Crystal Nucleation Kinetics Research Articles

Templated Nucleation of Clotrimazole and Ketoprofen on Polymer Substrates.

The use of different template surfaces in crystallization experiments can directly influence the nucleation kinetics, crystal growth, and morphology of active pharmaceutical ingredients (APIs). Consequently, templated nucleation is an attractive approach to enhance crystal nucleation kinetics and preferentially nucleate desired crystal polymorphs for solid-form drug molecules, particularly large and flexible molecules that are difficult to crystallize. Herein, we investigate the effect of polymer templates on the crystal nucleation of clotrimazole and ketoprofen with both experiments and computational methods. Crystallization was carried out in toluene solvent for both APIs with a template library consisting of 12 different polymers. In complement to the experimental studies, we developed a computational workflow based on molecular dynamics (MD) and derived descriptors from the simulations to score and rank API-polymer interactions. The descriptors were used to measure the energy of interaction (EOI), hydrogen bonding, and rugosity (surface roughness) similarity between the APIs and polymer templates. We used a variety of machine learning models (14 in total) along with these descriptors to predict the crystallization outcome of the polymer templates. We found that simply rank-ordering the polymers by their API-polymer interaction energy descriptors yielded 92% accuracy in predicting the experimental outcome for clotrimazole and ketoprofen. The most accurate machine learning model for both APIs was found to be a random forest model. Using these models, we were able to predict the crystallization outcomes for all polymers. Additionally, we have performed a feature importance analysis using the trained models and found that the most predictive features are the energy descriptors. These results demonstrate that API-polymer interaction energies are correlated with heterogeneous crystallization outcomes.

Preferred Crystallographic Orientation via Solution Bathing for High‐Performance Inverted Perovskite Photovoltaics

AbstractThe meticulous control of crystal facets in polycrystalline perovskite films offers valuable insights into the photoelectric properties, varying significantly with different orientations. Exploring effective means to regulate these facets is crucial, and further revealing the underlying mechanisms is needed. Here, the research employed green solution bathing to obtain high‐quality perovskite films with preferred crystallographic orientation. In brief, eco‐friendly 2‐pentanol is used as the solvent, and functional molecules 2‐(dimethylaminomethyl)‐4‐(2‐aminoethylthiomethyl)thiazole (DAT) are introduced into the solution bathing as the solute. By introducing DAT molecules, precise control over perovskite crystal nucleation kinetics is achieved, resulting in films with a preferential (100) facet orientation. Conversely, films without DAT exhibited distinct (111) facet orientation. The regulation of DAT on perovskite film crystal facet is verified through theoretical and crystallographic analyses. Theoretical calculations show that S atom of DAT binds most strongly to the (100) facet of FAPbI3, promoting surface energy reduction and thermodynamic enhancement, favoring (100) crystal orientation. Crystallographic characterization further proved the regulation effect. In addition, PL/TRPL tests confirm the regulation of DAT on superior photoelectric properties of (100)‐oriented perovskite films. The work introduces a novel approach and preparation process for regulating the crystal facets orientation of polycrystalline perovskite films.

Monitoring Aqueous Sucrose Solutions Using Droplet Microfluidics: Ice Nucleation, Growth, Glass Transition, and Melting.

Freezing and freeze-drying processes are commonly used to extend the shelf life of drug products and to ensure their safety and efficacy upon use. When designing a freezing process, it is beneficial to characterize multiple physicochemical properties of the formulation, such as nucleation rate, crystal growth rate, temperature and concentration of the maximally freeze-concentrated solution, and melting point. Differential scanning calorimetry has predominantly been used in this context but does have practical limitations and is unable to quantify the kinetics of crystal growth and nucleation. In this work, we introduce a microfluidic technique capable of quantifying the properties of interest and use it to investigate aqueous sucrose solutions of varying concentration. Three freeze-thaw cycles were performed on droplets with 75-μm diameters at cooling and warming rates of 1 °C/min. During each cycle, the visual appearance of the droplets was optically monitored as they experienced nucleation, crystal growth, formation of the maximally freeze-concentrated solution, and melting. Nucleation and crystal growth manifested as increases in droplet brightness during the cooling phase. Heating was associated with a further increase as the temperature associated with the maximally freeze-concentrated solution was approached. Heating beyond the melting point corresponded to a decrease in brightness. Comparison with the literature confirmed the accuracy of the new technique while offering new visual data on the maximally freeze-concentrated solution. Thus, the microfluidic technique presented here may serve as a complement to differential scanning calorimetry in the context of freezing and freeze-drying. In the future, it could be applied to a plethora of mixtures that undergo such processing, whether in pharmaceutics, food production, or beyond.

