Hysteresis curves reveal the microscopic origin of cooperative CO2 adsorption in diamine-appended metal-organic frameworks.

Diamine-appended metal-organic frameworks (MOFs) of the form Mg2(dobpdc)(diamine)2 adsorb CO2 in a cooperative fashion, exhibiting an abrupt change in CO2 occupancy with pressure or temperature. This change is accompanied by hysteresis. While hysteresis is suggestive of a first-order phase transition, we show that hysteretic temperature-occupancy curves associated with this material are qualitatively unlike the curves seen in the presence of a phase transition; they are instead consistent with CO2 chain polymerization, within one-dimensional channels in the MOF, in the absence of a phase transition. Our simulations of a microscopic model reproduce this dynamics, providing a physical understanding of cooperative adsorption in this industrially important class of materials.

Design Rules for Self-Assembly of 2D Nanocrystal/Metal-Organic Framework Superstructures.

We demonstrate the guiding principles behind simple two dimensional self-assembly of MOF nanoparticles (NPs) and oleic acid capped iron oxide (Fe3 O4 ) NCs into a uniform two-dimensional bi-layered superstructure. This self-assembly process can be controlled by the energy of ligand-ligand interactions between surface ligands on Fe3 O4 NCs and Zr6 O4 (OH)4 (fumarate)6 MOF NPs. Scanning transmission electron microscopy (TEM)/energy-dispersive X-ray spectroscopy and TEM tomography confirm the hierarchical co-assembly of Fe3 O4 NCs with MOF NPs as ligand energies are manipulated to promote facile diffusion of the smaller NCs. First-principles calculations and event-driven molecular dynamics simulations indicate that the observed patterns are dictated by combination of ligand-surface and ligand-ligand interactions. This study opens a new avenue for design and self-assembly of MOFs and NCs into high surface area assemblies, mimicking the structure of supported catalyst architectures, and provides a thorough fundamental understanding of the self-assembly process, which could be a guide for designing functional materials with desired structure.

Irregular model DNA particles self-assemble into a regular structure.

DNA nanoparticles with three-fold coordination have been observed to self-assemble in experiment into a network equivalent to the hexagonal (6.6.6) tiling, and a network equivalent to the 4.8.8 Archimedean tiling. Both networks are built from a single type of vertex. Here we use analytic theory and equilibrium and dynamic simulation to show that a model particle, whose rotational properties lie between those of the vertices of the 6.6.6 and 4.8.8 networks, can self-assemble into a network built from three types of vertex. Important in forming this network is the ability of the particle to rotate when bound, thereby allowing the formation of more than one type of binding motif. The network in question is equivalent to a false tiling, a periodic structure built from irregular polygons, and possesses 40 particles in its unit cell. The emergence of this complex structure, whose symmetry properties are not obviously related to those of its constituent particles, highlights the potential for creating new structures from simple variants of existing nanoparticles.

Configurational entropy and effective temperature in systems of active Brownian particles.

We propose a method to determine the effective density of states and configurational entropy in systems of active Brownian particles by measuring the probability distribution function of potential energy at varying temperatures. Assuming that the entropy is a continuous and monotonically increasing function of energy, we provide support that two-dimensional systems of purely repulsive active Brownian spheres can be mapped onto an equilibrium system with a Boltzmann-like distribution and an effective temperature. We find that the effective temperature depends even for a large number of particles on system size, suggesting that active systems are non-extensive. In addition, the effective Helmholtz free energy can be derived from the configurational entropy. We verify our results regarding the configurational entropy by using thermodynamic integration of the effective Helmholtz free energy with respect to temperature.

Dynamic self-organization of side-propelling colloidal rods: experiments and simulations.

In recent years, there is a growing interest in designing artificial analogues of living systems, fueled not only by potential applications as 'smart micro-machines', but also by the demand for simple models that can be used to study the behavior of their more complex natural counterparts. Here, we present a facile, internally driven, experimental system comprised of fluorescently labeled colloidal silica rods of which the self-propulsion is powered by the decomposition of H2O2 catalyzed by a length-wise half Pt coating of the particles in order to study how shape anisotropy and swimming direction affect the collective behavior. We investigated the emerging structures and their time evolution for various particle concentrations in (quasi-)two dimensional systems for three aspect ratios of the rods on a single particle level using a combination of experiments and simulations. We found that the dynamic self-organization relied on a competition between self-propulsion and phoretic attractions induced by phoresis of the rods. We observed that the particle clustering behavior depends on the concentration as well as the aspect ratio of the rods. Our findings provide a more detailed understanding of dynamic self-organization of anisotropic particles and the role the propulsion direction plays in internally driven systems.

