It is shown that, close to the origin, the correlation function [y(r)] of any N-component sample with interfaces made up of planar facets is always a third-degree polynomial in r. Hence, the only monotonically decreasing terms present in the asymptotic expansion of the relevant small-angle scattered intensity are the Porod [-2y'(0+)/h 4] and the KirstePorod [4')(3)(0 +)/h 6] contributions. The latter contribution is non-zero owing to the contributions arising from each vertex of the interphase surfaces. The general vertex contribution is evaluated in closed form and the )'(3)(0+) values relevant to the regular polyhedra are reported.

No abstract

No abstract

No abstract

Porod's law extended to the sixth-order term can be written I = (Ke/s 4 + K6/s6)U2 (s,o ") where I is the scattered intensity, s = 2(sin8)/,~, 0 being half the scattering angle and a the wavelength used; U2(s, tr) describes the interphase profile and tr is a measure of the width of the interphase transition zone. Kp and K6 are two constants. In the same way as Kp can be related to the specific area, K6 is related to a pure number 8 called here 'angulosity'. For an angulous body, 0 always is negative and can easily be calculated when its geometry is simple. It does not depend on the dimensions of the body. It is shown in the present paper thatso that, in a two-phase system, the ratio K6/Kp represents the angulosity per unit area S of the interface between the phases. A least-squares analysis of the experimental small-angle X-ray scattering (SAXS) curve gives the values of Kp, K6 and 0-. The method was successfully applied in the case of telechelic ionomers to characterize their ionic aggregates. These aggregates present a larger angulosity than that of a parallelepiped. Their volume is relatively small and only contains a small number of ions. The results agree with the results obtained by other techniques. It can be concluded from this that the introduction of the s -6 term into Porod's law is judicious and allows the structure of the phases to be better characterized.