Copolymerization System Research Articles

Visualization of Bivariate Sequence Length–Chain Length Distribution in Free Radical Copolymerization

Copolymer properties and processability depend on copolymer microstructure, i.e., copolymer composition and monomer unit arrangements along the copolymer chains. To predict the ultimate properties of copolymers, one needs complete information on the length and position of sequences of each monomer type in every chain. A versatile kinetic Monte Carlo code is developed and applied for the simulation of typical free radical copolymerizations. The code allows explicit monitoring of every growing chain during the course and at the end of polymerization, can account for comonomer systems of any arbitrary reactivity ratios (r1 and r2) over the full range of monomer composition. Meanwhile, it eliminates the need for solving arrays of differential equations arising from deterministic modeling approaches. Since the code virtually synthesizes billions of copolymer molecules and keeps in storage information on each and every copolymer chain in the system, it allows for detailed statistical analysis. The simulator visualizes the bivariate sequence length–chain length distribution for typical copolymerization systems and examples with: r1 < 1 and r2 < 1; r1 > 1 and r2 < 1; (r1 × r2) = 1; and r1 = r2 = 1, and is also applied successfully to an experimental scenario described in the literature.

Steady State and Equilibrium in Reversible Copolymerization at Constant Comonomer Concentrations

Selected aspects of copolymerization processes carried on at constant comonomer concentrations are analyzed theoretically and modeled by Monte Carlo method. It is confirmed that some combinations of initial parameters lead to stationary conditions of copolymer formation for both irreversible and reversible systems which can be regarded as the first‐order Markov chain process. However, this study shows that for many copolymerization systems the stationary conditions are attained only at high number‐average degree of polymerization DPn, and for some reversible copolymerizations, attaining equilibrium, stationary conditions are not observed at all. The analysis shows that the chain length distribution (CLD) for copolymerization carried out under steady state conditions at constant comonomer concentrations, equal to equilibrium concentrations for infinitely high DPn, is approximately described by the modified Bessel and exponential functions. This type of CLD is analytically proved and confirmed by the Monte Carlo simulations for the analogous homopolymerization process.

A DFT study of the ring-opening polymerization mechanism of l-lactide and ε-caprolactone using aluminium salen-type initiators: Towards an understanding of their reactivities in homo- and copolymerization

The initiation and first propagation steps of the ring-opening polymerization (ROP) of l-lactide (l-LA) and ε-caprolactone (ε-CL) mediated by aluminium salen-type initiators with formulae LAlOCH3 (LH2=N,N'-bis(salicylidene)-1,2-ethylenediamine (1a) and N,N',-bis(salicylidene)-2,2-dimethyl-1,3-propanediamine (1b) as well as their corresponding 3,5-dichloro-substituted counterparts, 2a and 2b, respectively) are investigated at the molecular level using density functional theory (DFT). The results show that, even though the apparent ROP mechanisms are similar for all systems studied, the activation barriers for the rate-limiting transition states are different and depend on the initiator. The reactivities of the initiators toward the ROP of the two monomers are predicted to increase in the order 1a <2a <1b <2b, in good agreement with experimentally and theoretically observed trends for systems with different bridging units and electronic properties of the ligand substituents. However, this does not entail similar reactivities in all polymerization processes. An explanation for this, here the different reactivities observed for homo- and copolymerization (for the two types of monomers) is found in their different binding affinities with the propagating active species. Several experimentally observed features, such as e.g. reaction rates, in other related homopolymerization and random copolymerization systems with these two monomers can also be rationalized.

Kinetics and mechanism of metallocene‐catalyzed olefin polymerization: Comparison of ethylene, propylene homopolymerizations, and their copolymerization

ABSTRACTA series of ethylene, propylene homopolymerizations, and ethylene/propylene copolymerization catalyzed withrac‐Et(Ind)2ZrCl2/modified methylaluminoxane (MMAO) were conducted under the same conditions for different duration ranging from 2.5 to 30 min, and quenched with 2‐thiophenecarbonyl chloride to label a 2‐thiophenecarbonyl on each propagation chain end. The change of active center ratio ([C*]/[Zr]) with polymerization time in each polymerization system was determined. Changes of polymerization rate, molecular weight, isotacticity (for propylene homopolymerization) and copolymer composition with time were also studied. [C*]/[Zr] strongly depended on type of monomer, with the propylene homopolymerization system presented much lower [C*]/[Zr] (ca. 25%) than the ethylene homopolymerization and ethylene–propylene copolymerization systems. In the copolymerization system, [C*]/[Zr] increased continuously in the reaction process until a maximum value of 98.7% was reached, which was much higher than the maximum [C*]/[Zr] of ethylene homopolymerization (ca. 70%). The chain propagation rate constant (kp) of propylene polymerization is very close to that of ethylene polymerization, but the propylene insertion rate constant is much smaller than the ethylene insertion rate constant in the copolymerization system, meaning that the active centers in the homopolymerization system are different from those in the copolymerization system. Ethylene insertion rate constant in the copolymerization system was much higher than that in the ethylene homopolymerization in the first 10 min of reaction. A mechanistic model was proposed to explain the observed activation of ethylene polymerization by propylene addition. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem.2017,55, 867–875

