Metastable Zone Width Data Research Articles

An integral model for determining the temperature-dependent interfacial energy and pre-exponential factor during the metastable zone width cooling process

By incorporating a temperature-dependent function of interfacial energy and a temperature-dependent pre-exponential factor inversely proportional to the solution viscosity, an integral model was developed according to classical nucleation theory to retrieve the nucleation parameters from the metastable zone width (MSZW) data. The developed model was applied to determine the temperature-dependent interfacial energy and pre-exponential factor during the cooling process from the MSZW data for phenacetin in ethanol experimentally measured in this work. For comparison, the interfacial energy and pre-exponential factor for phenacetin in ethanol at various operating temperatures were determined from the induction time data based on the conventional method. The results indicated that the temperature-dependent interfacial energy and pre-exponential factor for phenacetin in ethanol obtained from the MSZW data based on the developed model were consistent with those obtained from the induction time data based on the conventional method.

Effect of Impurities on Solubility and Metastable Zone Width of Manganese Sulfate Monohydrate

AbstractRecovering manganese from waste batteries is an important issue to promote the development of new energy. Herein, nickel sulfate and cobalt sulfate, representative impurities in waste battery leachate, are selected to examine their influence on the crystallization thermodynamics and crystal nucleation of manganese sulfate monohydrate. This work assessed alterations in solubility and metastable zone width (MSZW) due to the presence of impurities. The results showed a decrease in manganese sulfate monohydrate solubility in water with increasing impurity concentrations of either nickel sulfate or cobalt sulfate. The effects of initial concentration, heating rate, and impurity concentration on MSZW demonstrated a consistent increase in MSZW as these factors increased. The MSZW data are fitted using the self‐consistent Nývlt‐like model and the classical 3D nucleation theory model. The results revealed a general increase in the nucleation rate constant, K, with increasing saturation temperature or decreasing nickel sulfate concentration. Conversely, the solid‐liquid interface energy, γ, generally decreases with increasing saturation temperature or decreasing nickel sulfate concentration. Based on the influence observed on the interface energy, a possible mechanism is proposed that suggests that impurities inhibit crystal nucleation through adsorption.

Comparison of the interfacial energy and pre-exponential factor for isonicotinamide in various solvents from the induction time and metastable zone width data

For isonicotinamide in methanol, acetone, acetonitrile, and ethyl acetate, the interfacial energy and pre-exponential factor from the MSZW data for isonicotinamide in each solvent were compared with those from the induction time data.

Antisolvent crystallization kinetics of different substances in solvent–antisolvent systems

Published experimental data of metastable zone width (MSZW) for the crystallization of four different solutes from their saturated solutions, determined as the maximum antisolvent content Δxmax, by addition of selected antisolvents as a function of feeding rate RA using theoretical equations based on power law (PL) and classical nucleation theory (CNT) are analyzed and trends of variations of the parameters of the equations and relationship between the parameters of the two approaches are discussed. With Δxmax taken in mole fraction of the antisolvent, from the analysis of the Δxmax(RA) data for the different investigated systems the following conclusions may be drawn:(1)The values of the parameters of the linear dependence of ln(Δxmax) on lnRA of the PL-based approach and those of the parameters of the linear dependence of (Δxmax)−2 on lnRA of the CNT-based approach are mutually related.(2)The preexponential factor A of the CNT, associated with the frequency of attachment of solute molecules with, and their detachment from, the growing three-dimensional nuclei, and their solute–solution interfacial energy γeff mainly depend on the product fa2, where f is the number of molecules or ions of solute per m3 in its saturated solution and a2 is the dimensionless solvent–antisolvent interaction parameter. The sequence of variation of γeff is opposite to that of the preexponential factor A.(3)The observed trend of variation of the nucleation constant K calculated from the analysis of antisolvent content Δxmax taken in mole fraction is similar to that of the A for different systems. However, A ≫ K and the ratio A/K ≈ 106.(4)The values of γeff obtained from the MSZW data of the investigated compounds are low and suggest the occurrence of their crystallization by heterogeneous nucleation.

Study on the nucleation kinetics of DL-methionine based on the metastable zone width of unseeded batch crystallization

The metastable zone width (MSZW) of DL-methionine aqueous solution for unseeded batch crystallization was measured by turbidity method. The spontaneous nucleation curves at different stirring rates (250 rpm, 350 rpm and 450 rpm) and cooling rates (18.0 K/h, 30.0 K/h and 42.0 K/h) were obtained by measuring the nucleation temperatures of solutions with saturation temperatures from 304.3 K to 341.9 K. The results show that the increase in saturation temperature and stirring rate makes the MSZW narrower. This is mainly because the enhanced mass transfer makes solute molecules more likely to collide and thus facilitate nucleation. Also the increase in cooling rate widen the MSZW for there is a time lag between nucleation and turbidity is detected. These data provide the operating boundary of crystallization and are important in production to obtain the desired crystal quality. Meanwhile, the nucleation kinetics is studied based on the MSZW data by five semi-empirical models in this work. And the interfacial energy between DL-methionine and water was determined, which decreases from 1.88 mJ·m2 to 0.99 mJ·m2 when temperature increases from 304.3 K to 341.9 K.

