Modeling Particle Size Distribution (PSD) in Emulsion Copolymerization Reactions in a Continuous Loop Reactor

A detailed dynamic mathematical model that describes the evolution of particle size distributions (PSDs) during emulsion copolymerization reactions in a continuous loop reactor was developed and compared with experimental data. The model is based on the assumption that two distinct particle populations exist: precursor particles and stable latex particles. Precursor particles are colloidally unstable and therefore may undergo coagulation with other precursors and be absorbed by stable latex particles. It is shown that the kinetic model is able to reproduce the rather complex dynamic behavior of the vinyl acetate/Veova10 emulsion copolymerization in a continuous loop reactor, including the development of oscillatory responses of PSDs during reaction start‐up. It is also shown that, for the studied polymerization system, oscillatory responses are obtained only when both particle populations are assumed to exist and when both coagulative and micellar particle nucleations are simultaneously considered.     

Production of porous suspension polymer beads with a narrow size distribution using a cross-flow membrane and a continuous tubular reactor

The work described focuses on a two-stage process for the production of large porous suspension polymer beads of defined particle size and narrow size distribution. Emulsification has been performed using purpose built cross-flow membrane equipment, which allows controlled production of large emulsion droplets with a much narrower size distribution. The work described compares the production of large emulsion droplets of monomer prepared both by agitation and using a cross-flow membrane. The effects of variations in the pore size of the membrane and flow-rates on the size of the emulsion droplets produced are also investigated. The second stage of the process is polymerisation of performed monomer emulsion droplets using a continuous tubular reactor. Samples polymerised using such a method show a narrower size distribution than similar systems polymerised as a batch.     

In Line Monitoring of VAc-BuA Emulsion Polymerization Reaction in a Continuous Pulsed Sieve Plate Reactor using NIR Spectroscopy

Summary: This work deals with the in line and in situ monitoring of the changes in residual monomer concentrations and polymer particle size in the process of emulsion copolymerization of vinyl acetate (VAc) and butyl acrylate (BuA) over the sections of a novel tubular reactor (pulsed sieve plate continuous reactor, PSPC) using NIR spectroscopy. Off-line measurements (gas chromatographic, gravimetric and dynamic light scattering) were used as reference for the development of the multivariate PLS calibration model. All NIR spectra were on-line collected with an IFS 28/N Bruker spectrometer using a probe (transflectance mode) immersed into the reaction medium. The calibration model and validation data were analyzed using the OPUS/QUANT software. The results indicated that there exists a good agreement between values from the NIR calibration models and the off-line reference measured experimental data. Moreover, the on-line NIR can detect efficiently the occurrence of disturbances during the polymerization reaction, a useful tool for the improving the process safety.     

Continuous Atom Transfer Radical Polymerization in a Tubular Reactor

The use of a tubular reactor for conducting living radical polymerizations by atom transfer radical polymerization (ATRP) was investigated. Solution polymerization experiments were performed with styrene and butyl acrylate to elucidate the influence of a continuous reaction process on conversion, molecular weight, and polydispersity compared to batch polymerization experiments. The continuous polymerizations were well controlled. Initial conversion was found to be slightly higher in the tubular reactor than in a batch polymerization run at similar conditions, while number average molecular weight and polydispersity are comparable between the continuous and batch processes. Residence time distribution studies showed the reactor exhibits nearly plug flow behavior.

     

Emulsion polymerization of styrene. I. Review of experimental data and digital simulation

Isothermal emulsion polymerization at 60°C of styrene in a batch reactor were studied by using sodium lauryl sulfate as surfactant and potassium persulfate as initiator source. The concentrations of surfactant and initiator were varied during the runs. The polymerization evolution was followed as samples were taken at regular intervals. These emulsion samples were analyzed for monomer conversion, rate of polymerization, as well as for the size and the size distribution of the particles. The molecular weight and molecular weight distribution were obtained by gel permeation chromatography. Our study showed that fresh nucleation takes place even at high conversion, causing a continuous shifting toward broadening of particle size distribution. Contrary to the theory of Smith and Ewart, which assumes a constant number of particles during interval II of the polymerization reaction, our digital simulation of the reaction presents better experimental results with a variable number of particles, and indicates that the Hui–Hamielec model for termination constant k_t as function of conversion is not applicable under our working conditions.     

