R. Mittelbach et O. Glatter, DIRECT STRUCTURE-ANALYSIS OF SMALL-ANGLE SCATTERING DATA FROM POLYDISPERSE COLLOIDAL PARTICLES, Journal of applied crystallography, 31, 1998, pp. 600-608
The internal structure of colloidal particles of spherical, rod-like o
r lamellar symmetry can be determined from small-angle scattering data
by means of the well established 'indirect Fourier transformation' te
chnique followed by the numerical deconvolution of the pair distance d
istribution function. The method works without any preliminary knowled
ge of the particles under investigation except a rough estimate of the
ir maximal size. However, its use has hitherto been restricted to mono
disperse or very weakly polydisperse systems. In this paper a new meth
od is presented that is capable of determining the radial scattering l
ength density distribution of particles in strongly polydisperse sampl
es and provides a parameter that quantifies the degree of polydispersi
ty present in the system. The only additional information necessary is
the function type which describes the size distribution of the partic
les under investigation in the best way possible. However, the method
is limited to polydisperse systems which may be characterized by only
one linear size parameter. In addition, it is now possible to represen
t the density profile by smooth spline functions, ie. the technique is
no longer restricted to step functions as basis functions. The mathem
atical procedure is outlined in detail and numerical results of simula
tions as well as of experimental data from small-angle neutron scatter
ing and small-angle X-ray scattering measurements of surfactant aggreg
ates in water and water/oil systems are given.