Determination Of Reactivity Ratios Research Articles

Determination of Reactivity Ratios of N-butyl Acrylate/methyl Methacrylate Copolymerization by NMR Spectroscopy

In this study, the reactivity ratios of n-butyl acrylate (BA) and methyl methacrylate (MMA) were investigated. The copolymerization reactions were performed in toluene at 70 oC, using azobisisobutyronitrile as the initiator. The composition of the initial monomer mixture and copolymers was easily determined with the help of proton nuclear magnetic resonance (1H-NMR) spectroscopy. The molar fractions of BA and MMA in the feed were varied to apply the linear methods of Fineman–Ross and Kelen - Tudos. The calculation gave the reactivity ratios and . The computed copolymer composition was relatively close to the real copolymers obtained, with a 5% deviation.

Accurate Determination of Reactivity Ratios for Copolymerization Reactions with Reversible Propagation Mechanisms

Accurate Determination of Reactivity Ratios for Copolymerization Reactions with Reversible Propagation Mechanisms

Quasi-alternating copolymerization of oxiranes driven by a benign acetate-based catalyst

Alternating copolymers are distinctly unique in comparison with other copolymers. Herein, an in-depth investigation of the oxyanionic ring-opening copolymerization of propylene oxide (PO) and allyl glycidyl ether (AGE) from benzyl alcohol (BnOH) activated with potassium acetate (KOAc) complexed by 18-crown-6 ether (18C6) is described. We demonstrate that the 18C6/KOAc complex is an efficient and benign catalytic system to promote copolymerization of both oxirane monomers, leading to well-defined polyethers with varied comonomer content and low dispersity values (ƉM < 1.20). Kinetic analysis confirmed the controlled nature of the (co)polymerization process, and the determination of reactivity ratios revealed a quasi-alternating copolymerization profile, according to the Fineman-Ross method. The comparison between the quasi-alternating-type PO/AGE copolymerization and block or gradient copolymerization revealed significant differences, to confirm the different sequence incorporation in the different topological copolymers. These results highlight the great potential of 18C6/KOAc-mediated copolymerization process for the controlled sythesis of a series of copolymer topologies.

Machine learning approach to polymer reaction engineering: Determining monomers reactivity ratios

In copolymerization, the monomers' reactivity ratios play an important role in shaping the final copolymer properties. Thus, the knowledge of reactivity ratio is essential to the polymer reaction engineering. However, the experimental methods of determining reactivity ratios are laborious and require many repetitions and testing at different compositions. Therefore, computational methods for determining the reactivity ratios based on the chemical structures of the reactants have attracted significant attention. Here, we demonstrate how machine learning enables the prediction of comonomers reactivity ratios based on the molecular structure of monomers. We combined multi-task learning, multi-inputs, and one of the state-of-the-art machine learning model – Graph Attention Network – to build a model capable of predicting reactivity ratios based on the monomers’ chemical structures. We found that the interpretable characteristics of Multi-Input-Multi-Output Graph Attention Network, along with its capability to learn chemical features facilitates the accurate prediction of the reactivity ratios. Such a predictive tool can be used in combination with macroscopic kinetic models to design new copolymers.

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.

In Situ Kinetics Reveal the Influence of Solvents and Monomer Structure on the Anionic Ring‐Opening Copolymerization of Epoxides

AbstractIn‐depth understanding of copolymerization kinetics and the resulting polymer microstructure is crucial for the design of materials with well‐defined properties. Further, insights regarding the impact of solvents on copolymerization kinetics allows for precisely tuned materials. In this regard, in situ 1H NMR spectroscopy enables precise monitoring of the living anionic ring‐opening copolymerization (AROP) of ethylene oxide (EO) with the glycidyl ethers allyl glycidyl ether (AGE) and ethoxy vinyl glycidyl ether (EVGE), respectively. Determination of reactivity ratios reveals slightly higher reactivity of both glycidyl ethers compared to EO, emphasizing a pronounced counterion chelation effect by glycidyl ethers in AROP. Implementation of density functional theory (DFT) calculations further illustrates the complexation capability of ether‐containing side groups in glycidyl ethers, in analogy to crown ethers (“crown ether effect”). Investigation of the copolymerization in i) THF‐d8 and ii) DMSO‐d6 shows an increasing disparity of reactivity ratios for both glycidyl ethers compared to EO, clearly related to decreasing solvent polarity.

