Non-uniqueness in determination of terminal and penultimate model reactivity ratios in the styrene-methyl methacrylate free-radical copolymerization system

The terminal and penultimate model reactivity ratios in the free-radical copolymerization of styrene and methyl methacrylate in bulk at 40°C were calculated by means of the simplex and scanning methods. Calculations showed that for the terminal model r₁ and r₂ vary in comparatively narrow ranges of 0.548–0.552 and 0.480–0.483, respectively. For the penultimate model, the most accurate reactivity ratios calculated by the simplex method, which were r₁₁ = 0.727, r₂₂ = 0.490, r₂₁ = 2.890, r₁₂ = 4.583, are surrounded with sets of reactivity ratio values of equal accuracy. The ranges of variation were found to be 0.711–0.746, 0.487–0.492, 2.810–2.970 and 4.213–5.049, respectively. Numerical values of the penultimate r-parameters calculated with the simplex method depend, due to the structure of the multidimensional space (r₁₁, r₂₂, r₂₁, r₁₂, σ), on the initial guess for the r-parameters. Use of the covariance matrix for the estimation of the indetermination ranges is discussed.     

Application of the monomer reactivity ratios to the kinetic‐model discrimination and the solvent‐effect determination for the styrene/acrylonitrile monomer system

The impact of reactivity ratios determined with the Nelder and Mead simplex method on the kinetic‐model discrimination and the solvent‐effect determination for the styrene/acrylonitrile monomer system was investigated. For the monomer system, the penultimate unit effect was inversely proportional to the polarity of the solvent: acetonitrile < N,N‐dimethylformamide < methyl ethyl ketone < toluene. Quantitatively, the penultimate unit effect could be correlated with an absolute value of the difference between the standard deviation of the reactivity ratios determined for the terminal and penultimate models. By application of the F test, the penultimate model was justified for copolymerization in toluene. The conclusion was less certain for polymerization in methyl ethyl ketone. With a scanning procedure based on the simplex method, it was found that an equivalent representation of the copolymer‐composition data could be achieved with multiple sets of penultimate‐model reactivity ratios. However, the relationship between the triad‐sequence distribution and copolymer composition depended on the reactivity‐ratio set chosen for the microstructure determination. The microstructure calculated with the penultimate‐model reactivity ratios determined with the simplex method from the initial guess (r₁₁ = r₁, r₂₁ = 1/r₂, r₂₂ = r₂, r₁₂ = 1/r₁) did not obey the general “bootstrap effect” rule. This observation still requires some theoretical interpretation. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 846–854, 2000     

Styrene—Acrylonitrile Copolymerization: Effect of Remote Units on the Reactivity of the Styrene-Ended Radicals

Application of the gas-liquid chromatographic method to the analysis of the process of styrene-acrylonitrile radical copolymerization, especially with a monomer mixture rich in styrene, provided evidence for penultimate and antepenultimate effects. Methods are given for the determination of the corresponding reactivity ratios:

r _A ≈ 0, r _AS = 0.55, r _ASS = 0.50, r _SSS = 0.25     

Fortran IV programs for the penultimate copolymerization model

Three programs have been written for calculations involving use of the penultimate copolymerization model. The first computes the penultimate reactivity ratios from composition-conversion data, without constraints, at any conversion. A nonlinear leastsquares technique using Marquardt's algorithm is employed. The second program computes the four optimum starting monomer feed ratios, M₁⁰/M₂⁰ which should be used by the experimenter from the penultimate reactivity ratios. These optimum feed ratios are obtained by choosing the conditions necessary to minimize the determinant of the variance-covariance matrix. The input for the first program includes estimates of known values of the penultimate reactivity ratios. By using these two programs sequentially the experimenter has an optimized experimental approach toward evaluating penultimate reactivity ratios at any conversion. Finally, a program has been provided to calculate composition–conversion data, given penultimate reactivity ratios.     

