Characteristics of the SAS correlation function of long cylinders with oval right section

Geometric parameters of isotropic ensembles of right cylinders from the small-angle-scattering correlation function

The scattered intensity of ensembles of right homogeneous quasi-diluted cylinders with constant oval right section (RS) and volume fraction phi are analyzed using the small-angle-scattering (SAS) correlation function (CF) gamma(r) = gamma(r, phi) in the isotropic two-phase approximation. A relation between the CF of the cylinder RS, beta(0)(r), and the CF of the single cylinder of height H, gamma(0)(r, H), allows the calculation of the explicit cylinder parameters of height, surface area, RS surface area, RS perimeter and volume. This is accomplished by evaluating the first two derivatives of gamma(0)(r) at r = 0. Without the assumption of an oval RS, neither H nor the RS surface area can be uniquely determined.