Determination of reactivity ratios for acrylic acid and its dimer from classical parameter estimation and Bayesian approach

AbstractThe reactivity ratios of acrylic acid (AA, M1) and its dimer β‐acroyloxypropionic acid (diAA, M2) are determined from cumulative copolymerization data by two different methods: classical parameter estimation (PE) by minimizing the objective function and a Bayesian analysis. Classical PE gives and at the minimum of the residual. From the Bayesian analysis, the probability distribution of the parameter sets is obtained, revealing the existence of parameter sets with rather the same probability. The influence of the number of data and the size of the measurement error are discussed.

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.

Kinetic analysis of continuous reaction data for RAFT and free radical copolymerization with acrylic and styrenic monomers

Free radical (FR) and Reversible Addition Fragmentation Chain Transfer (RAFT) copolymerization rates for styrenic monomers in bulk and aqueous reactions were accelerated by acrylic comonomers, whose own rates were both delayed and decreased. The effect was found with styrenics as low as 0.6% by mole, and is directly observable from Automatic Continuous Online Monitoring of Polymerization reactions (ACOMP) data. Rapid radical transfer from acrylic to styrenic comonomer, through lower energy radical resonance stabilization in styrenics, was the suspected cause. FR and RAFT rates were equal, suggesting that FR termination controlled radical concentrations and rates. Despite strongly changing concentrations of initiator and comonomer radicals during reactions, the Quasi-Steady-State Approximation was demonstrated to hold. While rates were identical, molecular weights showed the characteristic increase with conversion for RAFT and decrease for FR. A new, generalized method for reactivity ratio determination was found and acceleration/deceleration behavior was consistently interpreted within a penultimate model.

Effect of anethole on the copolymerization of vinyl monomers

Copolymerization behavior of Anethole with common vinyl monomers, determination of reactivity ratios via nonlinear least square method and the effect of Anethole on molecular weight and branching of copolymers produced via batch and semi-batch processes were reported.

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

Bulk Organocatalytic Synthetic Access to Statistical Copolyesters from l-Lactide and ε-Caprolactone Using Benzoic Acid.

The development of synthetic strategies to produce statistical copolymers based on l-lactide (l-LA) and ε-caprolactone (CL), denoted as P(LA- stat-CL), remains highly challenging in polymer chemistry. This is due to the differing reactivity of the two monomers during their ring-opening copolymerization (ROcP). Yet, P(LA- stat-CL) materials are highly sought after as they combine the properties of both polylactide (PLA) and poly(ε-caprolactone) (PCL). Here, benzoic acid (BA), a naturally occurring, cheap, readily recyclable, and thermally stable weak acid, is shown to trigger the organocatalyzed ring-opening copolymerization (OROcP) of l-LA and CL under solvent-free conditions at 155 °C, in presence of various alcohols as initiators, with good control over molar masses and dispersities (1.11 < Đ < 1.35) of the resulting copolyesters. Various compositions can be achieved, and the formation of statistical compounds is shown through characterization by 1H, 13C, and diffusion ordered spectroscopy NMR spectroscopies and by differential scanning calorimetry, as well as through the determination of reactivity ratios ( rLA = 0.86, rCL = 0.86), using the visualization of the sum of squared residuals space method. Furthermore, this BA-OROcP process can be exploited to access metal-free PLA- b-P(LA- stat-CL)- b-PLA triblock copolymers, using a diol as an initiator. Finally, residual traces of BA remaining in P(LA- stat-CL) copolymers (<0.125 mol %) do not show any cytotoxicity toward hepatocyte-like HepaRG cells, demonstrating the safety of this organic catalyst.

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...

The poly(propylene oxide-co-ethylene oxide) gradient is controlled by the polymerization method: determination of reactivity ratios by direct comparison of different copolymerization models

An investigation of the copolymerization of EO and PO by in situ1H NMR spectroscopy reveals striking differences in the monomer gradient, depending on the polymerization method.

