How to design an icosahedral quasicrystal through directional bonding.

Icosahedral quasicrystals (IQCs) are materials that exhibit long-range order but lack periodicity in any direction. Although IQCs were the first reported quasicrystals1, they have been experimentally observed only in metallic alloys2, not in other materials. By contrast, quasicrystals with other symmetries (particularly dodecagonal) have now been found in several soft-matter systems3-5. Here we introduce a class of IQCs built from model patchy colloids that could be realized experimentally using DNA origami particles. Our rational design strategy leads to systems that robustly assemble in simulations into a target IQC through directional bonding. This is illustrated for both body-centred and primitive IQCs, with the simplest systems involving just two particle types. The key design feature is the geometry of the interparticle interactions favouring the propagation of an icosahedral network of bonds, despite this leading to many particles not being fully bonded. As well as furnishing model systems in which to explore the fundamental physics of IQCs, our approach provides a potential route towards functional quasicrystalline materials.

Phases of surface-confined trivalent colloidal particles.

Patchy colloids promise the design and modelling of complex materials, but the realization of equilibrium patchy particle structures remains challenging. Here, we assemble pseudo-trivalent particles and elucidate their phase behaviour when confined to a plane. We observe the honeycomb phase, as well as more complex amorphous network and triangular phases. Structural analysis performed on the three condensed phases reveals their shared structural motifs. Using a combined experimental and simulation approach, we elucidate the energetics of these phases and construct the phase diagram of this system, using order parameters to determine the phase coexistence lines. Our results reveal the rich phase behaviour that a relatively simple patchy particle system can display, and open the door to a larger joined simulation and experimental exploration of the full patchy-particle phase space.

Structural characterization of systems with competing interactions confined in narrow spherical shells.

Systems with short-range attraction and long-range repulsion can form ordered microphases in bulk and under confinement. In fact, confinement has been proven to be a good strategy to induce the formation of novel ordered microphases that might be appealing to the development of functional nanomaterials. Using Grand Canonical Monte Carlo (GCMC) simulations, we study a model colloidal system with competing interactions under confinement in narrow spherical shells at thermodynamic conditions under which the hexagonal phase is stable in bulk. We observe the formation of three parent ordered structures formed by toroidal clusters and two spherical clusters (Type I), toroidal clusters and one spherical cluster (Type II), and toroidal clusters alone (Type III), depending on the radius of the confining shell, that can often coexist with other related structures derived from these parent ones by a simple transformation, in which the system is divided into two hemispheres that are rotated with respect to each other by a given angle. We propose a general method to characterize and predict the structures obtained under confinement in spherical shells in systems able to self-assemble into a hexagonal phase in bulk. We also show that deforming the spherical shells into ellipsoidal ones affects the structure of the system in such a way that helical structures are favoured by prolate ellipsoids and toroidal structures by oblate ellipsoids.

Estimation of bubble cavitation rates in a symmetrical Lennard-Jones mixture by NVT seeding simulations.

The liquid-vapor transition starts with the formation of a sufficiently large bubble in the metastable liquid to trigger the phase transition. Understanding this process is of fundamental and practical interest, but its study is challenging because it occurs over timescales that are too short for experiments but too long for simulations. The seeding method estimates cavitation rates by simulating a liquid in which a bubble is inserted, thus avoiding the long times needed for its formation. In one-component systems, in the NpT ensemble, the bubble grows or redissolves depending on whether its size is larger or smaller than the critical size, whereas in the NVT ensemble (i.e., at constant number of particles, volume, and temperature), the critical bubble can remain in equilibrium. Provided that a good criterion is used to determine the bubble size, this method, combined with the Classical Nucleation Theory (CNT), gives cavitation rates consistent with those obtained by methods independent of the CNT. In this work, the applicability of NVT seeding to homogeneous cavitation in mixtures is demonstrated, focusing on a partially miscible symmetrical binary Lennard-Jones (LJ) liquid at a temperature within the mixing regime. At the same stretching pressure, cavitation rates are higher in the binary mixture than in the pure liquid due to the lower interfacial free energy of the mixture. Curiously, the cost of creating a bubble is similar in the pure and binary LJ liquids at the same metastability, Δµ/Δµspin, with Δµ being the difference in chemical potential between the metastable liquid and coexistence, and Δµspin between the spinodal and coexistence.

