Diffusion-limited kinetics of the solution-solid phase transition of molecular substances

In situ counter-diffusion crystallization and long-term crystal preservation in microfluidic fixed targets for serial crystallography

Compared with batch and vapor diffusion methods, counter diffusion can generate larger and higher-quality protein crystals yielding improved diffraction data and higher-resolution structures. Typically, counter-diffusion experiments are conducted in elongated chambers, such as glass capillaries, and the crystals are either directly measured in the capillary or extracted and mounted at the X-ray beamline. Despite the advantages of counter-diffusion protein crystallization, there are few fixed-target devices that utilize counter diffusion for crystallization. In this article, different designs of user-friendly counter-diffusion chambers are presented which can be used to grow large protein crystals in a 2D polymer microfluidic fixed-target chip. Methods for rapid chip fabrication using commercially available thin-film materials such as Mylar, propyl-ene and Kapton are also detailed. Rules of thumb are provided to tune the nucleation and crystal growth to meet users' needs while minimizing sample consumption. These designs provide a reliable approach to forming large crystals and maintaining their hydration for weeks and even months. This allows ample time to grow, select and preserve the best crystal batches before X-ray beam time. Importantly, the fixed-target microfluidic chip has a low background scatter and can be directly used at beamlines without any crystal handling, enabling crystal quality to be preserved. The approach is demonstrated with serial diffraction of photoactive yellow protein, yielding 1.32 Å resolution at room temperature. Fabrication of this standard microfluidic chip with commercially available thin films greatly simplifies fabrication and provides enhanced stability under vacuum. These advances will further broaden microfluidic fixed-target utilization by crystallographers.

The Current Understanding of Mechanistic Pathways in Zeolite Crystallization

Zeolite catalysts and adsorbents have been an integral part of many commercial processes and are projected to play a significant role in emerging technologies to address the changing energy and environmental landscapes. The ability to rationally design zeolites with tailored properties relies on a fundamental understanding of crystallization pathways to strategically manipulate processes of nucleation and growth. The complexity of zeolite growth media engenders a diversity of crystallization mechanisms that can manifest at different synthesis stages. In this review, we discuss the current understanding of classical and nonclassical pathways associated with the formation of (alumino)silicate zeolites. We begin with a brief overview of zeolite history and seminal advancements, followed by a comprehensive discussion of different classes of zeolite precursors with respect to their methods of assembly and physicochemical properties. The following two sections provide detailed discussions of nucleation and growth pathways wherein we emphasize general trends and highlight specific observations for select zeolite framework types. We then close with conclusions and future outlook to summarize key hypotheses, current knowledge gaps, and potential opportunities to guide zeolite synthesis toward a more exact science.

The elementary reactions for incorporation into crystals

The growth rates of crystals are largely dictated by the chemical reaction between solute and kinks, in which a solute molecule severs its bonds with the solvent and establishes new bonds with the kink. Details on this sequence of bond breaking and rebuilding remain poorly understood. To elucidate the reaction at the kinks we employ four solvents with distinct functionalities as reporters on the microscopic structures and their dynamics along the pathway into a kink. We combine time-resolved in situ atomic force microscopy and x-ray and optical methods with molecular dynamics simulations. We demonstrate that in all four solvents the solute, etioporphyrin I, molecules reach the steps directly from the solution; this finding identifies the measured rate constant for step growth as the rate constant of the reaction between a solute molecule and a kink. We show that the binding of a solute molecule to a kink divides into two elementary reactions. First, the incoming solute molecule sheds a fraction of its solvent shell and attaches to molecules from the kink by bonds distinct from those in its fully incorporated state. In the second step, the solute breaks these initial bonds and relocates to the kink. The strength of the preliminary bonds with the kink determines the free energy barrier for incorporation into a kink. The presence of an intermediate state, whose stability is controlled by solvents and additives, may illuminate how minor solution components guide the construction of elaborate crystal architectures in nature and the search for solution compositions that suppress undesirable or accelerate favored crystallization in industry.

Crystal Structure and Twisted Aggregates of Oxcarbazepine Form III

Polymorphism and crystal habit play vital roles in dictating the properties of crystalline materials. Here, the structure and properties of oxcarbazepine (OXCBZ) form III are reported along with the occurrence of twisted crystalline aggregates of this metastable polymorph. OXCBZ III can be produced by crystallization from the vapor phase and by recrystallization from solution. The crystallization process used to obtain OXCBZ III is found to affect the pitch, with the most prominent effect observed from the sublimation-grown OXCBZ III material where the pitch increases as the length of aggregates increases. Sublimation-grown OXCBZ III follows an unconventional mechanism of formation with condensed droplet formation and coalescence preceding nucleation and growth of aggregates. A crystal structure determination of OXCBZ III from powder X-ray diffraction methods, assisted by crystal structure prediction (CSP), reveals that OXCBZ III, similar to carbamazepine form II, contains void channels in its structure with the channels, aligned along the c crystallographic axis, oriented parallel to the twist axis of the aggregates. The likely role of structural misalignment at the lattice or nanoscale is explored by considering the role of molecular and closely related structural impurities informed by crystal structure prediction.

