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Nucleation plays a critical role in the birth of crystals and is associated with a vast array of phenomena, such as protein crystallization and ice formation in clouds. Despite numerous experimental and theoretical studies, many aspects of the nucleation process, such as the polymorph selection mechanism in the early stages, are far from being understood. Here, we show that the hitherto unexplained excess of particles in a face-centered-cubic (fcc)-like environment, as compared to those in a hexagonal-close-packed (hcp)-like environment, in a crystal nucleus of hard spheres can be explained by the higher order structure in the fluid phase. We show using both simulations and experiments that in the metastable fluid phase, pentagonal bipyramids, clusters with fivefold symmetry known to be inhibitors of crystal nucleation, transform into a different cluster, Siamese dodecahedra. These clusters are closely similar to an fcc subunit, which explains the higher propensity to grow fcc than hcp in hard spheres. We show that our crystallization and polymorph selection mechanism is generic for crystal nucleation from a dense, strongly correlated fluid phase.

Leveraging the anisotropic shape of DNA-functionalized nanoparticles holds potential for shape-directed crystallization of a wide collection of superlattice structures. Using coarse-grained molecular dynamics simulations, we study the self-assembly of a binary mixture of cubic gold nanoparticles, which are functionalized by complementary DNA strands. We observe the spontaneous self-assembly of simple cubic (SC), plastic body-centered tetragonal (pBCT), and compositionally disordered plastic body-centered tetragonal (d-pBCT) phases due to hybridization of the DNA strands. We systematically investigate the effect of length, grafting density, as well as rigidity of the DNA strands on the self-assembly behavior of cubic nanoparticles. We measure the potential of mean force between DNA-functionalized nanocubes for varying rigidity of the DNA strands and DNA lengths. Using free-energy calculations, we find that longer and flexible DNA strands can lead to a phase transformation from SC to the pBCT phase due to a gain in entropy arising from the orientational degrees of freedom of the nanocubes in the pBCT phase. Our results may serve as a guide for self-assembly experiments on DNA-functionalized cubic nanoparticles.

We introduce a machine-learning approach to predict the complex non-Markovian dynamics of supercooled liquids from static averaged quantities. Compared to techniques based on particle propensity, our method is built upon a theoretical framework that uses as input and output system-averaged quantities, thus being easier to apply in an experimental context where particle resolved information is not available. In this work, we train a deep neural network to predict the self intermediate scattering function of binary mixtures using their static structure factor as input. While its performance is excellent for the temperature range of the training data, the model also retains some transferability in making decent predictions at temperatures lower than the ones it was trained for, or when we use it for similar systems. We also develop an evolutionary strategy that is able to construct a realistic memory function underlying the observed non-Markovian dynamics. This method lets us conclude that the memory function of supercooled liquids can be effectively parameterized as the sum of two stretched exponentials, which physically corresponds to two dominant relaxation modes.

Using a grand-canonical Landau-de Gennes theory for colloidal suspensions of bent (banana-shaped) rods, we investigate how spatial deformations in the nematic director field affect the local density of twist-bend and splay-bend nematic phases. The grand-canonical character of the theory naturally relates the local density to the local nematic order parameter S. In the splay-bend phase, we find S and hence the local density to modulate periodically along one spatial direction. As a consequence the splay-bend phase has the key symmetries of a smectic rather than a nematic phase. By contrast we find that S and hence the local density do not vary in space in the twist-bend phase, which is therefore a proper nematic phase. The theoretically predicted one-dimensional density modulations in splay-bend phases are in agreement with recent simulations.

Combinatorial metamaterials are metamaterials designed by combining fundamental building blocks, unit cells, picked from a discrete set. This discretized design space allows us to explore the limitless structural complexity of metamaterials in a controlled manner. However, analytical and conventional numerical approaches have difficulty in efficiently navigating this large design space, which grows exponentially with system size. Here we employ machine learning techniques to explore combinatorial metamaterial designs. We show that a trained convolutional neural network is able to classify never before seen configurations into those supporting system-wide periodic deformations in one dimension, line modes, and those who do not with over 99% accuracy. This suggests that the network has correctly learned to identify the set of design rules for the presence of a line mode. To study the scalability of this long-correlation classification problem, we investigate the relation between network complexity and configuration size. Our work provides insight into application and scaling of neural networks with regard to complex discrete structure-property maps.

