How to calculate structure factors of self-assembling anisotropic particles

Abstract

We put forward a theoretical approach to analyse the structure factors obtained experimentally for solutions of self-assembling anisotropic particles. This method is applicable for any system of particles forming chains in thermodynamic equilibrium and is based on studying the behaviour of the centre–centre structure factor first peak. In order to calculate the structure factor analytically, we first derive the radial distribution function. For that we use the combination of the density functional theory and density expansion of the pair correlation functions. The first theory allows for the equilibrium chain formation, and the second takes into account particles' shape anisotropy at the level of the Gay–Berne potential. We apply our method to describe centre–centre structure factors of self-assembling short DNA duplexes with various semiaxes ratios. Extensive comparison of the theoretical predictions with the Monte Carlo simulation data shows a very good agreement. We show that the particle shape anisotropy exerts a crucial influence on the behaviour of the structure factors.