Emergent Insulator-Metal Transition with Tunable Optical and Electrical Gap in Thin Films of a Molecular Conducting Composite

Composites exhibit unique synergistic properties emerging when components with different properties are combined. The tuning of the energy bandgap in the electronic structure of the material allows designing tailor-made systems with desirable mechanical, electrical, optical, and/or thermal properties. Here, we study an emergent insulator-metal transition at room temperature in bilayered (BL) thin-films comprised of polycarbonate/molecular-metal composites. Temperature-dependent resistance measurements allow monitoring of the electrical bandgap, which is in agreement with the optical bandgap extracted by optical absorption spectroscopy. The semiconductor-like properties of BL films, made with bis(ethylenedithio)-tetrathiafulvalene (BEDT-TTF or ET) α-ET2I3 (nano)microcrystals as two-dimensional molecular conductor on one side and insulator polycarbonate as a second ingredient, are attributed to an emergent phenomenon equivalent to the transition from an insulator to a metal. This made it possible to obtain semiconducting BL films with tunable electrical/optical bandgaps ranging from 0 to 2.9 eV. A remarkable aspect is the similarity close to room temperature of the thermal and mechanical properties of both composite components, making these materials ideal candidates to fabricate flexible and soft sensors for stress, pressure, and temperature aiming at applications in wearable human health care and bioelectronics.

Precrystallization solute assemblies and crystal symmetry

Solution crystallization is a part of the synthesis of materials ranging from geological and biological minerals to pharmaceuticals, fine chemicals, and advanced electronic components. Attempts to predict the structure, growth rates and properties of emerging crystals have been frustrated, in part, by the poor understanding of the correlations between the oligomeric state of the solute, the growth unit, and the crystal symmetry. To explore how a solute monomer or oligomer is selected as the unit that incorporates into kinks and how crystal symmetry impacts this selection, we combine scanning probe microscopy, optical spectroscopy, and all-atom molecular simulations using as examples two organic materials, olanzapine (OZPN) and etioporphyrin I (EtpI). The dominance of dimeric structures in OZPN crystals has spurred speculation that the dimers preform in the solution, where they capture the majority of the solute, and then assemble into crystals. By contrast, EtpI in crystals aligns in parallel stacks of flat EtpI monomers unrelated by point symmetry. Raman and absorption spectroscopies show that solute monomers are the majority solute species in solutions of both compounds. Surprisingly, the kinetics of incorporation of OZPN into kinks is bimolecular, indicating that the growth unit is a solute dimer, a minority solution component. The disconnection between the dominant solute species, the growth unit, and the crystal symmetry is even stronger with EtpI, for which the (010) face grows by incorporating monomers, whereas the growth unit of the (001) face is a dimer. Collectively, the crystallization kinetics results with OZPN and EtpI establish that the structures of the dominant solute species and of the incorporating solute complex do not correlate with the symmetry of the crystal lattice. In a broader context, these findings illuminate the immense complexity of crystallization scenarios that need to be explored on the road to the understanding and control of crystallization.

Influence of cooling rate on ice crystallization and melting in sucrose-water system

The ice crystallization and melting in systems where the equilibrium state is difficult to reach is one of the growing areas in pharmaceutical freeze-drying research. The quality of the final freeze-dried product depends on the parameters of the cooling step, which affect the ice nucleation and growth. In this paper, we present a DSC study of ice crystallization and melting in a sucrose-water system. Using two different types of thermal cycles, we examine the influence of cooling and heating rates on the thermal behavior of sucrose-water solutions with water contents between 50 and 100 wt%. The DSC results show that low cooling rates provide crystallization at higher temperatures and lead to lower amount of nonfreezing water. Consequently, the glass transition and ice melting properties observed upon heating depend on the cooling conditions in the preceding step. Based on the experimental results, we investigate the reasons for the existence of the two steps on DSC heating curves in sucrose-water systems: the glass transition step and the onset of ice melting. We show that diffusion of water can be the limiting factor for ice growth and melting in the sucrose-water system when the amorphous phase is in a liquid state. In particular, when the diffusion coefficient drops below 10^-14 m²/sec, the ice crystals growth or melting becomes strongly suppressed even above the glass transition temperature. Understanding the diffusion limitations in the sucrose-water system can be used for the optimization of the freeze-drying protocols for proteins and probiotics.

