Penultimate unit effects in the free‐radical copolymerization of styrene with acrylonitrile according to theoretical thermochemistry

Penultimate unit effects in the free‐radical copolymerization of styrene with acrylonitrile were investigated by the consideration of the theoretical thermochemistry of three subsequent propagation steps in the copolymerization process at 298 K and the electronic properties of the relevant reactants. The total energies, zero‐point energies incorporating a 0.96 scale factor, and thermal enthalpy corrections for all optimized structures were computed with the B3LYP density functional theory and the 6‐311G(d,p) basis set. The penultimate unit effect on the enthalpy of reaction for elementary propagation reactions ranged from ?1.2 to 2.7 kcal/mol. The enthalpies of elementary copolymerization propagation reactions showed that penultimate unit effects depended not only on the γ substituent itself but also on the terminal unit of the growing radical and the monomer being attached. The exothermicity of the addition of radicals, varying in the penultimate unit for a given monomer, was lower for more polar radicals and smaller Mulliken charges at the radical atom, except for radicals with a CN substituent placed in the γ position when they reacted with acrylonitrile. For the latter system, the repulsive interactions between the CN substituent and nitrile group of the monomer being added contributed to the reaction enthalpy. Almost no penultimate unit effect was detected upon spin distribution at the radical atom, and this probably indicated the absence of the independent implicit penultimate model. The results obtained strengthen the concept of the inseparability of implicit and explicit penultimate unit effects in radical copolymerization. However, it appears that for the styrene–acrylonitrile copolymerization system, the explicit penultimate model prevails over the implicit penultimate model. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 3592–3603, 2002     

Further evidence for the inseparability of the theoretical enthalpic terminal and penultimate unit effects in the radical copolymerization of styrene with acrylonitrile

The theoretical enthalpies of propagation reactions at 0 K without zero‐point vibrational energy corrections according to terminal and penultimate models of the radical copolymerization of styrene with acrylonitrile are reported from molecular orbital calculations at the following levels of theory and basis sets: HF/6‐31G(d); B3‐LYP/6‐31G(d); B3‐LYP/6‐311G(d,p) and B3‐LYP/6‐311+G(3df)//6‐311G(d,p). Both the enthalpic terminal and penultimate unit effects, determined according to the theoretical thermochemistry, depend on the level of theory and basis set used for the molecular orbital calculations. The best performing B3LYP/6‐311+G(3df)//B3LYP/6‐311G(d,p) procedure gives theoretical enthalpies for the addition of styrene and acrylonitrile to CH that differ from experimental values by 0.6 and 1.6 kcal mol^?1, respectively. An analysis of the results obtained here leads to the conclusion that at least for the styrene–acrylonitrile monomer system, that is, a monomer system known as one of the few systems that do not conform to terminal model composition and microstructure equations, the enthalpic terminal unit effects seem to depend on the penultimate units of the growing radical. This finding, together with the outcome from our previous work on the dependence of the penultimate effects on the terminal units in a growing macroradical, indicates the inseparability of the enthalpic terminal (implicit) and explicit penultimate unit effects on the radical copolymerization. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1778–1787, 2003     

Theoretical study of the free‐radical copolymerization of styrene with methyl methacrylate: Comparative study to the styrene–acrylonitrile monomer system

Enthalpic and electronic terminal and penultimate unit effects in the free‐radical copolymerization of styrene (S) with methyl methacrylate (M) were investigated by quantum mechanical calculations at 0 and 298 K. Total energies, zero‐point energies scaled by a 0.96 factor, and thermal enthalpy corrections for all optimized structures were computed at the B3‐LYP/6‐31G(d) level of theory. Differences in enthalpies for elementary propagation reactions at 0 and 298 K did not exceed 0.6 kcal/mol. Enthalpic effects of the replacement of S by M in the penultimate position of the growing radicals in elementary copolymerization propagation reactions (enthalpic penultimate unit effects) were always positive, ranging from 1.2 to 3.3 kcal/mol at 298 K. The values suggested that the elementary propagation reactions involving more S units in the growing polymer chain ends should be slightly thermodynamically preferred. A comparison of these results with those for the S–acrylonitrile monomer system showed that the most crucial feature differentiating enthalpic effects for the two monomer systems is the replacement of M by acrylonitrile in the reaction pair CH₃‐S‐M · + M → CH₃‐S‐M‐M · and CH₃‐M‐M · + M → CH₃‐M‐M‐M ·. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 1557–1565, 2004     

Penultimate unit effects in free radical copolymerization

The penultimate unit effects (PUEs) on the propagation, termination, and reversible addition-fragmentation chain transfer (RAFT) processes in free radical copolymerization are discussed on the basis of recent publications. The propriety of the implicit and explicit PUE models in propagation and chain transfer processes is commented. The penultimate termination model with the geometric-mean approximation and the related rate equation are highlighted.     

