Concentration profiles and contrast factors

We now focus on the behavior of the mixture as a.function of T at constant overall composition in order to compare the predictions of the model with the results of the experimental study. Specifically, we consider the trajectory paths I and II indicat(Hl in Fig. 4.18, which correspond to the mass fi actions m a (dtosen in the experimental study. Sehcinmel ( t al. [lUfi] showed that along these trajectories the Porod parameter Ip (see Section 4.8.1) does not change with temperature, whicli indicates that the mean composition of the mixture in the pore stays constant for all temperatures. 

We adopt the following prescription to compare the measured contrast factors, ko and kp (sec Section 4.8.1), with, those predicted by our model. The densities, and of the first layer at the pore wall and the mean densities, andp, inside the remaining pore space arc given by 

To achieve the stable phase of constant mean concentration, w, for fixed temperature T, we have to distinguish two scenarios. If the state is in the one-phase region (outside the shaded regions in Fig. 4.18), then the differential chemical potential A/i couples naturally to and behaves monotonically with the concentration w a- Therefore, A t has to be varied until the chosen value of u A is reached. On the other hand, for states in the phase coexistence 

With the above prescriptions we can compute the density profiles of all stable phases along paths I and II in Fig. 4.18, respectively. FVom these density profiles, we calculate the contrast parameters using Eqs. (4.155) and, if necessary, Eqs. (4.156) and (4.157) to compare them with the values extracted from the experiments. 

Hero wo consider the behavior of the confined water-rich liquid mixlmc (mean mass fraction of amphiphile wa = 0.25) on the trajectory I in Fig. 4.18. SANS measurements of the intensity I q) [106] show that I q) is independent of temperature in the experimental range (10 — 70°C). In terms of Eq. (4.144), this implies that within this temperature range the two contrast parameters, kc. and kp, remain constant, which is surprising in view of the fact that the mixture undergoes a pha.se separation in this temperature range. 

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