Estimating Reactivity Ratios From Triad Fraction Data

Reactivity 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.     

Calorimetric monitoring of emulsion copolymerization reactions

An approach for monitoring both the overall conversion and the cumulative copolymer composition in emulsion copolymerization systems via calorimetric measurements was developed. The approach was checked by carrying out batch emulsion copolymerizations of methyl methacrylate/n-butyl acrylate, n-butyl acrylate/vinyl acetate, and methyl methacrylate/vinyl acetate and comparing calorimetric based estimations with off-line determinations of both the overall conversion and the cumulative copolymer composition. A good agreement was achieved for most of the cases studied. © 1993 John Wiley & Sons, Inc.     

Emulsion co- and terpolymerization of styrene,methyl methacrylate,and methyl acrylate. I. Experimental determination and model prediction of composition drift and microstructure in batch reactions

In Part I of this series the reactivity ratios of the comonomer pair methyl acrylate-methyl methacrylate were determined with low-conversion bulk polymerizations. It was shown that the binary reactivity ratios of the systems styrene-methyl acrylate, styrene-methyl methacrylate, and methyl acrylate-methyl methacrylate describe composition drift in low-coversion bulk terpolymerizations with these monomers reasonably well. A computer model was developed to simulate the composition drift in emulsion co- and terpolymerizations. The composition drift in two batch emulsion copolymerization systems (styrene-methyl acrylate and methyl acrylate-methyl methacrylate) and one emulsion terpolymerization system (styrene-methyl acrylate-methyl methacrylate) was investigated both experimentally and with the model. Experimental results were compared with model calculations. The copolymer chemical composition distributions (CCD) were determined with gradient polymer elution chromatography (GPEC®). This technique was also used for the first time to obtain information about the extent of composition drift in emulsion terpolymerizations. Cumulative terpolymer compositions were determined with ³H-NMR as a function of conversion and with this information the three-dimensional CCD was obtained. The composition drift was analyzed with respect to free radical copolymerization kinetics (reactivity ratios) and monomer partitioning. It was shown that in most emulsion copolymerizations the composition drift is mainly determined by the reactivity of the monomers and to a lesser extent by monomer partitioning, except in systems where there is a large difference in water solubility. The model predictions for cumulative terpolymer composition as a function of conversion and the three-dimensional terpolymer CCD showed excellent agreement with the experiments. The GPEC® elution chromatogram of the terpolymer was found to be in accordance with the predicted CCD and the experimentally determined CCD. © 1996 John Wiley & Sons, Inc.     

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

Copolymers 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     

Ethyl Acrylate‐Hydroxyethyl Acrylate and Hydroxyethyl Acrylate‐Methacrylic Acid: Reactivity Ratio Estimation from Cross‐linked Polymer Using High Resolution Magic Angle Spinning Spectroscopy

Solution free radical copolymerizations of hydroxyethyl acrylate/methacrylic acid (HEA/MAA) and ethyl acrylate/hydroxyethyl acrylate (EA/HEA) have been conducted in m‐xylene (60 wt% solvent level) over the temperature range of 70–130°C using tert‐butyl peroxybenzoate as initiator. High resolution magic angle spinning spectroscopy (HR–MAS) and 2D–NMR have been utilized to characterize the copolymer gel for copolymer composition. The reactivity ratio values 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. Also, Arrhenius‐type reactivity ratio expressions have been developed that describe how reactivity ratios vary with temperature.     

