Dense periodic packings of tori

Tabular Potentials for Monte Carlo Simulation of Supertoroids with Short-Range Interactions

We describe a methodology for constructing tabular potentials of supertoroids with short-range interactions, which requires the calculation of the volume of overlap of these shapes for many relative positions and orientations. Recent advances in the synthesis of anisotropic colloids have made experimental realizations of such particles feasible and have increased the practical impact of fundamental simulation studies of these families of shapes. This extends our recent work on superquadric potentials to now include a family of ring-like shapes with a hole in the middle. Along with the addition of supertoroids, the ability to make tables for nonidentical particles and particle pairs with multiple, disconnected overlap volumes was added. Using newly developed extensions to a previously published algorithm, we produced tabular potentials for all of these new cases. The algorithmic developments in this work will enable Monte Carlo simulations of a wider variety of shapes to predict thermodynamic properties over a range of conditions.

Assembly of porous smectic structures formed from interlocking high-symmetry planar nanorings

Materials comprising porous structures, often in the form of interconnected concave cavities, are typically assembled from convex molecular building blocks. The use of nanoparticles with a characteristic nonconvex shape provides a promising strategy to create new porous materials, an approach that has been recently used with cagelike molecules to form remarkable liquids with "scrabbled" porous cavities. Nonconvex mesogenic building blocks can be engineered to form unique self-assembled open structures with tunable porosity and long-range order that is intermediate between that of isotropic liquids and of crystalline solids. Here we propose the design of highly open liquid-crystalline structures from rigid nanorings with ellipsoidal and polygonal geometry. By exploiting the entropic ordering characteristics of athermal colloidal particles, we demonstrate that high-symmetry nonconvex rings with large internal cavities interlock within a 2D layered structure leading to the formation of distinctive liquid-crystalline smectic phases. We show that these smectic phases possess uniquely high free volumes of up to ∼95%, a value significantly larger than the 50% that is typically achievable with smectic phases formed by more conventional convex rod- or disklike mesogenic particles.

A Geometric-Structure Theory for Maximally Random Jammed Packings

Maximally random jammed (MRJ) particle packings can be viewed as prototypical glasses in that they are maximally disordered while simultaneously being mechanically rigid. The prediction of the MRJ packing density ϕMRJ, among other packing properties of frictionless particles, still poses many theoretical challenges, even for congruent spheres or disks. Using the geometric-structure approach, we derive for the first time a highly accurate formula for MRJ densities for a very wide class of two-dimensional frictionless packings, namely, binary convex superdisks, with shapes that continuously interpolate between circles and squares. By incorporating specific attributes of MRJ states and a novel organizing principle, our formula yields predictions of ϕMRJ that are in excellent agreement with corresponding computer-simulation estimates in almost the entire α-x plane with semi-axis ratio α and small-particle relative number concentration x. Importantly, in the monodisperse circle limit, the predicted ϕMRJ = 0.834 agrees very well with the very recently numerically discovered MRJ density of 0.827, which distinguishes it from high-density "random-close packing" polycrystalline states and hence provides a stringent test on the theory. Similarly, for non-circular monodisperse superdisks, we predict MRJ states with densities that are appreciably smaller than is conventionally thought to be achievable by standard packing protocols.