Equilibrium phases of one-patch colloids with short-range attractions.

Inspired by experimental studies of short-ranged attractive patchy particles, we study with computer simulations the phase behavior and the crystalline structures of one-patch colloids with an interaction range equal to 5% of the particle diameter. In particular, we study the effects of the patch surface coverage fraction, defined as the ratio between the attractive and the total surface of a particle. Using free-energy calculations and thermodynamic integration schemes, we evaluate the equilibrium phase diagrams for particles with patch coverage fractions of 30%, 50% and 60%. For a 60% surface coverage fraction, we observe stable lamellar crystals consisting of stacked bilayers that directly coexist with a low density fluid. Inside the coexistence region, we observe the formation of lamellar structures also in direct NVT simulations, indicating that the barrier of formation is low and experimental realization is feasible. For sufficiently strong interactions, these structures spontaneously assemble from the fluid in simulations, suggesting that they might also easily form in experimental systems. In the Janus case, i.e. at 50% surface coverage fraction, no lamellar structures are formed, and the stable crystals are similar to those that have been found previously for a longer interaction range (i.e. 20% of the particle diameter). At 30% coverage fraction, we identify novel 'open' crystal structures with large unit cells of up to 14 particles that are stable in the strong interaction limit.

Cooperative polymerization of one-patch colloids.

We numerically investigate cooperative polymerization in an off-lattice model based on a pairwise additive potential using particles with a single attractive patch that covers 30% of the colloid surface. Upon cooling, these particles self-assemble into small clusters which, below a density-dependent temperature, spontaneously reorganize into long straight tubes. We evaluate the partition functions of clusters of all sizes to provide an accurate description of the chemical reaction constants governing this process. Our calculations show that, for intermediate sizes, the partition functions retain contributions from two different structures, differing in both energy and entropy. We illustrate the microscopic mechanism behind the complex polymerization process in this system and provide a detailed evaluation of its thermodynamics.

Predicting crystals of Janus colloids.

We present a numerical study on the phase diagram for a simple model of Janus colloids, including ordered and disordered structures. Using a range of techniques, we generate a set of crystal structures and investigate their relative stability field in the pressure-temperature and temperature-density planes by means of free-energy calculations and thermodynamic integration schemes. We find that despite the Janus colloids' simple architecture, they form stable crystal structures with complicated bond-topologies on an underlying face-centered-cubic or hexagonal-close-packed lattice. In addition, we find a phase consisting of wrinkled bilayer sheets, competing with both the fluid and the crystal phases. We detect a metastable gas-liquid coexistence which displays a micellization-driven re-entrant behavior.

Layout of ancient Greek papyri through lead-drawn ruling lines revealed by Macro X-Ray Fluorescence Imaging.

The use of lead-drawn ruling lines by ancient scribes for the layout of Greek papyrus rolls was known to us only from classical authors and was postulated by a few scholars in modern times. In situ application of noninvasive Macro X-Ray Fluorescence Imaging Spectroscopy (MA-XRF) to unrolled papyri from Herculaneum, dating from about 200 BC to the 1st century AD, has provided the first direct evidence of such practice in ancient book production. The key experimental proof of periodic lines drawn in lead was gathered by a highly sensitive MA-XRF mobile instrument, which allowed detection of ultra-low trace residues of metals with detection limits that rival synchrotron light instruments. Elemental distribution maps of Pb have revealed three different systems of textual layout in ancient papyrus rolls and have resolved the dispute around so-called Maas' Law, by delivering experimental proof that slanted text columns were a deliberate aesthetic choice of scribes.

Phase diagram of one-patch colloids forming tubes and lamellae.

We numerically calculate the equilibrium phase diagram of one-patch particles with 30% patch coverage. It has been previously shown that in the fluid phase these particles organize into extremely long tubelike aggregates (G. Munaò et al. Soft Matter 2013, 9, 2652). Here, we demonstrate by means of free-energy calculations that such a disordered tube phase, despite forming spontaneously from the fluid phase below a density-dependent temperature, is always metastable against a lamellar crystal. We also show that a crystal of infinitely long packed tubes is thermodynamically stable, but only at high pressure. The full phase diagram of the model, beside the fluid phase, displays four different stable crystals. A gas-liquid critical point, and hence a liquid phase, is not detected.