Using computer simulations, we study the isotropic-to-nematic nucleation in a fluid of colloidal hard rods as well as in a mixture of colloidal rods and non-adsorbing polymer. In order to follow the transformation of the system from the isotropic to the nematic phase, we use a new cluster criterion that enables us to distinguish the nematic clusters from the isotropic fluid phase. Applying this criterion in Monte Carlo simulations, we find two different regimes depending on the supersaturation. At low supersaturation we find nucleation and growth, while at higher supersaturation spinodal decomposition is observed. We determine the height of the nucleation barrier, and we study the structure as well as the shape of the nematic clusters. We discuss our simulation results in the light of classical nucleation theory.

Using simulations, we study the diffusion of rod-like guest particles in a smectic environment of rod-like host particles. We find that the dynamics of guest rods across smectic layers changes from a fast nematic-like diffusion to a slow hopping-type dynamics via an intermediate switching regime by varying the length of the guest rods with respect to the smectic layer spacing. We determine the optimal rod length that yields the fastest and the slowest diffusion in a lamellar environment. We show that this behavior can be rationalized by a complex 1D effective periodic potential exhibiting two energy barriers, resulting in a varying preferred mean position of the guest particle in the smectic layer. The interplay of these two barriers controls the dynamics of the guest particles yielding a slow, an intermediate and a fast diffusion regime depending on the particle length., To be published in Physical Review Letters

The influence of geometry on the local and global packing of particles is important to many fundamental and applied research themes, such as the structure and stability of liquids, crystals and glasses. Here we show by experiments and simulations that a binary mixture of hard-sphere-like nanoparticles crystallizing into a MgZn(2)Laves phase in bulk spontaneously forms icosahedral clusters in slowly drying droplets. Using advanced electron tomography, we are able to obtain the real-space coordinates of all the spheres in the icosahedral clusters of up to about 10,000 particles. The local structure of 70-80% of the particles became similar to that of the MgCu(2)Laves phase. These observations are important for photonic applications. In addition, we observed in simulations that the icosahedral clusters nucleated away from the spherical boundary, which is distinctly different from that of the single species clusters. Our findings open the way for particle-level studies of nucleation and growth of icosahedral clusters, and of binary crystallization. The authors investigate out-of-equilibrium crystallization of a binary mixture of sphere-like nanoparticles in small droplets. They observe the spontaneous formation of an icosahedral structure with stable MgCu(2)phases, which are promising for photonic applications.

We studied the formation of supraparticles from nanocrystals confined in slowly evaporating oil droplets in an oil-in-water emulsion. The nanocrystals consist of an FeO core, a CoFe2O4 shell, and oleate capping ligands, with an overall diameter of 12.5 nm. We performed in situ small- and wide-angle X-ray scattering experiments during the entire period of solvent evaporation and colloidal crystallization. We observed a slow increase in the volume fraction of nanocrystals inside the oil droplets up to 20%, at which a sudden crystallization occurs. Our computer simulations show that crystallization at such a low volume fraction is only possible if attractive interactions between colloidal nanocrystals are taken into account in the model as well. The spherical supraparticles have a diameter of about 700 nm and consist of a few crystalline face-centered cubic domains. Nanocrystal supraparticles bear importance for magnetic and optoelectronic applications, such as color tunable biolabels, color tunable phosphors in LEDs, and miniaturized lasers.

Periodic nano- or microscale structures are used to control light, energy and mass transportation. Colloidal organization is the most versatile method used to control nano- and microscale order, and employs either the enthalpy-driven self-assembly of particles at a low concentration or the entropy-driven packing of particles at a high concentration. Nonetheless, it cannot yet provide the spontaneous three-dimensional organization of multicomponent particles at a high concentration. Here we combined these two concepts into a single strategy to achieve hierarchical multicomponent materials. We tuned the electrostatic attraction between polymer and silica nanoparticles to create dynamic supracolloids whose components, on drying, reorganize by entropy into three-dimensional structured materials. Cryogenic electron tomography reveals the kinetic pathways, whereas Monte Carlo simulations combined with a kinetic model provide design rules to form the supracolloids and control the kinetic pathways. This approach may be useful to fabricate hierarchical hybrid materials for distinct technological applications.

