Polymorph specific RMSD local order parameters for molecular crystals and nuclei: α-, β-, and γ-glycine

Crystal nucleation is important for many processes including pharmaceutical crystallization, biomineralization, and material synthesis. The progression of structural changes which occur during crystal nucleation are often described using order parameters. Polymorph specific order parameters have been developed for crystallization of spherically symmetric particles; however, polymorph specific order parameters for molecular crystals remain a challenge. We introduce template based polymorph specific order parameters for molecular crystals. For each molecule in a simulation, we compute the root mean squared deviation (RMSD) between the local environment around the molecule and a template of the perfect crystal structure for each polymorph. The RMSD order parameters can clearly distinguish the α-, β-, and γ-glycine polymorph crystal structures in the bulk crystal and also in solvated crystallites. Surface melting of glycine crystallites in supersaturated aqueous solution is explored using the newly developed order parameters. The solvated α-glycine crystallite has a thinner surface melted layer than the γ-glycine crystallite. α-glycine forms first out of aqueous solution, so surface melted layer thickness may provide insight into interfacial energy and polymorph selection.     

Order parameters for the multistep crystallization of clathrate hydrates

Recent reports indicate that the crystallization of clathrate hydrates occurs in multiple steps that involve amorphous intermediates and metastable clathrate crystals. The elucidation of the reaction coordinate for clathrate crystallization requires the use of order parameters able to identify the reactants, products, and intermediates in the crystallization pathway. Nevertheless, existing order parameters cannot distinguish between amorphous and crystalline clathrates or between different clathrate crystals. In this work, we present the first set of order parameters that discern between the sI and sII clathrate crystals, the amorphous clathrates, the blob of solvent-separated guests and the liquid solution. These order parameters can be used to monitor the advance of the crystallization and for the efficient implementation of methods to sample the rare clathrate nucleation events in molecular simulations. We illustrate the use of these order parameters in the analysis of the growth and the dissolution of clathrate crystals and the spontaneous nucleation and growth of clathrates under conditions of high supercooling.     

Evidence for a size dependent nucleation mechanism in solid state polymorph transformations

This study applies aimless shooting and likelihood maximization to determine the molecular mechanism in the solid state polymorph transformation in terephthalic acid from over 500 candidate order parameters. The crystals examined here extend the range of crystal sizes considered in our previous work (J. Amer. Chem. Soc. 2007, 129, 4714) and reveal a change in the mechanism with increasing system size. As the crystal size increases beyond that studied in our previous work, the polymorph transformation mechanism changes from a global distortion of the crystal to a local corner nucleation mechanism. In the corner nucleation mechanism, the interfacial area between the two polymorphs is minimized for a given nucleus size. However, this mechanism differs from classical nucleation theory in that the molecular level details are essential to describe the nucleation process, which involves nonspherical domains at the corner of the crystal. These new findings suggest that there is a range of sizes for which corner nucleation is the dominant mechanism of polymorph transitions, thus implying that different mechanistic regimes exist for nucleation based on crystal size. From a computational standpoint, this study demonstrates the utility of aimless shooting and likelihood maximization to identify nonintuitive reaction coordinates in complex systems.     

Cross-nucleation between ROY polymorphs

Cross-nucleation between polymorphs is a newly discovered phenomenon important for understanding and controlling crystal polymorphism. It contradicts Ostwald's law of stages and other theories of crystallization in polymorphic systems. We studied the phenomenon in the spontaneous and seeded melt crystallization of 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile (ROY), currently the most polymorphic system of known structures. We observed extensive and sometimes selective cross-nucleation between ROY polymorphs. Certain polymorphs could not nucleate without the aid of others. The new polymorph was found to be more or less thermodynamically stable than the initial one but to always grow faster than or as fast as the initial one. The temperature and surface characteristics of the seed crystals affected the occurrence of cross-nucleation. Our results show that the pathway of crystallization in polymorphic systems is not determined solely by the initial nucleation, but also by cross-nucleation between polymorphs and the different growth rates of polymorphs. This study identified a new metastable polymorph of ROY, the 10th of the family.     