The Ambiguous Functions of the Precursors That Enable Nonclassical Modes of Olanzapine Nucleation and Growth

One of the most consequential assumptions of the classical theories of crystal nucleation and growth is the Szilard postulate, which states that molecules from a supersaturated phase join a nucleus or a growing crystal individually. In the last 20 years, observations in complex biological, geological, and engineered environments have brought to light violations of the Szilard rule, whereby molecules assemble into ordered or disordered precursors that then host and promote nucleation or contribute to fast crystal growth. Nonclassical crystallization has risen to a default mode presumed to operate in the majority of the inspected crystallizing systems. In some cases, the existence of precursors in the growth media is admitted as proof for their role in nucleation and growth. With the example of olanzapine, a marketed drug for schizophrenia and bipolar disorder, we demonstrate that molecular assemblies in the solution selectively participate in crystal nucleation and growth. In aqueous and organic solutions, olanzapine assembles into both mesoscopic solute-rich clusters and dimers. The clusters facilitate nucleation of crystals and crystal form transformations. During growth, however, the clusters land on the crystal surface and transform into defects, but do not support step growth. The dimers are present at low concentrations in the supersaturated solution, yet the crystals grow by the association of dimers, and not of the majority monomers. The observations with olanzapine emphasize that detailed studies of the crystal and solution structures and the dynamics of molecular association may empower classical and nonclassical models that advance the understanding of natural crystallization, and support the design and manufacture of promising functional materials.

Olanzapine crystal symmetry originates in preformed centrosymmetric solute dimers

The symmetries of a crystal are notoriously uncorrelated to those of its constituent molecules. This symmetry breaking is typically thought to occur during crystallization. Here we demonstrate that one of the two symmetry elements of olanzapine crystals, an inversion centre, emerges in solute dimers extant in solution prior to crystallization. We combine time-resolved in situ scanning probe microscopy to monitor the crystal growth processes with all-atom molecular dynamics simulations. We show that crystals grow non-classically, predominantly by incorporation of centrosymmetric dimers. The growth rate of crystal layers exhibits a quadratic dependence on the solute concentration, characteristic of the second-order kinetics of the incorporation of dimers, which exist in equilibrium with a majority of monomers. We show that growth by dimers is preferred due to overwhelming accumulation of adsorbed dimers on the crystal surface, where it is complemented by dimerization and expedites dimer incorporation into growth sites.

Transformation of siderite to goethite by humic acid in the natural environment

Humic acid (HA) is particularly important in iron-bearing mineral transformations and erosion at the water-mineral boundary zone of the Earth. In this study, three stages of the possible pathway by which HA causes mineral transformation from siderite to goethite are identified. Firstly, a Fe(II)-HA complex is formed by chelation, which accelerates the dissolution and oxidation of Fe(II) from the surface of siderite. As the Fe(II)-HA complex retains Fe atoms in close proximity of each other, ferrihydrite is formed by the agglomeration and crystallization. Finally, the ferrihydrite structurally rearranges upon attachment to the surface of goethite crystals and merges with its structure. The influence of low concentrations of HA (0-2 mg/L) on phosphate adsorption is found to be beneficial by the inducing of new mineral phases. We believe that these results provide a greater understanding of the impact of HA in the biogeochemical cycle of phosphate, mineral transformation.

Temperature-dependent growth of protein crystals with temperature-independent solubility: case study of apoferritin

Combined diffusion- and interface-controlled crystal growth analysis elucidates the temperature-dependent growth kinetics of protein crystals at a relatively small variation of supersaturation.

The pathway and kinetics of hierarchical assembly of ionic oligomers into a lyotropic columnar phase

Ionic benzene-1,3,5-tricarboxamide (BTA) molecules can self-assemble into hollow cylinders which further arrange into columnar phases in water. In situ investigations suggest a multi-step pathway of supramolecular assembly via formation of dispersed molecular aggregates followed by a less ordered intermediate phase before the equilibrium columnar phase is formed. The pathway and kinetics of the formation of lyotropic LC phases through hierarchical supramolecular assembly are similar to non-classical crystallization, in line with an emerging holistic view on crystallization and self-assembly.

Structuring of Organic Solvents at Solid Interfaces and Ramifications for Antimalarial Adsorption on β-Hematin Crystals

A critical aspect of material synthesis is solvent structuring at solid-liquid interfaces, which can impact the adsorption of solute and growth modifiers on an underlying substrate. In general, the impact of solvent structuring on molecular sorbate interactions with solid sorbents is poorly understood. This is particularly true for processes that occur in organic media, such as hematin crystallization, which is crucial to the survival of malaria parasites. Here, we use chemical force microscopy and molecular modeling to analyze the interactions between functional moieties of known antimalarials and the interface between β-hematin crystals and a mixed organic (octanol)-aqueous solvent. We show that the β-hematin surface, patterned in parallel hydrophobic and hydrophilic stripes, engenders the assembly of up to five layers of octanol molecules aligned parallel to the crystal surface. In contrast, studies of solvent structuring on a disordered glass surface reveal that octanol molecules align perpendicular to the interface. The distinct octanol arrays direct molecule adsorption at the respective interfaces. At both substrates, we also find stabilized pockets of aqueous nanophase lining the surfaces. A combination of experimental analyses and modeling of solvent structuring provides crucial insights into the association of hematin molecules with growing crystals as well as the adsorption and mobility of antimalarial drugs. Moreover, our findings offer a general perspective on the collective behaviors of complex organic solvents that may apply to a broad range of interactions at solid-liquid interfaces.

