Modeling Of Free Radical Polymerization Research Articles

All-dry free radical polymerization inside nanopores: Ion-milling-enabled coating thickness profiling revealed “necking” phenomena

Conformal coating of nanopores with functional polymer nanolayers is the key to many emerging technologies such as miniature sensors and membranes for advanced molecular separations. While the polymer coatings are often used to introduce functional moieties, their controlled growth under nanoconfinement could serve as a new approach to manipulate the size and shape of coated nanopores, hence, enabling novel functions like molecular separation. However, precise control of coating thickness in the longitudinal direction of a nanopore is limited by the lack of a characterization method to profile coating thickness within the nanoconfined space. Here, we report an experimental approach that combines ion milling (IM) and high-resolution field emission scanning electron microscopy (FESEM) for acquiring an accurate depth profile of ultrathin (∼20 nm or less) coatings synthesized inside nanopores via initiated chemical vapor deposition (iCVD). The enhanced capability of this approach stems from the excellent x–y resolution achieved by FESEM (i.e., 4.9 nm/pixel), robust depth (z) control enabled by IM (step size as small as 100 nm with R2 = 0.992), and the statistical power afforded by high-throughput sampling (i.e., ∼2000 individual pores). With that capability, we were able to determine with unparalleled accuracy and precision the depth profile of coating thickness and iCVD kinetics along 110-nm-diameter nanopores. That allowed us to uncover an unexpected coating depth profile featuring a maximum rate of polymerization at ∼250 nm underneath the top surface, i.e., down the pores, which we termed “necking.” The necking phenomenon deviates considerably from the conventionally assumed monotonous decrease in thickness along the longitudinal direction into a nanopore, as predicted by the diffusion-limited kinetics model of free radical polymerization. An initiator-centric collision model was then developed, which suggests that under the experimental conditions, the confinement imposed by the nanopores may lead to local amplification of the effective free radical concentration at z ≤ 100 nm and attenuation at z ≥ 500 nm, thus contributing to the observed necking phenomenon. The ion-milling-enabled depth profiling of ultrathin coatings inside nanopores, along with the initiator-mediated coating thickness control in the z-direction, may serve to enhance the performance of size-exclusion filtration membranes and even provide more flexible control of nanopore shape in the z dimension.

Modeling of Free-Radical Polymerization under Periodic Photoinitiation

Modeling of Free-Radical Polymerization under Periodic Photoinitiation

Effect of Confinement on the Synthesis of PMMA in AAO Templates and Modeling of Free Radical Polymerization

The hierarchical surface structure of polymer materials leads to unique properties which are of both academic and commercial interest. In this work we explore the ability to replicate the well-defined surface structure of anodic aluminum oxide (AAO) templates by in situ polymerization of methyl methacrylate. When the reaction is conducted inside the templates, the rate of polymerization was significantly higher and molecular weight was reduced, as compared to the reaction in bulk. These observations were explained using a mathematical model to describe the polymerization based on free-volume theory and confinement effects. As the dimensions of the template are reduced, a catalytic effect on the rate of initiator decomposition leads to a faster polymerization rate in the early stages of polymerization. In addition, due to the confined reaction volume, the rate of termination is increased in the latter stages of the reaction. The two confinement effects combine to lead to lower molecular weight polymers of ...

Monte Carlo Modeling of Free Radical Polymerization in Microflow Reactors

A Monte Carlo algorithm is developed to simulate the radical polymerization and copolymerization in microflow reactor. The algorithm couples the stochastic reaction process, based on Gillespie's theory, with material diffusion and flow. The simulation results agree well with the experimental kinetic data reported in the literature. The method can be used to predict the polymerization kinetics, molecular weight and molecular weight distribution, and composition and sequence length distribution (both instantaneous and cumulative) of the polymer products obtained from microflow reactors. The effects of various reaction parameters, such as flow rate, initial concentration, and temperature, on the polymerization kinetics are also discussed.

