Finite volume method as the numerical method for new emulsion polymerization tubular reactor with internal angle baffles

A finite volume method is used to solve a determinist mathematical model and to analyze the performance of an alternative design for an emulsion polymerization reactor with internal angular baffles as static mixer. It is assumed to be a steady‐state, cylindrical one‐dimensional model having a fully developed laminar plug flow. The Smith‐Ewart model is used to estimate the monomer conversion, the kinetics is of Arrhenius type, and laminar finite‐rate model is assumed to compute chemical source terms. The objective of this work is to develop the finite volume method for the new emulsion polymerization tubular reactor with internal angle baffles. The performance of the alternative reactor is compared with continuous tubular reactor with constant reaction temperature. The simulations were validated with experimental results for the isothermal and tubular reactor, with a good concordance. The results with baffles were better than without baffles in relation to desired properties such as particle size and viscosity. The problem is sufficiently well solved by finite volume method. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 6037–6048, 2006     

Kinetic modeling of an unsaturated polyester resin using two complementary techniques: Near infrared spectroscopy and heat flux sensors

This article concerns the characterization of the polymerization kinetics of an unsaturated polyester resin containing a large excess of styrene. For this type of resin, DSC measurements happen to not be satisfactory. Two complementary techniques were then used: an in situ near infrared spectroscopy and a PVT mold equipped with heat flux sensors. This article describes these two experimental devices and the methods used to obtain the experimental data. By monitoring the evolutions of unsaturated polyester and styrene conversions with near infrared spectroscopy, it was possible to identify two different chemical mechanisms occurring during the resin cure responsible for the measured two‐peaks thermograms. Their relative importance was quantified. A kinetic model representative of these two coupled reactions was established and its parameters evaluated from the thermal analysis. This model was able to predict the kinetic behavior of the resin outside of the domain of study, even at high temperature, where the second peak of the thermogram vanishes while the final conversion decreases. This model was also able to simulate the resin cure during experiments with an imposed heating rate. POLYM. ENG. SCI. 45:846–856, 2005. © 2005 Society of Plastics Engineers     

Correlation analysis of epoxy/amine resin cure,structure and chemorheological behavior in RTM processes

At the reactive mould‐filling stage in resin transfer moulding (RTM) processes, the correlation analysis of epoxy/amine resin cure, structure and chemorheological behavior plays a key role in the optimum control of RTM processes. A new methodology used to simulate the reactive resin flow in RTM processes with edge effect is presented in this article. The recursive approach and the branching theory are used to describe the evolution of molecular structure and resin viscosity, respectively. And then the resin flow process is simulated by means of a semi‐implicit iterative calculation method and the finite volume method. The results reveal the proposed resin cure‐structure‐viscosity model provides excellent agreement with the experimental viscosity data during the RTM filling process. It is also observed that the curing reaction causes the inhomogeneous distribution of resin conversion and resin molecular weight in the mould cavity, which will result in the spatially structural and performance inhomogeneities in the finished products. With the injection temperature or the edge width increasing, the discrepancy of resin conversion and resin molecular weight in the mould cavity is more evident. This study is helpful for understanding the complicated relationship among the processing variables, resin structures, and properties. POLYM. COMPOS., 2011. © 2011 Society of Plastics Engineers     

New emulsion polymerization tubular reactor with internal angular baffles: Reaction temperature effect

Deterministic models of physicochemical, mathematical, and computational sciences were used for modeling and simulation of emulsion homopolymerization process of styrene with baffles into tubular reactor (TR) as static mixer. Modeling and simulation were approximate to steady state, cylindrical one‐dimensional model, fully developed laminar plug flow, and they were solved with finite volume method and programmed with Fortran language. Also, the Smith‐Ewart model was considered to estimate the monomer conversion and Arrhenius chemical kinetics was considered as laminar finite‐rate model to compute chemical source. The experimental‐inductive and mathematical‐deductive methods were applied for obtaining mass balance results and properties characterization. The objective is to model, to simulate, and to analyze the emulsion polymerization reactor performance with internal‐inclined angular baffles, and to compare with continuous TR in variable reaction temperature. The predictions were validated with experimental results for the isothermic and TR, with a good concordance. The results in no isothermal conditions without and with baffles were better than in isothermal conditions without and with baffles in relation to the desired properties. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 2572–2581, 2006     

