A stochastic formulation for the description of the crystal size distribution in antisolvent crystallization processes

A stochastic approach to describe the crystal size distribution dynamics in antisolvent based crystal growth processes is here introduced. Fluctuations in the process dynamics are taken into account by embedding a deterministic model into a Fokker‐Planck equation, which describes the evolution in time of the particle size distribution. The deterministic model used in this application is based on the logistic model, which shows to be adequate to suit the dynamics characteristic of the growth process. Validations against experimental data are presented for the NaCl–water–ethanol antisolvent crystallization system in a bench‐scale fed‐batch crystallization unit. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

On‐line control of crystal properties in nonisothermal antisolvent crystallization

The issues regarding the design and implementation of on‐line optimal control strategies of crystal properties in nonisothermal antisolvent crystallization processes to control particles’ mean size and standard deviation are dealt. The one‐dimensional Fokker–Planck equation is used to represent the dynamic characteristics of the crystal growth and generate iso‐mean and iso‐standard deviation curves. Using controllability tools it is demonstrated that the system is ill conditioned in the whole operational range, posing limitations on the achievable control performance. To circumvent the problem, a control strategy is formulated by pairing crystals’ mean size with antisolvent feed rate and manipulating temperature to control the standard deviation. A novel digital image‐texturing analysis approach is discussed and implemented to track crystals’ size distribution along the experiment and providing the on‐line information for further feedback control action. Subsequently, alternative control strategies are implemented and tested to achieve a desired crystal size distribution. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2188–2201, 2015     

溶析结晶在医药领域的研究进展

结晶作为一种传统的分离和提纯工艺，广泛运用于医药、化工、材料等领域。随着对结晶工艺的深入研究和对晶体产品质量越来越高的要求，结晶不再仅仅用于物质的分离和提纯，更重要的是根据产品功能的需要，制备特定结构的晶体。作为结晶的重要组成部分，溶析结晶因其操作简单、能耗相对较低、适用于热敏性物质等优势受到了广泛的关注。本文从溶析结晶相较于其他溶液结晶的不同点出发，重点介绍了溶析结晶热力学、溶析结晶动力学和工艺过程的研究，以及与溶析结晶相关的超临界流体技术和球形结晶技术。溶析结晶热力学关注了溶解度的测定方法和如何通过相图来确定合适的操作条件；溶析结晶动力学，详细描述了间歇、连续溶析结晶动力学模型的建立；工艺过程的研究，包括溶析剂与含有待结晶物质混合、结晶过程的控制和优化。同时本文对溶析结晶目前存在的问题进行了总结，并对未来的发展作了展望。     

Effects of UV‐irradiation on the nonisothermal crystallization kinetics of polypropylene

The influences of UV‐induced photodegradation on the nonisothermal crystallization kinetics of polypropylene (PP) were investigated by differential scanning calorimetry. The Avrami analysis modified by Jeziorny, Ozawa method, and a method modified by Liu were employed to describe the nonisothermal crystallization process of unexposed and photodegraded PP samples. Kinetics studies reveal that the rates of nucleation and growth may be affected differently by photodegradation. A short‐term UV‐irradiation may accelerate the overall nonisothermal crystallization process of PP, but a long‐term UV‐irradiation should impede it. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci, 2006     

硝酸钙-磷酸-水-异丙醇体系中溶析结晶工艺研究

酸解液中氮磷的高效分离是发展硝酸法湿法磷酸的关键技术之一。提出采用溶析结晶使酸解液中磷以磷酸钙盐形式析出从而达到氮磷分离的研究思路。以异丙醇为溶析剂,通过单因素实验考察了溶析剂加入比（异丙醇与模拟酸解液质量比）、温度、五氧化二磷质量分数、溶析时间对析出晶体物相结构以及磷析出率的影响。结果表明,溶析时间不会影响析出晶体物相结构,增大溶析剂加入比、升高温度、降低五氧化二磷质量分数都会使得析出的晶体由磷酸二氢钙转变成磷酸氢钙。通过对比磷析出率得出适宜的工艺条件：溶析剂加入比为3∶1、温度为5.0 ℃、五氧化二磷质量分数为30%、溶析时间为1.0 h,在此条件下磷析出率可达73.58%。     

Evaluation of nonisothermal crystallization kinetic models for linear poly(phenylene sulfide)

