and Mehran Kardar¹

¹ Department of Physics, Massachusetts Institute of Technology - Cambridge, MA 02139, USA
² Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University - Tel Aviv 69978, Israel

^a magrebi@mit.edu

Received: 21 September 2011
Accepted: 24 October 2011

Abstract

We consider polymers attached to the tip of a cone, and the resulting force due to entropy loss on approaching a plate (or another cone). At separations shorter than the polymer radius of gyration R_g, the only relevant length scale is the tip-plate (or tip-tip) separation h, and the entropic force is given by . The universal amplitude can be related to (geometry dependent) correlation exponents of long polymers. We compute for phantom polymers, and for self-avoiding (including star) polymers by ϵ-expansion, as well as by numerical simulations in 3 dimensions.