We study polymorph selection in a model of charged colloids, with a focus on the higher-order structure prior to and during nucleation. Specifically, we carry out molecular dynamics simulations of a repulsive Yukawa system with a slightly softened (Weeks-Chandler-Andersen) core. We consider the case where the interaction is long-ranged and the BCC crystal is stable, and also intermediate- and short-ranged cases where the FCC crystal is stable. We use two methods for structure identification, the topological cluster classification (TCC) [A. Malins et al., J. Chem. Phys. 139, 234506 (2013)] and the bond orientational order parameter analysis of W. Lechner and C. Dellago [J. Chem. Phys.129, 114707 (2008)]. Under conditions of high supersaturation, appropriate to experiments with colloids, we find that the system forms a precursor state in which the particles are hexagonally ordered. ~That is to say, the precursors are indistinguishable from an HCP crystal using the bond orientational order parameters. This ordering occurs at state points both when the body-centred cubic crystal is the stable phase, and also when the face-centred cubic crystal is stable. In all cases, the stable polymorph forms from the precursor phase in a second stage. Although at freezing, the fluid is very much more ordered when the interactions are short-ranged (when FCC is stable), at the supersaturations where nucleation occurs in our simulations, the higher-order structure of the metastable fluids is almost identical for the long-, short-, and intermediate-ranged systems when measured with the TCC.
In many systems, nucleation of a stable solid may occur in the presence of other (often more than one) metastable phases. These may be polymorphic solids or even liquid phases. In such cases, nucleation of the solid phase from the melt may be facilitated by the metastable phase because the latter can "wet" the interface between the parent and the daughter phases, even though there may be no signature of the existence of metastable phase in the thermodynamic properties of the parent liquid and the stable solid phase. Straightforward application of classical nucleation theory (CNT) is flawed her…
Most substances can crystallise into two or more different crystal lattices, called polymorphs. Despite this, there are no systems in which we can quantitatively predict the probability of one competing polymorph forming, instead of the other. We address this problem using large scale (hundreds of events) studies of the competing nucleation of the alpha and gamma polymorphs of glycine. In situ Raman spectroscopy is used to identify the polymorph of each crystal. We find that the nucleation kinetics of the two polymorphs is very different. Nucleation of the alpha polymorph starts off slowly but…
DNA-coated colloids can self-assemble into an incredible diversity of crystal structures, but applications of this technology are limited by poor understanding and control over the dynamical crystallization pathways. To address this challenge, we use microfluidics to quantify the self-assembly dynamics of DNA-programmed colloidal crystals, from thermally-activated nucleation through reaction-limited and diffusion-limited phases of crystal growth. Our detailed measurements of the temperature and concentration dependence of the kinetics at all stages along the crystallization pathway provide a s…
Understanding the driving forces behind the nucleation of different polymorphs is of great importance for material sciences and the pharmaceutical industry. This includes understanding the reaction coordinate that governs the nucleation process as well as correctly calculating the relative free energies of different polymorphs. Here we demonstrate, for the prototypical case of urea nucleation from melt, how one can learn such a 1-dimensional reaction coordinate as a function of pre-specified order parameters, and use it to perform efficient biased all-atom molecular dynamics simulations. The r…
We determine the full kinetic phase diagram for nucleation and growth of crystal phases in a suspension of charged colloids. We calculate nucleation barrier heights for face-centered cubic (fcc) and body-centered cubic (bcc) crystal phases for varying screening lengths and supersaturations using the seeding approach in extensive simulations. Using classical nucleation theory, we determine for the entire metastable fluid region the crystal polymorph with the lowest nucleation barrier. Surprisingly, we find a regime close to the triple point where metastable bcc can form due to a lower nucleatio…
When a system undergoes a transition from a liquid to a solid phase, it passes through multiple intermediate structures before reaching the final state. However, our knowledge on the exact pathways of this process is limited, mainly due to the difficulty of realizing direct observations. Here, we experimentally study the evolution of symmetry and density for various colloidal systems during liquid-to-solid phase transitions, and visualize kinetic pathways with single-particle resolution. We observe the formation of relatively-ordered precursor structures with different symmetries, which then c…
Using computer simulations we investigate the homogeneous crystal nucleation in suspensions of colloidal hard dumbbells. The free energy barriers are determined by Monte Carlo simulations using the umbrella sampling technique. We calculate the nucleation rates for the plastic crystal and the aperiodic crystal phase using the kinetic prefactor as determined from event driven molecular dynamics simulations. We find good agreement with the nucleation rates determined from spontaneous nucleation events observed in event driven molecular dynamics simulations within error bars of one order of magnit…