Bistability of propagating front with spin‐mode in a frontal polymerization of trimethylopropane triacrylate

We have studied a nonlinear dynamic behaviour in a frontal polymerization process. Frontal polymerization is a mode of converting a monomer into a polymer via a localized reaction zone that propagates as a front. Interest in studying the dynamic behaviour of such propagating fronts is growing. Many studies focus on the spin‐mode front propagation characterized by a nonplanar front having one or more high temperature regions which move in a helical path along the axis of the reaction vessel. In this study, the bistable character of the spin‐mode induced by reaction vessel diameter has been analyzed. First, a reactor with a discontinuously varying diameter for preliminary tests, and second, a conical reactor with a continuously varying diameter have been used. We have obtained evidence of bistability of the spin‐mode front in the frontal polymerization of trimethylopropane triacrylate under certain reaction conditions. Copyright © 2003 Society of Chemical Industry     

Rheological,mechanical, and morphological studies of epoxy/poly(methyl methacrylate) semi‐interpenetrating polymer networks

Semi‐interpenetrating polymer networks (semi‐IPNs) of epoxy resin and poly(methyl methacrylate) (PMMA) were synthesized. Methyl methacrylate (MMA) was polymerized by free radical mechanism with azo‐bis‐isobutyronitrile in the presence of oligomeric epoxy resin (DGEBA), and hexahydrophthalic anhydride as crosslinking agent. The gelation and vitrification transitions during cure/polymerization processes have been examined using parallel‐plates rheological technique. From differential scanning calorimetry and rheological techniques, it was suggested that both curing and polymerization processes occur simultaneously. However, the gelation time was longer for the semi‐IPN than those observed for the cure of pure DGEBA or polymerization of MMA. The gelation time increased significantly when 5% of MMA was employed, suggesting a diluent effect of the monomer. Higher amount of MMA resulted in a decrease of gel time, probably because of the simultaneous polymerization of MMA during the curing process. Structural examination of the semi‐IPNs, using scanning electron microscopy, revealed phase separation in nanoscale size for semi‐IPNs containing PMMA at concentrations up to 15%. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2007     

Modeling of Emulsion Copolymerization of 2‐Hydroxyethyl Methacrylate and Styrene

A mathematical model is developed to describe the reaction behavior of emulsion copolymerization systems where significant polymerization occurs in both the latex particle and aqueous phases. 2‐Hydroxyethyl methacrylate (HEMA) and styrene system was used to illustrate the development of a batch reactor. The model considers the gel and glass effects and monomer transfer. The principal model parameters are taken from the literature. Copolymerization reactivity ratios were estimated using a nonlinear least‐squares procedure. Model predictions have been compared with experimental data on monomer conversion.     

Vacuum‐assisted resin transfer molding model

A model of the vacuum‐assisted resin transfer molding (VARTM) process is developed that includes the most important aspects of the processing physics. The model consists of several submodels, such as preform mechanics, Darcy flow, wicking flow, and void formation. The preform mechanics model treats the preform as a linearly elastic, one‐dimensional (1D) solid. However, the key physical process is the lubrication of the preform due to fluid wetting, and this is modeled as a reduction in preform modulus, an easily measurable parameter. Residual stress, three‐dimensional (3D) structural behavior, and nonlinearity are neglected, but can all be included. The fluid flow model of capillary wicking is not tacked onto the Darcy equation as a modified boundary condition, as was previously done. The wicking is treated simply, but more realistically, by performing a force balance on the fluid in a pore. Balancing the capillary pressure and the viscous drag allows the development of a wicking front that precedes the main Darcy flow front to an extent that depends on several easily measurable factors. It is this wicking front that is responsible for the small void formation that reduces the quality of VARTM parts, relative to resin transfer molding (RTM) parts. POLYM. COMPOS. 26:477–485, 2005. © 2005 Society of Plastics Engineers     

