Estimation Of Reactivity Ratios Research Articles

A robust and high-throughput measurement platform for monomer reactivity ratios from surface-initiated polymerization

This article describes a robust approach to measure monomer reactivity ratios from surface-initiated copolymerization, by measuring composition of statistical copolymer brush surfaces using X-ray photoelectron spectroscopy. Statistical copolymer brushes were prepared from various monomer feeds by surface-initiated radical copolymerization at room temperature under ultraviolet (UV) irradiation. The copolymer brush composition data were fit to the terminal copolymerization kinetic model resulting in point estimates for the monomer reactivity ratios that are in good agreement with values measured under bulk reaction conditions. Additionally, a high-throughput approach was demonstrated to measure reactivity ratios using a single substrate exhibiting a gradient in copolymer brush composition. This high-throughput approach significantly reduces the time and effort required to generate reliable and reproducible point estimates of reactivity ratios, and these values are in good agreement with values obtained from both the discrete sample surface measurements and classical bulk analytical methods.

Reactivity Ratio Estimation from Cumulative Copolymer Composition Data

AbstractThe goal is to present an alternative technique for reactivity ratio estimation in copolymerization. Typically, reactivity ratios are estimated using the instantaneous copolymer composition equation, based on low conversion copolymer composition data. However, using experimental data from the full copolymerization trajectory would, in principle, be more advantageous, and shy away from commonly used restrictive assumptions. Estimation using cumulative copolymerization data and models eliminates the difficulties associated with stopping reactions at low conversion, while one gains to study the full polymerization trajectory. The error‐in‐variables‐model (EVM) method is used for parameter estimation. Two cumulative model forms, the analytical integration of the differential composition equation and the one resulting from the direct numerical integration of this equation, are employed. Using these two types of models improves the reactivity ratio estimation and, in particular, the latter model form is a more reliable and direct method of estimating reactivity ratios. magnified image

A new general approach to determine more accurate comonomer reactivity ratios in controlled/living radical copolymerization systems

In controlled/living radical copolymerization (atom transfer radical copolymerization in this study) and in any other living chain-growth copolymerization, the possible preferential addition of one of the comonomers onto the (macro)initiator-derived (macro)radical can affect the copolymer composition, especially at low conversion; this results in inaccurate comonomer reactivity ratio estimation by the classic approach. A new general approach is introduced in this article, which allowed us to exclude the influence of the possible preferential addition of one of the comonomers onto the (macro)initiator-derived (macro)radical on the copolymer composition at any conversion. According to this approach, copolymer chain grown during time t (t ≠ 0) is considered to be, in fact, the macroinitiator terminated with one of the comonomers under study, which will further grow during the time interval Δt′ = t′ − t [where any reaction time t′ is considered to be grater than reaction time t, i.e. t′ > t] from a comonomer mixture with composition of f(t) [where f(t) is the molar ratio of comonomer i to comonomer j in the comonomer mixture] at time t. In such a situation, it is possible to obtain individual comonomer conversions [xi(Δt′) and xj(Δt′)], the overall comonomer conversion [xov(Δt′)], and the cumulative average copolymer composition for the copolymer formed during Δt′, from which more accurate comonomer reactivity ratios can be calculated by the various low- or high-conversion methods, depending on the overall comonomer conversion. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011

Estimating Reactivity Ratios From Triad Fraction Data

AbstractReactivity ratio estimation is a non‐linear estimation problem. Typically, reactivity ratios are estimated using the instantaneous copolymer composition equation, otherwise known as the Mayo‐Lewis model, based on low conversion (<5%) copolymer composition data. However, there are other instantaneous models, which can be used to estimate reactivity ratios, such as the instantaneous triad fraction equations. The aim of this paper is to determine the potential improvement in reactivity ratio estimates when triad fraction data is used in place of and in combination with copolymer composition data. The interest in using triad fraction data in parameter estimation, stems from the fact that there are a greater number of responses measured (six triad fractions) compared to composition leading to data with theoretically more information content. In principle this should lead to reactivity ratio estimates having less uncertainty. In this study, the parameter estimates are obtained by employing the error in variables model (EVM), assuming a multiplicative error structure. Several case studies involving published literature data for different copolymer systems are presented. As the case studies demonstrate in general more precise estimates can be obtained from triad fraction data. Combining the triad fraction with composition data leads to little additional improvement. However, discrepancies arise between reactivity ratios estimated from composition data compared with those obtained from triad fraction data depending upon the copolymer system. Those copolymer systems exhibiting more heterogeneity due to phase separation during polymerization may be showing more discrepancy.

