The mechanism of the formation of enantiotropic polymorphs of carisbamate in solution crystallization

The nucleation kinetics, as a function of supersaturation level, was studied for carisbamate, a polymorphic crystalline compound, in methanol, ethanol, 2-propanol and water. The induction times in nucleation kinetics varied markedly with respect to relative supersaturation in the range 1.3–2.3. At the same relative supersaturation, the induction time for carisbamate in methanol is the shortest, increasing in order from ethanol, 2-propanol, and then water. The interfacial tensions γ between carisbamate and methanol, ethanol, 2-propanol, and water were estimated from their induction times based on nucleation theory and were found to be about 3.6, 4.1, 4.5, and 5.7 mJ/m², respectively. These values were of same order of magnitude as those obtained from solubility data. The equation that displays the influence of interfacial tension, supersaturation and temperature on crystallization kinetics was derived, and found to be consistent with experimental observations. The mechanism of enantiotropic polymorphism for carisbamate in the solvents is illustrated. Using interfacial tension values determined for single solvents, the polymorphic form resulting from crystallization in mixed and pure solvent systems could be predicted with good accuracy.     

The induction time,interfacial energy and growth mechanism of maltitol in batch cooling crystallization

Maltitol is crystallized with seeds by cooling mode in industry, often with large amount of fine crystals and wide crystal size distribution. To eliminate the fine nucleation, it's necessary to understand the nucleation kinetics. In this work, the solubility of maltitol in water was measured by the gravimetric method, the nucleation kinetics of maltitol in batch cooling crystallization was investigated using focus beam reflectance measurement (FBRM), and a novel method was proposed to determine the induction time from the trend of the crystal median chord given by FBRM. Based on the relationship between the induction time and the supersaturation, the nucleation mechanism was obtained, including homogenous nucleation at high supersaturation and heterogenous nucleation at low supersaturation. Additionally, combining the classical nucleation theory (CNT) and Arrhenius’ principle, the crystal‐solution interfacial energy and the energy barrier of homogenous nucleation were calculated. From the scanning electron microscope (SEM) images, the growth mechanism of maltitol was identified as surface nucleation growth and the surface entropy factor calculated from the kinetic analyses of t_ind data corroborated this growth mechanism.     

Advancements (and challenges) in the study of protein crystal nucleation and growth; thermodynamic and kinetic explanations and comparison with small-molecule crystallization

This paper reviews advancements and some novel ideas (not yet covered by reviews and monographs) concerning thermodynamics and kinetics of protein crystal nucleation and growth, as well as some outcomes resulting therefrom. By accounting the role of physical and biochemical factors, the paper aims to present a comprehensive (rather than complete) review of recent studies and efforts to elucidate the protein crystallization process. Thermodynamic rules that govern both protein and small-molecule crystallization are considered firstly. The thermodynamically substantiated EBDE method (meaning equilibration between the cohesive energy which maintains the integrity of a crystalline cluster and the destructive energies tending to tear-up it) determines the supersaturation dependent size of stable nuclei (i.e., nuclei that are doomed to grow). The size of the stable nucleus is worth-considering because it is exactly related to the size of the critical crystal nucleus, and permits calculation of the latter. Besides, merely stable nuclei grow to visible crystals, and are detected experimentally. EBDE is applied for considering protein crystal nucleation in pores and hydrophobicity assisted protein crystallization. The logistic functional kinetics of nucleation (expressed as nuclei number density vs. nucleation time) explains quantitatively important aspects of the crystallization process, such as supersaturation dependence of crystal nuclei number density at fixed nucleation time and crystal size distribution (CSD) resulting from batch crystallization. It is shown that the CSD is instigated by the crystal nucleation stage, which produces an ogee-curve shaped CSD vs. crystal birth moments. Experimental results confirm both the logistic functional nucleation kinetics and the calculated CSD. And even though Ostwald ripening modifies the latter (because the smallest crystals dissolve rendering material for the growth of larger crystals), CSD during this terminal crystallization stage retains some traces of the CSD shape inherited from the nucleation stage. Another objective of this paper is to point-out some biochemical aspects of the protein crystallization, such as bond selection mechanism (BSM) of protein crystal nucleation and growth and the effect of electric fields exerted on the process. Finally, an in-silico study on crystal polymorph selection is reviewed.     