The nonisothermal crystallization kinetics of linear Poly(phenylene sulfide) (PPS) was studied with differential scanning calorimetry. Ozawa theory, Jeziorny model, and Mo equation were applied to describe the crystallization kinetics and to determine the crystallization parameters and mechanism of the linear PPS resin. The crystallization activation energies were also calculated using Kissinger formula and Flynn‐Wall‐Ozawa equation, respectively. According to the Ozawa model, it is found that instantaneous nucleation takes place during crystallization of PPS; the Ozawa exponent m is 3 in initial stage of crystallization; as the crystallization temperature decreases, the value of m reduces, and the growth rate of crystal almost keeps a constant. The Avrami exponent n obtained from Jeziorny model fluctuate around 1.84. Based on the Jeziorny model, the crystallization rate increases with increasing the cooling rate, but it does not change any longer when the cooling rate rise to a certain value. Mo equation also exhibits great advantages in treating the nonisothermal crystallization kinetics of PPS. The activation energy E of nonisothermal crystallization process of PPS is calculated to be −162.73 kJ/mol by the Kissinger formula, and the mean value of E determined by Flynn‐Wall‐Ozawa equation is −152.40 kJ/mol. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

PEN非等温冷结晶动力学的研究

采用差示扫描量热(DSC)法对聚萘二甲酸乙二醇酯(PEN)的非等温冷结晶动力学进行研究;通过改变升温速率,讨论了PEN冷结晶起始温度与峰顶温度之间存在差值的原因;对比了两种不同的冷结晶起始点的确定方法对冷结晶动力学常数的影响。结果表明:以DSC曲线偏离基线作为PEN冷结晶的起始点,得到的表观Avrami指数很大;用基线延长线与DSC曲线的切线的交点作为冷结晶的起始点和结束点,得到的表观Avrami指数为2.55,且不随升温速率的变化而变化,与等温熔融热结晶方法得到的结果接近,具有相似的结晶生长方式。     

Two courses in the nonisothermal primary crystallization of poly(butylene terephthalate)

Nonisothermal crystallization behavior of poly(butylene terephthalate) (PBT) was investigated by means of differential scanning calorimetry. The nonisothermal crystallization kinetic process was analyzed and relative kinetic parameters were obtained with the Avrami and Liu–Mo equations. The results demonstrate a heterogeneous nucleation mechanism. It was found that the nonisothermal primary crystallization of PBT was composed of two courses. Course I corresponded to the two‐dimensional formation process of the lamellae, and the corresponding relative crystallinity (X_t) was less than 15%. Course II was concerned with the three‐dimensional growth process of the spherulite, and X_t changed from 15 to 90%. The secondary crystallization began when X_t was greater than 90%. According to the Flynn–Wall–Ozawa equation, the activation energies for course I, course II, and secondary crystallization were calculated to be ?120, ?210, and ?100 kJ/mol, respectively. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

Simulation of crystallization kinetics and morphology during nonisothermal crystallization in short fiber reinforced composites

Computer simulation for the nonisothermal crystallization of short fiber reinforced composites is presented. The pixel coloring technique is implemented to the study of crystal morphology evolution as well as the crystallization kinetics. A parametric study is used to explore the influences of thermal conditions and fibers on the crystallization in the reinforced system. We particularly focus on the roles of cooling rate, initial temperature, nucleation density on fibers, fiber content, fiber length, and fiber diameter. The results indicate that cooling rate is a significant factor to the crystallization kinetics as well as the morphology. The initial temperature only affects the crystallization kinetics and has minor impact on the morphology. The additional fibers have a dual effect on the crystallization. They depress the crystallization rate by hindering the spherulitic growth and accelerate the crystallization rate by providing nucleation sites. The constraining effect is mainly dependent on fiber content, whereas the enhancing effect is mainly determined by fiber surface and fiber nucleation density as well as surface nucleation mode. Present results are hoping to give more insight about the crystallization in short fiber reinforced composites and be more helpful to the industrial application. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

PTT非等温结晶动力学研究

采用差示扫描量热仪对PTT进行非等温结晶研究。利用不同动力学模型对其结晶过程进行处理, 并将PTT与PET及PBT的非等温结晶过程进行对比。结果表明:Jeziorny方程和Ozawa方程都可以很好的 描述PTT,PET,PBT的非等温结晶过程;采用结合Avrami方程和Ozawa方程的处理方法,得到了3种聚酯的 结晶速率的大小关系:PBT>PTT>PET。通过计算Ziabicki结晶能力参数,得到3种聚酯的结晶能力的顺序 为:PBT>PTT>PET。     

