In situ monitoring and control of lysozyme concentration during crystallization in a hanging drop

Fiber optic Raman spectroscopy combined with a partial least-squares regression model was demonstrated as a monitor of lysozyme concentration during crystallization in a hanging drop experiment in real time. Raman spectral features of the buffer and protein were employed to build the regression model. The use of fiber optic technology coupled with Raman spectroscopy, which is ideal for use with aqueous solutions, results in a powerful noninvasive probe of the changing environment within the solution. Lysozyme concentrations were monitored in experiments at a constant reservoir ionic strength. Data from these uncontrolled experiments were used to determine rates of supersaturation, induction times, and the number and size of the resultant lysozyme crystals. Control experiments were performed by introducing step changes in the reservoir ionic strength. The step changes were initiated by comparing in situ rates of supersaturation with the rates of supersaturation calculated from the uncontrolled data. Monitoring the concentration changes of the lysozyme within the hanging drop permits a measurement of the level of supersaturation of the system and enhances the possibility of dynamic control of the crystallization process.     

Crystallization of zinc lactate in presence of malic acid

The influence of malic acid, which acts as an impurity on the cooling crystallization of zinc lactate is investigated in this paper by monitoring the relative supersaturation and the number of crystals during crystallization. The presence of malic acid increases the solution solubility and makes the metastable zone wider; it also changes the habit of the crystal. The purity of the final products is shown to be influenced by the amount and size of seed crystals, cooling rate, seeding temperature and final temperature, but appears to depend mainly on the particle size and level of supersaturation. Residual supersaturation thresholds are observed that depend on the final temperature. A model is proposed to predict the steady-state supersaturation value from the final temperature at a given impurity concentration. This model is based on Kubota and Gibbs equations.     

Mechanism of aggregation and intergrowth of crystals during bulk crystallization from solutions

Available literature data on aggregation kinetics of crystals of a number of salts during their bulk crystallization from solutions have been analysed. The proposed earlier mechanism of aggregation and intergrowth of crystals during bulk crystallization owing to formation of nucleus‐bridges between crystals was tested and confirmed. The aggregation kinetics of crystals was described by the familiar Smoluchowski equation for coagulation of colloidal particles. However, in a bulk crystallization process, the aggregation constant in this equation decreased as supersaturation in a solution lowered. An expression for the aggregation constant in this equation was proposed. The proposed mechanism of crystal intergrowth duringt bulk crystallization allowed evaluating the specific surface energy of tested salts, which turned out to be in reasonable agreement with published literature data. It was concluded that the intergrowth of crystals during bulk crystallization from solutions proceeded via formation of nucleus‐bridges between crystals. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Growth kinetics of sodium perborate from batch crystallization

The size distribution of sodium perborate crystals was continually monitored using a Malvern sizer during batch crystallization from aqueous solutions carried out under falling supersaturation established at the experiment onset. The growth rate was determined from the time shift of the crystal size distribution expressed in cumulative oversize numbers. The size independent overall growth rate was first order with respect to supersaturation for crystals larger than 150 μm. Crystals between 20 and 150 μm exhibited a significant size-dependent growth rate. Furthermore, the fraction of crystals smaller than 20 μm, formed by primary nucleation, grew extremely slowly or did not grow at all.     

A Stochastic Model for Nucleation Kinetics Determination in Droplet-Based Microfluidic Systems

The measured induction times in droplet-based microfluidic systems are stochastic and are not described by the deterministic population balances or moment equations commonly used to model the crystallization of amino acids, proteins, and active pharmaceutical ingredients. A stochastic model in the form of a Master equation is formulated for crystal nucleation in droplet-based microfluidic systems for any form of nucleation rate expression under conditions of time-varying supersaturation. An analytical solution is provided to describe the (1) time evolution of the probability of crystal nucleation, (2) the average number of crystals that will form at time t for a large number of droplets, (3) the induction time distribution, and (4) the mean, most likely, and median induction times. These expressions are used to develop methods for determining the nucleation kinetics. Nucleation kinetics are determined from induction times measured for paracetamol and lysozyme at high supersaturation in an evaporation-based high-throughput crystallization platform, which give low prediction errors when the nucleation kinetics were used to predict induction times for other experimental conditions. The proposed stochastic model is relevant to homogeneous and heterogeneous crystal nucleation in a wide range of droplet-based and microfluidic crystallization platforms.     

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.     

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.     