Freezing point depression of salt aqueous solutions using the Madrid-2019 model.

Salt aqueous solutions are relevant in many fields, ranging from biological systems to seawater. Thus, the availability of a force-field that is able to reproduce the thermodynamic and dynamic behavior of salt aqueous solutions would be of great interest. Unfortunately, this has been proven challenging, and most of the existing force-fields fail to reproduce much of their behavior. In particular, the diffusion of water or the salt solubility are often not well reproduced by most of the existing force-fields. Recently, the Madrid-2019 model was proposed, and it was shown that this force-field, which uses the TIP4P/2005 model for water and non-integer charges for the ions, provides a good description of a large number of properties, including the solution densities, viscosities, and the diffusion of water. In this work, we assess the performance of this force-field on the evaluation of the freezing point depression. Although the freezing point depression is a colligative property that at low salt concentrations depends solely on properties of pure water, a good model for the electrolytes is needed to accurately predict the freezing point depression at moderate and high salt concentrations. The coexistence line between ice and several salt aqueous solutions (NaCl, KCl, LiCl, MgCl2, and Li2SO4) up to the eutectic point is estimated from direct coexistence molecular dynamics simulations. Our results show that this force-field reproduces fairly well the experimentally measured freezing point depression with respect to pure water freezing for all the salts and at all the compositions considered.

Formation and internal ordering of periodic microphases in colloidal models with competing interactions.

Theory and simulations predict that colloidal particles with short-range attractive and long-range repulsive interactions form periodic microphases if there is a proper balance between the attractive and repulsive contributions. However, the experimental identification of such structures has remained elusive to date. Using molecular dynamics simulations, we investigate the phase behaviour of a model system that stabilizes a cluster-crystal, a cylindrical and a lamellar phase at low temperatures. Besides the transition from the fluid to the periodic microphases, we also observe the internal freezing of the clusters at a lower temperature. Finally, our study indicates that, for the chosen model parameters, the three periodic microphases are kinetically accessible from the fluid phase.

Programming patchy particles to form three-dimensional dodecagonal quasicrystals.

Model patchy particles have been shown to be able to form a wide variety of structures, including symmetric clusters, complex crystals, and even two-dimensional quasicrystals. Here, we investigate whether we can design patchy particles that form three-dimensional quasicrystals, in particular targeting a quasicrystal with dodecagonal symmetry that is made up of stacks of two-dimensional quasicrystalline layers. We obtain two designs that are able to form such a dodecagonal quasicrystal in annealing simulations. The first is a one-component system of seven-patch particles but with wide patches that allow them to adopt both seven- and eight-coordinated environments. The second is a ternary system that contains a mixture of seven- and eight-patch particles and is likely to be more realizable in experiments, for example, using DNA origami. One interesting feature of the first system is that the resulting quasicrystals very often contain a screw dislocation.

Structural and Dynamical Behaviour of Colloids with Competing Interactions Confined in Slit Pores.

Systems with short-range attractive and long-range repulsive interactions can form periodic modulated phases at low temperatures, such as cluster-crystal, hexagonal, lamellar and bicontinuous gyroid phases. These periodic microphases should be stable regardless of the physical origin of the interactions. However, they have not yet been experimentally observed in colloidal systems, where, in principle, the interactions can be tuned by modifying the colloidal solution. Our goal is to investigate whether the formation of some of these periodic microphases can be promoted by confinement in narrow slit pores. By performing simulations of a simple model with competing interactions, we find that both the cluster-crystal and lamellar phases can be stable up to higher temperatures than in the bulk system, whereas the hexagonal phase is destabilised at temperatures somewhat lower than in bulk. Besides, we observed that the internal ordering of the lamellar phase can be modified by changing the pore width. Interestingly, for sufficiently wide pores to host three lamellae, there is a range of temperatures for which the two lamellae close to the walls are internally ordered, whereas the one at the centre of the pore remains internally disordered. We also find that particle diffusion under confinement exhibits a complex dependence with the pore width and with the density, obtaining larger and smaller values of the diffusion coefficient than in the corresponding bulk system.

