SCATTERING PROPERTIES OF THE LEVELED-WAVE MODEL OF RANDOM MORPHOLOGIES

In the leveled-wave model, random porous morphologies are stimulated by discrete maps of continuous stochastic standing waves generated by adding sinusoids over suitable distributions of wave vectors and phase constants. The mathematical structures obtained this way appear to be useful models for certain kinds of random geometries, such as the bicontinuous morphologies that occur in microemulsions and porous glasses. Properties of the leveled-wave method are developed, and the scattering behavior is derived. Scattering from an arbitrary three-phase system can be analyzed by adding different instances of scattering from a generalized film morphology in which the scattering phase is confined to the interior of the interspatial region bounded by two leveled-wave interfaces that are separated everywhere. General results for this interspace scattering are derived. Fractal surfaces, dimension 2 less-than-or-equal-to D less-than-or-equal-to 3, are incorporated into the leveled-wave scheme by using a wave-number distribution having an appropriate long-tailed asymptotic behavior. Scenarios are discussed for the scattering as D --> 2 from above and for D --> 3 from below. For D = 3 the asymptotic scattering falls faster than algebraically as the scattering wave vector Q --> infinity.