Modeling the curing kinetics for a modified bismaleimide resin using isothermal DSC

The kinetics of curing for a modified bismaleimide (BMI) resin was investigated to ascertain a suitable cure model for the material. The resin system used in this study was composed of 4,4′‐bismaleimidodiphenylmethane (BMIM) and 0,0′‐diallyl bisphenol A (DABPA, DABA). The BMIM was the base monomer and the DABPA was the modified agent. A series of isothermal DSC runs provided information about the kinetics of cure in the temperature range 170–220°C. Regardless of the different temperatures, the shape of the conversion curves was similar, and this modified BMI resin system underwent an nth‐order cure reaction. Kinetic parameters of this BMI resin system, including the reaction model, activation energy, and frequency factor, were calculated. From the experimental data, it was found that the cure kinetics of this resin system can be characterized by a first‐order kinetic model. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 3338–3342, 2004     

Modeling the chemorheological behavior of epoxy/liquid aromatic diamine for resin transfer molding applications

The analysis of the chemorheological behavior of an epoxy prepolymer based on a diglycidylether of bisphenol‐A (DGEBA) with a liquid aromatic diamine (DETDA 80) as a hardener was performed by combining the data obtained from Differential Scanning Calorimetry (DSC) with rheological measurements. The kinetics of the crosslinking reaction was analyzed at conventional injection temperatures varying from 100 to 150°C as experienced during a Resin Transfer Molding (RTM) process. A phenomenological kinetic model able to describe the cure behavior of the DGEBA/DETDA 80 system during processing is proposed. Rheological properties of this low reactive epoxy system were also measured to follow the cure evolution at the same temperatures as the mold‐filling process. An empirical model correlating the resin viscosity with temperature and the extent of reaction was obtained to carry out later a simulation of the RTM process and to prepare advanced composites. Predictions of the viscosity changes were found to be in good agreement with the experimental data at low extents of cure, i.e., in the period of time required for the mold‐filling stage in RTM process. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 4228–4237, 2006     

Modeling of a Buss‐Kneader as a polymerization reactor for acrylates. Part I: Model validation

The Buss‐Kneader is generally known as a compounding device. Although a reasonable number of papers have been published on extruders as polymerization reactors, only little is known about the behavior of the Buss‐Kneader when used as a polymerization reactor. Its good mixing properties in the radial and axial directions make it a suitable reactor for exothermal polymerization reactions. This paper describes experiments with the co‐polymerization of n‐butyl acrylate and hydroxyethyl methacrylate in a Buss‐Kneader. For model calculations the Buss‐Kneader was treated as a plug flow reactor with axial dispersion. Experimental results on axial temperature profile, monomer conversion and molecular weight are compared with model calculations. Model parameters are based on independently measured data on the heat transfer coefficient, axial dispersion and polymerization kinetics.     

Multipurpose carbon fiber sensor design for analysis and monitoring of the resin transfer molding of polymer composites

The resin transfer molding (RTM) process is taking an ever‐growing place among the manufacturing technologies of polymer composite parts because of its numerous advantages. However, consistent production of high‐quality parts is difficult to achieve and requires better understanding of the process and good control of the raw materials. Part‐to‐part variations are inevitable as a result of uncarefully controlled molding environments and unidentifiable or undetected disturbances that cannot be completely eliminated or accounted for. Despite of many efforts to understand and model the fundamental physical and chemical behavior of materials during processing, there is no reliable system able of predicting the optimum processing parameters to manufacture high‐quality parts in a productive way. In this context, this work aims to develop systems allowing the monitoring of the whole RTM process (from preforming to resin curing) and that are reliable, cheap, and easy to use on production line. We have chosen to investigate the potential of the electric and dielectric carbon fiber sensors, which have already proved to be suitable for in service damage monitoring and preventive maintenance without any integration issues. However, the development of the continuous electric sensor has been limited by the polarization of the resin under the direct current. The flow front and the cure monitoring of the resin has been achieved with the dielectric sensor, energized by an alternative current preventing the polarization. Additionally, the ability of this carbon fiber sensor to evaluate the thickness of dry reinforcements and to measure online the actual unsaturated permeability of reinforcements has been demonstrated. POLYM. COMPOS., 26:717–730, 2005. © 2005 Society of Plastics Engineers     

