Packing confined hard spheres denser with adaptive prism phases

Structures of the First Epitaxial Layer Created in Colloidal Heteroepitaxy

Brownian dynamics simulations have been performed to investigate the structural dependence of the first epitaxial layer in colloidal heteroepitaxy. When the epitaxial particles were larger than the substrate particles and the interactions were dominated by the depletion force, a hexagonal structure formed on a closely packed hexagonal substrate. The orientation of this hexagonal structure varied with the size ratio of the epitaxial to substrate particles to make the interaction between the substrate and epitaxial particles strong. When the sizes of the substrate and epitaxial particles were similar, long-period structures formed instead of hexagonal structures to strengthen the interaction between the substrate and epitaxial layer at the expense of the interaction between particles in the first epitaxial layer.

Phase Reentrances and Solid Deformations in Confined Colloidal Crystals

A simple geometric constraint often leads to novel, complex crystalline phases distinct from the bulk. Using thin-film charge colloidal crystals, a model system with tunable interactions, we study the effects of geometric constraints. Through a combination of experiments and simulations, we systematically explore phase reentrances and solid deformation modes concerning geometrical confinement strength, identifying two distinct categories of phase reentrances below a characteristic layer number, N_{c}: one for bcc bulk-stable and another for fcc bulk-stable systems. We further verify that the dominant thermodynamic origin is the nonmonotonic dependence of solids' free energy on the degree of spatial confinement. Moreover, we discover transitions in solid deformation modes between interface-energy and bulk-energy dominance: below a specific layer number, N_{k}, geometric constraints generate unique soft deformation modes adaptive to confinement. These findings on the N-dependent thermodynamic and kinetic behaviors offer fresh insights into understanding and manipulating thin-film crystal structures.

Structures Formed by Particles with Shoulderlike Repulsive Interaction in Thin Systems

When particles are constructed in thin systems between two parallel flat walls, structures that are not observed in bulk systems are created and the created structures change, depending on the width between the walls. In this study, the structures formed by particles constructed in thin systems were investigated through performing isothermal-isobaric Monte Carlo simulations, where the interaction between the particles is given by the hard-core square shoulder potential. By controlling the width of the shoulder-like repulsive interaction and the system width, several novel structures such as the connection of rhombuses and the square lattice of the (100) face of the body-centered cubic lattice were created.

Comment on the applicability of the Gurvich rule for estimation of pore volume in microporous zeolites

This comment seeks to establish a relation between two definitions of the pore volume of a microporous crystalline material. According to the first definition based on the Gurvich rule, the volume of the pores can be estimated from the saturated amount of vapour adsorbed, using the bulk liquid density of adsorbate as the conversion factor. The second definition is based on a purely geometric consideration of the porous space. With argon as the adsorbate and all-silica zeolite structures from the International Zeolite Association (IZA) database as the model adsorbents, we generate adsorption data using Grand Canonical Monte Carlo simulations and structural characteristics of the materials from the Poreblazer PB4.0 software. Under confinement in zeolitic pores, adsorbed argon forms structures very different from the liquid-like configurations. However, the pore volumes of these materials obtained from the Gurvich may deviate positively or negatively from the reference geometric value. Considering simply the geometric features of the materials, such as the pore volume itself or the pore size distribution, it proved to be difficult to anticipate how the volume from the Gurvich rule would deviate from the geometric volume for a particular structure. Overall, volume from the Gurvich rule agrees with the geometric volume within 25% error for 82% of the structures from the IZA database. As an additional outcome of this study, we provide a comprehensive database of textural characteristics and simulated argon adsorption data for all-silica zeolites, which can be used as reference values for the assessment of the quality of the microporous samples of all-silica zeolites in future experimental studies.