Spatiotemporal protein crystal growth studies using microfluidic silicon devices

Fundamental investigations of protein crystallization using miniaturized microfluidic silicon devices were presented towards achieving spatiotemporal nucleation and subsequent post-nucleation growth. The developed microfluidic silicon device was typically composed of crystal growth cell, reservoir cell, and optionally of heater elements for supersaturation control. A specific fine pattern area in the growth cell which was fabricated on the silicon substrate with doped p- and n-type silicon layers, served as spatially selective nucleation site of dissolved protein molecules through electrostatic attractive force. In a model material, hen egg white lysozyme, a large number of crystals were grown on the defined nucleation site evenly spaced from each other, whereas parasitic crystal growth positioned around the selective nucleation site, was suppressed by the effects of electrostatic repulsive force between the doped silicon surface and charged protein molecules. A possible crystallization mechanism of describing the heterogeneous nucleation during the initial stage and during the growth of the crystal at the electrolyte–semiconductor silicon surface is proposed and discussed.     

Investigation of nucleation kinetics and crystal defects of HMX

The nucleation kinetics of HMX (cyclotetramethylene tetranitramine, C₄H₈N₈O₈) in γ‐butyrolactone was studied in cooling process by induction time method. The laser scattering method was used to measure the solubility data and metastable region of HMX in γ‐butyrolactone. The induction time was measured over a range of supersaturation at different temperatures. Then, the nucleation mechanism of HMX in γ‐butyrolactone was investigated by analysis the relationships between induction time and supersaturation. The results indicated homogeneous nucleation dominated at high supersaturation of S >1.35, while the heterogeneous nucleation dominated at low supersaturation of S < 1.35. The values of interfacial tension at different final temperatures were calculated to indicate the ability of HMX to be crystallized. The growth mechanism of HMX was investigated by the data fitting applying different growth mechanism models and identified as two‐dimensional nucleation‐mediated (2D) growth. Finally, the effects of supersaturation and temperature on the crystal defects were analyzed based on the nucleation kinetics. When the temperature is below 303.15K, homogeneous nucleation dominated the nucleation process at higher supersaturation. Fine HMX crystals with more defects were produced. On the contrary, heterogeneous nucleation mechanism dominated at lower supersaturation. large regular HMX crystals with fewer defects were formed when the temperature is above 318.15K.     

F-及SiF2-6对α型半水硫酸钙结晶成核及形貌的影响

本文模拟了半水法湿法磷酸生产过程中α型半水硫酸钙(α-HH)的结晶过程。在30%P₂O₅,反应温度95 ℃,过饱和度S=1.64~2.10条件下,通过浊度仪监测溶液中浊度变化,测定了不同F^-及SiF^2-₆浓度下α-HH结晶诱导时间,采用经典成核理论公式计算了α-HH的临界晶核半径及成核速率,并通过扫描电子显微镜(SEM)、X射线衍射(XRD)、X射线光电子能谱(XPS)表征分析了F^-及SiF^2-₆对α-HH结晶过程的影响。结果表明:随着F^-、SiF^2-₆浓度的升高,α-HH晶体的结晶诱导时间延长,表面能和临界晶核半径都增大,然而成核速率减小。当过饱和度S=1.64时,加入0.06 mol·L^-1 F^-,α-HH结晶诱导时间延长了465 s,成核速率减小到0.403×10²⁹ 晶核数·cm^-3·s^-1,然而,加入0.06 mol·L^-1 SiF^2-₆,α-HH结晶诱导时间延长了710 s,成核速率减小到0.339×10²⁹晶核数·cm^-3·s^-1。SiF^2-₆对α-HH晶体抑制成核作用大于F^-。F^-、SiF^2-₆阻碍了α-HH晶体沿C轴方向生长,使得晶体长径比减小,晶体形貌向短柱状变化。F^-、SiF^2-₆影响了α-HH晶体(200)、(310)、(400)晶面衍射峰强度和结晶度。控制半水法湿法磷酸中F^-及SiF^2-₆浓度水平,可以得到短柱状的α-HH晶体,有利于过滤洗涤。     

