Crossover from Normal to Anomalous Diffusion in Systems of Field-Aligned Dipolar Particles

Using molecular dynamics simulations we investigate the translational dynamics of particles with dipolar interactions in homogenous external fields. For a broad range of concentrations, we find that the anisotropic, yet normal diffusive behavior characterizing weakly coupled systems becomes anomalous both parallel and perpendicular to the field at sufficiently high dipolar coupling and field strength. After the ballistic regime, chain formation first yields cagelike motion in all directions, followed by transient, mixed diffusive-superdiffusive behavior resulting from cooperative motion of the chains. The enhanced dynamics disappears only at higher densities close to crystallization.

Figure 1

(a) MSDs for $\lambda =3$ at $H^{*}=0$ and 10; (b) Simulation snapshot at $\lambda =3$ and $H^{*}=10$; (c) Anisotropy ratio as a function of dipolar coupling strength.

Figure 2

(a)–(b) MSDs for $\lambda =7$ and $H^{*}=0$, 10, 100. (b) Includes data for two system sizes; the box indicates the subdiffusive regime. (c)–(e) Corresponding snapshots.

Figure 3

(a),(b) Distinct van Hove functions ($\lambda =7$, $H^{*}=100$). (c),(d) Trajectories of two initially neighboring particles (insets show a larger time scale).

Figure 4

(a),(b) The functions $G_s^{\parallel (\perp )}$ at $t^{*}=20$ with corresponding instantaneous data (colors according to the covered distance). Insets: non-Gaussian parameters ${\alpha }_{\parallel (\perp )}(t)$. (c),(d) Snapshots with particles colored according to the code in (a) and (b).

Figure 5

MSDs (a) parallel (b) perpendicular to $\mathbf{H}$ at various densities ${\rho }^{*}$ ($\lambda =7$, $H^{*}=100$, $N=864$). Part (c) is a snapshot at ${\rho }^{*}=0.8$.