Efficient event-driven simulations of hard spheres

 Hard spheres are arguably one of the most fundamental model systems in soft matter physics, and hence a common topic of simulation studies. Event-driven simulation methods provide an efficient method for studying the phase behavior and dynamics of hard spheres under a wide range of different conditions. Here, we examine the impact of several optimization strategies for speeding up event-driven molecular dynamics of hard spheres and present a light-weight simulation code that outperforms existing simulation codes over a large range of system sizes and packing fractions. The presented differences in simulation speed, typically a factor of five to ten, save significantly on both CPU time and energy consumption and may be a crucial factor for studying slow processes such as crystal nucleation and glassy dynamics.

Connectedness percolation of fractal liquids

We apply connectedness percolation theory to fractal liquids of hard particles, and make use of a Percus-Yevick liquid state theory combined with a geometric connectivity criterion. We find that in fractal dimensions the percolation threshold interpolates continuously between integer-dimensional values, and that it decreases monotonically with increasing (fractal) dimension. The influence of hard-core interactions is significant only for dimensions below three. Finally, our theory incorrectly suggests that a percolation threshold is absent below about two dimensions, which we attribute to the breakdown of the connectedness Percus-Yevick closure.

Assembly and Dynamic Analysis of Square Colloidal Crystals via Templated Capillary Assembly

Capillary assembly has the ability to engineer centimeter-sized regions of discrete colloidal superstructures and microarrays. However, its use as a tool for directing crystallization of colloids into surface-bound nonclose-packed arrays is limited. Furthermore, the use of quantitative particle tracking tools to investigate evaporative assembly dynamics is rarely employed. In this contribution, we use templated capillary assembly to fabricate square-packed lattices of spherical, organosilica colloids using designed patterned boundaries. Particle tracking algorithms reveal that the assembly of square-packed regions is controlled by the interplay between confinement-driven nuclei formation and osmotic pressure-driven restructuring. We find that the incorporation of a square template increases the yield of particles bearing four nearest neighbors (Z_n = 4) from 4 to 39%, obtained using a heavier and more viscous solvent. Maximal square-packed domains occur at specific initial particle concentrations (1.75-2.25 wt % or φ = 0.013-0.017), indicating that rearrangements are a function of osmotic force. We use particle tracking methods to dynamically monitor conversions between square and hexagonal packing, revealing a cyclical transition between 4 and 6 coordinated particles throughout meniscus recession. Our method is highly scalable and inexpensive and can be adapted for use with different particle sizes and compositions, as well as for targeted open-packed geometries. Our findings will inform the large area, defect-free assembly of nonclose-packed lattices of unexplored varieties that are necessary for the continued expansion of colloid-based materials with vast applications in optical electronics.

Self-assembled multi-layer simple cubic photonic crystals of oppositely charged colloids in confinement

Designing and fabricating self-assembled open colloidal crystals have become one major direction in the soft matter community because of many promising applications associated with open colloidal crystals. However, most of the self-assembled crystals found in experiments are not open but close-packed. Here, by using computer simulation, we systematically investigate the self-assembly of oppositely charged colloidal hard spheres confined between two parallel hard walls, and we find that the confinement can stabilize multi-layer NaCl-like (simple cubic) open crystals. The maximal number of layers of stable NaCl-like crystals increases with decreasing inverse screening length. More interestingly, at finite low temperature, the large vibrational entropy can stabilize some multi-layer NaCl-like crystals against the most energetically favoured close-packed crystals. In the parameter range studied, we find up to 4-layer NaCl-like crystals to be stable in confinement. Our photonic calculation shows that the inverse 4-layer NaCl-like crystal can already reproduce the large photonic band gaps of the bulk simple cubic crystal, which open in the low frequency range with a low dielectric contrast. This suggests new possibilities of using confined colloidal systems to fabricate open crystalline materials with novel photonic properties.