We survey our research on modeling the mechanisms of control of uniformity in growth of nanosize and colloid particles. The former are produced as nanocrystals, by burst-nucleation from solution. The latter, colloid-size particles, are formed by self-assembly (aggregation) of the nanocrystals. In the colloid particle synthesis, the two dynamical processes are coupled, and both are governed by diffusional transport of the respective building blocks (monomers). The interrelation of the two processes allows for synthesis of narrow size distribution colloid dispersions which are of importance in m…
We review theoretical explanation of mechanisms of control of uniformity in growth of nanosize particles and colloids. The nanoparticles are synthesized as nanocrystals, by burst nucleation from solution. The colloids are self-assembled by aggregation of these nanocrystals. The two kinetic processes are coupled, and both are driven by diffusional transport. The interrelation of the two processes allows for formation of narrow-size-distribution colloid dispersions which are of importance in many applications. We review a mathematical model of cluster growth by capture of diffusing "singlets." B…
We report a numerical study of the rate of crystal nucleation in a binary suspension of oppositely charged colloids. Two different crystal structures compete in the thermodynamic conditions under study. We find that the crystal phase that nucleates is metastable and, more surprisingly, its nucleation free energy barrier is not the lowest one. This implies that, during nucleation, there is insufficient time for sub-critical nuclei to relax to their lowest free-energy structure. Such behavior is in direct contradiction with the common assumption that the phase that crystallizes most readily is t…
Recent experiments have shown how nematically-ordered tactoid shaped actin droplets can be reorganized and divided by the action of myosin molecular motors. In this paper, we consider how similar morphological changes can potentially be achieved under equilibrium conditions. Using simulations, both atomistic and continuum, and a phenomenological model, we explore how the nucleation dynamics, shape changes, and the final steady state of a nematic tactoid droplet can be modified by interactions with model adhesive colloids that mimic a myosin motor cluster. Our results provide a prescription for…
We study the conditions under which and how an imposed cluster of fixed colloidal particles at prescribed positions triggers crystal nucleation from a metastable colloidal fluid. Dynamical density functional theory of freezing and Brownian dynamics simulations are applied to a two-dimensional colloidal system with dipolar interactions. The externally imposed nucleation clusters involve colloidal particles either on a rhombic lattice or along two linear arrays separated by a gap. Crystal growth occurs after the peaks of the nucleation cluster have first relaxed to a cutout of the stable bulk cr…
We explore crystallisation and polymorph selection in active Brownian particles with numerical simulation. In agreement with previous work [Wysocki $\textit{et al.}$ $\textit{Europhys. Lett.}$, $\textbf{105}$ 48004 (2014)], we find that crystallisation is suppressed by activity and occurs at higher densities with increasing $Péclet$ number ($Pe$). While the nucleation rate decreases with increasing activity, the crystal growth rate increases due to the accelerated dynamics in the melt. As a result of this competition we observe the transition from a nucleation and growth regime at high $Pe$ to…
The free energy landscape responsible for crystallization can be complex even for relatively simple systems like hard sphere and charged stabilized colloids. In this work, using hard-core repulsive Yukawa model, which is known to show complex phase behavior consisting of fluid, FCC and BCC phases, we studied the interplay between the free energy landscape and polymorph selection during crystallization. When the stability of the BCC phase with respect to the fluid phase is gradually increased by changing the temperature and pressure at a fixed fluid-FCC stability, the final phase formed by crys…
A recent description of diffusion-limited nucleation based on fluctuating hydrodynamics that extends classical nucleation theory predicts a very non-classical two-step scenario whereby nucleation is most likely to occur in spatially-extended, low-amplitude density fluctuations. In this paper, it is shown how the formalism can be used to determine the maximum probability of observing \emph{any} proposed nucleation pathway, thus allowing one to address the question as to their relative likelihood, including of the newly proposed pathway compared to classical scenarios. Calculations are presented…
We use Brownian Dynamics simulations in combination with the umbrella sampling technique to study the effect of shear flow on homogeneous crystal nucleation. We find that a homogeneous shear rate leads to a significant suppression of the crystal nucleation rate and to an increase of the size of the critical nucleus. A simple, phenomenological extension of classical nucleation theory accounts for these observations. The orientation of the crystal nucleus is tilted with respect to the shear direction.
