Mayo-Lewis Model Research Articles

Revealing the Monomer Gradient of Polyether Copolymers Prepared Using N‐Heterocyclic Olefins: Metal‐Free Anionic versus Zwitterionic Lewis Pair Polymerization

AbstractN‐Heterocyclic olefin (NHO)‐based polymerization pathways for the copolymerization of ethylene oxide (EO) and propylene oxide (PO) are investigated in detail. Employing in situ 1H NMR spectroscopy, both an organocatalytic, anionic polymerization setup (system A) and a zwitterionic, Lewis pair‐type approach (system B) are studied comparatively. The obtained kinetics data are fitted to the non‐terminal model (Jaacks and Ideal Integrated) and terminal Mayo–Lewis model (Meyer Lowry) to determine the reactivity ratios, revealing striking differences in copolyether microstructure and achievable molar masses. While for the metal‐free catalysis (system A) reactivity ratios of rEO = 3.4 and rPO = 0.30 are found, indicating a soft gradient structure, the presence of Mg(HMDS)2 (system B) entails exclusively zwitterionic propagation. This results in enhanced selectivity, displaying corresponding parameters of rEO = 7.9 and rPO = 0.13, in line with the proposed monomer‐activated mechanism. The block‐like, strongly tapered copolyether microstructure is also reflected in the thermal properties, showing a melting point for the latter sample and much higher molar masses (Mn >50 000 g mol−1). Notably, this study not only identifies capable polymerization systems for EO/PO, but also underlines that via in situ 1H NMR kinetics key questions regarding the polymerization mechanism can be illuminated quickly and reliably, simplifying access to essential structure‐property relations.

Reactivity Ratios Estimation of the Free‐Radical Polymerization of Itaconic Acid and N‐Vinyl‐2‐Pyrrolidone by the Error‐in‐Variables Methodology

AbstractDesigned copolymers require an understanding of the relative reactivity ratios of the monomer pair and a proper regression technique that can extract this data from the experiments. An implementation of the error‐in‐variables method previously describes in the literature is written and made available for use, along with an high‐performance liquid chromatography (HPLC) methodology for acquiring the kinetic data for the regression analysis of the itaconic acid and N‐vinyl‐2‐pyrrolidone (IA/NVP) free‐radical copolymerization system. From the data, it is observed that higher initial mole fractions of IA in the reaction medium change the reaction kinetics, limiting the validity of the Mayo–Lewis model to a narrow range of initial mole fractions of IA. This effect is not observed at molar fractions below 10%, enabling the parameters to be estimated. The performance of the developed algorithm is satisfactory, and within less than 5% error when applied to data found in the literature. The parameters estimated by the algorithm for the IA/NVP system are r1 = 0.3046 and r2 = 0.0170, with IA as compound 1. A rather large deviation is observed for r1 and this is attributed to measurement errors associated with the low IA concentrations and high initial reaction rates.

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.

Practical Prediction of Heteropolymer Composition and Drift.

Composition drift in batch polymerizations is a well-known phenomenon and can lead to composition gradients in polymers synthesized using controlled polymerization methodologies. With known reactivity ratios of monomers, the drift, and thus resultant gradient copolymer, can be designed by adjusting reagent ratios and targeted conversions. Although such prediction is straightforward, it is seldom done, likely due to the perceived difficulty and unfamiliarity for nonspecialists. We seek to remedy this by providing the communities using copolymerswith an easy-to-use program called Compositional Driftwhich isbased on the Mayo-Lewis model and the penultimate model of monomer addition, using Monte Carlo methodology. This tool can also be applied to predict composition in nondrifting polymerizations.Herein we supply this tool to the community, showcasing two recent examples of use to guide experimental design and understanding of heteropolymers (RHP).

