Dependence of computed copolymer reactivity ratios on the calculation method. II. Effects of experimental design and error structure

Two calculation methods for estimating reactivity ratios, one method based on the differential Alfrey-Mayo equation and one based on the integrated form of this model, are compared with respect to precision and bias. Both methods are characterized by the use of information about the monomer feed composition only and are assumed to be valid up to high conversion. As only monomer feed composition has to be analyzed, several sampling designs are feasible. Two extreme designs can be distinguished. One consists of repetitive sampling of the initial and final monomer feed mixture, whereas the other consists of sequential sampling during the course of the reaction. The influence of both designs of the calculated r-values is investigated by means of simulation. In the present paper the second calculation method, based on the integrated form, is solved by a nonlinear least squares method considering errors in both variables. This method required additional information about the errorstructure of the data. As this information is mostly of approximate nature, the influence of misspecification of this error structure on the calculated r-values is also examined.     

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.     

Die Copolymerisation von Vinylacetat und Divinyladipat. Vernetzung und Cyclisierung

The reactivity ratios for the vinyl acetate-divinyl adipate system are determined. Both valuesr _{V Ac} andr _{DV A} are near to unity. The reactivity of the pendent double bond is very low and soluble polymers are formed far over the critical conversion calculated with anr-value of the pendent double bonds equal to unity. Contrary to this a high portion of intramolecular cyclization occurs, presumably leading to chain units of the type amounting to 10% of the total number of divinyl adipate units in the chain in systems with an initial monomer concentration of 95% and to 23% in systems with a monomer concentration of 50%. The reactivity ratio of the pendent double bond is estimated. The main reason for the high conversion for gel formation is the low rate of intermolecular reaction of pendent double bonds. In this respect cyclization plays a minor role.     

Die Copolymerisation von Vinylacetat und Divinyladipat. Vernetzung und Cyclisierung

The reactivity ratios for the vinyl acetate-divinyl adipate system are determined. Both valuesr _{V Ac} andr _{DV A} are near to unity. The reactivity of the pendent double bond is very low and soluble polymers are formed far over the critical conversion calculated with anr-value of the pendent double bonds equal to unity. Contrary to this a high portion of intramolecular cyclization occurs, presumably leading to chain units of the type amounting to 10% of the total number of divinyl adipate units in the chain in systems with an initial monomer concentration of 95% and to 23% in systems with a monomer concentration of 50%. The reactivity ratio of the pendent double bond is estimated. The main reason for the high conversion for gel formation is the low rate of intermolecular reaction of pendent double bonds. In this respect cyclization plays a minor role.

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Copolymerization and Copolymers of Styrene N-(2,4,6-Tribromophenyl) Maleimide with Styrene

Kinetic studies of the free radical copolymerization of N-(2,4,6- tribromophenyl) maleimide (TBPMI) with styrene in solution were carried out. The thermal and flammability characteristics of the resulting polymers were also investigated. The monomer reactivity ratios were found to be r ₁ = 0.006 ± 0.0026 (TBPMI) and r ₂ = 0.086 ± 0.0023, and the activation energy of the copolymerization reaction was E_a = 73.6 kJ/mol. The resulting copolymers showed an alternating structure regardless to the monomer feed composition. The molecular weights of the copolymers obtained are relatively high and gradually increase by increasing the TBPMI fraction in the feed, whereas the T_g's showed similar values (540 K) for the equimolar ratio of the comonomers. The course of copolymerization up to high conversion was followed by microcalorimetry and is characterized by a remarkable increase of the initial reaction rate as the fraction of TBPMI was increased; it is also higher at higher total monomer concentrations. However, the overall conversion decreases when the fraction of TBPMI is higher than the equimolar ratio. The thermal stability of the alternating copolymers is higher than that of polystyrene, and their mixture showed appreciable flame-retardant properties, as demonstrated by a limiting oxygen index measurement.     

Studies of the polymerization of diallyl compounds. XXXVII. Copolymerizations of diallyl phthalate with dialkyl fumarates

Diallyl phthalate (DAP) was copolymerized with dialkyl fumarates, including diethyl fumarate (DEF), di-n-butyl fumarate (DBF), and di-n-octyl fumarate (DOF) by using 2,2′-azobisisobutyronitrile as an initiator at 60°C. Both rate and degree of copolymerization were quite enhanced compared with the homopolymerization of DAP and the maximum rate was found at the molar ratio of 1:1 in the monomer feed. The cyclization of DAP was almost exclusively suppressed in the Copolymerization. Gelation was promoted from 25% of the gel-point conversion for the DAP homopolymerization to 9% of the minimum one observed. Copolymerizability of DAP (M₁) with dialkyl fumarates (M₂) was quite high, with the following monomer reactivity ratios M₂, r₁, r₂: DEF, 0.01, 1.25; DBF, 0.02, 1.01; DOF, 0.02, 0.96. These results are discussed in mechanistic detail.     