Ion dissolution mechanism and kinetics at kink sites on NaCl surfaces

Desolvation barriers are present for solute-solvent exchange events, such as ligand binding to an enzyme active site, during protein folding, and at battery electrodes. For solution-grown crystals, desolvation at kink sites can be the rate-limiting step for growth. However, desolvation and the associated kinetic barriers are poorly understood. In this work, we use rare-event simulation techniques to investigate attachment/detachment events at kink sites of a NaCl crystal in water. We elucidate the desolvation mechanism and present an optimized reaction coordinate, which involves one solute collective variable and one solvent collective variable. The attachment/detachment pathways for Na⁺ and Cl^- are qualitatively similar, with quantitative differences that we attribute to different ion sizes and solvent coordination. The attachment barriers primarily result from kink site desolvation, while detachment barriers largely result from breaking ion-crystal bonds. We compute ion detachment rates from kink sites and compare with results from an independent study. We anticipate that the reaction coordinate and desolvation mechanism identified in this work may be applicable to other alkali halides.

A classical view on nonclassical nucleation

Understanding and controlling nucleation is important for many crystallization applications. Calcium carbonate (CaCO₃) is often used as a model system to investigate nucleation mechanisms. Despite its great importance in geology, biology, and many industrial applications, CaCO₃ nucleation is still a topic of intense discussion, with new pathways for its growth from ions in solution proposed in recent years. These new pathways include the so-called nonclassical nucleation mechanism via the assembly of thermodynamically stable prenucleation clusters, as well as the formation of a dense liquid precursor phase via liquid-liquid phase separation. Here, we present results from a combined experimental and computational investigation on the precipitation of CaCO₃ in dilute aqueous solutions. We propose that a dense liquid phase (containing 4-7 H₂O per CaCO₃ unit) forms in supersaturated solutions through the association of ions and ion pairs without significant participation of larger ion clusters. This liquid acts as the precursor for the formation of solid CaCO₃ in the form of vaterite, which grows via a net transfer of ions from solution according to z Ca²⁺ + z CO₃^2- → z CaCO₃ The results show that all steps in this process can be explained according to classical concepts of crystal nucleation and growth, and that long-standing physical concepts of nucleation can describe multistep, multiphase growth mechanisms.

CRYSTAL GROWTH. Crystallization by particle attachment in synthetic, biogenic, and geologic environments

Field and laboratory observations show that crystals commonly form by the addition and attachment of particles that range from multi-ion complexes to fully formed nanoparticles. The particles involved in these nonclassical pathways to crystallization are diverse, in contrast to classical models that consider only the addition of monomeric chemical species. We review progress toward understanding crystal growth by particle-attachment processes and show that multiple pathways result from the interplay of free-energy landscapes and reaction dynamics. Much remains unknown about the fundamental aspects, particularly the relationships between solution structure, interfacial forces, and particle motion. Developing a predictive description that connects molecular details to ensemble behavior will require revisiting long-standing interpretations of crystal formation in synthetic systems, biominerals, and patterns of mineralization in natural environments.

Amplification of salt-induced polymer diffusiophoresis by increasing salting-out strength

The role of salting-out strength on (1) polymer diffusiophoresis from high to low salt concentration, and (2) salt osmotic diffusion from high to low polymer concentration was investigated. These two cross-diffusion phenomena were experimentally characterized by Rayleigh interferometry at 25 °C. Specifically, we report ternary diffusion coefficients for polyethylene glycol (molecular weight, 20 kg·mol(-1)) in aqueous solutions of several salts (NaCl, KCl, NH4Cl, CaCl2, and Na2SO4) as a function of salt concentration at low polymer concentration (0.5% w/w). We also measured polymer diffusion coefficients by dynamic light scattering in order to discuss the interpretation of these transport coefficients in the presence of cross-diffusion effects. Our cross-diffusion results, primarily those on salt osmotic diffusion, were utilized to extract N(w), the number of water molecules in thermodynamic excess around a macromolecule. This preferential-hydration parameter characterizes the salting-out strength of the employed salt. For chloride salts, changing cation has a small effect on N(w). However, replacing NaCl with Na2SO4 (i.e., changing anion) leads to a 3-fold increase in N(w), in agreement with cation and anion Hofmeister series. Theoretical arguments show that polymer diffusiophoresis is directly proportional to the difference N(w) - n(w), where n(w) is the number of water molecules transported by the migrating macromolecule. Interestingly, the experimental ratio, n(w)/N(w), was found to be approximately the same for all investigated salts. Thus, the magnitude of polymer diffusiophoresis is also proportional to salting-out strength as described by N(w). A basic hydrodynamic model was examined in order to gain physical insight on the role of n(w) in particle diffusiophoresis and explain the observed invariance of n(w)/N(w). Finally, we consider a steady-state diffusion problem to show that concentration gradients of strong salting-out agents such as Na2SO4 can produce large amplifications and depletions of macromolecule concentration. These effects may be exploited in self-assembly and adsorption processes.

