Kinetics of Nucleation and Crystal Growth

This paper deals with homogeneous and heterogeneous primary nucleation and the atomistic model of heterogeneous primary and secondary nucleation. Three aspects of crystal growth mechanisms will be taken into account: growth by two-dimensional nucleation, the so-called birth and spread model, spiral growth without and with consideration of the influence of diffusion, and finally adhesive growth. An equation for the estimation of the growth rate of imperfect crystals including dislocations, published by Mersmann [1], is discussed. The influence of additives on nucleation and crystal growth, respectively, will be exemplarily explained for several model systems. The effect of growth rate dispersion (GRD) is described. Therefore, some experimental results concerning growth rates and different ways to influence growth are represented and discussed. Furthermore, a model explaining the effect of GRD is represented.     

Unusual Crystal Growth Kinetics of (RS)‐Ibuprofen from Ethanolic Solutions

The solubility, secondary nucleation threshold, and growth kinetics of (RS)‐ibuprofen have been studied in an aqueous ethanol solvent. The metastable zone for secondary nucleation is very narrow at lower temperatures in this range, but greatly enlarged at higher temperatures. The crystal growth kinetics not only display significant dispersion of growth rates, but also a dead zone that is dependent on the growth rates of the crystals. Faster growing crystals display almost no dead zone, whereas the smallest crystals have a large dead zone. The size of the dead zone is largely responsible for the dispersion of crystal growth rates, perhaps due to differences in the thermodynamic stability of the different crystals. The mechanism of growth rate dispersion relates to that of the dead zone.     

GROWTH RATES OF POTASSIUM SULPHATE CRYSTALS OF DIFFERENT SURFACE QUALITIES IN THE SIZE RANGE FROM 10-100 μm

Growth rate data of surface-integration controlled growing potassium sulphate crystals in the size range. 10-100μm are presented. The experiments were carried out in an agitated vessel crystallizer. The crystal growth rates were calculated from the shift of the population distributions with time as measured by a Coulter-Counter. In particular the effect of different surface qualities on the growth rates was investigated and clearly demonstrated. The existence of a growth rate dispersion (GRD) was shown for crystals in an agitated crystallizer. This is a new observation since previously this effect was only investigated for stagnant solutions in the case of the above mentioned range of crystal sizes.     

Needle Crystal Morphology Explained

The morphology of needle shaped crystals is, usually, ill‐predicted when using the common attachment energy approach. Here we explain the needle shape of triacylglycerol crystals on the basis of a two‐dimensional nucleation growth mechanism. For that the edge energies of 2D nuclei on the surfaces of the various crystal faces is determined and turns out to be much lower than expected when applying the attachment energy criteria. The edge energies are found by determining the connected nets of the various faces that follow from the crystal structure and the interaction energies between the molecules. The results are confirmed by Monte Carlo simulations.     

Modeling the crystallization of proteins and small organic molecules in nanoliter drops

Drop‐based crystallization techniques are used to achieve a high degree of control over crystallization conditions in order to grow high‐quality protein crystals for X‐ray diffraction or to produce organic crystals with well‐controlled size distributions. Simultaneous crystal growth and stochastic nucleation makes it difficult to predict the number and size of crystals that will be produced in a drop‐based crystallization process. A mathematical model of crystallization in drops is developed using a Monte Carlo method. The model incorporates key phenomena in drop‐based crystallization, including stochastic primary nucleation and growth rate dispersion (GRD) and can predict distributions of the number of crystals per drop and full crystal size distributions (CSD). Key dimensionless parameters are identified to quickly screen for crystallization conditions that are expected to yield a high fraction of drops containing one crystal and a narrow CSD. Using literature correlations for the solubilities, growth, and nucleation rates of lactose and lysozyme, the model is able to predict the experimentally observed crystallization behavior over a wide range of conditions. Model‐based strategies for use in the design and optimization of a drop‐based crystallization process for producing crystals of well‐controlled CSD are identified. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Control of well‐defined crater structures on the surface of biaxially oriented polypropylene film by adding nucleators