Effect of trace sodium polystyrene sulfonate on the solubility, nucleation and crystallization of thiourea from metastable zone width data

The nucleation parameters from two deterministic approaches; the self-consistent Nývlt-like approach (SCA) and the linearized integral nucleation-only (NO) approach, were used to examine the effect of sodium polystyrene sulfonate (NaPSS) on the metastable zone width (MSZW) of Thiourea (TU) in aqueous solution. The addition of NaPSS enhanced the interfacial tensions, γ, of TU (2.52–3.27 mJ.m−2 for SCA model and 1.91–2.95 mJ.m−2 for NO model) leading to increased apparent nucleation progression, m, (1.54–3.44). The MSZW and growth of TU crystals in the presence of NaPSS occurs by instantaneous and heterogeneous nucleation. NaPSS delayed the nucleation of TU, a factor which correlates with increased TU crystal size distribution (38.1 μm in water to ∼ 88.36 μm). High values of m also correspond to observed lower solubility of TU in the presence of NaPSS. Finally, molecular modelling shows NaPSS strongly binds to the TU crystal surfaces during crystallization, inhibiting the nucleation.

Comparison of the Nucleation Kinetics Obtained from the Cumulative Distributions of the Metastable Zone Width and Induction Time Data.

A linearized integral model based on classical nucleation theory is applied in this work to determine the interfacial energy and pre-exponential factor using a linear plot from the cumulative distributions of the metastable zone width (MSZW) data for some systems reported in the literature, including isonicotinamide, butyl paraben, dicyandiamide, and salicylic acid. Based on the same criterion for the nucleation point, the interfacial energy and pre-exponential factor are determined using the conventional linear regression method from the cumulative distributions of the induction time data for the same systems. The results indicate that the interfacial energy and pre-exponential factor calculated from the MSZW data are consistent with those calculated from the induction time for the studied systems.

Comparison of the Nucleation Parameters of Aqueous l-glycine Solutions in the Presence of l-arginine from Induction Time and Metastable-Zone-Width Data

Induction time and metastable-zone-width (MSZW) data for aqueous l-glycine solutions in the presence of l-arginine impurity were experimentally measured using a turbidity probe in this study. The nucleation parameters, including the interfacial free energy and pre-exponential nucleation factor, obtained from induction time data, were compared with those obtained from MSZW data. The influences of lag time on the nucleation parameters were examined for the induction time data. The effects of l-arginine impurity concentration on the nucleation parameters based on both the induction time and MSZW data were investigated in detail.

On the linear and integral models for metastable zone width determined by solution cooling method

From a consideration of fundamental concepts of metastable zone width (MSZW), as determined by the maximum undercooling ΔTm that a solution saturated at temperature T0 can withstand without crystallization as a function of cooling rate RL, final equations of three deterministic approaches, namely: solute-supply, integral nucleation and integral nucleation-plus-growth models, based on classical three-dimensional nucleation theory are derived in a consistent manner, and then used to analyze the published experimental data of ΔTm of glycine–water, glutaric acid–acetic acid and potassium tetraborate tetrahydrate–water systems saturated at different temperatures T0. From analysis of the experimental data of MSZW of glycine–water system trends of variations in the values of the nucleation kinetic parameters of the equation of the classical nucleation theory, obtained by the determininstic integral nucleation model and the conventional stochastic theory, are compared and discussed. It was found that: (1) equation of the simple solute-supply approach satisfactorily explains the dependence of ΔTm of solutions on cooling rate RL at their different saturation temperature T0, and enables to estimate nucleation parameters such as preexponential factor A and solid–solution interfacial solution γeff associated with nucleation, and (2) the values of γeff obtained from the MSZW data are relatively low and suggest the occurrence of crystallization by heterogeneous nucleation. Finally, the nature of nucleation encountered in MSZW measurements by the polythermal method is discussed.

