Contractile actuation and dynamical gel assembly of paramagnetic filaments in fast precessing fields

Flexible superparamagnetic filaments are studied under the influence of fast precessing magnetic fields using simulations and a continuum approximation analysis. We find that individual filaments can be made to exert controllable tensile forces along the precession axis. These forces are exploited for microscopic actuation. In bulk, the filaments can be rapidly assembled into different configurations whose material properties depend on the field parameters. The precession frequency affects filament aggregation and conformation by changing the net torques on the filament ends. Using a time-dependent precession angle allows considerable freedom in choosing properties for filament aggregates. As an example, we design a field that twists chains together to dynamically assemble a self-healing gel.

Figure 1

Helical contraction. (a) Schematic of the boundary conditions on a contracting helix. (b) Frame from MD simulation using LAMMPS with a 40-bead magnetic filament connecting two inert test masses. Under the influence of a precessing field with $M>0$, the helix attempts to contract to the $x-y$ plane. Here $\epsilon =40, {\mu }^2{\sigma }^{-3}=4kT$, and $\beta =\pi /2$. (c) If $M<0$, the filament attempts to align with the $z$ axis and forms planar solutions. Both bending and magnetic energy costs are localized to hairpin turns, so the state is metastable.

Figure 2

Effects of precession frequency and bending modulus on aggregation for 80-bead filaments with ${\mu }^2{\sigma }^{-3}=4kT$ and $\gamma \sigma =10$ (Lennard-Jones units). For sufficiently low frequencies and bending moduli, the torque on filament ends forces filaments to aggregate in metastable spirals instead of branching networks.

Figure 3

Achieving twisting with a magnetic drive. (a) Path traced by the driving field with $\omega =2.5, {\omega }_2=1.0$, and ${\beta }_0=0.5$ over $t\in [0,4\pi ]i$ (top) and $[0,\pi ]$ (bottom). (b) The twisted cross-links created by this drive with the parameters $\mu =2.0$ and $\epsilon =80.0$. Further simulation details are given in the SM. (c)Increasing chain length and system density creates a system-spanning network of cross-linked filaments. The succeeding panels are the results of altering the magnetic drive parameters as noted: (d) ${\beta }_0=0.4$; (e) ${\beta }_0=0.6$; (f) ${\omega }_2=2.0$; (g) ${\omega }_2=0.5$; (h) $\omega =25, {\omega }_2=10$; (i) $\omega =0.25, {\omega }_2=0.1$.