Integrated B2B‐NMPC control strategy for batch/semibatch crystallization processes

The uncertainty in crystallization kinetics is of major concern in manufacturing processes, which can result in deterioration of most model‐based control strategies. In this study, uncertainties in crystallization kinetic parameters were characterized by Bayesian probability distributions. An integrated B2B‐NMPC control strategy was proposed to first update the kinetic parameters from batch to batch using a multiway partial least‐squares (MPLS) model, which described the variances of kinetic parameters from that of process variables and batch‐end product qualities. The process model with updated kinetic parameters was then incorporated into an NMPC design, the extended prediction self‐adaptive control (EPSAC), for online control of the final product qualities. Promising performance of the proposed integrated strategy was demonstrated in a simulated semibatch pH‐shift reactive crystallization process to handle major crystallization kinetic uncertainties of L‐glutamic acid, wherein smoother and faster convergences than the conventional B2B control were observed when process dynamics were shifted among three scenarios of kinetic uncertainties. © 2017 American Institute of Chemical Engineers AIChE J, 2017     

Crystallization kinetics of poly(3‐hydroxybutyrate‐co‐3‐hydroxyvalerate)/clay nanocomposites

The preparation and properties of nanocomposites, consisting of a poly(3‐Hydroxybutyrate‐co‐3‐hydroxyvalerate) and an organophilic clay are described. The effect of organophilic clay on the crystallization behavior of (PHBV) was studied. A differential scanning calorimeter (DSC) was used to monitor the energy of the crystallization process from the melt. During the crystallization process from the melt, the organophilic clay led to an increase in crystallization temperature (T_c) of PHBV compared with that for plain PHBV. During isothermal crystallization, dependence of the relative degree of crystallization on time was described by the Avrami equation. The addition of organophilic clay caused an increase in the overall crystallization rate of PHBV, but did not influence the mechanism of nucleation, and growth of the PHBV crystals and the increase caused by a small quantity of clay is move effective than that large one. The equilibrium melting temperature of PHBV was determined as 186°C. Analysis of kinetic data according to nucleation theories showed that the increase in crystallization rate of PHBV in the composite is due to the decrease in surface energy of the extremity surface. The mechanical test shows that the tensile strength of hybrid increased to 35.6 MPa, which is about 32% higher than that of the original PHBV with the incorporation of 3 wt % clay, and the tensile modulus was also increased. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 93: 655–661, 2004     

Non-Isothermal crystallization of isotactic polypropylene in dotriacontane. I: Effects of dilution,cooling rate,and nucleating agent addition on overall crystallization kinetics

The overall non-isothermal crystallization kinetics for nucleated and non-nucleated isotactic polypropylene (iPP) in dotriacontane systems was investigated. Adipic acid was used as the nucleating agent. Crystallization peak temperature was determined via differential scanning calorimetry as a function of the experimentally controlled variables iPP concentration, cooling rate, and nucleating agent concentration. The influence of these variables on crystallization mechanism and spherulitic structure as implied by the Ozawa and Ziabicki analyses was determined. The non-isothermal crystallization kinetics presented here are the first for iPP-diluent systems with and without nucleating agent.     

Strain-induced crystallization behavior of poly(ether ether ketone) (PEEK)

Strain-induced crystallization of poly(ether ether ketone) (PEEK) was studied by the use of a parallel plate rheometer. The experimental variables included preheating time, crystallization temperature, and shear rate. The crystallization kinetics were characterized by means of an induction time defined as the time elapsed from the start of shearing to the onset of crystallization. The experimental results showed that the induction time for strain-induced crystallization of PEEK was significantly shorter than that for crystallization under quiescent condition, and that strain-induced crystallization was much less temperature dependent than quiescent crystallization. The activation energy for strain-induced crystallization was found to be 0.035kcal/mole, which was considerably smaller than the reported activation energy for quiescent crystallization. Photomicrographs of the sheared specimens indicated that PEEK crystallites orient along the flow direction.     

Crystallization kinetics of poly(phenylene sulfide) (PPS) and PPS/carbon fiber composites

The evolution of crystallinity of neat PPS and of the carbon fiber reinforced polymer under different processing conditions is studied. Crystallization from the amorphous state at low temperatures (cold crystallization), crystallization from the melt during cooling, and crystal melting processes are analyzed using calorimetric techniques under both isothermal and nonisothermal conditions. Cold and melt crystallization kinetics are described using an Avrami equation and an Arrhenius expression for the temperature dependence of the kinetic constant. Also, the melting kinetics of the, reinforced and of the unreinforced polymer are studied in this work. The effect of carbon fibers on the crystallization kinetics of PPS is analyzed, and a comparison of the crystallization behavior of PPS and other semicrystalline thermoplastic matrices, such as poly(etheretherketone) (PEEK), is presented.     

