Stochastic hydrodynamics is a central tool in the study of first order phase transitions at a fundamental level. Combined with sophisticated free energy models, e.g. as developed in classical Density Functional Theory, complex processes such as crystallization can be modeled and information such as free energy barriers, nucleation pathways and the unstable eigenvector and eigenvalues determined. The latter are particularly interesting as they play key roles in defining the natural (unbiased) order parameter and the nucleation rate respectively. As is often the case, computational realities restrict the size of system that can be modeled and this makes it difficult to achieve experimental conditions for which the volume is effectively infinite. In this paper, the use of open boundary conditions is discussed. By using an open system, the calculations become much closer to experimental conditions however, the introduction of open boundary conditions raises a number of questions concerning the stochastic model such as whether the fluctuation-dissipation relation is preserved and whether stationary points on the free energy surface remain stationary points of the dynamics.

We present a fundamental framework for the study of crystallization based on a combination of classical density functional theory and fluctuating hydrodynamics that is free of any assumptions regarding order parameters and that requires no input other than molecular interaction potentials. We use it to study the nucleation of both droplets and crystalline solids from a low-concentration solution of colloidal particles using two different interaction potentials. We find that the nucleation pathways of both droplets and crystals are remarkably similar at the early stages of nucleation until they diverge due to a rapid ordering along the solid pathways in line with the paradigm of "non-classical" crystallization. We compute the unstable modes at the critical clusters and find that despite the non-classical nature of solid nucleation, the size of the nucleating clusters remains the principle order parameter in all cases, supporting a "classical" description of the dynamics of crystallization. We show that nucleation rates can be extracted from our formalism in a systematic way. Our results suggest that in some cases, despite the non-classical nature of the nucleation pathways, classical nucleation theory can give reasonable results for solids but that there are circumstances where it may fail. This contributes a nuanced perspective to recent experimental and simulation work, suggesting that important aspects of crystal nucleation can be described within a classical framework.

Impurities control the formation of bio-crystals and can fully paralyze crystal growth at low levels of supersaturation. Traditional impurity models predict that an escape from this so-called “dead zone” requires an increase in the driving force (i.e. supersaturation). In this work, using protein crystals as a model system, we uncover an alternative escape route from the dead zone that does not involve an increase in supersaturation. We demonstrate that the merger of a protein cluster with the crystal surface triggers the formation of an ordered multi-layered island. The newly created surface on top of the resulting 3D island is initially devoid of impurities and therefore characterized by near-pure step growth kinetics. The accelerated step advancement on this relatively uncontaminated surface limits the available time for impurities to adsorb on the emerging terraces and by extension their resulting surface density. Cluster-mediated crystal growth occurring in heterogeneous media can therefore lead to stop-and-go dynamics, which offers a new model to explain crystallization taking place under biological control (e.g. biomineralization).

Classical density functional theory for finite temperatures is usually formulated in the grand-canonical ensemble where arbitrary variations of the local density are possible. However, in many cases the systems of interest are closed with respect to mass, e.g., canonical systems with fixed temperature and particle number. Although the tools of standard, grand-canonical density functional theory are often used in an ad hoc manner to study closed systems, their formulation directly in the canonical ensemble has so far not been known. In this work, the fundamental theorems underlying classical DFT are revisited and carefully compared in the two ensembles showing that there are only trivial formal differences. The practicality of DFT in the canonical ensemble is then illustrated by deriving the exact Helmholtz functional for several systems: the ideal gas, certain restricted geometries in arbitrary numbers of dimensions, and, finally, a system of two hard spheres in one dimension (hard rods) in a small cavity. Some remarkable similarities between the ensembles are apparent even for small systems with the latter showing strong echoes of the famous exact of result of Percus in the grand-canonical ensemble.