Rounded Layering Transitions on the Surface of Ice.

Understanding the wetting properties of premelting films requires knowledge of the film's equation of state, which is not usually available. Here we calculate the disjoining pressure curve of premelting films and perform a detailed thermodynamic characterization of premelting behavior on ice. Analysis of the density profiles reveals the signature of weak layering phenomena, from one to two and from two to three water molecular layers. However, disjoining pressure curves, which closely follow expectations from a renormalized mean field liquid state theory, show that there are no layering phase transitions in the thermodynamic sense along the sublimation line. Instead, we find that transitions at mean field level are rounded due to capillary wave fluctuations. We see signatures that true first order layering transitions could arise at low temperatures, for pressures between the metastable line of water-vapor coexistence and the sublimation line. The extrapolation of the disjoining pressure curve above water-vapor saturation displays a true first order phase transition from a thin to a thick film consistent with experimental observations.

The influence of confinement on the structure of colloidal systems with competing interactions.

Colloidal systems with competing interactions have a complex phase diagram with several periodic microphases, in which particles are arranged in lamellae, cylinders or clusters. Using grand canonical Monte Carlo simulations, we investigate how the structure of the colloidal fluid can be modified by confinement in channels with different cross-section geometries and sizes. We pay particular attention to the hexagonal cylindrical phase since it is the most susceptible to form new structures from. In particular, we considered pores with elliptical, triangular, squared, hexagonal, and wedged-cylindrical cross-sections. Our results show that the structure of the confined fluid depends on the commensurability of the bulk periodic structure with the confining cross-section of the channel. We also find that the structure of the confined fluid can be modified by inserting wedges of appropriate geometry and size. These geometrical modifications of the confining pores can be exploited for the controlled assembly of colloidal structures.

Assembly of Helical Structures in Systems with Competing Interactions under Cylindrical Confinement.

The behavior under confinement of nanoparticles interacting with the short-range attraction and long-range repulsion potential is studied by means of Monte Carlo simulations in the grand canonical ensemble. The study is performed at thermodynamic conditions at which a hexagonal cylindrical phase is the most stable phase in bulk. In these conditions, cylindrical confinement promotes the formation of helical structures whose morphology depends upon both the pore radius and boundary conditions. As the pore radius increases, the fluid undergoes a series of structural transitions going from single to multiple intertwined helices to concentric helical structures. When the pore ends are closed by planar walls, ring and toroidal clusters are formed next to these walls. Dependent upon the cylinder length, molecules away from the pore edges can either keep growing into ring and toroidal aggregates or arrange into helical structures. It is demonstrated that the system behaves in cylindrical confinement in the same way as the block copolymer systems. Such behavior has not been observed for the colloidal systems in cylindrical confinement with only repulsive interactions.

Structure and water attachment rates of ice in the atmosphere: role of nitrogen.

In this work we perform computer simulations of the ice surface in order to elucidate the role of nitrogen in the crystal growth rates and crystal habits of snow in the atmosphere. In pure water vapor at temperatures typical of ice crystal formation in cirrus clouds, we find that basal and primary prismatic facets exhibit a layer of premelted ice, with thickness in the subnanometer range. For partial pressures of 1 bar, well above the expected values in the troposphere, we find that only small amounts of nitrogen are adsorbed. The adsorption takes place onto the premelted surface, and hardly any nitrogen dissolves within the premelting film. The premelting film thickness does not change either. We quantify the resulting change of the ice/vapor surface tension to be in the hundredth of mN m-1 and find that the structure of the pristine ice surface is not changed in a significant manner. We perform a trajectory analysis of colliding water molecules, and find that the attachment rates from direct ballistic collision are very close to unity irrespective of the nitrogen pressure. Nitrogen is however at sufficient density to deflect a fraction of trajectories with smaller distance than the mean free path. Our results show explicitly that the reported differences in growth rates measured in pure water vapor and a controlled nitrogen atmosphere are not related to a significant disruption of the ice surface due to nitrogen adsorption. On the contrary, we show clearly from our trajectory analysis that nitrogen slows down the crystal growth rates due to collisions between water molecules with bulk nitrogen gas. This clarifies the long standing controversy of the role of inert gases on crystal growth rates and demonstrates their influence is solely related to the diffusion limited flow of water vapor across the gas phase.