Determination of the Radical Reactivity Ratios of 2-(N-Ethylperfluorooctanesulfonamido)ethyl Acrylate and Methacrylate in Copolymerizations with N,N-Dimethylacrylamide by in Situ 1H NMR Analysis As Established for Styrene–Methyl Methacrylate Copolymerizations

A model system of styrene (St) and methyl methacrylate (MMA) was copolymerized in an NMR tube at 60 °C using 2,2′-azobis(isobutyronitrile) as the initiator and pyridazine as an internal standard to optimize an in situ 1H NMR spectroscopic method for determining reactivity ratios by generating data at hundreds of instantaneous comonomer compositions (244 data points from 8 to 91 mol % St) starting with only nine initial comonomer compositions. The radical reactivity ratios of styrene (rSt = 0.697 ± 0.010) and methyl methacrylate (rMMA = 0.491 ± 0.007) were determined by nonlinear least-squares fitting of a Mayo–Lewis plot of the instantaneous copolymer composition as a function of the comonomer feed composition using the terminal model and MINITAB statistical software, in which the copolymer composition was calculated by assuming that all comonomer consumed was converted to copolymer without side reactions; the results were similar to accepted literature values for the terminal and implicit penultimate models. After correcting for changes in the “lock” value at the initial stages of the copolymerization (because of solids formed in the sealed NMR tube), the same technique was used to determine the reactivity ratios of 2-(N-ethylperfluorooctanesulfonamido)ethyl acrylate (FOSA; rFOSA = 1.624 ± 0.048) and 2-(N-ethylperfluorooctanesulfonamido)ethyl methacrylate (FOSM; rFOSM = 2.876 ± 0.083) in their radical copolymerizations with N,N-dimethylacrylamide (DMA; rDMA = 1.126 ± 0.031 with FOSA; rDMA = 0.859 ± 0.026 with FOSM).

Conventional Oxyanionic versus Monomer-Activated Anionic Copolymerization of Ethylene Oxide with Glycidyl Ethers: Striking Differences in Reactivity Ratios.

Detailed understanding of the monomer distribution in copolymers is essential to tailor their properties. For the first time, we have been able to utilize in situ 1H NMR spectroscopy to monitor the monomer-activated anionic ring opening copolymerization (AROP) of ethylene oxide (EO) with a glycidyl ether comonomer, namely, ethoxy ethyl glycidyl ether (EEGE). We determine reactivity ratios and draw a direct comparison to conventional oxyanionic ROP. Surprisingly, the respective monomer reactivities differ strongly between the different types of AROP. Under conventional oxyanionic conditions similar monomer reactivities of EO and EEGE are observed, leading to random structures (rEO = 1.05 ± 0.02, rEEGE = 0.94 ± 0.02). Addition of a cation complexing agent (18-crown-6) showed no influence on the relative reactivity of EO and EEGE (rEO = rEEGE = 1.00 ± 0.02). In striking contrast, monomer-activated AROP produces very different monomer reactivities, affording strongly tapered copolymer structures (rEO = 8.00 ± 0.16, rEEGE = 0.125 ± 0.003). These results highlight the importance of understanding reactivity ratios of comonomer pairs under certain polymerization conditions, at the same time demonstrating the ability to generate both random and strongly tapered P(EO-co-EEGE) polyethers by simple one-pot statistical anionic copolymerization. These observations may be generally valid for the copolymerization of EO and glycidyl ethers.

Determination of reactivity ratios for the copolymerization of poly(acrylic acid‐co‐itaconic acid)

ABSTRACTMonomer reactivity ratios are important parameters used in copolymerization kinetics to predict the rate of polymerization, copolymer composition and monomer sequence length, and by extension, molecular weight and distribution of the final product. Batch aqueous solution copolymerizations of acrylic acid (AA) and itaconic acid (IA) are performed at various feed compositions. Polymerizations are categorized into low (&lt;11 wt %) conversion and higher (&lt; 30 wt %) conversion data sets for analysis. Due to the limited solubility of IA in the reaction mixture, the feed composition of IA in all polymerizations is constrained to lower than 25 mol %. Conversion is determined by gravimetric methods, and copolymer composition via 1H‐NMR spectroscopy. All data are analyzed using the error‐in‐variables model (EVM) method. Two analyses are used, one with the EVM approach and another with a novel Direct Numerical Integration (DNI) coupled with the EVM method. The DNI/EVM approach yields values of rAA = 0.36 and rIA = 1.62 for the reactivity ratios. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016, 133, 44014.