Reactive Crystallization Kinetics Study of Boehmite in Ammonia Solution by Adding Ammonium Aluminum Sulfate

As an important intermediate product in new techniques for extracting alumina from coal fly ash, boehmite is obtained by the reaction between ammonium aluminum sulfate and ammonia. The reactive crystallization kinetics of boehmite is investigated using a continuous steady-state method. The Mydlarz and Jones (MJ3) models are in considerable agreement with the experimental results by a non-linear regression method; furthermore, crystal nucleation and growth rate equations are proposed. The results revealed that the suspension density and agitation rates present considerable influence on nucleation. Additionally, high levels of supersaturation are not conducive for crystal growth, and the supersaturation index for crystal growth was small due to its poor water solubility. Moreover, the maximum d0.5 (average particle size) was 27.968 μm under the agitation condition and the feed rates of 250 r/s and 0.5 g/10 min. Fast crystal growth speed is associated with the crystal structure’s high AlO6-unit and bulk-oxygen content. Our study on crystal nucleation and growth kinetics will be beneficial to the industrial production of boehmite.

Desupersaturation dynamics in solutions with applications to bovine and porcine insulin crystallization

Evolution of crystal ensembles in supersaturated solutions is studied at the initial and intermediate stages of bulk crystallization. An integro-differential model includes fluctuations in crystal growth rates, initial crystal-size distribution and arbitrary nucleation and growth kinetics of crystals. Two methods based on variables separation and saddle-point technique for constructing a complete analytical solution to this model are considered. Exact parametric solutions based on these methods are derived. Desupersaturation dynamics is in good agreement with the experimental data for bovine and porcine insulin. The method based on variables separation has a strong physical limitation on exponentially decaying initial distribution and leads to the distribution function increasing with time. The method based on saddle-point technique leads to a dome-shaped crystal-size distribution function decreasing with time and has no strong physical limitations. The latter circumstance makes this method more reasonable for describing the kinetics of bulk crystallization in solutions and melts.

Decoding the role of triacylglycerol composition in the milk fat crystallisation behaviour: A study using buffalo milk fat fractions

The role of triacylglycerols (TAGs) composition in milk fat crystallisation is evaluated from a new perspective by correlating the crystal structures and their predicted TAG contributors. Four different TAG groups, defined by their fatty acid (FA) chain length and saturation are proposed to explain the crystallisation behaviour of different milk fat samples, namely TAGs containing (i) fully saturated long chain FAs, (ii) single unsaturated long-chain FA and (iii) multi unsaturated long-chain FAs, as well as (iv) short-chain FAs. Samples containing different TAGs proportions were obtained from two-step dry fractionation of buffalo milk fat. Liquid chromatography and mass spectrometry (LCMS) was employed to determine the TAGs composition. The crystallisation characteristics were evaluated using small-angle X-ray scattering (SAXS), differential scanning calorimetry (DSC) and polarised light microscopy. The results confirm that fully saturated long chain TAGs are responsible for the formation of high melting point 2L-crystals (d-spacing: 44.1–49.7 Å), whilst the low melting point 3L-crystals (64.4–72.8 Å) are mainly contributed by long chain TAGs containing unsaturated fatty acids. Further, the crystallisation inhibiting effect of asymmetrical TAGs, containing short chain fatty acid (C4-6) is evident. As a final point, effects of the four TAG groups, each given with a specific composition, were examined closely also with respect to their influence on the nucleation and polymorphic transformation kinetics of milk fat crystals.