POLYACRYLONITRILE PRECURSORS FOR CARBON FIBER WITH IMIDOCARBOX YLIC ACID UNITS: COPOLYMERIZATION OF ACRYLONITRILE WITH MALEIMIDOBENZOIC ACID

ABSTRACT

4-Maleimidobenzoic acid (MBA) was explored as a comonomer in polyacrylonitrile (PAN) precursors for carbon fiber. The copolymerization of acrylonitrile (AN) with MBA was carried out in DMF. The reactivity of MBA was considerably less than that of AN, which was manifested as a negative reactivity ratio for the former. The r _MBA- values from ?0.24 to ?0.33 and r _AN values of 1.07 were obtained by Kelen-Tudos and extended Kelen-Tudos methods. The penultimate reactivity ratios were determined by both linear and non-linear methods. The values were r ₁=0.0093, r ₁′=0.0132, r ₂=1.063 and r ₂′=1.625. The relative MBA concentration in the copolymer decreased drastically on enhancing its content in the monomer mixture. The penultimate model could satisfactorily explain the feed-copolymer composition profile for the whole composition range. MBA caused a decrease in the apparent copolymerization rate and molecular weight in agreement with the observed trends in the reactivity ratios. A statistical prediction of monomer sequences based on reactivity ratios implied that MBA existed as a lone monomer unit between the long sequences of AN units. This sequence distribution is suited for the efficiency of MBA in cyclisation reaction, which stabilizes PAN during its pyrolysis. Optimum thermal stabilization effect and char yield were observed for copolymers with around 3 mol% MBA in the chain.     

Search for a Steric Penultimate Effect: Copolymerization of 2,3,4-Trimethyl-3-pentyl Methacrylate with Styrene

The hindered monomer, 2,3,4-trimethyl-3-pentyl methacrylate (I), was synthesized for penultimate effect studies. Since it readily homopoiymerized (km¹¹¹≠ 0) and readily copolymerized with styrene, copolymerizations of I with styrene were carried out at 60°C in benzene with AIBN as initiator. The conversion to copolymer and the copolymer composition were determined by using GLC techniques. Composition-conversion data was analyzed by performing a computerized nonlinear least-squares fitting to the integrated form of the penultimate model equation. The experimental design included the use of optimized M¹°/M²° ratios. The penultimate reactivity ratios calculated from these data were r¹′ = 0.23, r¹′= 0.59, r² = 0.59, r²′ = 1.34. Thus, when I is the penultimate unit, a terminal styryl radical prefers to add styrene, whereas when styrene is the penultimate unit, terminal styryl radicals prefer to add I. These results constitute the best evidence for a steric penultimate effect yet available in the literature from composition-conversion studies. However, the case is not yet proved. Further studies to strengthen this conclusion are proposed.     

A study of the relative reactivity of maleic anhydride and some maleimides in free radical copolymerization and terpolymerization

Composition data for the free radical copolymerization of maleic anhydride with N-phenylmaleimide in toluene at 60°C have been obtained. Relative reactivity ratios in terminal and penultimate models using nonlinear least-squares optimization routine have been determined. The standard error was found to be somewhat smaller in the penultimate model, but is still larger than the uncertainty estimated for the copolymer composition. Terpolymers of maleic anhydride and styrene with maleimide, N-butylmaleimide, N-phenylmaleimide, and N-carbamylmaleimide were obtained. On the basis of analysis of the product composition at various monomer feeds the relative reactivity of maleic anhydride and maleimides in these reactions is compared and the influence of the structure of thesemonomers on the rate of some chain growth reactions is discussed.     

Solvent and kinetic penultimate unit effects in the copolymerization of acrylonitrile with itaconic acid

Copolymerization of acrylonitrile (AN) with itaconic acid (IA) in dimethylformamide (DMF) and DMF/water mixture was investigated at enhanced concentrations of the latter. Analysis of the copolymer composition revealed the existence of a marked penultimate unit effect with respect to radicals terminated in AN. The reactivity of IA was considerably less than that of AN, manifested as a negative reactivity ratio for the former. The r_IA values ranging from −0.28 to −0.50 and r_AN values ranging from 0.53 to 0.70, were obtained by Kelen-Tudo's (KT) and extended KT methods. The penultimate reactivity ratios were determined by both linear and non-linear methods. The values ranged from r₁=0.009 to 0.01, r₁^′=0.0015 to 0.0043, r₂=0.54 to 0.69 and r₂^′=0.9 to 1.03. The reactivity of AN radical towards IA decreased about twofold when the latter formed the penultimate group. The penultimate model explained an acceptable rational feed-copolymer composition profile for the whole composition range. Addition of water decreased the reactivity of IA slightly. IA caused a decrease in the apparent copolymerization rate in agreement with the observed trends in the reactivity ratios; presence of water caused a further decrease in the rate of polymerization. A statistical prediction of monomer sequences based on reactivity ratios implied that IA existed as a lone monomer unit between the long sequences of AN units.     

