A multi-scale CFD model has been developed to describe the particle behavior in a polyolefin fluidized bed reactor (FBR). The model consists of a CFD model incorporating a single particle model and a population balance model (PBM). The main particle behavior in the FBR can be calculated using the multi-scale model. The multi-scale model is tested by comparing simulation results with experimental data. Three cases including CFD coupled with PBM, CFD–PBM coupled with the single particle model without consideration of external diffusion, and multi-scale CFD model under consideration of external diffusion are developed to further examine the model. The simulations demonstrate that both intraparticle mass and heat transfers, which are ignored by these conventional CFD–PBM models, have significant effects on the particle behavior.

**A multi-scale CFD has been developed to describe the particle behavior in a polymerization FBR**. The multi-scale model is tested by comparing simulation results with experimental data. The simulations demonstrate that both the intraparticle mass and heat transfer significantly impact the particle behavior.

The scope of this work is to explain the multi-scale polymerization process modeling framework, comprising of polymerization kinetics (micro-scale), system thermodynamics (meso-scale), and reactor performance (macro-scale) as well as to present the methodology for developing a mathematical model for catalytic olefin polymerization. Guidelines for tuning the kinetic model parameters are proposed. This review aims to provide basic knowledge and understanding regarding catalytic olefin polymerization kinetics and offers the starter-kit tools for developing similar works.

**This work presents the basic framework** for catalytic olefin polymerization kinetic modeling. It provides an insight for a better understanding of the kinetic models, offering the starter-kit tools for developing similar approaches in the complex but extremely interesting area of polymerization kinetic reaction engineering.

On-line monitoring of polymerization reactions in microreactors is investigated by confocal Raman microscopy (CRM). Two different types of experiments are carried out: solution polymerizations and miniemulsion polymerizations. The solution polymerization experiments are performed with either styrene or butyl acrylate (BA) monomers, while toluene is used as solvent in both cases. BA is the only monomer used in the miniemulsion polymerizations. Conversion is determined by CRM for different residence times and the results are compared with the ones obtained gravimetrically. The good agreement achieved in all the experiments demonstrates that CRM is an appropriate technique to on-line monitoring the kinetics of polymerizations performed in microreactors.

**Use of confocal Raman microscopy to monitor kinetics of homogeneous and heterogeneous polymerizations in microreactors is being reported.** The adequacy of the technique is demonstrated through several experiments performed at different residence time for solution and miniemulsion polymerizations. The method also allows getting the conversion evolution along the microreactor length by changing the position of the Raman microscope.

The copolymerization kinetics of hydroxyethyl methacrylate (HEMA) with either ethylene glycol dimethacrylate (EGDMA) or diethylene glycol dimethacrylate (DEGDMA) in the presence of RAFT controllers is studied using a mathematical model recently developed in our group. The model is based on the concept of multifunctional polymer molecules. The cases of conventional and controlled homopolymerizations of HEMA as well as the RAFT copolymerization of HEMA/EGDMA and HEMA/DEGDMA are addressed and are in good agreement with available experimental data. The bulk/solution version of the model is used as first approximation of the behavior of a RAFT dispersion copolymerization of HEMA/EGDMA carried out in supercritical carbon dioxide.

**The growth of hydrogels from HEMA and EGDMA (or DEGDMA) with controlled structures is studied with the aid of** a comprehensive mathematical model previously developed by us. Bulk and solution copolymerizations are addressed and the bulk situation is used to approximate the behavior of a RAFT dispersion copolymerization of HEMA/EGDMA in scCO_{2}.

Filtrodynamic behavior of trans-filter time-dependent pressure signals Δ*P*(*t*) is determined for membrane and frit filters using latex spheres of varying diameter *D*. Membrane data are best interpreted via a time-dependent, accreting filtration bed, based on Darcy's law. A single parameter, permeability *k*, describes each membrane/particle pair. For small particles, *k* increases with increasing *D*, then becomes *D*-independent for large ones. Predictable behavior for polydisperse mixtures of small spheres is obtained. The mechanism and behavior of filtration for non-membrane metallic frits is dramatically different, and better described by a previous “characteristic loading” model. Use of frit and membrane filters in series allowed monitoring each filter's separate response to particle accumulation.

The filtrodynamic behavior of trans-filter time-dependent pressure signals is determined for membrane and frit filters using latex spheres of varying diameter *D*. An accretion model based on Darcy's law best describes the mechanism of membrane filters. Non-membrane metallic frits reveal a different mechanism and behavior of filtration that is better described by the “characteristic loading” model.

