Unbinding Transitions of Polymers or Membranes in Two Dimensions

Abstract

Membranes can be thought of as (d − 1)-dimensional objects fluctuating in d-dimensional space, where usually d = 3. The fluctuations of membranes are governed by their bending energy, in contrast to the fluctuations of interfaces, which are controlled by surface tension (see, for example, Ref.1). Continuum models for both fluid² and crystalline³ membranes have recently been proposed. Membranes are believed to be crumpled⁴ for all temperatures T > 0 in spatial dimension d < 3, and to have a crumpling transition at finite temperatures for d > 3. The analysis of these models is rather difficult, even for free membranes. In studying unbinding transitions, it is often useful to look at sytems in reduced spatial dimension d = 2. In this case, membranes become indistingushable from polymers, 1-dimensional objects in d-dimensional space.⁵ Some of the results presented here may therefore be studied experimentally for polymers adsorbed on a flat substrate.