Determination of reactive crystallization kinetics of 5‐(difluromethoxy)‐2‐mercapto‐1H‐benzimidazole in a batch crystallizer

5‐(difluromethoxy)‐2‐mercapto‐1H‐benzimidazole (DMB) was crystallized via the reaction between sodium salt of DMB and acetic acid. In this work, we firstly measured the solubility data of DMB in binary ethanol‐water mixture at different temperatures. Then, the reactive crystallization kinetics of DMB was determined in the batch crystallizer. Based on the population balance and mass balance, the kinetics model of reactive crystallization process of DMB was established. And the nucleation rate, size‐independent crystal growth and agglomeration kernel were determined by method of classes. Finally, based on the population balance, numeric simulation was done using the above crystallization kinetics in order to verify its reliability.     

一维TiO2纳米管光催化降解气相苯的动力学研究

采用水热法制备出一维TiO₂纳米管,并将其应用于光催化降解气相苯。探讨了TiO₂用量、TiO₂面积、苯的初始浓度等因素对光催化性能的影响,并研究其降解动力学规律。结果表明,催化剂用量为0.5 g,面积为180 cm²,苯的初始浓度为480 mg/m³时,苯的去除率最高可达66%。并且随着催化剂用量和面积的增加,气相苯的降解率均随之升高,但其影响却逐渐减弱。而气相苯的初始浓度对光催化降解率的影响较大,且其过程符合拟一级动力学规律,可用L-H模型描述,并确定其反应方程为r=0.003 8C_t/(1+0.587C_t)。     

Model for sintering polydispersed glass particles

We propose a model to describe the sintering kinetics of polydispersed glass particles, having no adjustable parameter. The model is based on three sintering stages: a pure `Frenkel' (F) first step, a mixed `Frenkel/Mackenzie–Shuttleworth' stage, and a third, pure `Mackenzie–Shuttleworth' (MS) step. The model considers sample shrinkage as the sum of the partial shrinkage of several clusters, each consisting of equally sized particles and each showing independent F or MS behavior. The overall set of clusters mimics the specimen's real particle size distribution. We then introduce the concept of neck forming ability – ξ_r, which allows the formation of necks among particles of different sizes, relaxing the clustering condition. Using experimental physical parameters: particle size distribution, viscosity, surface energy, and the theoretical ξ_r, the model describes well the sintering kinetics of an alumino-borosilicate glass powder having polydispersed, irregular shaped particles in a variety of temperatures. The sintering kinetics of the real powder is slower, but not far from the calculated kinetics of a monodispersed distribution containing only particles of average size. Thus the model provides a tool for estimating the sintering kinetics of real glass powders, for any size distribution and temperature, thus minimizing the number of laboratory experiments.     

Parallel simulation of random fractal growth using dynamic lattice liquid (DLL) model

The dynamic lattice liquid (DLL) model is proposed as a universal tool for investigating various aggregation processes. This model allows to perform simulations in systems with constant number of particles and explicit presence of a solvent. The fractals growth is investigated in the systems with different initial concentration of cluster forming particles. It is shown that fractal dimension increases with increasing initial concentration of particles which build up the cluster. The presented results show that DLL algorithm properly reflects structural and dynamic properties of such process.     

Efficient solution of a batch crystallization model with fines dissolution

In this paper, an efficient and accurate numerical method is proposed for solving a batch crystallization model with fines dissolution. The dissolution of small crystals (fines dissolution) is useful for improving the quality of a product. This effectively shifts the crystal size distribution (CSD) towards larger crystal sizes and often makes the distribution narrower. The growth rate can be size-dependent and a time-delay in the dissolution unit is also incorporated in the model. The proposed method has two parts. In the first part, a coupled system of ordinary differential equations (ODEs) for moments and solute mass is numerically solved in the time domain of interest. These discrete values are used to get growth and nucleation rates in the same time domain. In the second part, the discrete growth and nucleation rates along with the initial CSD are used to construct the final CSD. The analytical expression for CSD is obtained by applying the method of characteristics and Duhamel's principle on the given population balance model (PBM). A Gaussian quadrature method, based on orthogonal polynomials, is used for approximating integrals in the ODE-system of moments and solute mass. The efficiency and accuracy of the proposed numerical method is validated by a numerical test problem.     

