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.

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.

Visualizing defect dynamics by assembling the colloidal graphene lattice.

Graphene has been under intense scientific interest because of its remarkable optical, mechanical and electronic properties. Its honeycomb structure makes it an archetypical two-dimensional material exhibiting a photonic and phononic band gap with topologically protected states. Here, we assemble colloidal graphene, the analogue of atomic graphene using pseudo-trivalent patchy particles, allowing particle-scale insight into crystal growth and defect dynamics. We directly observe the formation and healing of common defects, like grain boundaries and vacancies using confocal microscopy. We identify a pentagonal defect motif that is kinetically favoured in the early stages of growth, and acts as seed for more extended defects in the later stages. We determine the conformational energy of the crystal from the bond saturation and bond angle distortions, and follow its evolution through the energy landscape upon defect rearrangement and healing. These direct observations reveal that the origins of the most common defects lie in the early stages of graphene assembly, where pentagons are kinetically favoured over the equilibrium hexagons of the honeycomb lattice, subsequently stabilized during further growth. Our results open the door to the assembly of complex 2D colloidal materials and investigation of their dynamical, mechanical and optical properties.

Self-Assembly of Optimally Packed Cylindrical Clusters inside Spherical Shells.

Systems with short-range attraction and long-range repulsion can form ordered microphases in bulk and under confinement. Using grand canonical Monte Carlo simulations, we study a colloidal system with competing interactions under confinement in narrow spherical shells at thermodynamic conditions at which the hexagonal phase of cylindrical clusters is stable in bulk. We observe spontaneous formation of different ordered structures. The results of the simulations are in a very good agreement with the predictions of a simple mathematical model based on the geometry and optimal packing of colloidal clusters. The results of the simulations and the explanation provided by a relatively simple geometric model may be helpful in manufacturing copolymer nanocapsules and may indicate possible ways of coiling DNA strands on spherical objects.

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.

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.

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.

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.

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.

How ice grows from premelting films and water droplets.

Close to the triple point, the surface of ice is covered by a thin liquid layer (so-called quasi-liquid layer) which crucially impacts growth and melting rates. Experimental probes cannot observe the growth processes below this layer, and classical models of growth by vapor deposition do not account for the formation of premelting films. Here, we develop a mesoscopic model of liquid-film mediated ice growth, and identify the various resulting growth regimes. At low saturation, freezing proceeds by terrace spreading, but the motion of the buried solid is conveyed through the liquid to the outer liquid-vapor interface. At higher saturations water droplets condense, a large crater forms below, and freezing proceeds undetectably beneath the droplet. Our approach is a general framework that naturally models freezing close to three phase coexistence and provides a first principle theory of ice growth and melting which may prove useful in the geosciences.

Confinement of Colloids with Competing Interactions in Ordered Porous Materials.

In this work, we explore the possibility of promoting the formation of ordered microphases by confinement of colloids with competing interactions in ordered porous materials. For that aim, we consider three families of porous materials modeled as cubic primitive, diamond, and gyroid bicontinuous phases. The structure of the confined colloids is investigated by means of grand canonical Monte Carlo simulations in thermodynamic conditions at which either a cluster crystal or a cylindrical phase is stable in bulk. We find that by tuning the size of the unit cell of these porous materials, numerous novel ordered microphases can be produced, including cluster crystals arranged into close packed and open lattices as well as nonparallel cylindrical phases.

Surface phase transitions and crystal habits of ice in the atmosphere.

With climate modeling predicting a raise of at least 2°C by year 2100, the fate of ice has become a serious concern, but we still do not understand how ice grows (or melts). In the atmosphere, crystal growth rates of basal and prism facets exhibit an enigmatic temperature dependence and crossover up to three times in a range between 0° and -40°. Here, we use large-scale computer simulations to characterize the ice surface and identify a sequence of previously unidentified phase transitions on the main facets of ice crystallites. Unexpectedly, we find that as temperature is increased, the crystal surface transforms from a disordered phase with proliferation of steps to a smooth phase with small step density. This causes the anomalous increase of step free energies and provides the long sought explanation for the enigmatic crossover of snow crystal growth rates found in the atmosphere.

Micelle-directed chiral seeded growth on anisotropic gold nanocrystals.

Surfactant-assisted seeded growth of metal nanoparticles (NPs) can be engineered to produce anisotropic gold nanocrystals with high chiroptical activity through the templating effect of chiral micelles formed in the presence of dissymmetric cosurfactants. Mixed micelles adsorb on gold nanorods, forming quasihelical patterns that direct seeded growth into NPs with pronounced morphological and optical handedness. Sharp chiral wrinkles lead to chiral plasmon modes with high dissymmetry factors (~0.20). Through variation of the dimensions of chiral wrinkles, the chiroptical properties can be tuned within the visible and near-infrared electromagnetic spectrum. The micelle-directed mechanism allows extension to other systems, such as the seeded growth of chiral platinum shells on gold nanorods. This approach provides a reproducible, simple, and scalable method toward the fabrication of NPs with high chiral optical activity.

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.

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.