Intensive vectors excess”

The coexistence conditions (12.68) that relate each excess intensive vector RK) to the chosen axis intensities R ) can also be written in terms of the conjugate extensive vectors R ) = X/). With the usual metric relationship between intensive and extensive vectors,... 

The biorthogonality property (12.4) then allows one to easily evaluate scalar products of each excess intensity RK) with basis axis vectors R ) or R ). The scalar product of extensive Xj) with (12.76) gives... 

Accordingly, we can solve the p homogeneous linear vector equations (12.66) for the p excess intensities RK) in terms of the chosen independent set of /-axis intensities R,). When each of the vector equations (12.66) is multiplied by ( L 1) and summed over A, the resulting solution is... 

Fig. 6 Excess scattering intensities from PAAm hydrogels measured at the scattering vector = 1 X 10 nm shown as...

It is important to note that the lamellar phase is thus stabilized by the balance of a negative interfacial tension (of the free oil/water interface covered by an amphiphilic monolayer), which tends to increase the internal area, and a repulsive interaction between interfaces. The result, Eq. (48), indicates that the scattering intensity in a lamellar phase, with wave vector q parallel to the membranes, should have a peak at nonzero q for d > d due to the negative coefficient of the q term in the spectrum of Eq. (40). just as in the microemulsion phase. This effect should be very small for strongly swollen lamellar phases (in coexistence with excess oil and excess water), as both very small [96]. Very similar behavior has been observed in smectic liquid crystals (Helfrich-Hurault effect) [122]. Experimentally, the lamellar phase under an external tension can be studied with the surface-force apparatus [123,124] simultaneous scattering experiments have to be performed to detect the undulation modes. 

We denote the excess structure factor per mass cocncentration of solution by S k) an simply call it the structure factor. Here by excess we mean the value for a solution minus that for its solvent. As before, k is the magnitude of the scattering vector. Textbooks of physical chemistry explain how S k) can be determined from measurements of the intensity of scattered light or X-ray or neutrons. For the polymer solution under consideration it can be shown that S k) is related to h r) by [15]... 

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