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

Abstract

An approximation for the small-angle scattering (SAS) correlation function (CF) β0(r) of a plane oval domainXis discussed. The approach is based on two parameters, the perimeteruand the surface areaSRS, ofX. The function β0(r) fixes the correlation function γ0(r) of the oval homogeneous rod with constant right sectionX. The mean chord lengthl1of such a rod is the root of the equation γ0(l1) = 1 − 8/(3π). For a dilute rod arrangement, the Porod lengthlpand γ′(l1), the value of the derivative of the sample CF atr=l1, are related by γ′(l1) = −4/(3πlp).