Modelling nucleation and particle growth in emulsion copolymerization in continuous loop reactors

A mathematical model for emulsion copolymerization in continuous loop reactors is presented. The flow pattern of the loop reactor can be represented by a loop formed by two tubular reactors with axial dispersion. The mathematical model combines this flow model with the physico-chemical characteristics of the emulsion copolymerization. The outputs of the model are monomer conversion, copolymer composition, particle size distribution and latex viscosity. The model was checked during the redox initiated emulsion copolymerization of vinyl acetate and veova 10 carried out in a completely automated continuous loop reactor.     

Data Reconciliation and Control in Styrene-Butadiene Emulsion Polymerizations

Summary: A nonlinear model-based predictive control (NLMPC) method was developed using a First Principles model of an emulsion copolymerization of carboxylated styrene butadiene rubber (XSBR). Copolymer composition, conversion and average molecular weights of the copolymer were chosen as the controlled variables due to their influence on the final product properties and quality. These properties, however, are rarely measured in-line due to the operational difficulties associated with their measurement. For this reason a soft-sensor using reaction calorimetry techniques was developed and used to infer reaction conditions, rates, species concentrations and polymer properties in a industrial scale emulsion polymerization reactor.     

Effect of nitrogen sources in batch and continuous cultures to lipase production byCandida rugosa

The interaction between medium components, microorganisms and the operational mode to produce lipase byCandida rugosa was studied. It has been observed as an emulsion formation between oleic acid and urea during continuous culture. Because of this emulsion, the nitrogen source cannot be assimilated by the cells. The lack of nitrogen source provoked a decrease in protein synthesis, being lipase synthesis suppressed. The change of the nitrogen source from urea to ammonium sulfate avoided the emulsion formation, allowing to reach biomass and lipase steady states in continuous cultures. In batch cultures, no effect of nitrogen source on lipase production and biomass was observed. The specific productivity in continuous culture was slightly higher than in batch cultures.     

EMULSION POLYMERIZATION IN A SEED-FED CONTINUOUS STIRRED-TANK REACTOR

A numerical method has been developed to predict the particle size distribution (PSD) of the product latex from a steady-state polydisperse-seeded continuous reactor. Simulations have been carried out for the emulsion polymerization of vinyl chloride based on the experimental conditions reported by Berens(l). The simulation results can be reasonably well fitted to the PSD data published by Berens. The radical desorption constant, k_d, for Berens’ vinyl chloride emulsion polymerization can be estimated by fitting the simulated PSD to experimental measurements. The simulation work presented in this article demonstrates that the combination of mathematical modeling and PSD measurements can be a useful tool in studying radical transport rates and aqueous phase termination phenomena. The simulation results also indicate that the continuum diffusion theory for free radical absorption by the particles leads to a better PSD fit than a model based on equal diffusion rates per unit area.     

Kinetics of the batch cationic emulsion polymerization of styrene: A comparative study with the anionic case

An in‐depth study on the kinetics of the cationic emulsion polymerization of styrene in a batch reactor is presented. This study is focused on the effect of the amount of the cationic surfactant dodecyltrimethylammonium bromide (DTAB), using two different cationic initiators: 2,2′‐azobisisobutyramidine dihydrochloride (AIBA), 2,2′‐azobis (N,N′‐dimethyleneisobutyramidine) dihydrochloride (ADIBA), on kinetics and colloidal features such as conversion, number of particles, number average of radicals per particle, mean particle diameter, and particle size distribution (PSD) of the polystyrene latices obtained by emulsion polymerization in a batch reactor. Furthermore, the results of the cationic emulsion polymerization were compared with its homologous anionic case. Using DTAB as cationic surfactant an expected increase in the total rate of polymerization was observed when the DTAB concentration increased. However, the total number of particles increased much more than in the anionic system. On the other hand, a dependence on the particle size of the rate of polymerization per particle together with the average number of radicals per particle was found. These differences between cationic and anionic emulsion polymerizations were explained taking into account the limited particle coagulation observed with cationic surfactants, and the high rate of radical formation of cationic initiators. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4461–4478, 2006     

