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 (H-0), bending rigidity (k(c)) 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 2k(c) + (k) over bar (c). As a result, the average droplet radius (R) as well as the droplet polydispersity sigma(R)/< R > behave consistently in the limit 2k(c) + (k) over bar (c) -> 0 whereas the conventional expressions are recovered in the limit 2k(c) + (k) over bar (c) -> infinity. It is demonstrated that association entropy effects may be quantified by a parameter k(s) with same dimension and order of magnitude as k(c) and (k) over bar (c). k(s) is found to be always negative and tends to decrease (R) and to increase sigma(R)/< 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 k(c)) but is independent of (k) over bar (c), in contrast to previous investigations where association entropy effects were neglected. (C) 2007 Elsevier B.V. All rights reserved.