Determination of nucleation parameters and the solid liquid interfacial energy of the KCl‐ethanol‐water system

The kinetic parameters of homogeneous nucleation of KCl in different ethanol‐water solvent mixtures were determined at 25°C from the experimental measurements of the width of the metastable zone at different cooling rates. The ethanol mass ratio in the ethanol water solvent mixture was varied from 0‐0.9 and the metastable zone width for each solvent mixture was measured under the cooling rates of 10, 20 and 30 K/h. The influence of ethanol ratio on the activity coefficient was calculated. It was found that increasing the ethanol ratio in the solvent mixture leads to an increase in the mean molal activity coefficient. The experimental results obtained showed that the increase in the ethanol ratio in the solvent widens the metastable zone for the crystallization of KCl. Also it has inferred from the calculations based on the classical nucleation theory that increasing of the ethanol ratio in the solvent mixture resulted in an increase of the nucleation rate order, increase of the critical size of nuclei and increase of the solid liquid interfacial energy. It has been found that the solid liquid interfacial energy can be good correlated with inversely proportionality to the solubility. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Metastable zone width for secondary nucleation and secondary nucleation inside the metastable zone

This study presents an evaluation of a new method, called zero growth activation free energy, used to determine the metastable zone width for the secondary nucleation case. It predicts the metastable zone width with a maximum error of 5‐10%. Estimation of the metastable zone width for different isothermal crystallization conditions can be modeled according to a chosen reference set of growth experiments carried out in the volume diffusion regime at different initial supersaturations, using seed crystals of a certain characteristic size. Moreover, the activation free energy of the secondary nucleation was estimated. The role of the enthalpy of immersion in the formation of secondary nucleation events inside the metastable zone was pointed out, as well as its effect in causing extra‐fast growth rate. Furthermore, sucrose crystal surface free energy was estimated. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

In situ determination of metastable zone width by a simple optical probe

The metastable zone width (MSZW), which denotes the region between the solubility curve and the onset of nucleation, is an important control parameter for successful operation of a solution crystallization process as it defines an operating boundary for the crystallization process. The MSZW can be approximated as the gap between the loci of cloud points that correspond to onset of nucleation and clear points that closely represent solubility. This work presents the design and application of a simple optical probe consisting of a line laser source, a light‐dependent resistor, and a simple processing circuit for in situ determination of onset of nucleation of a crystallization process. Three different crystallization processes, namely, cooling crystallization of glycine, cooling crystallization of L‐asparagine monohydrate, and anti‐solvent crystallization of glycine, are investigated to assess the performance of the in situ probe. In all the cases, the cloud points and clear points are conveniently detected by sharp changes in output voltage of the probe with reasonable accuracy. The presented optical probe can be used as a simple and inexpensive alternative tool in the area of crystallization process monitoring.     

Solubility and metastable zone width of DL‐tartaric acid in aqueous solution

Solubility and metastable zone width (MSZW) of DL‐tartaric acid (DL‐TA) in aqueous solution have been determined. Solubility of DL‐TA was measured in the temperature range from 0 to 50 °C at atmospheric pressure by means of the conventional polythermal method using Turbidity Monitoring Technique, which was verified by a gravimetric method. The dissolution enthalpy and entropy of DL‐TA were then calculated from the solubility data using van't Hoff equation. Two approaches was used to estimate the nucleation kinetics from the measured metastable zone width data, the self‐consistent approach and the approach based on 3D nucleation. In addition, the metastable zone width slightly decreases with increasing agitation rate and was independent of working volume.     

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.     

Effect of Urea on Metastable Zone Width,Induction Time and Nucleation Parameters of Ammonium Dihydrogen Orthophosphate

Enhancement of the metastable zone width in ammonium dihydrogen ortho phosphate (ADP) was achieved by the addition of the organic compound Urea to ADP solution. The metastable zone width studies were carried out for various temperature cooling rates and the nucleation parameters are studied. The induction period was studied and the critical nucleation parameters calculated based on classical theory for homogeneous nucleation are discussed. The critical nucleation parameters increase with the increase in concentration of doping.     

Temperature control of protein crystal nucleation

The thermal variant of the classical nucleation‐growth‐separation principle is shown, both theoretically and experimentally, to be a reliable tool for studying protein crystal nucleation. The classical nucleation theory is used to elucidate the temperature dependence of crystal nucleus size. A one‐to‐one ratio of the number density of nuclei formed to crystals grown to visible size is achieved using the nucleation‐growth‐separation method. The experiments conducted in such a way show that new nuclei are prevented from appearing while avoiding any crystal loss due to dissolution. The same method is used to study experimentally the interval of growth temperatures where the number density of (nucleated) crystals is relatively insensitive to the growth temperature. It is argued that this temperature interval corresponds to the width of the so‐called metastable zone.     

