Time-dependent clustering and magnetization in magnetic colloidal suspensions

This work analyzes the influence of the time-dependent clustering aggregation process on the transient and equilibrium magnetization of a monodisperse magnetic colloidal suspension under a uniform magnetic field <i>via</i> Brownian dynamics simulations. The clustering aggregation process is characterized by microstructural properties, such as the nucleation-growth factor, 〈<i>n</i>_c(<i>t</i>)〉, mean cluster size, 〈<i>N</i>_c(<i>t</i>)〉, kinetic exponent, <i>z</i>, effective radius, 〈<i>R</i>_eff〉, and radial distribution function, <i>g</i>(<i>r</i>). These are analyzed in terms of the volume fraction, <i>ϕ</i>, the dipolar coupling parameter, <i>λ</i>, and the Langevin parameter, <i>α</i>. Here, <i>λ</i> and <i>α</i> measure the magnetic dipole-dipole interaction energy and the magnetic field-dipole interaction energy relative to the thermal energy, respectively. The magnetization in transient and equilibrium regimes is analyzed relative to these microstructural properties for different values of <i>ϕ</i>, <i>λ</i>, and <i>α</i>. The analysis of the microstructural properties reveals a reduction in the dipolar chain growth at higher <i>λ</i> and <i>ϕ</i> values in the range of 1 < <i>α</i> < 10, which contrasts with the increase observed for low values of the same parameters. This reduction is caused by the lateral interactions between the chains formed. For higher <i>ϕ</i> and <i>λ</i> values, these interactions lead to side-by-side coupling of the long-dipolar chains that enhances the transient and equilibrium magnetization. The equilibrium magnetization values have been compared with some predictive models, showing a significant discrepancy at 0.01 ≤ <i>α</i> ≤ 10, which involves the aforementioned range of <i>α</i>. Also, the Langevin magnetic susceptibility, <i>χ</i>_L, used in these models provides a way to characterize dilute suspensions with strong magnetic interparticle interactions (<i>χ</i>_L ≥ 0.09). These results may contribute to formulating more accurate models to predict magnetization of these suspensions.