Copolymerization of 4-methyl-1,3-dioxene-4 with maleic anhydride and terpolymerization with styrene as the third component

Copolymerization of 4-methyl-1,3-dioxene-4 with maleic anhydride was carried out. The monomer reactivity ratio was determined to be r₁ = 0.18, r₂ ～ 0 in terminal model and r₁ = 0.015, r₁′ = 0.224, r₂′ = r₂′ = 0 in the penultimate model. Calculations of run number, linkage probabilities, and number-average chain length in the terminal model and comparison of n (mole ratio of each monomer unit content in copolymer) in each model with the experimental value was made. From these results, the obtained polymer was confirmed to be alternating. Terpolymerization of 4-methyl-1,3-dioxene-4 with maleic anhydride and styrene was also carried out. The agreement of the experimental value (titration by indicator or electroconductivity) of maleic anhydride content with the theoretical value confirms that the terpolymer has a DMS triad sequence.     

Determination of the reactivity ratios of methyl acrylate with the vinyl acetate,vinyl 2,2-dimethyl-propanoate,and vinyl 2-ethylhexanoate

The course of composition drift in copolymerization reactions is determined by reactivity ratios of the contributing monomers. Since polymer properties are directly correlated with the resulting chemical composition distribution, reactivity ratios are of paramount importance. Furthermore, obtaining correct reactivity ratios is a prerequisite for good model predictions. For vinyl acetate (VAc), vinyl 2,2-dimethyl-propanoate also known as vinyl pivalate (VPV), and vinyl 2-ethylhexanoate (V2EH), the reactivity ratios with methyl acrylate (MA) have been determined by means of low conversion bulk polymerization. The mol fraction of MA in the resulting copolymer was determined by ¹H-NMR. Nonlinear optimization on the thus-obtained monomer feed–copolymer composition data resulted in the following sets of reactivity ratios: r_MA = 6.9 ± 1.4 and r_VAc = 0.013 ± 0.02; r_MA = 5.5 ± 1.2 and r_VPV = 0.017 ± 0.035; r_MA = 6.9 ± 2.7 and r_V2EH = 0.093 ± 0.23. As a result of the similar and overlapping reactivity data of the three methyl acrylate–vinyl ester monomer systems, for practical puposes these data can be described with one set of reactivity data. Nonlinear optimization of all monomer feed–copolymer composition data together resulted in r_MA = 6.1 ± 0.6 and r_VEst = 0.0087 ± 0.023. © 1994 John Wiley & Sons, Inc.     

Pulsed laser terpolymerization of styrene,methyl methacrylate and methyl acrylate

The propagation rate coefficient of the terpolymerization of styrene, methyl methacrylate and methyl acrylate in bulk was successfully determined at three different monomer compositions. The temperature was varied between 18 and 80°C. The resulting data at 50°C were not in agreement with predictions according to the terminal model with binary reactivity ratios that have been determined by fitting copolymer composition data with the terminal model. This indicates that here also the penultimate unit affects the kinetics.     

Modelling copolymerization kinetics

The 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.     

Effect of the substituents on radical copolymerization of dialkyl fumarates with some vinyl monomers

Radical copolymerization of dialkyl fumarates (DRF) with various vinyl monomers was carried out in benzene at 60°C. The monomer reactivity ratios, r₁ and r₂, were determined from the comonomer-copolymer composition curves. The relative reactivity of DRFs with various ester substituents toward a polystyryl radical was revealed to depend on both steric and polar effects of the ester groups. It has also been clarified that α-substituents of the polymer radical have a significant role in addition of DRF, from the comparison of the monomer reactivity ratios determined in copolymerizations with monosubstituted and 1,1-disubstituted ethylenes. The absolute cross-propagation rate constants were also evaluated and discussed. © 1992 John Wiley & Sons, Inc.     