Reviews of modern physics 91(3), 030001 (2019). doi:10.1103/RevModPhys.91.030001, Ninety years! As the first spinoff of the Physical Review launched in 1929, Reviews of ModernPhysics (RMP) has tracked the progress of physics during a time of explosive growth of the field.Originally one journal, the Physical Review has not only split into the more specialized journals weknow today, but the scope, breadth, and depth of topics covered could hardly have been imagined byJohn Tate, Sr., the editor in chief who started RMP. Yet RMP is still published quarterly. So whyhasn’t RMP grown at the same prodigious rate? The research that informs these reviews isprogressing faster, but writing a review that is broadly accessible and that will remain relevant fordecades has therefore become more difficult. RMP’s role is to find authors who are up to thischallenge.At the April 2019 editorial board meeting we resolved to reaffirm our mission of providing thecommunity with articles that capture the essence of the field, with introductions and conclusions thatare accessible to students (our most junior colleagues who will carry science into the future) and thatcommunicate how and why the topic has fascinated scientists and provided an arena for newparadigms, theories, and connections between subfields. To this end, we will implement even higherstandards for our submissions: not only will submitted manuscripts be reviewed by experts, they willalso be reviewed by qualified non-experts from nearby subfields to ensure broad accessibility.Though this is, of course, a greater burden on our referees and authors, we believe that it is necessaryto publish “classic” articles and keep RMP vital for many years to come.We look forward to continuing to serve the community., Published by APS, College Park, Md.

Assembling binary mixtures of nanoparticles into crystals, gives rise to collective properties depending on the crystal structure and the individual properties of both species. However, quantitative 3D real-space analysis of binary colloidal crystals with a thickness of more than 10 layers of particles has rarely been performed. Here we demonstrate that an excess of one species in the binary nanoparticle mixture suppresses the formation of icosahedral order in the self-assembly in droplets, allowing the study of bulk-like binary crystal structures with a spherical morphology also called supraparticles. As example of the approach, we show single-particle level analysis of over 50 layers of Laves phase binary crystals of hard-sphere-like nanoparticles using electron tomography. We observe a crystalline lattice composed of a random mixture of the Laves phases. The number ratio of the binary species in the crystal lattice matches that of a perfect Laves crystal. Our methodology can be applied to study the structure of a broad range of binary crystals, giving insights into the structure formation mechanisms and structure-property relations of nanomaterials., 3D real-space analysis of thick nanoparticle crystals is non-trivial. Here, the authors demonstrate the structural analysis of a bulk-like Laves phase by imaging an off-stoichiometric binary mixture of hard-sphere-like nanoparticles in spherical confinement by electron tomography, enabling defect analysis on the single-particle level.

Colloidal particles with site-specific directional interactions, so called “patchy particles”, are promising candidates for bottom-up assembly routes towards complex structures with rationally designed properties. Here we present an experimental realization of patchy colloidal particles based on material independent depletion interaction and surface roughness. Curved, smooth patches on rough colloids are shown to be exclusively attractive due to their different overlap volumes. We discuss in detail the case of colloids with one patch that serves as a model for molecular surfactants both with respect to their geometry and their interactions. These one-patch particles assemble into clusters that resemble surfactant micelles with the smooth and attractive sides of the colloids located at the interior. We term these clusters “colloidal micelles”. Direct Monte Carlo simulations starting from a homogeneous state give rise to cluster size distributions that are in good agreement with those found in experiments. Important differences with surfactant micelles originate from the colloidal character of our model system and are investigated by simulations and addressed theoretically. Our new “patchy” model system opens up the possibility for self-assembly studies into finite-sized superstructures as well as crystals with as of yet inaccessible structures.

