On the prediction of crystal shape distributions in a steady-state continuous crystallizer

Zhang and Doherty [2004. Simultaneous prediction of crystal shape and size for solution crystallization. A.I.Ch.E. Journal 50, 2101-2112] have provided a one-dimensional analysis of crystallization based on the assumption that the relative face-specific growth rates of a (2-D) crystal are independent of supersaturation and hence invariant with time. Subsequent work by these authors [Zhang, Y., Sizemore, J.P., Doherty, M.F., 2006. Shape evolution of 3-dimensional faceted crystals. A.I.Ch.E. Journal 52, 1906-1915) consider shape evolution of single three-dimensional crystals with morphological changes. In this work, we present a multidimensional population balance approach accounting for dependence of the relative face-specific growth rates on supersaturation, a situation more commonly encountered. For example, Joshi and Paul [1974. Effect of supersaturation and fluid shear on habit and homogeneity of potassium dihydrogen phosphate crystals. Journal of Crystal Growth 22, 321-327] and Mullin and Whiting [1980. Succinic acid crystal-growth rates in aqueous solution. Industrial & Engineering Chemistry Fundamentals 19, 117-121] report face-specific growth rates with different dependence on the supersaturation. Thus it has been observed that there exists significantly different crystal shapes in a crystallizer [Yang, G., Kubota, N., Sha, Z., Louhi-Kultanen, M. Wang, J., 2006. Crystal shape control by manipulating supersaturation in batch cooling crystallization. Crystal Growth and Design 6, 2799-2803]. Consequently, the population of crystals at any instant will have widely varying crystal shapes and sizes depending upon the initial crystal shape and size distribution. Computations are presented for the shape distributions of the crystal population emerging from a steady-state continuous crystallizer for two cases: (1) feed without crystals including nucleation for the formation of new crystals, and (2) feed with seed crystals of known shape, with suppressed nucleation. In the range of mean residence times investigated, the calculated crystal volume distributions for the first case show geometrically dissimilar shapes without morphological variations. However, in the second case, because the feed crystals of the chosen shape were susceptible to morphological changes, the volume distributions display this feature with shape and size distributions for each of a number of different morphologies. By varying operating conditions such as the flow rate, the inlet supersaturation, and the shapes of feed crystals, the proposed model can clearly be used to manipulate the crystal shape and size distributions and their morphologies.     

Comparison of different solubility equations for modeling in cooling crystallization

In this paper we evaluate the sensitivity of using different solubility models on cooling crystallization. Specifically, the cooling crystallization of acetaminophen in ethanol is investigated. Empirical, correlative thermodynamic (namely van Laar, Wilson, and NRTL) and predictive thermodynamic (namely MOSCED, NRTL-SAC, and UNIFAC) models are considered. Equilibrium solubility model prediction determines the predicted supersaturation profile. The different solubility equations are used within a population balance model for prediction of crystal size properties. Incorrect prediction of the supersaturation profile results in incorrect prediction of crystal size distribution. The NRTL model was found to be more accurate at predicting equilibrium solubility and consequently crystal size. After the solubility sensitivity is evaluated, two methods are proposed to make the crystallization model more robust against solubility model errors.     

Crystallization of high purity ammonium meta-tungstate for production of ultrapure tungsten metal

The growth mechanism of Ammonium Meta-Tungstate (AMT) crystal was interpreted as two-step model. Growth rates of AMT crystals were measured in a fluidized bed crystallizer. The effects of temperature, supersaturation and crystal size on the crystal growth were investigated. The contribution of the diffusion step increased with the increase of temperature, crystal size and supersaturation. The nucleation kinetics from measurements on the width of the metastable region of Ammonium Meta-Tungstate (AMT) was also evaluated. The crystal size distribution from a programmed cooling crystallization system was predicted by the numerical simulation of a mathematical model using the kinetics of nucleation and crystal growth. It was also observed that the shape of AMT crystals was changed during the growth period. This paper was presented at The 5th International Symposium on Separation Technology-Korea and Japan held at Seoul between August 19 and 21, 1999.     