DTA peak shift studies of primary crystallization in glasses

Following the recognition during the last decade that knowledge of the shift in the exothermic crystallization DTA peak as a function of pre-DTA isothermal heat-treatment times and temperatures, can provide quantitative information about the crystallization kinetics, there has been renewed interest in DTA investigations of crystallization of glasses. Most studies to date, however, have focussed on the kinetics of polymorphic crystallization (where the compositions of the crystal and the parent glass are the same). These studies have established that the DTA peak shifts to lower temperatures with increased pre-DTA heat-treatment times and JMAK-based formalisms have been developed to extract the steady state nucleation rate from the DTA peak shift data. In this paper, we report new results on the DTA peak shift in systems undergoing primary crystallization (where the compositions of the crystal and glass are different). The DTA results show that the exothermic peak temperature decreases initially but increases later on, becoming significantly larger than the initial value, with increase in the pre-DTA heat-treatment time at a fixed temperature. This increase at long times has not been reported previously and is qualitatively different than the monotonic decrease reported for polymorphic crystallization. To rationalize these new results, a model of primary crystallization has been developed which includes homogeneous nucleation, diffusion-controlled growth, Gibbs-Thomson effect, and a mean field soft-impingement correction during growth. Based on this model and experimental results, it is concluded that the initial shift to lower temperatures is due to an increase in the number of nuclei (as concluded previously by others for the case of polymorphic crystallization) and the later shift towards high temperatures in our experiments is due to diffusion-controlled growth during the pre-DTA heat treatment.     

Kinetics of protein crystal nucleation and growth in the batch method

We have applied the Johnson–Mehl–Avrami–Kolomogorov (JMAK) theory of crystal nucleation and growth to the problem of protein crystallization in the batch method. Without integrating the JMAK equation explicitly, we use dimensional analysis to derive a general formula for the half-life for decay of the protein supersaturation. This formula includes a dimensioned group and an arbitrary dimensionless function. We integrate the JMAK equation exactly for the special case where the growth rate is independent of the supersaturation and the nucleation rate is proportional to its square. This gives an equation for the time decay of the supersaturation and a formula for the half-life in which all arbitrary dimensionless functions are evaluated. The results are consistent not only with Von Weimarn's rule, which asserts that the average size of a crystal increases as the supersaturation decreases, but also with our experimental results for crystallization of lysozyme, in which the half-life at fixed pH decreases with increasing ionic strength and decreasing temperature.     

Evaluation of nucleation rate by in‐situ focused beam reflectance measurement in an unseeded batch cooling crystallization

Nucleation kinetics in the cooling crystallization of hexahydro‐1,3,5‐trinitro‐1,3,5‐triazine (RDX) from γ‐butyrolactone was studied by converting total counts/s measured by in situ focused beam reflectance measurement (FBRM) into number of crystals. The classical nucleation rate model, which is derived exclusively from the thermodynamic state for the nucleation and molecular collision frequency, was found to be inadequate to describe the experimentally measured nucleation rates. However, the nucleation rates predicted by the modified classical nucleation rate model, inclusive of an additional temperature term, were found to be in good agreement with those measured in the present work. Furthermore, the metastable zone widths are also found to be more accurately predicted by the modified classical nucleation rate model than the classical approach, which assumes that the mass‐based nucleation rate is an exponential function of supersaturation and is equal to the supersaturation rate.     