PET/TiO2复合材料非等温结晶行为的研究

采用表面接枝和聚合改性的方法,分别以γ-缩水甘油醚氧丙基三甲基硅烷(GPS)和甲基丙烯酸甲酯(MMA)对纳米二氧化钛(TiO_2)进行表面修饰,通过熔融共混制得聚对苯二甲酸乙二醇酯(PET)/GPS- TiO_2和PET/聚甲基丙烯酸甲酯(PMMA)-TiO_2纳米复合材料,用差示扫描量热法研究了其复合材料的非等温结晶行为,利用不同动力学模型对其结晶过程进行处理。结果表明：未处理的纳米TiO_2提高了PET的熔融温度和结晶温度;而经表面接枝的GPS-TiO_2和PMMA-TiO_2对PET的熔融温度和结晶温度的影响并不显著;不同表面特性的纳米TiO_2降低了PET的结晶度,但经表面接枝后的纳米TiO_2其影响程度减弱;用Jezi- omy法和莫志深法处理PET/TiO_2纳米复合材料的非等温结晶过程比较理想,PET,PET/PMMA-TiO_2,PET/ TiO_2,PET/GPS-TiO_2复合材料的结晶速率依次减小。     

Isothermal and nonisothermal crystallization kinetics of nylon-11

Analysis of the isothermal, and nonisothermal crystallization kinetics of Nylon-11 is carried out using differential scanning calorimetry. The Avrami equation and that modified by Jeziorny can describe the primary stage of isothermal and nonisothermal crystallization of Nylon-11. In the isothermal crystallization process, the mechanism of spherulitic nucleation and growth are discussed; the lateral and folding surface free energies determined from the Lauritzen–Hoffman equation are ς = 10.68 erg/cm² and ς_e = 110.62 erg/cm²; and the work of chain folding q = 7.61 Kcal/mol. In the nonisothermal crystallization process, Ozawa analysis failed to describe the crystallization behavior of Nylon-11. Combining the Avrami and Ozawa equations, we obtain a new and convenient method to analyze the nonisothermal crystallization kinetics of Nylon-11; in the meantime, the activation energies are determined to be −394.56 and 328.37 KJ/mol in isothermal and nonisothermal crystallization process from the Arrhonius form and the Kissinger method. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 70: 2371–2380, 1998     

Synthesis and nonisothermal crystallization kinetics of thermoplastic polyamide-6 elastomers

Three kinds of thermoplastic polyamide-6 elastomers (TPAEs) with varying polytetramethyleneglycol (PTMG) contents of 10, 20, and 30 wt % were prepared via a one-pot polymerization synthetic route and named as TPAE1, TPAE2, and TPAE3, respectively. First, their structures were investigated by Fourier transform infrared spectroscopy, proton nuclear magnetic resonance spectroscopy, scanning electron microscope, and X-ray diffraction. The obtained results confirmed that targeted TPAEs were successfully synthesized and the unit cell of crystallization in TPAEs with α form was confirmed. Subsequently, the thermal properties of prepared TPAEs were characterized by differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) measurements, respectively. DSC curves showed that melting points of synthesized TPAEs were in the range of 209.2–215.9 °C. Moreover, TGA results showed TPAEs possess good thermal stability and cannot be decomposed under 300 °C. Additionally, the modified Avrami's equation, Ozawa's theory, and Mo's method were employed to investigate the nonisothermal crystallization kinetics of prepared TPAEs. It is found that the Mo's method exhibited great advantages in treating the nonisothermal crystallization kinetics of prepared TPAEs. Meanwhile, the crystallization kinetics and halftime are influenced by the contents of PTMG and follows a nonlinear fashion in agreement with the trend inactivation energies calculated by the Kissinger method. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136, 47388.     