Correlation between quantity of defect and supersaturation in RDX crystallization using γ-butyrolactone and water as solvent

The crystallization of RDX (cyclotrimethylenetrinitramine) was carried out using cooling crystallization. Effect of cooling rate and antisolvent to solvent ratio on the inclusion was studied. Qualitative observation of internal crystal defects was performed by optical microscopy with matching refractive index. The quantitative amount of inclusions was determined by measuring concentration of solid. Effect of the cooling rate and the antisolvent to solvent ratio on supersaturation was investigated. The supersaturation affected significantly the inclusion of mother liquor inside the crystals. The higher supersaturation induced the more agglomeration, that caused the formation of the more inclusions inside RDX crystals. From morphological study, defect is formed in course of transformation from plate-like to polygon shape. An empirical correlation of the inclusion fraction of RDX with the relative supersaturation was obtained.     

Monitoring the particle size and shape in the crystallization of paracetamol from water

In this work, a technique capable of restoring bidimensional particle size distributions from images of the particles in suspension is applied to the seeded cooling crystallization of paracetamol from water. The effects of cooling rate and stirring rate on the final particle size and shape are studied and the average growth rates along different directions of particles are found to be strongly dependend on supersaturation. This observation is in line with previous studies, though in this work it has been established for the first time using populations of particles. The technique was capable of quantifying changes in particle size and shape, indicating particle sizes and shapes that correlated well with observations from electron microscopy images.     

Estimation of number of surface crystals on sodium fluoride mother crystal in crystallization

A simple model was developed to explain the surface crystals found on the clear mother crystal face. The surface crystals on the mother crystal in the reaction crystallization of sodium were mathematically estimated by using a model based on two-dimensional secondary nucleation and two-step growth mechanisms. The model predicted that the surface crystals found on the mother crystal would be sensitive to the reactant concentration and agitation speed due to their influence on the interfacial supersaturation in the crystal growth. As the bulk supersaturation increased and the molecular transport was facilitated, the number of surface crystals on the mother crystal also increased, because the interfacial supersaturation built up on the mother crystal surface was enhanced. The prediction of the number of the surface crystals on the mother crystal appeared to be consistently comparable with experimental results.     

How to measure supersaturation?

The existing methods for the measurement of supersaturation can be generalized insofar that physical properties are used that show a dependence on concentration of the measurands for supersaturation. The influence of impurities, foreign particles, or ions on the metastable zone width and on the kinetics of nucleation and crystal growth cannot be detected by most of the described methods. Thus, it is necessary to develop a supersaturation sensor which considers the actual crystallization process itself in its measurement method. The idea of that is to induce crystallization on the surface of the sensor by generating an additional supersaturation by cooling and to observe the time-dependent development of the formation of solid matter on the surface which leads finally to incrustation. Assuming a constant cooling rate and constant properties of the sensor surface, the starting time of the incrustation on the sensor surface depends only on the prevailing supersaturation in the process solution. Experimental results obtained for inorganic (KNO₃) and organic (adipic acid) crystallizing solutes proved the working of the new sensor.     

Polymorphism of D-mannitol: Crystal structure and the crystal growth mechanism

The polymorphism of D-Mannitol(mannitol) is reviewed in this paper. It was found that the structure of the stable form is consistent in most literatures, but different authors have given different information about the two metastable forms. Therefore the commonly used nomenclature of mannitol was summarized based on the crystal unit cell parameters with the help of X-ray powder diffraction. Moreover, the crystal growth mechanism of mannitol polymorphs was summarized. Considering the lack of kinetic data for the metastable form especially, a reported method was attempted to apply to δ mannitol in an aqueous cooling crystallization process based on the induction time previously measured, and it was identified that the growth of the δ form follows the two-dimensional(2D) nucleationmediated mechanism. The results also indicate that the method based on induction time and supersaturation should have the potential to be expanded to the metastable polymorphs for the growth property study in a bulk system.     

Morphology, reorganization and stability of mesomorphic nanocrystals in isotactic polypropylene

The morphology and thermodynamic stability of crystals of isotactic polypropylene (iPP) were analyzed as a function of the path of crystallization by atomic force microscopy (AFM) and differential scanning calorimetry (DSC). Samples were melt-crystallized at different rates of cooling using a “controlled rapid cooling technique”, and subsequently annealed at elevated temperature. Mesomorphic equi-axed domains with a size less than 20 nm were obtained by fast cooling from the melt at a rate larger about 100 K s⁻¹. These domains stabilize on heating by growing in chain direction and cross-chain direction, to reach a maximum size of about 40-50 nm at a temperature of 433 K, with the quasi-globular shape preserved. Annealing at 433 K additionally triggers formation of different types of lamellae. It is suggested that these lamellae either develop by coalescence of nodules, or by recrystallization from the melt. The transition from the disordered mesomorphic structure, evident at ambient temperature after fast crystallization, to monoclinic structure on heating at about 340 K occurs at local scale within existing crystals, and cannot be linked to complete melting of mesomorphic domains and recrystallization of the melt. The temperature of melting of initial mesomorphic domains, after reorganization at elevated temperature, is identical to the temperature of melting of rather perfect lamellae, obtained by initial slow melt-crystallization, followed by annealing. The close-to-identical temperatures of melting of these crystals of largely different shapes are confirmed by model calculations, using the Gibbs-Thomson equation. Modeling of the melting temperature reveals that nodular crystals, stabilized by annealing at high temperature, exhibit a similar fold-surface as lamellar crystals.     

