Tubular vesicles and effective fourth-order membrane elastic theories

¹ Laboratoire de Physico-Chimie Théorique, Ecole Supérieure de Physique et de Chimie Industrielles de la Ville de Paris, 10 rue Vauquelin, F-75231 Paris Cédex 05, France
² Dipartimento di Fisica del Politecnico di Torino and Istituto Nazionale di Fisica della Materia, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy

Received: 25 November 1996
Accepted: 2 June 1997

Abstract

We discuss the phase diagram of fourth-order membrane elastic theories for systems with internal degrees of freedom. The presence of scalar or more generally tensorial fields coupled to the membrane curvature renormalizes the elastic constants and destabilizes flat membranes. A simple analysis of the second-order curvature elasticity indicates that spherical or saddle-like membranes shapes will be favored. By taking into account the fourth-order stabilizing terms, we show that tubular shapes can form the most stable state. Hence non-chiral tubular vesicles can be explained on the basis of simple mean-field elasticity. Tubules may appear when an in-plane tensorial (or vectorial) field is coupled to the difference between the membrane principal curvatures.