Ground state of dipolar hard spheres confined in channels

We investigate the ground state of a classical two-dimensional system of hard-sphere dipoles confined between two hard walls. Using lattice sum minimization techniques we reveal that at fixed wall separations, a first-order transition from a vacuum to a straight one-dimensional chain of dipoles occurs upon increasing the density. Further increase in the density yields the stability of an undulated chain as well as nontrivial buckling structures. We explore the close-packed configurations of dipoles in detail, and we find that, in general, the densest packings of dipoles possess complex magnetizations along the principal axis of the slit. Our predictions serve as a guideline for experiments with granular dipolar and magnetic colloidal suspensions confined in slitlike channel geometry.

Phase diagram of hard squares in slit confinement

This work shows a complete phase diagram of hard squares of side length σ in slit confinement for H < 4.5, H being the wall to wall distance measured in σ units, including the maximal packing fraction limit. The phase diagram exhibits a transition between a single-row parallel 1-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{\square }}$$\end{document}□ and a zigzag 2-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat{\diamond }$$\end{document}◇ˆ structures for H_c(2) = (2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt{{\bf{2}}}$$\end{document}2 − 1) < H < 2, and also another one involving the 1-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{\square }}$$\end{document}□ and 2-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{\square }}$$\end{document}□ structures (two parallel rows) for 2 < H < H_c(3) (H_c(n) = n − 1 + \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt{{\bf{2}}{\boldsymbol{n}}-{\bf{1}}}$$\end{document}2n−1/n is the critical wall-to-wall distance for a (n − 1)-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{\square }}$$\end{document}□ to n-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\diamond }$$\end{document}◇ transition and where n-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\diamond }$$\end{document}◇ represents a structure formed by tilted rectangles, each one clustering n stacked squares), and a triple point for H_t \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{\simeq }}$$\end{document}≃ 2.005. In this triple point there coexists the 1-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{\square }}$$\end{document}□, 2-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{\square }}$$\end{document}□, and 2-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat{\diamond }$$\end{document}◇ˆ structures. For regions H_c(3) < H < H_c(4) and H_c(4) < H < H_c(5), very similar pictures arise. There is a (n − 1)-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{\square }}$$\end{document}□ to a n-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\diamond }$$\end{document}◇ strong transition for H_c(n) < H < n, followed by a softer (n − 1)-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{\square }}$$\end{document}□ to n-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{\square }}$$\end{document}□ transition for n < H < H_c(n + 1). Again, at H \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{\gtrsim }}$$\end{document}≳ n there appears a triple point, involving the (n − 1)-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{\square }}$$\end{document}□, n-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{\square }}$$\end{document}□, and n-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\diamond }$$\end{document}◇ structures. The similarities found for n = 2, 3 and 4 lead us to propose a tentative phase diagram for H_c(n) < H < H_c(n + 1) (n ∈ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{{\mathbb{N}}}}$$\end{document}ℕ, n > 2), where structures (n − 1)-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{\square }}$$\end{document}□, n-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{\square }}$$\end{document}□, and n-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\diamond }$$\end{document}◇ fill the phase diagram. Simulation and Onsager theory results are qualitatively consistent.

Attraction Controls the Entropy of Fluctuations in Isosceles Triangular Networks

We study two-dimensional triangular-network models, which have degenerate ground states composed of straight or randomly-zigzagging stripes and thus sub-extensive residual entropy. We show that attraction is responsible for the inversion of the stable phase by changing the entropy of fluctuations around the ground-state configurations. By using a real-space shell-expansion method, we compute the exact expression of the entropy for harmonic interactions, while for repulsive harmonic interactions we obtain the entropy arising from a limited subset of the system by numerical integration. We compare these results with a three-dimensional triangular-network model, which shows the same attraction-mediated selection mechanism of the stable phase, and conclude that this effect is general with respect to the dimensionality of the system.

