Layering transitions for adsorbing polymers in poor solvents

¹ Department of Mathematics and Statistics, The University of Melbourne 3010, Australia
² School of Mathematical Sciences, Queen Mary, University of London Mile End Road, London E1 4NS, UK

Corresponding authors: j.krawczyk@ms.unimelb.edu.au aleks@ms.unimelb.edu.au t.prellberg@qmul.ac.uk andrewr@ms.unimelb.edu.au

Received: 13 December 2004
Accepted: 19 April 2005

Abstract

An infinite hierarchy of layering transitions exists for model polymers in solution under poor solvent or low temperatures and near an attractive surface. A flat histogram stochastic growth algorithm known as FlatPERM has been used on a self- and surface interacting self-avoiding walk model for lengths up to 256. The associated phases exist as stable equilibria for large though not infinite length polymers and break the conjectured Surface Attached Globule phase into a series of phases where a polymer exists in specified layer close to a surface. We provide a scaling theory for these phases and the first-order transitions between them.