Effects of L-Aspartic acid on the step retreat kinetics of calcite

Effects of L-Aspartic acid (L-Asp) on step retreat kinetics in the dissolution of calcite were investigated. The step retreat velocities under surface-controlled kinetics were determined from in-situ atomic force microscopic observations using an improved flow-through system. Comparison of the present results with those obtained under a mixed kinetics condition revealed that the addition of L-Asp promotes the transport process in the calcite dissolution through acid–base and/or complex forming reactions in the diffusion boundary layer. Additionally, promotion of the acute and obtuse step retreats by the L-Asp additive was observed under surface-controlled kinetics. This report is the first to clarify that L-Asp promotes surface processes in the dissolution of calcite.     

沉淀法制备纳米ZrO2粉末过程中团聚体形成与控制的研究

依据沉淀过程的动力学分析,研究了沉淀法制备纳米ZrO2粉末团聚体的形成机理及控制技术.实验结果表明:在沉淀反映过程中,当晶粒聚集形成胶粒的初始聚集过程成为控制过程时,粉末的团聚体形成于沉淀反映过程;当胶粒聚集形成三维网络状更大聚集体的二次聚集过程成为控制过程时,团聚体形成于干燥煅烧过程.沉淀过程中,同时引入合适的胶体保护剂和络合剂可以控制初始和二次聚集过程,从根本上控制了胶粒的聚集特征,因而控制了粉末的团聚状态.     

Oxygen and carbon transfer during solidification of semiconductor grade silicon in different processes

A model is established for comparing the solute distribution resulting from four solidification processes currently applied to semiconductor grade silicon: Czochralski pulling (CZ), floating zone (FZ), 1D solidification and electromagnetic continuous pulling (EMCP). This model takes into account solid–liquid interface exchange, evaporation to or contamination by the gas phase, container dissolution, during steady-state solidification, and in the preliminary preparation of the melt. For simplicity, the transfers are treated in the crude approximation of perfectly mixed liquid and boundary layers. As a consequence, only the axial (z) distribution can be represented. Published data on oxygen and carbon transfer give a set of acceptable values for the thickness of the boundary layers. In the FZ and EMCP processes, oxygen evaporation can change the asymptotic behaviour of the reference Pfann law. In CZ and in 1D-solidification, a large variety of solute profile curves can be obtained, because they are very sensitive to the balance between crucible dissolution and evaporation. The CZ process clearly brings supplementary degrees of freedom via the geometry of the crucible, important for the dissolution phenomena, and via the rotation rate of the crystal and of the crucible, important for acting on transfer kinetics.     

Synthesis of PbTe‐SnTe particles by thermal decomposition of salts to create nano‐structured thermoelectric materials

Micro‐ and nanocrystalline particles of Pb‐Sn‐Te mixed crystals were synthesized using thermal decomposition and chemical interaction of lead acetate, tin oxalate and tellurium powder mixture in H₂ atmosphere. For the process parameter optimization data of thermal gravimetry (TG), X‐ray diffraction (XRD), electronic microscopy (TEM, SEM) and measurements of the specific surface of particles were used. Additionally the influence of gas phases on the decomposition kinetics, crystal structure, size, specific surface of the particles, gains composition and the physical properties were analyzed. Seebeck coefficient values increased and conductivity decreased with decreasing tin concentration. The presented method for preparing PbTe‐SnTe polydisperse particles is developed to create nano‐structured thermoelectric materials with high figure of merit. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Growth and dissolution kinetics of potassium sulfate in pure solutions and in the presence of Cr3+ ions

