Transformation of phase size distribution into scattering intensity

A practical method of calculating the small‐angle scattering intensity and the density correlation function from the phase size distribution is presented for a sample with a random two‐phase morphology. The correlation function can be calculated in terms of joint probability distribution functions of the phase size distributions of the two individual phases with information from the chord length distribution. The phase size distribution is approximated as a weighted sum of exponentials, which is then transformed analytically into the correlation function and hence the small‐angle scattering for any combination of phase size distributions of the two phases. This represents an extension of the Debye method for materials with more complex phase size distributions. The inverse problem of calculating the phase size distributions from the small‐angle scattering requires a thermodynamic model or simplifying approximation. An example of the reverse transformation is given for a nanoporous polymer thin film. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3070–3080, 2004