Stochastic Simulation of Droplet Interactions in Suspension Polymerization of Vinyl Chloride

In this paper a population balance based mathematical model is presented for describing suspension polymerization of vinyl chloride. The properties of the polymer product and the behaviour of the stirred batch polymerization reactor are investigated by simulation. Two-phase kinetics model of free radical polymerization is used, and heat balance is also included into the model. Beside the coalescence and breakage phenomena, are taken interchanges of species and heat between the droplets induced by collisions into account forming a complex threescale system. The motion of droplets in the physical space of the polymerization reactor, the breakage, coalescence and coalescence/ redispersion processes are simulated by using a coupled continuous time – Monte Carlo method.

Percipitation copolymerization of acrylamide and acrylic acid: Determination of reactivity ratio by various methods

AbstractCopolymers of acrylamide ( AM ) and acrylic acid ( AA) were prepared by precipitation polymerization method at 65 °C in the ethyl acetate as solvent. Copolymer composition was determined by elemental analysis. Monomer reactivity ratios were determined in low conversions. Mayo-Lewis, Finemann-Ross, Inverted Finemann-Ross, Ezrielev-Brokhina-Roskin, Kelen-Tudos, Extended Kelen-Tudos and Mao-Huglin methods, as linear methods, and Tidwell-Mortimer, as nonlinear method, were applied to calculate rAM and rAA r reactivity ratios. Monomer reactivity ratios of AM and AA were obtained 0.46 and 0.28, respectively. Comparing of reactivity ratios of AM and AA in this work by other solvents showed that hydrogen bonding and ionic strength are important parameters that can affect the reactivity ratios of monomers. Moreover, microstructure of copolymers was determined using reactivity ratios and conditional probability based on the kinetic model for free-radical polymerization.

Modeling of Free Radical Polymerization of Azobenzene-based Linear Polymers

ABSTRACTModeling of free radical polymerizations of the liquid-crystalline monomer 6-[4-(4-heptyloxyphenylazo)phenoxy]hexylacrylate using the PREDICI software package is reported. The model accounts for all elemental reactions that were identified to be important for radical polymerizations of acrylate-type monomers. On the basis of butyl acrylate kinetic data a remarkable agreement between number average molar masses from modelling (Mn,sim) and from experiments (Mn,exp) is observed: Mn,sim = 17800 g·mol−1 and Mn,exp = 17400 g·mol−1. Similarly, dispersity values of 1.8 and 1.6 were determined via modelling and experiments, respectively. It is shown that the assumption of butyl acrylate kinetics provides a reasonable approximation even for acrylate-based monomers having mesogenic substituents.

APPLICATION OF GENETIC ALGORITHM TO DETERMINE KINETIC PARAMETERS OF FREE RADICAL POLYMERIZATION OF VINYL ACETATE BY MULTI-OBJECTIVE OPTIMIZATION TECHNIQUE

A Multi-objectiv e optimization procedure has been developed to determine some kinetic parameters of free radical polymerization of vinyl acetate based on genetic algorithm. For this purpose, mathematical modeling of free radical polymerization of vinyl acetate is carried out first and then selected kinetic parameters are optimized by minimizing objective functions defined from comparing experimental data and mathematical modeling outcomes. A ranking procedure is applied to classificatio n of solutions, and a Pareto optimal set filter is used to preserve the non- dominated solutions on the basis of Pareto optimality definition. Results show by this optimization technique, kinetic parameters are calculated in reasonable time and computational costs near the global optimum without scalarization of objective functions into a single objective function.

