Iterative parameter estimation for extraction of crystallization kinetics of potassium chloride from batch experiments

Extraction of crystallization kinetics, the fundamental information which governs the performance of a crystallization process, is characterized by experimental difficulties in MSMPR and mathematical difficulties in batch crystallization. Here, a rigorous approach is taken to estimate kinetic parameters from a batch crystallizer. The two step LaxWendorff technique is adapted for the solution of the population balance in a batch crystallizer and an iterative self-correcting least squares algorithm is implemented for the estimation of the kinetic parameters. The need for multi-response estimation as opposed to single-response from terminal CSD is demonstrated. The kinetics extracted are average ones, representing primary and secondary nucleation kinetics. It is found that the kinetic parameters estimated by multi-response technique have a superior predictive capability as opposed to those obtained using the terminal CSD only. An advantage of the proposed algorithm is that the measurement of course of supersaturation, which is difficult to perform, is not required.     

膜辅助添加晶种的过硫酸铵冷却结晶在线监测与过程调控

冷却结晶是经典的溶液结晶过程,常用于分离溶解度随温度变化较大的物质,制备高品质晶体产品。直接进行降温会导致成核速率不可控,得到的晶体产品质量差。在工业中通常选择在溶液结晶介稳区内投放适量晶种来诱导成核,但晶种制备过程复杂,而且成功的添加晶种过程取决于晶种的粒度分布、数量、投放时机和操作人员的经验等因素,降低了产品质量的批次重复性。本文利用聚四氟乙烯（PTFE）中空纤维膜组件为结晶溶液和冷却液提供换热界面,结晶溶液温度降低,在膜界面处形成较均匀的过冷度梯度,进而在低过饱和度下发生异相成核,实现膜辅助添加晶种的过硫酸铵冷却结晶过程调控。膜组件中产生的晶种进入结晶釜中继续生长,将成核和生长过程进行解耦。在线结晶检测系统捕捉到的照片证实了通过控制膜组件使用温度和时长两个操作参数便可得到具有较好的形貌、较窄的粒度分布的晶种。相比直接冷却结晶,在相近的降温速率下,膜辅助添加晶种过程制备的晶体产品具有更大的平均粒径,且粒度分布更集中,表面更加光滑。因此,膜辅助冷却结晶呈现了良好的成核控制能力,有望实现晶种自动制备和添加功能,为高附加值晶体产品的冷却结晶过程开发提供了新方向。     

聚丙烯／滑石粉复合材料的等温结晶动力学

用差示扫描量热法(DSC)研究聚丙烯(PP)及PP／滑石粉复合材料的等温结晶过程。用Avrami方程全面分析PP／滑石粉的等温结晶动力学，并由此获得相关的动力学参数；用Kissinger方程研究滑石粉对PP／滑石粉复合材料结晶活化能的影响。研究表明：加入滑石粉后明显提高PP／滑石粉复合材料的结晶速率和结晶度；证明滑石粉能促进PP材料的结晶，并在PP结晶过程中起到异相成核作用。PP／滑石粉复合材料的等温结晶过程属于典型的异相成核机理。     

间歇冷却结晶过程的模拟

The general mathematical model for batch cooling crystallization was established based on the population balance equation considering the change of slurry volume, and simulated with crystallization thermodynamics,kinetics and mass balance employing bed voidage. In the system of vitamin C-water-ethanol, reliability of this model was verified by comparison between simulation results and experimental data. The effects of operation parameters on product quality can be systematically investigated by modeling simulation.     

半芳香族聚酰胺6T/6I/6的合成及其非等温结晶动力学研究

采用成盐、高温溶液缩聚两步法成功制备了半芳香族聚酰胺（PA）6T/6I/6。通过傅里叶变换红外光谱（FTIR）、氢核磁共振（¹H⁃NMR）分析了其分子链结构,并对其力学性能进行了测试表征,利用差示扫描量热法（DSC）对PA6T/6I/6的非等温结晶动力学进行了研究,使用Jeziorny法、Oazawa法和莫志深法修正的Avrami方程分别分析了PA6T/6I/6的非等温结晶行为。结果表明,通过Jeziorny法处理发现结晶过程分为主期结晶和次期结晶2个阶段,主期结晶阶段Avrami指数在1.08~1.09之间,晶体为异相成核,呈一维针状生长,次期结晶阶段Avrami指数在2.13~2.21之间,晶体为二维片状生长方式;Ozawa法处理曲线相关性低,表明不适用于描述PA6T/6I/6的非等温结晶过程;莫志深法修正的Avrami方程能较好地描述结晶过程,a值在0.89~0.90之间,F（T）值在7.24~15.85之间;采用Kissinger方程计算求得PA6T/6I/6的非等温结晶活化能为-294.17 kJ/mol。     