Modeling Strategies for the Propagation of Terminal Double Bonds During the Polymerization of N‐Vinylpyrrolidone and Experimental Validation

Based on a recently suggested reaction mechanism, which involves the production and propagation of terminal double bonds (TDBs), kinetic models for the polymerization of N‐vinylpyrrolidone in aqueous solution are developed. Two modeling strategies, the classes and the pseudodistribution approach, are applied to handle the multidimensional property distributions that result from this reaction mechanism and to get detailed structural property information, e.g., on the chain length distribution and the distribution of TDBs. The structural property information is then used to develop reduced models with significantly lower computational effort, which can be used for process design, on‐line applications or coupled to computational fluid dynamic simulations. To validate the derivations, the models are first compared against each other and finally to experimental results from a continuous stirred tank reactor. The evolution of monomer conversion and molecular weight average data as well as molecular weight distributions can be represented very well by the models that are derived in this article. These results support the correctness of the reaction mechanism predicted by quantum mechanical simulations.     

A perturbation solution for batch extraction with double emulsions: role of continuous phase mass transfer resistance

The effect of the continuous phase mass transfer resistance on solute extraction with double emulsions in a batch reactor is investigated. A model presented by Ho et al. (1982) for diffusion controlled mass transfer into the double emulsions is solved by perturbation analysis. In the case of a significant continuous phase mass transfer resistance, the extraction of solute is a function of the inverse Biot modulus, m. For values of m greater than 0.01 the external phase resistance must be taken into account in order to accurately predict extraction rates. Such conditions will exist when double emulsion drops are relatively small or when stirring rates in the batch extractor are low.     

Emulsion copolymerization of styrene and methyl methacrylate. II. Molecular weights

A mathematical model for the time evolution of both number-average molecular weight and weight-average molecular weight is described. The model results in a set of ordinary differential equations and its application is not limited by the maximum number of radicals per particle. The model was used to analyze the effect of the monomer molar ratio in the initial charge on the weight-average molecular weight during the emulsion copolymerization of styrene and methyl methacrylate in a batch reactor.     

Forced Oscillations in a Nonisothermal Continuous Polymerization Reactor

A dynamic model of a nonisothermal continuous stirred tank polymerization reactor is developed to predict product molecular weight distribution parameters. Deliberate oscillations in operating variables were programmed into the model and the resulting time-averaged reactor performance indices compared with that for optimum steady-state operation. Results indicate that periodic operation does influence polymerization reactor performance, particularly with regard to time-averaged molecular weight polydispersity. Significant resonant behavior was encountered with molecular weight properties at low frequencies.     

Nitroxide‐Mediated Polymerization of Styrene in a Continuous Tubular Reactor

Summary: Nitroxide‐mediated polymerization of styrene in a continuous tubular reactor has been demonstrated for the first time. The polymerization kinetics in the tubular reactor are similar to those in a batch reactor. The number average molecular weight increases linearly with conversion, and chain extension experiments were successful, indicating that the living nature of the polymerization is maintained in the tubular reactor.

Evolution of molecular weight as measured by GPC for chain‐extended latex in continuous tubular reactor.     