A linearized integral model for determining the nucleation parameters from metastable zone width data

By incorporating the combined effect of nucleation and growth rates on the crystallite size distribution, a linearized integral model was proposed in this work according to classical nucleation theory to determine the nucleation parameters from the metastable zone width (MSZW). Instead of the nucleation pre-exponential factor, the combined constant of nucleation and growth was introduced to account for the combined effect of nucleation and growth rates crystallite size distribution at the nucleation point. From the MSZW data of aqueous L-glycine solutions at different cooling rates for various initial saturation temperatures, the values of the interfacial energy and the combined constant of nucleation and growth were determined and discussed by using the proposed model in this work, as well as various models reported in the literature. The results indicated that the proposed model in this work leads to a lower value of the interfacial energy and a poorer fit of the data than those by the classical 3D nucleation theory approach.

Effect of L-valine impurity on the nucleation parameters of aqueous L-glutamic acid solutions from metastable zone width data

Effect of L-valine on the metastable zone width (MSZW) of aqueous L-glutamic acid solutions saturated at 45 °C at various cooling rates was studied and examined by using various models based on the classical nucleation theory. From the MSZW data for each impurity concentration, values of the pre-exponential nucleation factor and interfacial energy were determined and discussed. It was found that the value of MSZW of the aqueous L-glutamic acid solutions is associated with heterogeneous nucleation and the value of the interfacial energy increases with impurity concentration.

A Linear Regression Model for Determining the Pre-Exponential Factor and Interfacial Energy Based on the Metastable Zone Width Data

A linear regression model is presented in this study to determine the pre-exponential factor and interfacial energy of the crystallized substance based on classical nucleation theory using the metastable zone width data. The nucleation event is assumed corresponding to a point at which the total number density of the nuclei has reached a fixed (but unknown) value. One equation is derived for any temperature-dependent functional form of the solubility. Another equation is derived for the van’t Hoff solubility expression. The pre-exponential factor and interfacial energy obtained from these two equations are found consistent for the studied systems, including glutamic acid, glycine, and 3-nito-1,2,4-triazol-5-one. The results obtained from these two equations are also compared with those obtained from the integral method and classical 3D nucleation theory approach.

Effects of succinic acid and adipic acid on the metastable width of glutaric acid in acetic acid

The influence of impurities on the solubility and metastable zone width (MSZW) of glutaric acid in acetic acid solution was studied. At T = (300.15–340.15) K, the presence of impurity succinic acid or adipic acid increases the solubility of glutaric acid in acetic acid solution, and the solubility increases with increasing mass fraction of impurities. In the study of the effects of saturation temperature, cooling rate, and impurities on MSZW, it was found that the MSZW widened with increasing cooling rate, but it narrowed with increasing saturation temperature and the mass fraction of impurities. The MSZW data was analyzed by using the self-consistent Nyvlt-like approach and the classical 3D nucleation theory-based approach to determine the nucleation kinetic parameters. The results show the increases of saturation temperature and the mass fraction of impurities significantly reduce the nucleation order m and the solid-liquid interfacial energy γ.

Determination of metastable zone width and nucleation kinetics for combined cooling and antisolvent crystallization of L-asparagine monohydrate in water-isopropanol mixture

The metastable zone width (MSZW) was measured for combined cooling and antisolvent crystallization of L-asparagine monohydrate (LAM) in water-isopropanol solution by conventional polythermal method. The effects of cooling rate, antisolvent flow rate and saturation temperature on the MSZW were investigated and analysed using both statistical and theoretical models. The relationship of MSZW with these factors are more complex compared to cooling-only or antisolvent-only crystallization. For each of these three factors, a range of values were determined where the MSZW behaves in a more predictable manner and follows the behaviour of cooling-only crystallization. The effect of antisolvent flow rate was more pronounced compared to cooling rate in case of combined cooling and antisolvent crystallization of LAM. The obtained MSZW data were also used for the estimation of nucleation kinetics using the method proposed by Kubota.

The temperature dependence of the pre-exponential factor and interfacial energy for aqueous glycine solutions based on the metastable zone width data

The metastable zone width (MSZW) data for aqueous glycine solutions at various saturation temperatures 308–328 K are experimentally measured using the turbidity probe in this work. The integral model based on classical nucleation theory is applied to determine the pre-exponential factor and interfacial energy using the measured MSZW data. It is found that the MSZW data of aqueous glycine solutions are fitted well to the integral model. The results indicate for glycine that the interfacial energy decreases with increasing temperature while the pre-exponential factor increases with increasing temperature. For comparison, self-consistent Nyvlt-like equation and classical 3D nucleation theory approach are also applied to determine the nucleation kinetics of glycine from the measured MSZW data.

