True reactivity ratios for styrene-methyl methacrylate copolymerization in bulk

The local composition concept has been adopted to account for the monomer partitioning effect in the vicinity of the growing macroradical in radical copolymerization. Local compositions were calculated in a two step procedure. In the first step the activity coefficients were calculated in the assumed model systems using the UNIFAC group contribution method

1 UNIFAC means UNIQUAC Functional Group Activity Coefficients, where UNIQUAC stands for Universal Quasichemical Activity Coefficients.

. Subsequently, the modified Wilson equation was applied for estimation of the Boltzmann factor in the derived formulae. Terminal and penultimate models for the bulk copolymerization were investigated. For both models corresponding formulae were derived relating copolymer composition with local mole fractions and the true reactivity ratios. Test calculations have been performed for the bulk styrene-methyl methacrylate system at 313.15 K.     

Terminal and Penultimate Reactivity Ratios in the Styrene-Acrylonitrile Free-Radical Copolymerization System in Bulk

ABSTRACT

The terminal and penultimate model reactivity ratios for the styrene-acrylonitrile monomer system in bulk have been investigated by the simplex and scanning method. It has been shown that Mayo-Lewis equation has an unique solution when determining the reactivity ratios according to the terminal model while for the penultimate model the non-uniqueness in determination of the reactivity ratios has been found. The numerical values of the penultimate r-parameters calculated with the simplex method depend on the initial guess for r-parameters.

Several sets of penultimate reactivity ratios for the styrene-acrylonitrile system in bulk have been found to be equal from mathematical point of view. The reactivity ratios with comparable standard deviation have an equivalent graphical representation on the copolymerization diagragm. It has been also confirmed that the penultimate model is a more appropriate of the models considered to describe the variation of the copolymer composition with the monomer feed. Taking into account previous results for the styrene-methyl methacrylate system in bulk it is thereby assumed that the occurrence non-uniqueness in determination of the penultimate model reactivity ratios does not depend on the monomer system.     

Triad distributions of 1,1-diphenylethylene–methyl acrylate copolymer determined from NMR study

The triad distributions of 1,1-diphenylethylene (D)–methyl acrylate (M) copolymers have been determined from NMR measurements and examined according to the terminal and penultimate models of copolymerization theory. As expected from the diamagnetic shielding by the phenyl rings of the nearest D units, the methoxy proton resonances were found to appear as three resolved peaks at 6.4–6.6 τ, 6.7–7.0 τ, and 7.2 τ, and have been assigned to the central M units of the triads MMM, MMD or DMM and DMD, respectively. The copolymer composition and the triad distributions observed are shown to agree better with the terminal model with the methyl acrylate reactivity ratio of 0.092 ± 0.010 than with the penultimate model.     

NON-LINEAR LEAST SQUARE CURVE FITTING OF COPOLYMERIZATION MODELS TO THE ALTERNATING TRIAD FRACTION OF COPOLYMERS OF STYRENE AND CITRACONIC ANHYDRIDE,AND COPOLYMERS OF STYRENE AND MALEIC ANHYDRIDE PREPARED IN N,N-DIMETHYLFORMAMIDE

Copolymers of styrene (ST) and citraconic anhydride (α-methylmaleic anhydride) (CA) were prepared in a very polar solvent, N,N-dimethylformamide (DMF), at 50.0°C with AIBN. The monomer unit triad fractions were determined by ¹³C NMR in acetone-d ₆ solution. Non linear least square (NLLS) curve fitting was performed for the copolymerization models of the terminal model, the penultimate unit effect model, the complex participation model, the complex dissociation model, and the so-called comppen model. The theoretical equations for the ST-centered alternating triad mole fraction were fitted by NLLS minimization routine to the triad fraction data of the ST-CA copolymers and that of the ST-maleic anhydride (MA) copolymers prepared in identical polymerization conditions. It was found that for rigidly alternating copolymers of ST-MA, the difference among the copolymerization models disappeared and all models merged together. The difference among the copolymerization models were somewhat more apparent for less alternating copolymers of ST-CA copolymers. The sum of squares values indicated that the copolymerization models, which involved some complex participation, fit the data better with the comppen model. This was a combination of a complex participation and penultimate unit effects, which performed best.     

