Copolymerization Reactivity Ratios Research Articles

The Importance of the Knowledge of Errors in the Measurements in the Determination of Copolymer Reactivity Ratios from Composition Data

AbstractOften the errors in the measurement of copolymerizations are not accurately determined or included in the calculation of reactivity ratios. Some knowledge of the errors in the initial monomer ratio, conversion, and copolymer composition is however essential to obtain reliable (unbiased) reactivity ratios with a realistic uncertainty. It is shown that the errors serve a trifold purpose; they can serve as weighing factors in the fit, they can be compared with the fit residues to decide whether the chosen model is adequate for the data and they can be used to construct a realistic joint confidence interval for the reactivity ratios. The best approach is to have an estimate of the individual errors in the copolymer composition, either from a thorough error propagation exercise or from replicate measurements. With these errors, the χ2‐joint confidence intervals can then be constructed which gives a realistic estimate of the errors in the reactivity ratios. Utilizing the Errors in Variables Method (EVM) is correct and useful, but only if the individual errors in all the variables in each experiment are more or less known.

IUPAC recommended experimental methods and data evaluation procedures for the determination of radical copolymerization reactivity ratios from composition data

The IUPAC method uses monomer composition, conversion, and copolymer composition to find reactivity ratios. Shown the optimal reactivity ratios in red and a 95% Confidence Interval in blue.

Microflow system for controlled synthesis of ethylene-vinyl acetate copolymers: Continuous copolymerization and kinetic study

Ethylene content in ethylene–vinyl acetate copolymers (EVA) is a key factor that determines its further usage. While conventional batch reactor for EVA synthesis faces the problem of heterogeneous reaction environment and temperature control. A microflow system was designed to avoid these problems and facilitate the synthesis of EVA with controlled ethylene content. Continuous flow synthesis of EVA by solution free radical copolymerization was realized homogeneously based on this microflow system. 13C NMR spectra indicate that EVA obtained in microflow system has less ethylene concentrated sequence than EVA obtained in batch reactor. By operating the microflow system in a stop-flow method, we developed a simple kinetic model of copolymerization and measured the reactivity ratios of ethylene and vinyl acetate copolymerization in tert-butyl alcohol and dimethyl carbonate. The microflow system is demonstrated to be a powerful tool in kinetic and mechanism study and engineering application of copolymerization processes involving monomers which are gas phase under conventional condition.

Free‐radical propagation rate coefficients

AbstractThe pulsed laser polymerization‐size‐exclusion chromatography (PLP‐SEC) technique has become the International Union of Pure and Applied Chemistry (IUPAC)‐recommended method for the accurate determination of propagation rate coefficients, kp, for radical polymerization. The fundamental insight provided by Heuts, Gilbert, and Radom into the relevance of transition state dynamics allows for an adequate understanding of the dependence of kp on radical chain length, solvent environment, and monomer conversion. The associated entropic effects are particularly pronounced in aqueous solution, but are also found in less polar media and with non‐polar monomers. Moreover, these arguments are applicable towards the interpretation of copolymerization reactivity ratios. The addition of sodium hydroxide to aqueous solutions of (meth)acrylic acid yields partially and even fully ionized systems with clearly reduced kp, which indicates the action of repulsive forces between the equally charged monomer and radical species. Increasing the concentration of monomer as well as the addition of salts may reverse this effect and increase kp due to counterion activity.

In-situ 1H NMR measurements of reactivity ratios and thermal properties for copolymerization of N-vinylpyrrolidone and 1-vinyl-3-butylimidazolium bromide

