Estimation Of Reactivity Ratios Research Articles

Bulk Free Radical Terpolymerization of Butyl Acrylate, 2-Methylene-1,3-Dioxepane and Vinyl Acetate: Terpolymer Reactivity Ratio Estimation.

This investigation introduces the first estimation of ternary reactivity ratios for a butyl acrylate (BA), 2-methylene-1,3-dioxepane (MDO), and vinyl acetate (VAc) system at 50 °C, with an aim to develop biodegradable pressure-sensitive adhesives (PSAs). In this study, we applied the error-in-variables model (EVM) to estimate reactivity ratios. The ternary reactivity ratios were found to be r12 = 0.417, r21 = 0.071, r13 = 4.459, r31 = 0.198, r23 = 0.260, and r32 = 55.339 (BA/MDO/VAc 1/2/3), contrasting with their binary counterparts, which are significantly different, indicating the critical need for ternary system analysis to accurately model multicomponent polymerization systems. Through the application of a recast Alfrey-Goldfinger model, this investigation predicts the terpolymer's instantaneous and cumulative compositions at various conversion levels, based on the ternary reactivity ratios. These predictions not only provide crucial insights into the incorporation of MDO across different initial feed compositions but also offer estimates of the final terpolymer compositions and distributions, underscoring their potential in designing compostable or degradable polymers.

Effect of alkyl methacrylate/glycidyl methacrylate copolymer backbone structure on mechanical properties of hydroxyurethane-crosslinked networks

The effect of cyclic carbonate functionalized polymer backbones on mechanical and rheological properties of hybrid thermoset resins with hydroxyurethane linkages via vegetable-oil derived diamine were investigated. Atom transfer radical polymerization (ATRP) of binary methyl, ethyl, butyl methacrylate (MMA, EMA, BMA) mixtures with glycidyl methacrylate (GMA) with various GMA initial molar fractions (fGMA = 0.1–0.9) were performed at 70 °C to create precursor backbones with modulated glass transition temperature (Tg). The copolymer compositions were essentially statistical as demonstrated by estimated reactivity ratios. MMA/GMA reactivity ratios were rMMA = 0.80 ± 0.09 and rGMA = 1.35 ± 0.09, which agreed with earlier studies while previously unreported EMA/GMA reactivity ratios were rGMA = 1.10 ± 0.09 and rEMA = 0.31 ± 0.09 and BMA/GMA reactivity ratios were rBMA = 0.67 ± 0.09 and rGMA = 1.45 ± 0.09. The synthesized copolymers were then carbonated, converting the pendent epoxy functional groups to cyclic carbonates. The carbonated copolymers were reacted with the vegetable oil-derived diamine Priamine 1074 to form relatively rigid side chains via hydroxyurethane linkages to the backbone. Degree of flexibility of backbones and cyclic carbonate functionality were manipulated to synthesize crosslinked networks with Young's moduli ranging from 395 MPa to 1250 MPa.

Estimation of Reactivity Ratios for Olefin Polymerization Catalysts—On the Importance of Thermodynamics

AbstractA systematic study of the impact of gas phase composition on the estimation of the reactivity ratios of a Ziegler–Natta catalyst during the gas phase copolymerization of ethylene with 1‐butene and 1‐hexene has been carried out. The results of the study show that if one uses a realistic equation of state to estimate the co‐ and anti‐solubility effects of multiple species in the gas phase, one can obtain a unique value of the reactivity ratio pair from any number of experiments. However, it is found that using only binary solubility data and ignoring the impact of chemically inert species on solubility will lead to the estimate of composition‐dependent reactivity ratio pairs.

Ethylene/1‐Hexene Copolymerization Kinetics and Microstructure of Copolymers Made with a Supported Metallocene Catalyst

AbstractEthylene/1‐olefin copolymers made with supported metallocenes in slurry or gas‐phase polymerization are often less homogeneous than those made with the same unsupported metallocene in solution polymerization. In particular, their molecular weight distributions are broader, having polydispersities higher than two, and sometimes their chemical composition distributions may even be bimodal. In our previous publication, we developed a mathematical model to describe the polymerization kinetics and polymer microstructure of ethylene homopolymers made with a supported metallocene catalyst. In this article, we extended that model to also cover the copolymerization of ethylene and 1‐hexene with the same supported catalyst. The copolymerizations are performed in parallel semibatch reactors using a metallocene catalyst supported on an inorganic porous carrier. 1‐Hexene concentration and polymerization time are the factors changed to investigate this system. Modeling results show that, as for the ethylene homopolymerization case, a three‐site model is needed to describe the molecular weight distributions of the copolymers, but their chemical compositions can be described with a single set of reactivity ratios. A single set of parameters is also enough to describe the copolymerization kinetics with this supported catalyst. A new method is also developed and tested to estimate reactivity ratios under composition drift in this article.