Investigation of metastable zone width of ammonium oxalate aqueous solutions

The metastable zone width of pure ammonium oxalate aqueous solutions, as represented by maximum supercooling ΔT_max, is investigated as functions of cooling rate R and saturation temperature T₀ by the polythermal method. The experimental results are discussed by using two recently advanced approaches: (1) self‐consistent Nývlt‐like approach based on a power‐law relationship between nucleation rate J and maximum supersaturation lnS_max, and (2) a novel approach based on the relationship between J and lnS_max described by the classical three‐dimensional nucleation theory. Analysis of the experimental data revealed that both approaches describe the experimental data on metastable zone width by the polythermal method reliably and provide useful information about the physical processes and parameters involved in nucleation kinetics. The values of various physical quantities predicted by both of these approaches are reasonable for a fairly‐soluble compound. A careful examination of the data on ΔT_max as a function of T₀ obtained by polythermal method and from density measurements showed that ΔT_max has a slight tendency to decrease with increasing saturation temperature T₀. The values of lnS_max at saturation temperature 303 K suggest that the metastable zone width of ammonium oxalate aqueous solutions is determined by primary nucleation in the polythermal method and by secondary nucleation during density measurements. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Study of lactose crystallization in water‐acetone solutions

This paper describes a study on the process of lactose crystallization using a water‐acetone solution. The selection of lactose was based on its significance for the pharmaceutical and food industries and on the fact that the crystallization of this organic compound has been little studied and is, unlike inorganic compounds, complex. The objective was to achieve lactose batch crystallization of solutions by analyzing the crystal growth under different operating conditions. To determine solubility curves, the experiments were carried out based on gravimetric methods. All the crystallization experiments were performed according to the methodology proposed by Nývlt in 1985, who uses the temperature at which the first crystals appear (nucleation) to establish the width of the metastable zone and the induction time. The results showed that crystals with different average diameters, shape factors, and recovered mass were obtained for different water‐acetone compositions. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A novel self‐consistent Nývlt‐like equation for metastable zone width determined by the polythermal method

Using a power‐law relation between three‐dimensional nucleation rate J and dimensionless supersaturation ratio S, and the theory of regular solutions to describe the temperature dependence of solubility, a novel Nývlt‐like equation of metastable zone width of solution relating maximum supercooling ΔT_max with cooling rate R is proposed in the form: ln(ΔT_max/T₀) = Φ + β lnR, with intercept Φ = {(1–m)/m }ln(ΔH_s/R_GT_lim) + (1/m)ln(f/KT₀) and slope β = 1/m. Here T₀ is the initial saturation temperature of solution in a cooling experiment, ΔH_s is the heat of dissolution, R_G is the gas constant, T_lim is the temperature of appearance of first nuclei, m is the nucleation order, and K is a new nucleation constant connected with the factor f defined as the number of particles per unit volume. It was found that the value of the term Φ for a system at saturation temperature T₀ is essentially determined by the constant m and the factor f. The value of the factor f for a solute–solvent system at initial saturation temperature T₀ is determined by solute concentration c₀. Analysis of the experiment data for four different solute‐water systems according to the above equation revealed that: (1) the values of Φ and m for a system at a given temperature depend on the method of detection of metstable zone width, and (2) the value of slope β = 1/m for a system is practically a temperature‐independent constant characteristic of the system, but the value of Φ increases with an increase in saturation temperature T₀, following an Arrhenius‐type equation with an activation energy E_sat. The results showed, among others, that solubility of a solute is an important factor that determines the value of the nucleation order m and the activation energy E_sat for diffusion. In general, the lower the solubility of a solute in a given solvent, the higher is the value of m and lower is the value of E_sat. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

L-精氨酸掺杂下ZTS溶液的稳定性研究

研究了L-精氨酸掺杂下硫脲硫酸锌(ZTS)溶液中的成核过程,测量了在不同掺杂浓度下ZTS溶液的亚稳区和诱导期.结果表明:随掺杂浓度的增加,溶液的亚稳区变宽,诱导期增大;根据经典成核理论计算了晶体的成核热、动力学参数,分析了溶液稳定性与掺杂浓度的关系,即随着L-精氨酸掺杂浓度的增加,溶液的稳定性得到明显提高.利用化学腐蚀法对ZTS晶体(100)面进行了腐蚀,并用光学显微镜对腐蚀面进行观察,得到了清晰的位错蚀坑.当L-精氨酸掺杂浓度为1.5mol;时,ZTS晶体(100)面位错蚀坑密度最小,适合高光学质量晶体的生长.     

