Surfactant films spontaneous curvature

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. 

The self-diffusion approach relies on the fact that molecular displacements over macroscopic distances are very sensitive to confinement and thus to microstructure. For example, we found that at the same composition (water, oil, surfactant), the ratio between water and oil self-diffusion coefficients could differ by a factor of 100 000. This also illustrates that the microstructure is primarily determined by the spontaneous curvature of the surfactant film and not by the oil-to-water ratio. Contributions to a better understanding of microemulsion structures with FT spin-echo NMR self-diffusion starting with Stilbs, included also Nilsson, Olsson, Soderman, Khan, Guering, Monduzzi, Ceglie, Das and many others in Lund. In this work [49-63], the access to suitable systems was very important. Here, the contacts with Friberg, Shinoda, Strey and Langevin played a central role. 

Figure 9 gives a generic picture, but the parameter controlling the spontaneous curvature is different for different surfactant systems. For nonionic surfactants, temperature controls the spontaneous curvature, changing it from positive (surfactant film curved toward oil) a low temperatures to negative at higher tempemtures. For other systems, salinity (for ionics), surfactant composition in a mixture, and cosurfactant and cosolvent concentrations are controlling parameters. The generic structural change as a function of the spontaneous curvature is demonstrated in Fig. 9. At markedly positive spontaneous curvatures we have...

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... 

We note that bicontinuity results from a particular spontaneous curvature of the surfactant films rather than from a certain solvent volume fraction, which is a secondary factor in determining microstructure. Note that for nonionic surfactants it was shown that the diffusion behavior was determined by temperature and not by solvent composition. For different systems at the same composition, we may have either water droplets, oil droplets, or a bicontinuous structure. An example is given in Fig. 17. Furthermore, one could argue that, to be consistent, all surfactant structures of infinite aggregates (including lamellar and hexagonal) should be described as percolated. 

Calculations [33] of self-diffusion in ordered bicontinuous structures have, as illustrated in Fig. 21, reproduced the main features of the experimental studies for a large number of microemulsion systems. (For others, a quantitative comparison is difficult because of large influences of effects other than obstruction, such as a high surfactant film concentration or incomplete segregation between domains.) Furthermore, the symmetry of the self-diffusion pattern around the crossover of the oil and water curves implies a symmetry also in structural changes. This symmetry is easy to understand in terms of structures that have a constant mean curvature surface, where changes in spontaneous curvature away from zero in the two directions should be equivalent except for the two solvents changing place. 

Figure 19 Double-oil diffusion experiment with nonionic surfactant, (a) Self-diffusion coefficients and (b) diffusion coefficient ratio A" as a function of temperature in a water-rich microemulsion with nonionic surfactant. A transition from oil-in-water droplets to a bicontinuous microstructure occurs with increasing temperature (decreasing spontaneous curvature of the C12E5 surfactant film). The maximum in K indicates that an attractive interaction between the micelles is operating prior to the formation of a bicontinuous structure. Kq = 1.69 is the diffusion coefficient ratio in the pure oil mixture and is indicated as a broken line in (b). Note that the initial decrease of the self-diffusion coefficients shows that the droplets grow in size before the bicontinuous transition. The phase boundary at 25.7 C is indicated as a vertical broken line. (Data from Ref 43.)...

Clearly, the siuface tension has a minimum when the spontaneous curvature of the surfactant film equals the mean ciuvature of the interface. The mean curvature for a flat interface is zero, larger than zero for an interface curving towards the oil (oil-in-water emulsions), and smaller than zero for a water-in-oil emulsion. Hence, a large positive spontaneous monolayer curvature, as for a strongly hydro-philic surfactant, favors oil-in-water emulsions and vice versa. The Kabalnov-Wennerstrom model also allows the thickness of the film to vary in order to minimize the free energy of hole formation, i.e., the mean curvature of... 

Under certain conditions, the radius of curvature of the interfacial film may become so large that the spherical configuration can evolve towards a sponge-type or bicontinuous structure. The water and oil domains are interconnected over macroscopic distances. Once again, the monomer plays a crucial role. By placing itself between surfactant molecules in the interfacial film, it modifies its spontaneous curvature. At present, only water-soluble monomers have been (co)polymerised, in the aqueous domains of bicontinuous microemulsions. Examples are the neutral monomer acrylamide, the anionic monomer sodium acrylate and the cationic monomer MADQUAT (methacryloyloxyethyltri-methylammonium chloride). 

The ability to form a lamellar liquid crystalline film depends on the spontaneous curvature of the surfactant aggregates, or the CPP, which is a convenient and intuitive description of the surfactant molecular structure. Kabalnov and Wennerstrbm [16] have shown that, for the formation of a water bridge between two water droplets, a large free energy is required for a surfactant with a high CPP, while the free energy required for a surfactant with a low CPP is lower. Hence, the stability of a surfactant double layer increases with an increase of the CPP of the surfactant. 

Relying on these data to answer the question of how the microemulsion structure is altered due to freezing is not a simple matter. Percolation is a term frequently used to describe microemuisions as having a bicontinuous structure. However, bicontinuity describes a situation with dynamic equilibrium structure that results from a particular spontaneous curvature of the surfactant films, with a minor contribution of the volume fraction of the specific solvent. Thus, at the same composition, different systems may have either water droplets, oil droplets, or a bicontinuous structure. Percolation , on the other hand, describes... 

ILs can be incorporated in the microemulsion formulation as substituents of the polar and nonpolar phases or as surfactants. In recent studies, Koetz and coworkers [103] showed that the role of cosurfactant can also be assumed by an IL in the stabilization of water-in-oil microemulsions. SDS- and CTAB-based water-in-toluene/ pentanol microemulsions have been formulated with the aid of ethyl-methylimidazolium hexylsulfate, [C2mim][CgSOJ. Their experimental results showed that replacing water by the IL increases the isotropic phase region of the system. The authors assume the formation of a palisade layer (Scheme 13.4), where the IL plays a similar role like a cosmfactant, changes the spontaneous curvature of the interfacial film, and decreases the droplet size. 

Figure 4.14. Effect of surfactant structure on the spontaneous curvature of surfactant films V is the volume of the surfactant tail, /c the extended length of the surfactant tail, and oq the effective area per head-group. Reproduced by permission of Elsevier Science (redrawn from Isrealachvilli (74))...

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