The size ratio effect on the microstructure and magnetization of a bidisperse magnetic colloidal suspension

This research examines how the size ratio influences the microstructure and time-dependent magnetization in a bidisperse magnetic colloidal suspension under a uniform magnetic field. Two types of particles model the bidisperse suspension: the small particles of radius <i>R</i>_s and the large particles of radius <i>R</i>_l. The size ratio, <i>ξ</i> = <i>R</i>_l/<i>R</i>_s, defines the particle size difference. The total volume fraction of the suspension, <i>ϕ</i>, is obtained from <i>ϕ</i> = <i>ϕ</i>_s + <i>ϕ</i>_l, where <i>ϕ</i>_s and <i>ϕ</i>_l are the volume fractions of the small and large particles, respectively. The magnetic dipole-dipole interaction among the small particles and the large ones is characterized by the dipolar coupling parameters <i>λ</i>_s and <i>λ</i>_l, respectively. The interactions among the applied magnetic field and the magnetic dipoles of the small and large particles are measured by the Langevin parameters <i>α</i>_s and <i>α</i>_l, respectively. This study performs Brownian dynamics (BD) simulations of a bidisperse suspension comprising <i>N</i> = 1000 particles, with <i>ϕ</i> = 10^-3 and <i>ϕ</i>_s = <i>ϕ</i>_l = 5 × 10^-4. Also, <i>α</i>_s ranges from 0 to 1000, and <i>λ</i>_s from 5 to 30. The size ratio, <i>ξ</i>, takes values of 1, 2 and 3. The values of <i>λ</i>_l and <i>α</i>_l are computed by the parameters aforementioned by assuming that all particles exhibit the same saturation magnetization. Our results show a rich variability in the microstructure as <i>ξ</i> increases. As the large particles increase in size, they exhibit a greater magnetic dipole moment, which induces a non-uniform local magnetic field around them. The surrounding small particles then aggregate with the large ones, driven by this local magnetic field. Small <i>α</i>_s values lead to the formation of flux-closure structures such as rings of small and large particles as well as shell-like structures, which consist of small particles surrounding the large ones. The formation of these microstructures directly affects time-dependent magnetization of the suspension, which exhibits a decay with time in the limit of long times. These findings have important implications for synthesizing magnetic colloidal suspensions with enhanced properties.