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

Homopolymerization and copolymerization of N‐(o‐/m‐/p‐chlorophenyl) itaconimide with methyl methacrylate was carried out by taking varying mole fractions (0.1 to 0.5) of N‐aryl substituted itaconimide monomers in the initial feed using azobisisobutyronitrile as an initiator and tetrahydrofuran as the solvent. The copolymer composition was determined by 1H‐NMR spectroscopy using the ratio of proton resonance signal intensity attributed to OCH3 of MMA (δ = 3.5–3.8 ppm) and the aromatic protons (δ = 7.0–7.5 ppm) of N‐(o‐/m‐/p‐chlorophenyl) itaconimide. The comonomer reactivity ratios were determined using Kelen–Tüdos and nonlinear error in variable methods. The reactivity ratios obtained by nonlinear error in variable methods were r1 (PI) = 1.26/r2 (MMA) = 0.35; r1 (MI) = 1.21/r2 (MMA) = 0.34; and r1 (OI) = 0.78/r2 (MMA) = 0.34. The carbonyl carbon signals of MMA (M) as well as N‐aryl itaconimide (I) copolymers were used for the determination of the sequence distribution of M‐ and I‐centered triads. The sequence distribution of M‐ and I‐centered triads determined from 13C{1H}‐NMR spectra of the copolymers are in good agreement with the triad concentrations calculated using the Alfrey–Mayo statistical model and Monte Carlo simulation method. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 91: 2016–2027, 2004

Copolymers 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.

The determination of reactivity ratios is simplified by using an excess of one monomer (M1) at a time large enough that the copolymers will have a very small content of the other monomer (M2). In this case chain propagation takes place almost exclusively by addition to polymer radicals with a terminal M1‐unit (P) and monomer consumption by propagation of P may be neglected. One reactivity ratio (r1) is obtained from monomer conversions by means of a simple integrated equation which is valid up to high conversions. A calculation is proposed in order to account for the neglected propagation via P. The other reactivity ratio (r2) is obtained from copolymerizations with excess M2.As the new method uses an integrated form of the MAYO equation it permits the determination of monomer conversions directly by gas chromatography of unreacted monomers. Thus, if desired, analysis of copolymers can be avoided. The gas chromatographic method has been tested with the radical copolymerization of styrene and methyl methacrylate.In ternary and quaternary copolymerizations the new method offers particular advantages.

Sequence control is critical for tuning polymer properties in high-end applications, where reactivity ratios serve as key parameters for analyzing and regulating sequences. Nevertheless, traditional determination methods exhibit low experimental efficiency and are typically confined to two-component copolymerization. Here, we develop a machine learning platform, which leverages a novel design of "reactivity ratio fingerprints" (rFPs) to determine reactivity ratios in binary and ternary copolymerizations. Deep learning models trained on millions of rFPs enable highly efficient (millisecond-level) determination from sparse experimental data (random monomer structures, arbitrary reaction design). This approach demonstrates outstanding versatility to analyze reactivity ratios under diverse conditions (e.g., temperature, solvent). Notably, rFP-guided reaction design promotes on-demand sequence tailoring, compatible with a wide range of binary and ternary monomer combinations. Kinetic investigations and glass transition characterizations support the formation of varied sequence structures, facilitating the identification of binary and ternary azeotropic copolymerizations. This work not only unveils an attractive strategy for determining reactivity ratios but also offers a generalizable framework for sequencing complicated chain structures toward property engineering.

Copolymers of poly( n-alkyl acrylates): synthesis, characterization, and monomer reactivity ratios

Dimethyl meta-isopropenyl benzyl isocyanate (TMI®) is a bifunctional monomer with an unsaturation and an isocyanate group. Bulk copolymerizations of TMI with styrene, methyl methacrylate, and n-butyl acrylate were investigated. Polymerizations were carried out to low conversions in sealed test tubes at 70°C. The copolymer composition was determined using Fourier transform infrared (FTIR) spectroscopy. The data were analyzed using the terminal, as well as restricted penultimate, model of copolymerization. The method of Kelen-Tudos was used to calculate the reactivity ratios according to the terminal model. A nonlinear regression analysis was also carried out. Low reactivity ratio values for TMI were obtained for the copolymerizations with styrene and methyl methacrylate as a result of the inability of TMI to undergo homopolymerization. The value was higher for the copolymerization with n-butyl acrylate. Composition diagrams were generated, and the range of TMI concentration in the monomer charge for the preferential incorporation of TMI in the copolymer was identified. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 67: 559–568, 1998

The new copolymers from different feed compositions of glycidyl methacrylate (GMA) and tetrahydrofurfuryl acrylate (THFA) were synthesized using free radical polymerization in toluene at 70±1 °C using benzoyl peroxide (BPO) as initiator. The polymers were characterized by 1H NMR, 13C NMR and FTIR spectroscopic techniques. The polydispersities of the copolymers suggest a strong tendency for chain termination by disproportionation. The glass transition temperature of the copolymers increases with increase in GMA content. The thermal stability of the copolymers increases with increase in THFA content. The copolymer compositions were determined using 1H NMR analysis. Reactivity ratios for GMA and THFA as determined by the Mao-Huglin method were r1=0.379 and r2=0.266. The results showed that all these copolymerizations are strictly linear systems describable by the Mayo-Lewis equation based on the terminal model and that accurate reactivity ratio data can be obtained.

