Modeling of poly(ethylene terephthalate) reactors: 5. A continuous prepolymerization process

A mathematical model for the continuous prepolymerization of BHET to PET, carried out in a series of stirred tank reactors, has been developed. The influence of process and operational variables on productivity, as well as the side-product formation (which controls the product quality), have been studied in a range as close to industrial practice as possible. The overall conclusions concerning the productivity profile, as well as some side products, appear to be substantiated from the available data in the open literature. The results of the mathematical model have been used to highlight the key process and operational variables that are likely to give the best productivity and product quality in industrial practice.     

Modelling of reversible poly(ethylene terephthalate) reactors

The second stage of batch poly(ethylene terephthalate) (PET) reactor with bis(2-hydroxyethyl) terephthalate (BHET) as the feed has been simulated. In this stage, the overall polymerization is not diffusion limited and is known to be a complex reaction. In this work it has been assumed to consist of polycondensation, reaction with monofunctional compounds (cetyl alcohol), redistribution, and cyclization reactions. The forward and reverse steps of each of these have been modelled in terms of the rate constants involving functional groups and the reacted bonds. The equations for the calculation of the molecular weight distribution (MWD) in batch reactors have been written and solved numerically. The MWD reported in this work is assumed to include the monofunctional products only, and, for the case where ethylene glycol is not removed from the reaction mass, it was found to be unaffected by the choice of the redistribution rate constant (k_r). Since the removal of ethylene glycol is not mass transfer controlled, its concentration in the reaction mass is assumed be given by the vapor–liquid equilibrium existing at the pressure applied on the reactor. In this work, the level of ethylene glycol concentration, y_g (?[G]/[P₁]₀), has been taken as a parameter, and, on application of vacuum, the MWD results were found to vary with k_r with the sensitivity increasing with y_g. It was then shown that the importance of the redistribution reaction is enhanced when the cyclization reaction also occurs. The effect of vacuum on the performance of the reactor has been studied by varying y_g. For y_g less than 0.01, the change in the MWD of the polymer becomes very small. The effects of polymerization temperature and initial concentration of monofunctional compounds on MWD were found to be small.     

Modeling of poly(ethylene terephthalate) reactors. I. A semibatch ester interchange reactor

A comprehensive model for a semibatch ester interchange reactor has been developed with a view to investigate the effect of various process and operational variables on the DMT conversion rate as well as the by-product formation. The influence of important variables such as EG-to-DMT ratio, catalyst concentration, and operational variables such as temperature and pressure has been considered. Definite conclusions concerning the choice of the desirable range of process and operational variables to maximize productivity and minimize by-product formation have been reached.     

Modeling of poly(ethylene terephthalate) reactors. II. A continuous transesterification process

A comprehensive mathematical model for a continuous transesterification process has been built so as to enable prediction of the influence of different process and operational variables on productivity and by-product formation. The influence of temperatures and temperature profiles, of residence time and residence time distribution, and also of the number of reactors in series has been investigated. The modeling has been done as close to the industrial practice as possible. Important pragmatic implications from the point of view of operation of continuous transesterification are highlighted.     

Modeling of poly(ethylene terephthalate) reactors: 4. A continuous esterification process

A mathematical model has been developed for the direct, continuous esterification process. Influence of process and operational variables, including temperature distribution, residence time distribution, bis(hydroxyethyl)terephthalate recycle, pressure, and ethylene glycol (EG) to terephthalic acid ratio on the reactor performance have been investigated in a range as close to industrial practice as possible. The variables influencing the amount of EG reflux (which governs the energy economy) and side products (which govern the product quality) have been discussed. This investigation provides an analysis of a continuous, direct esterification process, and the results indicate strategies for optimizing productivity and product quality.     