Investigation of nonisothermal crystallization of hydroxyapatite/ethylene‐vinyl acetate (HA/EVA) composite

Hydroxyapatite/ethylene‐vinyl acetate (HA/EVA) composites were prepared by injection molding and characterized by X‐ray diffraction (XRD) and attenuated total multiple reflection infrared (ATR‐IR) spectroscopy. The nonisothermal crystallization behavior of HA/EVA composites at different cooling rates and with different HA content were examined by differential scanning calorimetry (DSC). The results exhibit the occurrence of interaction between HA and EVA, and the HA particles in EVA matrix act as effective nucleation agent. The addition of HA influences the mechanism of nucleation and growth of EVA crystallites. HA particles, as nucleus, are efficient to promote EVA crystallization at early stage but prevent EVA crystal growth in the late stage. The EVA crystallization in the composite is mainly through heterogeneous nucleation. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Studies on the phase structure,mechanical, rheological properties,and nonisothermal crystallization kinetics of the PEN/SCF composites

Short carbon fiber reinforced poly(ethylene 2,6‐naphthalate) composites (PEN/SCF) were prepared by twin‐screw extruder. The structure, mechanical, rheological properties, and nonisothermal crystallization kinetics of the composites were investigated by scanning electron microscope, universal tester, and differential scanning calorimetry. The results suggest that there is better interaction between SCF and PEN matrix, which leads to an increase in the tensile strength, Young's modulus, and impact strength of the composites with proper contents of SCF. Rheological behavior of the PEN/SCF composites melt is complicated, combining a dilate fluid at lower shear rate and a pseudoplastic fluid at higher shear rate. Moreover, the flow activation energy of the composites suggests that the melt with more SCF has higher sensitivity to the processing temperature. In conclusion, the composite with 5–10 wt % content of SCF has better properties. The Avrami equation modified by Jeziorny and Ozawa theory was used, respectively, to fit the primary stage of nonisothermal crystallization of various composites. The Avrami exponents n are evaluated to be 2.6–3.1 for the neat PEN and 3.4–4.8 for PEN/SCF composites, and the SCF served as nucleation agent accelerates the crystallization rate of the composites, and more the content of SCF faster the crystallization rate. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

有机膜精确调控传质的新型溶析结晶及过程强化

溶析结晶是一种环保、高效的结晶方法,在温敏性、低溶解度物系的晶体生产领域具有不可替代的重要作用。但是,传统溶析结晶过程中溶液过饱和度的时空均一性差,传质调控为微米级尺度,容易爆发成核,是亟待解决的关键问题。本文提出利用聚醚砜（PES）中空纤维膜,为溶析剂与结晶溶液之间的传质提供均匀稳定的界面,实现结晶溶液与溶析剂的精确混合和结晶过程强化,开发了一种新型的溶析结晶传质调控技术。溶析剂在压力差驱动下均匀渗透通过有机膜,在结晶溶液一侧的膜外表面形成溶析剂液膜层,通过表面液膜的不断更新,将传统溶析结晶的毫米级宏观混合转变为亚微米级尺度的微观混合,实现过饱和度的均匀分布。同时,这层液膜的存在,避免了结晶溶液直接接触膜表面,有效地解决了异相成核附着导致膜污染的问题。实验中,对壳程流速做出周期性改变后,渗透通量可即时发生一致的线性响应变化,证实有机膜调控传质过程的精确性和灵敏性。PES膜重复使用多次后,渗透通量仍可以保持稳定。相比传统的滴加式溶析结晶,在相同的溶析剂传质速率下,有机膜调控过程制备的晶体产品,形貌更加规整、粒径分布更集中。因此,在溶析剂精确传质和抗污染方面,有机膜调控的溶析结晶过程均表现出良好的性能,为药物、大分子结晶的高效工业化制备开拓了新的思路。     

Synthesis and nonisothermal crystallization kinetics of biodegradable poly(ethylene terephthalate-co-ethylene succinate)s

In the current work, a series of biodegradable poly(ethylene terephthalate-co-ethylene succinate)s (P[ET-co-ES]s) were prepared via a traditional melting polycondensation method. First of all, the structures of prepared copolymers were characterized by nuclear magnetic resonance and Fourier transform infrared measurements. Meanwhile, the thermal properties of prepared samples were analyzed by differential scanning calorimetry and thermogravimetric analysis measurements, respectively. Subsequently, the mechanical properties of the P(ET-co-ES)s were evaluated, the tensile strength of P(ET-co-ES)s decreased with increasing of PES content in copolymer, however, corresponding P(ET-co-ES)s exhibited better elongation at break. Next, the biodegradability of P(ET-co-ES)s was evaluated using lipase as degrading enzyme. The results presented that the biodegradability of P(ET-co-ES)s improved with PES content, the corresponding results were supported by scanning electron microscopy test. Finally, the Mo's modified Avrami equation was employed to analyze the nonisothermal crystallization kinetics of prepared copolymers. The results showed the addition of the PES component improved the crystallization properties of the prepared P(ET-co-ES)s. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2020 , 137, 48422.