Bulk Free‐Radical Copolymerization of n‐Butyl Acrylate and n‐Butyl Methacrylate: Reactivity Ratio Estimation

The reactivity ratios for the bulk free‐radical copolymerization of n‐butyl acrylate (BA)/n‐butyl methacrylate (BMA) are estimated at 80 °C. By performing a series of low conversion runs including replicate runs, the reactivity ratios are estimated as rBA = 0.460 and rBMA = 2.008. Runs to high conversions are then conducted at three different feed compositions (fBMA = 0.2, 0.5, and 0.8) to validate the reactivity ratios. The composition data from the high conversion experiments show good agreement with the estimated reactivity ratios in the integrated form of the Mayo–Lewis model. The molecular weight, gel content, and glass transition temperature of BA/BMA copolymers are also determined. image

Features of styrene copolymerization with sodium p-styrenesulfonate in solvents of different polarities

The copolymerization of sodium p-styrenesulfonate with styrene is studied in solvents that form homogeneous solutions with mixtures of these monomers and differ in polarity: DMFA, a mixture of 1,4-dioxane with DMF, DMSO, and a DMSO-water mixture. It is shown that the diagrams of the copolymer composition depend on the type of solvent and that their shapes do not obey the Mayo-Lewis model. The copolymers become substantially enriched with styrene units during an increase in the solvent polarity. The main cause of deviation from the classical scheme of binary copolymerization is the selective solvation of growing macroradicals with styrene. This effect becomes more pronounced during an increase in the solvent polarity and a decrease in its dissolving ability with respect to polystyrene and during polymer separation into a heterophase. This conclusion is confirmed by the dependence of the copolymer composition on the initiator concentration.

Routes to carboxylic acid functional acrylonitrile copolymers via N‐tert‐butyl‐N‐(1‐diethylphosphono‐2,2‐dimethylpropyl) free nitroxide based nitroxide‐mediated polymerization

AbstractStyrene (S)/acrylonitrile [AN; initial acrylonitrile molar feed compositions (fAN,0's) = 0.10–0.86) and tert‐butyl methacrylate (tBMA)/AN (fAN,0 = 0.10–0.80) copolymers were synthesized at 90°C in 50 wt % 1,4‐dioxane solutions with a unimolecular initiator, N‐(2‐methylpropyl)‐N‐(1‐diethylphosphono‐2,2‐dimethylpropyl)‐O‐(2‐carboxylprop‐2‐yl) hydroxylamine [BlocBuilder (BB)]. In the tBMA/AN copolymerizations, 8.0–8.5 mol % N‐tert‐butyl‐N‐(1‐diethylphosphono‐2,2‐dimethylpropyl) free nitroxide relative to BB was added. The S/AN copolymers exhibited narrow, monomodal molecular weight distributions (MWDs) with low polydispersities [weight‐average molecular weight (Mw)/number‐average molecular weight (Mn) = 1.14–1.26], and the Mn versus monomer conversion (X) plots were relatively linear (Mn = 18.1 kg/mol, X ≈ 0.7); this suggested that pseudo‐living behavior was approached. AN proved to be an effective controlling comonomer for tBMA because the tBMA/AN copolymers exhibited narrow monomodal MWDs with Mw/Mn = 1.17–1.50 and relatively linear Mn versus X plots to reasonably high X values (Mn = 15.6 kg/mol, X ≈ 0.6). The AN and S monomer reactivity ratios were rAN = 0.07 ± 0.01 and rS = 0.27 ± 0.02 (Fineman–Ross) and rAN = 0.10 ± 0.01 and rS = 0.28 ± 0.02 (Kelen–Tüdos), respectively; these values were in good agreement with conventional free‐radical polymerization. Error‐in‐variables model (EVM) analysis indicated that the use of cumulative composition S/AN data was more effective than typical approaches using low‐X data with the Mayo–Lewis model. The AN and tBMA reactivity ratios [rAN = 0.07 ± 0.01 and rtBMA = 1.24 ± 0.20 (Fineman–Ross) and rAN = 0.14 ± 0.01 and rtBMA = 0.89 ± 0.19 (Kelen–Tüdos)] were similar to those reported for related alkyl methacrylate/AN conventional radical copolymerizations. EVM analysis suggested significant experimental error was associated with the tBMA/AN system, and this warrants further investigation. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012