Kinetics of copolymerization—VI Investigation of copolymer composition in the system acrylonitrile—methyl acrylate-dimethylformamide

The compositions of copolymers formed under different copolymerization conditions were studied for the system acrylonitrile-methyl acrylate-dimethylformamide at 50°C. The relationship between the compositions of the feed and the copolymer cannot be described with sufficient accuracy either by the classical copolymerization equation or by the equation derived from the penultimate model. The systematic deviations observed on application of the classical composition equation can be qualitatively well interpreted in terms of the hot radical theory.     

The mechanism of copolymerization of maleic anhydride with styrene and with vinyl acetate

A nonaqueous potentiometric direct titration method was used to determine the composition diagrams for the copolymerization of maleic anhydride with styrene and with vinyl acetate in methyl ethyl ketone at 50°C. The data were analyzed using nonlinear least-squares minimization routines to fit composition equations for the terminal, penultimate, and complex models directly. The applicability of each model to both systems were evaluated statistically. The penultimate model was found to best describe both systems, although in the case of the maleic anhydride/vinyl acetate system this was only a small improvement over the terminal model. Although significant comonomer complexation occurs in both systems, the complex model did not provide statistically significant improvement in fit to the data compared with the terminal model.     

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.     

Chain statistics and heat of reaction in random copolymerization

Copolymer chain-statistics and other properties including the heat of copolymerization are derived using the joint concepts of the mean-length of the sequences of each species along the copolymer chain and the number of transitions from sequences of one species to the other. The approach originated in papers of Smoluchowski going back to 1915. By systematic use of the approach, classical relationships are derived for both the terminal and the penultimate models of copolymerization. Relationships are given for the heat of copolymerization and the spectroscopic determination of the monomer reactivity ratios. The simultaneous use of the terminal and penultimate models for specific comonomer species is discussed.     

全氟甲基乙烯基醚和其它含氟单体乳液共聚合的竞聚率测定

分别通过气相色谱法测定了全氟甲基乙烯基醚 (PMVE)与偏氟乙烯 (VDF)以及PMVE与四氟乙烯(TFE)二元乳液共聚反应中的气相单体组成和共聚物组成 ,然后用非线性回归法 (RREVM )计算得TFE PMVE及VDF PMVE乳液共聚合反应的表观竞聚率分别为γTFE =3 89和γPMVE =0 0 5以及γVDF =1 0 6和γPMVE =0 11.结合已经测定的TFE VDF二元乳液共聚的表观竞聚率 ,计算了由VDF TFE PMVE三元乳液共聚合反应合成的共聚物组成 ,后者与由1 9F NMR实测的共聚物组成吻合     

A Two‐Step Interval and Modified Rosenbrock Method for Kinetic Parameter Estimation in Copolymerization Systems: A Robust and Reliable Approach

Summary: The kinetics of solution free radical copolymerization of isobutyl methacrylate (i‐BMA) and lauryl methacrylate (LMA) in benzene, initiated with 2,2‐azoisobutyronitrile (AIBN) were studied at different monomer feed compositions at low conversion levels. In order to avoid the complications of copolymerization kinetics, the pseudo‐kinetic rate constant method was applied in constant and variable volume polymerization systems. A two‐step procedure based on interval analysis and the modified Rosenbrock method was used to estimate the kinetic parameters of copolymerization. In the first step, initiation, coupled propagation‐termination and transfer rate parameters were determined from steady state kinetic equations using interval analysis. Since the objective function is non‐linear, non‐convex and has multiple local optima, a robust computational technique, based on the Interval Newton/Generalized Bisection (IN/GB) algorithm, was developed to solve this set of non‐linear algebraic equations. This method was used with mathematical and computational guarantees of certainty to find the global optimum. In the second step, the system of mole balance, population balance and moment equations, which are highly stiff ordinary differential equations, were discritized and solved by the modified Rosenbrock method. The results of the first computational step were inserted as an active or equality constraint in the second step to calculate the individual elementary rate parameters of the reaction. Statistical analysis indicated that the copolymer composition is well described by the terminal unit model (TUM), but the implicit penultimate unit effect (IPUE) model of Fukuda and coworkers is more suitable for describing the rate data. In contrast to most previously studied systems, it was found that propagation and coupled rate parameters are greater than those predicted by the TUM.