Terpolymerization of Triisopropylsilyl Acrylate,Methyl Methacrylate,and Butyl Acrylate: Reactivity Ratio Estimation

Ternary monomer reactivity ratios of triisopropylsilyl acrylate (SiA), methyl methacrylate (MMA), and n‐butyl acrylate (BA), as common monomers in self‐polishing coatings (SPCs) binders are obtained using experimental data collected from free radical bulk polymerization at 70 °C. Different terpolymerizations at low and medium‐high conversions are performed at optimized feed compositions. Estimations are made using the error‐in‐variables model (EVM) framework, applying the recast form of the Alfrey–Goldfinger (AG) model and a direct numerical integration (DNI) approach to the collected data. Estimations from individual low and medium‐high conversion data are compared to those found with the combined data (full conversion range data). The highest certainty in point estimates are obtained with analysis of the full conversion range data. Furthermore, the reactivity ratios determined from the combined data fall between those found with analysis of individual low and medium‐high conversion data, another corroboration of reliable data collection. Reactivity ratios determined from analysis of the combined data (r_SiA/MMA = 0.4185, r_MMA/SiA = 1.3754, r_SiA/BA = 0.8739, r_BA/SiA = 0.5736, r_BA/MMA = 0.3692, r_MMA/BA = 1.7919) are used in the recast AG model to predict cumulative terpolymer composition as a function of conversion. The experimental data and model prediction show satisfactory agreement.     

Preparation of silicone‐graft copolymers by homogeneous radical copolymerization in supercritical carbon dioxide

Copolymerizations of 1,1‐dihydroperfluorooctyl methacrylate (FOMA; M₁) and methacryloxypropyl‐terminated polydimethylsiloxane [M‐PDMS (M_n = 5.9 K); M₂] and homopolymerization of M‐PDMS in supercritical CO₂ are described. The homopolymerization of M‐PDMS proceeded homogeneously without difficulty to produce oligomers (M_n = 30 K). The copolymerizations of FOMA and M‐PDMS also proceeded homogeneously over a wide monomer feed ratio. The ratio of M‐PDMS incorporated into the copolymer obtained was almost equal to the monomer feed ratio even up to the high conversion. The reactivity ratio r₁ was determined to be 1.66. DSC examination of the copolymers indicated a microphase‐separated morphology consisting of poly‐FOMA (PFOMA) and PDMS domains for all copolymer compositions. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 1139–1145, 2000     

Emulsion copolymerization of styrene and methyl methacrylate

Chain transfer constants to monomer have been measured by an emulsion copolymerization technique at 44°C. The monomer transfer constant (ratio of transfer to propagation rate constants) is 1.9 × 10^?5 for styrene polymerization and 0.4 × 10^?5 for the methyl methacrylate reaction. Cross-transfer reactions are important in this system; the sum of the cross-transfer constants is 5.8 × 10^?5. Reactivity ratios measured in emulsion were r₁ (styrene) = 0.44, r₂ = 0.46. Those in bulk polymerizations were r₁ = 0.45, r₂ = 0.48. These sets of values are not significantly different. Monomer feed compcsition in the polymerizing particles is the same as in the monomer droplets in emulsion copolymerization, despite the higher water solubility of methyl methacrylate. The equilibrium monomer concentration in the particles in interval-2 emulsion polymerization was constant and independent of monomer feed composition for feeds containing 0.25–1.0 mole fraction styrene. Radical concentration is estimated to go through a minimum with increasing methyl methacrylate content in the feed. Rates of copolymerization can be calculated a priori when the concentrations of monomers in the polymer particles are known.     

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.     