Classical density functional theory is used to determine the fluid-solid surface tensions for low-index faces of crystals of hard spheres and Lennard-Jones particles. The calculations make use of the recently introduced explicitly stable fundamental measure theory model for hard spheres, and we show that this gives state-of-the-art accuracy compared to simulation. For the Lennard-Jones system, results are presented for both solid-liquid and solid-vapor interfaces, and in both cases the FCC results compare favorably with existing results from the literature. We find that the BCC crystal has significantly lower solid-liquid surface tension than the FCC structure. For the solid-vapor interface, our results indicate that the BCC phase is unstable with respect to transition to the HCP structure, in agreement with various zero-temperature results in the literature.

We report the investigation of various experimental conditions and their influence on polymorphism of 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile, commonly known as ROY. These conditions include an in-house-developed microfluidic chip with controlled mixing of parallel flows. We observed that different ROY concentrations and different solvent to antisolvent ratios naturally favored different polymorphs. Nonetheless, identical samples prepared with different mixing methods, such as rotation and magnetic stirring, consistently led to the formation of different polymorphs. A fourth parameter, namely the confinement of the sample, was also considered. Untangling all those parameters and their influences on polymorphism called for an experimental setup allowing all four to be controlled accurately. To that end, we developed a novel customized microfluidic setup allowing reproducible and controlled mixing conditions. Two parallel flows of antisolvent and ROY dissolved in solvent were infused into a transparent microchannel. Next, slow and progressive mixing could be obtained by molecular diffusion. Additionally, the microfluidic chip was equipped with a piezoceramic element, allowing the implementation of various mixing rates by acoustic mixing. With this device, we demonstrated the importance of parameters other than concentration on the polymorphism of ROY.

We use classical density functional theory (cDFT) to calculate fluid-solid surface tensions for fcc and bcc crystals formed by hard spheres and Lennard-Jones (LJ) particles. For hard spheres, our results show that the recently introduced ``explicitly stable'' functionals perform as well as the state of the art, and for both interaction potentials, our results compare well to simulation. We use the resulting bulk and interfacial energies for LJ to parametrize a capillary model for the free energy of small solid clusters and thereby determine the relative stability of bcc and fcc LJ clusters. We show a crossover from bcc to fcc stability as cluster size increases, thus providing insight into long-standing tension between simulation results and theoretical expectations. We also confirm that the bcc phase in contact with a vapor is unstable, thus extending earlier zero-temperature results. Our Letter demonstrates the potential of cDFT as an important tool in understanding crystallization and polymorphism.

A new kinetic Monte Carlo simulation approach for crystal growth from solution is presented. The simulations include an explicit representation of an extended volume of solution above the crystal face and realistically treats voids within the forming crystal, step overhangs and concentration gradients in the mother solution. The effect of impurities on step growth is investigated and it is shown that the results depend on a complex interplay between concentration gradients in solution driven by the consumption of material during step growth, the lifetime of impurities on the crystal surface and the geometry of the steps.

The original derivation of power functional theory [M. Schmidt and J. M. Brader, J. Chem. Phys. 138, 214101 (2013)] is reworked in some detail with a view to clarifying and simplifying the logic and making explicit the various functional dependencies. We note various issues with the original development and suggest a modification that allows us to avoid them. In the process, we also suggest an alternative interpretation of our results, which bears surprising similarities to classical density functional theory.

We examine the effect of rough surfaces on crystal nucleation by means of kinetic Monte Carlo simulations. Our work makes use of three-dimensional kMC models, explicit representation of transport in solution and rough surfaces modeled as randomly varying height fluctuations (roughness) with exponentially decaying correlation length (topology). We use Forward-Flux Sampling to determine the nucleation rate for crystallization for surfaces of different roughness and topology and show that the effect on crystallization is a complex interplay between the two. For surfaces with low roughness, small clusters form on the surface but as clusters become larger they are increasingly likely to be found in the bulk solution while rougher surfaces eventually favor heterogeneous nucleation on the surface. In both cases, the rough surface raises the local supersaturation in the solution thus leading to another mechanism of enhanced nucleation rate.