Copolymerization is a powerful tool for tuning the properties of synthetic polymers. In chain-growth polymerization, copolymer microstructure is controlled by the relative reactivity of comonomers, quantified by copolymer reactivity ratios. Yet, the complex macromolecular reactivity captured by reactivity ratios precludes the prediction of the resultant microstructures by intuition, and the established theory to understand reactivity ratios (i.e., Q-e scheme) has not been updated substantially since the development of quantum mechanics. Here, we combine modern computation, data science, and experimental validation to gain a detailed structure–reactivity understanding of the electronic, energetic, and steric parameters that govern comonomer reactivity. Using >450 reactivity ratios identified from primary literature sources, a combination of parametrization from density functional theory and data science methods identified discrete structure–reactivity relationships in free radical copolymerization. We demonstrate that the electronics of the radical species and the sterics of the monomers, neither of which were captured in the previous Q-e scheme, are pivotal to understanding the copolymerization reactivity. Experimentally measured reactivity ratios of a previously unstudied monomer combination validated the models, demonstrating the potential predictive power of this work to understand the comonomer sequence a priori. This work provides a framework to understand polymer microstructure from first-principles by relating specific and interpretable attributes of monomer structure to comonomer reactivity.

The copolymers of N-vinylcarbazole/methyl acrylate (V/M) of different compositions were prepared by solution polymerisation using 2,2’-Azobisisobutyronitrile (AIBN) as an initiator and their composition was determined from quantitative 13C{1H} NMR spectroscopy. Reactivity ratios for the comonomers were calculated using the Kelen–Tudos (KT) and non-linear error in variable methods (EVM). The complete spectral assignment of the overlapping 1H and 13C{1H} spectra of the copolymers were done with the help of Distortionless Enhancement by Polarization Transfer (DEPT), two dimensional heteronuclear single quantum correlation (HSQC) and total correlated spectroscopy (TOCSY). The assignments of various compositional sequences were done in the carbon resonance signals of the methoxy region of M unit, the methine region of both V and M units and the methylene region of both V and M units.

The copolymerization reactivity ratios for 2-ethoxyethyl methacrylate (EOEMA) with dodecyl methacrylate (DDMA) or styrene (ST) were estimated. Polymerization was performed by using tert-butyl peroxy-2-ethylhexanoate (0.01 mol dm−3) as initiator, isothermally (70 °C) to low conversions (< 10 wt.%) in a wide range of copolymer compositions (every 10 mol-% steps). For the DDMA/EOEMA copolymerization both monomers prefer to react with EOEMA: r (DDMA) = 0.82 and r (EOEMA) = 1.26 with r (DDMA) × r (EOEMA) = 1, which results in the random copolymerization. For the ST/EOEMA copolymerization reactivity ratios are r (ST) = 0.59 and r (EOEMA) = 0.49 indicating a higher reactivity with opposite monomer, while the alternation tendency is not highly pronounced. The probabilities for formations of dyad and triad monomer sequences in dependence on monomer compositions were calculated from the obtained reactivity ratios. With the share increase of ST or DDMA in copolymers surface properties changed from hydrophilic to hydrophobic. Glass transition temperature of copolymer increased with the increase of ST and decrease of DDMA. The molar mass distribution and thermal degradation of synthesized copolymers were also determined and discussed. The reactivity ratios enable optimization of copolymer properties for a given application as polyelectrolytes, drug delivery systems and multifunctional additives for improvement of rheological properties of lubricating oils.

Methacrylonitrile/methylmethacrylate (A/M) copolymers were prepared by bulk polymerization. The 13C DEPT-135 (distortionless enhancement by polarization transfer) spectrum was used to differentiate between the carbon resonance signals of methyl, methoxy, and methylene units in the copolymers (A/M). Comonomer reactivity ratios were determined using Kelen–Tudos and non-linear error in variable methods. 2D heteronuclear single quantum correlation (HSQC) and total correlated spectroscopy (TOCSY) spectra were used to resolve the complex 1H NMR spectrum.

The reactivity ratios for the copolymerization of a first‐generation dendronized monomer with styrene and different acrylates are determined. The obtained ratios as well as the copolymer compositions that can be expected are discussed in detail. The influence of the dendron on the polymerization potential of the monomer is estimated by comparing its reactivity to those of linear systems as well as using higher generations of the dendronized monomer. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013

The new acrylic monomer 4-benzyloxycarbonyl phenyl acrylate (BCPA) was synthesized and copolymerized with methyl methacrylate (MMA) in ethyl methyl ketone at 70±1°C using benzoyl peroxide as a free radical initiator. The copolymers were characterized by FT-IR, 1H-NMR and 13C-NMR spectroscopic techniques. The compositions of the copolymers were determined by 1H-NMR analysis. The reactivity ratios of the monomers were determined using the Fineman–Ross (r1=0.6085 and r2=1.7251), Kelen–Tüdös (r1=0.6085 and r2=1.7276), Ext. Kelen–Tüdös (r1=0.6083 and r2=1.7963) and nonlinear error-in-variables model methods (r1=0.6627 and r2=1.7858). The solubilities of the polymers were tested in various polar and non-polar solvents. The elemental analysis was determined by a Perkin–Elmer C–H analyzer. The molecular weights (M¯ w and M¯ n) of the copolymers were determined by gel permeation chromatography. Thermogravimetric analysis of the polymers reveals that the thermal stability of the copolymers decreases with an increase in the mole fraction of MMA in the copolymers. Glass transition temperature of the copolymers was found to increase with an increase in the mole fraction of BCPA in the copolymers.

On the determination of monomer reactivities in copolymerization

On the preparation of acrylic acid/vinyl acetate copolymers with constant composition — 1. Copolymerization reactivity ratios