While it is common to add anti‐blocking agents to biaxially oriented polypropylene (BOPP) films for general use in order to prevent blocking against each other, the technology of crater‐like film surface roughness formed on the BOPP films without any additives is well known in the industrial BOPP film areas. Numerous studies have been reported on the crater‐like film surface roughness on the BOPP films since the 1980s, but its formation mechanism and the controlling method of the crater‐like film surface roughness are yet to be clarified. In our previous reports, we presented a new hypothesis of crater formation mechanism from a new point of view on sheet morphology and crater shape on the BOPP film surface. It was strongly influenced by the crystal grain shape in the surface layer of PP sheet. In this report, it was clarified that a nucleator has a big influence on the formation of the crystal grains in the surface layer of PP sheets and on the formation of craters. In addition, craters did not form on the BOPP films stretched from the sheet of which the skin layer with crystal grain was shaved, even though β crystal still remained. It was clarified that the crystal grain is trans‐crystal from the observation using TEM. Therefore, it is concluded that the existence of β crystals in the surface layer of PP sheets is not essential in order to produce craters on BOPP films, but trans‐crystals are necessary to form the craters. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 130: 3555–3564, 2013     

在玻璃上合成有取向的silicalite-1分子筛膜及其生长机理

引言 分子筛膜具有规则的微孔结构、良好的化学和热稳定性,在气体分离、催化膜反应器、化学传感器以及分子筛改性电极等方面有广泛的应用前景[1-2],是催化和分离新材料领域的研究热点之一.     

Crystal structure changes during isothermal crystallization, cooling and heating of linear polyethylene

The dynamic process of crystal structure change during isothermal crystallization, cooling and heating of linear polyethylene with different molecular weight and polydispersity was followed by wide-angle X-ray diffraction (WARD) measurement. From the WARD data, variations of unit cell parameters a and b and changes in crystallinity were estimated. During isothermal crystallization, both cell parameters were found to decrease with time, suggesting that the crystal structure was becoming more perfect. With an increase in molecular weight or crystallization temperature, the rate of crystal perfection and the attainable crystallinity were found to decrease. This behavior can be explained by the formation of thicker lamellae, which probably have a lower degree of defects and a reduced surface-to-volume ratio in the crystals. Upon cooling and heating, the cell parameters appeared to contract and expand accordingly. The thermal contraction and expansion of parameter a is considerably larger than that of b, which probably results from the weaker intra-chain interactions along the a-axis, which is perpendicular to the spherulite growth direction.     

Crystal Morphology Controlling of TATB by High Temperature Anti‐Solvent Recrystallization

The spheroidizing of TATB (1,3,5‐triamino‐2,4,6‐trinitrobenzene) can help to control preferred orientation and anisotropic expansion of TATB based PBXs, as well as to improve crystal quality, desensitizing efficiency, packing density, and even explosive energy. In this paper, TATB crystals with different morphology were obtained by high temperature recrystallization from anti‐solvents. TATB was dispersed into DMSO and heated to dissolve. Water as an anti‐solvent was added to the solution with different conrol parameters. We designed additional experiments to study the particular influence of these parameters. It was shown that the crystal morphology is strongly affected by the stirring rate and the amount of water added. The recrystallized TATB samples have similar thermal stability as starting TATB, but higher densities and purities, which indicates that the quality of TATB crystals was improved. By slowly adding an appropriate amount of water and cooling, regular crystals of TATB were obtained, which proves that water is a good morphology modifier for TATB.     

Kinetic roughening transition and missing regime transition of melt crystallized polybutene-1 tetragonal phase: growth kinetics analysis

The morphology and lateral growth rate of isotactic polybutene-1 (it-PB1) have been investigated for crystallization from the melt over a wide range of crystallization temperatures from 50 to 110°C. The morphology of it-PB1 crystals is a rounded shape at crystallization temperatures lower than 85°C, while lamellar single crystals possess faceted morphology at higher crystallization temperatures. The kinetic roughening transition occurs around 85°C. The nucleation and growth mechanism for crystallization does not work below 85°C, since the growth face is rough. However, the growth rate shows the supercooling dependence derived from the nucleation and growth mechanism. The nucleation theory seems still to work even for rough surface growth. Possible mechanisms for the crystal growth of this polymer are discussed.     