Antagonistic cooperativity between antimalarials controlling hematin crystallization by attenuation of step pinning WENCHUAN MA1, JAMES F. LUTSKO2, JEFFREY D. RIMER1, PETER G. VEKILOV1,3 1 Department of Chemical and Biomolecular Engineering, University of Houston, 4726 Calhoun Road, Houston, TX 77204-4004, USA, vekilov@uh.edu 2 Center for Nonlinear Phenomena and Complex Systems, CP 231, University Libre de Bruxelles, Boulevard du Triomphe, 1050 Bruxelles, Belgium 3 Department of Chemistry, University of Houston, 3585 Cullen Blvd., Houston, TX 77204-5003, USA

Standard solid-on-solid models of crystal growth represent the appearance and disappearance of molecules on the crystal surface as stochastic events. Here, in order to model more realistically the growth of crystals from solution, we introduce a dynamic model of the fluid in contact with the crystal surface and in this way account explicitly for mass transport in the solution. We present our hybrid model and establish its relation to standard SOS simulations while demonstrating explicit effects of mass transport that are usually ignored in SOS simulations. We then introduce flow in the solution in directions parallel to the crystal surface and observe dramatic effects on crystal growth for flows perpendicular to the step front as well as for flows parallel to the step. In order to understand the latter, quite unexpected feature, we study the effect of flow on isolated islands on a crystal surface and show that flow in the solution can induce spontaneous movement of 2D islands on the crystal surface.

The derivation of the state of the art tensorial versions of Fundamental Measure Theory (a form of classical Density Functional Theory for hard spheres) is reexamined in the light of the recently introduced concept of global stability of the density functional based on its boundedness [Lutsko and Lam, Phys. Rev. E 98, 012604 (2018)2470-004510.1103/PhysRevE.98.012604]. It is shown that within the present paradigm, explicit stability of the functional can be achieved only at the cost of giving up accuracy at low densities. It is argued that this is an acceptable trade-off since the main value of DFT lies in the study of dense systems. Explicit calculations for a wide variety of systems show that a proposed explicitly stable functional is competitive in all ways with the popular White Bear models while sharing some of their weaknesses when applied to non-close-packed solids.

The standard model of classical density-functional theory (cDFT) for pair potentials consists of a hard-sphere functional plus a mean-field term accounting for long ranged attraction. However, most implementations using sophisticated fundamental measure hard-sphere functionals suffer from potential numerical instabilities either due to possible instabilities in the functionals themselves or due to implementations that mix real- and Fourier-space components inconsistently. Here we present a new implementation based on a demonstrably stable hard-sphere functional that is implemented in a completely consistent manner. The present work does not depend on approximate spherical integration schemes and so is much more robust than previous algorithms. The methods are illustrated by calculating phase diagrams for the solid state using the standard Lennard-Jones potential as well as a new class of potentials recently proposed by Wang et al. [Phys. Chem. Chem. Phys. 22, 10624 (2020)PPCPFQ1463-907610.1039/C9CP05445F]. The latter span the range from potentials for small molecules to those appropriate to colloidal systems simply by varying a parameter. We verify that cDFT is able to semiquantitatively reproduce the phase diagram in all cases. We also show that for these problems computationally cheap Gaussian approximations are nearly as good as full minimization based on finite differences.

Recent theories of nucleation that go beyond classical nucleation theory predict that diffusion-limited nucleation of both liquid droplets and of crystals from a low-density vapor (or weak solution) begins with long-wavelength density fluctuations. This means that in the early stages of nucleation, "clusters" can have low density but large spatial extent, which is at odds with the classical picture of arbitrarily small clusters of the condensed phase. We present the results of kinetic Monte Carlo simulations using forward flux sampling to show that these predictions are confirmed, namely, that on average, nucleation begins in the presence of low-amplitude, but spatially extended density fluctuations thus confirming a significant prediction of the nonclassical theory.