Frustrated packing in a granular system under geometrical confinement

Optimal packings of uniform spheres are solved problems in two and three dimensions. The main difference between them is that the two-dimensional ground state can be easily achieved by simple dynamical processes while in three dimensions, this is impossible due to the difference in the local and global optimal packings. In this paper we show experimentally and numerically that in 2 + ε dimensions, realized by a container which is in one dimension slightly wider than the spheres, the particles organize themselves in a triangular lattice, while touching either the front or rear side of the container. If these positions are denoted by up and down the packing problem can be mapped to a 1/2 spin system. At first it looks frustrated with spin-glass like configurations, but the system has a well defined ground state built up from isosceles triangles. When the system is agitated, it evolves very slowly towards the potential energy minimum through metastable states. We show that the dynamics is local and is driven by the optimization of the volumes of 7-particle configurations and by the vertical interaction between touching spheres.

Diverging Time Scale in the Dimensional Crossover for Liquids in Strong Confinement

We study a strongly interacting dense hard-sphere system confined between two parallel plates by event-driven molecular dynamics simulations to address the fundamental question of the nature of the 3D to 2D crossover. As the fluid becomes more and more confined the dynamics of the transverse and lateral degrees of freedom decouple, which is accompanied by a diverging time scale separating 2D from 3D behavior. Relying on the time-correlation function of the transversal kinetic energy, the scaling behavior and its density dependence is explored. Surprisingly, our simulations reveal that its time dependence becomes purely exponential such that memory effects can be ignored. We rationalize our findings quantitatively in terms of an analytic theory which becomes exact in the limit of strong confinement.

Spatial confinement governs orientational order in patchy particles

Orientational order in condensed matter plays a key role in determining material properties such as ferromagnetism, viscoelasticity or birefringence. We studied purely orientational ordering in closely-packed one-patch colloidal particles confined between flat substrates, where the particles can only rotate and are ordered via the sticky interaction between the patches. For the first time, we experimentally realized a rich variety of mesoscopic patterns through orientational ordering of colloids by controlling patch size and confinement thickness. The combination of experiment and numerical simulation reveals the decisive role of confinement: An ordered state(s) is selected from the (meta)stable options in bulk when it is commensurate with the system geometry and boundary conditions; otherwise, frustration induces a unique order. Our study offers a new means of systematic control over mesoscopic structures via orientational ordering in patchy particles. The system would also possess unique functionalities through the rotational response of the particles to external stimuli.

Net, excess and absolute adsorption and adsorption of helium

The definitions of absolute, excess and net adsorption in microporous materials are used to identify the correct limits at zero and infinite pressure. Absolute adsorption is shown to be the fundamental thermodynamic property and methods to determine the solid density that includes the micropore volume are discussed. A simple means to define when it is necessary to distinguish between the three definitions at low pressure is presented. To highlight the practical implications of the analysis the case of adsorption of helium is considered in detail and a combination of experiments and molecular simulations is used to clarify how to interpret adsorption measurements for weakly adsorbed components.

Confined disordered strictly jammed binary sphere packings

Disordered jammed packings under confinement have received considerably less attention than their bulk counterparts and yet arise in a variety of practical situations. In this work, we study binary sphere packings that are confined between two parallel hard planes and generalize the Torquato-Jiao (TJ) sequential linear programming algorithm [Phys. Rev. E 82, 061302 (2010)] to obtain putative maximally random jammed (MRJ) packings that are exactly isostatic with high fidelity over a large range of plane separation distances H, small to large sphere radius ratio α, and small sphere relative concentration x. We find that packing characteristics can be substantially different from their bulk analogs, which is due to what we term "confinement frustration." Rattlers in confined packings are generally more prevalent than those in their bulk counterparts. We observe that packing fraction, rattler fraction, and degree of disorder of MRJ packings generally increase with H, though exceptions exist. Discontinuities in the packing characteristics as H varies in the vicinity of certain values of H are due to associated discontinuous transitions between different jammed states. When the plane separation distance is on the order of two large-sphere diameters or less, the packings exhibit salient two-dimensional features; when the plane separation distance exceeds about 30 large-sphere diameters, the packings approach three-dimensional bulk packings. As the size contrast increases (as α decreases), the rattler fraction dramatically increases due to what we call "size-disparity" frustration. We find that at intermediate α and when x is about 0.5 (50-50 mixture), the disorder of packings is maximized, as measured by an order metric ψ that is based on the number density fluctuations in the direction perpendicular to the hard walls. We also apply the local volume-fraction variance σ(τ)(2)(R) to characterize confined packings and find that these packings possess essentially the same level of hyperuniformity as their bulk counterparts. Our findings are generally relevant to confined packings that arise in biology (e.g., structural color in birds and insects) and may have implications for the creation of high-density powders and improved battery designs.

