Scaling behaviour of the structure factor of chain-forming ferrofluids at low wave vectors

A. O. Ivanov - S. S. Kantorovich - E. S. Pyanzina

Department of Mathematical Physics, Urals State University, 51 Lenin Av., 620083 Ekaterinburg, Russia

Abstract
Computer simulations of the structure and scattering in chain-forming ferrofluids have revealed an anomalous behaviour of the structure factor S(q) at low values of the wave vector q. In the region q σ < π (σ stands for the particle diameter), the structure factor obeys the power-law decrease S(q) ∼ q^−D, and the scaling exponent D is close to unity. This feature holds true for the ferrofluids with a rather high dipolar coupling constant λ = m² / k_BT σ³ (m is the particle magnetic moment, and k_BT is the thermal energy), λ > 4. The discovered anomaly was explained in terms of ferroparticle aggregates, the most probable structure of which is evidently the chain one. In this report the chain model of a ferrofluid at the high dipolar strength λ is used to study theoretically the scaling low-q behaviour of the structure factor. The radial distribution function is determined on the base of the statistic algorithm commonly used in computer simulations, and the structure factor is calculated according to its definition as the Fourier transform of the radial distribution function. The log-log plot of the structure factor S against wave vector q shows the linear dependence in the region 1 < qσ < π for low concentrated chain-forming ferrofluids. These theoretical predictions are in a good qualitative and quantitative agreement with the simulation results. Figs 3, Refs 17.