Mesophases in mixtures of water and polyoxyethylene surfactant: Variations of repeat spacing with temperature and composition

Lamellar (L ) and hexagonal (H ₁) mesophases, formed in mixtures of water and polyethylene oxide (PEO) oleylethers (average EO-numbers 5 (a), 8.5 (b) and 14 (c)) and pure hexaoxyethylene dodecylether (d), were investigated with small-angle X-ray diffraction. Analysis of repeat spacings shows a deviation from linear one- and two-dimensional swelling ofL andH ₁, respectively, when a transition to a mesophase with a larger curvature of the interface is approached. With regard toL , in this respect similar behaviour is observed for a pure surfactant (d) and a surfactant with an EO-length distribution (b). It is proposed that, through the formation of aggregates of limited extent, water filled pores in the mesophases arise. This is confirmed by analysis of the intensity ratio of diffraction maxima of first and second order inL . Models for finite aggregates are introduced. These consist of (1) lamellae, infinite in one direction and with variable lengthL in a direction perpendicular to the first, with cylindrical edges and (2) cylinders with variable lengthL bounded by spherical caps. According to these models, under certain conditions, finite aggregates may be formed without an increase of the interfacial area per surfactant molecule. Applying the models to the regions where non-linear swelling is observed, reasonable values forL are found, which decrease progressively when the phase transition is approached.