Crystallization kinetics for simulation of processing of various polyesters

The approach to determine crystallization kinetic parameters based on the DSC nonisothermal crystallization experiments is applied to poly(butylene terephthalate) (PBT) and poly(ethylene‐2,6‐naphthalate) (PEN). The differential form of the Nakamura equation and master curve approach are used. The isothermal induction times are obtained from nonisothermal induction times according to the concept of induction time index. The correction of temperature lag between the DSC furnace and the sample is incorporated. The corrected nonisothermal crystallization kinetic data is shifted with respect to an arbitrarily chosen reference temperature to obtain the master curve. By fitting the obtained master curve with the Hoffman‐Lauritzen equation, the model parameters for the crystallization rate constant are obtained. The relative crystallinity measured at different cooling and heating rates is described by these model parameters. © 2006 Wiley Periodicals, Inc. J Appl PolymSci 102: 2847–2855, 2006     

Synthetic Mica Investigations: III, Precision-Controlled Electric Furnaces for Temperatures to 1500°C

Three furnaces using silicon carbide heating elements are described, including (1) a utility furnace for melting and testing, (2) a precisioncontrolled (± 1/2°C.) crystallization furnace, and (3) a rectangular crystallization furnace. Schematic drawings of the furnaces and a simplified wiring diagram for the heating elements are included. One composite controller is described from a functional viewpoint, with a block-diagram presentation. A complete circuit diagram of this controller also is incorporated. The use of saturable core reactors in regulating power to electric furnaces is advocated; reactors permit the control of electricity in a manner similar to adjustment of the flow of water by means of a valve.     

Isothermal crystallization of isotactic polypropylene in dotriacontane. I: Effect of nucleating agent addition on overall crystallization kinetics

The overall isothermal crystallization kinetics for nucleated and non-nucleated isotactic polypropylene (iPP)-dotriacontane systems was investigated. Adipic acid was used as the nucleating agent. Half-time was determined via differential scanning calorimetry as a function of the experimentally controlled variables dilution, crystallization temperature, and the addition of nucleating agent. The influence of these variables on crystallization mechanism and spherulitic structure, as implied by the Avrami analysis, was determined. The influence of these variables on fold surface energy was examined by the Lauritzen and Hoffman analysis.     

Description of PVT behavior of an industrial polypropylene–EPR copolymer in process conditions

An experimental procedure is presented to describe the PVT behavior of multiphase polymeric materials in a wide range of cooling rates. In particular, the procedure is applied to a typical multiphase industrial polymer, that is, an industrial polypropylene–ethylene‐propylene rubber (iPP–EPR) copolymer with a small percentage of talc. The volume evolution is described combining specific volumes of different phases present in the material. All phases are described simply by thermal expansion and compressibility coefficients drawn either from the literature or from low and high temperature (i.e., below and above the iPP crystallization range) standard PVT data. Crystallization evolution of iPP is described by the Nakamura nonisothermal formulation of the Avrami–Evans crystallization kinetic model. Model parameters are identified by comparison with both standard calorimetric results and final densities of thin samples solidified during quenches conducted with cooling rates of several hundreds of K/s. It is also shown that identification of crystallization kinetic parameters by means of calorimetric data only leads to misleading results for cooling rates larger than those adopted in the calorimetric tests. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 267–278, 2001     

Effect of nano-nucleating agent addition on the isothermal and nonisothermal crystallization kinetics of isotactic polypropylene

Using differential scanning calorimetry (DSC) technique, a comparative study has been made of the isothermal and nonisothermal crystallization kinetics of nonnucleated isotactic polypropylene (iPP) and of nucleated iPP with 0.5 wt% of single-walled carbon nanotubes (SWCNTs) as a nucleating agent. The Avrami exponents (n) of iPP and nucleated iPP are close to 3.0 for isothermal crystallization. These results indicate that the addition of nucleating agents did not change the crystallization growth patterns of the neat polymer and that crystal growth was heterogeneous three-dimensional spherulitic. The results show that the addition of SWCNTs can shorten the crystallization half-time (t _1/2) and increase the crystallization rate of iPP. In the nonisothermal crystallization process, the Ozawa model failed to describe the crystallization behavior of nucleated iPP. The Cazé–Chuah model successfully described the nonisothermal crystallization process of iPP and its nanocomposite. A kinetic treatment based on the Ziabicki theory is presented to describe the kinetic crystallizability, in order to characterize the nonisothermal crystallization kinetics of iPP and nucleated iPP. Polarized light microscopy (PLM) experiments reveal that SWCNTs served as nucleating sites, resulting in a decrease of the spherulite size.     