High temperature copolymerization of styrene/ethyl acrylate: Reactivity ratio estimation in bulk and solution

AbstractStyrene/ethyl acrylate (Sty/EA) free‐radical copolymerizations have been conducted in bulk with and without initiator and in solution using p‐xylene and m‐xylene (30 wt% and 60 wt% solvent level) at 100°C and 130°C. The monomer reactivity ratio values and their temperature dependence have been determined from low conversion copolymer composition data using the computer software package RREVM, which is based on the error in variables model (EVM) method. Copolymer composition data at low conversion confirmed the Mayo–Lewis model at both temperatures. The reactivity ratio values of the Sty/EA system do not seem to change with dilution by nonpolar solvents at low concentration from the reactivity ratio values obtained in bulk with and without initiator. However, xylene isomers were found to have a slight effect on the reactivity ratio value of ethyl acrylate when high solvent concentration was utilized. © 2004 Wiley Periodicals, Inc. Adv Polym Techn 23: 186–195, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/adv.20009

Determination of monomer reactivity ratios in styrene/2-ethylhexylacrylate copolymer

The monomer reactivity ratios for styrene/2-ethylhexylacrylate in bulk at 80°C were investigated by studying the resulting copolymer composition via 1H-NMR. Composition results were summarized and various methods were employed to estimate the reactivity ratios including the use of the Error-in-Variables-Model (EVM) approach by using the Mayo–Lewis model. The estimates of the reactivity ratios from the EVM method are found to be rs = 0.979 and rEHA = 0.292. The resulting copolymer has a tendency toward alternation with an azeotrope of f(styrene) = 0.972. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 3368–3370, 2004

The effect of monomer preferential solvation in radical copolymerization: Reactivity ratios and compositional distribution

The effects of preferential solvation of monomers by polymer coils in homogeneous radical copolymerization at low conversion (5–7%) have been studied for styrene-acrylonitrile, styrenemethacrylic acid, styrene-acrylamide, styrene-acrylic acid, styrene-butyl methacrylate, vinyl acetate-2-methyl-5-vinyl-pyridine and vinyl acetate-2-vinyl pyridine. In the simplest cases, the copolymer composition and microstructure can be described by the Mayo-Lewis model with the apparent or effective monomer reactivity ratios: r 2 = r 2 0γ, r 1 = r 1 0 γ , where r 1 0, r 2 0 are ideal reactivity ratios defined by the monomer structure, γ is the monomer distribution coefficient. The most fundamental effect of preferential solvation is the relation between the copolymer composition and molecular weight caused by the dependence of preferential solvation coefficient γ upon the length of a growing chain. This dependence leads to two previously unknown types of chemical heterogeneity of low-conversion copolymers, viz. intra- and intermolecular gradient chemical heterogeneity.

The Microstructure of Poly(Isobutylene-co-p-Methylstyrene) by NMR Spectroscopy

Abstract The microstructure of isobutylene-para-methylstyrene (IB-pMeSt) copolymers was studied by NMR spectroscopy. 1H- and 13C-NMR spectra were used to obtain overall copolymer compositions. 13C-NMR signals were assigned in terms of triad monomer sequences, and triad distributions were obtained over a wide copolymer composition range. According to statistical tests, the IB-pMeSt copolymerization cannot be described by zero- (Bernoullian) or first-order Markov models because reactivity ratios r IB and r pMeSt were found to change with the monomer feed composition. Additional insight into the microstructure of IB-pMeSt copolymers was gained by calculating sequence numbers, run numbers, and sequence lengths from triad distributions. Further, the Kelen-Tudos plot showed a distinct curvature indicating that the Kelen-Tudos method, applied over the entire monomer feed composition range, cannot give meaningful reactivity ratios for this monomer pair. Evidently the simple two-parameter Mayo-Lewis model is inade...