Rapid Assessment of Crystal Nucleation and Growth Kinetics: Comparison of Seeded and Unseeded Experiments.

In this work, we outlined an experimental workflow enabling the rapid assessment of primary and secondary nucleation and crystal growth kinetics. We used small-scale experiments in agitated vials with in situ imaging for crystal counting and sizing to quantify nucleation and growth kinetics of α-glycine in aqueous solutions as a function of supersaturation at isothermal conditions. Seeded experiments were required to assess crystallization kinetics when primary nucleation is too slow, especially at lower supersaturations often encountered in continuous crystallization processes. At higher supersaturations, we compared results from seeded and unseeded experiments and carefully analyzed interdependencies of primary and secondary nucleation and growth kinetics. This approach allows for the rapid estimation of absolute values of primary and secondary nucleation and growth rates without relying on any specific assumptions about functional forms of corresponding rate expressions used for estimation approaches based on fitting population balance models. Quantitative relationships between nucleation and growth rates at given conditions provide useful insights into crystallization behavior and can be explored to rationally manipulate crystallization conditions for achieving desirable outcomes in batch or continuous crystallization processes.

Automated and Material-Sparing Workflow for the Measurement of Crystal Nucleation and Growth Kinetics

Automated and Material-Sparing Workflow for the Measurement of Crystal Nucleation and Growth Kinetics

Discovery of a new polymorph of clotrimazole through melt crystallization: Understanding nucleation and growth kinetics.

Clotrimazole (CMZ) is a classical antifungal drug for studying crystallization. In this study, a new CMZ polymorph (Form 2) was discovered during the process of nucleation and growth rate determination in the melt. High-quality single crystals were grown from melt microdroplets to determine the crystal structure by x-ray diffraction. Form 2 is metastable and exhibits a disordered structure. The crystal nucleation and growth kinetics of the two CMZ polymorphs were systematically measured. Form 2 nucleates and grows faster than the existing form (Form 1). The maximum nucleation rate of Forms 1 and 2 was observed at 50 °C (1.07 Tg). The summary of the maximum nucleation rate temperature of CMZ and the other six organic compounds indicates that nucleation near Tg in the supercooled liquid is a useful approach to discovering new polymorphs. This study is relevant for the discovering new drug polymorphs through an understanding of nucleation and growth kinetics during melt crystallization.

Ultrahigh-quality large single crystal preparation using the modified seed crystal-induced crystallization method with precision-controlled temperature gradient

• Centimeter-size Cs 4 PbBr 6 single crystals were synthesized by novel method. • The growth, nucleation kinetics of large single crystals was investigated. • All the Cs 4 PbBr 6 single crystals emit intense greenish PL signals under UV lamp. • This technique has great potential for large-scale industrial production. Inorganic perovskites, particularly Cs4PbBr6, possess great potential applications for radiation detection, photonic and optoelectronic devices due to their peculiar yet robust photoluminescence properties and spectral color purity. Herein, a facile and industrial route to synthesize centimeter-size (1.2×1.1×0.8 cm3) Cs4PbBr6 single crystals was developed by modified seed crystal induced the precision-controlled temperature-gradient crystallization method. The effects of the temperature and supersaturation on growth, nucleation kinetics of large Cs4PbBr6 single crystals have been investigated. Our findings will provide a new strategy for the fabrication of large perovskite-related single crystals and could further strengthen their competitiveness for the field of lighting or display.