Suspension and bulk polymerizations of vinyl acetate (VAc) are performed in several experimental conditions, using cyanomethyl methyl(phenyl) carbamodithioate as the chain transfer agent (CTA). The polymerization kinetics are monitored in batch for bulk polymerizations, showing an inhibitory period at the beginning of the reaction runs, despite the particular experimental conditions used. More accurate control over the molecular properties of the synthesized poly(vinyl acetate) (PVAc) is achieved when high concentrations of CTA are used. Similar experimental conditions are applied to prepare PVAc particles via suspension polymerization of VAc in the presence of small amounts of CTA. It is possible to produce spherical particles with a narrow particle size distribution and predominant spherical morphology. Although the reactions yield low control over the molecular weight properties, it is possible to use the synthesized particles as macro-CTAs and promote chain extension reactions to extend the chain length of the PVAc.

**Poly(vinyl acetate) is synthesized via bulk and suspension RAFT polymerizations using a dithiocarbamate compound as chain transfer agent (CTA).** It is shown that the control over the molecular properties is highly sensitive to the monomer/CTA ratio. The proposed approach enables the production of poly(vinyl acetate) particles and allows for posterior chain extension, also facilitating the synthesis of microparticles with complex molecular architectures.

Poly(methyl methacrylate)-*b*-poly(styrene) (PMMA-*b*-PSt) block copolymer is synthesized successfully via seeded emulsion polymerization in the presence of 1,1-diphenylethylene (DPE). First, emulsion polymerization of MMA is carried out with KPS as initiator in the presence of DPE, giving a DPE-containing PMMA precursor with the ability of reactivation by simply heating. The emulsion polymerization behavior of MMA in the presence of DPE is investigated. The second monomer styrene (St) is then polymerized in PMMA seed emulsion and the block copolymer is successfully obtained. The formation of PMMA-*b*-PSt block copolymer is confirmed by ^{1}H NMR and gel permeation chromatography. Dynamic light scattering is used to monitor the particle diameters, and suggests that the particles grow without secondary nucleation occurring.

**The behavior of methyl methacrylate in emulsion polymerization in the presence of 1,1-diphenylethylene is investigated by the analysis of instantaneous number MWD.** The block copolymer PMMA-*b*-PSt is successfully prepared by simply heating the PMMA seed emulsion controlled by DPE in the presence of second monomer St.

A mathematical model is developed to simulate condensation polymerization of 1,3-propanediol to produce polytrimethylene glycol (PO3G) polyether. The model includes improved mass-transfer expressions that account for nonzero concentrations of water and monomer inside nitrogen bubbles and for increasing overall bubble surface area due to increases in bubble residence time. An objective function that accounts for the mole fractions of evaporated monomer, water and propanal is considered for parameter estimation. Improvements in the predicted monomer and water concentrations in the polymer and evaporation rates of monomer and water can be observed compared to a previous model. However, predictions of degree of polymerization do not improve noticeably. Recommendations including revisions of the chemical mechanism to include additional reactions and accounting for evaporation of linear and cyclic oligomers in future models are suggested.

**A mathematical model is developed to simulate condensation polymerization of 1,3-propanediol. The model includes improved mass-transfer expressions** that account for nonzero concentrations of water and monomer inside bubbles and for changing the overall bubble surface area. Improvements in the predicted unreacted monomer, water concentrations, and evaporation of the monomer and water can be observed in comparison to the previous model.

In this paper, the state estimation of semi-continuous and batch processes for a set of emulsion polymerization reactions is addressed. Specifically, the autocovariance least-squares (ALS) and the moving horizon estimation (MHE) techniques are implemented to determine the covariance matrices and monitor the reactions in two steps, respectively. A collection of four polymerization reaction data sets that include gravimetric analysis are considered and used for validation of the proposed methods. The major process states estimated are the overall heat transfer coefficient and the conversion. The estimation results are in good agreement with the experimental data, independently of the initial overall heat transfer coefficient employed. They also indicate that a unique set of covariance matrices can represent the four reactions studied. The developed procedure offers a robust alternative for state estimation of industrial and experimental polymerization systems.

**Moving horizon estimation is an optimization-based filter that can address non-linear and constrained systems**. A monitoring procedure with statistical parameters estimated by the autocovariance least-squares technique is proposed and validated with experimental emulsion polymerization reaction data. The estimation results are compared with gravimetric analysis and the effect of the initial estimate is also evaluated, showing that the procedure is robust.