Effect of particle size on salt-induced diffusiophoresis compared to Brownian mobility

For ternary polymer-salt-water systems at low polymer concentration (0.5%, w/w), we have experimentally investigated the effect of polymer size on polymer diffusiophoresis (i.e., polymer migration induced by a salt concentration gradient) and salt osmotic diffusion (i.e., salt migration induced by a polymer concentration gradient). Specifically, Rayleigh interferometry was employed to measure ternary diffusion coefficients for aqueous solutions of poly(ethylene glycol) (PEG) and KCl at 25 °C. Our investigation focused on four polymer molecular masses (from 10 to 100 kg mol(-1)) and two salt concentrations (0.25 and 0.50 M). To describe and examine our experimental results, we introduced a normalized diffusiophoresis coefficient as the ratio of polymer diffusiophoresis to polymer Brownian mobility. This coefficient was found to increase with polymer molecular mass, thereby demonstrating that the relative importance of polymer diffusiophoresis compared to its intrinsic Brownian mobility increases with particle size. The observed behavior was linked to preferential hydration (water thermodynamic excess) and hydration (bound water) of the macromolecule. The ratio of salt osmotic diffusion to binary salt-water diffusion approximately describes the nonuniform spatial distribution of salt along a static polymer concentration gradient at equilibrium. The significance of polymer diffusiophoresis, especially at high PEG molecular mass, was examined by considering a steady-state diffusion problem showing that salt concentration gradients can produce large enhancements and depletions of polymer concentration. This work is valuable for understanding and modeling the effect of salt concentration gradients on diffusion-based transport of polymers with applications to interfacial processes.

Atomic mechanism of dynamic electrochemical lithiation processes of MoS₂ nanosheets

Layered molybdenum disulfide (MoS2) has been studied for decades for its diversity of structure and properties, where the structural dynamic evolution during lithium intercalation is an important but still indistinct, controversial topic. Here the electrochemical dynamic process of MoS2 nanosheets upon lithium intercalation has been systematically investigated by in situ high-resolution transmission electron microscopy. The results indicate that the lithiated MoS2 undergoes a trigonal prismatic (2H)-octahedral (1T) phase transition with a lithium ion occupying the interlayer S-S tetrahedron site in the 1T-LiMoS2. A pseudoperiodic structural modulation composed of polytype superlattices is also revealed as a consequence of the electron-lattice interaction. Furthermore, the shear mechanism of the 2H-1T phase transition has been confirmed by probing the dynamic phase boundary movement. The in situ real-time characterization at atomic scale provides a great leap forward in the fundamental understanding of the lithium ion storage mechanism in MoS2, which should be also of help for other transition metal dichalcogenides.

ZnO nanocubes with (101) basal plane photocatalyst prepared via a low-frequency ultrasonic assisted hydrolysis process

The crystallographic plane of the ZnO nanocrystals photocatalyst is considered as a key parameter for an effective photocatalysis, photoelectrochemical reaction and photosensitivity. In this paper, we report a simple method for the synthesis of a new (101) high-energy plane bounded ZnO nanocubes photocatalyst directly on the FTO surface, using a seed-mediated ultrasonic assisted hydrolysis process. In the typical procedure, high-density nanocubes and quasi-nanocubes can be grown on the substrate surface from a solution containing equimolar (0.04 M) zinc nitrate hydrate and hexamine. ZnO nanocubes, with average edge-length of ca. 50 nm, can be obtained on the surface in as quickly as 10 min. The heterogeneous photocatalytic property of the sample has been examined in the photodegradation of methyl orange (MO) by UV light irradiation. It was found that the ZnO nanocubes exhibit excellent catalytic and photocatalytic properties and demonstrate the photodegradation efficiency as high as 5.7 percent/μg mW. This is 200 times higher than those reported results using a relatively low-powered polychromatic UV light source (4 mW). The mechanism of ZnO nanocube formation using the present approach is discussed. The new-synthesized ZnO nanocubes with a unique (101) basal plane also find potential application in photoelectrochemical devices and sensing.

The edge termination controlled kinetics in graphene chemical vapor deposition growth

The kinetics of graphene CVD growth is dominated by the type of edge passivation.

Does Solution Viscosity Scale the Rate of Aggregation of Folded Proteins?

Viscosity effects on the kinetics of complex solution processes have proven hard to predict. To test the viscosity effects on protein aggregation, we use the crystallization of the protein glucose isomerase (gluci) as a model and employ scanning confocal and atomic force microscopies at molecular resolution, dynamic and static light scattering, and rheometry. We add glycerol to vary solvent viscosity and demonstrate that glycerol effects on the activation barrier for attachment of molecules to the crystal growth sites are minimal. We separate the effects of glycerol on crystallization thermodynamics from those on the rate constant for molecular attachment. We establish that the rate constant is proportional to the reciprocal viscosity and to the protein diffusivity. This finding refutes the prevailing crystal growth paradigm and illustrates the application of fundamental kinetics laws to solution crystallization.