Insights into the molecular mechanism underlying polymorph selection

We use molecular simulations to study polymorph selection during the crystallization of charge-stabilized colloidal suspension. By modifying the conditions of crystallization, we invert the stability of two polymorphs and induce the formation of crystallites whose structure is predominantly that of the stable polymorph. However, our simulations reveal that kinetics play a major role not only during the nucleation step but also in the growth mechanism. The growth of postcritical crystallites of the stable polymorph proceeds through a complex mechanism involving the cross-nucleation of a third metastable polymorph followed by the conversion of this third polymorph into the stable structure.     

Polymorph selection during the crystallization of Yukawa systems

Using molecular-dynamics simulations, we study the crystallization of supercooled liquids of charge-stabilized colloidal suspensions, modeled by the Yukawa (screened-Coulomb) potential. By modifying the value of the screening parameter lambda, we are able to invert the stability of the body-centered cubic (bcc) and face-centered cubic (fcc) polymorphs and study the crystal nucleation and growth in the domain of stability of each polymorph. We show that the crystallization mechanism strongly depends on the value of lambda. When bcc is the stable polymorph (lambda=3), the crystallization mechanism is straightforward. Both kinetics and thermodynamics favor the formation of the bcc particles and polymorph selection takes place early during the nucleation step. When fcc is the stable polymorph (lambda=10), the molecular mechanism is much more complex. First, kinetics favor the formation of bcc particles during the nucleation step. The growth of the post-critical nucleus proceeds through the successive cross-nucleation of the stable fcc polymorph on the metastable hcp polymorph as well as of the hcp polymorph on the fcc polymorph. As a result, polymorph selection occurs much later, i.e., during the growth step, than for lambda=3. We then extend our findings established in the case of homogeneous crystal nucleation to a situation of practical interest, i.e., when a seed of the stable polymorph is used. We demonstrate that the growth from the (111) face of a perfect fcc crystal into the melt proceeds through the same mechanisms.     

Molecular recognition controls the organization of mixed self-organized bis-urea-based mineralization templates for CaCO(3)

To investigate the role and importance of nondirectional electrostatic interactions in mineralization, we explored the use of Langmuir monolayers in which the charge density can be tuned using supramolecular interactions. It is demonstrated that, in mixed Langmuir monolayers of bis-ureido surfactants containing oligo(ethylene oxide) and ammonium head groups associated with matching or nonmatching spacers between the two urea groups, the organization is controlled by molecular recognition. These different organizations of the molecules lead to different nucleation behavior in the mineralization of calcium carbonate. The formation of modified calcite and vaterite crystals was induced selectively by different phases of mixed monolayers, and they were characterized by SEM, TEM, and SAED. To understand the influence of the mixed Langmuir monolayers on the crystallization process, we studied the mixtures by means of (pi-A) isotherms and Brewster angle microscopy observations. Infrared reflection-absorption spectroscopy experiments were also performed on Langmuir-Schaefer films. From these results, we conclude that the local organization of the two systems discussed here gives rise to differences in both charge density and flexibility that together determine not only polymorph selection and the nucleation face but also the morphology of the resulting crystals.     

On the mechanism of crystalline polymorph selection by polymer heteronuclei

The phase-selective crystallization of acetaminophen (ACM) using insoluble polymers as heteronuclei was investigated in a combined experimental and computational effort to elucidate the mechanism of polymer-induced heteronucleation (PIHn). ACM heteronucleates from supersaturated aqueous solution in its most thermodynamically stable monoclinic form on poly(n-butyl methacrylate), whereas the metastable orthorhombic form is observed on poly(methyl methacrylate). When ACM crystals were grown through vapor deposition, only the monoclinic polymorph was observed on each polymer. Each crystallization condition leads to a unique powder X-ray diffraction pattern with the major preferred orientation corresponding to the crystallographic faces in which these crystal phases nucleate from surfaces of the polymers. The molecular recognition events leading to these outcomes are elucidated with the aid of computed polymer-crystal binding energies using docking simulations. This investigation illuminates the mechanism by which phase selection occurs during the crystallization of ACM using polymers as heteronuclei, paving the way for the improvement of methods for polymorph selection and discovery based on heterogeneous nucleation promoters.     