Inferential sensors for estimation of polymer quality parameters: Industrial application of a PLS-based soft sensor for a LDPE plant

Low-density polyethylene (LDPE) and ethylene vinyl acetate (EVA) copolymers are produced in free radical polymerization using reactors at extremely high pressure. The reactors require constant monitoring and control in order to minimize undesirable process excursions and meet stringent product specifications. In industrial settings, polymer quality is mainly specified in terms of melt flow index (MI) and density. These properties are difficult to measure and usually unavailable in real time, which leads to major difficulty in controlling product quality in polymerization processes. Researchers have attempted first principles modeling of polymerization processes to estimate end use properties. However, development of detailed first principles model for free radical polymerization is not a trivial task. The difficulties involved are the large number of complex and simultaneous reactions and the need to estimate a large number of kinetic parameters. To overcome these difficulties, some researchers considered empirical neural network models as an alternative. However, neural network models provide no physical insight about the underlying process. We consider data-based multivariate regression methods as alternative solution to the problem. In this paper, some recent developments in modeling polymer quality parameters are reviewed, with emphasis given to the free radical polymerization process. We present an application of PLS to build a soft-sensor to predict melt flow index using routinely measured process variables. Issues of data acquisition and preprocessing for real industrial data are discussed. The study was conducted using data collected form an industrial autoclave reactor, which produces LDPE and EVA copolymer using free radical polymerization. The results indicated that melt index (MI) can be successfully predicted using this relatively straightforward statistical tool.

FREE-RADICAL RETROGRADE-PRECIPITATION POLYMERIZATION: A MATHEMATICAL MODELING STUDY OF POLYMERIZATION OF STYRENE IN DIETHYL ETHER

Polymerizing a monomer above the lower critical solution temperature (LCST) of its polymer-monomer-(non)solvent mixture has demonstrated better control characteristics than conventional free-radical polymerization kinetics. Reaction kinetics of polymerization in a poor solvent are strongly influenced by heat and mass transfer properties, as understood from modeling the transport phenomena in our earlier work. The study has now been extended to model the reaction kinetics in a styrene-diethyl ether system. The model was based on the CCS model for free radical polymerization, with the modification proposed by Achilias-Kiparissides. Computer simulation results agree well with those obtained from experiments carried under similar conditions, with the onset of phase separation as the only adjustable parameter. Drawbacks of the model are lack of analysis for the effect of monomer concentration and the absence of an appropriate radical trapping mechanism.

Secondary Reactions in the High-Temperature Free Radical Polymerization of Butyl Acrylate

Secondary reactions have a marked effect on butyl acrylate polymerization rate and polymer structure under the high-temperature free radical reaction conditions typically used for production of solvent-based acrylic coatings resins. The low monomer concentrations characteristic of semibatch starved-feed reactor operation lead to significant rates of intramolecular transfer, resulting in a tertiary radical center capable of termination, monomer addition, or β-scission. The rate coefficients for these reactions are estimated from monomer concentrations, polymer molecular weights, and NMR analyses of quaternary branch points and macromer end groups for a series of semibatch experiments with varying monomer and polymer concentrations. A classical free radical polymerization model is insufficient for the description of this complex system. Thus, a mechanistic model including the additional reactions has been formulated and is shown to provide a good representation of the experimental results.

Molecular Weight Distribution Modeling of Radical Polymerization in a CSTR with Long Chain Branching through Transfer to Polymer and Terminal Double Bond (TDB) Propagation

The modeling of free radical polymerization with long chain branching in a CSTR is addressed. Long branches are assumed to be created by transfer to polymer and by insertion of active terminal double bonds (TDBs). Such TDBs may be produced by transfer to monomer and termination by disproportionation. The modeling approach is based on population balances being solved using a Galerkin finite element method (FEM). Two different models have been derived. The “TDB classes” model employs different equations for each class of chains with a certain number of TDBs. The “TDB moment distribution” uses the pseudodistribution method developed by us before22 for simultaneous molecular weight/degree of branching distribution modeling. Model calculations have been performed for the case of poly(vinyl acetate) (PVAc). In the case of the maximum one TDB per chain, the two models prove to be mathematically equivalent. An increase of TDB propagation rate leads to a broadening of chain length distribution (CLD) and sometimes to a more pronounced “shoulder” at long chain lengths. The significant concentration range extends to extremely long chain lengths (1010)well within a gel regimebut the model could fully cover this. Quite remarkably, concentrations of living chains are higher than those of dead chains in this region. The average number of TDBs per chain could be calculated and turns out to be constant at shorter chain lengths, but becomes lower for longer chains. This is explained by the combined action of chain growth by TDB propagation, which implies TDB consumption as well, and transfer to polymer. For the case of more than one TDB per chain, the two models yield different results depending on closure relationships. The TDB moment distribution model revealed that the longest chains carry tens of thousands of TDBs. The classes model strongly underestimates the number of TDBs and hence the reactivity of the dead chains to TDB propagation. The results show the effect of dead chains with many TDBs acting as cross-linkers for living chains. As an interesting trend, it was observed that with increasing TDB propagation rate an increasing fraction of monomer units existing in polymer chains is present in fewer, but extremely long living, chains.