Phase diagrams and kinetics of phase transitions in protein solutions

The phase behavior of proteins is of interest for fundamental and practical reasons. The nucleation of new phases is one of the last major unresolved problems of nature. The formation of protein condensed phases (crystals, polymers, and other solid aggregates, as well as dense liquids and gels) underlies pathological conditions, plays a crucial role in the biological function of the respective protein, or is an essential part of laboratory and industrial processes. In this review, we focus on phase transitions of proteins in their properly folded state. We first summarize the recently acquired understanding of physical processes underlying the phase diagrams of the protein solutions and the thermodynamics of protein phase transitions. Then we review recent findings on the kinetics of nucleation of dense liquid droplets and crystals. We explore the transition from nucleation to spinodal decomposition for liquid-liquid separation and introduce the new concept of solution-to-crystal spinodal. We review the two-step mechanism of protein crystal nucleation, in which mesoscopic metastable protein clusters serve as precursors to the ordered crystal nuclei. The concepts and mechanisms reviewed here provide powerful tools for control of the nucleation process by varying the solution thermodynamic parameters.

Solvent-mediated amorphous-to-crystalline transformation of nitrendipine in amorphous particle suspensions containing polymers

The amorphous-to-crystalline transformation of nitrendipine was investigated using Raman spectroscopy and X-ray powder diffraction (XRPD). The nucleation and growth rate of crystalline nitrendipine in a medium containing poly (vinyl alcohol) (PVA) and polyethylene glycol (PEG 200) were quantitatively determined using image analysis based on polarized light microscopy. The findings from the image analysis revealed that the transformation process occurred through the dissolution of amorphous drug precipitate followed by the nucleation and growth of the crystalline phase with the amorphous precipitate acting as a reservoir for maintaining the supersaturation. The rates of nucleation and crystal growth of nitrendipine decreased with an increase in PEG 200 concentration in organic phase from 0% to 75% (v/v). Increasing the PVA concentration in water phase from 0.1% to 1.0% (w/w) also decreased the rates of nucleation and crystal growth, however, an increase in PVA concentration from 1.0% to 2.0% (w/w) did not result in a further decrease in the rates of nucleation and crystal growth. An increase in drug concentrations in the organic phase from 10 mg/ml to 30 mg/ml led to faster nucleation rates. However, a further increase in drug concentration to 100mg/ml decelerated the growth of nitrendipine crystals. Combining image analysis of polarized light micrographs together with Raman spectroscopy and XRPD provided an in-depth insight into solid state transformations in amorphous nitrendipine suspensions.

Control of Gibbs free energy relationship between hen egg white lysozyme polymorphs under application of an external alternating current electric field

The distribution of phases between bulk (tetragonal structure) and spherulitic crystals for hen egg white lysozyme was controlled under application of an external alternating current electric field. The distribution of phases differed depending on differences in the magnitude of the electrostatic energy contribution to the respective chemical potentials of the two solid phases. Therefore, the Gibbs free energy relationship between the two solid phases could be controlled by changing the frequency of the applied external electric field. Such a method of controlling the Gibbs free energy relationship among polymorphs would be adaptable to many kinds of protein.

Multisite models to determine the distribution of kink sites adjacent to low-energy edges

Kink sites play a critical role in crystal growth. The incorporation of a growth unit into a kink site (1) maintains the free energy of the edge constant and (2) creates another site with the same properties. These properties allow growth through successive incorporation events to proceed in a self-sustaining manner such that the equilibrium spacing between kinks is maintained on average. Traditionally the distributions of kink sites have been determined using a single-site model whereby the probabilities of encountering a kink site adjacent to an edge and encountering a disturbance along an edge are assumed equivalent. In this paper, we develop multisite models that determine the probabilities of encountering kink sites; with the requirement that they obey both properties necessary for growth through successive self-sustaining incorporation events. The probabilities determined using the multisite models diverge significantly from the single-site model for edges with intermolecular interactions ≲6k(b)T between successive molecules. The implications of these findings for the development of predictive crystal shape models and experimental analysis are discussed.

Control of effect on the nucleation rate for hen egg white lysozyme crystals under application of an external ac electric field

The effect of an external ac electric field on the nucleation rate of hen egg white lysozyme crystals increased with an increase in the concentration of the precipitant used, which enabled the design of an electric double layer (EDL) formed at the inner surface of the drop in the oil. This is attributed to the thickness of the EDL controlled by the ionic strength of the precipitant used. Control of the EDL formed at the interface between the two phases is important to establishing this novel technique for the crystallization of proteins under the application of an external ac electric field.