A one-dimensional and two-dimensional model of the frontal reaction of epoxy compounds by aromatic amines in tubular flux reactors is investigated. The influence of relevant kinetic factors (velocity, activation energy, and others) on the velocity of the traveling front, the heat regimes of the reactor, and the geometric dimensions of the reactor is studied. An optimal steady-state condition of the tubular reactor under continuous action is determined. Profiled armored carbon and glass plastics forming laboratory installation are constructed, as derived from the obtained theoretical results. It is shown that the theoretical and practical results are in satisfactory agreement. Several physico-mechanical properties (e.g., bending strength, longitudinal modulus of elasticity), as based on the reactor wall temperature, angle of armoring, and tension are determined.

**This work reports on the observation of reaction fronts of polymers in tubular reactors and its successful numerical description.** It is shown that frontal reaction of epoxy oligomers occurs by aromatic amines and that simulations in one- and two-dimensional setups agree well with the experiments. Furthermore, nonlinear dynamical regimes such as oscillations of front velocity and geometric changes of the front shape are detected.

Polymer chain microstructure is one of the most important characteristics determining the end-use properties of the latexes, and it is defined mainly in the reactor. In this work, the influence of the emulsion or miniemulsion process as well as that of the batch or continuous tubular reactor on the microstructure of the *n*-butyl acrylate containing latexes is analyzed. It is found that, under similar experimental conditions, miniemulsion polymerization leads always to lower gel content than emulsion, because of the higher average monomer concentration during polymerization. Further, emulsion polymerizations performed in the continuous tubular reactor allow to obtain free-gel containing latexes, if the pre-emulsion feed is sonicated prior to enter into the reactor. In addition, the better control of the temperature on the tubular reactors leads to narrower molecular weight distribution latexes than the batch reactors in emulsion polymerization.

**Strategies to obtain poly( n**

The relative importance of the higher solubility of *n*-hexane (with respect to ethylene) and its associated heat of sorption on the thermal behavior of the growing polymer particles during gas phase ethylene polymerization on supported catalysts are investigated. It is found that if a polymerizing particle begins to heat-up, the partial desorption of a condensable solute in a gaseous state helps to attenuate the temperature rise in the polymer particles, decreasing the risk of local hot spots.

**The relative importance of the higher solubility of n**

Owing to their good cost-performance ratio polyolefins are very attractive polymers which are used in a variety of applications. However, painting or bonding of PP parts can cause problems due to inadequate adhesiveness. Today, different methods are available for pretreating the surface in order to improve its adhesive properties. These methods have the disadvantage that they are carried out as an additional fabrication step. Depending on the type of pretreatment this leads to high equipment and energy costs. In situ surface modification during molding is a new method to avoid such disadvantages. It was applied up to now for different thermoplastics. In this paper its application for the surface modification of polyolefins is reported. The differences in the processing details due to the use of a liquid modifier, which is advantageous for polyolefins, to the solid modifier films used, e.g., for polycarbonate are identified.

**The surface of polyolefin parts is modified during injection molding using reactive polymer mixtures and radical reactions.** Best results are obtained with liquid modifiers. The paper identifies the special conditions on using liquids for reactions during injection molding.

Surfactant-free bio-based latexes are synthesized by generating miniemulsions via in situ surfactant formation while using as a precursor a component that is already available after the synthesis of the monomer. In this work, the oleic acid (OA) remaining after the synthesis of the OA derivative 2-hydroxy-3-(methacryloxy)propyl oleate (MOA) monomer is used to generate in situ surfactants. The conditions to achieve stable miniemulsions are evaluated and the resultant systems are successfully polymerized. These environmentally friendly polymeric materials provide transparent and glossy films.

**Miniemulsification of a bio-based monomer by in situ surfactant technique and further polymerization is being reported.** The non-reacted oleic acid present in the production of the fatty acid derivative monomer is successfully used as precursor to generate the surfactant. Surfactant-free bio-based latexes forming transparent and glossy films are achieved.

**Cover:** A multi-phase, multi-zone mathematical model is developed to describe the dynamic operation of an industrial high-pressure flash separator for a ternary (ethylene-vinyl acetate-EVA) system. The model takes into account the complex gas carry-under and liquid droplets carry-over phenomena occurring in the separator as well as the monomer mass transfer rate from the dispersed liquid droplets to the gas phase and the bubble formation in the liquid zone. Further details can be found in the article by P. Pladis, A. Baltsas, V. Kanellopoulos and C. Kiparissides on page 392.