Copolymerization of 2,3,4,5,6‐Pentafluorostyrene and Methacrylic Acid by Nitroxide‐Mediated Polymerization: The Importance of Reactivity Ratios

Amphiphilic block copolymers of 2,3,4,5,6‐pentafluorostyrene (PFS) and methacrylic acid (MAA) are synthesized via nitroxide‐mediated polymerization (NMP). It is established that to obtain a controlled copolymerization a minimum of 40 mol% of PFS is required, which is significantly greater than other copolymerization systems such as using 4.5–8 mol% styrene or 1 mol% of 9‐(4‐vinylbenzyl)‐9H‐carbazole to control the copolymerization of methacrylates. It is surmised that this lack of control is due to the reactivity ratios that favor the addition of MAA rather than PFS (rPFS = 0.14, rMAA = 6.97). However this reactivity ratio pair suggests that a one‐shot delayed injection approach can be utilized to synthesize almost pure block copolymers in one pot. Therefore, poly(PFS)‐b‐(PFS‐ran‐MAA) block copolymers are synthesized by a one‐shot delayed addition of MAA. While the concentration of irreversibly terminated chains is evident these results suggest a promising route to the synthesis of fluorinated amphiphilic block copolymers by NMP. image

Copolymer of lactide and ε-caprolactone catalyzed by bimetallic Schiff base aluminum complexes

A series of copolymers of lactide (LA) and e-caprolactone (e-CL) with different monomer feed ratios were achieved using three kinds of bimetallic Schiff aluminum complexes as catalysts. The ratios of LA and e-CL units in different copolymers and the average segments length were determined by NMR analysis. The comparative kinetic study of L-LA/e-CL and rac-LA/e-CL copolymerization systems showed that the polymerization rate of LA was faster than e-CL, and L-LA showed polymerization rate slightly faster than rac-LA. It was inferred that the copolymers achieved by these complexes were gradient copolymers with gradual change in distribution of LA and e-CL units. The thermal properties of these copolymers were characterized by DSC analysis, which showed that the glass transition temperature (Tg) of these copolymers changed regularly according to the pro-portion change of two structural units.

Metal-Free Alternating Copolymerization of CO2 with Epoxides: Fulfilling “Green” Synthesis and Activity

Polycarbonates were successfully synthesized for the first time through the anionic copolymerization of epoxides with CO2, under metal-free conditions. Using an approach based on the activation of epoxides by Lewis acids and of CO2 by appropriate cations, well-defined alternating copolymers made of CO2 and propylene oxide (PO) or cyclohexene oxide (CHO) were indeed obtained. Triethyl borane was the Lewis acid chosen to activate the epoxides, and onium halides or onium alkoxides involving either ammonium, phosphonium, or phosphazenium cations were selected to initiate the copolymerization. In the case of PO, the carbonate content of the poly(propylene carbonate) formed was in the range of 92-99% and turnover numbers (TON) were close to 500; in the case of CHO perfectly alternating poly(cyclohexene carbonate) were obtained and TON values were close to 4000. The advantages of such a copolymerization system are manifold: (i) no need for multistep catalyst/ligand synthesis as in previous works; (ii) no transition metal involved in the copolymer synthesis and therefore no coloration of the samples isolated; and (iii) no necessity for postsynthesis purification.