Copolymerization with depropagation: A study of α‐methyl styrene/methyl methacrylate in bulk at elevated temperatures

Previously published material on the α‐methyl styrene/methyl methacrylate (α‐MS/MMA) copolymer system at temperatures above the ceiling temperature of α‐MS has focused on low‐conversion results. Several attempts have been made to estimate copolymer reactivity ratios from experimental data, but in most cases errors are present in the determination of copolymer composition variables. In this article, the results of rigorous parameter estimations, as applied to two sets of equations developed independently by P. Wittmer (Adv Chem 1971, 99, 140–174) and H. Kruger, J. Bauer, and J. Rubner (Makromol Chem 1987, 188, 2163–2175), are discussed. Experimental data for the copolymer system at low conversions, as well as over the full conversion range, are presented, covering a temperature range of 60–140 °C. A comparison of the data trends with traditional copolymer systems indicates that the reversibility of both MMA and α‐MS must be considered when composition, polymerization rate, or molecular weight equations are being developed. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 1981–1990, 2000     

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     

用~(13)CNMR研究丁苯阴离子共聚体系中各活性种的竞聚率

本文利用~(13)CNMR测试数据,计算了丁苯阴离子共聚体系中各活性种的竞聚率,得到了与动力学数据较一致的结果,对阴离子聚合反应Markov级数问题进行了讨论,并对用积分法计算高转化率下共聚物二元组组成进行了探索。     

α-甲基苯乙烯与苯乙烯阴离子共聚合研究——Ⅱ.共聚组成及单体表观竞聚率

 本文研究了以正丁基锂为引发剂、四氢呋喃为极性添加剂,在环己烷中进行α-甲基苯乙烯与苯乙烯阴离子共聚合。通过共聚组成及聚合活性种研究,由反应机理推导了该体系的共聚组成方程,求得了不同[THF]下的表观竞聚率值r₁和r₂。     

α-甲基苯乙烯与苯乙烯阴离子共聚合研究——Ⅱ.共聚组成及单体表观竞聚率

本文研究了以正丁基锂为引发剂、四氢呋喃为极性添加剂,在环己烷中进行α-甲基苯乙烯与苯乙烯阴离子共聚合。通过共聚组成及聚合活性种研究,由反应机理推导了该体系的共聚组成方程,求得了不同[THF]下的表观竞聚率值(?)和(?)。     

Estimation of Reactivity Ratios in the Copolymerization of Styrene and VeoVa‐10

The 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.     

Estimation of monomer reactivity ratios by nonlinear least-squares procedure with consideration of the weight of experimental data

To obtain the optimum values of the monomer reactivity ratios for the copolymerization systems with largely different reactivities between both monomers, a nonlinear least-squares procedure which took into account the weights of experimental data, was proposed and discussed. The weights of the data were treated for the errors arisen from the amounts of monomers charged, the densities of monomers, the weights of copolymer formed, and the composition of copolymer. The least-squares procedure with the consideration of the weights was applicable to both differentiated equation and integrated equation derived by Lewis and Mayo. This procedure was applied to radical copolymerizations of α-substituted crotonic esters with styrene, and reasonable monomer reactivity ratios were obtained. It was noted that errors from the copolymer composition were more important than those from the other factors and that the use of the integrated equation was recommended even when the copolymers were isolated at low conversions.     

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 experimental data. The application of the method is illustrated using simulated data disturbed with random errors.     

Model prediction of batch emulsion copolymerization as a function of conversion: A sensitivity analysis

Recently a model has been developed capable of predicting absolute monomer concentrations and their ratios in the polymer, aqueous, and monomer droplet phases as a function of conversion in batch emulsion copolymerizations without using any adjustable parameters. In this article the sensitivity of model predictions of composition drift toward deviations of 10% in all model parameters (maximum swellabilities of monomer in the polymer phase, water solubilities, reactivity ratios, and monomer and polymer densities) was estimated using the monomer combination methyl methacrylate-styrene as an example. From the sensitivity analysis it can be concluded that the reactivity ratios are the most important parameters affecting composition drift. The effects of deviations in maximum swellabilities and monomer and polymer densities on composition drift can be neglected, while the water solubility is important only in those cases where the amount of monomer in the aqueous phase cannot be neglected as compared with the total monomer amount. © 1994 John Wiley & Sons, Inc.     