Kinetic study of atom transfer radical homo- and copolymerization of styrene and methyl methacrylate initiated with trichloromethyl-terminated poly(vinyl acetate) macroinitiator

Atom transfer radical bulk copolymerization of styrene (St) and methyl methacrylate (MMA) was performed in the presence of CuCl/PMDETA as a catalyst system and trichloromethyl-terminated poly(vinyl acetate) telomer as a macroinitiator at 90°C. The overall monomer conversion was followed gravimetrically and the cumulative average copolymer composition at moderate to high conversion was determined by 1H NMR spectroscopy. Reactivity ratios of St and MMA were calculated by the extended Kelen–Tudos (KT) and Mao–Huglin (MH) methods to be rSt=0.605±0.058, rMMA=0.429±0.042 and rSt=0.602±0.043, rMMA=0.430±0.032, respectively, which are in good agreement with those reported for the conventional free-radical copolymerization of St and MMA. The 95% joint confidence limit was used to evaluate accuracy of the estimated reactivity ratios. Results showed that in the controlled/living radical polymerization systems such as ATRP, more reliable reactivity ratios are obtained when copolymer composition at moderate to high conversion is used. Good agreement between the theoretical and experimental composition drifts in the comonomer mixture and copolymer as a function of the overall monomer conversion was observed, indicating the accuracy of reactivity ratios calculated by copolymer composition at the moderate to high conversion. Instantaneous copolymer composition curve and number-average sequence length of comonomers in the copolymer indicated that the copolymerization system tends to produce a random copolymer.

Copolymerization of 2-[3-(2H-Benzotriazol-2-yl)-4-hydroxyphenyl]ethyl Methacrylate with Styrene

Radical copolymerization of 2-[3-(2H-benzotriazol-2-yl)-4-hydroxyphenyl]ethyl methacrylate (M1) with styrene (M2) at 70 °C in 1,4-dioxane was investigated and the reactivity ratios were determined. The copolymerization was carried out as batch copolymerization to a low conversion or as copolymerization with a continuous addition of monomers at higher instantaneous conversion. The monomer reactivity ratios of the copolymerizable UV stabilizer 2-[3-(2H-benzotriazol-2-yl)-4-hydroxyphenyl]ethyl methacrylate with styrene were determined using the Finemann-Ross plot for both copolymeration techniques. The estimated reactivity ratios were r1 = 0.588 and r2 = 0.6 for the technique of continuous addition of monomers and r1 = 0.462 and r2 = 0.476 and for the batch experiment. The copolymerization exhibited an azeotrope at f1 = 0.507, thus a copolymer with microstructure close to the alternating one was formed at this ratio of comonomers.

High-Temperature Bulk Copolymerization of Methyl Methacrylate and Acrylonitrile: III. Thermal Polymerization

The thermally initiated copolymerization of methyl methacrylate and acrylonitrile has been studied in the bulk phase. Experiments for estimating reactivity ratios were conducted at 120°C and 140°C. Feed composition constraint approaches were used to design the reactivity ratio experiments. The error in variables model (EVM) method was employed to evaluate the reactivity ratios and analyze the error. The results showed that the reactivity ratios did not vary significantly with temperature up to 140°C for both thermally initiated and experiments with initiator. Full conversion range experiments were also conducted at 140°C. The rate of reaction, copolymer composition, M¯ n , M¯ w , and glass transition temperatures of samples were measured.

Hydroxylated Poly(N-isopropylacrylamide) as Functional Thermoresponsive Materials