Controlling Orientational and Translational Order of Iron Oxide Nanocubes by Assembly in Nanofluidic Containers

We demonstrate that spatial confinement can be used to control the orientational and translational order of cubic nanoparticles. For this purpose we have combined X-ray scattering and scanning electron microscopy to study the ordering of iron oxide nanocubes that have self-assembled from toluene-based dispersions in nanofluidic channels. An analysis of scattering vector components with directions parallel and perpendicular to the slit walls shows that the confining walls induce a preferential parallel alignment of the nanocube (100) faces. Moreover, slit wall separations that are commensurate with an integer multiple of the edge length of the oleic acid-capped nanocubes result in a more pronounced translational order of the self-assembled arrays compared to incommensurate confinement. These results show that the confined assembly of anisotropic nanocrystals is a promising route to nanoscale devices with tunable anisotropic properties.

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.

Confinement Induced Plastic Crystal-to-Crystal Transitions in Rodlike Particles with Long-Ranged Repulsion

Colloidal particles in geometrical confinement display a complex variety of packing structures different from their three-dimensional (3D) bulk counterpart. Here, we confined charged rodlike colloids with long-ranged repulsions to a thin wedge-shaped cell and show, by quantitative 3D confocal microscopy, that not only their positional but also their orientational order depends sensitively upon the slit width. Synchronized with transitions in lattice symmetry and number of layers confinement induces plastic crystal-to-crystal transitions. A model analysis suggests that this complex sequence of more or less rotationally ordered states originates from the subtle competition between the electrostatic repulsion of a rod with the wall and with its neighbors.

Fundamental measure theory for the electric double layer: implications for blue-energy harvesting and water desalination

Capacitive mixing (CAPMIX) and capacitive deionization (CDI) are promising candidates for harvesting clean, renewable energy and for the energy efficient production of potable water, respectively. Both CAPMIX and CDI involve water-immersed porous carbon (supercapacitors) electrodes at voltages of the order of hundreds of millivolts, such that counter-ionic packing is important for the electric double layer (EDL) which forms near the surfaces of these porous materials. Thus, we propose a density functional theory (DFT) to model the EDL, where the White-Bear mark II fundamental measure theory functional is combined with a mean-field Coulombic and a mean spherical approximation-type correction to describe the interplay between dense packing and electrostatics, in good agreement with molecular dynamics simulations. We discuss the concentration-dependent potential rise due to changes in the chemical potential in capacitors in the context of an over-ideal theoretical description and its impact on energy harvesting and water desalination. Compared to less elaborate mean-field models our DFT calculations reveal a higher work output for blue-energy cycles and a higher energy demand for desalination cycles.

Deriving fundamental measure theory from the virial series: consistency with the zero-dimensional limit

Fundamental measure theory (FMT) for hard particles has great potential for predicting the phase behavior of colloidal and nanometric shapes. The modern versions of FMT are usually derived from the zero-dimensional limit, a system of at most one particle confined in a collection of cavities in the limit that all cavities shrink to the size of the particle. In Phys. Rev. E 85, 041150 (2012), a derivation from an approximated and resummed virial expansion was presented, whose result was not fully consistent with the FMT from the zero-dimensional limit. Here we improve on this derivation and obtain exactly the same FMT functional as was obtained earlier from the zero-dimensional limit. As a result, further improvements of FMT based on the virial expansion can now be formulated, some of which we suggest in the outlook.

