A new method of estimating monomer reactivity ratios in copolymerization by linear regression methods

Sequential gas-liquid chromotographic analysis of the reaction mixture throughout a copolymerization reaction in conjuction with the improved curve-fitting I (integrated form) method, which accounts for measurements errors in both variables, allows accurate estimation of the monomer reactivity ratios. In this article an alternative method is presented for estimating r values in copolymerization with linear regression only, which is especially suited to cases in which one or two of the r values is close to 1. In these cases the improved curve-fitting I method tends to converge slowly because of the numerical instability of the integrated copolymerization equation. The use of the new method is illustrated for the estimation of the r values for ethylene and vinyl acatate in benzene at 35 kg/cm² and 62°C. The linear regression method was also tried on other copolymerizations and the results are compared with those obtained from the improved curve-fitting I method. The limits of the applicability of the linear regression method were determined by simulated sequential sampling experiments. It appears that the new method is applicable when the product of the r values is between 0.001 and 2, provided both monomer conversions are large enough compared with the measurements error.     

Analysis of the linear methods for determining copolymerization reactivity ratios. II. A critical reexamination of cationic monomer reactivity ratios

A thorough examination of some cationic copolymerization systems by a new method has shown that many published r values have to be corrected significantly and that some are erroneous and meaningless, because for these systems the conventional copolymer compositions equation does not hold. Available information in regard of cationic copolymerizations has been treated in terms of three classes: (a) Systems in which the conventional copolymer composition equation adequately describes the copolymerization mechanism and previous authors justifiably used the two parameter model to calculate reactivity ratios. Our results show that the discrepancy between published r values and the more precise values obtained in this work is about ±23%. (b) Systems in which the approximations implicit in the conventional copolymer composition equation do not hold and the calculated r values are erroneous and misleading. Monomer pairs comprising monomers of significantly different reactivities belong to this class indicating that in copolymerizations in general and in cationic copolymerizations in particular a strong cast system exists, i.e., copolymerization can readily occur within the cast (between monomers of similar reactivities); however, only with difficulty if at all between casts (between monomers of differing reactivities). (c) Systems in which the use of the copolymer composition equation is completely unjustified, the calculated r values are meaningless and in some cases the existence of true copolymers is questioned.     

Comparative recalculation of the monomer reactivity ratios in copolymerization for styrene and methyl methacrylate

The monomer reactivity ratios (MMRs) in radical copolymerization for styrene and methyl methacrylate were recalculated by five different methods using literature copolymerization data. The use of approximate 95% confidence limits and their visual inspection helps to separate possibly biased copolymer composition data. The recalculated mean MRR values were r₁ (styrene) = 0.501 ± 0.031 and r₂ = 0.472 ± 0.031. The results of the linear least-squares calculation procedures seldom approach the quality of the nonlinear least-squares analysis according to the method of Tidwell and Mortimer.     

Radical copolymerization of styrene and alkyl methacrylates: monomer reactivity ratios and thermal properties

Copolymers containing styrene and alkyl methacrylate (n-butyl-, n-hexyl-, or stearyl methacrylate) at different compositions have been prepared by radical copolymerization. The monomer reactivity ratios were estimated using the Finemann-Ross, the inverted FR and the Kelen-Tüdos graphical methods. Structural parameters of the copolymers were obtained calculating the dyad monomer sequence fractions. The effect of the size of the alkyl methacrylate on the copolymer structure is discussed. The glass transition temperature, T_g of the copolymers with butyl and hexyl methacrylate was examined in the frame of several theoretical equations allowing the prediction of these T_g values. The best fit was obtained using methods that take into account the monomer sequence distribution of the copolymers. The copolymers of styrene with stearyl methacrylate exhibited the characteristic melting endotherm, due to the crystallinity of the methacrylate sequences and the polystyrene glass transition temperature.     

Bounds for reactivity indices

Lower and upper bounds are derived for bond number, localization energy and atom self-polarizability of alternant hydrocarbons. It is proved that in acyclic polyenes the maximal bond number is 1, 2 and 3, respectively for primary, secondary and tertiary carbon atoms.     

A microcomputer program for estimation of copolymerization reactivity ratios

A 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.     

Improved methods of estimating monomer reactivity ratios in copolymerization by considering experimental errors in both variables

Existing methods of calculating monomer reactivity ratios in copolymerization are reviewed briefly, evaluated, and classified according to their mathematical and computational similarities. More attention is paid to procedures based on the integrated copolymer equation with which calculation of r values is performed most often by electronic computer. Unfortunately, until now all procedures have shown shortcomings because the real-error structure of the observations has not been taken into account. A new algorithm that does account correctly for measurement errors in both variables is described. A computational method is illustrated for copolymerization data obtained from quantitative gas chromatographic analysis of the monomer feed throughout the reaction. It is shown that the actual error structure of the variables corresponds to the assumed error structure. Reliability of the estimates is substantially increased, compared with the existing methods. Standard deviations of the monomer reactivity ratios are given and appear to be in good agreement with reality.     