生物基尼龙56的等温结晶性能研究

采用差示扫描量热仪和带有热台的偏光显微镜对生物基尼龙56的等温结晶性能进行了研究。用Avrami方程对等温结晶过程及其动力学进行了分析,得出Avrami指数(n值)在2.30~3.37之间,推测其晶体生长方式为三维球状生长;采用Arrhenius方程计算了生物基尼龙56的等温结晶活化能(ΔE)为-99.04 kJ/mol。偏光显微镜研究证实了上述推测,同时发现球晶半径与结晶时间呈线性关系,求得了球晶的生长速率。     

手性药物结晶拆分的研究进展

手性是自然界和生物体中广泛存在的一种性质,约半数以上的药物活性成分含有手性中心,受手性分子的空间立体选择性影响,手性对映体药物往往较其外消旋体表现出更高的活性、更低的副作用,因而,精准制备手性单一对映体药物具有非常重要的研究意义。目前,手性外消旋体拆分是制备单一对映体的最高效、便捷的途径,而结晶拆分是实现手性单一对映体分离最为重要且广泛应用的技术。综述了近年来手性药物结晶拆分的研究进展,梳理了结晶拆分研究的发展历程,重点介绍了基于经典拆分方法（非对映体成盐拆分和优先结晶）和近年来发展的基于优先富集和Viedma熟化的对映体拆分新技术以及结晶拆分的强化方法,并简述了色谱、膜分离等其他手性外消旋体分离方法。最后,对手性药物的结晶拆分方法进行了总结和展望。     

Optimal operation of batch enantiomer crystallization: From ternary diagrams to predictive control

In this work, the modeling and control of batch crystallization for racemic compound forming systems is addressed in a systematic fashion. Specifically, a batch crystallization process is considered for which the initial solution has been pre‐enriched in the desired enantiomer to enable crystallization of only the preferred enantiomer. A method for determining desired operating conditions (composition of the initial pre‐enriched solution and temperature to which the mixture must be cooled for maximum yield) for the batch crystallizer based on a ternary diagram for the enantiomer mixture in a solvent is described. Subsequently, it is shown that the information obtained from the ternary diagram, such as the maximum yield attainable from the process due to thermodynamics, can be used to formulate constraints for an optimization‐based control method to achieve desired product characteristics such as a desired yield. The proposed method is demonstrated for the batch crystallization of mandelic acid in a crystallizer with a fines trap that is seeded with crystals of the desired enantiomer. The process is controlled with an optimization‐based controller to minimize the ratio of the mass of crystals obtained from nuclei to the mass obtained from seeds while maintaining the desired enantioseparation. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1618–1637, 2018     

不同催化体系所得聚酯的等温结晶研究

用DSC法对三氧化二锑 (Sb2 O3)、氟钛酸钾 (K2 TiF6 )、钛酸四丁酯 (Ti(OC4 H9) 4)及乙二醇锑(S -2 4) 4种催化体系所得聚酯进行等温结晶研究 ,求得了结晶速率常数 (k)和Avrami指数 (n)。结果表明 ,锑系催化剂所得聚酯的结晶速度总体大于钛系催化剂所得聚酯 ,其中以Sb2 O3催化所得聚酯结晶速度最快 ,而Ti(OC4 H9) 4催化所得聚酯结晶速度最慢。DTA结果表明锑系催化剂所得聚酯冷结晶温度低于钛系催化剂所得聚酯 ,与结晶速度测试结果相一致。     

PTT的等温与非等温结晶动力学研究

采用DSC方法对聚对苯二甲酸丙二酯进行等温与非等温结晶动力学研究,利用不同动力学模型对其结晶过程进行分析.结果表明,在等温结晶过程中,Avrami指数n和半结晶时间随着结晶温度的升高而增大,结晶速率常数K随着结晶温度的升高而减小;在非等温结晶的过程中,结晶动力学常数Zc和相对过冷度△Tc随着降温速率的提高而上升,Avr...     