Nucleation

Crystallization starts with nucleation and control of nucleation is crucial for the control of the number, size, perfection, polymorphism and other characteristics of crystalline materials. This is particularly true for crystallization in solution, which is an essential part of processes in the chemical and pharmaceutical industries and a major step in physiological and pathological phenomena. There have been significant recent advances in the understanding of the mechanism of nucleation of crystals in solution. The foremost of these are the two-step mechanism of nucleation and the notion of the solution-crystal spinodal. According to the two-step mechanism, the crystalline nucleus appears inside pre-existing metastable clusters of size several hundred nanometers, which consist of dense liquid and are suspended in the solution. While initially proposed for protein crystals, the applicability of this mechanism has been demonstrated for small molecule organic materials, colloids, polymers, and biominerals. This mechanism helps to explain several long-standing puzzles of crystal nucleation in solution: nucleation rates which are many orders of magnitude lower than theoretical predictions, the significance of the dense protein liquid, and others. At high supersaturations typical of most crystallizing systems, the generation of crystal embryos occurs in the spinodal regime, where the nucleation barrier is negligible. The solution-crystal spinodal helps to understand the role of heterogeneous substrates in nucleation and the selection of crystalline polymorphs. Importantly, these ideas provide powerful tools for control of the nucleation process by varying the solution thermodynamic parameters.

Dynamics of Biomineralization and Biodemineralization

In order to understand the fundamental processes leading to biomineralization, this chapter focuses on the earliest events of homo/heterogeneous nucleation from an initial supersaturated solution phase and subsequent growth involving various possible precursor phases (amorphous or crystalline) to the final mineral phase by specific template and other influences. We also discuss how the combination of macroscopic constant composition and microscopic atomic force microscopy provides insights into the physical mechanisms of crystal growth and phase stability and the influences of proteins, peptides or other small molecules.Biodemineralization reactions of tooth enamel and bone may be inhibited or even suppressed when particle sizes fall into certain critical nanoscale levels. This phenomenon actually involves particle-size-dependent critical conditions of energetic control at the molecular level. Clearly, this dissolution termination is a kinetic phenomenon and cannot be attributed to reaction retardation as a result of surface modification by additives. Almost all biomineralized structures are highly hierarchical at many different length scales. At the lowest level they often consist of tiny crystals, typically tens to hundreds of nanometers. This size is not arbitrary; rather, it seems to give biominerals such as bone and tooth remarkable physical characteristics.

Subnanometer atomic force microscopy of peptide-mineral interactions links clustering and competition to acceleration and catastrophe

In vitro observations have revealed major effects on the structure, growth, and composition of biomineral phases, including stabilization of amorphous precursors, acceleration and inhibition of kinetics, and alteration of impurity signatures. However, deciphering the mechanistic sources of these effects has been problematic due to a lack of tools to resolve molecular structures on mineral surfaces during growth. Here we report atomic force microscopy investigations using a system designed to maximize resolution while minimizing contact force. By imaging the growth of calcium-oxalate monohydrate under the influence of aspartic-rich peptides at single-molecule resolution, we reveal how the unique interactions of polypeptides with mineral surfaces lead to acceleration, inhibition, and switching of growth between two distinct states. Interaction with the positively charged face of calcium-oxalate monohydrate leads to formation of a peptide film, but the slow adsorption kinetics and gradual relaxation to a well-bound state result in time-dependent effects. These include a positive feedback between peptide adsorption and step inhibition described by a mathematical catastrophe that results in growth hysteresis, characterized by rapid switching from fast to near-zero growth rates for very small reductions in supersaturation. Interactions with the negatively charged face result in formation of peptide clusters that impede step advancement. The result is a competition between accelerated solute attachment and inhibition due to blocking of the steps by the clusters. The findings have implications for control of pathological mineralization and suggest artificial strategies for directing crystallization.

Determination of the transition-state entropy for aggregation suggests how the growth of sickle cell hemoglobin polymers can be slowed

Sickle cell anemia is associated with the mutant hemoglobin HbS, which forms polymers in red blood cells of patients. The growth rate of the polymers is several micrometers per second, ensuring that a polymer fiber reaches the walls of an erythrocyte (which has a 7-microm diameter) within a few seconds after its nucleation. To understand the factors that determine this unusually fast rate, we analyze data on the growth rate of the polymer fibers. We show that the fiber growth follows a first-order Kramers-type kinetics model. The entropy of the transition state for incorporation into a fiber is 95 J mol(-1) K(-1), very close to the known entropy of polymerization. This agrees with a recent theoretical estimate for the hydrophobic interaction and suggests that the gain of entropy in the transition state is due to the release of the last layer of water molecules structured around contact sites on the surface of the HbS molecules. As a result of this entropy gain, the free-energy barrier for incorporation of HbS molecules into a fiber is negligible and fiber growth is unprecedentedly fast. This finding suggests that fiber growth can be slowed by components of the red cell cytosol, native or intentionally introduced, which restructure the hydration layer around the HbS molecules and thus lower the transition state entropy for incorporation of an incoming molecule into the growing fiber.

Sickle-cell haemoglobin polymerization: is it the primary pathogenic event of sickle-cell anaemia?