Copolymerization with Depropagation

Free-radical copolymerizations of styrene with α-methylstyrene and methyl methacrylate and of acrylonitrile with α-methylstyrene have been carried out in the approximate regions of the ceiling temperatures of α-methylstyrene and methyl methacrylate. A theoretical treatment of copolymerization emphasizing the thermodynamic reversibility of particular propagation reactions has been compared with a kinetic treatment of copolymerization which emphasizes penultimate unit effects on the same propagation reactions. The former is found to adequately describe experimental copolymer composition data over a wide range of temperatures and over the complete range of monomer feed composition.     

Free-Radical Copolymerization of Methyl Methacrylate and α-Methacrylophenone. I. Reactivity Ratios

The free-radical copolymerization of methyl methacrylate and methacrylophenone (MAP) initiated by azobisisobutyroni-trile at 60°C has been studied in ethylbenzene solution and in bulk. The process is characterized by a competitive Diels-Alder condensation of methacrylophenone and by a very low reactivity of methacrylophenone-terminated macroradicals in propagation reactions. The experimental composition data are consistent with a terminal unit model: r_A = 1.77 ± 0.02, r_B = 0.110 ± 0.006. Copolymerization with depropagation of methacrylophenone-terminated growing chains and copolymerization affected by penultimate effects have been tested as optimized possible models to take into account the inability of MAP to undergo homopolymerization.     

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.     

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.     

Copolymerization kinetics of methyl methacrylate-styrene obtained by PLP-MALDI-ToF-MS

The combination of MALDI-ToF-MS and pulsed laser polymerization has been used to study the propagation rate coefficients for the copolymer system styrene-methyl methacrylate. For the first time, complete information regarding mode of termination, reactivity of photoinitiator-derived radicals, copolymer molecular mass, chemical composition, and copolymerization rates is obtained interrelated. The polymerizations were carried out in bulk with varying styrene concentrations at a temperature of 15.2 degrees C by an excimer pulsed laser with varying frequencies. Both chemical composition distributions and molecular weight distributions were determined by MALDI-ToF-MS. The data were fitted to the implicit penultimate unit model and have resulted in new point estimates of the monomer and radical reactivity ratios for the copolymer system styrene-methyl methacrylate: r(St) = 0.517, r(MMA) = 0.420, s(St) = 0.296, s(MMA) = 0.262. Comparison between Monte Carlo simulations and the obtained results further confirmed the very successful combination of pulsed laser copolymerization experiments with MALDI-ToF-MS. The obtained results are believed to be the most accurate and complete set of copolymerization parameters to date.     

Copolymerization of vinyl acetate with ethyl α-cyanocinnamate

Trisubstituted ethylene, ethyl α-cyanocinnamate, is readily copolymerized with vinyl acetate by a conventional radical initiator. Terminal, penultimate, and “complex” copolymerization models were applied by using the data of composition of the copolymers obtained in bulk and by copolymerization in benzene, ethyl acetate, and chloroform. The model based on the participation of the monomer complexes describes satisfactorily the deviation from the terminal copolymerization model. The proton NMR analyses of the monomer mixtures indicate that the interaction between the monomers leads to the formation of weak monomer complexes. Kinetic studies of the initial rate dependence on the total monomer concentration and monomer feed composition enabled us to evaluate the degree of participation of the free uncomplexed monomers and the monomer complex in the propagation reactions. The contribution of the complexed monomers in the propagation stages increases with the increase in total monomer concentration. The initial rate of the copolymerization is proportional to the square root of the initiator concentration, thus confirming the bimolecular termination of the macrochains. The rate constants of the addition reactions of the complex and free monomers were evaluated from the kinetic studies. The quantitative kinetic treatment provided information regarding the relative weight of the termination reaction and indicated that the termination in the system occurs predominantly by the cross-termination reaction between two growing polymer radicals with different kinds of monomer units at the ends. Additional information on the termination in this system was obtained from viscosity measurements.     