Kinetics and modeling of free radical polymerization of N-vinylformamide

Free radical polymerization kinetics of N-vinylformamide was investigated in bulk and in aqueous solution. The molecular weight development with N-vinylformamide conversions was measured using a gel permeation chromatography (GPC). The bulk process showed a typical “gel effect” from the beginning of the polymerization. The molecular weight increased steadily at low conversion and leveled off at high conversion. In the solution polymerization, the “gel effect” became less pronounce with decreasing monomer concentration. When the monomer concentration was less than 40wt%, no auto-acceleration was observed from the time-conversion curves. The kp/kt1/2 values of the polymerization system were determined using the initial rates of bulk polymerization and the number average molecular weight data at 50, 60 and 70°C. A kinetic model based on free volume theory was proposed to describe the polymerization kinetics and molecular weight development. The model agreed with the time-conversion and conversion-average molecular weight data.

Polyester cure monitoring by means of different techniques

AbstractThe cure of a set of polyester resin samples having different styrene contents has been monitored by means of Fourier transform infrared (FTIR) spectroscopy, differential scanning calorimetry (DSC), rheometry, and ultrasonic measurements. FTIR and DSC experimental data were used to calculate the cure kinetics using a freeradical polymerization model (multiple steps) and also an empirical model that considers the curing to involve only a single step. The dependence of viscosity on the degree of curing has been investigated at different shear rates. Finally, correlations among the results from the different techniques have been established and discussed in terms of the curing mechanism.

Kinetic modeling of free radical polymerization of styrene initiated by the bifunctional initiator 2,5-dimethyl-2,5-bis(2-ethyl hexanoyl peroxy)hexane

This paper deals with the kinetic study of bulk free radical polymerization of styrene initiated with the commercial bifunctional initiator 2,5-dimethyl-2,5-bis(2-ethyl hexanoyl peroxy)hexane (Lupersol 256). The polymerization kinetics is investigated by DSC measurement for temperatures between 80 and 110°C and for initiator initial concentration from 0.115 up to 0.46 mol%. The experimental conversion and reaction rate are compared and discussed with the calculated values. For modeling the polymerization rate, a reaction scheme similar to the one given by Yoon and Choi (Polymer 1992;33(21):4582–4591) has been used and adapted. A detailed diffusional and semi-empirical model proposed by Chiu et al. (Macromolecules 1983;16(3):348–357) has been modified by Rouge (Etude de la polymérisation radicalaire du styrène initiée par un amorceur bifonctionnel dans un réacteur tubulaire à recyclage, Diploma work, DC, EPF, Lausanne, 1997) in order to describe these results. The model allows the description of the number molecular weight, but the polydispersity is underestimated for conversion higher than 70%. For temperature higher than 100°C, thermal initiation must be taken into account. The efficiency factor is found close to 1, but seems to decrease for temperatures above 100°C.