Nitroxide‐mediated free‐radical copolymerization of styrene with butyl acrylate

Controlled free‐radical copolymerization of styrene (S) and butyl acrylate (BA) was achieved by using a second‐generation nitroxide, N‐tert‐butyl‐N‐[1‐diethylphosphono‐(2,2‐dimethylpropyl)] nitroxide (DEPN), and 2,2‐azobisisobutyronitrile (AIBN) at 120 °C. The time‐conversion first‐order plot was linear, and the number‐average molecular weight increased in direct proportion to the ratio of monomer conversion to the initial concentration, providing copolymers with low polydispersity. The monomer reactivity ratios obtained were r_S = 0.74 and r_BA = 0.29, respectively. To analyze the convenience of applying the Mayo–Lewis terminal model, the cumulative copolymer composition against conversion and the individual conversion of each monomer as a function of copolymerization time were studied. The theoretical values of the propagating radical concentration ratio were also examined to investigate the copolymerization rate behavior. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4168–4176, 2004     

Graft polymers with macromonomers. II. Copolymerization kinetics of methacrylate-terminated polystyrene and predicted graft copolymer structures

Copolymerization studies of methacrylate-terminated polystyrene macromonomers (M₁) with several comonomers (M₂) verified the modified kinetic scheme and permitted prediction of graft polymer compositions and structures. Instantaneous and cumulative copolymer compositions, average graft distributions, and grafts per molecule are predicted from FORTRAN IV or BASIC programs. The r₂ relative reactivity ratios determined from styrene copolymerization (0.61) or from low conversion acrylic monomer in aqueous suspension (～0.4) had good agreement with literature values (about 0.6 and 0.4, respectively). Decreased macromonomer reactivity determined at high acrylic monomer conversions was attributed to phase separation phenomena. The Macromers also exhibited lower reactivity than predicted when copolymerized with acrylic monomers in DMSO/benzene solutions (r₂ ～ 0.8).     

Solvent effects on free-radical polymerization, 4. Modelling of hompolymerization

A new so-called reactant-solvent complex model is proposed to describe the effect of solvent on chain propagation in homopolymerization. It takes into account complex formation of both monomer and radical with solvent by equilibria. Evaluation methods presented permit to estimate the complex equilibrium constant K which is assumed to be nearly the same for both monomer and radical complexation and the relative reactivity ratio r₁₁, for complexed monomer. Measured reaction rates as function of monomer concentration are needed for calculations.     

Real-Time FTIR Monitoring of the Carbocationic Copolymerization of Isobutylene with Styrene

The carbocationic copolymerization of isobutylene (IB) and styrene (St) was investigated using real time FTIR monitoring. Depending on the concentration of the individual monomers, and their ratio in the feed, initial rapid monomer consumption was observed. Instantaneous reactivity ratios (r_IB(inst) and r_St(inst)) obtained from apparent rate constants of monomer consumption strongly depended on concentration.     

Polymerization behavior of 2,2,6,6-tetramethylpiperidinyl methacrylate: A monomer carrying a hindered amine group

Copolymers of 2,2,6,6-tetramethylpiperidinyl methacrylate (TPMA) with styrene (S) and with methyl methacrylate (MMA) were synthesized using AIBN as initiator. S–TPMA copolymers from feed ranging from 0.10–0.80 mole fractions TPMA and MMA-TPMA copolymers from feed of 0.04–0.85 mole fractions TPMA were used in the determination of monomer reactivity ratios r₁, r₂. Four different methods were employed in the calculations of r₁ and r₂ and all calculated results were in good agreement with each other. The structure of S–TPMA copolymers was inferred to be of an alternating nature while that of MMA–TPMA copolymers was random. Both copolymers are potential hindered amine light stabilizers (HALS) and are expected to be less extractable from, and more compatible with, polystyrene and poly(methyl methacrylate) base polymers.     

Polymers from multifunctional isocyanates 14. Alternating copolymers from isocyanato alkenes: Copolymerization of 2-propenyl isocyanate with trimethylsilyl methacrylate as electron acceptor monomer

The copolymerization of 2-propenyl isocyanate ( 1 ) with trimethylsilyl methacrylate ( 2 ) has been investigated. 1 is an electron donor monomer with little tendency to undergo homopolymerization, while 2 is an electron acceptor monomer, capable of free radical homopolymerization. Polymerization to low conversion in benzene gave copolymers with preferential incorporation of 2 and a tendency towards alternating copolymers with increasing amounts of 1 in the feed (1 : 1.13 with a 9 : 1 feed ratio of monomers 1 : 2 ). The glass transition temperatures of the amorphous polymers are in the range from 100–70°C, with a T_g of poly(trimethylsilyl methacrylate) being 135°C. Desilylation occurs in the presence of water, causing an exothermal reaction above the glass transition temperature probably with formation of amides, a reaction that can be used for crosslinking. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 611–616, 1998     

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.     