This article shows how the method of instantaneous distributions can be used to model the microstructures of polymers made under different polymerization conditions. The three main distributions investigated are the distributions of chain length (CLD), chemical or comonomer composition (CCD), and long chain branching (LCBD). It is also explained how the method of instantaneous distributions can be combined with reactor models to calculate the cumulative distribution of polymers made in reactors having different residence time distributions, spatial and time gradients. Finally, the usefulness of this mathematical modeling technique is illustrated in several case studies involving olefin polymerization. Extensions for free-radical polymerization are covered in the appendices.

**Instantaneous distributions are analytical solutions that describe several aspects of polymer microstructures at a given instant of time.** Cumulative distributions are obtained by integrating instantaneous solutions over time and reactor volume. The method of instantaneous distributions is a powerful technique that can be used to describe many aspects of the polymer molecular architecture at low computational cost.

The polymerization that IUPAC terms reversible-deactivation radical polymerization is a controlled radical polymerization technique (CRP) that allows producing polymers with tailored properties without the stringent conditions typical in ionic polymerization. A theoretical analysis is presented of the influence of operating and design conditions on the product properties for the nitroxide-mediated copolymerization (NMP) of styrene and α-methyl styrene. Several reactor configurations are analyzed, with different feeding policies and temperature profiles. To this end a mathematical model is developed to predict copolymer average properties and the complete bivariate MWD. The results help establishing design parameters and optimal operating policies to obtain desired copolymer microstructures.

**A mathematical model is presented of the nitroxide mediated copolymerization of styrene and α-methyl styrene,** capable of predicting the average properties of the resulting material and the full bivariate molecular weight distribution. It is applied to different reactor configurations with several feeding policies and temperature profiles. The model shows promise for its application in an optimization tool for controlled radical polymerization processes.

A kinetic model including the cyclic propagation (cyclization) is proposed for the nitroxide-mediated radical copolymerization of styrene–divinylbenzene. The method involves a balance of sequences of units, which connect a radical center and a pendant double bond present in the same polymer chain. The rate constant for cyclization was considered a function of the sequence length. Good agreement between the model predictions and experimental data for solution and suspension controlled copolymerizations was found. The rate constant of cyclization for the smallest ring (3 monomeric units) was estimated to be 700 s^{−1} at 90 °C, and the activation energy was estimated to be 32 500 cal mol^{−1}.

**The concept of sequence (number of monomeric units connecting a radical center and a pendant double bond present in the same polymer chain)** is proposed to model cyclization in NMRP of styrene–divinylbenzene. The cyclization rate constant is considered to be a function of the sequence length. The model predictions were validated with experimental data, by adjusting only one parameter, the cyclization rate constant for the smallest ring (with 3 monomeric units).

Nitroxide-mediated polymerization of styrene-divinylbenzene has been modeled using generating functions of length distributions, pseudo-kinetic propagations, and numerical fractionation with the crosslinking rate depending on generation. Cyclization reactions are tackled by balances of sequences, yielding fair predictions of the measured pendant double bond concentration. With reduction in crosslinking, agreement for the experiments at 90 °C between predicted and measured weight-average, molecular weight, and weight fraction of gel is observed. A much higher relative crosslinking reactivity is observed at 130 °C as compared to 90 °C, likely an effect of the chain mobility.

**Three modeling approaches for the NMRP of styrene–divinylbenzene are studied and compared with experiments.** A hypothetical reduction of reactivity is tested for the crosslinking reactions involving polymer molecules belonging to different generations, yielding simultaneous agreement of predicted and measured weight-average molecular weight and weight fraction of gel.

PEGDA hydrogels copolymerized with NVP using free-radical photopolymerization are used in biomedical applications. These networks consist of a poly(acrylate-*co*-vinyl pyrrolidone) backbone crosslinked with PEG chains whose crosslink density is dependent on the backbone molecular weight and composition. Insight into the network structure and characterization of the backbone molecular weight and composition is achieved by considering hydrogel degradation through ester bond hydrolysis resulting in the release of PEG and poly(acrylic acid-*co*-vinyl pyrrolidone). A model is developed to determine the influence of kinetic constants and phenomena on the backbone formation and is compared to experimental data. Results indicate that the backbone molecular weight is related to the amount of NVP and unaffected by polymerization time.

**PEG diacrylate hydrogels photopolymerized with NVP are used in biomedical applications.** The network structure of these biomaterials is highly dependent on the molecular weight and composition of the copolymer backbone which dictates the resultant hydrogel properties. Insight into the copolymer backbone formation is achieved by hydrogel degradation and subsequent characterization of the degradation products using experimental measurements and computational modeling.