The forced gas sweeping process for semibatch melt polycondensation of poly(ethylene terephthalate)

The experimental and modeling studies are presented on the melt polycondensation of poly(ethylene terephthalate) by a gas sweeping process. In this process, low molecular weight prepolymer is polymerized to a higher molecular weight polymer in a molten state at ambient pressure as ethylene glycol is removed by nitrogen gas bubbles injected directly to the polymer melt through a metal tube. In the temperature range of 260–280°C, the rate of polymerization by the gas sweeping process is quite comparable to that of conventional high vacuum process. The effects of nitrogen gas flow rate and reaction temperature on polymerization rate and polymer molecular weight were investigated. Polymer molecular weight increases with an increase in gas flow rate up to certain limits. A dynamic mass transfer–reaction model has been developed, and the agreement between experimental data and model simulations was quite satisfactory. The effect of ethylene glycol bubble nucleation on the polymerization has also been investigated. It was observed that the presence of nucleated ethylene glycol bubbles induced by the bulk motion of polymer melt has negligible impact on the polymerization rate and polymer molecular weight. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 1388–1400, 2001     

Modeling of poly(ethylene terephthalate) reactors. IX. Solid state polycondensation process

A mathematical model for simulation of industrial process of solid state polycondensation of poly(ethylene terephthalate) (PET) has been developed. The model eliminates errors evident in the earlier models by proper formulation. The model results have been validated by experimental data in the literature. It enables prediction of the influence of particle shape, size, temperature, etc. on the polycondensation process correctly in all different regimes of operation, apart from bringing out the importance of gas-side resistance, influence of carrier gas, etc. for the first time.     

Modeling of semibatch direct esterification reactor for poly(ethylene terephthalate) synthesis

A comprehensive kinetic model for a semibatch direct esterification reactor has been developed. The solid-liquid equilibirium of terephthalic acid was considered in the modeling. Effects of the monomer feed ratio, reaction temperatures, and oligomer addition on the conversion, degree of polymerization, and the formation of diethylene glycol were studied. © 1996 John Wiley & Sons, Inc.     

Modeling of poly(ethylene terephthalate) reactors: 6. A continuous process for final stages of polycondensation

A mathematical model of a continuous polycondensation reactor used in the finishing stages is developed. This axial dispersion model predicts the directions in which mixing, and other process and operational variables, will influence the progress of polycondensation. The available pilot plant data have been compared with the model predictions. In view of the neglect of the side reactions in our model, the comparison is only approximate but appears reasonable. The analysis developed is used to highlight certain critical design considerations.     

A modeling of semibatch reactors for melt transesterification of dimethyl terephthalate with ethylene glycol

A mathematical model of a semi batch reactor was developed to investigate the oligomerization reactions in the melt transesterification of dimethyl terephthalate with ethylene glycol catalyzed by metal acetate catalyst. The detailed kinetic scheme based on the molecular species model is used to estimate the conversion of methyl ester groups and the concentrations of various oligomeric species. The numerical simulation of the model shows that the oligomerization reactions lower the overall conversion of methyl ester end groups. Effects of ethylene glycol/dimethyl terephthalate mole ratios, reaction temperature and, catalyst concentration on the conversion, oligomer concentration, oligomer molecular weight, and molecular weight distribution were also analyzed.     

Poly(ethylene terephthalate)/polypropylene microfibrillar composites. III. Structural development of poly(ethylene terephthalate) microfibers

Poly(ethylene terephthalate) was extruded, solid‐state‐drawn, and annealed to simulate the structure of poly(ethylene terephthalate) microfibers in a poly(ethylene terephthalate)/polypropylene blend. Differential scanning calorimetry and wide‐angle X‐ray scattering analyses were conducted to study the structural development of the poly(ethylene terephthalate) extrudates at different processing stages. The as‐extruded extrudate had a low crystallinity (～ 10%) and a generally random texture. After cold drawing, the extrudate exhibited a strong molecular alignment along the drawing direction, and there was a crystallinity gain of about 25% that was generally independent of the strain rates used (0.0167–1.67 s^?1). 2θ scans showed that the strain‐induced crystals were less distinctive than those from melt crystallization. During drawing above the glass‐transition temperature, the structural development was more dependent on the strain rate. At low strain rates, the extrudate was in a state of flow drawing. The resultant crystallinity hardly changed, and the texture remained generally random. At high strain rates, strain‐induced crystallization occurred, and the crystallinity gain was similar to that in cold drawing. Thermally agitated short‐range diffusion of the oriented crystalline molecules was possible, and the resultant crystal structure became more comparable to that from melt crystallization. Annealing around 200°C further increased the crystallinity of the drawn extrudates but had little effect on the texture. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 104: 137–146, 2007     