Modeling of free radical polymerization up to high conversion. II. Development of a mathematical model

In free radical polymerization diffusion-controlled processes take place simultaneously to the normal chemical reactions. Despite extensive efforts to model such processes a consistent model for the design of a polymerization reactor has not yet been established. In this article a semiempirical model describing the conversion, polymerization degree, and molecular weight distribution (MWD) for the free radical polymerization is developed for the entire course of the reaction. The model includes the change of termination, propagation, transfer, and initiation rate. By simultaneous parameter estimation from the conversion and degrees of polymerization data the model parameters have been determined for isothermal polymerizations of methyl methacrylate (MMA) and styrene (ST). The simulation results for the conversion, degrees of polymerization, and MWD are in good accordance with experimental data for suspension and bulk polymerization of MMA and ST up to very high conversions. The influence of diffusion on the propagation rate in case of polymerization of MMA is negligible compared to the influence of the cage effect on the radical efficiency; in case of ST polymerization both effects must be included in the kinetic model. The model presented is also tested for polymerizations conducted in the presence of solvent and/or chain transfer agents.

Modeling of free radical polymerization up to high conversion. I. A method for the selection of models by simultaneous parameter estimation

A systematic quantitative method for the selection of models for the high-conversion free radical polymerization exhibiting gel and glass effects has been developed. Four representative models were selected from the literature and were compared on the basis of the same experimental data. All models describe the isothermal time-conversion data over the entire conversion range for a single type and loading of initiator well. Models that are not considering the effect of molecular weight of the polymers on the diffusion of macro radicals fail to describe the time-conversion data if the concentration of the initiator varies at the same time. By simultaneous fitting of the conversion and polymerization degree data it was shown that the Marten-Hamielec model and its extended form (Panke-Stickler-Hamielec model) were not able to describe the number average polymerization degree Pn at the final conversion, where the glass effect occurs. This occurred because both models neglect the change of the radical efficiency f in this region, which has more effect on Pn than the change of the propagation rate coefficient (see part II of this series). © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 63: 1649–1661, 1997

Modeling of free radical polymerization up to high conversion. I. A method for the selection of models by simultaneous parameter estimation

A systematic quantitative method for the selection of models for the high-conversion free radical polymerization exhibiting gel and glass effects has been developed. Four representative models were selected from the literature and were compared on the basis of the same experimental data. All models describe the isothermal time-conversion data over the entire conversion range for a single type and loading of initiator well. Models that are not considering the effect of molecular weight of the polymers on the diffusion of macro radicals fail to describe the time-conversion data if the concentration of the initiator varies at the same time. By simultaneous fitting of the conversion and polymerization degree data it was shown that the Marten-Hamielec model and its extended form (Panke-Stickler-Hamielec model) were not able to describe the number average polymerization degree Pn at the final conversion, where the glass effect occurs. This occurred because both models neglect the change of the radical efficiency f in this region, which has more effect on Pn than the change of the propagation rate coefficient (see part II of this series).

Use of neural networks for modeling of olefin polymerization in high pressure tubular reactors

AbstractNeural network computing is one of the fastest growing fields of artificial intelligence due to its ability to “learn” nonlinear relationships. This article presents the approach of back propagation neural networks for modeling of free radical polymerization in high pressure tubular reactors. Industrial data were used to train the network for prediction of the temperature profile along the reactor, as well as polymer properties such as density, melt flow index, and molecular weight averages. Comparisons were made between the neural network and mechanistic model predictions published in the literature. Results showed the promising capability of a neural network as an alternative approach to model polymeric systems. © 1994 John Wiley & Sons, Inc.

Modeling and experimental studies of aqueous suspension polymerization processes. 1. Modeling and simulations

The modeling and simulation of free radical polymerizations in different processes (bulk, solution, suspension, emulsion, dispersion) should not require altered sets of kinetic rate constants for the same monomer or monomer mixture system. Appropriate handling of the different physical picture in each process and an accurate description of all the elemental steps (physical and chemical phenomena) can result in universal models built on the common kinetic mechanism of free-radical polymerizations. In this work we have extended our homogeneous free radical polymerization model to consider the suspension polymerization of partially water-soluble monomers. Simulation results from this model are compared to experimental results from the literature and from our own suspension polymerization experiments