Correlation, structural parameters from measured scattering intensity

Nonetheless, by using the Fourier transform and two other mathematical operations, convolution and correlation, we can obtain several important structural parameters fiom the experimentally measured scattered intensity. The usual assumption is that the system can be represented by two-phases, with either sharp or difiuse boundaries between the phases. Some structural parametas of interest include average separation distance between the phases specific surface, Og average thicknesses cf the two phases and width of the boundary between phases, if diffose. These parameters are obtained from the "auto-correlation" function of p(x), which is a specific type of convolution. 

Attempt of correlating the molecular structures and experimental data, for example, cmc, and the thermodynamic parameters of micellization (enthalpy, entropy, and free energy), rests on the assumption that they have been calculated by a consistent procedure this point needs further consideration. At the outset, it should be noticed that there are systematic differences between the results, for example, the cmc, obtained by using distinct experimental techniques. The reason is that the function plotted (absorbance of micelle-solubilized dye, conductivity, surface tension, light scattering intensity, etc.) versus [surfactant] measures different averages of the various species in solution. Examples are surface tension that primarily depends on monomer concentration and solubilization of (water-insoluble) dye that depends mainly on the total amount of micelles present. The consequence is that cmc measured from surface tension will always be lower than cmc measured by dye solubilization [28]. In fact, values of the cmc of the same surfactant, determined by different groups, by the same technique show differences. For example, fifty-four erne s determined by the same technique for Cj NMe Br (measurements at 25°C) differ by 22% [29]. 

---