Particle shape manipulation and optimization in cooling crystallization involving multiple crystal morphological forms

A population balance model for predicting the dynamic evolution of crystal shape distribution is further developed to simulate crystallization processes in which multiple crystal morphological forms co‐exist and transitions between them can take place. The new model is applied to derive the optimal temperature and supersaturation profiles leading to the desired crystal shape distribution in cooling crystallization. Since tracking an optimum temperature or supersaturation trajectory can be easily implemented by manipulating the coolant flowrate in the reactor jacket, the proposed methodology provides a feasible closed‐loop mechanism for crystal shape tailoring and control. The methodology is demonstrated by applying it to a case study of seeded cooling crystallization of potash alum. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Induction Time in Crystallization Fouling on Heat Transfer Surfaces

This work deals with the induction period in crystallization fouling on heat transfer surfaces. While the crystal growth period can be calculated, the influencing effects in the initial stage of crystallization fouling are not fully understood and quantified so far. To identify the factors influencing the induction time, experiments with calcium sulfate were performed on modified surfaces. As surface parameters the free surface energy, roughness and topography were determined by drop shape analysis and/or AFM. The visual information by microscopic studies with a SEM shows different behavior in the initial stage of crystallization on modified surfaces at constant process conditions. These microscopic findings could be verified with induction times of fouling experiments, leading to a prediction of the induction time based on surface parameters and supersaturation of the salt solution.     

Semi‐quantitative Study on the Inclusion in Cooling Crystallization of RDX Using Various Solvents

Inclusion entrapped inside the crystals prepared in the cooling crystallization of cyclotrimethylenetrinitramine (RDX) from solution was studied. Effect of supersaturation on the inclusion formation was also studied in crystallization using solvents. Solvents such as acetone (AC), cyclohexanone (CH), dimethylsulfoxide (DMSO), N‐methylpyrrolidone (NMP), γ‐butyrolactone (BL), and their mixtures with water were investigated. The quantitative amount of inclusions entrapped in the RDX crystallized in various solvents was related to the supersaturation. The inclusion fraction in the crystals was affected by the supersaturation and the solvent. In order to decrease the inclusion fraction, in the low supersaturation, AC and CH were recommended, while in high supersaturation, NMP and DMSO were desirable. Eventually the solvent effect on the inclusion was grasped by considering the supersaturation effect.     

Model-based object recognition to measure crystal size and shape distributions from in situ video images

To achieve robust control of industrial crystallization processes, it is necessary to measure the sizes, shapes, and polymorphic forms (i.e., internal structures) of the developing crystal population. This paper describes a model-based object recognition algorithm designed to extract crystal size and shape information from noisy, in situ crystallization images. The effectiveness of the algorithm is demonstrated using in situ images obtained at low, medium, and high solids concentrations during an α-glycine cooling crystallization in water. With respect to measurements obtained through manual image analysis by human operators, the algorithm gives reasonably accurate size and shape measurements. The algorithm is sufficiently fast to enable real-time monitoring for typical cooling crystallization processes.     

A study on crystallization kinetics of pentaerythritol in a batch cooling crystallizer

The crystallization kinetics of pentaerythritol (PeE) in aqueous solution in the presence of impurity or not in a batch cooling crystallizer was explored. Also, the solubility and the nucleation and crystal growth kinetics of PeE in aqueous solution were investigated. A second-order dependence of PeE growth rate on supersaturation is observed in pure PeE-water system. The crystal growth rate of PeE-water system in the presence of impurity is proportional to the supersaturation to the 3.5 power. The nucleation and crystal growth behaviors for PeE-water system in a batch cooling crystallizer were grasped according to Mersmann's criteria. The nucleation in this crystallizer was found to act with heterogeneous nucleation. In this system, it suggests that the crystal growth is controlled by a complex mechanism behavior of surface integrated and diffusion limited. Simplified relation was derived for calculation of mean crystal size of product crystals from the batch cooling crystallizer. The obtained relation was verified by a set of experiments.     