Kinetics and intimate mechanism of protein crystal nucleation

Experimental and theoretical investigations on protein crystal nucleation are reviewed. Various experimental applications of the classical principle, which requires separation of the nucleation and growth stages of the crystallization process, are described. Temperature control is used most frequently, hypergravity and concentration changes being auxiliary techniques. Nucleation time-lags are measured by imposing temperature evoked supersaturation gradients. Application perspectives are revealed. Nucleation rates are measured according to the classical principle mentioned above, and energy barriers for crystal nucleation and numbers of molecules constituting the critical nuclei are calculated. Surprisingly, although requiring unusually high supersaturation, protein crystal nucleation occurs much more slowly than that with small molecule substances. On this basis novel notions are suggested for the elementary mechanism of protein crystal bond formation. Due to the selection of the crystalline bonding patches a successful collision between protein molecules, resulting in the formation of a crystalline connection, requires not only sufficiently close approach of the species, but also their proper spatial orientation. Imposing a rigid steric constraint, the latter requirement postpones the crystal nucleus formation. Besides, it was shown that cluster coalescence is not a factor, hampering the protein crystal nucleation. The comparison of the model predictions with experimental results proved that nucleation kinetics is governed by kinetic (not by energetic) factors.     

Induction time in crystallization of gas hydrates

The kinetics of the initial stage of crystallization of one-component gas hydrates in aqueous solutions are analyzed. The temporal evolution of the volume of hydrate crystallized and the moles of gas consumed are determined. Expressions are derived for the supersaturation dependence of the hydrate crystallite growth rate and the induction time in hydrate crystallization. These expressions are used for revealing how additives in the solution that act as kinetic inhibitors of hydrate crystallization can affect the induction time of the process. The results obtained are applied to crystallization of methane, ethane and cyclopropane hydrates.     

Effect of phosphonate additive on crystallization of gypsum in phosphoric and sulfuric acid medium

Understanding the mechanisms of growth and inhibition during crystallization of calcium sulfate is of primary importance for many industrial applications. For instance, inhibition of the crystallization process may be required to prevent scale formation in pipes, boilers, heat exchangers, reactors, reverse osmosis membrane surfaces, cooling water systems, secondary oil recovery utilizing water flooding techniques and desalination evaporators, etc. On the other hand, control growth and morphology of gypsum crystals is desired in achieving higher filtration rate and higher productivity of phosphoric acid from phosphate rocks. In this regard, this basic study is carried out to understand effect of Aminotris (methylenephosphonic acid (ATMP) on calcium sulfate dihydrate (gypsum) crystallization. The time elapsed between the achievement of supersaturation and the appearance of a solid phase (termed as induction time) is measured under different supersaturation ratios ranging from 1.018 to 1.979. The data are used to calculate the surface energy, critical nucleus size, and crystal growth rates of gypsum under different conditions. The results show that, the induction time decreases exponentially with increasing the supersaturation ratio. In addition, the surface energy decreases with ATMP compared to the baseline (without ATMP). Interestingly, with addition of the ATMP, the crystals mean and median diameters are found to decrease. The inhibition efficiency ranges from 16% to 59% depending on supersaturation ratio.     

Determination of metastable zone width for combined anti-solvent/cooling crystallization

The metastable zone width (MSZW), induction time and primary nucleation kinetics have been measured and estimated for simultaneous anti-solvent and cooling crystallization of paracetamol in iso-propanol/water solution. ATR-FTIR spectroscopy and laser back-scattering are used to measure the solute concentration and primary nucleation event, respectively. Response surface analysis was applied to find the contribution of the crystallization mechanism on the MSZW and obtain a statistical model for quick estimation of the MSZW. Two theoretical approaches for the estimation of nucleation rate kinetic parameters from experimental data are presented. The methods are obtained by modifying the classical Nyvlt's correlation for simultaneous cooling/anti-solvent crystallizations. The nucleation order n for primary nucleation was deduced from the slope of a linear plot of log(MSZW) vs. log(cooling and anti-solvent rates). The induction time was also estimated by changing the classical methods for combined cooling and anti-solvent crystallization.     