Polynomial ARMA model identification for a continuous styrene polymerization reactor using on‐line measurements of polymer properties

The multiinput–multioutput identification for a continuous styrene polymerization reactor using a polynomial ARMA model is carried out by both simulation and experiment. The pseudorandom multilevel input signals are applied for model identification in which input variables are the jacket inlet temperature and the feed flow rate, whereas the output variables are the monomer conversion and the weight‐average molecular weight. The use of a polynomial ARMA model for identification of the multivariable polymerization reaction system is validated by simulation study. For the experimental corroboration, correlations are developed to convert the on‐line measurements of density and viscosity of the reaction mixture to the monomer conversion and the weight‐average molecular weight. The on‐line values of the conversion and weight‐average molecular weight turn out to be in good agreement with the off‐line measurements. Despite the complex and nonlinear features of the polymerization reaction system, the polynomial ARMA model is found to satisfactorily describe the dynamic behavior of the polymerization reactor. Therefore, one may apply the polynomial ARMA model to the optimization and control of polymerization reactor systems. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 76: 1889–1901, 2000     

Studies on the synthesis of low molecular weight,one‐dimensional polyanilines prepared by fast emulsion polymerization using (n‐dodecylbenzenesulfonic acid)/HCl emulsifiers

Low molecular weight polyaniline nanotubes were prepared by fast emulsion polymerization in the presence of both n‐dodecylbenzenesulfonic acid (DBSA) and HCl(aq). The anilinium monomers associated with DBSA emulsifiers were found to self‐arrange into strands of associated cylindrical micelles before polymerization, as monitored by their optical activity and optical image. In the presence of some HCl(aq), the monomer‐associated cylindrical micelles expanded and the polymerization rate could be speeded up. It was found that the low molecular weight (viscosity‐averaged molecular weight) polyaniline obtained can easily lead to the formation of highly conductive, one‐dimensional nanotubes or nanofibers monitored by the variation of optical activities and λ_max of the UV–visible–near IR spectra during polymerization. The DBSA/HCl ratio played an important role in the eventual properties and morphologies of the one‐dimensional polyanilines, which can be illustrated by conductivity, SEM and transmission electron microscopy measurements. The resultant one‐dimensional polyaniline nanotubes can be arranged into a layered structure by orientation, illustrated by AFM and wide‐angle X‐ray diffraction. © 2012 Society of Chemical Industry     

Impact of radiation attenuation and temperature evolution on monomer conversion of dimethacrylate‐based resins with a photobleaching photoinitiator

The photopolymerization process of a dimethacrylate copolymer system activated by the camphorquinone (CQ)/amine photoinitiator system (1 wt%), was experimentally studied under nonisothermal conditions in 1‐ and 2‐mm thick samples by measuring double bond conversion, temperature rise and radiation attenuation through the sample during polymerization. The peak temperature in 1‐ or 2‐mm thick samples irradiated at 5 mW/cm² was 29 and 38°C, respectively. The temperature evolution during polymerization was also predicted by solving the energy balance coupled with the kinetic expressions for the reaction rate. Radiation attenuation as a function of depth by the photobleachable CQ results in spatial and temporal variation in the local rates of the kinetic steps involved. General relationships for spatiotemporal variations in concentration of a photobleaching initiator, in systems where attenuation and initiator consumption are taken into account, were used to compute local polymerization rates. The effects of radiation attenuation, photobleaching of the photoinitiator and variation of cure temperature at different depths into the resin, all compete to determine the double bond consumption. The increased radiation attenuation in the 2‐mm thick sample was accompanied by a higher cure temperature compared with the 1‐mm thick sample, and as a result, the monomer conversion averaged over the sample thickness in the 1‐ and 2‐mm thick samples was the same. Results obtained in this research highlight the inherent interlinking of thermal and radiation attenuation effects in bulk photopolymerizing systems. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers     