Mechanism of Influence of Organic Impurity on Crystallization of Sodium Sulfate

To promote the development of crystallization technology for recovering salt from high salinity wastewater, the effect of organic impurity on crystallization of sodium sulfate was investigated by using phenol as a representative organic impurity. The effect of phenol on crystallization thermodynamics of sodium sulfate was evaluated by measuring solubility data of sodium sulfate in water in the presence of phenol. It was found that the existence of phenol could suppress the solubility of sodium sulfate in water. The effect of organic impurity on crystal nucleation was performed by measuring the metastable zone width (MSZW) and induction time of sodium sulfate. Two models (self-consistent Nývlt-like equation and Classical 3D nucleation theory) were used to analyze the experimental data. It was found that Classical 3D nucleation theory (3D CNT) can better explain the effect of phenol on nucleation. From both MSZW data and induction time data, it was found that the existence of phenol will apparently increase...

Nucleation kinetics from metastable zone widths for sonocrystallization of l-phenylalanine

This study investigates the effect of ultrasound on metastable zone width (MSZW) during crystallization of l-phenylalanine from aqueous solution. The solubility of l-phenylalanine in water was measured gravimetrically in the temperature range of 293.15–333.15K. The MSZW was measured by conventional polythermal method for four different cooling rates at five different saturation temperatures in absence and presence of ultrasound. The MSZW increased with increase in cooling rates and decreased with increase in saturation temperature. The application of ultrasound considerably reduced the MSZW for all the experiments. The obtained MSZW data are analysed using four different approaches to calculate various nucleation parameters. In presence of ultrasound, the apparent nucleation order decreased and nucleation rate constant increased significantly.

Determination of metastable zone width of potassium sulfate in aqueous solution by ultrasonic sensor and FBRM

The metastable zone width (MSZW) and nucleation kinetics of potassium sulfate in the aqueous solution were investigated. MSZW was measured using both the ultrasonic velocity sensor and the focused beam reflectance measurement (FBRM) at different cooling rate, stirring rate and impurities concentration (aluminum ions and silicon ions), and the effects of these conditions on MSZW were discussed in details. In addition, the accuracy and sensitivity of detectors to measure the nucleation temperature of potassium sulfate in the aqueous solution were compared between the ultrasonic velocity sensor and FBRM over a wider range of operating conditions. Although two detectors measured MSZW with an acceptable accuracy, the ultrasonic velocity sensor had a higher sensitivity to the phase transition of potassium sulfate in solution since it directly detected the concentration change of potassium sulfate in solution. Furthermore, both self-consistent Nývlt-like equation method and classical 3D nucleation theory approach were applied to estimate MSZW of potassium sulfate in aqueous solution. According to these classical theories, the nucleation kinetics parameters were calculated based on the measured MSZW data for potassium sulfate aqueous solution with 40°C, 50°C and 60°C saturation temperature, respectively. It was found two approaches could describe MSZW of potassium sulfate aqueous system very well.

Thermodynamic properties of 3-chlorophthalic anhydride and 4-chlorophthalic anhydride and their application for purification method development

Development and design of crystallization process strongly depend on accurate solid-liquid equilibrium data. In this paper, the solubility of 3-chlorophthalic anhydride and 4-chlorophthalic anhydride in methyl acetate+cyclohexane binary solvent mixtures was determined from T=(283.15 to 328.15) K by gravimetric method under atmospheric pressure. The results show that the solubility of 3-chlorophthalic anhydride and 4-chlorophthalic anhydride increases with the increasing of temperature at constant solvent composition. At fixed temperature, the solubility of 3-chlorophthalic anhydride increases with mole fraction of methyl acetate increasing. Nevertheless, the solubility of 4-chlorophthalic anhydride displays a maximum with the solvent composition changing. To extend the applicability range of the solubility data, experimental solubility data in binary solvent mixtures was correlated by the modified Apelblat equation, the CNIBS/R-K equation and the Jouyban-Acree equation. It is found that the correlated data is in good agreement with the experimental data. The metastable zone width (MSZW) of 3-chlorophthalic anhydride and 4-chlorophthalic anhydride were also determined by the polythermal method at three different cooling rates. Finally, the cooling crystallization process of 3-chlorophthalic anhydride was designed to separate and purify 3-chlorophthalic anhydride according to its solubility and MSZW data.

Comparison of the interfacial energy and pre-exponential factor calculated from the induction time and metastable zone width data based on classical nucleation theory

The pre-exponential factor and interfacial energy obtained from the metastable zone width (MSZW) data using the integral method proposed by Shiau and Lu [1] are compared in this study with those obtained from the induction time data using the conventional method (ti∝J−1) for three crystallization systems, including potassium sulfate in water in a 200mL vessel, borax decahydrate in water in a 100mL vessel and butyl paraben in ethanol in a 5mL tube. The results indicate that the pre-exponential factor and interfacial energy calculated from the induction time data based on classical nucleation theory are consistent with those calculated from the MSZW data using the same detection technique for the studied systems.