Colloids and Surfaces A: Physicochemical and Engineering Aspects 183 – 185 (2001) 159 – 169 Shape fluctuations of microemulsion droplets: a neutron spin – echo study Thomas Hellweg a , Michael Gradzielski b , Bela Farago c , Dominique Langevin d, * a TU Chemnitz, Institut fu ¨r Physik, Materialforschung und Flu ¨ssigkeiten, D-09107 Chemnitz, Germany b Uniersita ¨t Bayreuth, Lehrstuhl fu ¨r Physikalische Chemie I, Uniersita ¨tsstr. 30, D-95440 Bayreuth, Germany c Institut Laue -Langein, Aenue des Martyrs, BP156, F -38042 Grenoble Cedex 9, France d Laboratoire de Physique des Solides, Uniersite ´ Paris -Sud, Ba ˆt. 510, F -91405 Orsay Cedex, France Abstract An alternative approach to the determination of the bending elastic constants of the surfactant film in droplet microemulsions was presented recently, which accounts for the viscosity differences of the liquids forming the microemulsion. In this work the approach will be applied to investigate a C 8 E 3 and C 10 E 4 based microemulsion containing the oil n -decane. The determined values for  and  ¯ are compared to results from macroscopic measurements. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Neutron spin – echo; Microemulsions; Bending elasticity; Shape fluctuations www.elsevier.nl/locate/colsurfa 1. Introduction Amphiphilic surfactant molecules self-assemble in a large variety of microstructures : micelles, either spherical, cylindrical [1] or disc-like, mono or bilayers, vesicles, etc. The self assembly can take place in water, in organic solvents (after- wards referred to as ‘oils’), or when both water and oil are used : in this case, the surfactant can help to solubilise the two otherwise immiscible liquids. If this happens, a microemulsion is obtained, with a microstructure made of either droplets (oil in water or water in oil) or of ex- tended surfactant layers separating oil and water domains and bicontinuous in oil and water. It has long been recognised that the type of structure observed is closely related to the spontaneous curvature C 0 of the surfactant assemblies [2]. By using an analogy with liquid crystals which also adopt layered structures, Helfrich [3] introduced a free energy associated to deviations from the ac- tual curvature of the microstructures and C 0 . If the surfactant layer is replaced by a mathematical surface (the neutral surface) of principal curva- tures C 1 and C 2 , this elastic energy per unit area is given by: * Corresponding author. Tel.: +33-1-69155351; fax: +33- 1-69156086. E-mail address: langevin@lps.u-psud.fr (D. Langevin). 0927-7757/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII:S0927-7757(01)00567-2