One of the main reasons for the current interest in colloidal nanocrystals is their propensity to form superlattices, systems in which (different) nanocrystals are in close contact in a well-ordered three-dimensional (3D) geometry resulting in novel material properties. However, the principles underlying the formation of binary nanocrystal superlattices are not well understood. Here, we present a study of the driving forces for the formation of binary nanocrystal superlattices by comparing the formed structures with full free energy calculations. The nature (metallic or semiconducting) and the size-ratio of the two nanocrystals are varied systematically. With semiconductor nanocrystals, self-organization at high temperature leads to superlattices (AlB(2), NaZn(13), MgZn(2)) in accordance with the phase diagrams for binary hard-sphere mixtures; hence entropy increase is the dominant driving force. A slight change of the conditions results in structures that are energetically stabilized. This study provides rules for the rational design of 3D nanostructured binary semiconductors, materials with promises in thermoelectrics and photovoltaics and which cannot be reached by any other technology.

Binary colloidal crystals offer great potential for tuning material properties for applications in, for example, photonics, semiconductors and spintronics, because they allow the positioning of particles with quite different characteristics on one lattice. For micrometer-sized colloids, it is believed that gravity and slow crystallization rates hinder the formation of high-quality binary crystals. Here, we present methods for growing binary colloidal crystals with a NaCl structure from relatively heavy, hard-sphere-like, micrometer-sized silica particles by exploring the following external fields: electric, gravitational, and dielectrophoretic fields and a structured surface (colloidal epitaxy). Our simulations show that the free-energy difference between the NaCl and NiAs structures, which differ in their stacking of the hexagonal planes of the larger spheres, is very small (≈0.002 k B T ). However, we demonstrate that the fcc stacking of the large spheres, which is crucial for obtaining the pure NaCl structure, can be favored by using a combination of the above-mentioned external fields. In this way, we have successfully fabricated large, 3D, oriented single crystals having a NaCl structure without stacking disorder.

We study bulk and interfacial properties of a model suspension of hard colloidal platelets with continuous orientations and vanishing thickness using both density functional theory, based on either a second virial approach or fundamental measure theory (FMT), and Monte Carlo (MC) simulations. We calculate the bulk equation of state, bulk isotropic-nematic (IN) coexistence, and properties of the (planar) free IN interface and of adsorption at a planar hard wall, where we find complete wetting of the nematic phase at the isotropic-wall interface upon approaching bulk IN coexistence. We investigate in detail the asymptotic decay of correlations at large distances. In all cases, the results from FMT and MC agree quantitatively. Our findings are of direct relevance to understanding interfacial properties of dispersions of colloidal platelets.

In continuation of our work in [A.P. Gantapara et al., Phys. Rev. Lett. 111, 015501 (2013)], we investigate here the thermodynamic phase behavior of a family of truncated hard cubes, for which the shape evolves smoothly from a cube via a cuboctahedron to an octahedron. We used Monte Carlo simulations and free-energy calculations to establish the full phase diagram. This phase diagram exhibits a remarkable richness in crystal and mesophase structures, depending sensitively on the precise particle shape. In addition, we examined in detail the nature of the plastic crystal (rotator) phases that appear for intermediate densities and levels of truncation. Our results allow us to probe the relation between phase behavior and building-block shape and to further the understanding of rotator phases. Furthermore, the phase diagram presented here should prove instrumental for guiding future experimental studies on similarly-haped nanoparticles and the creation of new materials., Comment: 19 pages, 12 figures

We study various manifestations of structural crossover in the properties of a binary mixture of hard-spheres. For homogeneous mixtures that are sufficiently asymmetric, there is a crossover line in the phase diagram such that for thermodynamic states that lie on one side, the decay of the three bulk pair correlation functions is oscillatory with a common wavelength approximately equal to the diameter of the smaller spheres, and for states on the other side, the common wavelength is approximately the diameter of the bigger spheres. Using density functional theory we show that structural crossover manifests itself in the intermediate range decay of i) the one-body density profiles of a hard-sphere mixture adsorbed at planar walls, ii) the effective (depletion) potential between two big hard-spheres immersed in the same binary mixture and iii) the solvation force, or excess pressure, of the same mixture confined between two planar hard-walls. We determine exactly the structural crossover line for a one-dimensional binary mixture of hard-rods and present evidence, based on density functional theory calculations and Monte-Carlo simulations, for structural crossover in homogeneous binary mixtures of hard-disks in two dimensions. By considering a multicomponent mixture of hard-spheres, with an appropriate bimodal distribution of diameters, we argue that structural crossover should still occur in the presence of polydispersity and that our results could be relevant to colloidal mixtures where correlation functions can be measured using real-space techniques.