Penultimate Unit Effects in Free-Radical Copolymerization. Number-Average Degree of Polymerization and Copolymerization Rate in Styrene/Methyl Methacrylate/Toluene System

Recently, Fukuda et al. showed from the measurements of absolute rate constants that in the free-radical copolymerization the propagation step obeys the penultimate model and the termination step is diffusion-controlled. Also Fukuda et al. proposed the “radical stabilization energy model” in the free radical copolymerization. To examine this copolymerization model, relationships between feed monomer composition f1 and number-average degree of polymerization Xn and between f1 and copolymerization rate Rp were investigated for the copolymerization of styrene and methyl methacrylate in toluene at 40°C. The composition of the copolymer F1 was determined by 1H NMR. The number-average molecular weight of the copolymer Mn was measured to calculate Xn by osmometry and size exclusion chromatography (SEC). By the so-called terminal model (the Mayo–Lewis model), the copolymer composition data was well described while the data of Xn and Rp Were not described. Alternatively, the model proposed by Fukuda et al. described well the composition data, the Xn data and the Rp data.

Pulsed Laser Copolymerization of Styrene and Maleic Anhydride

Pulsed laser polymerization (PLP) has been done for the free radical copolymerization of styrene (monomer 1) and maleic anhydride (monomer 2) at 25,35, and 50 OC in butanone (methyl ethyl ketone (MEK) and acetonitrile (Acn) using AIBN as photoinitiator. The mean values for the propagation rate constant, (k,), were determined and found to be independent of solvent. Copolymer compositions were measured as a function of comonomer ratio in an isothermal continuous stirred reactor using MEK as solvent over a temperature range from 60 to 140 C. The combination of these data and the data from PLP experiments were used in model discrimination by multivariate nonlinear regression. The best description of this copolymerization is obtained from the penultimate unit model. No convergence could be reached in a multivariate nonlinear regression of the combined data set to the complex participation model. The mean k, is well described by the Mayo-Lewis model, where copolymer composition shows some deviation from the model. Numerical inspection reveals that invoking complex participation leads to a good fit of the copolymer composition data but very bad agreement with the mean k, data. The comonomer pair showed several peculiarities compared to systems described in the literature so far. Extremely high molecular weight copolymer was formed during the PLP experiments, the amount being dependent, among others, on solvent. Furthermore, large amounts of oligomers, i.e., dimers and trimers, are formed under PLP conditions. Two possible explanations for the anomalies of this comonomer pair are discussed. First, diradical initiation could account for the observed phenomena. Laser pulses are thought to excite electron donor-acceptor complexes, resulting in diradicals, which may initiate copolymerization. Second, dark polymerization might give rise to formation of high molecular weight copolymer. Due to significant or even total light absorption, part of the monomer solution is unaffected by the laser pulses.

Copolymerization of a novel substituted methacrylamide with methyl methacrylate

The copolymerization behaviour of the adduct of N′, N′-dimethylaminopropyl methacrylamide and epichlorohydrin (DMAPMA-Epi) and methyl methacrylate (MMA) was investigated. The reactivity ratios for the MMA (1)/DMAPMA-Epi (2) couple in solution, using various regression methods based on the Mayo-Lewis model, are r 1 = 1.73 and r 2 = 0.03. The Q and e values for DMAPMA-Epi are estimated to be 0.23 and −1.32 respectively. On the basis of the reactivity ratios, theoretical curves for the instantaneous copolymer composition throughout conversion have been calculated.

Solvent effects on the copolymerization of styrene with maleic anhydride: determination of apparent reactivity ratios from the penultimate unit model

A method for optimization of monomer feed composition to obtain the most accurate reactivity ratios has been described by Tidwell and Mortimer. The proposed method is more generally applicable than for use with the Mayo-Lewis model and copolymer composition vs monomer feed composition data. By means of a simulated example involving the penultimate unit models the effect of experimental design in the determination of reactivity ratios is clearly demonstrated. The same technique is adapted to the copolymerization of styrene with maleic anhydride. Apparent reactivity ratios are obtained for polymerization in toluene, butanone and N,N′-dimethylformamide. There appears to be a significant solvent effect. This paper provides an indication that the highest obtainable accuracy of apparent reactivity ratios depends on the values of the reactivity ratios themselves. Interpretation of the experimental results in terms of the bootstrap model leads to the conclusion that there is no dependence of monomer sequence distribution vs copolymer composition on the solvent. Quantitative interpretation is hampered most probably by the absence of maleic anhydride homopolymerization.