Sickle cell anaemia is associated with a mutant haemoglobin, HbS, which forms polymers in the red blood cells of patients. The primary role of the HbS polymerization for the pathophysiology has been questioned: observations in patients and model organisms contradict deterministic scenarios of sickling crises triggered by polymerization. However, results with knock-out sickle-cell mice, which were cured by delaying HbS polymerization, reconfirm polymerization's primary role. To reconcile the contradictory observations, this article reviews recent findings on two steps in polymerization: homogeneous nucleation of fibres, and their growth. The fibre growth is faster by far than for any other protein ordered structure. This is due to a negligible free-energy barrier for incorporation into a fibre, determined by an entropy gain, stemming from the release of water molecules structured around HbS. The kinetics of fibre nucleation have shown that the formation of the polymer nucleus is preceded by a metastable droplet of a dense liquid. The properties of the dense liquid are sensitive functions of solution composition, including components in micro- and nanomolar amounts. This mechanism allows low-concentration solution components to strongly affect the nucleation kinetics, accounting for the high variability of the disease. These insights can potentially be utilized for control of HbS polymerization and treatment of the disease.

Self-assembly of 1-D organic semiconductor nanostructures

This review focuses on the molecular design and self-assembly of a new class of crowded aromatics that form 1-D nanostructures via hydrogen bonding and pi-pi interactions. These molecules have a permanent dipole moment that sums as the subunits self assemble into molecular stacks. The assembly of these molecular stacks can be directed with electric fields. Depending on the nature of the side-chains, molecules can obtain the face-on or edge-on orientation upon the deposition onto a surface via spin cast technique. Site-selective steady state fluorescence, time-resolved fluorescence, and various types of scanning probe microscopy measurements detail the intermolecular interactions that drive the aromatic molecules to self-assemble in solution to form well-ordered columnar stacks. These nanostructures, formed in solution, vary in their number, size, and structure depending on the functional groups, solvent, and concentration used. Thus, the substituents/side-groups and the proper choice of the solvent can be used to tune the intermolecular interactions. The 1-D stacks and their aggregates can be easily transferred by solution casting, thus allowing a simple preparation of molecular nanostructures on different surfaces.

Role of molecular charge and hydrophilicity in regulating the kinetics of crystal growth

The composition of biologic molecules isolated from biominerals suggests that control of mineral growth is linked to biochemical features. Here, we define a systematic relationship between the ability of biomolecules in solution to promote the growth of calcite (CaCO3) and their net negative molecular charge and hydrophilicity. The degree of enhancement depends on peptide composition, but not on peptide sequence. Data analysis shows that this rate enhancement arises from an increase in the kinetic coefficient. We interpret the mechanism of growth enhancement to be a catalytic process whereby biomolecules reduce the magnitude of the diffusive barrier, Ek, by perturbations that displace water molecules. The result is a decrease in the energy barrier for attachment of solutes to the solid phase. This previously unrecognized relationship also rationalizes recently reported data showing acceleration of calcite growth rates over rates measured in the pure system by nanomolar levels of abalone nacre proteins. These findings show that the growth-modifying properties of small model peptides may be scaled up to analyze mineralization processes that are mediated by more complex proteins. We suggest that enhancement of calcite growth may now be estimated a priori from the composition of peptide sequences and the calculated values of hydrophilicity and net molecular charge. This insight may contribute to an improved understanding of diverse systems of biomineralization and design of new synthetic growth modulators.

Nucleation of Protein Crystals under the Influence of Solution Shear Flow

Several recent theories and simulations have predicted that shear flow could enhance, or, conversely, suppress the nucleation of crystals from solution. Such modulations would offer a pathway for nucleation control and provide a novel explanation for numerous mysteries in nucleation research. For experimental tests of the effects of shear flow on protein crystal nucleation, we found that if a protein solution droplet of approximately 5 microL (2-3 mm diameter at base) is held on a hydrophobic substrate in an enclosed environment and in a quasi-uniform constant electric field of 2 to 6 kV cm(-1), a rotational flow with a maximum rate at the droplet top of approximately 10 microm s(-1) is induced. The shear rate varies from 10(-3) to 10(-1) s(-1). The likely mechanism of the rotational flow involves adsorption of the protein and amphiphylic buffer molecules on the air-water interface and their redistribution in the electric field, leading to nonuniform surface tension of the droplet and surface tension-driven flow. Observations of the number of nucleated crystals in 24- and 72-h experiments with the proteins ferritin, apoferritin, and lysozyme revealed that the crystals are typically nucleated at a certain radius of the droplet, that is, at a preferred shear rate. Variations of the rotational flow velocity resulted in suppression or enhancement of the total number of nucleated crystals of ferritin and apoferritin, while all solution flow rates were found to enhance lysozyme crystal nucleation. These observations show that shear flow may strongly affect nucleation, and that for some systems, an optimal flow velocity, leading to fastest nucleation, exists. Comparison with the predictions of theories and simulations suggest that the formation of ordered nuclei in a "normal" protein solution cannot be affected by such low shear rates. We conclude that the flow acts by helping or suppressing the formation of ordered nuclei within mesoscopic metastable dense liquid clusters. Such clusters were recently shown to exist in protein solutions and to constitute the first step in the nucleation mechanism of many protein and nonproteinsystems.