A study of primary nucleation of calcium oxalate monohydrate: II. Effect of urinary species

Kidney stones consist of various organic and inorganic compounds. Calcium oxalate monohydrate (COM) is the main inorganic constituent of kidney stones. However, the mechanisms for the formation of calcium oxalate kidney stones are not well understood. In this regard, there are several hypotheses including nucleation, crystal growth and/or aggregation of formed COM crystals. The effect of some urinary species such as oxalate, calcium, citrate, and protein on nucleation and crystallization characteristics of COM is determined by measuring the weight of formed crystals and their size distributions under different chemical conditions, which simulate the urinary environment. Statistical experimental designs are used to determine the interaction effects among various factors. The data clearly show that oxalate and calcium promote nucleation and crystallization of COM. This is attributed to formation of a thermodynamically stable calcium oxalate monohydrate resulting from supersaturation. Citrate, however, inhibits nucleation and further crystal growth. These results are explained on the basis of the high affinity of citrate to combine with calcium to form soluble calcium citrate complexes. Thus, citrate competes with oxalate ion for binding to calcium cations. These conditions decrease the amount of free calcium ions available to form calcium oxalate crystals. In case of protein (mucin), however, the results suggest that no significant effect could be measured of mucin on nucleation and crystal growth. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Growth kinetics and capture of impurities during gas phase crystallization

This article summarizes recent published and unpublished results obtained primarily in our laboratory in gas phase crystallization. Section I presents some conditions for growth from the vapour via a thin, but nevertheless macroscopic, liquid film covering the growing crystal. In section 2, we discuss the conclusion that the growth by chemical vapour deposition (CVD) at least in the practically important cases of Si and GaAs occurs via a dense monomolecular layer. In section 3, the energy transfer from lattice vibrations to intramolecular vibrations in an adsorbed molecule is considered. It turns out that the effective intramolecular “temperature” may be noticeably lower than the crystal temperature. Correspondingly, the chemical decomposition rate of the adsorbed molecule may be at least 10 times lower than that found according to Boltzmann's law. It is shown in section 4 that the nucleation of the next lattice layer in the diffusion field of the previously created steps gives a growth rate versus supersaturation law which differs from the Burton-Cabrera-Frank (BCF) law. Morphologically this mechanism of self-consistent nucleation manifests itself in systems of concentric steps. These systems, but not the spirals, play a dominant role in NaCl growth and evaporation under a molecular beam. The same situation can occur in the CVD of silicon also. In section 5, the kinetics of condensation of NaCl on platinum group metals is shown to be drastically dependent on the monomolecular coverage of the metal substrate with carbom. These results may be understood if we suppose that the carbon coverage decreases the NaCl-on-metal adsorption enengy, mean adsorption time and path, and consequently, the nucleation and growth rates. In section 6, applying the self-consistent nucleation concept of section 4 to molecular beam condensation allows us to find the amount of impurities captured by the growing crystal relative to the amount in the beam source.     

Influence of a polyacrylate antiscalant on gypsum nucleation and growth

Calcium sulphate dihydrate (gypsum) crystallization was studied under conditions, of supersaturation and temperature, simulating a brackish water desalination unit using solar energy. The effect of an commercial sodium salt of poly(acrylic acid), based compound known as RPI, on homogeneous nucleation and growth of gypsum was also examined. Gypsum was precipitated by mixing aqueous CaCl₂ and Na₂SO₄ solutions. It was found that, with increasing temperature or supersaturation, the induction time decreases and the growth rate increases. By using classical nucleation theory, the interfacial tension and the nucleation rate values were estimated. It was shown that the interfacial tension is temperature dependent. The addition of increasing quantities of RPI, in the same conditions of temperature and supersaturation, prolongs the induction time, decreases the nucleation rate and increases the interfacial tension. The addition mode of RPI (in calcium or in sulphate solution) was found as an important parameter in controlling the inhibition process of gypsum crystallization. XRD and SEM analysis showed that RPI antiscalant strongly affected the texture and the morphology of the deposit gypsum. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Growth kinetics on the (100) and (001) faces of TGS crystals