Crystallization and precipitation

This paper deals with the design and operation of cooling and evaporation crystallizers and precipitators for reaction crystallization. It will be shown that the median crystal size, L₅₀, of a crystalline product and the crystal size distribution (CSD) mainly depend on the crystallization kinetics, e.g. the rates of nucleation and crystal growth, and that these kinetics are controlled by supersaturation. Therefore, the main objective in crystallization and precipitation is to choose and to maintain the optimal supersaturation with respect to product quality at all times and all locations in the crystallizer or precipitator.     

Stress from crystallization of salt

The thermodynamic and kinetic factors influencing crystallization pressure are reviewed for cases including capillary rise and evaporation, cyclic wetting and drying, and hydration of cement. Under equilibrium conditions, where the crystal is surrounded by a film of solution, high stresses are expected only in small pores, but when that film is discontinuous (as may occur during drying), high stresses can arise even in large pores. High crystallization pressure requires a substantial supersaturation of the pore liquid. In the case of sodium sulfate, supersaturation results from the difference in solubility between the anhydrate and decahydrate phases; for ettringite, supersaturation may develop following the cooling from elevated temperatures. During the hydration of Portland cement, crystallization pressure may result from the growth of ettringite and/or calcium hydroxide.     

Crystal Growth in Drowning‐Out Crystallization using a T‐Mixer

The kinetics of nucleation and crystal growth in drowning‐out crystallization using a T‐mixer were estimated using crystal size distribution, taking into account a size‐independent growth. At the conditions of the feed compositions investigated, the product weight mean size changed from 7–29 μm when the residence time varied between 0.32 and 0.61 s. Nucleation and growth rates were expressed simply as a function of the residence time. The T‐mixer can be used to generate high levels of supersaturation due to inducing micro‐mixing effects. The particle size correlated well with the ratio of growth rate to nucleation rate. Finally, the particle size obtained in drowning‐out crystallization using a T‐mixer was found to be proportional to the 1.69^th power function of the residence time.     

基于PBM的L-谷氨酸粒度分布控制优化

针对β型L-谷氨酸冷却结晶过程,为获取期望粒度分布,采用特征曲线法（MOCH）来建立关于粒度相关生长率的种群平衡方程（PBE）,然后通过对种群平衡模型（PBM）参数辨识后确定最优过饱和度及控温曲线。由于辨识模型参数的目标函数具有非线性和非凸型性,因而采用少量经济性的批量冷却结晶实验,结合图像分析晶种和产品粒度分布得到的统计数据,拟合模型参数。根据实际要求的结晶过程时间,为达到目标粒度分布,通过优化结晶过程的过饱和度获得最优调温曲线,实现基于恒定过饱和度的晶体生长过程优化控制。实验结果表明通过优化的控温曲线,实现了基于最优过饱和度控制的期望目标粒度分布。     

FOX-7晶体的制备和热性质

为了解FOX-7晶体形状和尺寸对其热性质的影响,通过冷却结晶和阻溶剂结晶的方法从DMF/H2O、NMP/H2O体系中获得FOX-7晶体.SEM结果表明,得到的晶体基本为延长的四面或六面棱柱和斜方菱晶两种类型,不同溶剂体系中得到晶体的尺寸不同和包含的颗粒数量也不同,超声处理得到的晶体具有单一形状,只是其表面较粗糙.DSC测试结果表明,不同结晶方式和不同溶剂体系中获得的FOX-7晶体的热性质有一定的差别.由此得出,不同的结晶方式和溶剂体系可以获得不同形状、尺寸和热性质的FOX-7晶体,而超声处理可以很好地控制晶体的形状.     

Effects of crystallization temperature on the polymorphic behavior of syndiotactic polystyrene

The influence of crystallization temperature on formation of the α- and β-form crystals of syndiotactic polystyrene (sPS) was investigated by X-ray diffraction and non-isothermal differential scanning calorimetry analysis. For sPS samples without any thermal history, the crystallization temperature must be the intrinsic factor controlling the formation the α and β-form crystals. Being crystallized at different cooling rate from the melt, sPS forms the β-form crystal until the temperature cooled down to about 230 °C, and α-form crystal can only be obtained when the temperature was below about 230 °C.