球形TiCl4/MgCl2催化剂引发丙烯气相聚合动力学

采用微机在线控制的半连续烯烃聚合反应器,在加压条件下进行了球形TiCl₄/MgC_l2催化剂催化的丙烯气相聚合,测定了单体瞬时聚合速率等重要的动力学数据,考察了不同聚合条件对聚合动力学的影响,并用Flory-Huggins方程估算了聚合物非晶区中的单体浓度C_m.研究表明聚合速率与C_m成正比;丙烯聚合速率在反应一开始就迅速衰减,之后是缓慢的衰减.提出了一个n级衰减的丙烯气相聚合动力学模型,根据实验数据拟合得到了模型的各个参数,其中活性中心的衰减级数为2.5,气相聚合的表观增长活化能为77.1 kJ•mol^-1.用该模型可以较好地模拟加压条件下的丙烯气相聚合动力学行为.     

ATR‐UV monitoring of methyl methacrylate miniemulsion polymerization for determination of monomer conversion

Attenuated Total Reflection (ATR) UV spectroscopy has been used to monitor monomer conversion in methyl methacrylate miniemulsion polymerization. It was found that the vinylic groups of methyl methacrylate strongly absorb the UV light with a maximum absorption at 225 nm. This absorption peak decreases as monomer is converted to polymer. The polymer has a strong absorption at a lower UV region. The results from this feasibility study indicate that ATR‐UV sensor technique has a great potential to be used for on‐line or in‐line process monitoring in emulsion and miniemulsion polymerization. With a partial least square (PLS) calibration model, very good prediction the monomer conversion was obtained. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 99: 1471–1475, 2006     

Three‐dimensional CFD‐PBM coupled model of the temperature fields in fluidized‐bed polymerization reactors

A three‐dimensional (3‐D) computational fluid dynamics model, coupled with population balance (CFD‐PBM), was developed to describe the gas–solid two‐phase flow in fluidized‐bed polymerization reactors. The model considered the Eulerian–Eulerian two‐fluid model, the kinetic theory of granular flow, the population balance, and heat exchange equations. First, the model was validated by comparing simulation results with the classical calculated data. The entire temperature fields in the reactor were also obtained numerically. Furthermore, two case studies, involving constant solid particle size and constant polymerization heat or evolving particle‐size distribution, polymerization kinetics, and polymerization heat, were designed to identify the model. The results showed that the calculated results in the second case were in good agreement with the reality. Finally, the model of the second case was used to investigate the influences of operational conditions on the temperature field. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

Simulation and optimization of the continuous tower process for styrene polymerization

The continuous tower process, a popular industrial process for the manufacture of polystyrene, was simulated and optimized. A kinetic model for the thermal polymerization of styrene, which takes into account the Trommsdorff effect and the volume change accompanying the reaction, was developed. This was used to formulate model equations for the continuous flow stirred tank reactor (CSTR) and plug flow reactor (several sections) in the tower process. The model can predict monomer conversion, number‐ and weight‐average molecular weights, polydispersity index (PDI), and temperature at various locations in the unit, under specified operating conditions. Multiobjective optimization of this process was also carried out, for which an adaptation of a genetic algorithm (GA) was used. The two objectives were maximization of the final monomer conversion and minimization of the PDI of the product. The conversion in the CSTR was constrained to lie within a desired range, and polymer having a specified value of the number‐average molecular weight was to be produced. The optimal solution was a unique point (no Pareto sets were obtained). The optimal solutions indicated that the tower process is operated under near‐optimal conditions. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 94: 775–788, 2004