A diosgenin-containing water-soluble polymer as model for the controlled release of brassinosteroids

Novel water-soluble polymers containing diosgenin moieties have been synthesized in order to study the proper conditions for the design of phytoactive formulations carrying brassinosteroid analogs. Samples are obtained by radical copolymerization between acrylamide (AM) and diosgenin monomaleate (DMM) at different initial feed compositions. The resulting copolymers present variable steroidal molar fractions ranging from 0.01 to 0.12, as calculated by means of 1H NMR spectroscopy. Mao–Huglin method is employed for the estimation of monomer reactivity ratios, which renders 16.884 and 0.0024 for AM and DMM, respectively. Surface tension measurements evidence that copolymers with steroidal content below 0.1 exhibit aqueous stability with micelle formation. Controlled release of diosgenin moieties is achieved through alkaline hydrolysis of the monomaleate ester and followed by conductometry. The process displays second order kinetics with a suitable rate constant value for agricultural applications (0.061 L mol−1 s−1). The proposed formulation can also be extended for other applications of steroidal compounds.

Ketene-based aliphatic polyketones obtained by cationic copolymerization of dimethylketene (DMK) with diethylketene (DEK) or diphenylketene (DPK): synthesis, characterization and reactivity ratio estimation

Cationic copolymerizations of different ketoketenes are conducted to explore the structure and properties of the afforded copolymers. Diethylketene (DEK) and diphenylketene (DPK) are both copolymerized with dimethylketene (DMK), via a cationic mechanism using the mixture AlCl3 / (CH3)3CCl as initiator. The experiments confirmed that two series of polyketones, containing a main DMK chain comprising few DEK or DPK units, are successfully obtained. The reactivity ratios are calculated. The structures and thermal performances of the obtained copolymers are discussed. An interesting DMK / DEK copolymer with a broad processing window was obtained (Tm = 164 °C, $${T}_{d}^{5\%}$$ = 259 °C).

The solution copolymerization of styrene and maleic anhydride in a continuous stirred tank reactor and its theoretical modelling

The synthesis of copolymers with a narrow chemical composition distribution (CCD) often requires a technological solution to overcome composition drift. Among the possible solutions, polymerization in a continuous stirred tank reactor (CSTR) is one of the most elegant. During steady state operation, the CCD is only determined by the statistical nature of the copolymerization without any broadening as typically observed in batch reactions. In this contribution, the mathematical description of the copolymerization of styrene and maleic anhydride in a CSTR is provided and experimental data are used to estimate reactivity ratios as well as to describe the copolymer composition as a function of steady state conversion.

Estimation of Reactivity Ratios in the Copolymerization of Styrene and VeoVa‐10

AbstractThe styrene and vinyl neodecanoate copolymerization system shows a strong tendency to form two separate homopolymers. In order to improve the feeding strategies and hence the copolymer uniformity, it is necessary to know the reactivity ratios between these monomers. The error‐in‐variables‐method (EVM) is the most recommended mathematical procedure for estimating these parameters. Experiments on free‐radical copolymerization in solution in sealed ampoules are carried out to provide data for the conversion (via gravimetry) and fractional monomer compositions (via Fourier transform mid‐infrared (mid‐FT‐IR) spectroscopy). These data allow estimation of the reactivity ratios. EVM appropriately takes into account the experimental errors in the data and allows determination of the reactivity ratio values by the Mayo–Lewis model (r1 = 28.60 and r2 = 1.23). The convergence and robustness of the method decrease considerably with a larger discrepancy between the reactivity values.

Fully Degradable Thioester-Functional Homo- and Alternating Copolymers Prepared through Thiocarbonyl Addition–Ring-Opening RAFT Radical Polymerization

