Eur. Phys. J. E (2011) 34: 79
https://doi.org/10.1140/epje/i2011-11079-6

Regular Article

Primitive interactions between inclusions on a fluid membrane: The role of thermal fluctuations

¹ Faculté des Sciences Ben M’sik, Laboratoire de Physique des Polymères et Phénomènes Critiques, P.O. Box 7955, Casablanca, Morocco
² Université Moulay Ismail, Meknès, Morocco

^* e-mail: benhamou.mabrouk@gmail.com
^** e-mail: benhamou_mabrouk@yahoo.fr
^*** e-mail: m.benhamou@univh2m.ac.ma

Received: 14 November 2010
Revised: 1 June 2011
Accepted: 25 July 2011
Published online: 10 August 2011

Abstract

Consider a fluid membrane decorated by moving hard or soft inclusions. The aim of this work is a quantitative study of the influence of thermal fluctuations on the three-dimensional primitive forces between these inclusions. Integrating over all membrane fluctuations, we obtain a general form giving the modified primitive interactions upon the transverse distance. The established formalism enables us to obtain the modified expression of some standard interaction potentials. In particular, for power-like potentials, we found a modified expression featuring the Whittaker function. The present formalism may be extended to other primitive interaction potentials. Finally, the main conclusion is that, decorated fluid membranes may be regarded as effective two-dimensional colloidal solutions where inclusions interact via the computed effective interactions.