In-situ 1H NMR was used to obtain the copolymerization reactivity ratios of n-vinylpyrrolidone (VP) and 3-butyl-1-vinylimidazolium bromide (BVIM[Br]) using D2O and V50 as solvent and initiator, respectively. The influence of the VP-BVIM[Br] monomer ratios was studied at 45, 50, and 55 °C using initial molar ratios of (30−70), (50−50), and (70−30), respectively. According to the monomer conversions, it was determined that electrostatic and thermodynamic effects controlled the reactions. As the reaction temperature increased, higher conversions were obtained, and in the VP-BVIM[Br] (70−30) ratio, the conversions were higher and close to 100 % at 50 and 55 °C. This result was attributed to the lower ionic strength in the initial reaction system (0.46 mol/L). The monomer reactivities were calculated using the Mao-Huglin method and it was found that for the (70−30) VP-BVIM[Br] molar ratio at 45, 50, and 55 °C, rVP=rBVIM[Br]=1, obtaining random copolymers. For the VP-BVIM[Br] (30−70) molar ratio at 45 °C, the reactivity of VP was higher than that of BVIM[Br], rVP= 2.1 > rBVIM[Br]= 0.7, and for the VP-BVIM[Br] (50−50) molar ratio at 50 and 55 °C, the reactivity of VP was lower than that of BVIM[Br], rVP= 0.5 < rBVIM[Br]= 1.1 and rVP= 1 < rBVIM[Br]= 1.5, respectively, obtaining a spontaneous gradient copolymer. The decomposition temperature of the copolymers depended on the initial molar ratio of the reaction mixture, finding that the higher the VP molar ratio, the higher the initial decomposition temperature (279 °C). Random copolymers reached higher Tg (174 °C) in comparison with those that featured a spontaneous gradient microstructure (152 °C).

Copolymerization Reactivity Ratio Inference: Determining Confidence Contours in Parameter Space via a Bayesian Hierarchical Approach

AbstractConfidence contours in parameter space are a helpful tool to compare and classify determined estimators. For more intricate parameter estimations of nonlinear nature or complex error structures, the procedure of determining confidence contours is a statistically complex task. For polymer chemists, such particular cases are encountered in determination of reactivity ratios in copolymerization. Hereby, determination of reactivity ratios in copolymerization requires nonlinear parameter estimation. Additionally, data may possess (possibly correlated) errors in both dependent and independent variables. A common approach for such nonlinear estimations is the error‐in‐variables model yielding statistically unbiased estimators. Regarding reactivity ratios, to date published procedures neglect the non‐Gaussian structure of the error estimates that is a consequence of the nonlinearity of the model. In this publication, this issue is addressed by employing a Bayesian hierarchical model, which correctly propagates the errors of all variables. The statistical procedure is discussed in chemist friendly language to encourage confident usage of the tool. The approach is based on a Python program requiring minimal installation effort. A detailed manual of the code is included in the appendix of this work, in an effort to make this procedure available to all interested polymer chemists.

An artificial neural network to predict reactivity ratios in radical copolymerization

An artificial neural network model is described which is capable of predicting reactivity ratios in radical copolymerization solely based on monomer chemical structures. It outperforms classical approaches, enabling prediction without kinetic data.

Synthesis and properties of surfactants for carbon nanotubes based on copolymers of 2-N-morpholinoethyl methacrylate with dodecyl methacrylate and styrene

The copolymerization reactivity ratios for 2-N-morpholinoethyl methacrylate (MEMA) with dodecyl methacrylate (DDMA) or styrene (ST) were estimated. The efficiency of the prepared polymers for dispersion of MWCNT in toluene was also studied. A wide range of copolymer compositions (all 10 mol% steps) were prepared using tert-butyl peroxy-2-ethylhexanoate (0.02 mol dm−3) as initiator isothermally (70 °C) to low conversions (< 10 wt%). In the case of DDMA/MEMA copolymerization, there is a slight tendency for both monomers to react more with MEMA. The reactivity ratios obtained are r(DDMA) = 0.86 and r(MEMA) = 1.05. The reactivity ratios for the copolymerization of ST/MEMA are both <1 and are r(ST) = 0.35 and r(MEMA) = 0.59, indicating a higher reactivity of each monomer with the other monomer. The addition of small amounts (10 mol%) of MEMA to DDMA homopolymer significantly increases its thermal stability (the temperature at 50 wt% loss is 46 °C higher). For ST/MEMA, the addition of MEMA gradually decreases the thermal stability (the temperature difference at 50 wt% loss between the homopolymers is 25 °C). The best dispersion of MWCNT in toluene is obtained with the ST/MEMA copolymer containing 42 mol% MEMA, as shown by UV–Vis measurements and visual inspections after the gravity test. The obtained results contribute to the further development of polymeric surfactants and stimuli-responsive polymers.

Using Triethylborane to Manipulate Reactivity Ratios in Epoxide-Anhydride Copolymerization: Application to the Synthesis of Polyethers with Degradable Ester Functions.

