A model-independent maximum-entropy method for the inversion of small-angle X-ray diffraction patterns

A model-independent maximum-entropy method is presented which will produce a structural model from small-angle X-ray diffraction data of disordered sy stems using no other prior information. In this respect, it differs from co nventional maximum-entropy methods which assume the form of scattering enti ties a priori. The method is demonstrated using a number of different simul ated diffraction patterns, and applied to real data obtained from perfluori nated ionomer membranes, in particular Nafion(TM), and a liquid crystalline copolymer of 1,4-oxybenzoate and 2,6-oxynaphthoate (B-N).