Interpreting the copolymerization of styrene with maleic anhydride and with methyl methacrylate in terms of the bootstrap model

The bootstrap model was proposed by Harwood to explain copolymer sequence distribution which is dependent only on copolymer composition in solvents which cause changes in the apparent reactivity ratios for a number of pairs of monomers. This work presents an explicit formulation of the equations describing copolymer composition and sequence distribution in terms of the bootstrap model for both the simple Mayo-Lewis model and the penultimate unit model. Inspection of these equations reveals the necessary and sufficient conditions for sequence distribution to be a function only of copolymer composition. The results of copolymerizations of styrene with methyl methacrylate and with maleic anhydride under various conditions are interpreted in terms of the bootstrap model.

Modelling copolymerization kinetics

AbstractThe composition and rate behavior of free radical copolymerizations is usually described by the Mayo‐Lewis (ML) model and the associated reactivity ratios, r1 and r2. Particularly with respect to rate, a number of systems have been found to be poorly described by the simple ML model and the penultimate unit effect (PUE) model has been suggested as an explanation. A small but significant amount of work has been done with small model analogues of polymer chains and with ESR which has established the chemical feasibility of a PUE. This paper reviews recent work with pulsed laser polymerization kinetic measurements which are successfully described in terms of a modified PUE. It is concluded that the strength of the PUE correlates inversely with the monomer reactivity ratio product, r1r2. The effect is important for rate, but not for composition.

A microcomputer program for estimation of copolymerization reactivity ratios

AbstractA user‐friendly program has been developed to estimate copolymerization reactivity ratios based on a nonlinear minimization algorithm. The use of an optimal experimental design for copolymerization when the Mayo–Lewis model applies is presented. The applicability of the program is demonstrated using actual and simulated experimental data.

Copolymerization propagation kinetics of styrene with alkyl acrylates

AbstractPropagation rate constants have been determined at two temperatures (298 K and 323 K) for the copolymerizations of styrene (STY) with methyl acrylate (MA) and STY with n‐butyl acrylate (BA) over a range of monomer feed compositions. A pulsed UV laser was used as an initiation source and gel permeation chromatography (GPC) was utilized to analyse the products. None of the copolymerizations conformed to the Mayo‐Lewis model, with respect to their propagation rate constants. The results were interpreted on the basis of a penultimate effect on the propagation reaction. In addition, Mark‐Houwink constants were determined for poly(MA) and poly(BA) in tetrahydrofuran (THF) at 298 K. These constants are given as [K(dm3 kg−1),α]: 7·88 × 10−3, 0·885 and 8·57 × 103, 0·865 for poly(MA) and poly(BA) respectively.

Copolymerization kinetics of 4‐methoxystyrene with methyl methacrylate and 4‐methoxystyrene with styrene: A test of the penultimate model

AbstractThe propagation kinetics for the copolymerization of 4‐methoxystyrene with methyl methacrylate and 4‐methoxystyrene with styrene have been investigated using a pulsed laser technique. The dependence of the copolymerization propagation rate constant on the monomer feed ratio shows a diviation from classic Mayo–Lewis model kinetics for 4‐methoxystyrene with methyl methacrylate but not for 4‐methoxystyrene with styrene. These results have been interpreted to indicate that a penultimate effect is apparent in the first monomer pair but not in the second. With r1r2 = 0.092 for the copolymerization of 4‐methoxystyrene with methyl methacrylate and r1r2 = 0.95 for 4‐methoxystyrene with styrene, it is suggested that a deviation of the product of the coplymerization reactivity ratios from unity may be an indication of the presence of a penultimate effect.