High‐order simulation of polymorphic crystallization using weighted essentially nonoscillatory methods

Most pharmaceutical manufacturing processes include a series of crystallization processes to increase purity with the last crystallization used to produce crystals of desired size, shape, and crystal form. The fact that different crystal forms (known as polymorphs) can have vastly different characteristics has motivated efforts to understand, simulate, and control polymorphic crystallization processes. This article proposes the use of weighted essentially nonoscillatory (WENO) methods for the numerical simulation of population balance models (PBMs) for crystallization processes, which provide much higher order accuracy than previously considered methods for simulating PBMs, and also excellent accuracy for sharp or discontinuous distributions. Three different WENO methods are shown to provide substantial reductions in numerical diffusion or dispersion compared with the other finite difference and finite volume methods described in the literature for solving PBMs, in an application to the polymorphic crystallization of L ‐glutamic acid. © 2008 American Institute of Chemical Engineers AIChE J, 2009     

Nonisothermal and isothermal crystallization kinetics of nylon‐12

The isothermal and nonisothermal crystallization behavior of Nylon 12 was investigated using differential scanning calorimetry (DSC). An Avrami analysis was used to study the isothermal crystallization kinetics of Nylon 12, the Avrami exponent (n) determined and its relevance to crystal growth discussed and an activation energy for the process evaluated using an Arrhenius type expression. The Lauritzen and Hoffman analysis was used to examine the spherulitic growth process of the primary crystallization stage of Nylon 12. The surface‐free energy and work of chain folding were calculated using a procedure reported by Hoffmann and the work of chain folding per molecular fold (σ) and chain stiffness of Nylon 12 (q) was calculated and compared to values reported for Nylons 6,6 and 11. The Jeziorny modification of the Avrami analysis, Cazé and Chuah average Avrami parameter methods and Ozawa equation were used in an attempt to model the nonisothermal crystallization kinetics of Nylon 12. A combined Avrami and Ozawa treatment, described by Liu, was used to more accurately model the nonisothermal crystallization kinetics of Nylon 12. The activation energy for nonisothermal crystallization processes was determined using the Kissinger method for Nylon 12 and compared with values reported previously for Nylon 6,6 and Nylon 11. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Fractional crystallization: Design alternatives and tradeoffs

Guildlines for the design of fractional crystallization processes to separate two-and three-solute mixtures are presented. By using solvent addition/removal, stream combination, and cooling/heating, these processes bypass regions of multiple saturation in the phase diagram and recover purse solutes. Design equations are formulated, and the constraints on the design variables are identified. also included is a discussion of the effect on recyle flows of changes in the design variables and an estimate of the cost of a fractional crystallization separation.     

Crystallization behavior of poly(lactic acid)/elastomer blends

Differential Scanning Calorimetry (DSC) was used to evaluate the crystallization behavior of poly(lactic acid) and its blends with elastomer. It has been observed that the cold crystallization temperature of the blends decreased as the weight fraction of elastomer increased as well as the onset temperature of cold crystallization also shifted to lower temperature. In non-isothermal crystallization experiments, the crystallinity of poly(lactic acid) increased with a decrease in the heating and cooling rate. The melt crystallization of poly(lactic acid) appeared in the low cooling rate (1, 5 and 7.5 °C/min). The presence of low elastomer tends also to increase the crystallinity of poly (lactic acid). The DSC thermogram at ramp of 10 °C/min showed the maximum crystallinity of poly(lactic acid) is 36.95% with 20 wt% elastomer contents in blends. In isothermal crystallization, the cold crystallization rate increased with increasing crystallization temperature in the blends. The Avrami analysis showed that the cold crystallization was in two stages process and it was clearly seen at low temperature. The Avrami exponent (n) at first stage was varying from 1.59 to 2 which described a one-dimensional crystallization growth with homogeneous nucleation, whereas at second stage was varying from 2.09 to 2.71 which described the transitional mechanism to three dimensional crystallization growth with heterogeneous nucleation mechanism. The equilibrium melting point of poly(lactic acid) was also evaluated at 176 °C.     