A mathematical model for the seeded emulsion copolymerization of styrene, butadiene, and an acidic monomer has been developed. The outputs of the model include monomer conversion, copolymer composition, solids content, average particle size, 4-PCH and 4-VCH concentrations, overall molecular weight distribution, gel content, distance between crosslinking points, acid distribution between phases, and amount of inactive polymer in the aqueous phase and its composition. The parameters of the model have been estimated using pilot-plant data and the model captures well the effect of the process variables on the latex characteristics.

**Styrene–butadiene latex (SB) is one of the major waterborne dispersed polymers with an annual production of about 2.9 × 10**^{6} **metric tons.** A mathematical model for the prediction of kinetics and polymer structure for the seeded emulsion copolymerization of styrene, butadiene, and an acidic monomer has been developed and its parameters estimated using pilot-plant data.

A novel formulation for addressing planning, scheduling, and control problems in a Methyl-Methacrylate CSTR is presented. Improved optimal solutions can be obtained by using a simultaneous solution approach where the interactions among these problems are explicitly taken into account, in contrast with the classical sequential or decoupled way to address it. In previous works a cyclic production strategy for addressing production patterns has been used. For real-time implementation an extended-horizon production strategy has been used. Moreover, the open-loop optimal dynamic transition trajectories among target polymerization grades are closed-loop implemented using a Nonlinear Model Predictive Control strategy for dealing with disturbance rejection and set-point tracking issues.

**In this work the interlinked problems of planning, scheduling, and control** by using a simultaneous solution approach are addressed. The optimization problem is cast as a MIDO/MINLP problem whose optimal solution is obtained only for a relatively small number of operating periods and binary variables.

A multiobjective dynamic optimization problem using conflicting performance objectives in polymerization systems is formulated. We use the dynamic one-dimensional mathematical model of a methyl-methacrylate cell cast reactor featuring monomer conversion and molecular weight distribution as the conflicting objectives. The aim is to compute the whole set of trade-off solutions comparing the performance of three well known procedures for addressing the solution of multiobjective optimization (MO) problems: normal boundary intersection, weighted sum, and epsilon-constraint. Using the air temperature profile as the manipulated variable, we demonstrate the dynamic optimal solutions obtained using the best trade-off solution from each one of the MO techniques.

**We formulate a multiobjective dynamic optimization problem (MOP) using conflicting performance objectives in a methyl-methacrylate cell cast reactor.** The aim is to compute the whole set of trade-off solutions comparing the performance of three well-known procedures for addressing the solution of MOP. The best trade-off solution is selected as the point on the trade-off curve in closest proximity to the utopia region.

This work analyzes the possible influence of the inevitable temperature and concentration fluctuations that take place inside typical stirred tank heterogeneous polymerization reactors on the evolution of kinetic variables. Preliminary analyses regarding the characteristic time constants for heat and mass transfer inside polymer particles that are suspended in a continuous phase are performed in order to evaluate how fast particles respond to perturbations along a dynamic trajectory inside the reactor. It is concluded that particles of typical heterogeneous systems can respond almost immediately to operation changes. For this reason, simulations are performed to evaluate the influence of the varying temperature and concentration fields on the evolution of kinetic variables. It is concluded that the effects caused by the inevitable fluctuations of temperature and concentration inside the vessel can be neglected in usual conditions of reaction of heterogeneous polymerization systems.

**The evolution of kinetic variables is regarded in light of possible impacts** of inevitable temperature and concentration fluctuations inside typical stirred tank heterogeneous polymerization. Elaborations of responding time constants of particles on perturbations inside the reactor are performed. Simulations disclose the effects of varying temperature and concentration fields inside the vessel.

A multi-phase, multi-zone mathematical model is developed to describe the dynamic operation of an industrial high-pressure flash separator for a ternary (Ethylene–Vinyl acetate–EVA) system. The proposed description of the high-pressure separator can take into account the complex gas carry-under and liquid droplets carry-over phenomena occurring during the non-equilibrium operation of the separator. Numerical simulations have been carried out to determine the effect of operating conditions on the dynamic operation and separation efficiency of a HPS unit operating in series with an industrial scale high-pressure EVA autoclave. The proposed model is capable of simulating the dynamic operation of an industrial-scale HPS over a wide range of operating conditions and EVA copolymer grades.

**A multi-phase, multi-zone mathematical model has been developed to describe the dynamic operation of an industrial high-pressure flash separator for a ternary (ethylene–vinyl acetate–EVA) system.** The model takes into account the complex gas carry-under and liquid droplets carry-over phenomena occurring in the separator.