Polythermal Nucleation Kinetics of NaHCO3-Na2CO3-H2O in the Presence of Polyectrolyte Additives

The particle size distribution (PSD) of substances is important to their transportation and packaging. The crystal nucleation kinetics measured from the metastable zone width (MSZW) and/or the induction time are vital to the control of the PSD. In this work, the existence of three polyelectrolyte additives (sodium polystyrene sulfonate (SPS), Polyacetic acid (PAA) and sodium carboxymethylcellulose (CMC)) showed varying effects on the MSZW and induction times of NaHCO3-Na2CO3-H2O system. SPS lowers the MSZW and induction time while both parameters were increased in the presence of CMC and PAA. The nucleation inhibition effects were observed to be prominent for both PAA and CMC resulting in observed finer PSDs as cooling rate, b increases from 0.5 K/min to 2.65 K/min. The PSD increases with b for both pure and SPS additive, whereas they decrease for both PAA and CMC.

Concentration dependence of the crystal nucleation kinetics in undercooled Cu-Ge melts.

The crystallization temperature of deeply undercooled Cu-Ge alloy melts is repeatedly measured. A statistical analysis is applied on the undercooling distributions obtained from nine different compositions, ranging from the pure semimetal (Ge) to the pure metal (Cu). By considering each undercooling distribution as an inhomogeneous Poisson process, the nucleation rates for every composition are calculated. The Thompson-Spaepen model for homogeneous nucleation in binary alloys is applied, enabling the estimation of nucleation parameters, such as kinetic pre-factors and interfacial energies, as a function of composition. Furthermore, the Turnbull coefficient α, a dimensionless solid-liquid interfacial energy constant, is also calculated as a function of alloy constitution, suggesting a dependence on the liquid composition. The composition-dependent changes of α are of considerable importance, since the α is originally defined for pure systems as a quantity dependent on crystal structure, and is nevertheless used for describing nucleation kinetics of binary and glass forming multi-component alloy systems.

Theoretical and Practical Studies on Effects of External Electrostatic Electric Field on Nucleation and Growth Kinetics of Protein Crystals

The crystallization technique where an electric field is applied is an extremely powerful tool to control the crystallization processes of various materials. In particular, the method with application of an external electrostatic electric field can have a significant effect on the phase equilibrium of the liquid and solid phases. This review demonstrates that the crystallization processes of proteins are significantly impacted by the application of an external electrostatic electric field: (1) Control of both the increase and decrease in the nucleation rate can be achieved by changing the applied frequency of the external electrostatic electric field. (2) The effect of the external electrostatic electric field on the nucleation rate can be controlled by regulating the thickness of the electric double layer (EDL) formed at the interface. (3) The quality of the grown crystals can be improved by an increase in the step free energy under application of an external electrostatic electric field at 1 MHz. The effect of the external electrostatic electric field on nucleation and growth kinetics during crystal growth of proteins is also discussed based on a thermodynamic perspective.

Relating Alkyl Chain Length of Additives to Wax Crystallization Inhibition: Toward the Rational Design of Pour Point Depressants

Precipitation of paraffin wax (long-chained n-alkanes) from engine oil and fuel distillates at low temperatures is generally prevented using low-dosage polymeric additives, known as pour point depressants (PPDs). The ability of a PPD to inhibit wax crystallization is largely determined by how well its alkyl side chains interact with the waxy components present in the base oil. The current study aims to elucidate the mechanism underpinning this structure–property relationship using docosane (n-C22H46) dissolved in a mixture of dodecane and toluene as a model waxy oil and the homologous series of paraffins as “tailor-made” additives. By determining the wax crystal nucleation kinetics using polythermal turbidimetry measurements, a direct link between the carbon chain length of the additive molecule and its ability to retard wax precipitation was established. Thermodynamic and structural analysis of the wax formation process using differential scanning calorimetry and small/wide-angle X-ray scattering techniques respectively revealed that the additive incorporates into the lamellar wax aggregates formed during the nucleation stage and subsequently impedes its crystallization. This mechanism is consistent with the cocrystallizing behavior of n-alkanes from multiparaffinic solutions to form a solid solution. Only additives with alkyl chains longer than the solute wax retarded nucleation and growth along the needle axis of the wax crystal because of the end-chain protrusion/bending disorder in the resultant lamellar wax crystal structure.

Characterization and Crystal Nucleation Kinetics of a New Metastable Polymorph of Piracetam in Alcoholic Solvents.