Cold Crystallization of PLLA Studied by Simultaneous SAXS and WAXS

Summary: The cold crystallization process of initially amorphous poly(L ‐lactic acid), PLLA, with two different molecular weights, during a heating at 2 °C/min, was investigated by DSC and time‐resolved simultaneous SAXS and WAXS, using synchrotron radiation. Equatorial scans of the isotropic 2D‐SAXS patterns showed that the average Bragg long period (L_B) of PLLA samples was approximately constant with the development of cold crystallization up to a temperature that corresponded to a melt/re‐crystallization process that took place before the nominal melting peak seen by DSC. L_B values were found to be higher for the high molecular weight material. This was in accordance with the higher melting temperature observed in the high molecular weight PLLA that implied the existence of thicker lamellae. WAXS results showed that the molecular weight did not apparently affect the crystal form and the final degree of crystallinity of PLLA. The Avrami parameters from WAXS and DSC were consistent, showing that the non‐isothermal cold crystallization of the two PLLA samples corresponded mainly to a three‐dimensional growth, although an imperfect crystallization process was involved at early times. The crystallization rate of PLLA, observed both by WAXS and DSC, decreased with increasing molecular weight.

SAXS profiles of PLLA2 as a function of temperature. The inset shows the 2D‐SAXS pattern obtained at 180 °C.     

高质量分数对二甲苯结晶动力学研究

利用间歇动态法研究高质量分数混合二甲苯中的对二甲苯结晶动力学,应用矩量变换法求解粒数衡算方程,通过测量结晶过程中的母液温度和对二甲苯质量分数的变化,由非线性优化法求解对二甲苯结晶动力学参数。实验结果表明,在自然降温和线性降温方式下,所得到的结晶动力学参数一致,而且能很好地模拟对二甲苯结晶过程的母液中对二甲苯质量分数的变化,相对误差大多在±0.5%以内,因而可以用来优化和模拟对二甲苯结晶过程。     

聚丙烯在溶液中的等温结晶行为

采用差示扫描量热仪（DSC）分析聚丙烯（PP）在2种不同溶剂中的等温结晶过程,并使用Avrami方程研究等温结晶动力学。 结果表明,晶体生长速率随着结晶温度的升高而降低。 同时,根据Lauritzen⁃Hoffman 二次成核理论,PP在溶液中的成核常数K_g和折叠表面自由能σ_e低于PP原料,反映了其在溶液中的结晶速率较高。     

Uniaxial Orientation and Crystallization Behavior of Amorphous Poly(ethylene terephthalate) Fibers

The effects of drawing conditions on the orientation and crystallinity of poly(ethylene terephthalate) (PET) fibers were investigated by using optical birefringence, sonic velocity, and wide-angle X-ray diffraction measurements, respectively. The preferred condition for preparation of uniaxially oriented amorphous PET fibers was suggested. The crystallization behavior of oriented PET fibers under relaxed and fixed length conditions was investigated by using differential scanning calorimetry (DSC). The multi-overlapping peaks were observed in the non-isothermal DSC curves of oriented PET fibers under relaxed condition. The kinetics of non-isothermal crystallization of oriented PET fibers under relaxed condition was analyzed by using an equation which takes the multi-crystallization processes into account. The kinetic parameters of every process were obtained and the crystallization mechanism was discussed. The crystallization behavior under fixed length condition differs from that under relaxed condition.     

Effect of nucleating agent addition on crystallization of isotactic polypropylene

The isothermal and nonisothermal crystallization kinetics of nonnucleated and nucleated isotactic polypropylene (iPP) were investigated by DSC and a polarized light microscope with a hot stage. Dibenzylidene sorbitol (DBS) was used as a nucleating agent. It was found that the crystallization rate increased with the addition of DBS. The influence of DBS on fold surface energy, σ_e, was examined by the Hoffman and Lauritzen nucleation theory. It showed that σ_e decreased with the addition of DBS, suggesting that DBS is an effective nucleating agent for iPP. Ozawa's theory was used to study the nonisothermal crystallization. It was found that the crystallization temperature for the nucleated iPP was higher than that for nonnucleated iPP. The addition of DBS reduced the Ozawa exponent, suggesting a change in spherulite morphology. The cooling crystallization function has a negative exponent on the crystallization temperature. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 69: 2089–2095, 1998     

Isothermal crystallization kinetics and melting behavior of polyamide 11/silica nanocomposites prepared by in situ melt polymerization