The growth kinetics and mechanisms on the (001) and (100) faces of TGS crystals were investigated. A phase contrast microscope with a CCD camera was used to observe the growth of the crystal. We found the growth on the (001) and (100) faces at high supersaturation was mainly controlled by a BCF surface diffusion mechanism. The kinetic data for the (100) face were also fitted by the nucleation and layer growth model of two-dimension nucleation at high supersaturation. Some important growth parameters for TGS crystals, such as edge energy, activation energy, and so on, were estimated.     

Effect of supersaturation on the crystallization of phenylbutazone polymorphs

The article describes the effect of degree of supersaturation, σ, on the crystallization of specific polymorphs of phenylbutazone from its methanolic solution at 20 °C. At low initial supersaturation, σ ≤ 2.0, the fraction of the metastable α polymorph in the crystallized product exceeds that of the δ polymorph, while at σ ≥ 5.0, the fraction of the stable δ polymorph increases in the crystallized product. The results are explained by the effect of supersaturation on the relative rates of nucleation and crystal growth of the polymorphs. Furthermore, the mechanism of nucleation and crystal growth also change with supersaturation. Supersaturated methanolic solutions of phenylbutazone exhibit a critical temperature at which the nucleation rates of the polymorphs decrease drastically. This effect is partly explained by the decreased mobility of phenylbutazone molecules at lower temperatures. Nucleation is most rapid when the crystallization temperature is close to the transition temperature, T_t(α ⟷ δ), between the polymorphs, α and δ. The nucleation rate decreases as the temperature difference between T_t(α ⟷ δ) and the crystallization temperature increases. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Supersaturation and crystal size distribution changes during the precipitation of Nickel ammonium sulphate hexahydrate

The desupersaturation of nickel ammonium sulphate aqueous solutions, during the precipitation of the hydrated salt, has been followed by refractive index measurements. The addition of seed crystals has a considerable effect on the desupersaturation process: the induction and latent periods and the crystal size distribution are all greatly reduced. The precipitated crystal size follows V . WEIMARN'S rules, viz, the median size (a) passes through a maximum with increasing supersaturation for a given crystallization time, and (b) decreases with increasing supersaturation, for precipitations which have virtually ceased. The crystal yield increases with both supersaturation and time, but the size distribution remains fairly constant with time for supersaturations, S > 2.     

Batch crystallization of soluble proteins: effect of precipitant, temperature and additive

Although techniques used for protein crystallization have been progressing greatly, successful crystallization is still largely empirical and operatordependent. The crystallization of biological macromolecules is a pretty complicated process involving numerous parameters, thus the detailed understanding of the effect of crystallization conditions on macromolecule crystallization is advantageous. In this study, we have investigated the effect of precipitant, temperature, and additive on the crystallization of lysozyme and chymotrypsinogen A. As the precipitant, sodium chloride is more effective to the crystallization of lysozyme, and ammonium sulfate is more suitable to the crystallization of chymotrypsinogen A. Temperature is found to have no effect on the crystal habit of chymotrypsinogen A, while lysozyme crystallization displays highly sensitive temperature dependence, gradually varied temperature can result in better crystal habit and quality of lysozyme crystals. Furthermore, non-electrolytic additives dimethyl sulfoxide (DMSO) and glycerol are found to not only to increase the protein's solubility, but also decrease the critical supersaturation S_c for explosive nucleation of highly supersaturated protein solution. It is suggested that these additives can affect the interactions between protein molecules, thermodynamic equilibrium, surface energy of the crystal, and nucleation process of protein crystallization.