Chiral photonic crystals from sphere packing.

Inspired by recent developments in self-assembled chiral nanostructures, we have explored the possibility of using spherical particles packed in cylinders as building blocks for chiral photonic crystals. In particular, we focused on an array of parallel cylinders arranged in a perfect triangular lattice, each containing an identical densest sphere packing structure. Despite the non-chirality of both the spheres and cylinders, the self-assembled system can exhibit chirality due to spontaneous symmetry breaking during the assembly process. We have investigated the circular dichroism effects of the system and have found that, for both perfect electric conductor and dielectric spheres, the system can display dual-polarization photonic band gaps for circularly polarized light at normal incidence along the axis of the helix. We have also examined how the polarization band gap size depends on the dielectric constant of the spheres and the packing fraction of the cylinders. Furthermore, we have explored the effects of non-ideality and found that the polarization gap persists even in the presence of imperfections and heterogeneity. Our study suggests that a cluster formed by spheres self-assembling inside parallel cylinders with appropriate material parameters can be a promising approach to creating chiral photonic crystals.

Densest packings from size segregation of particles in geometric confinement.

A correlation between density maximization and size segregation for packings of polydisperse particles in geometric confinement has been discovered, through the derivation of a general solution for the densest-packed zigzag arrangements of polydisperse particles. This solution is a size-graded structure in which the larger a particle the closer it is located to either end of the system, such that the smaller particles in the interior are encapsulated by the larger ones away from it. Any pair of different-sized adjacent particles is a grain-boundary-like configuration that reduces the overall packing efficiency of the system, and this solution corresponds to a minimization of excess-volume contributions from grain-boundary-like configurations of different-sized particles as a result of the clustering of equal- or like-sized particles. Our findings provide new insights into how structural order of polydisperse particles emerges in confined settings.

Shape-Anisotropy-Induced Ordered Packings in Cylindrical Confinement.

Densest possible packings of identical spheroids in cylindrical confinement have been obtained through Monte Carlo simulations. By varying the shape anisotropy of spheroids and also the cylinder-to-spheroid size ratio, a variety of densest possible crystalline structures have been discovered, including achiral structures with specific orientations of particles and chiral helical structures with rotating orientations of particles. Our findings reveal a transition between confinement-induced chiral ordering and shape-anisotropy-induced orientational ordering and would serve as a guide for the fabrication of crystalline wires using anisotropic particles.

Electrostatic Self-Assembly: Understanding the Significance of the Solvent.

The electrostatic deposition of particles has become a very effective route to the assembly of many nanoscale materials. However, fundamental limitations to the process are presented by the choice of solvent, which can either suppress or promote self-assembly depending on specific combinations of nanoparticle/surface/solvent properties. A new development in the theory of electrostatic interactions between polarizable objects provides insight into the effect a solvent can have on electrostatic self-assembly. Critical to assembly is the requirement for a minimum charge on a surface of an object, below which a solvent can suppress electrostatic attraction. Examples drawn from the literature are used to illustrate how switches in behavior are mediated by the solvent; these in turn provide a fundamental understanding of electrostatic particle-surface interactions applicable to many areas of materials science and nanotechnology.

Progress in the theory of electrostatic interactions between charged particles.

In this perspective we examine recent theoretical developments in methods for calculating the electrostatic properties of charged particles of dielectric materials. Particular attention is paid to the phenomenon of like-charge attraction and we investigate the specific conditions under which particles carrying the same sign of charge can experience an attractive interaction. Given favourable circumstances, it is shown that even weakly polarisable materials, such as oil droplets and polymer particles, can experience like-charge attraction. Emphasis is also placed on the numerical accuracy of the multipole approach adopted in many electrostatic solutions and on the importance of establishing strict convergence criteria when addressing problems involving particulate materials with high dielectric constants.

Scaling analysis of negative differential thermal resistance.

Negative differential thermal resistance (NDTR) can be generated for any one-dimensional heat flow with a temperature-dependent thermal conductivity. In a system-independent scaling analysis, the general condition for the occurrence of NDTR is found to be an inequality with three scaling exponents: n(1)n(2) < -(1+n(3)), where n(1) ∈ (-∞,+∞) describes a particular way of varying the temperature difference, and n(2) and n(3) describe, respectively, the dependence of the thermal conductivity on an average temperature and on the temperature difference. For cases with a temperature-dependent thermal conductivity, i.e. n(2) ≠ 0, NDTR can always be generated with a suitable choice of n(1) such that this inequality is satisfied. The results explain the illusory absence of a NDTR regime in certain lattices and predict new ways of generating NDTR, where such predictions have been verified numerically. The analysis will provide insights for a designing of thermal devices, and for a manipulation of heat flow in experimental systems, such as nanotubes.

Electrostatic force between a charged sphere and a planar surface: a general solution for dielectric materials.

Using the bispherical coordinate system, an analytical solution describing the electrostatic force between a charged dielectric sphere and a planar dielectric surface is presented. This new solution exhibits excellent numerical convergence, and is sufficiently general as to allow for the presence of charge on both the sphere and the surface. The solution has been applied to two examples of sphere-plane interactions chosen from the literature, namely, (i) a charged lactose sphere interacting with a neutral glass surface and (ii) a charged polystyrene sphere interacting with a neutral graphite surface. Theory suggests that in both cases the electrostatic force makes a major contribution to the experimentally observed attraction at short sphere-plane separations, and that the force is much longer ranged than previously suggested.

Densest columnar structures of hard spheres from sequential deposition.

The rich variety of densest columnar structures of identical hard spheres inside a cylinder can surprisingly be constructed from a simple and computationally fast sequential deposition of cylinder-touching spheres, if the cylinder-to-sphere diameter ratio is D is an element of [1,2.7013]. This provides a direction for theoretically deriving all these densest structures and for constructing such densest packings with nano-, micro-, colloidal, or charged particles, which all self-assemble like hard spheres.

Heat conduction in the nonlinear response regime: scaling, boundary jumps, and negative differential thermal resistance.

We report a numerical study on heat conduction in one-dimensional homogeneous lattices in both the linear and the nonlinear response regime, with a comparison among three prototypical nonlinear lattice models. In the nonlinear response regime, negative differential thermal resistance (NDTR) can occur in both the Frenkel-Kontorova model and the phi4 model. In the Fermi-Pasta-Ulam- beta model, however, only positive differential thermal resistance can be observed, as shown by a monotonous power-law dependence of the heat flux on the applied temperature difference. In general, it was found that NDTR can occur if there is nonlinearity in the onsite potential of the lattice model. It was also found that the regime of NDTR becomes smaller as the system size increases, and eventually vanishes in the thermodynamic limit. For the phi4 model, a phenomenological description of the size-induced crossover from the existence to the nonexistence of a NDTR regime is provided.

Transition from the exhibition to the nonexhibition of negative differential thermal resistance in the two-segment Frenkel-Kontorova model.

An extensive study of the one-dimensional two-segment Frenkel-Kontorova (FK) model reveals a transition from the counterintuitive existence to the ordinary nonexistence of a negative-differential-thermal-resistance (NDTR) regime, when the system size or the intersegment coupling constant increases to a critical value. A "phase" diagram which depicts the relevant conditions for the exhibition of NDTR was obtained. In the existence of a NDTR regime, the link at the segment interface is weak and therefore the corresponding exhibition of NDTR can be explained in terms of effective phonon-band shifts. In the case where such a regime does not exist, the theory of phonon-band mismatch is not applicable due to sufficiently strong coupling between the FK segments. The findings suggest that the behavior of a thermal transistor will depend critically on the properties of the interface and the system size.