Polyamide 11 (PA 11)/silica nanocomposites were prepared via in situ melt polymerization by the dispersion of hydrophobic silica in 11‐aminoundecanoic acid monomer. Their isothermal crystallization process and melting behaviors were analyzed by differential scanning calorimetry. The isothermal crystallization kinetics was analyzed by the Avrami equation. The obtained data showed that the model of nucleation and growth of PA 11 was not affected after the incorporation of silica and was a mixture with two‐dimensional, circular, three‐dimensional growth with thermal nucleation. Double and single melting peaks were observed depending on the crystallization temperature. The equilibrium melting point of samples was evaluated, and the spherulites growth kinetics parameters and fold surface free energy were further calculated according to the classical theories. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

蒸氨废水化学沉淀除氟结晶动力学模型

以质量扩散-表面反应两步结晶理论为基础,推导出氟化钙沉淀结晶动力学模型,以蒸氨废水为研究对象,氯化钙为沉淀剂,采用间歇结晶和在线粒度监测技术测定了氟化钙结晶动力学数据,采用非线性优化技术获得了氟化钙结晶动力学模型参数,并对该模型进行了实验验证,结果表明模型及模型参数效果良好,模型值与实验值平均相对误差为3.37%。氟化钙沉淀结晶过程属于表面反应控制过程,氟化钙存在明显的聚结现象。模型模拟结果表明:钙离子浓度一定时,氟离子初始浓度越高则初始阶段氟离子浓度下降越快,初始氟离子浓度过高或过低,最终均不利获得较低的氟离子浓度;适当提高操作温度可以促进氟离子的净化,但温度过高则不利。     

A comparative study of polypropylene nucleated by individual and compounding nucleating agents. I. Melting and isothermal crystallization

In this study, melting and isothermal crystallization behaviors of polypropylene (PP) nucleated with different nucleating agents (NAs) have been comparatively studied. α‐phase NA 1,3 : 2,4‐bis (3,4‐dimethylbenzylidene) sorbitol (DMDBS, Millad 3988), β‐phase NA aryl amides compound (TMB‐5), and their compounds were introduced into PP matrix, respectively. The crystallization and melting characteristics as well as the crystallization structures and morphologies of nucleated PP were studied by differential scanning calorimetry (DSC), wide angle X‐ray diffraction (WAXD), and polarized light microscopy (PLM). As indicated by previous work that a few amounts of α‐phase NA (DMDBS) or β‐phase NA (TMB‐5) has apparent nucleation effect for PP crystallization. However, the crystallization of PP nucleated with compounding NAs is dependent on the content of each NA. In the sample of PP with 0.1 wt % DMDBS and 0.1 wt % TMB‐5, the nucleation efficiency of TMB‐5 is much higher than that of DMDBS and PP crystallization is mainly nucleated by TMB‐5, and in this condition, β‐phase PP is the main crystallization structure. For the sample of PP with 0.2 wt % DMDBS and 0.2 wt % TMB‐5, 0.2 wt % DMDBS has higher nucleation efficiency than 0.2 wt % TMB5, and α‐phase is the main crystalline structure in this sample. The isothermal crystallization kinetics and crystallization structure have been analyzed in detail in this work. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Thermal properties and isothermal crystallization of syndiotactic polypropylenes: Differential scanning calorimetry and overall crystallization kinetics

Isothermal crystallization and subsequent melting behavior of five samples of syndiotactic polypropylene are presented. Crystallization studies were carried out in the temperature range of 60°C to 97.5°C using a differential scanning calorimeter (DSC). Subsequent DSC scans of isothermally crystallized samples exhibited double melting endotherms. The high melting peak was concluded to be the result of the melting of crystals formed by recrystallization during the reheating process. Overall crystallization kinetics was studied based on the traditional Avrami analysis. Analysis of crystallization times based on the modified growth rate theory suggested that, within the crystallization temperature range studied, the syndiotactic polypropylenes crystallize in regime III. Kinetic crystallizability parameters also were evaluated, and were found to be in the range of 0.41°C s⁻¹ to 2.14°C s⁻¹. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 75: 44–59, 2000     

青霉素G钠盐结晶机理与媒晶剂的研究

运用Laplace变换法 ,简化了间歇结晶过程的数学模型 ,并计算了青霉素G钠盐在加与不加媒晶剂两种情况下 ,真空闪蒸结晶过程的动力学参数 ;用激光法测定了青霉素G钠盐在上述两种情况下的结晶介稳区宽度 ,通过实验对比表明 ,媒晶剂对结晶介稳区宽度、结晶动力学等有一定程度的影响 ;在此基础上进行了对青霉素G钠盐一步法结晶新工艺的初步探索 ,为新工艺进一步开发研究指明了方向