Optimization of the polycondensation stage of poly(ethylene terephthalate) reactors

A general kinetic scheme for the polycondensation step of the PET formation has been used to establish the mole balance equations of various functional groups in batch reactors. An objective function has been defined which aims to attain a desired degree of polymerization in the shortest time, has a specified level of diethylene glycol group content, and minimizes the other side products. Using the control vector iteration procedure, an optimum temperature profile has been calculated. The computations suggest that a high temperature should be used initially which must be lowered as the time of reaction increases for limiting the formation of side products.     

Immobilization of poly(ethylene oxide) on poly(ethylene terephthalate) using a plasma polymerization process

Poly(ethylene oxide) (PEO) has been covalently immobilized on poly(ethylene terephthalate) (PET) films using a radio frequency glow discharge polymer deposition process, followed by chemical coupling. Amino or hydroxyl groups were introduced onto the surface of the PET by exposing the films to allylamine and allyl alcohol plasmas. These functional groups were activated with cyanuric chloride, and then they were reacted with PEO. ESCA and water contact angle studies were used to characterize the surfaces of these films during the different stages of the reaction. The films containing the higher molecular weight PEO exhibited an increase in the ? C? O? peak of the C_ls ESCA spectrum and an increase in oxygen content on the film surfaces. Increasing the molecular weight of the PEO attached to the PET also resulted in an increased wettability of the films.     

Flame-retardant poly(ethylene terephthalate)

Poly(ethylene terephthalate) containing hexabromobenzene, tricresyl phosphate, or a combination of triphenyl phosphate and hexabromobenzene, pentabromotoluene, or octabromobiphenyl was extruded or spun at 280°C into monofilaments or low-denier yarn, respectively. Only combinations of the phosphorus- and halogen-containing compounds resulted in flame-retardant poly(ethylene terephthalate) systems, without depreciating their degree of luster and color quality. The melting temperature, the reduced viscosity, and the thermal stability above 400°C of these flame-retardant systems were in most cases comparable to those of poly(ethylene terephthalate) itself. Phosphorus-bromine synergism was proposed with flame inhibition occurring mostly in the gas phase.     

Blends of poly(ethylene terephthalate) and poly(butylene terephthalate)

Commercial grade poly(ethylene terephthalate), (PET, intrinsic viscosity = 0.80 dL/g) and poly(butylene terephthalate), (PBT, intrinsic viscosity = 1.00 dL/g) were melt blended over the entire composition range using a counterrotating twin‐screw extruder. The mechanical, thermal, electrical, and rheological properties of the blends were studied. All of the blends showed higher impact properties than that of PET or PBT. The 50:50 blend composition exhibited the highest impact value. Other mechanical properties also showed similar trends for blends of this composition. The addition of PBT increased the processability of PET. Differential scanning calorimetry data showed the presence of both phases. For all blends, only a single glass‐transition temperature was observed. The melting characteristics of one phase were influenced by the presence of the other. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 98: 75–82, 2005     

Synthesis and characterization of copolymers of poly(ethylene terephthalate) and cyclohexane dimethanol in a semibatch reactor (including the process model)

