Study of Schultz distribution to model polydispersity of microemulsion droplets

Abstract

We have employed a histogram analysis method to study the spectra obtained by small-angle neutron scattering (SANS) in order to investigate the size distribution of a model water-in-oil three-component microemulsion. It is found that the often used Schultz distribution function is indeed one of the reasonable choices to represent the moderately polydispersed droplet system. Analysis based on mean spherical approximations of the SANS data and inverse Laplace transformation of quasi-elastic light scattering data, assuming a Schultz distribution, yield consistent results compared with the histogram method. The polydispersity index, M/R, found in the model microemulsion is roughly constant at larger R, but increases at small R, consistent with a theory proposed by Safran.

On the composition fluctuations of reverse micelles

“…The number of the AOT molecules in the dry reverse micelle (W = 0) was found from this fitting to be equal to 22 in accordance with the studies [42][43][44] within the scatter of their data. Also there is an accordance between the water pool sizes calculated from the formula (44) and those reported in the studies [3,7,6] (except for the values at W < 5 where the methods used in the cited studies are too inaccurate). In view of the fact that the length of the hydrophobic tail of the surfactant is about 1 nm, this fitting also is in satisfactory accordance with the formula R h = 0.175W + 1.5 nm, 0 6 W 6 30, obtained in the study [11] for the hydrodynamic radius of the reverse micelles in heptane.…”

New insights of the nucleation and growth process of gold nanoparticles via in situ coupling of SAXS and XANES

“…It is common to use the Schulz-Zimm distribution for polydisperse particles [22]. Hence the scattering intensity is given by…”

SERS enhancement of gold nanospheres of defined size

“…It is common to use the Schulz-Zimm distribution for polydisperse particles. [60] Hence the scattering intensity is given by I(q) = scale · ∞ 0 f (r)P 2 (qr)dr (3) An analytical solution of that integral can be found in Kotlarchyk and Chen. [61] …”