Small-angle scattering intensity behaviours of cylindrical, spherical and planar lamellae

Analytical asymptotic expressions for the small-angle scattering intensities of cylindrical, spherical and planar lamellar grains are determined. Denoting the lamellar spacing by D and the number of lamellae by N, it is found that in the corresponding Porod plots, the positions of the main peaks, whatever the shape, are nearly given by , where k is a positive integer. At a fixed number of lamellar grains, the heights of the main peaks in the three cases increase with N as N³, N⁴ and N², respectively. The satellite peaks are much more structured for cylindrical and spherical lamellae than for planar ones. The momentum-transfer (h) range in which the asymptotic expressions turn out to be accurate is .