A novel microfluidic device that subjects a solution to a constant shear flow was developed. By taking advantage of the linear velocity profile in a lid driven flow configuration, small volumes (10(-5) L) can be subjected to a constant shear profile with a shear rate between 0.1 and 100 s(-1) at accurately controlled temperatures between 20 and 50 degrees C. The tunable shear can be maintained for extensive and fully controlled times. A dedicated microscope setup for visualization enables the on-chip detection of micron-sized crystals, particles, and aggregates. The influence of shear on the crystallization process of the reference protein lysozyme was studied. The results indicate that shear rates between 1 and 10 s(-1) decrease solubility and promote nucleation not only in the supersaturated and metastable zones of the phase diagram, but also in the undersaturated zone. A monotonically increasing nucleation rate was observed for shear rates between 1 and 10 s(-1). It is anticipated that the presented methodology can shed light on a variety of phase transitions that are influenced by flow.

Ubiquitous processes in nature and the industry exploit crystallization from multicomponent environments 1 – 5 ; however, laboratory efforts have focused on the crystallization of pure solutes 6 , 7 and the effects of single growth modifiers 8 , 9 . Here we examine the molecular mechanisms employed by pairs of inhibitors in blocking the crystallization of haematin, which is a model organic compound with relevance to the physiology of malaria parasites 10 , 11 . We use a combination of scanning probe microscopy and molecular modelling to demonstrate that inhibitor pairs, whose constituents adopt distinct mechanisms of haematin growth inhibition, kink blocking and step pinning 12 , 13 , exhibit both synergistic and antagonistic cooperativity depending on the inhibitor combination and applied concentrations. Synergism between two crystal growth modifiers is expected, but the antagonistic cooperativity of haematin inhibitors is not reflected in current crystal growth models. We demonstrate that kink blockers reduce the line tension of step edges, which facilitates both the nucleation of crystal layers and step propagation through the gates created by step pinners. The molecular viewpoint on cooperativity between crystallization modifiers provides guidance on the pairing of modifiers in the synthesis of crystalline materials. The proposed mechanisms indicate strategies to understand and control crystallization in both natural and engineered systems, which occurs in complex multicomponent media 1 – 3 , 8 , 9 . In a broader context, our results highlight the complexity of crystal–modifier interactions mediated by the structure and dynamics of the crystal interface.

Recent advances in classical density functional theory are combined with stochastic process theory and rare event techniques to formulate a theoretical description of nucleation, including crystallization, that can predict nonclassical nucleation pathways based on no input other than the interaction potential of the particles making up the system. The theory is formulated directly in terms of the density field, thus forgoing the need to define collective variables. It is illustrated by application to diffusion-limited nucleation of macromolecules in solution for both liquid-liquid separation and crystallization. Both involve nonclassical pathways with crystallization, in particular, proceeding by a two-step mechanism consisting of the formation of a dense-solution droplet followed by ordering originating at the core of the droplet. Furthermore, during the ordering, the free-energy surface shows shallow minima associated with the freezing of liquid into solid shells, which may shed light on the widely observed metastability of nanoscale clusters.

While in principle, finite temperature density functional theory (ftDFT) should be a powerful tool for the study of crystallization, in practice this has not so far been the case. Progress has been hampered by technical problems which have plagued the study of the crystalline systems using the most sophisticated Fundamental Measure Theory models. In this paper, the reasons for the difficulties are examined and it is proposed that the tensor functionals currently favored are in fact numerically unstable. By reverting to an older, more heuristic model it is shown that all of the technical difficulties are eliminated. Application to a Lennard-Jones fluid results in a demonstration of power of ftDFT to describe crystallization in a highly inhomogeneous system. First, we show that droplets attached to a slightly hydrophobic wall crystallize spontaneously upon being quenched. The resulting crystallites are clearly faceted structures and are predominantly HCP structures. In contrast, droplets in a fully periodic calculational cell remain stable to lower temperatures and eventually show the same spontaneous localization of the density into u0027atomsu0027 but in an amorphous structure having many of the structural charactersitics of a glass. A small change of the protocol leads, at the same temperature, to the formation of crystals, this time with the FCC structure typical of bulk Lennard-Jones solids. The FCC crystals have lower free energy than the amorphous structures which in turn are more stable than the liquid droplets. It is demonstrated that as the temperature is raised, the free energy differences between the structures decreases until the solid clusters become less stable than the liquid droplets and spontaneously melt. The presence of energy barriers separating the various structures is therefore clearly demonstrated.