Study on the Growth of Triglycinsulphate Single Crystals

Crystallization of TGS at 52.0°C - above the transition point - has been studied in a wide range of supersaturation of the solution (σ = 0 to 10⁻²). The rates of growth of {110} and {001} faces were measured as a function of supersaturation at constant hydrodynamical conditions (Re = 3.4 · 10⁻³). Further, the influence of hydrodynamical conditions on the growth of {110} faces at constant supersaturation (σ = 4.2 · 10⁻³) was established. The parameters of the experimentally found dependences are determined on the basis of the surface-diffusion model of BURTON . CABRERA and FRANK . From these dependences follows that the growth rate of the {110} faces is already almost limited by the volume diffusion of TGS molecules towards the crystal surface, while in the case of {001} faces the surface diffusion mechanism of crystallization is clearly manifested. Dislocation densities in the crystals have been determined by means of etching technique. The number of dislocations increases with increasing supersaturation; hence, supersaturation of the solution together with the processes taking place in the regeneration zone surrounding the seed determine the number of dislocations in the crystal volume and thus the resulting structural perfection of single crystals. Investigation of the spontaneous redistribution of domains showed that the growth rate of TGS crystals influences the dielectric properties to much smaller extent than does chemical purity.     

Growth aspects of barium oxalate monohydrate single crystals in gel medium

Single crystals of barium oxalate monohydrate (BaC₂O₄.H₂O, BOM) were grown in pure form by controlled diffusion of Ba²⁺ using the gel technique at different temperatures. Starting from aqueous Ba²⁺ chloride (BaCl₂) and acetic acid (C₂H₂O₄) in gel, this method offers a low‐cost and an easiest alternative to other preparation methods for the production of barium oxalate bulky single crystals. The optimal conditions for the growth of BOM crystals in silica gel were found by investigating different growth parameters such as gel pH, gel aging and crystallization temperature. Irrespective of all such crystallization environments, growth rate of the crystals were initially less and then exhibited supersaturation effect leading to non‐linearity. Gel aging and temperature has profound effect on nucleation density that resulted less number of crystals of maximum size in the gel matrix. Perfect single crystals were grown on gels of higher pH. The macropore morphology and porosity was controlled by changing age of the gel. It has been found that temperature has a fabulous effect in controlling the nucleation density by altering the supersaturation conditions for the formation of critical nuclei. The entire growth kinetics informed that the grown crystals were derived by the one dimensional diffusion controlled process. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Part 1: Kinetics and mechanism of the crystallization process

The kinetics of spontaneous crystallization of sodium chloride from aqueous‐ethanol solutions were studied. During the crystallization the electrical conductance and optical transmission of the supersaturated solutions were measured automatically. For monitoring of the total surface of growing potassium chloride crystals at the crystallization the turbidimetric method was used. The growth rate and activation energy were determined. The crystal growth rate was proportional to supersaturation. When the volume fraction of ethanol in solution increased from 14.85 to 29.72%, the activation energy of the growth process did not change and was about 50 kJ· mol^‐1. Aggregation of the crystals was found. The aggregation kinetics of the crystals may be described approximately by the famous Smoluchowski equation for coagulation of colloidal particles. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Agglomeration of NTO on the surface of HMX particles in water‐NMP solvent

A sensitive explosive was coated with a less sensitive explosive in order to improve stability while maintaining explosion performance. Agglomeration of 3‐nitro‐1,2,4‐triazole‐5‐one (NTO) on the surface of cyclotetramethylene tetranitramine (HMX) crystals in water‐N ‐methyl‐2‐pyrrolidone (NMP) solvent was performed by cooling crystallization. Phenomena for coating by crystallization and agglomeration were studied by in‐situ measurement. The agglomeration kinetic for the coating of NTO on HMX crystals was correlated with the 3rd power of the solution supersaturation and the 2nd power of the number of the suspended particles. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spontaneous crystallization of potassium chloride from aqueous and aqueous‐ethanol solutions Part 1: Kinetics and mechanism of the crystallization process

Kinetics of spontaneous crystallization of potassium chloride from aqueous and aqueous‐ethanol solutions were studied. During the crystallization of the salt the electrical conductance and optical transmission of the supersaturated solutions were measured automatically. For monitoring of the total surface of growing potassium chloride crystals at the crystallization the turbidimetric method was used. The growth rate and activation energy of the crystals were determined. The crystal growth rate was proportional to supersaturation. When the volume fraction of ethanol in the solution increased from 0 to 25.76%, the activation energy of the growth process did not change and was about 60 kJ·mol^‐1. Aggregation of the crystals was found. The aggregation kinetics of the crystals may be described approximately by the famous Smoluchowski equation for coagulation of colloidal particles. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Crystallization mechanisms of acicular crystals