Perspective on metal-mediated polar monomer/alkene copolymerization

A major unsolved problem in polymer synthesis is the design of efficient metal-mediated systems for the copolymerization of alkenes with polar vinyl monomers, such as acrylates and methacrylates. There are several reasons for the absence of efficient transition metal-based insertion copolymerization catalysts. First, following insertion, the ester group of the acrylate coordinates to the metal thereby hindering subsequent monomer coordination. A second reason stems from the preferred 2,1-insertion of acrylates into metal-carbon bonds resulting in the placement of the ester group on the α-carbon. This makes the metal-alkyl species particularly prone to homolysis because of the enhanced stability of the resultant alkyl radical, one that is essentially the same as the propagating species in radical-initiated acrylate polymerization. In this perspective we focus on this issue of facile metal-carbon bond homolysis, especially following acrylate insertion, using examples from our own work. We suggest ways to circumvent these issues, for example forcing 1,2-insertion by imposing steric crowding at the metal. Finally, we discuss the danger of relying on radical traps as probes for polymerization mechanism. Radical traps can react with metal-hydrides and attenuate metal-centered nonradical reactions. However, even when radical traps fail to stop an observed polymerization, it may be wrong to conclude that a nonradical mechanism is at work since the traps can be destroyed under certain reaction conditions.     

Polymerization and copolymerization in associated monomer aggregates

The polymerization of acrylic acid in bulk is controlled by linear plurimolecular H-bonded aggregates of the monomer which lead to the formation of a syndiotactic polymer. Polar solvents do not dissociate these aggregates unless high dilutions are reached. In contrast, “normal” kinetics are observed in the presence of 10–20 per cent toluene, n-hexane or chloroform. The polymerization of methacrylic acid is not affected to the same extent by molecular aggregates. In the copolymerization of acrylic acid with methyl acrylate or acrylonitrile, the reactivity ratios are altered by solvents. The acrylic acid content is higher in copolymers formed in bulk than in toluene solution. But similar effects are observed in the presence of DMF which does not dissociate the aggregates of acrylic acid; moreover, copolymerization data obtained with methacrylic acid indicate that other factors may be involved in determining reactivity ratios.Acrylamide also forms H-bonded aggregates and its copolymerization behaviour is strongly affected by solvents. No simple correlation holds, however, between reactivity ratios and extent of association.A very strict control of chain propagation occurs when 4-vinylpyridine is polymerized in the presence of polycarboxylic acids. A considerable rate increase was observed when vinylpyridine was grafted into polytetrafluoroethylene films which contained poly(acrylic acid) branches. This effect is explained by assuming that the pyridine groups form strong associations with the carboxylic sites, thereby providing a very favourable orientation of the vinyl groups for chain propagation.     

Strategies for computing chemical reactivity indices

 Two recent articles [(2000) J Am Chem Soc 122: 2010, (2001) J Am Chem Soc 123: 2007] have explored electron-density-based and external-potential-based chemical reactivity indices. In this article, methods are presented for computing these indices from the output of a Kohn–Sham density functional theory calculation. Received: 18 October 2000 / Accepted: 4 April 2001 / Published online: 9 August 2001     

Studies on monomer reactivity ratios. II. A charge-transfer model

A charge-transfer model is proposed for the treatment of monomer reactivity ratios in free-radical bulk polymerization. The procedure involves the assignment of three parameters to each monomer, which can be interpreted as being related to the energies of the highest occupied monomer orbital, the singly occupied radical orbital, and the lowest lying virtual orbital of the monomer. Parameters are found for 17 monomers and computed reactivity ratios for a large number of copolymer systems are tabulated and compared with experiment. Similarities of the present model and the electronegativity scheme are discussed.     

The temperature dependence of the monomer reactivity ratios in the copolymerization of styrene with α-substituted cinnamic acids

Styrene has been copolymerized with α-methyl [carboxyl-¹⁴C]cinnamic acid, α-phenyl [carboxyl-¹⁴C]cinnamic acid and ethyl benzylidene [carboxyl-¹⁴C]cyanoacetate at temperatures between 40 and 130°, using azoisobutyronitrile as initiator. The compositions of the copolymers have been determined by liquid scintillation counting; a simplified form of the copolymer composition equation was used to determine the reactivity ratios of the polystyryl radical. Arrhenius parameters have been derived. With the α-methyl and α-phenyl substituted acids, the pre-exponential factors favour self propagation, which predominates. With the smaller α-cyano substituent, self propagation is also favoured by the pre-exponential factors; however, cross propagation, favoured by the energies of activation, predominates. The effect of substitution by methyl or phenyl groups in the α-position of cinnamic acid is much greater than that found with the methyl or phenyl esters.     