In this study, we developed a poly(N-isopropylacrylamide)-based thermoresponsive polymeric material with a high content of hydroxyl groups. We newly designed the functional monomer, N-(2-hydroxyisopropyl)acrylamide (HIPAAm), considering maintaining the continuous and repeated structure of the isopropylamide group after copolymerization and the monomer reactivity ratios. The thermoresponsive polymer was derived by conventional radical copolymerization of HIPAAm with N-isopropylacrylamide (NIPAAm) in high yield. Estimation of monomer reactivity ratios, r(1) and r(2), supported the almost random sequence of the comonomers. The obtained copolymers showed a very sensitive phase transition and/or separation in response to temperature in aqueous media although they have many hydrophilic parts, and their thermoresponsive behavior was not affected by the pH. Furthermore, the cloud points of these copolymers closely depended on the HIPAAm content and could be easily controlled by adding salts. HIPAAm is expected to regulate the phase transition and/or separation temperature of the NIPAAm-based copolymers while maintaining their desirable sensitive thermoresponse. Differential scanning calorimetric analysis showed that dehydration of the polymer chains occurring in phase transition became incomplete with increasing HIPAAm content. Moreover, it was found that poly(NIPAAm-co-HIPAAm) having a high content of the HIPAAm unit showed liquid-liquid phase separation involving coacervation. The sizes of the coacervate droplets were relatively monodisperse and very minimal. Poly(NIPAAm-co-HIPAAm) is valuable for use in biomedical fields such as bioseparation.

High temperature bulk copolymerization of methyl methacrylate and acrylonitrile. I. Reactivity ratio estimation

The copolymerization of methyl methacrylate and acrylonitrile has been studied in the bulk phase. Experiments for estimating reactivity ratios were conducted at 60, 100, 120, and 140°C. Tidwell–Mortimer and the feed composition constraint approaches were used to design the experiments. The error in variables model (EVM) method was employed to evaluate the reactivity ratios and analyze the error involved. The results show that the reactivity ratios do not vary significantly with temperature up to 140°C. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 843–851, 2006

Styrene/Methacrylic Acid Monomer Reactivity Ratio Estimation in Bulk and Solution at High Temperatures

: Styrene/methacrylic acid (Sty/MAA) free radical copolymerizations have been conducted in bulk and in m-xylene solution (60 wt% solvent level) at 100 and 130°C using tert-butyl peroxybenzoate as initiator. Monomer reactivity ratios 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. It was found that the reactivity ratio values change with dilution by m-xylene from the values obtained in bulk at both temperatures.

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

Synthesis of random terpolymers and determination of reactivity ratios of N‐carboxyanhydrides of leucine, β‐benzyl aspartate, and valine

AbstractThe copolymerization and terpolymerization of leucine‐N‐carboxyanhydride, β‐benzyl aspartate‐ N‐carboxyanhydride, and valine‐N‐carboxyanhydride in dioxane, initiated with triethylamine, were investigated to determine the random nature of the terpolymer composition for potential applications as targeting drug delivery carriers. 1H NMR was used to obtain the actual monomer compositions of the polymers. The reactivity ratio of each monomer was determined with Fineman–Ross, Kelen–Tüdös, and nonlinear least‐squares curve‐ fitting methods. The product of the estimated reactivity ratios from the monomers in the binary copolymerizations indicated that random polymers were predominantly formed. On the basis of the reactivity ratios determined from the binary copolymers, Alfrey–Goldfinger equations were used to estimate the compositions of the terpolymers. There was no statistical difference between the actual monomer compositions and the calculated compositions of the terpolymers; this validated the reactivity ratios estimated by Fineman–Ross, Kelen–Tüdös, and nonlinear least‐squares curve‐ fitting methods. Therefore, the poly(leucine‐β‐Bzl‐ aspartate‐valine) synthesized in this study was primarily a random terpolymer. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 317–325, 2004

Estimation of monomer reactivity ratios in free‐radical solution copolymerization of lauryl methacrylate–isobutyl methacrylate

AbstractCopolymers of isobutyl methacrylate (i‐BMA) and lauryl methacrylate (LMA) were prepared by free‐radical solution copolymerizations at 70 °C with azobisisobutyronitrile (AIBN) as an initiator. The synthesis of these copolymers was investigated over a wide composition range both at low and high conversion levels. Copolymer compositions were determined from the %C, %H, and %O contents of copolymer by elemental analysis. Monomer reactivity ratios were estimated by analyzing composition data with nonlinear least‐squares (NLLS) models based on Marquardt optimization and van Herk methods. The point estimates, 95% individual confidence intervals and 95% joint confidence intervals are obtained from differential and integral approaches. Even though no explicit integral form for penultimate unit model (PUM) is available, a numerical approach is developed for integral estimation of reactivity ratios from PUM. A simulator program was developed which upon coupling of experimental data, NLLS analysis, and D‐optimal criteria calculates the best optimized values of monomer reactivity ratios and monomer feed compositions in a sequential and iterative order for terminal and penultimate unit models. Moreover, the simulator has the capibilities to calculate all features of van Herk method, maximum compositional drift in each monomer feed composition, and data reconciliation. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 112–129, 2004