Roughness of growth faces of polymer crystals: Evidence from morphology and implications for growth mechanisms and types of folding

It is proposed that the growth faces of lamellar polymer crystals can have an equilibrium roughness (or crenellation). This can explain why some polymer crystals show no evidence of faceting. Support for this idea comes from the extensive theoretical developments on the nature of crystal surfaces. The characteristic habits of polyethylene are analysed in terms of a roughness which, on the {110} faces, increases progressively over a temperature range of about 100°C. At a temperature near 110°C the roughness becomes sufficient for there to be no free energy penalty for arbitrary crystal shapes (e.g. rounded) compared with one bounded by {110} faces. Above this temperature of crystallization most of the habits which are observed are leaf-shaped, with an apex along 〈010〉. Below 110°C{110} facets (or microfacets) are normally seen. There is no positive evidence that faces approximately parallel to (100) planes, observed for crystallization temperatures in the range 80°–110°C, are ever other than rough. The relative rates of growth on the {110} compared with the (100) increase with temperature, since {110} faces predominate at low but not high temperatures of crystallization. These changes are attributed to the increase in roughness with temperature on the {110} faces. The existence of surface disorder (roughness) requires that the binding energy between units in the crystal is comparable with KT. Hence this unit is probably several monomer units of polyethylene (rather than, for example, a complete stem which contains a hundred or more monomers). There is therefore a surface lattice on the growth faces with twenty or more units in the direction perpendicular to the lamellae. Monte Carlo calculations are cited for lattices of 20 by 50 units. These show that a cooperative increase in surface roughness with temperature and a transition between faceted and non-faceted growth can be expected for lattices of such limited extents. No explicit allowance has been made as yet for the consequences of the units being linked into chains and, for that reason, not being able to arrive or leave the surface independently. It is noted that changes in the alkane lattice with temperature indicate a possible evolution in binding energy, and in mobility, and hence may influence surface roughness. Theories of crystallization in polymers have normally assumed a growth surface which is molecularly smooth in equilibrium, and have emphasised nucleation events. Since this paper shows that the equilibrium structure may often be rough, it may be necessary to re-examine the basis of these theories. A brief review is included of the experimental evidence for surface nucleation events: nucleation may be a more important barrier at low temperatures than at high. The type of folding will be influenced by equilibrium roughness just as it will be by kinetic roughness, and some comparisons are made with neutron scattering results on this topic. The degree of adjacent folding is higher in the faceted regime as expected. Brief comments are made on the applicability of this idea to polymers other than polyethylene.     

添加剂对氨基酸晶体生长的影响

氨基酸大多生长为针状或片状晶习,存在堆密度低、流动性差等问题,严重影响产品后加工处理过程。因此,实现氨基酸晶习的定向调控具有重要意义。添加剂对氨基酸晶习调控直接有效,广泛应用于工业生产中。本文主要从抑制和促进晶体生长两个角度,综述了添加剂对氨基酸晶体生长的作用机理。添加剂对晶体生长的抑制机理主要有两点：一是添加剂分子吸附到晶面上,阻碍溶质分子的扩散和聚集;二是添加剂分子嵌入晶格并占据生长位点。而添加剂促进晶体生长的机理为：添加剂加快了溶质分子在晶体表面的聚集速度、使晶体表面粗糙化和降低了溶剂层脱除能垒。最后,针对添加剂对氨基酸晶体生长影响的研究,从晶体工程的角度提出了通过分子模拟设计的添加剂定向控制氨基酸晶体生长,从而调控晶习的展望。     