Improved numerical inversion methods for the recovery of bivariate distributions of polymer properties from 2D probability generating function domains

Abstract The 2D probability-generating function technique is a powerful method for modeling bivariate distributions of polymer properties. It is based on the transformation of bivariate population balance equations using 2D probability generating functions (pgf) followed by a recovery of the distributions from the transform domain by numerical inversion. A key step of this method is the inversion of the pgf transforms. Available numerical inversion methods yield excellent results for pgf transforms of distributions with independent dimensions with similar orders of magnitude, for example bivariate molecular weight distributions in copolymerization systems. However, numerical problems are found for 2D distributions in which the independent dimensions have very different ranges of values, such as the molecular weight distribution-branching distribution in branched polymers. In this work, two new 2D pgf inversion methods are developed, which regard the pgf as a complex variable. The superior accuracy of these innovative methods makes them suitable for recovering any type of bivariate distribution. This enhances the capabilities of the 2D pgf modeling technique for simulation and optimization of polymer processes. An application example of the technique in a polymeric system of industrial interest is presented.

Effect of supercritical CO2 on the copolymerization behavior of cyclohexene oxide/CO2 and copolymer properties with DMC/Salen‐Co(III) catalyst system

ABSTRACTThe copolymerization of cyclohexene oxide (CHO) and carbon dioxide (CO2) was carried out under supercritical CO2 (scCO2) conditions to afford poly (cyclohexene carbonate) (PCHC) in high yield. The scCO2 provided not only the C1 feedstock but also proved to be a very efficient solvent and processing aid for this copolymerization system. Double metal cyanide (DMC) and salen‐Co(III) catalysts were employed, demonstrating excellent CO2/CHO copolymerization with high yield and high selectivity. Surprisingly, our use of scCO2 was found to significantly enhance the copolymerization efficiency and the quality of the final polymer product. Thermally stable and high molecular weight (MW) copolymers were successfully obtained. Optimization led to excellent catalyst yield (656 wt/wt, polymer/catalyst) and selectivity (over 96% toward polycarbonate) that were significantly beyond what could be achieved in conventional solvents. Moreover, detailed thermal analyses demonstrated that the PCHC copolymer produced in scCO2 exhibited higher glass transition temperatures (Tg ∼ 114 °C) compared to polymer formed in dense phase CO2 (Tg ∼ 77 °C), and hence good thermal stability. Additionally, residual catalyst could be removed from the final polymer using scCO2, pointing toward a green method that avoids the use of conventional volatile organic‐based solvents for both synthesis and work‐up. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016, 54, 2785–2793

Evolution of Chain Microstructure and Kinetics of Reaching Equilibrium in Living Reversible Copolymerization

Theoretical considerations and Monte Carlo simulations have proved that the microstructure of copolymer chains in living reversible copolymerization can be effectively described by the first‐order Markov chain process only when the system space of this process reaches chain lengths above the number‐average degree of polymerization (DPn). The time scale of equilibration depends mostly on DPn of the product, rate constants of depropagation, as well as on the equilibrium microstructure of copolymer. During the process, evolution encompasses, besides the chain‐length distribution like in homopolymerization, also the chain microstructure. The kinetically determined microstructure (gradient, alternate, etc.) observed in the first stage of copolymerization is related to reactivity ratios. It evolves into the equilibrium microstructure, determined exclusively by the equilibrium constants and initial conditions. Discussion of this evolution together with the statistical description of the reversible binary copolymerization systems at various stages of equilibration is given. image

Allylamine and Allyl Alcohol Plasma Copolymerization: Synthesis of Customizable Biologically‐Reactive Three‐Dimensional Scaffolds

Plasma copolymerization is a powerful plasma‐enhanced chemical vapor deposition (PECVD)‐based technique, and offers a distinct advantage over single‐precursor PECVD of being able to deposit films with tunable functionality by adjusting the plasma precursor ratio. Here, an allylamine/allyl alcohol plasma copolymerization system was used to modify two‐dimensional (2D) and three‐dimensional (3D) substrates for biomedical applications. Films with customizable and predictable nitrogen and oxygen content, as well as surface wettability, were deposited on both Si wafers and 3D polymer scaffolds across a range of copolymerization conditions. Additionally, the bioreactivity of plasma‐modified materials was evaluated using both human dermal fibroblast and E coli attachment studies.

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...

A general theory of kinetics and thermodynamics of steady-state copolymerization

Kinetics of steady-state copolymerization has been investigated since the 1940s. Irreversible terminal and penultimate models were successfully applied to a number of comonomer systems, but failed for systems where depropagation is significant. Although a general mathematical treatment of the terminal model with depropagation was established in the 1980s, a penultimate model and higher-order terminal models with depropagation have not been systematically studied, since depropagation leads to hierarchically-coupled and unclosed kinetic equations which are hard to solve analytically. In this work, we propose a truncation method to solve the steady-state kinetic equations of any-order terminal models with depropagation in a unified way, by reducing them into closed steady-state equations which give the exact solution of the original kinetic equations. Based on the steady-state equations, we also derive a general thermodynamic equality in which the Shannon entropy of the copolymer sequence is explicitly introduced as part of the free energy dissipation of the whole copolymerization system.

