Scattering of intersecting spherical particles in the Rayleigh-Gans approximation

In this work a novel semianalytical procedure to calculate the exact scattering behavior of complex particles made of intersecting spheres in the Rayleigh-Gans approximation is presented. Pickering emulsions, Janus particles, and lock and key particle colloids are particular cases of particles built from intersecting spheres. The proposed methodology is based on the decomposition of the complex particle as a sum of simpler components whose scattering properties can be evaluated using a simple integral. The procedure is developed for any number of spheres that intersect in pairs but it can be directly extended to intersections that involve more than two spheres at the same time. Some examples are presented to illustrate the application of the model to: (i) the study of the sensitivity of scattering spectra to detect complex particles from approximated model particles; (ii) the detection of different degrees of penetration of one particle into the other; (iii) the identification of the location of the cavity in particles that intersect with a spherical surface of contact; and (iv) the follow up of the evolution of a complex particle from a mix of its components.