Gel-induced selective crystallization of polymorphs

Although nanoporous materials have been explored for controlling crystallization of polymorphs in recent years, polymorphism in confined environments is still poorly understood, particularly from a kinetic perspective, and the role of the local structure of the substrate has largely been neglected. Herein, we report the use of a novel material, polymer microgels with tunable microstructure, for controlling polymorph crystallization from solution and for investigating systematically the effects of nanoconfinement and interfacial interactions on polymorphic outcomes. We show that the polymer microgels can improve polymorph selectivity significantly. The polymorphic outcomes correlate strongly with the gel-induced nucleation kinetics and are very sensitive to both the polymer microstructure and the chemical composition. Further mechanistic investigations suggest that the nucleation-templating effect and the spatial confinement imposed by the polymer network may be central to achieving polymorph selectivity. We demonstrate polymer microgels as promising materials for controlling crystal polymorphism. Moreover, our results help advance the fundamental understanding of polymorph crystallization at complex interfaces, particularly in confined environments.     

Polymorph selection during the crystallization of softly repulsive spheres: the inverse power law potential

Using hybrid Monte Carlo molecular simulations, we study crystallization from the melt of softly repulsive spheres interacting through an inverse power law potential. We work at fixed supercooling (i.e., at a temperature 25% below the melting temperature) and consider three systems, defined by different values for the inverse power exponent n: n = 5, n = 6.67, and n = 10. Modifying the value of n allows us to study the onset of crystallization in the domain of stability of the body-centered cubic (bcc) phase (n = 5 and n = 6.67) and in the domain of stability of the face-centered cubic (fcc) phase (n = 10). We show that, for the three systems, polymorph selection does not take place during crystal nucleation since the structure of the critical nuclei obtained for the three systems is not well defined. However, our results demonstrate that polymorph selection takes place during the growth step since growth proceeds either into the stable bcc phase for the two smaller values of n (n = 5 and n = 6.67) or into the stable fcc phase for the larger value of n (n = 10). We also show that we did not achieve complete control of polymorphism for n = 10. The growth step gives rise to either slowly growing crystallites composed of two blocks of different structures (the stable fcc form and the metastable bcc form) or rapidly growing crystallites of the metastable bcc form.     

Crystals of Benzamide,the First Polymorphous Molecular Compound,Are Helicoidal

The growth of spontaneously twisted crystals is a common but poorly understood phenomenon. An analysis of the formation of twisted crystals of a metastable benzamide polymorph (form II ) crystallizing from highly supersaturated aqueous and ethanol solutions is given here. Benzamide, the first polymorphic molecular crystal reported (1832), would have been the first helicoidal crystal observed had the original authors undertaken an analysis by light microscopy. Polymorphism and twisting frequently concur as they are both associated with high thermodynamic driving forces for crystallization. Optical and electron microscopies as well as electron and powder X‐ray diffraction reveal a complex lamellar structure of benzamide form II needle‐like crystals. The internal stress produced by the overgrowth of lamellae is shown to be able to create a twist moment that is responsible for the observed non‐classical morphologies.     

Crystals of Benzamide,the First Polymorphous Molecular Compound,Are Helicoidal

The growth of spontaneously twisted crystals is a common but poorly understood phenomenon. An analysis of the formation of twisted crystals of a metastable benzamide polymorph (form II ) crystallizing from highly supersaturated aqueous and ethanol solutions is given here. Benzamide, the first polymorphic molecular crystal reported (1832), would have been the first helicoidal crystal observed had the original authors undertaken an analysis by light microscopy. Polymorphism and twisting frequently concur as they are both associated with high thermodynamic driving forces for crystallization. Optical and electron microscopies as well as electron and powder X-ray diffraction reveal a complex lamellar structure of benzamide form II needle-like crystals. The internal stress produced by the overgrowth of lamellae is shown to be able to create a twist moment that is responsible for the observed non-classical morphologies.     

