Self-diffusion sponge phases

Anderson and Wennerstrom [33] calculated the geometrical obstruction factors of the self-diffusion of surfactant and solvent molecules in ordered bicontinuous microstructures, which serve as good approximations also for the disordered bicontinuous microemulsions and L3 (sponge) phases. The geometrical obstruction factor is defined as the relative diffusion coefficient DIDq, where D is the diffusion coefficient in the structured surfactant system and Z)q is the diffusion coefficient in the pure solvent. In a bicontinuous microemulsion the geometrical obstruction factor depends on the water/oil ratio. An expansion around the balanced (equal volumes of water and oil) state gives, to leading order. 

By making the IL component more surfactant-like, for example, by using EmimHexSO, in the presence of SDS, a broad isotropic phase channel can be produced [16]. More comprehensive investigations show that all types of microemulsions can be observed in the phase channel. Cryo-SEM micrographs show the transition from droplets to a sponge phase, accompanied by a characteristic change of the rednced self-diffusion coefficient obtained by NMR diffusion experiments. 

Self-diffusion data from bicontinuous structures contain, in principal, information on the average coordination number of the microstructure. The experimental results can, however, not be compared with the theoretical results directly. There is an additional reduction of D/Dq due to solvation of the surfactant film (a lateral friction felt by the solvent molecules in the solvent layers closest to the film) and an obstruction due to the finite film volume. These effects, which both increases with the surfactant-to-solvent ratio can however be included in the model, as will be discussed for the case of the sponge phase in one of the following sections. Extending the model to include solvation, however, introduces additional parameters which will affect the uncertainty. 

Figure 17.25. The variation of the reduced water self-diffusion coefficient with 0s in the sponge (filled symbols) and the bicontinuous cubic (open symbols) phases. The continuous line corresponds to D /D = 0.66 — 0.770s and is a linear fit to the data from the sponge phase (data are taken from ref. (31))...

Diffusion data from a sponge phase can also be analysed by using the model calculations of Anderson and Wennerstrom (15) (as discussed above) in connection with self-diffusion data from a balanced microemulsion. For the case of a bilayer structure, we have the following ... 

Here, and are, respectively, the water and surfactant self-diffusion coefficients in the sponge phase ... 

Figure 17.27. Self-diffusion coefficients of water ( , ), oil (a, a) and surfactant (O, ) in the bicontinuous cubic and oil-rich sponge phases of the Ci2E5-water-tetradecane system. The C12E5-to-water weight ratio is kept constant at 60/40, and the diffusion coefficients are plotted as a function of the oil volume fraction, o- Experiments were performed at the following temperatures in the cubic phase at o = 0-41 and 0.44, T = 20°C in the cubic phase at o = 0.48, T = 23°C in the sponge phase at o = 0.61, T = 25°C. The fact that the diffusion constants are essentially the same in the two phases demonstrates that the ordered (cubic) and disordered (sponge) structures are very similar (data taken from ref. (37))...

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