Applications of the crystallization process in the pharmaceutical industry

The applications of the crystallization technique in the pharmaceutical industry as a purification and separation process for the isolation and synthesis of pure active pharmaceutical ingredients (API), co-crystals, controlled release pulmonary drug delivery, and separation of chiral isomers are briefly discussed using a few case studies. The effect of process variables and solvent on the polymorphism and morphology of stavudine is discussed. The implementation of external control in the form of feedback and real-time optimal control using cooling and antisolvent crystallization of paracetamol in water-isopropyl alcohol is introduced. Two methods to prepare micron-sized drug particles, namely, micro-crystallization and polymer-coated API-loaded magnetic nanoparticles for pulmonary drug delivery, are discussed. The significance of co-crystals in drug administration is highlighted using the theophylline-nicotinamide co-crystal system. Resolution of chloromandelic acid derivatives, a racemic compound, is achieved using direct crystallization and diastereomeric salts crystallization. The crystal structures of diastereomeric salts of chloromandelic acid and phenylethylamine are determined. The structure comparison between the less soluble and more soluble salts shows that weak interactions such as CH/π interactions and van der Waals forces contribute to chiral recognition when the hydrogen bonding patterns are similar.     

Effect of nucleating agents on the crystallization of poly(3‐hydroxybutyrate‐co‐3‐hydroxyvalerate)

The effect of nucleating agents on the crystallization behavior of poly(3‐hydroxybutyrate‐co‐3‐hydroxyvalerate) (PHBV) was studied. A differential scanning calorimeter was used to monitor the energy of the crystallization process from the melt and melting behavior. During the crystallization process from the melt, nucleating agent led to an increase in crystallization temperature (T_c) of PHBV compared with that for plain PHBV (without nucleating agent). The melting temperature of PHBV changed little with addition of nucleating agent. However, the areas of two melting peaks changed considerably with added nucleating agent. During isothermal crystallization, dependence of the relative degree of crystallization on time was described by the Avrami equation. The addition of nucleating agent caused an increase in the overall crystallization rate of PHBV, but did not influence the mechanism of nucleation and growth of the PHB crystals. The equilibrium melting temperature of PHBV was determined as 187°C. Analysis of kinetic data according to nucleation theories showed that the increase in crystallization rate of PHBV in the composite is due to the decrease in surface energy of the extremity surface. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 2145–2152, 2002     

Isothermal and nonisothermal crystallization kinetics of a semicrystalline copolyterephthalamide based on poly(decamethylene terephthalamide)

The isothermal and nonisothermal crystallization kinetics of a semicrystalline copolyterephthalamide based on poly(decamethylene terephthalamide) (PA‐10T) was studied by differential scanning calorimetry. Several kinetic analyses were used to describe the crystallization process. The commonly used Avrami equation and the one modified by Jeziorny were used, respectively, to describe the primary stage of isothermal and nonisothermal crystallization. The Avrami exponent n was evaluated to be in the range of 2.36–2.67 for isothermal crystallization, and of 3.05–5.34 for nonisothermal crystallization. The Ozawa analysis failed to describe the nonisothermal crystallization behavior, whereas the Mo–Liu equation, a combination equation of Avrami and Ozawa formulas, successfully described the nonisothermal crystallization kinetics. In addition, the value of crystallization rate coefficient under nonisothermal crystallization conditions was calculated. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 94: 819–826, 2004     

Crystallization Behaviors of PbSe Quantum Dots in Silicate Glasses

This study, composed of three parts, aims at studying the crystallization behaviors of PbSe quantum dots (QDs) in silicate host glasses. Firstly, due to the importance of the choice of base glass for the QDs' crystallization, the selection of base glass compositions, the glass fragility, and glass formation ability (GFA) are discussed in details, and the results show that the selected glass compositions have an intermediate fragility and accordingly an intermediate glass transition temperature range among a wide variety of inorganic glass systems together with a good GFA/glass stability (GS). Thus, this base glass is suitable as the host glass in which PbSe QDs crystallize. Secondly, the experimental results on PbSe QDs' crystallizations are presented, and the results show that PbSe QDs can precipitate from silicate glasses favorably with no other chemical compounds precipitation, and the optimized temperature for PbSe QDs crystallization is 600°C. Lastly, the classical nucleation theory is used to analyze the PbSe QD crystallization behaviors in host glasses. The steady‐state nucleation rates and the growth rates of PbSe QDs as well as the time–temperature transformation (TTT) curves are calculated. The results indicate that the free surface energy between the PbSe nuclei and the host glass has great influence on the nucleation rates of PbSe QDs, while it has less effect on the growth rates of PbSe QDs; the crystallization behaviors of PbSe QDs with different volume fractions can be described well by the TTT curves while keeping the dimensionless empirical constant, α, unchanged for one certain curve.