The temperature dependence of the monomer reactivity ratios in the copolymerization of styrene with methyl and ethyl cinnamates

Styrene (M₁) has been copolymerized with the methyl and the ethyl esters (M₂) of cinnamic acid (carboxyl ¹⁴C) at temperatures between 40 and 130°, using azoisobutyronitrile as initiator. The compositions of the copolymers have been determined by liquid scintillation counting; since [M₁ ? [M₂], a simplified form of the copolymer composition equation could be used for determining the reactivity ratio r₁ graphically. Arrhenius parameters have been derived; the energies of activation favour cross propagation whereas the frequency factors favour self propagation. Although the latter effect slightly predominates, there is no evidence of significant steric effects. These esters thus resemble cinnamic acid when copolymerized with styrene.Styrol (M₁) wurde bei Temperaturen zwischen 40 und 130° und AiBN als Initiator mit dem Methyl- und Äthylester (M₂) der Zimtsäure (¹⁴C-COO) copolymerisiert. Die Copolymerenzusammensetzung wurde durch Flüssigscintillation bestimmt. Für [M₁] ? [M₂] konnte eine vereinfachte Form der Copolymerisationsgleichung angewandt werden um r₁ graphisch zu bestimmen. Die Arrhenius-Parameter wurden abgeleitet; die Aktivierungsenergien begünstigen das gekreuzte Wachstum während die Hǎufigkeitsfaktoren das Eigenwachstum begünstigen. Obwohl der letztereEffekt leicht überwiegt, wurde kein Hinweis auf sterische Hinderung gefunden. In der Copolymerisation mit Styrol verhalten sich diese Ester wie die freie Zimtsäure.     

Effect of pressure on free-radical copolymerization kinetics. III. An improved method of measuring monomer reactivity ratios under high-pressure conditions

To investigate high-pressure copolymerizations a sampling technique has been developed enabling continual on-line GLC analysis of the reaction mixture. As a result more reliable kinetic data are obtained. This new “sequential sampling” method, allowing the use of gaseous monomers, has been tested for the copolymerization of ethylene with vinyl propionate at 118 MPa and 335 K with tert-butyl alcohol as solvent. The results are compared with those obtained with the “quenching” method used so far, which yields compositional data on the reaction mixture before and after the high-pressure stage, only. It is shown that the “sequential sampling” method is the most adequate method of determining high-pressure monomer reactivity ratios. Furthermore, it is an important safety feature that the present procedure can be easily remote controlled. The present experimental method is neither restricted to copolymerization nor to gas-chromatographic analysis of the reaction mixture.     

Effect of pressure on free radical copolymerization kinetics. II. Novel methods of measuring monomer reactivity ratios under high-pressure conditions

Two new techniques for the determination of monomer reactivity ratios in copolymerization under high-pressure conditions have been developed, viz., the “sandwich” and the “quenching” method. Both methods are based on repeated quantitative gas chromatographic analysis of the reaction mixture during the low-pressure stages preceding and succeeding the high-pressure stage, of which the kinetics is under investigation. Application of the “sandwich” method implies the occurrence of reaction during both low-pressure stages and consequently the low-pressure kinetic data are required to obtain the transition points of low to high pressure and vice versa. These points constitute the initial and final conditions of the relevant high-pressure reaction. On the contrary, in the “quenching” method no reaction occurs during the low-pressure stages, owing to the lower temperature and the high activation energy of the initiator decomposition. As a consequence, the initial and final conditions of the high-pressure stage can be determined by a simple averaging procedure. Both methods have been tested for the ethylene—vinyl acetate copolymerization at 62°C and 600 kg/cm² with tert-butyl alcohol as solvent, and appear to lead to almost identical monomer reactivity ratios, although the “quenching” method is slightly preferred in case of copolymerization reactions. Both methods are particularly valuable when one of the reactants is gaseous or the reaction produces a gas. Further merits and drawbacks of both methods are discussed.     

Free‐radical copolymerization of vinyl esters using fluoroalcohols as solvents: The solvent effect on the monomer reactivity ratio

Free‐radical copolymerizations of vinyl acetate (VAc = M₁) and other vinyl esters (= M₂) including vinyl pivalate (VPi), vinyl 2,2‐bis(trifluoromethyl)propionate (VF6Pi), and vinyl benzoate (VBz) with fluoroalcohols and tetrahydrofuran (THF) as the solvents were investigated. The fluoroalcohols affected not only the stereochemistry but also the polymerization rate. The polymerization rate was higher in the fluoroalcohols than in THF. The accelerating effect of the fluoroalcohols on the polymerization was probably due to the interaction of the solvents with the ester side groups of the monomers and growing radical species. The difference in the monomer reactivity ratios (r₁, r₂) in THF and 2,2,2‐trifluoroethanol was relatively small for all reaction conditions and for the monomers tested in this work, whereas r₁ increased in the VAc‐VF6Pi copolymerization and r₂ decreased in the VAc‐VPi copolymerization when perfluoro‐tert‐butyl alcohol was used as the solvent. These results were ascribed to steric and monomer‐activating effects due to the hydrogen bonding between the monomers and solvents. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 220–228, 2000