Homogeneous nucleation is formulated within the context of fluctuating hydrodynamics. It is shown that for a colloidal or macromolecular system in the strong damping limit the most likely path for nucleation can be determined by gradient descent in density space governed by a nontrivial metric fixed by the dynamics. The theory provides a justification and extension of more heuristic equilibrium approaches based solely on the free energy. It is illustrated by application to liquid-vapor nucleation where it is shown that, in contrast to most free energy-based studies, the smallest clusters corre…
A recently formulated description of homogeneous nucleation for Brownian particles in the over-damped limit based on fluctuating hydrodynamics is used to determine the nucleation pathway, characterized as the most likely path (MLP), for the nucleation of a dense-concentration droplet of globular protein from a dilute solution in a small, finite container. The calculations are performed by directly discretizing the equations for the MLP and it is found that they confirm previous results obtained for infinite systems: the process of homogeneous nucleation begins with a long-wavelength, spatially…
A general theory of nucleation for colloids and macromolecules in solution is formulated within the context of fluctuating hydrodynamics. A formalism for the determination of nucleation pathways is developed and stochastic differential equations for the evolution of order parameters are given. The conditions under which the elements of Classical Nucleation Theory are recovered are determined. The theory provides a justification and extension of more heuristic equilibrium approaches based solely on the free energy. It is illustrated by application to the low-concentration/high-concentration tra…
The monomer surface mobility is the single most important parameter that decides the nucleation density and morphology of islands during thin film growth. During template-assisted surface growth in particular, low surface mobilities can prevent monomers from reaching target sites and this results in a partial to complete loss of nucleation control. While in atomic systems a broad range of surface mobilities can be readily accessed, for colloids, owing to their large size, this window is substantially narrow and therefore imposes severe restrictions in extending template-assisted growth techniq…
Mixtures of ideal polymers with hard spheres whose diameters are smaller than the radius of gyration of the polymer, exhibit extensive immiscibility. The interfacial tension between demixed phases of these mixtures is estimated, as is the barrier to nucleation. The barrier is found to scale linearly with the radius of the polymer, causing it to become large for large polymers. Thus for large polymers nucleation is suppressed and phase separation proceeds via spinodal decomposition, as it does in polymer blends.
The discrepancy in nucleation rate densities between simulated and experimental hard spheres remains staggering and unexplained. Suggestively, more strongly sedimenting colloidal suspensions of hard spheres nucleate much faster than weakly sedimenting systems. In this work we consider firstly the effect of sedimentation on the structure of colloidal hard spheres, by tuning the density mismatch between solvent and colloidal particles. In particular we investigate the effect on the degree of five fold symmetry present. Secondly we study the size of density fluctuations in these experimental syst…
We study the effect of shear flow on homogeneous crystal nucleation, using Brownian Dynamics simulations in combination with an umbrella sampling like technique. The symmetry breaking due to shear results in anisotropic radial distribution functions. The homogeneous shear rate suppresses crystal nucleation and leads to an increase of the size of the critical nucleus. These observations can be described by a simple, phenomenological extension of classical nucleation theory. In addition, we find that nuclei have a preferential orientation with respect to the direction of shear. On average the lo…
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 like the polymorph selection mechanism in the early stages are far from being understood. Here, we show that the excess of particles in a face-centred-cubic (fcc)-like environment with respect to those in a hexagonal-close-packed (hcp)-like environment in a crystal nucleus of hard spheres as observed in simulations and experiments can b…
Ice formation is ubiquitous in nature, with important consequences in a variety of environments, including biological cells, soil, aircraft, transportation infrastructure and atmospheric clouds. However, its intrinsic kinetics and microscopic mechanism are difficult to discern with current experiments. Molecular simulations of ice nucleation are also challenging, and direct rate calculations have only been performed for coarse-grained models of wate. For molecular models, only indirect estimates have been obtained, e.g. by assuming the validity of classical nucleation theory. We use a path sam…
We study low-salt, binary aqueous suspensions of charged colloidal spheres of size ratio Phi = 0.57, number densities below the eutectic number density n_E, and number fractions of p = 1.00-0.40. The typical phase obtained by solidification from a homogeneous shear-melt is a substitutional alloy of body centred cubic structure. In strictly gas-tight vials, the polycrystalline solid is stable against melting and further phase transformation for extended times. For comparison, we prepare the same samples also by slow and mechanically undisturbed deionization in commercial slit cells. These cells…
According to classical nucleation theory, a crystal grows from a small nucleus that already bears the symmetry of its end phase - but experiments with colloids now reveal that, from an amorphous precursor, crystallites with different structures can develop.
