ABSTRACT

The above discussion is based on the assumption that ohc is constant. If ohc depends on the concentration, the slope of the log d versus log ¢he plot may deviate from -1 even if Eq. (25) holds true. To determine the thickness ohc' the line shape of SAXS has been analyzed. If we assume that layer displacement fluctuations are independent of the transverse position, the scattering intensity can be written in terms of the form factor of a membrane P(q) and the structure factor S(q) as [109]

I(q) = (2njd)P(q)S(q)/l (26)

In the calculation of P(q), the membrane was assumed to be composed of three layers: one hydrophobic layer and two hydrophilic layers [108]. Then /(q) can be expressed as a function of 8hc and a parameter correlated with the layer displacement fluctuations. These parameters have been determined by the least-square fitting of q4I(q) because l(q) is inversely proportional to q4 . Figure 15 (left) shows examples of observed li(q) and least-squares fits

Figure 15 (right) shows the temperature dependence of SAXS patterns at 48 wt %; logarithm of the scattering intensity versus scattering vector q. Note that a broad component is superimposed on the first diffraction peak at 55 and 60°C. The filled and open triangles in Fig. 11 indicate the presence and absence of the broad component, respectively. It can be seen from the figure that the broad component is observed in the region where fw is relatively large. The observation of such a broad component has already been reported for the C16E6 system by Holmes and co-workers [111], who assign it to the reflection from the water-filled defects. This assignment is consistent with the strong correlation between fw and the appearance of the broad component in the present system. Imai and co-workers [114] have measured SAXS by using an oriented sample with the thickness of about 50 J.lm. They have shown that the broad component ·corresponds to the diffraction along the direction of membranes, also consistent with the interpretation of

-l

Holmes and co-workers. Even if the water-filled defects do not exist, the decrease in the absolute value of the slope of the log d versus log <he plot indicates the increase in the mean curvature of the interface for aggregates [115,116]. Such a variation in interfacial curvature has been confirmed by measurements of quadrupolar splitting of 2H20 (~v) [108].