Interaction of Particles Structure Factor

As mentioned above, measurements at finite concentrations lead to a non-vanishing influence of the structure factor S(q). For the overwhelming majority of the latex systems studied by SAS-experiments so far, colloid stability has been achieved by a screened Coulomb interaction [5,62,63]. The structure factor of such a system of particles interacting through a Yukawa-potential has been extensively studied theoretically by Klein and coworkers (see Ref. [63] and further citations given there) who extended the treatment to polydisperse systems. 

In principle, SAXS is suitable for determining the structure factor S(q) from experimental results. It will become apparent, however, that the influence of particle interaction in suspensions of latex particles is restricted to very small q-val- 

Polydispersity plays an important role for S(q) as well [63]. Here a discussion of the alterations effected to S(q) in the case of hard sphere interaction will suffice. For this purpose S(q) of a system of hard spheres maybe obtained from the Percus-Yevick theory [66] generalized by Vrij and coworkers [67,68] to polydis-perse systems. The solid line in Fig. 6 displays S(q) resulting for a system of hard spheres with a Gaussian size distribution characterized by a standard deviation of 7.5%. The main feature induced by polydispersity is the much weaker side minimum of S(q) as compared to the monodisperse case. Hence, a finite width of the size distribution will tend to smear out the oscillations of S(q) at higher q. 

Very often SAXS-measurements need to be conducted at rather high concentrations to obtain a good counting statistics. The considerations related to S(q) now demonstrate that the SAXS-analysis can indeed be done at a rather high concentration provided the q-value is not too small. 

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