Nucleation of pseudo hard-spheres and dumbbells at moderate metastability: appearance of A15 Frank-Kasper phase at intermediate elongations.

Crystal nucleation of repulsive hard-dumbbells from the sphere to the two tangent spheres limit is investigated at moderately high metastability by brute-force molecular dynamics simulations. Nucleation rates are in good agreement with previous simulations of hard-spheres and dumbbells. Icosahedral structures formed by twinned face-centred-cubic tetrahedra sharing five-fold symmetry axes and icosahedral centers are often found in spheres and dumbbells with either small (L/σ = 0.1 and 0.2) and large (L/σ = 1) elongations. These structures are incompatible with long range crystalline order but are able to survive up to quite large sizes. In contrast, at intermediate elongations (L/σ = 0.3), corresponding roughly to the bond length of molecular nitrogen, the fluid crystallizes into three distinct solid structures, namely, a low density plastic crystal, a hexagonal close-packed plastic crystal (with the same structure as ß-N2), and an A15 Frank-Kasper phase (cP8 structure corresponding to δ-N2). At the lower pressures studied the hexagonal close packed plastic crystal is the most stable phase, but at the higher pressures the stable phase is an orientationally ordered solid designated as CP1 that is never spontaneously formed in our crystallization simulations.

Programming patchy particles to form complex periodic structures.

We introduce a scheme to design patchy particles so that a given target crystal is the global free-energy minimum at sufficiently low temperature. A key feature is a torsional component to the potential that only allows binding when particles have the correct relative orientations. In all examples studied, the target crystal structures readily assembled on annealing from a low-density fluid phase, albeit with the simpler target structures assembling more rapidly. The most complex example was a clathrate with 46 particles in its primitive unit cell. We also explored whether the structural information encoded in the particle interactions could be further reduced. For example, removing the torsional restrictions led to the assembly of an alternative crystal structure for the BC8-forming design, but the more complex clathrate design was still able to assemble because of the greater remaining specificity.

Assembly of clathrates from tetrahedral patchy colloids with narrow patches.

Here, we revisit the assembly of colloidal tetrahedral patchy particles. Previous studies have shown that the crystallization of diamond from the fluid phase depends more critically on patch width than on the interaction range: particles with patches narrower than 40° crystallize readily and those with wide patches form disordered glass states. We find that the crystalline structure formed from the fluid also depends on the patch width. Whereas particles with intermediate patches assemble into diamond (random stacking of cubic and hexagonal diamond layers), particles with narrow patches (with width ≈20° or less) crystallize frequently into clathrates. Free energy calculations show that clathrates are never (in the pressure-temperature plane) thermodynamically more stable than diamond. The assembly of clathrate structures is thus attributed to kinetic factors that originate from the thermodynamic stabilization of pentagonal rings with respect to hexagonal ones as patches become more directional. These pentagonal rings present in the fluid phase assemble into sII clathrate or into large clusters containing 100 particles and exhibiting icosahedral symmetry. These clusters then grow by interpenetration. Still, the organization of these clusters into extended ordered structures was never observed in the simulations.

Adsorption of water, methanol, and their mixtures in slit graphite pores.