A new polymorph of the drug active pharmaceutical ingredient piracetam (Form VI) has been discovered and characterized by X-ray powder diffraction (PXRD), solid-state Raman, attenuated total reflectance infrared spectroscopy, and differential scanning calorimetry. The PXRD diffractogram of Form VI shows a distinct peak at 24.2° (2θ) that distinguishes it from the previously known polymorphs and solvates. Form VI is metastable with respect to the previously known polymorphs Form II and Form III; in ethanol solution at 288 K, Form VI transforms into Form II within 15 min, while in isopropanol solution Form VI is kinetically stable for at least 6 h. A total of 1200 crystal nucleation induction time experiments of piracetam in ethanol and isopropanol solutions have been conducted, in sets of 40–80 repeat experiments carried out at different temperatures and solute concentrations. Each solution nucleated as a single polymorph, and each set of repeat experiments resulted in different proportions of Form II, Form III, and Form VI, with Form VI dominating at low nucleation temperatures and Form II at higher nucleation temperatures. The induction time data for Form VI at 288 K have been evaluated within the framework of the classical nucleation theory. At equal driving force, nucleation of Form VI is less obstructed in ethanol than in isopropanol, as captured by a lower interfacial energy and higher pre-exponential factor in ethanol. The proportion of Form VI obtained at a comparable driving force increases in the order ethanol < isopropanol.

Two-step crystal nucleation kinetics: Solution of the master equation

The master equation of two-step nucleation is numerically solved with parameters characterizing isothermal homogeneous nucleation of ice crystals and water droplets in steam below the water freezing temperature. The time dependences of the crystal and droplet size distributions and nucleation rates as well as of the nucleation rate of ice crystals in the droplets are determined at different constant supersaturations. The stationary values of these nucleation rates are obtained in a wide supersaturation range. It is found that when the crystallization of the water droplets is slower than their growth, the stationary rate of two-step crystal nucleation is orders of magnitude lower than the corresponding stationary rate of one-step crystal nucleation. As to the stationary nucleation rate of the water droplets, it is practically unaffected by the ice crystals nucleating and growing in both the droplets and the steam. Finally, the delay times of the different nucleation processes are determined and it is found that at both low and high supersaturations the delay time of the two-step crystal nucleation is negative because of the presence of high initial peak in the nonstationary rate of this process. The results obtained provide unprecedented mechanistic insight into the kinetics of two-step crystal nucleation.

In-Situ Transmission Electron Microscopy Observation of Germanium Growth on Freestanding Graphene: Unfolding Mechanism of 3D Crystal Growth During Van der Waals Epitaxy.

Breakthroughs in cutting-edge research fields such as hetero-integration of materials and the development of quantum devices are heavily bound to the control of misfit strain during heteroepitaxy. While remote epitaxy offers one of the most intriguing avenues, demonstrations of functional hybrid heterostructures are hardly possible without a deep understanding of the nucleation and growth kinetics of 3D crystals on graphene and their mutual interactions. Here, the kinetics of such processes from real-time observations of germanium (Ge) growth on freestanding single layer graphene (SLG) using in-situ transmission electron microscopy are unraveled. This powerful technique provides a unique opportunity to observe new and yet unexplored phenomena, which are not accessible to the standard ex situ characterizations. Through direct observations, remote interactions are elucidated between Ge crystals through the graphene layer in double heterostructures of Ge/graphene/Ge. Notably, the data show real-time evidence of vertical Ge atoms diffusion through the graphene layer. This phenomenon is attributed to the remote interactions of Ge atoms through the graphene lattice, due to its interatomic interaction transparency. Additionally, key mechanisms governing nucleation and initial growth in graphene were systematically determined. These findings enlighten the growth mechanism of graphene and provide a new pathway for disruptive hybrid semiconductor-graphene devices.