Model‐Based Production of Polymer Chains Having Precisely Designed End‐to‐End Gradient Copolymer Composition and Chain Topology Distributions in Controlled Radical Polymerization, A Review

Polymer chain microstructures, such as copolymer composition distribution (CCD) and topology, play an important role in determining materials properties of the polymer products. The design and control of polymer chain microstructures represents an important task in macromolecular reaction engineering. Semi‐batch copolymerization with the model‐based design of comonomer feeding policies provides a powerful approach enabling precision production of CCD, topology, and their combined structures in controlled radical copolymerization systems. Various novel polymer products with predesigned CCDs and topologies have been successfully prepared by the approach. This article highlights the recent progresses in this area.

Mechanisms of orientational and photoelastic birefringence generation of methacrylates for the design of zero–zero‐birefringence polymers

The intrinsic birefringence Δn0 and photoelastic coefficient C of poly(methyl methacrylate), poly(2,2,2‐trifluroethyl methacrylate), poly(phenyl methacrylate), and poly(2,2,3,3,3‐pentafluorophenyl methacrylate) were determined. We categorized these methacrylate polymers into four birefringence‐types, even though their molecular structures differed only by the substituents on the side chains. Based on the results of Δn0 and C, novel polymers that exhibit neither orientational nor photoelastic birefringence, i.e., zero–zero‐birefringence polymers, were designed and synthesized by quaternary copolymerization system. Furthermore, we confirmed that the mechanisms of orientational birefringence and photoelastic birefringence generation were different in these methacrylate polymers. The conformation of the repeat unit of the polymers was nearly constant during the generation of orientational birefringence. In contrast, the conformation of the repeat unit of the polymers changed during the generation of photoelastic birefringence in the glassy state. These findings demonstrated the reasonability of evaluating orientational and photoelastic birefringence separately, as well as the adequacy of the classification of polymers into four birefringence‐types. Given these results and the fact that zero–zero‐birefringence polymers could be prepared successfully by four‐birefringence type monomers, we demonstrated the reasonability of the method for designing the zero–zero‐birefringence polymers. POLYM. ENG. SCI., 55:1330–1338, 2015. © 2015 Society of Plastics Engineers

Modeling of Kinetics of Sodium Methacrylate and Methacrylic Acid Amide Copolymerization

Experimental studies of sodium methacrylate and methacrylic acid amide copolymerization in aqueous solutions were accomplished under isothermal conditions. A mathematical model of the sodium methacrylate and methacrylic acid amide copolymerization in concentrated aqueous solutions was proposed. This model allows predicting the monomer conversion and molecular weight of copolymer. The model considers the change of initiation efficiency and chain termination rate on increase of the copolymerization system viscosity. A comparison of experimental data with calculations was performed based on the developed mathematical model.

Efficient solvent‐free alternating copolymerization of CO2 with 1, 2‐epoxydodecane and terpolymerization with styrene oxide via heterogeneous catalysis

ABSTRACTThe alternating copolymerization of CO2 with the terminated epoxides anchoring long alkyl groups is rarely reported because of their low reactivity and polycarbonate selectivity. This work describes a well‐controlled solvent‐free copolymerization of CO2 with 1, 2‐epoxydodecane (EDD) with a long electron‐donating alkyl group via the catalysis of Zn‐Co(III) double metal cyanide complex catalyst. The productivity of the catalyst was up to 2406 g polymer/g Zn, that is, EDD conversion was 99.2%. The alternating degree of CO2‐EDD copolymers were more than 99% and had high number‐average molecular weights (Mns) of &gt;100 kg mol−1, while only 1.0 wt % 4‐decyl‐1,3‐dioxolan‐2‐one (DC) were detected. Moreover, by introducing styrene oxide (SO) with electron‐withdrawing phenyl group into EDD‐CO2 copolymerization system, a new random terpolymer with either electron‐withdrawing or electron‐donating side groups was produced with single glass transition temperatures (Tgs) in a wide range from 3 to 56 °C, which might be potentially used as biodegradable elastomers or plastics. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015, 53, 737–744

