Membrane stress tensor in the presence of lipid density and composition inhomogeneities
Laboratoire Matière et Systèmes Complexes (MSC), Université Paris Diderot 7 & UMR CNRS 7057, 10 rue Alice Domon et Léonie Duquet, F-75205, Paris Cedex 13, France
2 Dipartimento di Scienze Fisiche and Sezione INFN, Università “Federico II”, Complesso Monte S. Angelo, I-80126, Napoli, Italy
Revised: 6 April 2011
Accepted: 5 May 2011
Published online: 26 May 2011
We derive the expression of the stress tensor for one- and two-component lipid membranes with density and composition inhomogeneities. We first express the membrane stress tensor as a function of the free-energy density by means of the principle of virtual work. We then apply this general result to a monolayer model which is shown to be a local version of the area-difference elasticity (ADE) model. The resulting stress tensor expression generalizes the one associated with the Helfrich model, and can be specialized to obtain the one associated with the ADE model. Our stress tensor directly gives the force exchanged through a boundary in a monolayer with density and composition inhomogeneities. Besides, it yields the force density, which is also directly obtained in covariant formalism. We apply our results to study the forces induced in a membrane by a local perturbation.
© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg, 2011