Surfactant films bending elasticity

D. Relation Between Surface Tension and Surfactant Film Bending Elasticity... 

L.T. Lee, D. Langevin, J. Meunier, K. Wong, and B. Cabane Film Bending Elasticity in Microemulsions Made with Nonionic Surfactants. Prog. Colloid Polymer Sci. 81, 209 (1990). 

Lee, L.T., Langevin, D., Meunier, J., Wong, K. andCabane, B. (1990) Film bending elasticity in microemulsions made with non-ionic surfactants. Progr. Colloid Polym. Sci., 81, 209-214. 

Elastic energy of a surfactant film. Please estimate the bending energy per unit area for a surfactant film with a bending rigidity of 10kbT and zero spontaneous curvature, which is at the interface of a drop of radius 5,20, and 100 nm. 

Hellweg, Th. and Langevin, D. (1998) Bending elasticity of the surfactant film in droplet microemulsions Determination by a combination of dynamic light scattering and neutron spin-echo spectroscopy. Phys. Rev. E, 57, 6825-6834. 

A theoretical basis for different shapes of microemulsions (even for small W/O or O/W volume fractions) has been established on the basis of the relationship between shape and interfacial curvature [350,351]. It is reasonable to expect that the relevant properties of the surfactant film are represented by a bending elasticity with a spontaneous curvature, Co (as was demonstrated for binary systems). If the elastic modulii k, ksT, the fluctuations in curvature of the film are very small, and the entropy associated with them can be neglected. The actual morphology is the result of the competition between the tendency to minimize the bending free energy (which prefers spheres of optimal radius of curvature, = l/c ) and the necessity to use up all of the water, oil, and surfactant... 

A variety of thermodynamic models qualitatively capture the central equilibrium and dynamic features of microemulsion behavior (41 5). These range from phenomenological models, which treat the oil-water interface as fluctuating membranes to lattice models which describes discrete surfactants interacting with oil and water. Membrane models range from simple cubic lattice descriptions to fluctuating film models that include curvature-dependent bending elasticity to prescribe lower limits on domain size. 

Microemulsion phase behavior and microstructure depend on two interfacial parameters, namely the spontaneous film curvature (the optimal curvature that the surfactant film attains) and the elasticity (bending modulus) of the surfactant film (Attwood, 1994 Sottmann and... 

By varying several parameters such as the W/O ratio, one can induce an inversion from an O/W to a W/O microemulsion and vice versa. The type of structure in the inversion domain depends essentially on the bending constant a characteristic of the elasticity of the surfactant layer [7]. If Ke is on the order of kT (where k is the Boltzmann constant and T absolute temperature), the persistence length of the film (i.e., the distance over which the film is locally flat) is microscopically small. The interfacial film is flexible and is easily deformed under thermal fluctuations. The phase inversion occurs through a bicontinuous structure formed of water and oil domains randomly interconnected [8,9]. The system is characterized by an average curvature around zero, and the solubilization capacity is maximum. When K kT, is large and the layers are flat over macroscopic distances. The transition occurs through a lamellar phase. 

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