СИНТЕЗ НОВЫХ БИОЛОГИЧЕСКИ АКТИВНЫХ ПОЛИМЕРНЫХ БИОКОНЪЮГАТОВ НА ОСНОВЕ ЛУПАНОВЫХ АЛЛИЛАМИДОВ

The work is devoted to the synthesis of new copolymers based on allylamides of betulonic and 2 hydroximinobetulonic acids and study of their cytotoxic activity. Allylamides of betulonic and 2 hydroximinobetulonic acids were prepared by the reaction of corresponding acids with allylamine in the presence of oxalyl chloride and triethylamine. It was established that the allylamides obtained do not homopolymerize, but copolymerize with low rates with acrylonitrile and N-vinylpyrrolidone in the presence of radical initiators The investigations of radical copolymerization of allylamides with acrylonitrile and N-vinyl­pyrrolidone showed that the resulting copolymers have a statistical distribution of the comonomer units in the macromolecule, wherein in the entire range of monomer concentrations the copolymers are enriched by the vinyl monomer units. The copolymerization rates are considerably reduced by increasing the content of allylamides in the initial monomer mixture in all copolymerization systems, the copolymerization rate of allylamide with acrylonitrile is higher than with N-vinylpyrrolidone. At the copolymerization in bulk with enhancing degree of conversion there is a gel-effect, which is associated with an increasing of the viscosity in the absence of solvent; at the copolymerization in solution gel-effect is absent. The structure of the copolymers obtained was determined by 1 H NMR spectroscopy. It was established that the products obtained are a mixture of copolymers of allyl amides and oligomers thereof. In the spectra of the reaction products a number of additions of the vinyl monomer with the participating of double bond of isopropylidene group is also observed. The copolymers obtained have a cytotoxic activity: the copolymer of allylamide of betulonic acid with N-vinylpyrrolidone exhibits 4-fold higher activity against MS culture when compared with the initial ally amide and is promising for developing new bioactive polymer bioconjugates.

Rational Design of Oxirane Monomers for Efficient Crossover Reactions in Concurrent Cationic Vinyl-Addition and Ring-Opening Copolymerization with Vinyl Ethers

Rational structural design of oxirane monomers is demonstrated here to be highly conducive to crossover reactions in the concurrent cationic vinyl-addition and ring-opening copolymerization of alkyl vinyl ethers and oxiranes. The key to the efficient crossover reactions was the smooth transformation of the once-formed oxirane-derived oxonium ion into the ring-opened carbocation, which then reacted with a vinyl monomer. For example, oxiranes that form resonance-stabilized, allyl-type carbocations (i.e., isoprene monoxide and butadiene monoxide) were polymerized through efficient crossover reactions in copolymerization with isopropyl vinyl ether, yielding copolymers composed of relatively short monomer sequences. In particular, the copolymerization of isoprene monoxide and isopropyl vinyl ether generated random or alternating-rich copolymers. The reaction using an oxirane that forms tertiary carbocations (isobutylene oxide) also proceeded via crossover reactions; however, the crossover frequency was lower, which resulted in a multiblock-like copolymer. In contrast to the three oxiranes that yielded copolymers, oxiranes that possibly result in secondary carbocations from their ring-opening (3,3-dimethyl-1,2-butylene oxide and 1,2-butylene oxide) hardly induced crossover reactions. In addition to the ease of carbocation generation via ring-opening, the nucleophilicity of the monomer and the reactivity of the oxirane-derived carbocations were shown to substantially affect the copolymerization behavior. These factors are discussed on the basis of the monomer reactivity ratios that were determined for the copolymerization systems using vinyl ethers with different reactivities, i.e., isopropyl vinyl ether or ethyl vinyl ether, toward oxiranes.

Photo-induced living cationic copolymerization of isobutyl vinyl ether and vinyl ether with carbazolyl groups

In this work, a fluorescent monomer 2-(9-carbazolyl) ethyl vinyl ether (CEVE) was synthesized in our lab, and its photo-induced living cationic copolymerization behavior with isobutyl vinyl ether (IBVE) was investigated in detail using diphenyliodonium chloride (DPICl)/2,2-dimethoxy-2-phenylacetophenone (DMPA) and zinc bromide (ZnBr2) initiating system in dichloromethane solution at 5 °C, −5 °C, and −15 °C, respectively. The living nature of this copolymerization system was confirmed by adding fresh comonomer method after the copolymerization almost finished. In addition, the obtained fluorescent copolymer poly(IBVE-co-CEVE) has a low glass transition temperature (T g), below −10 °C.