A method for determining reactivity ratios whenn copolymerizations are influenced by penultimate group effects

A novel kinetic treatment is proposed for the copolymerization of two monomers M₁ and M₂ when terminal −M₂· groups are susceptible to penultimate group effects. If [M₁] ⪢ [M₂], as is possible experimentally when M₂ is radioactively labelled, a value of the reactivity ratio r₁ which is independent of penultimate group effects can be obtained. This value is then used to find values for the other reactivity ratios. The method involves a solution for reactivity ratios by means of intersecting curves, each curve representing a given monomer feed ratio and copolymer composition ratio.     

Microstructure of ethylene–vinyl chloride copolymers. I. Direct verification of terminal radical effects on copolymerization by a simplified NMR approach

The sequence distributions of monomer units in a series of high-pressure, bulk ethylene–vinyl chloride copolymers have been determined by high-resolution NMR spectroscopy. The concentrations of EE, VV, and EV (VE) monomer pairs or diads were used with NMR-determined compositions to calculate, in addition to the sequence distribution parameters, the reactivity ratio product for the system. Inclusion of feed data allowed the calculation of individual reactivity ratios. Well within experimental error, the reactivity ratio product (r₁r₂ = 0.7) determined from microstructure analysis—independent of monomer feed data—was equal to that determined by the standard Fineman-Ross technique. Terminal monomer unit effects on the copolymerization were observed. The nonrandom structures result from a copolymerization described by first-order Markoffian statistics.     

Penultimate effects in methyl methacrylate-4-vinyl pyridine copolymers

From the ¹H-NMR spectra of methyl methacrylate (M₁)-4-vinyl pyridine (M₂) radical copolymers with various monomer ratios, the reactivity ratios have been found using the penultimate model (r₁₁ = 1.51 r₂₁ = 0.10 r₂ = 0.24) and the co-isotactic alternating addition probability (σ = 0.5) as the best fit of the pentad distribution between the three parts of the methoxy signal.     

Determination of microstructure and glass-transition temperature of acrylonitrile-methyl acrylate copolymers by 13C-NMR spectroscopy

Acrylonitrile-methyl acrylate (A/M) copolymers of different monomer compositions were prepared by bulk polymerization using free radical initiator (benzoyl peroxide). Copolymer compositions were determined by elemental analyses and comonomer reactivity ratios were determined by the nonlinear least squares errors-in-variables methods (EVM). Terminal and penultimate reactivity ratios have been calculated using the observed monomer triad sequence distribution determined from ¹³C{¹H}-NMR spectra. The triad sequence distribution was used to calculate diad concentrations, conditional probability parameters, number-average sequence lengths, and run number in the copolymers. The observed triad sequence concentrations determined from ¹³C{¹H}-NMR spectrum agreed well with those calculated from reactivity ratios. Glass transition temperatures (T_g) of various copolymers determined from DSC gave good agreement with those obtained from NMR. © 1992 John Wiley & Sons, Inc.     

An Error in Variables Method for Determining the Implicit Penultimate Copolymerization Ratios by On‐Line Monitoring of Reactions

Summary: In copolymerization systems with implicit penultimate effect, there are two radical reactivity ratios, s_a and s_b, which influence the reaction kinetics in addition to the monomer reactivity ratios, r_a and r_b, which govern the copolymer composition. Here, an error in variables method has been developed to determine s_a and s_b. It is based on continuous on‐line monitoring of the polymerization process, where monomer and polymer concentrations are measured through the monitoring of two independent properties of the system. The ratios and the corresponding χ² values were found by taking into account errors emanating from measurements and from calibration of the instruments. It is shown that the kinetic data allows both ratios to be found if both monomer reactivity ratios are less than one. If the system is near ideality (r_ar_b ≅ 1) or if both reactivities are greater than one, only an average radical reactivity ratio, , can be reliably determined.

The 2σ confidence contours for the 3 individual experiments. The reactivity ratios are r_a = 0.5, r_b = 0.2, s_a = 0.3, s_b = 0.4. For clarity the contours are plotted as functions of 1/s_a and 1/s_b.