The radical ring-opening polymerization (RROP) of thionolactones provides access to thioester backbone-functional copolymers but has, to date, only been demonstrated on acrylic copolymers. Herein, the thionolactone dibenzo[c,e]oxepane-5-thione (DOT) was subjected to azobisisobutyronitrile (AIBN)-initiated free-radical homopolymerization, which produced a thioester-functional homopolymer with a glass-transition temperature of 95 °C and the ability to degrade exclusively into predetermined small molecules. However, the homopolymerization was impractically slow and precluded the introduction of functionality. Conversely, the reversible addition–fragmentation chain-transfer (RAFT)-mediated copolymerization of DOT with N-methylmaleimide (MeMI), N-phenylmaleimide (PhMI), and N-2,3,4,5,6-pentafluorophenylmaleimide (PFPMI) rapidly produced well-defined copolymers with the tendency to form alternating sequences increasing in the order MeMI ≪ PhMI < PFPMI, with estimated reactivity ratios of rDOT = 0.198 and rPFPMI = 0.0078 for the latter system. Interestingly, defects in the alternating structure were more likely caused by (degradable) DOT–DOT sequences rather than (nondegradable) MI–MI sequences, which was confirmed through the paper spray mass spectrometric analysis of the products from aminolytic degradation. Upon the aminolysis of backbone thioesters, maleimide repeating units were ring-opened, forming bisamide structures. Conversely, copolymer degradation through a thiolate did not result in imide substitution but nucleophilic para-fluoro substitution on PFPMI comonomer units, indicating the ability of DOT–MI copolymers to degrade under different conditions and to form differently functional products. The RROP of thionolactones has distinct advantages over the RROP of cyclic ketene acetals and is anticipated to find use in the development of well-defined degradable polymer materials.

Making the Most of Parameter Estimation: Terpolymerization Troubleshooting Tips

Multi-component polymers can provide many advantages over their homopolymer counterparts. Terpolymers are formed from the combination of three unique monomers, thus creating a new material that will exhibit desirable properties based on all three of the original comonomers. To ensure that all three comonomers are incorporated (and to understand and/or predict the degree of incorporation of each comonomer), accurate reactivity ratios are vital. In this study, five terpolymerization studies from the literature are revisited and the ‘ternary’ reactivity ratios are re-estimated. Some recent studies have shown that binary reactivity ratios (that is, from the related copolymer systems) do not always apply to ternary systems. In other reports, binary reactivity ratios are in good agreement with terpolymer data. This investigation allows for the comparison between previously determined binary reactivity ratios and newly estimated ‘ternary’ reactivity ratios for several systems. In some of the case studies presented herein, reactivity ratio estimation directly from terpolymerization data is limited by composition restrictions or ill-conditioned systems. In other cases, we observe similar or improved prediction performance (for ternary systems) when ‘ternary’ reactivity ratios are estimated directly from terpolymerization data (compared to the traditionally used binary reactivity ratios). In order to demonstrate the advantages and challenges associated with ‘ternary’ reactivity ratio estimation, five case studies are presented (with examples and counter-examples) and troubleshooting suggestions are provided to inform future work.

The role of pH, ionic strength and monomer concentration on the terpolymerization of 2-acrylamido-2-methylpropane sulfonic acid, acrylamide and acrylic acid

The current study examines the effects of important factors (namely, pH, ionic strength and monomer concentration) on the terpolymerization of 2-acrylamido-2-methylpropane sulfonic acid (AMPS), acrylamide (AAm) and acrylic acid (AAc). A good understanding of how these factor levels affect terpolymerization reactivity ratios, and terpolymer composition, microstructure and molecular weight paves the way for the synthesis of custom-made polymers for specific applications. For the range of conditions studied, ionic strength has the greatest influence on reactivity ratios; results indicate that cross-over behavior exists for AMPS-based reactivity ratios. No clear correlation is observed between pH and reactivity ratio estimates (for 5 ≤ pH ≤ 9), but parameter estimation results suggest that the incorporation of acidic comonomers (AMPS and AAc) is affected by pH within this range. Finally, monomer concentration has a dominant impact on molecular weight averages, even when other factors are varied.

Solvent Effects on Radical Copolymerization Kinetics of 2-Hydroxyethyl Methacrylate and Butyl Methacrylate.

2-Hydroxyethyl methacrylate (HEMA) is an important component of many acrylic resins used in coatings formulations, as the functionality ensures that the chains participate in the cross-linking reactions required to form the final product. Hence, the knowledge of their radical copolymerization kinetic coefficients is vital for both process and recipe improvements. The pulsed laser polymerization (PLP) technique is paired with size exclusion chromatography (SEC) and nuclear magnetic resonance (NMR) to provide kinetic coefficients for the copolymerization of HEMA with butyl methacrylate (BMA) in various solvents. The choice of solvent has a significant impact on both copolymer composition and on the composition-averaged propagation rate coefficient (kp,cop). Compared to the bulk system, both n-butanol and dimethylformamide reduce the relative reactivity of HEMA during copolymerization, while xylene as a solvent enhances HEMA reactivity. The magnitude of the solvent effect varies with monomer concentration, as shown by a systematic study of monomer/solvent mixtures containing 50 vol%, 20 vol%, and 10 vol% monomer. The observed behavior is related to the influence of hydrogen bonding on monomer reactivity, with the experimental results fit using the terminal model of radical copolymerization to provide estimates of reactivity ratios and kp,HEMA.

