  We investigate the formation of chains of superparamagnetic iron oxide
nanoparticles (SPIONs) in a rotating magnetic field, combining two
well-explored chain-forming systems: larger micron-scale beads in a rotating
magnetic field, and SPIONs in a static field. This simple combination is
interesting because it features self-assembly that occurs both far from
equilibrium and at a finite temperature, with the better-explored systems
constituting respectively its zero temperature and near-equilibrium limits.
Theories applicable to either of the two limits qualitatively predict the chain
length distributions, except that chains in our experiments are shorter, which
we attribute to the simultaneous presence of thermal fluctuations and fluid
shear forces that work in concert to break chains apart. Our most striking
result is that the disorder in the SPION chains gradually dissipates over a
timescale of tens of minutes, about two orders of magnitude slower than the
characteristic chain assembly time. The disorder dissipation can be sped up by
increasing particle concentration and solution ionic strength, both of which
increase the speed of chain assembly. This strongly suggests that the
improvement in chain order with time is not due to thermal fluctuations but
rather to energy imparted by the self-assembly process, which continually
causes chains to grow and break apart, even when a steady state distribution
has obtained. More generally, our results indicate that self-assembly away from
equilibrium may sometimes lead to better ordered assemblies than under
near-equilibrium conditions.