青霉素亚砜结晶生长与成核动力学

利用Mydlarz 和 Jones 模型（MJ2）,对乙酸丁酯中青霉素亚砜的成核与生长动力学进行研究。通过矩量法对MJ2模型进行处理后,利用晶体产品的粒度分布计算得到青霉素亚砜的生长速率与成核速率,然后利用最小二乘法拟合回归求解出成核与生长动力学方程参数。通过实验设计考察了过饱和度、温度与搅拌速度对青霉素亚砜晶体成核和生长过程的影响。研究表明青霉素亚砜晶体生长速率随过饱和度比的增加呈现指数型增长,确定青霉素亚砜晶体生长属于晶体表面生长控制过程。由于高速搅拌会增加青霉素亚砜晶体的破碎,促进了二次成核过程,随着搅拌速度的增加,晶体生长速率出现小幅下滑,而成核速率则明显升高。青霉素亚砜成核与生长动力学研究将有助于工业生产过程优化。     

Crystal growth dispersion in an MSMPR crystallizer — a mathematical model

According to the literature, one of the formation mechanisms of crystal growth rate dispersion consists in each individual crystal growing at an adequate constant rate, with different rates however for different crystals. In the present paper, this case has been described on the basis of a population density of nuclei, making use of the classical exponential dependence amongst others. Differences between n and n have been interpreted. The dependencies describing the population density of crystals n have been presented and a simplified method for their calculation proposed.     

镀液流速对高速镀锌层粗糙度及织构的影响

利用自制的模拟重力高速电镀槽,通过扫描电子显微镜(SEM),X射线衍射(XRD)和粗糙度仪检测,研究了在硫酸盐镀锌过程中,镀液流速对镀锌层形貌、各晶面择优取向度和粗糙度的影响.结果发现,镀液流速对镀层的微观形貌影响:流速大时镀层结晶细致、平整,流速较小时镀层结晶粗大、凹凸不平;镀液流速对各晶面的择优取向度影响较小;且镀层的粗糙度随镀液流速的增加呈线性下降规律,并建立了镀液流速与镀层粗糙度之间的数学关系式:Ra=a bv;对该式的进一步探讨佐证了镀层厚度和电流密度对镀层粗糙度的影响规律.     

Crystal Growth of F‐Phlogopite from Glasses of the SiO2–Al2O3–MgO–K2O–F System

A study on the devitrification of fluorophyllosilicate glass precursors is presented. The research has been focused on the early stages of the crystallization process and shows the variation in the crystallization mechanism with increasing the fluorine content. The devitrification process has been studied by means of differential scanning calorimetry (DSC) and field‐emission scanning electron microscopy (FESEM). These complementary techniques established that both surface (heterogeneous nucleation) and volume (internal homogeneous nucleation) mechanisms are present in the crystallization process of fluorophlogopite‐based glasses, the latter being predominant. By increasing the percentage of fluorine in the parent glass, a variation in the location of the first crystals developed from the internal volume of the glass toward the external surface was observed. Such an alteration in the crystallization mechanism was also checked by examining the microstructure of crystallized samples prepared under short‐time treatments.     

Effect of Homolog Doping on Surface Morphology and Mass‐Loss Rates from PETN Crystals: Studies using Atomic Force Microscope and Thermogravimetric Analysis

Pentaerythritol tetranitrate (PETN) is an important energetic material, whose performance as a secondary explosive depends strongly on the density as well as flow porosity of powdered material, which in turn is governed by the size and surface properties of the PETN crystallite particles. Historically there has been evidence that the surface properties of PETN particles can be strongly influenced by the presence of homolog impurities of PETN, in particular, dipentaerythritol hexanitrate (diPEHN) and tripentaerythritol octanitrate (triPEON), although not many systematic studies characterizing such influence exist. In this work we employ thermogravimetric analysis (TGA) to measure mass‐loss rates at elevated temperatures and show that doping with a small amount of diPEHN and triPEON can reduce the mass‐loss rate from PETN single‐crystal surfaces by as much as 35 % as compared to undoped crystals. Arrhenius plots of mass‐loss rates as a function of temperature suggest that the reduction in evaporation is not due to the change in activation barrier of the molecular evaporation process, but perhaps due to the impedance to the receding motion of the steps by the immobile impurities on the surface. Removal of surface impurities through gentle washing with ethanol leads to enhanced mass‐loss rate relative to pure PETN suggesting a roughened surface morphology. Some surface roughening in doped crystals is supported by Atomic force microscopy (AFM) images of growth layers that show evidences of growth layer stacking and rough edges. We also find that a larger amount of impurity added to the original solution does not necessarily lead to a more highly doped crystal, which could perhaps be interpreted as PETN crystals being able to accommodate only up to a certain weight percent of homolog impurities.     