Mesocrystals: inorganic superstructures made by highly parallel crystallization and controlled alignment

Controlled self-organization of nanoparticles can lead to new materials. The colloidal crystallization of non-spherical nanocrystals is a reaction channel in many crystallization reactions. With additives, self-organization can be stopped at an intermediary step-a mesocrystal-in which the primary units can still be identified. Mesocrystals were observed for various systems as kinetically metastable species or as intermediates in a crystallization reaction leading to single crystals with typical defects and inclusions. The control forces and mechanism of mesocrystal formation are largely unknown, but several mesocrystal properties are known. Mesocrystals are exiting examples of nonclassical crystallization, which does not proceed through ion-by-ion attachment, but by a modular nanobuilding-block route. This path makes crystallization more independent of ion products or molecular solubility, it occurs without pH or osmotic pressure changes, and opens new strategies for crystal morphogenesis.     

Enantioselective Crystallization of Chiral Inorganic Crystals of ϵ-Zn(OH)2 with Amino Acids

Many inorganic materials can form crystals, but little is known about their enantioselective crystallization. Herein, we report on the enantioselective crystallization of ϵ-Zn(OH)₂ (Wulfingite) chiral crystals by using amino acids. Crystals of ϵ-Zn(OH)₂ were crystallized from supersaturated sodium hydroxide and zinc nitrate aqueous solutions in the presence of l - or d -arginine. All of the chiral measurements, such as selective chiral adsorption by circular dichroism (CD), chiral chromatography, and polarimetry measurements, clearly show chiral discrimination during the crystallization of ϵ-Zn(OH)₂. In addition, a new method has been developed for identifying chirality in crystals by using electron paramagnetic resonance (EPR). Although the values of chiral induction of the ϵ-Zn(OH)₂ crystals obtained are somewhat low, these values are still significant because they demonstrate that enantioselectivity during the crystallization of chiral inorganic crystals with chiral additives can be achieved. The method can be applied to many chiral inorganic systems. Understanding and controlling the crystallization of chiral inorganic crystals is important for gaining knowledge on the interaction of chiral molecules with inorganic surfaces. This knowledge can lead to an understanding of basic scientific questions such as the evolution of homochirality in biomolecules and the development of chiral inorganic crystals for a variety of purposes such as asymmetric catalysis and optical applications.     

Role of liquid polymorphism during the crystallization of silicon

Using molecular simulation, we establish the pivotal role played by liquid polymorphs during the crystallization of silicon. When undercooled at a temperature 20% below the melting point, a silicon melt is under the form of the highly coordinated, high-density liquid (HDL) polymorph. We find that crystallization starts with the formation, within the HDL liquid, of a nanosized droplet of the least stable liquid polymorph, known as the almost tetracoordinated low-density liquid (LDL) polymorph. We then show that the crystalline embryo forms within the LDL droplet, close to the interface with the surrounding HDL liquid, thereby following a pathway associated with a much lower free energy barrier than the direct formation of the crystalline embryo from the HDL liquid would have required. This implies that, for substances exhibiting liquid polymorphs, theories, like the classical nucleation theory, and empirical rules, like Ostwald's rule, should be modified to account for the role of liquid polymorphs in the nucleation process.     

Molecular simulation of cross-nucleation between polymorphs

Recent experiments report that an early nucleating crystalline structure (or polymorph) may nucleate another polymorph. We use molecular dynamics simulations to model this phenomenon known as cross-nucleation. We study the onset of crystallization in a liquid of Lennard-Jones particles cooled at a temperature 22% below the melting temperature. We show that growth proceeds through the successive cross-nucleation of the metastable hexagonal close-packed (hcp) polymorph on the stable face-centered cubic (fcc) polymorph and of the stable fcc polymorph on the metastable hcp polymorph. This finding is in agreement with the experimental results which demonstrated that the cross-nucleation of a stable polymorph on a metastable polymorph is just as likely as the cross-nucleation of a metastable polymorph on a stable polymorph. We then extend our findings established in the case of the homogeneous crystal nucleation to a situation of practical interest, i.e., when a seed of the stable polymorph is used. By studying the crystal growth from the (111) plane of a perfect fcc crystal, we show that, again, growth proceeds through the cross-nucleation of the hcp and fcc structures.     