Variation of number average molecular weight of the copolymer in polymerization system for various initial monomer feed compositions at different reaction times (solid lines are computed results).     

An experimental verification of statistical discrimination between the terminal and penultimate copolymerization models

In this article, the modified Buzzi–Ferraris model discrimination method was used to design experiments to discriminate between the terminal and penultimate models for styrene methyl methacrylate (STY/MMA) copolymerization. The measured variables were ¹³C-NMR peak areas. The peak area assignments of Aerdts⁸ were used. After nine experiments, the terminal model was picked over the penultimate model at 99.99% confidence. More importantly, the experimental data showed that computer simulated data used in previous studies were realistic, and the conclusions drawn from the simulation studies were valid. This experimental verification continues to show that the use of statistical model discrimination techniques can improve our ability to discriminate between competing copolymerization models. © 1996 John Wiley & Sons, Inc.     

Copolymerization of Vinyl Chloride and Sulfur Dioxide. III. Evaluation of the Copolymerization Mechanism

The mechanism of copolymerization of vinyl chloride (V) with sulfur dioxide (S) to form a variable composition polysulfone with average V:S molar ratio n ≥ 1 is examined. The copolymerization deviates from Lewis-Mayo behavior above -78°C. Alternative models for propagation involving (1) penultimate and pen-penultimate unit effects, (2) complex participation, and (3) depropagation are considered quantitatively by comparison of calculated and experimental copolymer/comonomer composition relationships and comonomer sequence distributions. Our theoretical modeling of the copolymerization shows that it is difficult to discriminate convincingly between alternative mechanisms. The penultimate and pen-penultimate effect models can account for the copolymer compositions, but not for the dilution effects which were observed provided the diluent is truly inert. The complex participation model can account for experimental behavior from -78 to -18°C by the assumption of addition of SV complexes, but it becomes rapidly less satisfactory at higher temperatures. Depropagation is the only model which can account for the compositions and dilution effects above 0°C. Progressive depropagation, with increasing temperature, of chains ending in the triad sequences ～SVS?, ～VVS?, and ～VSV? can explain the observed behavior over the entire comonomer composition and temperature range, but involvement of comonomer complexes in the propagation reactions is highly likely below 0°C.     

Special Forms of Copolymer Composition Equations

A theoretical explanation is presented for the experimentally observed binary copolymer composition equations in the form of y = Kx^a, where y is the ratio of the numbers of two monomers being incorporated in the polymer, x is the number or concentration ratio of the two monomers in the feed, and K and “a” are constants characteristic of the copolymerization system. The value of “a,” found experimentally, ranges from 0 to near 4. It is shown that the composition equation of this form with a = 0, 1, 2, 3, and 4 can be obtained under various limiting conditions from the conventional copolymer composition equations which take into account the terminal and penultimate effects. This simplification is often accompanied with reduction in the order of Markovian comonomer sequence distribution statistics associated with the original standard composition equations. It is also pointed out that the conventional composition equations can account for y = Kx^a with noninteger “a” for limited experimental ranges of x.     

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.     