In this contribution, we present an experimental investigation of the growth of four different organic molecules produced at industrial scale with a view to understand the crystallization mechanism of acicular or needle-like crystals. For all organic crystals studied in this article, layer-by-layer growth of the lateral faces is very slow and clear, as soon as the supersaturation is high enough, there is competition between growth and surface-activated secondary nucleation. This gives rise to pseudo-twinned crystals composed of several needle individuals aligned along a crystallographic axis; this is explained by regular over- and inter-growths as in the case of twinning. And when supersaturation is even higher, nucleation is fast and random.In an industrial continuous crystallization, the rapid growth of needle-like crystals is to be avoided as it leads to fragile crystals or needles, which can be partly broken or totally detached from the parent crystals especially along structural anisotropic axis corresponding to weaker chemical bonds, thus leading to slower growing faces. When an activated mechanism is involved such as a secondary surface nucleation, it is no longer possible to obtain a steady state. Therefore, the crystal number, size and habit vary significantly with time, leading to troubles in the downstream processing operations and to modifications of the final solid-specific properties.These results provide valuable information on the unique crystallization mechanisms of acicular crystals, and show that it is important to know these threshold and critical values when running a crystallizer in order to obtain easy-to-handle crystals.     

Crystallization of proteins under an external electric field

An external electric field affects the crystallization of proteins when applied under some conditions of temperature, pH, and precipitating agent composition. As suggested in the theoretical part of this paper, it produces large protein concentration gradients inside the mother liquor leading to a local supersaturation area in the crystallization solution. Such an experiment has been used for the first time on the crystallization of a protein. The effects of an external electric field on the crystallization of hen egg-white lysozyme at 293 K, pH 4.5, and two NaCl concentrations (0.6–0.7 M) have been investigated using the vapor diffusion method. The application of electric field results in a smaller number of crystals with larger size. The crystals grew at the droplet surface, near the cathode. The nucleation rate is drastically reduced and this experimental method could be used to control the number of crystals in the droplet.     

Solvent freeze out crystallization of lysozyme from a lysozyme‐ovalbumin mixture

Hen egg white lysozyme (HEWL) crystallization conditions from an ovalbumin‐lysozyme mixture were found by screening tests and further located in pseudo‐phase diagrams. This information was used to set up the initial conditions for the solvent freeze out (SFO) process. The process uses the freezing of ice to create the supersaturation for the proteins to crystallize out of the solution. The crystallization of HEWL (15 mg/mL) out of a lysozyme‐ovalbumin mixture (1.7 mg/mL) is carried out by SFO. Under the reported conditions, a crystallization yield of 69 % was obtained. A mean crystal size of 77.8 µm was enhanced in a crystallization time of 15.1 h. The lysozyme nature of the crystals is proven by SDS PAGE and enzymatic activity tests. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Crystallization kinetics of MgSO4 · 7 H2O at higher ranges of the driving force

By means of batch crystallization technique the crystallization kinetics of MgSO₄ · 7 H₂O at 25 °C at higher ranges of the supersaturation from pure aqueous solutions was investigated. It was observed that the growth rate highly depends on the habit of crystals and on their ratio of length to width, respectively. This ratio is a function of the initial supersaturation of each crystal.     

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.     

Deposition of bulk GaN from solution in gallium under high N2 pressure on silicon carbide and sapphire substrates

Results of high-pressure directional growth of GaN on foreign substrates: SiC, sapphire and GaN/sapphire MOCVD templates are presented. The role of nitrogen pressure and supersaturation in the growth process is discussed. The conditions for stable growth of the nitride are determined. The results of the crystallization process are compared with those obtained for directional growth on pressure grown GaN crystals.     

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。     

Crystallization kinetics of MgSO4 · 7 H2O in presence of tenside

The effect of sodium dodecyl sulfate (SDS) on crystallization kinetics and crystal habit of MgSO₄ · 7 H₂O from aqueous solutions at 25 °C was investigated in batch experiments. It highly depends on the supersaturation level. Both increasing supersaturation and rising concentration of the tenside promote the production of needle-like crystals but the influence of the driving force is much more pronounced. SDS increases the crystallization rate and the linear crystal growth rate in length direction of the crystals. To a high degree it also influences properties of the crystallizing solution such as surface tension and viscosity.