The anionic ring-opening copolymerization (ROCOP) of epoxides, namely of ethylene oxide (EO), with anhydrides (AH) generally produces strictly alternating copolymers. With triethylborane (TEB)-assisted ROCOP of EO with AH, statistical copolymers of high molar mass including ether and ester units could be obtained. In the presence of TEB, the reactivity ratio of EO (rEO), which is normally equal to 0 in its absence, could be progressively raised to values lower than 1 or higher than 1. Conditions were even found to obtain rEO equal or close to 1. Samples of P(EO-co-ester) with minimal compositional drift could be synthesized; upon basic degradation of their ester linkages, these samples afforded poly(ethylene oxide) (PEO) diol samples of narrow molar mass distribution. In other cases where rEO were lower or higher than 1, the PEO diol samples eventually isolated after degradation exhibited a broader distribution of molar masses because of the compositional drift of initial P(EO-co-ester) samples.

Impact of Macromonomer Molar Mass and Feed Composition on Branch Distributions in Model Graft Copolymerizations.

Graft polymers are useful in a versatile range of material applications. Understanding how changes to the grafted architecture, such as the grafting density (z), the side-chain degree of polymerization (Nsc), and the backbone degree of polymerization (Nbb), affect polymer properties is critical for accurately tuning material performance. For graft-through copolymerizations, changes to Nsc and z are controlled by the macromonomer degree of polymerization (NMM) and the initial fraction of the macromonomer in the feed (fMM0), respectively. We show that changes to these parameters can influence the copolymerization reactivity ratios and, in turn, impact the side-chain distribution along a graft polymer backbone. Poly((±)-lactide) macromonomers with NMM values as low as ca. 1 and as high as 72 were copolymerized with a small-molecule dimethyl ester norbornene comonomer over a range of fMM0 values (0.1 ≤ fMM0 ≤ 0.8) using ring-opening metathesis polymerization (ROMP). Monomer conversion was determined using 1H nuclear magnetic resonance spectroscopy, and the data were fit with terminal and nonterminal copolymerization models. The results from this work provide essential information for manipulating Nsc and z while maintaining synthetic control over the side-chain distribution for graft-through copolymerizations.

Determination of Reactivity Ratios from Binary Copolymerization Using the k-Nearest Neighbor Non-Parametric Regression.

This paper proposes a new method for calculating the monomer reactivity ratios for binary copolymerization based on the terminal model. The original optimization method involves a numerical integration algorithm and an optimization algorithm based on k-nearest neighbour non-parametric regression. The calculation method has been tested on simulated and experimental data sets, at low (<10%), medium (10–35%) and high conversions (>40%), yielding reactivity ratios in a good agreement with the usual methods such as intersection, Fineman–Ross, reverse Fineman–Ross, Kelen–Tüdös, extended Kelen–Tüdös and the error in variable method. The experimental data sets used in this comparative analysis are copolymerization of 2-(N-phthalimido) ethyl acrylate with 1-vinyl-2-pyrolidone for low conversion, copolymerization of isoprene with glycidyl methacrylate for medium conversion and copolymerization of N-isopropylacrylamide with N,N-dimethylacrylamide for high conversion. Also, the possibility to estimate experimental errors from a single experimental data set formed by n experimental data is shown.

Sustainable Myrcene-Based Elastomers via a Convenient Anionic Polymerization.

Soluble heterocomplexes consisting of sodium hydride in combination with trialkylaluminum derivatives have been used as anionic initiating systems at 100 °C in toluene for convenient homo-, co- and ter-polymerization of myrcene with styrene and isoprene. In this way it has been possible to obtain elastomeric materials in a wide range of compositions with interesting thermal profiles and different polymeric architectures by simply modulating the alimentation feed and the (monomers)/(initiator systems) ratio. Especially, a complete study of the myrcene-styrene copolymers (PMS) was carried out, highlighting their tapered microstructures with high molecular weights (up to 159.8 KDa) and a single glass transition temperature. For PMS copolymer reactivity ratios, rmyr = 0.12 ± 0.003 and rsty = 3.18 ± 0.65 and rmyr = 0.10 ± 0.004 and rsty = 3.32 ± 0.68 were determined according to the Kelen–Tudos (KT) and extended Kelen–Tudos (exKT) methods, respectively. Finally, this study showed an easy accessible approach for the production of various elastomers by anionic copolymerization of renewable terpenes, such as myrcene, with commodities.