Bulk Free‐Radical Co‐ and Terpolymerization of n‐Butyl Acrylate/2‐Ethylhexyl Acrylate/Methyl Methacrylate

Abstractn‐Butyl acrylate (BA), 2‐ethylhexyl acrylate (EHA), and methyl methacrylate (MMA) are commonly used monomers in pressure‐sensitive adhesive formulations. The bulk free‐radical copolymerizations of BA/EHA, MMA/EHA, and BA/MMA are studied at 60 °C to demonstrate the use of copolymer reactivity ratios for the prediction of BA/MMA/EHA terpolymer composition. The reactivity ratios for BA/EHA and MMA/EHA copolymer systems are determined using low conversion experiments; BA/MMA reactivity ratios are already known from the literature. The reactivity ratio estimates for the BA/EHA system are r BA = 0.994 and r EHA = 1.621 and the estimates for MMA/EHA are r MMA = 1.496 and r EHA = 0.315. High conversion experiments are conducted to validate the reactivity ratios. The copolymer reactivity ratios are shown to predict terpolymer composition of high conversion BA/MMA/EHA experiments.

Synthesis and characterization of hydrolytically degradable poly(N-vinylcaprolactam) copolymers with in-chain ester groups

Poly(N-vinylcaprolactam) (PNVCL) is attracting increasing interest as a polymer for biomedical application. However, it is not biodegradable, which is an important drawback for such applications. The present paper describes the synthesis and characterization of novel thermosensitive PNVCL copolymers able to hydrolytically degrade, which were prepared by the RAFT/MADIX copolymerization of NVCL and 5,6-benzo-2-methylene-1,3-dioxepane (BMDO). The RAFT/MADIX polymerization process displayed a moderate degree of control under the experimental conditions employed as proven by GPC measurements. The formation of the NVCL-BMDO copolymers was demonstrated by 1H NMR analyses which showed the presence of the in-chain ester groups resulted from the ring-opening polymerization of BMDO. The BMDO content of the copolymers was much lower than in the feed, indicating a higher reactivity of NVCL, which was confirmed through the estimation of the monomer reactivity ratios by applying the non-linear least squares method to fit the experimental results to the Lowry-Meyer integrated form of the Mayo-Lewis copolymer composition equation. The glass transition temperature of the copolymers diminished with the BMDO unit concentration within the chain. The phase transition temperature of the copolymers in 0.5-wt% aqueous solution decreased with the BMDO content as proven by transmittance measurements, in agreement with the increasing hydrophobic character. The degradability of the copolymers was demonstrated by the hydrolysis of the in-chain ester groups in 1-N KOH solution. The degraded polymer displayed a higher phase transition temperature than the original polymer, as expected. The results described within this paper may find applications for the synthesis of new biomaterials.

A kinetic study, thermal analysis and kinetic modeling on homo and copolymerization of 2-(N,N-diethylamino)ethyl methacrylate and PEGMA

Copolymers containing 2-(N,N-diethylamino)ethyl methacrylate (DEAEMA) and poly(ethylene glycol) methyl ether methacrylate with Mn = 500 g mol−1 (PEGMA500) are one of the most promising combinations of smart polymers with biocompatibility character for uses in medical applications. The homo and the copolymerization processes of these polymers have been studied via free radical polymerization in ethanol, resulting in first-order kinetics with respect to monomer in the homopolymerization for DEAEMA, and PEGMA500 when a high ratio initiator:monomer (≥1:100) is used. Additionally, the overall polymerization rate is ½ – order with respect to initiator concentration for DEAEMA, but it is not valid for the PEGMA500 polymerization. The value of kp/kt1/2 is estimated to be 0.39 L1/2 mol−1/2 s−1/2 for DEAEMA at 70 °C, while those values corresponding to PEGMA500 homopolymerization show a strong dependency of kt on the length of growing radicals. The estimated reactivity ratios (rDEAEMA = 0.81 ± 0.20 and rPEGMA500 = 0.73 ± 0.18 estimated by Tidwell and Mortimer method) predict the formation of copolymer with nonideal random sequence and an azeotropic composition. Thermal properties were also analyzed, the glass-transition temperature (Tg) values of poli(DEAEMA-co-PEGMA500) copolymers were measured and compared with Gibbs-Di Marzio equation. The experiments were well represented by a basic copolymerization model, considering the terminal model.

