Small-angle x-ray scattering from solution of rodlike particles with length distribution

The scattering function of rods with a constant radius, 8 Å, and a length distribution of the Schulz–Zimm type was calculated on a computer as a model of helical synthetic polypeptide. The influence of length and length distribution on the scattered intensity of small-angle x-ray scattering was clarified. As length grows and length distribution broadens it is difficult to obtain reliable values of molecular weight and radius of gyration from a Zimm plot. The influence of length distribution on the mass per unit length, M_q, and the radius of gyration of the cross section, 〈S〉^1/2, from the Guinier plot of the cross-sectional factor decreases as the length increases, and reliable values of M_q and 〈S〉^1/2 can be obtained even for rods with wide distribution for rods more than 600 Å long. In particular, it is pointed out that the value of 〈S〉^1/2 is little influenced by length and length distribution.