The growth and dissolution kinetics of potassium sulfate was studied based on single crystal measurements. The growth rate is correlated to the supersaturation with power low equation. At all the temperatures studied, the growth rate order lies in the range of 1‐1.5 with the surface integration process as the controlling step. The estimated value of the activation energy of growth is 39.4 kJ/mol. The dissolution rate order decreases with increasing the temperature. The diffusion step is controlling the dissolution process. The addition of 5 ppm Cr³⁺ ions reduces the growth rate. Both growth rate dispersion and dissolution rate dispersion occur in the growth and dissolution processes of potassium sulfate. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Growth and dissolution of equally‐sized insulin crystals

A protocol for growing sets of nearly uniform size crystals was devised and tested experimentally. The experiments were centered on insulin because of its medical significance however the method is applicable to other substances as well (C.N. Nanev, V.D. Tonchev, F.V. Hodzhaoglu, Protocol for growing insulin crystals of uniform size, J. Cryst. Growth 375 (2013)10–15). Now, both growth and dissolution of equally‐sized crystals are described quantitatively by a common analytical model. In our model the emphasis is put on the dissolution case when crystals number and/or size are sufficiently large to secure reaching solubility, while some non‐dissolved crystalline substance is still remaining. Quantitative results are obtained for the relations between dimensionless values of crystal size, solution concentration and time elapsed, the assumption simplifying our calculations being that the crystals retain their shape during the entire dissolution process.     

Chemical reaction kinetics leading to the first Stober silica nanoparticles – NMR and SAXS investigation

²⁹Si-NMR and ¹³C-NMR were used in methanol and ethanol to monitor the intermediates or hydrolyzed monomers that lead to the formation of the first primary particles as detected by small angle X-ray scattering. This identification was facilitated by using initial NH₃ and H₂O levels at the lower end of those experienced in Stober synthesis to slow the reaction kinetics. We found that [NH₃] and [H₂O] control the balance between hydrolysis of tetraethylorthosilicate (TEOS) and the condensation of its hydrolyzed monomers. Transesterification between methanol and TEOS did occur; however, it was negligible compared to the production of hydrolyzed intermediates. The first nanostructures appear at a hydrolyzed monomer concentration around 0.1 M, indicating that formation of the primary structures is thermodynamically controlled by a supersaturation of the intermediate species. Differences in particle size between methanol and ethanol are attributed to thermodynamic interactions between the solvent and the hydrolyzed intermediates.     

Synthesis of lead telluride particles by thermal decomposition method for thermoelectric applications

The lead telluride fine crystalline particles were synthesized using thermal decomposition and chemical interaction of lead acetate and tellurium powder mixture in reducing atmosphere (H₂). For the process control, thermal gravimetry (TG), the different‐scanning calorimetry (DSC), X‐ray diffraction (XRD), electronic microscopy (SEM) and measurements of the specific surface of particles were used. Additionally the influence of gas phases on the decomposition kinetics, crystal structure, size, specific surface of the particles and the physical properties were analyzed. Seebeck coefficient values increased with decreasing synthesis temperature and increasing specific surfaces of the powder. The presented method of preparing lead telluride polydisperse particles is developed to create nano‐structured thermoelectric materials with high figure of merit.     

Dissolution rate and mechanism of solid MgO particles in synthetic ladle slags

Four types of slag with different basicity, MgO and Al₂O₃ content were used to simulate the synthetic ladle slag. The dissolution behavior of MgO particles was then investigated using the direct dissolution method. The results show that the dissolution rate of MgO particles strongly depends on the slag composition and temperature. At the initial stage, the dissolution rate shows a good linear relation with time. Once spinel product forms around the MgO core, the dissolution rate decreases remarkably. The formation and function of the inner slag layer between the MgO core and the spinel product were investigated in detail. The inner slag layer is possible to act as a transfer passage for Mg element from the MgO core to the spinel product. The rate-limiting step of MgO dissolution is determined by the diffusion of spinel product toward the bulk slag.     

The Influence of Impurities on Crystallization Kinetics of Sodium Chloride

The influence of impurities on the crystallization kinetics of NaCl was investigated in a fluidized bed crystallizer. The growth and dissolution rates were related to the supersaturation and impurity concentrations. The effect of different impurities on the growth rate of NaCl crystals can be divided into thermodynamic effects where the impurities influence the solubility and kinetic effects where the impurities will suppress the growth rate compared to the pure NaCl. A mathematical model describing crystal growth rates from aqueous solution as a function of impurity concentration is presented. The model explains impurity concentration effects on the crystal growth rate in terms of an impurity effectiveness factor and a Langmuir adsorption isotherm for the impurity.     