Alternating Copolymerization of Styrene and N-(4-Bromophenyl)Maleimide

Abstract

Free radical copolymerization of styrene (St) and N(4-bro-mophenyl)maleimide (4BPMI) in dioxane solution gave an alternating copolymer in all proportions of feed comonomer compositions. The monomer reactivity ratios were found to be r ₁, = 0.0218 ± 0.0064 (St) and r ₂, = 0.0232 ± 0.0112 (4BPMI), and the activation energy of the copolymerization reaction for the equimolar ratios of comonomer was E _a, = 51.1 kJ/mol. The molecular weights of the copolymers obtained are relatively high, the T _g's showed similar values (490 K), and the thermal stability is higher than that of polystyrene. The initial rate of copolymerization depends on the total concentration of the comonomers and the maximum occurred at higher 4BPMI mol fractions; however, the overall conversion is highest at equimolar comonomer composition. It has been shown that a charge-transfer complex participates in the process of copolymerization. The initial reaction rate was measured as a function of the monomer molar ratios, and the participation of the charge-transfer complex monomer and the free monomers was quantitatively estimated.     

Radiation-induced polymerization of tetrafluoroethylene and 1,2,3,4,5-pentafluorostyrene at high pressure

Tetrafluoroethylene (A) and 1,2,3,4,5-pentafluorostyrene (B) were irradiated at 15°C at autogenous pressure by use of 30–92 mole-% A and at 5000 atm by use of 42–99.9 mole-% A. The high-pressure results indicate that the reactivity ratio r_A for monomer addition to A-ended radicals is 0.005; the other reactivity ratio r_B appears to vary from 15 to 60 generally increasing with the A content of the charge. At autogenous pressure r_A is small, but a precise determination is not possible because of the very low polymerization rate when the A content of the charge is high. However, if r_A is less than 0.01, then values of r_B vary from 15 to 50, again generally increasing with the A content of the charge. Mixtures of A and B exhibit positive deviations from Raoult's Law. Activity coefficients were measured at autogeneous pressure and used in an attempt to correct r_B for the nonideality of solution. The range of r_B was reduced only slightly to 8–27, and charges with high A contents now generally gave low values of r_B; consequently, this approach was not regarded as a success. Another attempt was made to account for the apparent variation in r_B by ascribing influence to the penultimate units of the radicals. Improved agreement between theoretical and observed compositions resulted, but significant discrepancies remained unexplained. Rate data agreed well with those calculated from a theoretical copolymer rate equation using values of r_A and r_B of 0.0045 and 40, respectively. The equation predicts an almost proportional decrease in rate with increasing proportions of A in the charge from 0 to 99 mole-% A.     

Synthesis and characterization of graft copolymers of methacrylonitrile/methacrylate mixtures onto amylomaize by the ceric ion method

Graft polymerizations of mixtures of methacrylonitrile with n-alkyl methacrylales onto amylomaize were carried out. The graft copolymers were characterized by both IR and ¹³C-NMR spectroscopies. The influence of the monomer feed on the grafting parameters has been studied. The variation of these parameters with the mole fraction of methacrylate in the feed for the first three systems studied, MAN/MMA, MAN/EMA and MAN/BMA, was similar: thus, percent grafting (%G, percent weight of grafted polymer with respect to grafted amylomaize), percent grafted amylomaize (%GA, percent weight of grafted amylomaize with respect to initial amylomaize), percent grafting conversion (%C_g, percent weight of grafted polymer with respect to initial monomer), and percent total conversion (%C_t, percent weight of total acrylic polymer with respect to initial monomer) were increased, but percent grafting efficiency (%GE, percent weight of graft copolymer with respect to total polymer) decreased. The system MAN/HMA presented values of grafting parameters lower than those of the previous systems. The optimum values were obtained at 0.6 HMA mole fraction in the monomer feed. When the number of carbon atoms of the n-alkyl group rises from 1 to 4, the increase of the n-alkyl group length gives rise to increases of the %G %C_g and %C_t values and decreases of the %GE and %GA values. For the largest methacrylate, the grafting reaction appears to be controlled by the lesser accessibility of the monomer to the active sites of the carbohydrate. © 1992 John Wiley & Sons, Inc.