Influence of bending energetics on the size, shape and polydispersity of droplet microemulsions

A theory for ellipsoidal shape fluctuating droplet microemulsions in the presence of excess discrete phase (Winsor I and II) is expounded that combines bending energetics of the amphiphilic monolayer at the droplet interface with thermodynamics of self-assembling solute and amphiphilic molecules. The theory relates the three bending elasticity constants spontaneous curvature (H0), bending rigidity (kc) and saddle-splay constant (k¯c) with interfacial tension, average size and shape and polydispersity of microemulsion droplets. It is demonstrated that the well-known conventional relations become modified as the entropy of self-assembling amphiphilic as well as solute molecules are taken into account, in particular at low values of the effective bending constant 2kc+k¯c. As a result, the average droplet radius 〈R〉 as well as the droplet polydispersity σR/〈R  〉 behave consistently in the limit 2kc+k¯c→0 whereas the conventional expressions are recovered in the limit 2kc+k¯c→∞. It is demonstrated that association entropy effects may be quantified by a parameter kS with same dimension and order of magnitude as kc and k¯c. kS is found to be always negative and tends to decrease 〈R〉 and to increase σR/〈R〉. Moreover, the average axial ratio of an oblate/prolate fluctuating droplet is found to be a strong function of the bending rigidity (the droplets become increasingly non-spherical with decreasing kc) but is independent of k¯c, in contrast to previous investigations where association entropy effects were neglected.