Salt Crystal Growth as Weathering Mechanism of Porous Stone on Historic Masonry

It is well known that in porous stones, NaCl precipitation on and beneath a surface depends on the solution supply and the evaporation rate according to the microclimate and the effective pore structure.In the present work, the study of salt crystal growth mechanisms in large heterogeneous systems like porous stone masonries is attempted. The historic masonries of the Medieval City of Rhodes act as a pilot, due to the intense marine environment and the climatic conditions in favour of NaCl crystallization into the highly porous stones.Weathered monument samples from various depths on masonries exposed to the sea are examined systematically under SEM and EPMA. The obtained results permit the differentiation of crystal growth patterns occurring during distinguished phases of the evaporation process within the porous stone masonry in depth.In the first phase, salt crystals grow favourably in the larger pores, connecting with the empty evaporation channels, and being supplied by solution from the next smaller pores. The isometric crystal habits attaining an equilibrium form correspond to those growing immersed in the solution, when a granular crust is formed.In a second phase, the crystals already exceed the pore size and overlap other smaller pores. As the rate of evaporation exceeds the solution supply, the solution retires and the substrate dries out, the area where the crystal contacts the solution is reduced, and consequently, columnar crystals grow.The pressure exerted by crystallization against the pore walls, when the crystals filling entirely the coarse pores continue growing, leads to disruption.     

冰晶尺寸及其对微波辅助冷冻干燥的影响

Freeze drying of an aqueous solution would result in the non-uniform distribution of solute concentration.Because ice is almost transparent to microwave, therefore such a non-uniform distribution may affect the microwave assisted freeze drying. The direct observation of the ice crystals formed under microscope reveals that the ice crystal sizes formed from de-ionized water depend on the cooling rate with fast cooling rate giving smaller ice crystals as expected. Once there is a sufficient amount of solute mixed with the de-ionized water, for example the reactive red,the size and its distribution are not very much dependent on either cooling rate or the final temperature provided there is sufficient time of cooling and the final temperature is not too low. The size of ice crystals formed within the solution of reactive red is usually below 100μm with a freezing rate of 1℃·min^-1 for a droplet of the size of less than 1 mm. A simplified simulation indicates that such a small ice crystal would not cause a significant non-uniform distribution of temperature for microwave assisted freeze drying. When the ice crystal size is larger than 5 mm, heat conduction from the solute concentrated region to the ice region mav need to be considered.     

Industrial batch crystallization of a plate-like organic product. In situ monitoring and 2D-CSD modelling. Part 2: Kinetic modelling and identification

The batch seeded cooling solution crystallization of a fine organic material, exhibiting a platelet-like habit, was investigated and a model of the time variations of the crystal size distribution (CSD) was designed using two-dimensional population balance equations. Activated surface secondary nucleation and attrition secondary nucleation mechanisms were considered, coupled with growth mechanisms of two main dimensions of the crystal, resulting in a set of eight kinetic parameters. The model relates the effects of the main batch operating conditions: seeding temperature, cooling rate and total area of the seed particles, on both the supersaturation profile and bi-dimensional CSD. Surface secondary nucleation occurs first since it is promoted by the introduction of seeds and remains active as long as the relative supersaturation exceeds a threshold value of about 16%. It vanishes below which could be expected as we deal with an activated mechanism. Contact secondary nucleation occurs later when the concentration of solid is sufficient. It is spread over time until supersaturation disappears at the end of the batch process. This contact secondary mechanism is assumed to be the dominant nucleation mechanism as it generates about two-thirds of the final crystal number. Sharp desupersaturation profile following the introduction of seeds, which was observed experimentally, is shown to be quantitatively described through the growth of seed particles. The termination of the batch process is more difficult to represent. Due to crystal attrition, distinct growth rates between initial and secondary crystals or growth rate dispersion might explain such difficulty.