Template-induced structure transition in sub-10 nm self-assembling nanoparticles

We report on the directed self-assembly of sub-10 nm gold nanoparticles confined within a template comprising channels of gradually varying widths. When the colloidal lattice parameter is mismatched with the channel width, the nanoparticles rearrange and break their natural close-packed ordering, transiting through a range of structural configurations according to the constraints imposed by the channel. While much work has been done in assembling ordered configurations, studies of the transition regime between ordered states have been limited to microparticles under applied compression. Here, with coordinated experiments and Monte Carlo simulations we show that particles transit through a more diverse set of self-assembled configurations than observed for compressed systems. The new insight from this work could lead to the control and design of complex self-assembled patterns other than periodic arrays of ordered particles.

Crystal phases of soft spheres systems in a slab geometry

We have identified the ground state configurations of soft particles (interacting via inverse power potentials) confined between two hard, impenetrable walls. To this end we have used a highly reliable optimization scheme at vanishing temperature while varying the wall separation over a representative range. Apart from the expected layered triangular and square structures (which are compatible with the three-dimensional bulk fcc lattice), we have identified a cascade of highly complex intermediate structures. Taking benefit of the general scaling properties of inverse power potentials, we could identify - for a given softness value - one single master curve which relates the energy to the wall separation, irrespective of the density of the system. Via extensive Monte Carlo simulations, we have performed closer investigations of these intermediate structures at finite temperature: we could provide evidence to which extent these particle arrangements remain stable over a relatively large temperature range.

Structural ordering of trapped colloids with competing interactions

The structure of colloids with competing interactions which are confined in a harmonic external trap potential is analyzed numerically by energy minimization in two spatial dimensions. A wealth of different cluster structures is found to be stable including clusters with a fringed outer rim (reminiscent to an ornamental border), clusters perforated with voids, as well as clusters with a crystalline core and a disordered rim. All cluster structures occur in a two-dimensional parameter space. The structural ordering can therefore be efficiently tuned by changing few parameters only providing access to a controlled fabrication of colloidal clusters.

Disordered strictly jammed binary sphere packings attain an anomalously large range of densities

Previous attempts to simulate disordered binary sphere packings have been limited in producing mechanically stable, isostatic packings across a broad spectrum of packing fractions. Here we report that disordered strictly jammed binary packings (packings that remain mechanically stable under general shear deformations and compressions) can be produced with an anomalously large range of average packing fractions 0.634≤φ≤0.829 for small to large sphere radius ratios α restricted to α≥0.100. Surprisingly, this range of average packing fractions is obtained for packings containing a subset of spheres (called the backbone) that are exactly strictly jammed, exactly isostatic, and also generated from random initial conditions. Additionally, the average packing fractions of these packings at certain α and small sphere relative number concentrations x approach those of the corresponding densest known ordered packings. These findings suggest for entropic reasons that these high-density disordered packings should be good glass formers and that they may be easy to prepare experimentally. We also identify an unusual feature of the packing fraction of jammed backbones (packings with rattlers excluded). The backbone packing fraction is about 0.624 over the majority of the α-x plane, even when large numbers of small spheres are present in the backbone. Over the (relatively small) area of the α-x plane where the backbone is not roughly constant, we find that backbone packing fractions range from about 0.606 to 0.829, with the volume of rattler spheres comprising between 1.6% and 26.9% of total sphere volume. To generate isostatic strictly jammed packings, we use an implementation of the Torquato-Jiao sequential linear programming algorithm [Phys. Rev. E 82, 061302 (2010)], which is an efficient producer of inherent structures (mechanically stable configurations at the local maxima in the density landscape). The identification and explicit construction of binary packings with such high packing fractions could have important practical implications for granular composites where density is critical both to material properties and fabrication cost, including for solid propellants, concrete, and ceramics. The densities and structures of jammed binary packings at various α and x are also relevant to the formation of a glass phase in multicomponent metallic systems.