A Generalized Least Square Model for the Determination of Monomer Reactivity Ratios in Free Radical Copolymerization Systems

AbstractThe reliable estimation of monomer reactivity ratios is a key problem in the development of process models, and, thus, is an important issue in both process design and control. Copolymers of isobutyl methacrylate (i‐BMA), and lauryl methacrylate (LMA) were prepared by free radical bulk copolymerization at 70 °C using 2,2′–azobisisobutyronitrile (AIBN) as initiator. The monomer reactivity ratios as well as the 95% confidence intervals were calculated from Fineman‐Ross, Ezrielev‐Brokhina‐Roskin, Kelen & Tudos, extended Kelen & Tudos and a linear iterative method proposed by Mao and Huglin. The estimation process was performed by applying nonlinear techniques based on Marquardt optimization, “ordinary least square” (OLS) and “generalized least square” (GLS) approaches and the results were compared with each other. The novel GLS estimator program developed during this study was employed to ascertain the shape of the copolymer composition curve and good agreement between experimental and calculated copolymer composition was obtained. Also, both real and simulated data was presented, which show GLS method is a statistically valid technique for estimating reactivity ratios by accounting response error structure. This new estimation method handles regression models with error terms that are heteroskedastic or serially correlated, or both.95% joint confidence interval for reactivity ratios from “NLLS” analysis.magnified image95% joint confidence interval for reactivity ratios from “NLLS” analysis.

Ethylene/1‐hexene copolymers synthesized with a single‐site catalyst: Crystallization analysis fractionation, modeling, and reactivity ratio estimation

AbstractA series of poly(ethylene‐co‐1‐hexene) samples made with rac‐ethylene bis(indenyl)zirconium dichloride/methylaluminoxane were analyzed by crystallization analysis fractionation (CRYSTAF). The nine samples had comonomer contents of 0–4.2 mol % 1‐hexene with a narrow range of molecular weights (34,000–39,000 g/mol). Because all the copolymer samples had narrow, unimodal chemical composition distributions, they were ideal as calibration standards for CRYSTAF. A linear calibration curve was constructed relating the peak crystallization temperature from CRYSTAF operated at a cooling rate of 0.1 °C/min and the comonomer content as determined by 13C NMR. Reactivity ratios for ethylene and 1‐hexene were estimated by the fitting of reactant liquid‐phase compositional data to the Mayo–Lewis equation. It was found that a value of the 1‐hexene reactivity ratio could not be unequivocally determined from the set of samples analyzed because the range of comonomer incorporation was too narrow. Stockmayer's bivariate distribution was used to model the fractionation process in CRYSTAF, and although a good fit to experimental CRYSTAF profiles was attained, the model did not fully describe the underlying crystallization phenomena. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2595–2611, 2002

Sulfobetaine zwitterionomers based on n‐butyl acrylate and 2‐ethoxyethyl acrylate: Monomer synthesis and copolymerization behavior

AbstractNew materials with potential applications for adhesives and coatings, based on copolymers containing zwitterionic pendent groups, were investigated. n‐Butyl acrylate and 2‐ethoxyethyl acrylate were copolymerized with a series of five zwitterionic sulfobetaine monomers. The structure of the monomers was varied in terms of the zwitterion intercharge spacing and the bulkiness of the alkyl substituents at the quaternary ammonium unit. Four of the five zwitterionic sulfobetaine methacrylate (SBM) monomers used in the study were synthesized. An evaluation of the reactivity ratios for the copolymer systems was performed with programs based on statistically sound techniques such as the error‐in‐variables model and the nonlinear‐least‐squares method. Reactivity ratio estimates for all 10 comonomer pairs were obtained, and they showed clear variations in reactivity with the structure of the SBM. In general, the more hydrophobic the SBM was, the lower its reactivity was with respect to the acrylate monomers. © 2002 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 40: 511–523, 2002; DOI 10.1002/pola.10138