Ample experimental evidence has been accumulated demonstrating that the formation of monodispersed colloids proceeds through a more complex mechanism, than the generally excepted diffusional "burst nucleation" process. Instead, the synthesis of narrow-size-distribution colloidal dispersions involves several stages, i.e., nuclei produced in a supersaturated solution, grow to nanosize subunits, which then aggregate to form much larger uniform secondary particles. To explain the size selection in such a series of processes, a kinetic model was developed which combined two growth/aggregation stage…
Non-aligning self-propelled particles with purely repulsive excluded volume interactions undergo athermal motility-induced phase separation into a dilute gas and a dense cluster phase. Here, we use enhanced sampling computational methods and analytic theory to examine the kinetics of formation of the dense phase. Despite the intrinsically nonequilibrium nature of the phase transition, we show that the kinetics can be described using an approach analogous to equilibrium classical nucleation theory, governed by an effective free energy of cluster formation with identifiable bulk and surface term…
We present modeling approaches to explain mechanisms of control of uniformity (narrow distribution) of sizes and shapes in synthesis of nanosize crystals and micron-size colloids. We consider those situations when the nanocrystals are formed by burst nucleation. The colloids are then self-assembled by aggregation of nanocrystals. The coupled kinetic processes are both controlled by diffusional transport, yielding well-defined colloid dispersions used in many applications. We address aspects of modeling of particle structure selection, ranging from nucleation to growth by aggregation and to mec…
An understanding of homogeneous nucleation of crystalline structure from a disordered medium such as a liquid remains an important unsolved problem in condensed matter physics. Guided by the results from a number of experiments on granular and colloidal systems in the past two decades, including in particular observations of homogeneous nucleation in colloidal and granular systems, we suggest an alternative to the statistical mechanics approach to static granular matter initiated by Edwards and Oakeshott in 1989.
We report simulations on the homogeneous liquid-fcc nucleation of charged colloids for both low and high contact energy values. As a precursor for crystal formation, we observe increased local order at the position where the crystal will form, but no correlations with the local density. Thus, the nucleation is driven by order fluctuations rather than density fluctuations. Our results also show that the transition involves two stages in both cases, first a transition liquid-bcc, followed by a bcc-hcp/fcc transition. Both transitions have to overcome free energy barriers, so that a spherical bcc…
We study the kinetics of the liquid-to-crystal transformation and of gel formation in colloidal suspensions of oppositely charged particles. We analyse, by means of both computer simulations and experiments, the evolution of a fluid quenched to a state point of the phase diagram where the most stable state is either a homogeneous crystalline solid or a solid phase in contact with a dilute gas. On the one hand, at high temperatures and high packing fractions, close to an ordered-solid/disordered-solid coexistence line, we find that the fluid-to-crystal pathway does not follow the minimum free e…
Nucleation is an activated process in which the system has to overcome a free energy barrier in order for a first-order phase transition between the metastable and the stable phases to take place. In the liquid-to-solid transition the process occurs between phases of different symmetry, and it is thus inherently a multi-dimensional process, in which all symmetries are broken at the transition. In this Focus Article, we consider some recent studies which highlight the multi-dimensional nature of the nucleation process. Even for a single-component system, the formation of solid crystals from the…
We analyze the geometric structure and mechanical stability of a complete set of isostatic and hyperstatic sphere packings obtained via exact enumeration. The number of nonisomorphic isostatic packings grows exponentially with the number of spheres $N$, and their diversity of structure and symmetry increases with increasing $N$ and decreases with increasing hyperstaticity $H \equiv N_c - N_{ISO}$, where $N_c$ is the number of pair contacts and $N_{ISO} = 3N-6$. Maximally contacting packings are in general neither the densest nor the most symmetric. Analyses of local structure show that the fra…
The ability to design synthesis processes that are out of equilibrium has opened the possibility of creating nanomaterials with remarkable physico-chemical properties, choosing from a much richer palette of possible atomic architectures compared to equilibrium processes in extended systems. In this work, we employ atomistic simulations to demonstrate how to control polymorph selection via cooling rate during nanoparticle freezing in the case of Ni$_3$Al, a material with a rich structural landscape. State-of-the-art free-energy calculations allow to rationalize the complex nucleation process, d…
Charged colloids can behave as Yukawa systems, with similar phase behaviour. Using particle- resolved studies, we consider a system with an unusually long Debye screening length which forms crystals at low colloid volume fraction ϕ ~ 0.01. We quantitatively compare this system with the Yukawa model and find that its freezing point is compatible with the theoretical prediction but that the crystal polymorph is not always that expected. In particular we find body-centred cubic crystals where face-centred cubic crystals are expected.
