Saddle-splay modulus of reverse microemulsions: Experimental determination using small-angle neutron scattering and dielectric relaxation spectroscopy

The elastic bending constants κ (elastic bending modulus) and κ (saddle-splay modulus) are key parameters for understanding the properties of microemulsions (MEs), vesicles, biological membranes, and other self-assembled amphiphilic molecular structures. The determination of κ is rather straight forward, whereas κ is quiet difficult to access experimentally. Nonetheless, the estimation of κ is crucial, owing to its importance in governing the intricate phase behavior, topology, and stability of these self-assembled structures. Here, we present an elegant protocol to determine the saddle-splay modulus of the spherical droplet phase of microemulsions using small-angle neutron scattering (SANS) and dielectric relaxation spectroscopy (DRS) techniques. The κ of AOT [sodium 1,4-bis(2-ethylhexoxy)-1,4-dioxobutane-2-sulfonate)]stabilized reverse MEs is estimated by probing their percolation transitions. Further, the effective elastic bending constant K is determined from the polydispersity of ME droplets measured using SANS, where the droplet deformations due to thermal fluctuations are described in terms of spherical harmonics. Strikingly, the ratio κ/κ lies in the acceptable range, -2<κ/κ<0, for the spherical droplet phase of MEs [R. H. Templer, B. J. Khoo, and J. M. Seddon, Langmuir 14, 7427 (1998)LANGD50743-746310.1021/la980701y], which further validates the proposed strategy to estimate the saddle-splay modulus.