超声波对甲硝唑溶液结晶热力学性质的影响

本文采用降温结晶的方法,在搅拌和超声波作用下,分别测量了甲硝唑溶液结晶成核的介稳区和诱导期.通过分析超声波对甲硝唑溶液结晶的介稳区、诱导期产生的影响,从扩散系数、温度及能量角度分析了超声波促进晶体成核作用的机理.通过比较搅拌和超声波下得到的产品,从理论上对影响晶体粒度及结晶产率的因素进行了分析.     

Nucleation and polymorphism explored via an easy-to-use microfluidic tool

We present an easy-to-use microfluidic set-up, easily transferable to the laboratory and determine an accurate method for metastable zone width measurement. We clearly define a zone in the phase diagram where nucleation is mononuclear. We nucleate a single crystal of metastable phase, which turns out to be stable. This approach holds promise for the control and the study of crystallization processes.     

Determination of nucleation kinetics of lovastatin in acetone solution

The metastable zone widths of lovastatin in acetone solution were determined at different temperatures, cooling rates and initial concentrations by polythermal method. It decreases with the increase of temperature and initial concentration, increases with the increase of cooling rate. The induction periods of lovastatin in acetone solution were also investigated as a function of supersaturation ratios. The crystal‐liquid interfacial tension, thus the fundermental nucleation parameters including Gibbs free energy change for the formation of critical nucleus, radius of critical nucleus and number of molecules in the critical nucleus have been gotten based on the classical homogeneous nucleation theory. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Determination of the phase diagram for the crystallization of L‐asparaginase II by a turbidity technique

Phase diagrams including the metastable zone width for the L‐asparaginase II from Escherichia coli with both PEG₆₀₀₀ and ethanol as a precipitant agent were determined, respectively. A turbidity technique giving results of nucleation and solubility limits in hours rather than in days was introduced. For the first time such data necessary for designing and controlling of crystallization processes of L‐asparaginase II are presented. Since the catalytical activity is an important parameter for L‐asparaginase II as an enzyme, a new type of phase diagram plotting the enzymatic activity as a function of temperature was established as well. Additionally, the crystalline L‐asparaginase II crystals with different shapes that formed in PEG₆₀₀₀ and ethanol, respectively, were also investigated by X‐ray Powder Diffraction (XRPD).     

A Study of the Metastable Zone in Nylon 12-Toluene Solution

The metastable zone for a nylon 12-toluene solution was determined in an established constant cooling rate apparatus. Supersaturation solubility curves and the equilibrium solubility curve are unparallel one to another. The metastable zone width under seeded conditions is dependent on the cooling rate, the retention time and the saturation temperature. And the metastable zone width under unseeded conditions is dependent on the cooling rate, the agitation rate and the saturation temperature. Through constant cooling rate crystallization experiments, two empirical correlations pertaining to the metastable zone of the solution have been found.     

Determination of nucleation kinetics of potassium tetraborate tetrahydrate

In this study, the metastable zone width of potassium tetraborate tetrahydrate was determined for four different temperatures and cooling rates. The induction period of potassium tetraborate tetrahydrate in aqueous solution was examined according to polythermal method by using visual observation. The induction period, which changes inversely proportional to the nucleation rate has been used to determine the interfacial tension between the potassium tetraborate tetrahydrate and aqueous solution. By using interfacial tension, the nucleation parameters such as Gibbs free energy change for the formation of critical nucleus, ΔG*, free energy of formation, ΔG, radius of critical nucleus, r and number of molecules in the critical nucleus, i* has been calculated. The effect of Li⁺ and Ca²⁺ impurities on metastable zone width has been studied. The metastable zone width of aqueous solution of potassium tetraborate tetrahydrate decreases with increasing impurity concentrations. The equilibrium saturation concentration change is high in the presence of Ca²⁺ ions while it is low in the presence of Li⁺ ions. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Crystallization of copper sulphate

Results of the studies of copper sulphate pentahydrate batch crystallization in the temperature range from 70 down to 30 °C are presented. In some of the experiments, free sulphuric acid has been added. The metastable zone width, nucleation and growth kinetic parameters, as well as the system kinetic constant were determined and compared with the data published in the literature.