Copolymers of conjugated dienes with maleic acid monoesters. IV. Reactivity ratios in copolymerization of isoprene with maleic acid monoesters

Research was carried out on copolymerization of isoprene with maleic acid monoesters in the presence of free radicals (AIBN). The aim of the study was to observe the effect of the different monoesters obtained with normal alcohols of the aliphatic series: monoethyl maleate, monopropyl maleate, monobutyl maleate, monoheptyl maleate, monolauryl maleate, and monocetyl maleate. On the basis of reactivity ratios determined by the Fineman-Ross method and compared with the Mayo-Lewis method, all the systems studied are typical cases of heterocopolymerization. The parameter r₁ is constant for this homologous series with the exception of the low terms. The experimental results agree with the ultimate model equation (with deviation at very high values of [M₁⁰]/[M₂⁰]), but not with the copolymer composition equation which considers the effect of the penultimate unity (penultimate model). Characterization of the sequential distribution is also presented (considering the effect of the terminal group only), and deviations of the experimental results are also discussed.     

Application of Markov chains to copolymerizations

Binary copolymerization is treated as a Markov chain process to calculate the distribution of the degree of polymerization for three different copolymerization models. The results for the terminal model according to Melville and Walling show considerable differences compared to the models according to Russo and Munari and Inagaki and Fukuda. Although these latter models start from different assumptions, one considering a penultimate effect in termination reactions, the other one a penultimate effect in propagation reactions, the results for these two models differ only slightly.     

四氟乙烯/偏氟乙烯乳液共聚反应的竞聚率测定

用亨利定律关联了四氟乙烯 (TFE) /偏氟乙烯 (VDF)乳液共聚合体系中的单体气相分压与其对应液相浓度间的关系 ,推导了用气相摩尔分数表示的共聚物组成方程式 .通过气相色谱和19F NMR分别测定了共聚反应前后气相单体组成和共聚物组成 ,用非线性回归法 (RREVM )计算TFE/VDF乳液共聚合反应表观竞聚率分别为γTFE=0 35和γVDF=0 6 3 .将实测的表观竞聚率代入共聚物组成方程计算共聚物组成与由19F NMR测定的结果一致 ,为进一步的工业放大试验提供科学依据     

Kinetic Study of Radical Polymerization VIII. A Comprehensive Study of Solution Copolymerization of Vinyl Acetate and Methyl Acrylate by 1H‐NMR Spectroscopy

Radical copolymerization reaction of vinyl acetate (VA) and methyl acrylate (MA) was performed in a solution of benzene‐d₆ using benzoyl peroxide (BPO) as the initiator at 60°C. Kinetic studies of this copolymerization reaction were investigated by on‐line ¹H‐NMR spectroscopy. Individual monomer conversions vs. reaction time, which was followed by this technique, were used to calculate the overall monomer conversion, as well as the monomer mixture and the copolymer compositions as a function of time. Monomer reactivity ratios were calculated by various linear and nonlinear terminal models and also by simplified penultimate model with r _2(VA)=0 at low and medium/high conversions. Overall rate coefficient of copolymerization was calculated from the overall monomer conversion vs. time data and k _p  . k _t ^?0.5 was then estimated. It was observed that k _p  . k _t ^?0.5 increases with increasing the mole fraction of MA in the initial feed, indicating the increase in the polymerization rate with increasing MA concentration in the initial monomer mixture. The effect of mole fraction of MA in the initial monomer mixture on the drifts in the monomer mixture and copolymer compositions with reaction progress was also evaluated experimentally and theoretically.     

Monte Carlo Study of Binary Copolymerizations. 1. Ultimate and Penultimate Effect,Applications

The Monte Carlo models of binary irreversible copolymeriza-tion with ultimate and penultimate effect are applied to the copolymerization of acrylic acid and methyl acrylate, and styrene and benzylidene malononitrile, respectively. The agreement with available experimental data is quite good. A comparative study between the formal kinetics model and the Monte Carlo model reveals that statements concerning the copolymer composition are robust, but statements concerning the sequence distribution are not always robust.