Determination of Reactivity Ratios of Copolymerization of Acrylamide (Am) and Methacryloxyethyltrimethyl Ammonium Chloride (Dmc) with Ultraviolet Initiation, and Their Sequence Length Distribution

The copolymer P(AM-DMC), one kind of cationic polyacrylamide, was synthesized by using acrylamide (AM) and methacryloxyethyltrimethyl ammonium chloride (DMC) as monomers with ultraviolet initiation. The copolymer was characterized by Fourier transform infrared spectroscopy. The composition of the copolymer was determined from the chlorine content by silver nitrate titration. The effects of monomer feed ratio and conversion on the composition of copolymer were discussed. Reactivity ratios were determined by the Fineman-Ross, Kelen-Tudos and Yezrielev-Brokhina-Roskin methods, indicating that their positive order calculation results were very different with those of reverse order, when the reactivity ratios were determined by Fineman-Ross. However, their positive order and reverse order calculation results were similar when the reactivity ratios were determined by the Kelen-Tudos and Yezrielev-Brokhina-Roskin methods. Therefore, the reactivity ratios were determined using the average results of the Kelen-Tudos and Yezrielev-Brokhina-Roskin methods. The reactivity ratios of AM and DMC were 2.3398 and 0.2285, respectively. This result showed that the copolymerization of AM and DMC was a non-ideal random copolymerization. Furthermore, the content of AM segments decreased with the increase of AM feed content, but the content of DMC segments increased. Moreover, the sequence length distribution was irregular and narrow, because AM was prone to homopolymerization.

Syntheses, characterization, and hydrolytic degradation of P(ε‐caprolactone‐co‐δ‐valerolactone) copolymers: Influence of molecular weight

ABSTRACTBiodegradable poly(ε‐caprolactone‐co‐δ‐valerolactone) copolymers were synthesized and investigated to study their behavior in aqueous medium. The copolyesters were produced by ring opening polymerization between ε‐caprolactone (CL) and δ‐valerolactone (VL) in bulk at 140°C using tin(II) octoate as catalyst. They were characterized by using 1H NMR, size exclusion chromatography, differential scanning calorimetry, and MALDI TOF mass spectrometry. Reactivity ratio determination gave an insight on their microstructure. Hydration, hydrolytic degradation, and biocide release of P(CL‐VL) films with different molecular weights values were studied. A one‐order kinetic whose rate constant decreases with copolymer macromolecular weight was observed. Although the molecular weight decrease remained relatively weak after 8 months of immersion, a correlation between molecular weight and hydrolysis rate was shown by high performance liquid chromatography‐mass spectrometry. The ability of the P(CL‐VL) films to release active compounds dispersed in the films was studied by atomic absorption spectroscopy. The release behavior of all copolymers was identical with a zero‐order kinetic. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016, 133, 43007.

Simple and Accurate Determination of Reactivity Ratios Using a Nonterminal Model of Chain Copolymerization

We propose a new method for the determination of reactivity ratios based on a nonterminal model of copolymerization kinetics. Within the context of this model, we derive simple, reactivity-ratio-dependent expressions whose solution relies solely on monomer consumption information spanning the full range of conversion. Utilizing this method, reactivity ratios are obtained for the aluminum chelate-catalyzed copolymerization of phenyl glycidyl ether and allyl glycidyl ether (rPGE = 1.56 ± 0.01 and rAGE = 0.66 ± 0.03) with monomer consumption monitored by in situ 1H NMR spectroscopy. Additionally, this approach is applied to experimental data extracted from the literature for other copolymerization systems encompassing a range of monomer types (styrenics, isoprene, lactones, lactide, and other cyclic ethers) and polymerization type (anionic, coordination, and zwitterionic) to obtain reactivity ratios under the mechanistic assumption of nonterminal model copolymerization kinetics. We present the nonterminal mo...