Determination of the reactivity parameters for the copolymerization of butyl acrylate with vinyl acetate

The composition of vinyl acetate–butyl acrylate copolymers obtained with batch emulsion polymerization have been studied by ¹H-NMR. Using the integrated copolymerization Meyer–Lowry equation, the apparent reactivity ratios of the two monomers were calculated as 10.67 for r₁, the reactivity ratio of butyl acrylate (BA), and 0.024 for r₂, the reactivity ratio of vinyl acetate (VAC). These results were compared with those obtained by other methods.     

Batch and semicontinuous emulsion copolymerization of vinyl acetat–butyl acrylate. I. Bulk,surface, and colloidal properties of copolymer latexes

Vinyl acetate (VAc)–butyl acrylate (BuA) comonomer mixtures with various composition were polymerized by batch and semicontinuous emulsion polymerization processes. PVAc and PBuA homopolymer latexes as well as the (VAc-BuA) copolymer latexes were characterized with respect to particle size, molecular weight, acid end groups on particle surfaces, and colloidal stability against electrolytes. The surface and colloidal properties of these latexes were also compared before and after aging and acid hydrolysis. The average particle size of batch latexes was independent of copolymer composition, whereas for semicontinuous latexes it decreased with increasing BuA content and was always lower than that of the corresponding batch latex. The molecular weight distribution (MWD) for batch latexes was narrower and much less dependent on composition than that of the semicontinuous latexes; bimodal MWD was found in most semicontinuous latexes with a substantial amount of low MW fraction. The total weak and strong acid end groups on particle surfaces for semicontinuous latexes is higher, and more dependent on composition, than the batch latexes. Acid-induced hydrolysis results in a drastic change in the type and concentration of the surface groups of the semicontinuous latex particles. Colloidal stability against electrolytes showed that both electrostatic (due to surface acid groups) and steric [due to surface poly(vinyl alcohol)] mechanisms are contributing. However, for semicontinuous latexes, increasing PVAc content above 50 mol % resulted in a proportional increase and ultimately dominant role of steric stabilization. The results were interpreted in terms of differences in reactivity ratios and water solubilities of the two monomers and their effects on the locus of initiation and growth in the two polymerization processes, as well as the monomer sequence within the polymer chain and degree of homogeniety of the copolymer composition within the particle.     

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.     

Composition control of copolymer in semibatch emulsion copolymerization. II. MMA/styrene/BMA three‐component system

In this study, polymers of the MMA/Styrene/BMA three‐component system were synthesized through either soapless semibatch emulsion copolymerization or soapless batch emulsion copolymerization technique. The optimal monomer feed flow rate was determined from the interphase partition laws, monomer reactivity ratios, and three or four times of iterative experimental procedures through semibatch emulsion copolymerization. As a result, the instantaneous composition of polymers could also be effectively controlled to get the desired final products. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 3253–3269, 2000     

Bulk Free‐Radical Co‐ and Terpolymerization of n‐Butyl Acrylate/2‐Ethylhexyl Acrylate/Methyl Methacrylate

n‐Butyl acrylate (BA), 2‐ethylhexyl acrylate (EHA), and methyl methacrylate (MMA) are commonly used monomers in pressure‐sensitive adhesive formulations. The bulk free‐radical copolymerizations of BA/EHA, MMA/EHA, and BA/MMA are studied at 60 °C to demonstrate the use of copolymer reactivity ratios for the prediction of BA/MMA/EHA terpolymer composition. The reactivity ratios for BA/EHA and MMA/EHA copolymer systems are determined using low conversion experiments; BA/MMA reactivity ratios are already known from the literature. The reactivity ratio estimates for the BA/EHA system are r _BA = 0.994 and r _EHA = 1.621 and the estimates for MMA/EHA are r _MMA = 1.496 and r _EHA = 0.315. High conversion experiments are conducted to validate the reactivity ratios. The copolymer reactivity ratios are shown to predict terpolymer composition of high conversion BA/MMA/EHA experiments.     

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.