Spontaneous crystallization of sodium chloride from aqueous‐ethanol solutions – Part 2: Mechanism of aggregation and coalescence of crystals

Published data on aggregation kinetics of sodium chloride crystals at its spontaneous crystallization from supersaturated aqueous‐ethanol solutions were analysed. It was found that the crystals coalesced through contact nucleus‐bridges between them according to the mechanism proposed by Polak. The kinetics of aggregation were described by the Smoluchowski equation for coagulation of colloidal particles. The kinetic coefficient of aggregation process depended on supersaturation, temperature of solution and other characteristics of the system. The specific surface energy of sodium chloride 0.95 mJ/m² was found. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Recrystallization of puerarin using the supercritical fluid antisolvent process

The purpose of this study was to investigate the influence of supercritical fluid (SCF) processing on the polymorphism of puerarin (Pur), a poorly soluble drug. The gas anti-solvent (GAS) technique was used to crystalize the drug in different conditions. The samples were analyzed by scanning electron microscopy and laser granulometry for changes in the habitus and particle size. The solid state was studied by X-ray powder diffraction (XRPD), differential scanning calorimetry (DSC), Fourier-transform infrared spectroscopy (FT-IR) and melting point determination. Finally, the dissolution and solubility tests were carried out. It was attested that compared with the commercial Pur in Crystal form I, at the optimum and most of conditions, Pur changed into crystal form II with more orderly and pure appearances. At the concentration of 60 mg/ml and at the solvent of methanol, two other new crystal forms (named form III and form IV) were produced. It was demonstrated that the particles mean diameter, size distribution and morphology can be strongly controlled through the manipulation of the process parameters and more importantly, Pur in the new crystal forms, which were not reported before with better physico-chemical properties could be produced by recrystalization by GAS.     

Simulation of surface structural relaxation kinetics in silica glass accelerated by water vapor

It is known that surface structural relaxation of silica glass takes place more rapidly than bulk structural relaxation, especially in the presence of water vapor. The effect of water vapor pressure, heat-treatment temperature and initial fictive temperature on the surface structural relaxation kinetics in silica glasses was investigated by measuring the change of the surface fictive temperature determined from the IR reflection peak shift of silica structural bands. The superimposed component of bulk structural relaxation was subtracted from the measured surface structural relaxation data to isolate the true surface structural relaxation kinetics. The obtained surface structural relaxation data as a function of fictive temperature, heating temperature and water vapor pressure were simulated with a model based on the diffusion equation with time-dependent surface concentration. The simulation model was used to predict the surface structural relaxation kinetics of the optical fiber having a high fictive temperature of ～ 1650 °C at 950 °C under 355 torr of water vapor, and it was confirmed that the present model can simulate surface structural relaxation of the fiber reasonably well.     

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)     

On‐line monitoring of lithium carbonate dissolution

Dissolution of lithium carbonate (Li₂CO₃) in aqueous solution was investigated using three on‐line apparatuses: the concentration of Li₂CO₃ was measured by electrical conductivity equipment; CLD (Chord Length Distribution) was monitored by FBRM (Focused Beam Reflectance Measurement); crystal image was observed by PVM (Particle Video Microscope). Results show dissolution rate goes up with a decrease of particle size, and with an increase in temperature; stirring speed causes little impact on dissolution; ultrasound facilitates dissolution obviously. The CLD evolution and crystal images of Li₂CO₃ powders in stirred fluid were observed detailedly by FBRM and PVM during dissolution. Experimental data were fitted to Avrami model, through which the activation energy was found to be 34.35 kJ/mol. PBE (Population Balance Equation) and moment transform were introduced to calculate dissolution kinetics, obtaining correlation equations of particle size decreasing rate as a function of temperature and undersaturation. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)