Binary vs. ternary reactivity ratios: Appropriate estimation procedures with terpolymerization data

There is a widely accepted analogy between copolymerization and terpolymerization mechanisms that has allowed researchers to use reactivity ratios obtained for binary pairs (from copolymerization experiments) in models dealing with terpolymerizations. However, binary reactivity ratios are not always applicable to terpolymerization systems; using the binary-ternary analogy (even as an approximation) requires making considerable assumptions about the system. When binary reactivity ratios are used to describe ternary systems, the consequences may include substantial differences in reactivity ratio estimates, poor composition prediction performance, and incorrect determination of product (terpolymer) characteristics. Experimental results and reactivity ratio estimation (via the error-in-variables-model) for the terpolymerization of 2-acrylamido-2-methylpropane sulfonic acid (AMPS), acrylamide (AAm) and acrylic acid (AAc) (and associated copolymers) are compared, all other conditions being equal.

Estimation of Reactivity Ratios in the RAFT Copolymerization of Styrene and Glycidyl Methacrylate

AbstractThe bulk reversible addition‐fragmentation chain transfer (RAFT) copolymerization of glycidyl methacrylate (GMA) and styrene (S) at several GMA molar feed fractions in the presence of 2‐cyano isopropyl dodecyl trithiocarbonate as RAFT agent and 1,10‐azobis(cyclohexane carbonitrile) as initiator is reported. The reaction conditions are similar to those used in the industrial production of crystal and high‐impact polystyrene by free radical polymerization with the purpose of synthesizing well‐defined copolymers in current industrial processes with only minor changes. Reactivity ratios calculated with linear Kelen–Tüdos, extended Kelen–Tüdos, and nonlinear regression (error in all variables) methods are reported. The results obtained suggest that the RAFT process modifies copolymer composition development. Increased preference for the monomer with the higher reactivity ratio is observed.

Computational Package for Copolymerization Reactivity Ratio Estimation: Improved Access to the Error-in-Variables-Model

The error-in-variables-model (EVM) is the most statistically correct non-linear parameter estimation technique for reactivity ratio estimation. However, many polymer researchers are unaware of the advantages of EVM and therefore still choose to use rather erroneous or approximate methods. The procedure is straightforward but it is often avoided because it is seen as mathematically and computationally intensive. Therefore, the goal of this work is to make EVM more accessible to all researchers through a series of focused case studies. All analyses employ a MATLAB-based computational package for copolymerization reactivity ratio estimation. The basis of the package is previous work in our group over many years. This version is an improvement, as it ensures wider compatibility and enhanced flexibility with respect to copolymerization parameter estimation scenarios that can be considered.

Parameter Estimation for an Inverse Nonlinear Stochastic Problem: Reactivity Ratio Studies in Copolymerization

A generalized polynomial chaos (gPC)‐based methodology is developed to estimate the reactivity ratio in copolymerization, where the reactivity ratio is assumed to be stochastic unknown and determined by comparing model predictions with limited experimental data. The estimation step is formulated as a stochastic inverse problem of finding the distributional stochastic reactivity ratio parameters with a maximum likelihood function. The results show that the gPC‐based reactivity ratio estimation is efficient and powerful, since it simultaneously provides the best estimates and their corresponding variances. Beyond achieving accurate estimation results, it is shown that the computational cost of the gPC‐based methodology is significantly lower than Markov chain Monte Carlo simulations, thus demonstrating the potential of the gPC method for dealing with other more complicated nonlinear problems. image

AMPS/AAm/AAc Terpolymerization: Experimental Verification of the EVM Framework for Ternary Reactivity Ratio Estimation

The complete error-in-variables-model (EVM) framework, consisting of both design of experiments and parameter estimation stages, is applied to the terpolymerization of 2-acrylamido-2-methylpropane sulfonic acid (AMPS, M1), acrylamide (AAm, M2) and acrylic acid (AAc, M3). This water-soluble terpolymer has potential for applications in enhanced oil recovery, but the associated terpolymerization kinetic characteristics are largely unstudied. In the current paper, EVM is used to design optimal experiments (for the first time in the literature), and reactivity ratios are subsequently estimated based on both low and medium-high conversion data. The results from the medium-high conversion data are more precise than those from the low conversion data, and are therefore used next to predict the terpolymer composition trajectory over the full course of conversion. Good agreement is seen between experimental data and model predictions, which confirms the accuracy of the newly determined ternary reactivity ratios: r12 = 0.66, r21 = 0.82, r13 = 0.82, r31 = 0.61, r23 = 1.61, r32 = 0.25.