Solvent effects in copolymerization

Extension of the Mayo-Lewis Model of copolymerization concerning solvent effects in free-radical polymerization is discussed on the basis of the bootstrap and penultimate unit effects.     

Copolymerization of styrene. V. Copolymerization with α-cyanocinnamamide

Copolymers of styrene with α-cyanocinnamamide were prepared by free radical initiation in bulk and in DMF solution and also by thermal initiation in bulk. The copolymerization parameters were determined by the conventional scheme of copolymerization and by an improved scheme taking into account the penultimate unit. Different values of the copolymerization parameters were obtained at the above mentioned different polymerization conditions, indicating the existence of a solvent effect. The influence of the comonomer on some of the basic properties, like intrinsic viscosity, solubility, melting range, and glass transition temperature and on some mechanical and behavior properties of the copolymers was studied in comparison with homopolystyrene.     

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.     

The termination reaction in free radical copolymerization. I. Methyl methacrylate and butyl- or dodecyl methacrylate

Using a spatially intermittent reactor, the absolute rate constant for the termination reaction in free radical copolymerization has been measured for the monomer pair methyl methacrylate (MMA)–butyl methacrylate (BMA). For the pair MMA–dodecyl methacrylate (DMA) the relative rate constant for termination has been measured. In both cases the termination rate constant was a monotonically changing function of the monomer feed composition. This function can be well approximated by a simple calculation of the enchained monomer units' contributions to the average segmental friction coefficient of the copolymer chain. An attempt to apply a previously derived theoretical treatment based on penultimate unit effects produced physically unrealistic results.     

Relative reactivity of chloroprene and methyl methacrylate toward initiator radicals

The relative rates of addition of chloroprene (CP) and methyl methacrylate (MMA) toward small model radicals structurally similar to the poly(MMA), poly(methacrylonitrile) and poly(styrene) radical was investigated following the method of Bevington and Huckerby [J Polym Sci Polym Chem 20 (1982) 2655]. Results indicate that these small radicals are significantly more selective toward CP than the corresponding polymer radicals, consistent with earlier reports that penultimate unit effects may be important in the copolymerisation of CP with MMA and styrene. As previous investigations of substituted dienes by the end-group method have given similar results for polymer radicals and small model radicals, this may constitute evidence for a penultimate unit effect that is predominantly electronic rather than steric in origin.     

Modeling and Experimentation of RAFT Solution Copolymerization of Styrene and Butyl Acrylate,Effect of Chain Transfer Reactions on Polymer Molecular Weight Distribution

Chain transfer reactions widely exist in the free radical polymerization and controlled radical polymerization, which can significantly influence polymer molecular weight and molecular weight distribution. In this work, the chain transfer reactions in modeling the reversible addition–fragmentation transfer (RAFT) solution copolymerization are included and the effects of chain transfer rate constant, monomer concentration, and comonomer ratio on the polymerization kinetics and polymer molecular weight development are investigated. The model is verified with the experimental RAFT solution copolymerization of styrene and butyl acrylate, with good agreements achieved. This work has demonstrated that the chain transfer reactions to monomer and solvent can have significant impacts on the number‐average molecular weight (M_n) and dispersity (Ð).     

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.     

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.     

Penultimate effect in radical copolymerization of 2‐trifluoromethylacrylates

Electron‐deficient 2‐trifluoromethylacrylates (TFMA) undergo radical copolymerization with electron‐rich norbornene derivatives, vinyl ethers, and styrene derivatives, which can be described by the penultimate model much better than by the commonly employed terminal model. In an attempt to directly observe the effect of the CF₃ group in the penultimate unit on the radical reactivity, we employed the Giese's mercury method. 4,4,4‐Trifluorobutyl and n‐butyl radicals produced from respective alkylmercuric chlorides were competitively reacted with t‐butyl 2‐trifluoromethylacrylate (TBTFMA) and t‐butyl methacrylate (TBMA) and the products analyzed with gas chromatography. While TBTFMA has been found to be about 24times more reactive than TBMA toward the n‐butyl radical, the former is about 12 times more reactive than the latter toward the 4,4,4‐trifluorobutyl radical. Thus, the reactivity of the propagating radical toward TBTFMA in comparison with TBMA is suppressed by a factor of two when the penultimate unit has the CF₃ group. We observed a sextet electron spin resonance of the TFMA propagating radical with a coupling constant of ca. 25 gauss between the β‐proton and β‐fluorine. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 1559–1565, 2008