Modified Porod's law estimate of the transition-layer thickness between two phases: test of triangular smoothing function

Abstract

An analytical method to estimate the thickness of the interface between two phases from small-angle scattering (SAS) data has been developed using Porod's law modified by a triangular smoothing function. The convolution with a `top-hat' function describing a sharp density profile results in a semi-sigmoidal density profile. This analytical method allows an interfacial layer thickness to be estimated from the negative slope of a Porod plot. The interfacial layer thickness (T) obtained from this model is related to similar models, namely a linear (E) and a sigmoidal density profile (σ) model, as follows:T= 21/2E= 2(61/2)σ, where σ is the standard deviation of the Gaussian function and does not represent the boundary thickness itself. The interfacial layer thickness obtained from any convolution method is a model-dependent parameter.