Although poly(ethylene terephthalate) (PET) has excellent basic properties, this polymer tends to crystallize rapidly and has a rather high melting temperature, a low glass‐transition temperature, and low impact on notched articles for some potential applications. Copolymerization is a reasonable method for improving the properties of PET. 1,4‐cyclohexane dimethanol (CHDM) is one of the most important comonomers for PET. In this research, PET and PET copolymers containing 5–30% CHDM were prepared from comonomer mixtures by two‐step melt polycondensation. The copolymers were synthesized in a home‐made laboratory setup. The first synthesis step was conducted under pressure, and the second was performed in vacuo at a high temperature (230–290°C). The microstructure of the synthesized copolymers was studied with Fourier transform infrared and nuclear magnetic resonance. The comonomer content in the polymer chain was determined from the nuclear magnetic resonance spectrum. The presence of the comonomer in the copolymer chain was random. Differential scanning calorimetry was used to study the thermal properties of the copolymers to detect changes in the polymer properties. CHDM reduced the heat of fusion and melting and glass‐transition temperatures of the PET copolymers. Process modeling was performed with mass balances of different functional groups and species. Equations of mass balances were integrated numerically. Numerical simulation and experimental results were in very good agreement. By modeling, the effects of the reaction temperature and feed molar ratio on the conversion and formation of diethylene glycol were studied. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Powdered poly(ethylene terephthalate)

The influence of the conditions of preparation on the properties of powdered poly(ethylene terephthalate) was followed from the point of view of its specific surface. The powdered poly(ethylene terephthalate) prepared by reprecipitation from the melt of 6-caprolactam has a porous and structured surface, and consequently, also a large specific surface in comparison with the powedered poly(ethylene terephthalate) prepared by mechanical milling. The specific surface value is influenced by the cooling rate of the initial homogeneous melt of poly(ethylene terephthalate)-6-caprolactam, by the concentration of poly(ethylene terephthalate) in this melt and by its molecular weight, by the water temperature at the extraction of 6-caprolactam from the tough mixed melt, by the drying temperature of the powdered poly(ethylene terephthalate), and by the content of residual 6-caprolactam in the powdered product. In the examined area, the specific surface value of the powdered poly(ethylene terephthalate) prepared by reprecipitation from the melt of 6-caprolactam ranged from 10 to 110 m²·g^?1.     

Two‐step photodegradation process of poly(ethylene terephthalate)

After investigating kinetics of the UV photodegradation of PET film samples having a thickness of 4.4 µm, we found that the photodegradation process takes place in two steps: a very rapid initial step followed by a normal step. This phenomenon is explained by using a concept of “weak links.” We have obtained the rate constants of degradation of the “normal links” k_N = 9.0 × 10⁻⁷ h⁻¹ and “weak links” k_W = 0.46 h⁻¹ and the number of scissions of weak links per molecules P_W = 0.22. For the samples treated by a UV stabilizer, we found k_N = 2.0 × 10⁻⁷ h⁻¹, k_W = 0.11 h⁻¹, and P_W = 0.27. The ratios of the rate constants of the untreated to treated samples are 4.2 for k_W and 4.5 for k_N. These results indicate that the UV stabilizer slows down the photodegradation rate of each step to the same extent, but hardly affects the number of scissions of weak links. Importantly, it is an implication that the lifetime of the PET thin film can be prolonged by a factor of 4.2 to 4.5 in the irradiation conditions used after being treated by the UV stabilizer. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 306–310, 1999     

Molecular weight control of poly(ethylene terephthalate) in extrusion process

A control strategy is developed to control molecular weight of recycled poly(ethylene terephthalate), PET, to overcome its degradation through an extrusion process. To obtain dynamic model of a twin screw extruder, steady‐state, and unsteady‐state experiments were performed. Discrete convolution models between inputs and outputs were obtained. Process inputs were considered as screw speed (SS), feed rate, and barrel temperatures and the output was viscosity average molecular weight (M_v) of the extrudate. SS and molecular weight of the product were chosen as the manipulated, controlled variable pair by considering singular value decomposition (SVD) technique. Model based PID controller and model predictive controller were used in the designed control scheme. By the simulation studies, both controllers were found to be successful for set‐point tracking, disturbance rejection cases; and were proven to be robust under modeling errors. POLYM. ENG. SCI., 54:459–465, 2014. © 2013 Society of Plastics Engineers