Study on the monomer reactivity ratio and performance of EPEG-AA (ethylene-glycol monovinyl polyethylene glycol–acrylic acid) copolymerization system

EPEG (ethylene-glycol monovinyl polyethylene glycol)-AA (acrylic acid) copolymerization is a typical representative of free radical copolymerization for the preparation of PCs that has been discussed and used increasingly in recent years. The calculation of the reactivity ratio can be used for the analysis of the monomers reactivity, which is of great significance to the study of copolymerization process. In this paper, combined with GPC test results, the monomer reactivity ratios in EPEG-AA copolymerization were calculated with the linear (Fineman–Ross, YBR, Kelen–Tüdös) methods and the nonlinear least square method, and the uncertainty of the methods were calculated. In addition, it has been found that compared with the widely used IPEG (isobutylene polyethylene glycol)-AA copolymerization, the monomer activity of EPEG is higher and closer with AA, so the copolymerization efficiency should be higher. This problem has been verified by experimental results, and the unity of theory and experiment has been realized. At the same time, the experimental results show that the PCs prepared by EPEG macromonomers have better dispersion of cement paste. To sum up, EPEG macromonomer will be more widely used in the future.

Copolymerization of Styrene and Pentadecylphenylmethacrylate (PDPMA): Synthesis, Characterization, Thermomechanical and Adhesion Properties.

The copolymerization of styrene (St) with a bioderived monomer, pentadecylphenyl methacrylate (PDPMA), via atom transfer radical polymerization (ATRP) was studied in this work. The copolymerization reactivity ratio was calculated using the composition data obtained from 1H NMR spectroscopy, applying Kelen-Tudos and Finemann-Ross methods. The reactivity ratio of styrene (r1 = 0.93) and PDPMA (r2 = 0.05) suggested random copolymerization of the two monomers with alternation. The copolymerization conversion increased with increasing PDPMA concentration of the feed, upto 70 wt % PDPMA, but decreased thereafter. The molecular weight determined by gel permeation chromatography was lower than the theoretical values and the polydispersity increased from 1.32 to 2.19, with increasing PDPMA content in the feed. The influence of styrene content on the glass transition and thermal decomposition behavior of the copolymers was studied by differential scanning calorimetry (DSC) and thermogravimetric analysis, respectively. Morphological characterization by transmission electron microscopy (TEM) revealed a phase separated soft core-hard shell type structure. The complex viscosity and adhesion properties like peel strength and lap shear strength of the copolymer on different substrates increased with increasing styrene content.

Experimental methods and data evaluation procedures for the determination of radical copolymerization reactivity ratios

Article Experimental methods and data evaluation procedures for the determination of radical copolymerization reactivity ratios was published on January 1, 2020 in the journal Chemistry International (volume 42, issue 1).

Effect of Catalyst Type on the Copolymerization of Styrene/1-Hexene and Exploring of Their Structural and Thermal Properties

The effect of catalyst type on styrene/1-hexene copolymerization reactions was investigated. The copolymerization reactions were performed using conventional free radical polymerization, atom transfer radical polymerization (ATRP) and Ziegler-Natta polymerization methods. Copolymers containing different 1-hexene compositions were synthesized and characterized by 1H NMR, GPC and DSC methods. The monomer reactivity ratios for free radical copolymerization were calculated using linear methods and found to be r1 ~ 25 and r2 → 0 for styrene and 1-hexene, respectively. The increases of 1-hexene mole fraction in ATRP synthesized copolymers showed that CuCl/L promotes 1-hexene cross propagation significantly. Furthermore, 1-hexene cannot participate in self-propagation reaction. In the polymerization assisted by supported Ziegler-Natta catalyst, the conversion of the reaction was increased with mole fraction of 1-hexene in the feed, which indicated the higher reactivity of this monomer. Finally, the thermal properties of copolymers were studied by DSC.

Correction to Recommendation for Accurate Experimental Determination of Reactivity Ratios in Chain Copolymerization

Correction to Recommendation for Accurate Experimental Determination of Reactivity Ratios in Chain Copolymerization

Toward Biodegradable Chain-Growth Polymers and Polymer Particles: Re-Evaluation of Reactivity Ratios in Copolymerization of Vinyl Monomers with Cyclic Ketene Acetal Using Nonlinear Regression with Proper Error Analysis

Recycling and biodegradability of chain-growth polymers is an important and growing topic. Introducing ester bonds in polymers via cyclic ketene acetals (CKAs) is an interesting route to create (bi...

Recommendation for Accurate Experimental Determination of Reactivity Ratios in Chain Copolymerization

A set of copolymerization data at prescribed reactivity ratios was numerically generated and then fit using common methods of data analysis including the copolymer equation, Fineman–Ross, Kelen–Tud...

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.