Bulk and solution copolymerization of methyl methacrylate and vinyl acetate

AbstractA series of batch, bulk and solution (in toluene) copolymerizations of methyl methacrylate and vinyl acetate was performed under various reaction conditions to high monomer conversions. In addition, low conversion bulk experiments were performed to estimate monomer reactivity ratios using the error in variables model method, based on terminal model (Mayo–Lewis) kinetics. A combination of the low and high conversion data with data from a previous study yielded reactivity ratio (r) estimates of 27.465 and 0.0102 for rMMA and rVAc, respectively, using the integrated copolymer composition (Meyer–Lowry) equation. In the high conversion experiments the effects of various factors on the reaction rate, cumulative copolymer composition, number‐ and weight‐average molecular weights, and molecular weight distribution were studied. The factors included the monomer feed composition, initiator concentration, temperature, solvent concentration, and the addition of n‐dodecyl mercaptan chain transfer agent. These factors were examined in light of the wide difference in the monomer reactivity ratios. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 82: 1238–1255, 2001

Use of the Maximum Likelihood Method for Composition Data Analysis in the Radical Copolymerization Terminal Model

A method based on the maximum likelihood principle has been used for the estimation of reactivity ratios in the terminal model of copolymerization from experimental composition data. This method assumes explicitly that all measured variables are subject to errors. If correct estimates of experimental errors are used the best values of parameters are obtained. In addition, this method can also be used for the copolymerization model validation and/or evaluation of the accuracy of the experi mental data. The application of the method is illustrated using simulated data disturbed with random errors.

Continuous solution copolymerization of ethylene with propylene using a constrained geometry catalyst system

Ethylene (E)/propylene (P) continuous solution copolymerization using the constrained geometry catalyst system, [CpMe4(SiMe2NtBu)]TiMe2 (CGC)/tris(pentafluorophenyl)boron/modified methylaluminoxane, was carried out at 3.45×103 kPa and 130, 140, and 150°C. Ethylene and propylene copolymers with a broad range of composition fractions were synthesized and characterized. The incorporation of propylene lowered the catalyst activity and increased chain termination reactions. The estimated reactivity ratios rE and rP were 2.89 and 0.324 at 130°C, 4.33 and 0.377 at 140°C, and 6.36 and 0.436 at 150°C, respectively. The relatively low rE and high rP values of CGC compared to other metallocene systems indicated a ready incorporation of propylene in ethylene/propylene copolymerization. The activation energies ΔEE and ΔEP were 56 and 21 kJ/mol, showing a more significant effect of polymerization temperature on rE than on rP. The reactivity ratios for normal propylene, inverted propylene, and ethylene were also estimated from the methylene sequence distributions.

Radical copolymerization of novel trifluorovinyl ethers with ethyl vinyl ether and vinyl acetate: Estimating reactivity ratios and understanding reactivity behavior of the propagating radical

Two novel trifluorovinyl ether (TFVE) monomers were copolymerized with either ethyl vinyl ether (EVE) or vinyl acetate (VAc) in a redox-initiated aqueous emulsion: 1-(2-phenoxyethoxy)-1,2,2-trifluoroethene (Ph-TFVE) and 1-[2-(2-ethoxyethoxy)ethoxy]-1,2,2-trifluoroethene (Et-TFVE). Previous studies demonstrated a propensity for radical hydrogen abstraction from the oligoether pendant group during the homopolymerization of Et-TFVE with continued propagation of the resulting radical, thereby providing the rationale to investigate the copolymerization of our new TFVEs with EVE or VAc. Reactivity ratios were estimated using the error-in-variables model from a series of bulk free radical copolymerizations of Ph-TFVE with EVE or VAc. The reactivity ratios were rPh-TFVE = 0.25 ± 0.07, rEVE = 0.016 ± 0.04; rPh-TFVE = 0.034 ± 0.04, rVAc =0.89 ±0.08. Partial hydrolysis of polymers containing VAc to vinyl alcohol (VA) resulted in two terpolymers: poly(Ph-TFVE-co-VAc-co-VA) and poly(Et-TFVE-co-VAc-co-VA), respectively. We investigated the possibility of hydrogen abstraction from VAc during polymerization by comparing the molar mass before and after hydrolysis. Abstraction from VAc was not apparent during polymerization; however, abstraction from the oligoether pendant group of Et-TFVE was again evident and was more significant for those copolymers having a greater fraction of Et-TFVE in the monomer feed. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 1344–1354, 2000