Isotropic-Nematic and Nematic-Nematic transitions from a homogeneous base state of a suspension of high aspect ratio, rod-like magnetic particles are studied for both Maier-Saupe and the Onsager excluded volume potentials. A combination of classical linear stability and asymptotic analyses provides insight into possible nematic states emanating from both the isotropic and nematic non-polarized equilibrium states. Local analytical results close to critical points in conjunction with global numerical results (Bhandar, 2002) yields a unified picture of the bifurcation diagram and provides a convenient base state to study effects of external orienting fields.
Using grand-canonical Monte Carlo simulations, we investigate the phase diagram of hard rods of length $L$ with additional contact (sticky) attractions on square and cubic lattices. The phase diagram shows a competition between gas-liquid and ordering transitions (which are of demixing type on the square lattice for $L ge 7$ and of nematic type on the cubic lattice for $L ge 5$). On the square lattice, increasing attractions initially lead to a stabilization of the isotropic phase. On the cubic lattice, the nematic transition remains of weak first order upon increasing the attractions. In the vicinity of the gas-liquid transition, the coexistence gap of the nematic transition quickly widens. These features are different from nematic transitions in the continuum.
Using overdamped Brownian dynamics simulations we investigate the isotropic-nematic (IN) transition of self-propelled rods in three spatial dimensions. For two well-known model systems (Gay-Berne potential and hard spherocylinders) we find that turning on activity moves to higher densities the phase boundary separating an isotropic phase from a (nonpolar) nematic phase. This active IN phase boundary is distinct from the boundary between isotropic and polar-cluster states previously reported in two-dimensional simulation studies and, unlike the latter, is not sensitive to the system size. We thus identify a generic feature of anisotropic active particles in three dimensions.
An ultra-fast quench is applied to binary mixtures of superparamagnetic colloidal particles confined at a two-dimensional water-air interface by a sudden increase of an external magnetic field. This quench realizes a virtually instantaneous cooling which is impossible in molecular systems. Using real-space experiments, the relaxation behavior after the quench is explored. Local crystallites with triangular and square symmetry are formed on different time scales and the correlation peak amplitude of the small particles evolves nonmonotonically in time in agreement with Brownian dynamics computer simulations.
Magneto-rheological elastomers (MREs) are functional materials that can be actuated by applying an external magnetic field. MREs comprise a composite of hard magnetic particles dispersed into a nonmagnetic elastomeric matrix. By applying a strong magnetic field, one can magnetize the structure to program its deformation under the subsequent application of an external field. Hard MREs, whose coercivities are large, have been receiving particular attention because the programmed magnetization remains unchanged upon actuation. Hence, once a structure made of a hard MRE is magnetized, it can be regarded as magnetized permanently. Motivated by a new realm of applications, there have been significant theoretical developments in the continuum description of hard MREs. By reducing the 3D description into 1D or 2D via dimensional reduction, several theories of hard magnetic slender structures such as linear beams, elastica, and shells have been recently proposed. In this paper, we derive an effective theory for MRE rods under geometrically nonlinear 3D deformation. Our theory is based on reducing the 3D magneto-elastic energy functional for the hard MREs into a 1D Kirchhoff-like description. Restricting the theory to 2D, we reproduce previous works on planar deformations. For further validation in the general case of 3D deformation, we perform precision experiments with both naturally straight and curved rods under either constant or constant-gradient magnetic fields. Our theoretical predictions are in excellent agreement with both discrete simulations and precision-model experiments. Finally, we discuss some limitations of our framework, as highlighted by the experiments, where long-range dipole interactions, which are neglected in the theory, can play a role.
The yet virtually unexplored class of soft colloidal rods with small aspect ratio is investigated and shown to exhibit a very rich phase and dynamic behavior, spanning from liquid to nearly melt state. Instead of nematic order, these short and soft nanocylinders alter their organization with increasing concentration from isotropic liquid with random orientation to one with preferred local orientation and eventually a multi-domain arrangement with local orientational order. The latter gives rise to a kinetically suppressed state akin to structural glass with detectable terminal relaxation, which, on increasing concentration reveals features of hexagonally packed order as in ordered block copolymers. The respective dynamic response comprises four regimes, all above the overlapping concentration of 0.02 g/ml: I) from 0.03 to 0.1 g/mol the system undergoes a liquid-to-solid like transition with a structural relaxation time that grows by four orders of magnitude. II) from 0.1 to 0.2 g/ml a dramatic slowing-down is observed and is accompanied by an evolution from isotropic to multi-domain structure. III) between 0.2 and 0.6 g/mol the suspensions exhibit signatures of shell interpenetration and jamming, with the colloidal plateau modulus depending linearly on concentration. IV) at 0.74 g/ml in the densely jammed state, the viscoelastic signature of hexagonally packed cylinders from microphase-separated block copolymers is detected. These properties set short and soft nanocylinders apart from long colloidal rods (with large aspect ratio) and provide insights for fundamentally understanding the physics in this intermediate soft colloidal regime, as well as and for tailoring the flow properties of non-spherical soft colloids.