We study the adsorption and wetting behaviour of colloidal hard spheres and colloidal rod-like particles at a planar hard wall using computer simulations. Our results show complete wetting by the hard-sphere crystal at the wall–fluid interface, and complete wetting by the nematic phase of the hard-rod fluid at the wall–isotropic fluid interface. In addition, we investigated the effect of polymer-mediated effective interactions on the wetting behaviour of colloidal spheres. The many-body character of the effective colloidal interactions yields an adsorption behaviour that differs enormously from those found for pairwise simple fluids; e.g., far from the triple point, we find three layering transitions in the partial wetting regime prior to a transition to complete wetting by the colloidal liquid.

After a brief review of the theory of sedimentation equilibria of colloidal systems, we consider the specific case of binary systems of hard sphere colloids and non-interacting polymer coils, the latter of vanishing buoyancy mass. The density profiles of the two components are calculated within density functional theory and using Monte Carlo simulations. Under appropriate conditions the profiles exhibit discontinuities or steeply varying regions associated with the interface separating colloid-rich and colloid-poor phases. The position of the interface is shown to be very sensitive to the strength of the gravitational field and, more surprisingly, to the total height L of the suspension. Phase coexistence in the absence of gravity is shown to be entirely suppressed beyond a critical ratio of the height L over the gravitational length of the colloids.

Using density functional theory and Monte Carlo simulations we investigate the Asakura-Oosawa-Vrij mixture of hard sphere colloids and non-adsorbing ideal polymers under selective confinement of the colloids to a planar slab geometry. This is a model for confinement of colloid-polymer mixtures by either two parallel walls with a semi-permeable polymer coating or through the use of laser tweezers. We find that such a pore favours the colloidal gas over the colloidal liquid phase and induces capillary evaporation. A treatment based on the Kelvin equation gives a good account of the location of the capillary binodal for large slit widths. The colloid density profile is found to exhibit a minimum (maximum) at contact with the wall for large (small) slit widths.

We investigate the fluid-fluid demixing phase transition of the Asakura-Oosawa model colloid-polymer mixture confined between two smooth parallel hard walls using density functional theory and computer simulations. Comparing fluid density profiles for statepoints away from colloidal gas-liquid coexistence yields good agreement of the theoretical results with simulation data. Theoretical and simulation results predict consistently a shift of the demixing binodal and the critical point towards higher polymer reservoir packing fraction and towards higher colloid fugacities upon decreasing the plate separation distance. This implies capillary condensation of the colloid liquid phase, which should be experimentally observable inside slitlike micropores in contact with a bulk colloidal gas.

We summarize the main results of our recent investigations of the interfacial properties of the simplest model of a colloid-polymer mixture, namely that introduced by Asakura & Oosawa and by Vrij, in which colloidPcolloid and colloid-polymer interactions are treated as hard sphere-like, while the polymer-polymer interaction is ideal (perfectly interpenetrating coils). In spite of its simplicity, we find that the model exhibits rich interfacial behaviour which depends on the size ratio q = gp/oc, where or, and oc denote the diameters of polymer and colloid, respectively. For highly asymmetric mixtures: q < 0.1547, an explicit and exact mapping of the binary mixture to an effective one-component Hamiltonian for the colloids allows one to perform computer simulations for inhomogeneous mixtures. We investigate a mixture with g = 0.1 and find th a t small amounts of polymer give rise to strong depletion effects at a hard wall. The colloid density at contact with the wall is several times greater than that for pure hard spheres at a hard wall. However, for states removed from the bulk fluid-solid coexistence curve we find no evidence of wall-induced crystallization. In order to treat less asymmetric cases, where stable fluid-fluid demixing occurs in bulk, we have designed a density functional theory specifically for this model mixture. For q = 0.6 we find a first order wetting transition from partial to complete wetting by the colloid-rich phase at the hard-wall-colloid-poor interface as the packing fraction q; of polymer in the reservoir is decreased. At a slightly higher value of $, there is a novel single layering transition, characterized by a jump in the densities in the first two adsorbed layers, as the bulk colloid packing fraction rlc is increased. The same density functional has been used to investigate the surface tension and colloid and polymer density profiles at the free interface between the demixed fluid phases.