Modeling molecular weight distribution in emulsion polymerization reactions with transfer to polymer

A mathematical model was developed for the computation of the dynamic evolution of molecular weight distributions (MWDs) during nonlinear emulsion polymerization reactions. To allow the direct computation of the whole MWD, an adaptive orthogonal collocation technique was applied. The model was validated with experimental methyl methacrylate/butylacrylate (BuA) semicontinuous and vinyl acrylate (VA)/Veova10 continuous emulsion polymerization results. Both systems considered introduce significant chain‐transfer reactions to polymer chains as a result of the presence of BuA and VA, respectively. The model developed was able to represent quite properly the kinetics and MWD of polymer samples during emulsion polymerizations. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3513–3528, 2001     

Design of Nonlinear Model‐Based Control Using Bifurcation Analysis for Solution Polymerizations Carried Out in Lumped‐Distributed Reactors

In order to implement nonlinear control, nonlinear system identification must be performed, however, there are open questions concerning this field of process control, for example, experimental planning, model structure selection, parameter estimation, and validation. Therefore, the study of nonlinear model identification is a relevant unsolved problem that needs to be handled for nonlinear control synthesis. This paper presents the use of bifurcation theory, dynamic and stability analysis for nonlinear identification, and control of polymerization reactors. Peroxide‐initiated styrene‐solution polymerization reactors (lumped‐distributed) are investigated: batch, continuous stirred‐tank reactor (CSTR), and tubular reactors. Open and closed loop analyses are carried out using jacket temperature and weight average molecular weight setpoints as the bifurcation parameters. Phenomenological mathematical models, neural network nonlinear models, and an experimental data from a polymerization unit are employed for validating the proposed methodology in order to implement confident nonlinear controllers.     

Modelling and simulation of styrene-acrylonitrile emulsion polymerization kinetics

The emulsion polymerization kinetics of the styrene-acrylonitrile system have been studied. A dynamic time-dependent model has been developed, which successfully describes the course of the conversion of styrene as compared with that of acrylonitrile. This model avoids the difficulties encountered by previous models when applied to high acrylonitrile-content polymers, and is able to predict the conversion process for both batch and continuous reactors. The model is aimed at the simulation and operation of composition-controlled semibatch and continuous processes.     

Emulsion terpolymerization of butyl acrylate/methyl methacrylate/vinyl acetate: Experimental results

A systematic study of the terpolymerization of butyl acrylate/methyl methacrylate/vinyl acetate (BA/MMA/VAc) was conducted. In this stage of the study, batch emulsion terpolymerizations were performed in a 5 L stainless steel pilot plant reactor. The experiments were designed using a Bayesian (optimal) technique. The polymers produced were characterized for conversion, composition, molecular weight, and particle size. Conversion, terpolymer composition, number- and weight-average molecular weight, and average particle size results are discussed in light of the influence of seven factors and the interaction of these factors. The factors studied include monomer feed composition, initiator concentration, chain transfer agent concentration, impurity concentration, initiator type, emulsifier concentration, and temperature. A “two-stage rate” phenomenon, similar to that occurring in bulk co- and terpolymerization and emulsion copolymerization of acrylic/vinyl acetate systems was observed in the conversion, composition and molecular weight data. Furthermore, an interesting yet often ignored effect of impurities on emulsion polymerization kinetics was explained. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35 : 1659–1672, 1997     

Modeling and Sensitivity Analysis of Particle Size Distribution and Chain Length Distribution in a Semibatch Emulsion Copolymerization Reactor

Summary: A comprehensive model is developed to predict the relationship between the particle size distribution and molecular weights of particles in an emulsion copolymerization reactor. A full population balance equation is used for the particle size distribution and extended to the model for the molecular properties using a continuous reactor approach. The numerical prediction clearly distinguishes the characteristics of molecular properties of particles by homogeneous nucleation from those by micellar nucleation with the dependence on the particle size. Sensitivity analysis of the proposed model under a variety of conditions shows that the compartmentalized feature of the emulsion system should be considered for better prediction of molecular properties, and provides information on the manipulated variables and lumped parameters which effectively decompose the correlation of both properties. Finally, a control strategy utilizing a lumped parameters tracking method is suggested for the regulation of both the particle size distribution and molecular properties.

Time evolution of number‐averaged molecular weights in the element under base conditions.