Investigation of non-ideal two-phase polymer structures by small-angle X-ray scattering

The mean square of the electron-density gradient, 〈|grad η|²〉 in isotropic structures is shown to be proportional to the fourth moment of the SAXS intensity distribution in reciprocal space ∫s⁴I(s)ds, as well as to the second derivative of the correlation function in the origin. In the case of two-phase structures with unsharp phase boundaries, these relations may be used to find the thickness E of the transition regions. As was shown by Ruland [J. Appl. Cryst. (1971). 4, 70–73] E can also be determined by analysis of the intensity in the tail of the SAXS pattern. This approach is used here to investigate the effect of E on the one-dimensional correlation function. In the application of both methods, separation of the SAXS intensity from the continuous background of liquid scattering constitutes a critical step. A procedure in which the background is represented by a curve of the type a + bsⁿ, where n is an even number, is found to work well for a number of polymers.