Nucleation and growth kinetics of CaCO3 crystals in the presence of foreign monovalent ions

The aim of this work is to study the effect of the presence of different monovalent ions (Na+, NH4+ and K+) on the nucleation and growth rates of CaCO3 precipitation. There is currently great interest in the precipitation of CaCO3 particles reusing CO2 rich flue gases and calcium-rich wastes, which implies the presence of foreign ions that can affect the crystallization process. Unseeded and seeded tests were carried out in a batch system to estimate the nucleation and growth kinetics, respectively. Tests with Na2CO3 and CaCl2 as precursors led to the classical calcite crystallization mechanism via vaterite formation at high supersaturations. On the other hand, the use of (NH4)2CO3 entailed lower pH and the presence of NH4+, which stabilized the vaterite and avoided its transformation into stable calcite crystals. Thus, faster nucleation kinetics by using Na2CO3 were obtained. To estimate the growth rate, tests with two initial seed loadings and types (micro and nano seed) were performed. The growth rate increased with the crystal size and decreased with the magma density. The results indicate that the ion effect on the growth rate seems to be related to the ionic radius of the foreign ion.

Crystal Nucleation and Growth in Cross-Linked Poly(ε-caprolactone) (PCL).

The crystal nucleation and overall crystallization kinetics of cross-linked poly(ε-caprolactone) was studied experimentally by fast scanning calorimetry in a wide temperature range. With an increasing degree of cross-linking, both the nucleation and crystallization half-times increase. Concurrently, the glass transition range shifts to higher temperatures. In contrast, the temperatures of the maximum nucleation and the overall crystallization rates remain the same, independent of the degree of cross-linking. The cold crystallization peak temperature generally increases as a function of heating rate, reaching an asymptotic value near the temperature of the maximum growth rate. A theoretical interpretation of these results is given in terms of classical nucleation theory. In addition, it is shown that the average distance between the nearest cross-links is smaller than the estimated lamellae thickness, which indicates the inclusion of cross-links in the crystalline phase of the polymer.

Unveiling relaxation and crystal nucleation interplay in supercooled germanium liquid

A well-designed study of the relationship between crystal nucleation and relaxation in supercooled liquids could clarify some critical issues in condensed matter science. In this article, we dwell on the kinetic spinodal temperature, TKS – where the times of first critical nucleus formation and structural relaxation curves cross over – and the Kauzmann temperature, TK – where the entropy of the supercooled liquid and crystal equalize. Germanium liquid was used as a model system, for which a reliable Stillinger-Weber potential and crystal nucleation kinetics are available. Using molecular dynamics (MD) simulations, we obtained the self-diffusion coefficient, D(T), and the shear viscosity, η(T), down to T=0.7·Tm, where Tm is the equilibrium melting temperature. In this way, three relaxation times were determined in the supercooled liquid: (i) via the shear viscosity, τη; (ii) the incoherent intermediate scattering function, τα; and (iii) the self-diffusion coefficient, τD. We found that τα(T)≈τD(T) and τη(T)<τα(T), corroborating the findings of recent experimental and computational studies conducted with other four substances. Hence, the viscosity only gives a lower bound to the intrinsic structural relaxation times,τα(T). We also compared the MD values of the atomic transport coefficient across the supercooled liquid/critical nucleus interface, D*, with those obtained by the classical nucleation theory (CNT) and found that the activation energies of D(T), η(T), and D*(T) are similar. The birth times of the first critical crystal nucleus at steady-state conditions, τ1(T), obtained in our previous study for the same material, were extrapolated to lower temperatures using the CNT for different sample sizes. We found that τ1(T) is much longer than the nucleation time-lags, confirming the establishment of the steady-state nucleation regime. A relevant finding is that the τα(T) and τ1(T) curves indeed cross over, confirming the existence of a kinetic spinodal for this liquid. Finally, we demonstrate that if the Kauzmann temperature existed for germanium, it would be located well below the TKS; hence, crystallization would intervene in the cooling path before the supercooled germanium liquid could reach TK, thus averting the entropy paradox, posed by Kauzmann in 1948. These findings shed light on several fundamental questions related to supercooled liquids.