Atomistic simulation of the homogeneous nucleation and of the growth of N2 crystallites

We report on a computer simulation study of the early stages of the crystallization of molecular nitrogen. First, we study how homogeneous nucleation takes place in supercooled liquid N(2) for a moderate degree of supercooling. Using the umbrella sampling technique, we determine the free energy barrier of formation for a critical nucleus of N(2). We show that, in accord with Ostwald's rule of stages, the structure of the critical nucleus is predominantly that of a metastable polymorph (alpha-N(2) for the state point investigated). We then monitor the evolution of several critical nuclei through a series of unbiased molecular dynamics trajectories. The growth of N(2) crystallites is accompanied by a structural evolution toward the stable polymorph beta-N(2). The microscopic mechanism underlying this evolution qualitatively differs from that reported previously. We do not observe any dissolution or reorganization of the alpha-like core of the nucleus. On the contrary, we show that alpha-like and beta-like blocks coexist in postcritical nuclei. We relate the structural evolution to a greater adsorption rate of beta-like molecules on the surface and show that this transition actually starts well within the precritical regime. We also carefully investigate the effect of the system size on the height of the free energy barrier of nucleation and on the structure and size of the critical nucleus.     

Molecular mechanism for the cross-nucleation between polymorphs

We use molecular simulations to study the early stages of crystallization in a supercooled liquid of Lennard-Jones particles. We observe the onset of concomitant polymorphism and demonstrate that this phenomenon results from the cross-nucleation of a metastable polymorph on the stable polymorph. We also show that cross-nucleation is selective as it only takes place between polymorphs of almost equivalent free energy. Our simulations provide detailed insights into the molecular mechanism underlying concomitant polymorphism and cross-nucleation between polymorphs.     

Atomic force microscopy studies of icosahedral virus crystal growth

Biological macromolecules and particularly viruses, provide excellent systems for the study of crystallization from solution because of their relatively large size. The kinetics of their crystallization is at least an order of magnitude less than for conventional systems, and their large size permits visualization, both of crystal lattices and individual particles, by techniques such as atomic force microscopy (AFM). This technique is especially powerful for biological macromolecules because it can be utilized in situ, in the crystallization mother liquor, over long periods of time without perturbing the growing crystals. We present here observations using AFM of the nucleation and growth of crystals of satellite tobacco mosaic virus, and some recordings as well of bromegrass mosaic virus. Correlations are made, where possible, with corresponding analyses using X-ray diffraction analysis.     

Tuning in-meso-crystallized lysozyme polymorphism by lyotropic liquid crystal symmetry

Lipid-based lyotropic liquid crystals (LLCs) show great potential for applications in fields as diverse as food technology, cosmetics, pharmaceutics, or structural biology. Recently, these systems have provided a viable alternative to the difficult process of membrane protein crystallization, owing to their similarities with cell membranes. Nonetheless, the process of in-meso crystallization of proteins still remains poorly understood. In this study, we demonstrate that in-meso crystal morphologies of lysozyme (LSZ), a model hydrophilic protein, can be controlled by both the composition and symmetry of the mesophase, inferring a possible general influence of the LLC space group on the protein crystal polymorphism. Lysozyme was crystallized in-meso from three common LLC phases (lamellar, inverse hexagonal, and inverse bicontinuous cubic) composed of monolinolein and water. Different mixing ratios of mesophase to crystallization buffer were used in order to tune crystallization both in the bulk mesophase and in excess water conditions. Two distinct mechanisms of crystallization were shown to take place depending on available water in the mesophases. In the bulk mesophases, protein nuclei form and grow within structural defects of the mesophase and partially dehydrate the system inducing order-to-order transitions of the liquid crystalline phase toward stable symmetries in conditions of lower hydration. The formed protein crystals eventually macrophase separate from the mesophase allowing the system to reach its final symmetry. On the other hand, when excess water is available, protein molecules diffuse from the water channels into the excess water, where the crystallization process can take place freely, and with little to no effect on the structure and symmetry of the lyotropic liquid crystals.