The phase-field crystal model is by now widely used in order to predict crystal nucleation and growth. For colloidal solidification with completely overdamped individual particle motion, we show that the phase-field crystal dynamics can be derived from the microscopic Smoluchowski equation via dynamical density functional theory. The different underlying approximations are discussed. In particular, a variant of the phase-field crystal model is proposed which involves less approximations than the standard phase-field crystal model. We finally test the validity of these phase-field crystal model…
Motivated by old experiments on colloidal suspensions, we report molecular dynamics simulations of assemblies of hard spheres, addressing crystallization and glass formation. The simulations cover wide ranges of polydispersity s (standard deviation of the particle size distribution divided by its mean) and particle concentration. No crystallization is observed for s > 0.07. For 0.02 < s < 0.07, we find that increasing the polydispersity at a given concentration slows down crystal nucleation. The main effect here is that polydispersity reduces the supersaturation since it tends to stabilise the…
A widely spread method of crystal preparation is to precipitate it from a supersaturated solution. In such a process, control of solution concentration is of paramount importance. Nucleation process, polymorph selection, and crystal habits depend crucially on this thermodynamic parameter. When performing simulations in the canonical ensemble as the crystalline phase is deposited the solution is depleted of solutes. This unavoidable modification of the thermodynamic conditions leads to significant artifact. Here we adopt the idea of the constant chemical potential molecular dynamics approach of…
The lack of detailed balance in active colloidal suspensions allows dissipation to determine stationary states. Here we show that slow viscous flow produced by polar or apolar active colloids near plane walls mediates attractive hydrodynamic forces that drive crystallization. Hydrodynamically mediated torques tend to destabilize the crystal but stability can be regained through critical amounts of bottom-heaviness or chiral activity. Numerical simulations show that crystallization is not nucleational, as in equilibrium, but is preceded by a spinodal-like instability. Harmonic excitations of th…
We study crystal nucleation under the influence of sedimentation in a model of colloidal hard spheres via Brownian Dynamics simulations. We introduce two external fields acting on the colloidal fluid: a uniform gravitational field (body force), and a surface field imposed by pinning a layer of equilibrium particles (rough wall). We show that crystal nucleation is suppressed in proximity of the wall due to the slowing down of the dynamics, and that the spatial range of this effect is governed by the static length scale of bond orientational order. For distances from the wall larger than this le…
We performed dynamic simulations of spheres with short-range attractive interactions for many values of interaction strength and range. Fast crystallization occurs in a localized region of this parameter space, but the character of crystallization pathways is not uniform within this region. Pathways range from one-step, in which a crystal nucleates directly from a gas, to two-step, in which substantial liquid-like clusters form and only subsequently become crystalline. Crystallization can fail because of slow nucleation from either gas or liquid, or because of dynamic arrest caused by strong i…
Homogeneous nucleation process of polyethylene (PE) is studied with full-atom molecular dynamic simulation. To account the complex shape with low symmetry and the peculiar intra-chain conformational order of polymer, we introduce a shape descriptor OCB coupling conformational order and inter-chain rotational symmetry, which is able to differentiate hexagonal and orthorhombic clusters from melt. With the shape descriptor OCB, we find that coupling between conformational and inter-chain rotational orderings results in the formation of hexagonal clusters first, which is dynamic in nature. Whilst …
Computer simulations of the fluid-to-solid phase transition in the hard sphere system were instrumental for our understanding of crystallization processes. But while colloid experiments and theory have been predicting the stability of several binary hard sphere crystals for many years, simulations were not successful to confirm this phenomenon. Here, we report the growth of binary hard sphere crystals isostructural to Laves phases, AlB$_2$, and NaZn$_{13}$ in simulation directly from the fluid. We analyze particle kinetics during Laves phase growth using event-driven molecular dynamics simulat…
The nucleation of crystals from the liquid melt is often characterized by a competition between different crystalline structures or polymorphs, and can result in nuclei with heterogeneous compositions. These mixed-phase nuclei can display nontrivial spatial arrangements, such as layered and onion-like structures, whose composition varies according to the radial distance, and which so far have been explained on the basis of bulk and surface free-energy differences between the competing phases. Here we extend the generality of these non-classical nucleation processes, showing that layered and on…