We study the effective interactions, structure, and the isothermal compressibility of a binary mixture interacting with pairwise additive pair potentials. By integrating out the degrees of freedom of species 2 in the partition sum we first show that a binary mixture can be mapped formally onto an effective one-component system with an effective Hamiltonian consisting of a structure-independent term, which contributes to the total pressure and chemical potential of the system, but does not affect the phase behavior, and a structure-dependent potential of mean force, which contains pair–, triplet–, and higher–body interactions. We then show that the 1-1 structure factor and pair correlation function, and the total isothermal compressibility of the mixture are equal to those of the effective one-component system, provided the mapping is exact. We illustrate and confirm these results by calculating the structure factors and pair correlation functions of the binary Asakura–Oosawa model, which is a simple model for colloid–polymer mixtures, and those of the corresponding one-component system for a size ratio such that the mapping onto an effective one-component Hamiltonian with a strictly pairwise potential of mean force is exact. The distinction between the osmotic and total compressibility of the mixture is emphasized.

We study a simple model for a wire which consists of alternate magnetic and non-magnetic segments. We are interested in the state of relative orientations of the disc-like magnetic segments. In particular, we investigated the ground state and the finite temperature phase diagram of the system, using ground state search, Mean field approximation and Monte Carlo simulations. We find a rich variety of orientational transitions.

Three's company: The first genuine ternary colloidal crystal (see picture) is composed of PbSe nanocrystals of two different diameters (blue and green) and of CdSe nanocrystals (red). Electron tomography shows that the superlattice is isostructural with the atomic lattice AIMgB4.

We show the existence of a fluid-fluid demixing transition in binary mixtures of nonadditive asymmetric hard-sphere mixtures by performing Gibbs ensemble Monte Carlo simulations for a size ratio of 0.1 and varying degrees of nonadditivity. We compare our results with the theoretical binodals obtained from the equation of state proposed by Barboy and Gelbart [J. Chem. Phys. 71, 3053 (1979)] and we find reasonable agreement for sufficiently large values of the nonadditivity parameter. Upon decreasing the nonadditivity parameter, we find that the fluid-fluid demixing region shifts to higher pressures and becomes narrower. For sufficiently small nonadditivities, we do not find a fluid-fluid demixing transition for total packing fractions $l0.5.$

We present a computer simulation study of a binary mixture of hard spherocylinders with different diameters (D1,D2) and the same lengths (L15L25L). We first study a mixture of spherocylinders with lengths L 515D2 and D150, which can be regarded as a mixture of rodlike colloids and ideal needles. We find clearly an entropy-driven isotropic-isotropic (I-I) demixing transition in this mixture. In addition, we study a mixture of spherocylinders with diameter ratio D1 /D250.1 and we investigated the I-I demixing transition as a function of the length L of the particles. We observe a stable I-I demixing for all values of L in the range of 3

We report computer simulations in the Grand canonical ensemble of a system of several alkanes between two solid surfaces. We computed the solvation force exerted by the fluid on the plates. The solvation force for linear decane oscillates with distance with a periodicity close to the width of the molecules. The branched alkanes ~2-methylundecane and 2-methylheptane! show a similar oscillatory behavior, however the oscillations are decreased and are shifted to the attractive regime. In addition, we computed the liquid-vapour equilibria by using Gibbs ensemble Monte-Carlo simulations of n-pentane confined in a slit of 9, 13, 17 Å. The critical temperature of the liquid-vapour coexistence shifts to lower temperatures upon confining. At a plate separation of 5 Å, no liquid-vapour equilibrium is found.