The behavior of water, methanol, and water-methanol mixtures confined in narrow slit graphite pores as a function of pore size was investigated by Monte Carlo, hybrid Monte Carlo, and Molecular Dynamics simulations. Interactions were described using TIP4P/2005 for water, OPLS/2016 for methanol, and cross interactions fitted to excess water/methanol properties over the whole range of concentrations, which provide a rather accurate description of water-methanol mixtures. As expected for hydrophobic pores, whereas pure methanol is adsorbed already from the gas phase, pure water only enters the pore at pressures well beyond bulk saturation for all pore sizes considered. When adsorbed from a mixture, however, water adsorbs at much lower pressures due to the formation of hydrogen bonds with previously adsorbed methanol molecules. For all studied compositions and pore sizes, methanol adsorbs preferentially over water at liquid-vapor equilibrium conditions. In pure components, both water and methanol are microscopically structured in layers, the number of layers increasing with pore size. This is also the case in adsorbed mixtures, in which methanol has a higher affinity for the walls. This becomes more evident as the pore widens. Diffusion of pure water is higher than that of pure methanol for all pore sizes due to the larger size of the methyl group. In mixtures, both components present similar diffusivities at all pore sizes, which is explained in terms of the coupling of molecular movements due to strong hydrogen bonding between methanol and water molecules. This is particularly evident in very narrow pores, in which pure methanol diffusion is completely impeded on the time scale of our simulations, but the presence of a small amount of water molecules facilitates alcohol diffusion following a single-file mechanism. Additionally, our results indicate that pure water diffusivities display a non-monotonous dependence of pore size, due to effects of confinement (proximity to a fluid-solid-fluid transition induced by confinement as reported in previous work) and the dynamic anomalies of water.

Study of Short-Chain Alcohol and Alcohol-Water Adsorption in MEL and MFI Zeolites.

In this paper, we present a comparative study of the adsorption behavior of short chain alcohols (pure and in aqueous solution) into silicalite-1 (MFI-type zeolite) and silicalite-2 (MEL-type zeolite). For quite some time, silicalite-1 has been the reference material to address the problem of adsorptive-based separation, mostly for hydrocarbon mixtures. Interestingly, being structurally close to silicalite-1, adsorption studies using silicalite-2 are scarce and to the best of our knowledge, a comparative study of their behavior for alcohol-water mixtures has not been published to date. We have here resorted to molecular simulation techniques to analyze the adsorption and diffusion phenomena in both zeolites at 25 and 50 °C for pure methanol, ethanol, 1-butanol, and water, and for some relevant compositions of alcohol/water mixtures. In addition to the dilute regime in the mixture, our study ranges from intermediate alcohol concentrations to alcohol-rich phases, relevant to alcohol purification processes. Besides, we have performed volumetric and calorimetric measurements of single-component adsorption of alcohols in pure silica MEL zeolite, which were used to validate the model potentials used in the simulations. We observe that the zigzag channels of MFI zeolite are most likely responsible for its somewhat higher affinity for alcohols. This leads to higher adsorption selectivities when compared to those of MEL zeolite. We have also found that the choice of water model strongly conditions water coadsorption into the zeolites and subsequently the predictions of the adsorbent's selectivity in alcohol/water systems. Despite considerable differences for adsorbed pure components, diffusivities of alcohol and water adsorbed from mixtures are relatively similar, as a consequence of the strong hydrogen bonds between hydroxyl groups and water.

Assembly of trivalent particles under confinement: from an exotic solid phase to a liquid phase at low temperature.

Using computer simulations, we study the phase diagram of a two-dimensional system of disk particles with three patches distributed symmetrically along the particle equator. The geometry of the particles is compatible with a honey-comb lattice at moderately low temperature and pressure, whereas it is expected that the system forms a close-packed triangular lattice at high temperature and pressure. The effect of patch size within the single bond per patch regime was investigated, and it was found that the topology of the phase diagram changes drastically with patch size. Interestingly, in particles with small patches (with a half opening angle of 10°), the fluid transforms upon increasing the pressure into a rather exotic phase that can be understood as a honey-comb lattice whose voids are filled continuously with additional particles that remain, on average, unbound. Eventually, all the voids are occupied so that particles are located at the positions of a triangular lattice, but only two thirds of the particles are orientationally ordered whereas the remaining one third can rotate almost freely as in a plastic crystal. At moderately low temperature, the fluid transforms into a nearly empty honey-comb lattice, whereas at high temperature it transforms directly into the almost filled lattice. Interestingly, for particles with big patches (with a half opening angle of 20°), the honey-comb and triangular lattices are separated by a liquid phase that remains stable down to fairly low temperatures. Less surprisingly, only particles with big patches exhibit an equilibrium gas-liquid separation.