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.     

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.     

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.     

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.     

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.     

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.     

Radical copolymerization of citraconic acid with styrene in dioxane solution

Styrene and citraconic acid (CA) were copolymerized in the dioxane solution ranging mole fraction of CA in feed from 0.1 to 0.9 at 70 °C. The terminal and penultimate models were used to fit the copolymer composition equation. Curve fitting, Mayo-Lewis, Joshi-Joshi, Fineman-Ross, Ezrielev-Brokhina-Roskin, Kellen-Tüd?s methods were used to solve the copolymer equation in terminal model. Besides these methods Solver in Excel 97 was used to solve copolymer equation in terminal and penultimate models of copolymerization. Experimental mole fractions of CA and those predicted from both models are agreed within the precision of the method used for the copolymer analysis, so the copolymer composition does not permit a definite choice of the adequate copolymerization model.     

A study of the influence of impurities when discriminating between the terminal and penultimate copolymerization models

We investigate the effect of the presence of reactive impurities during copolymerization on mathematical model discrimination and determine if impurities adversely affect the model discrimination process, depending on the criteria and response(s) used. Nonlinear mechanistic process models are employed in a multiresponse statistical discrimination scenario. The investigation also considers, via several case studies, the extremely interesting question of whether impurity effects could lead to incorrect choices about the copolymerization mechanism itself (terminal versus penultimate model). The answers to the above questions are that reactive impurities do affect the model discrimination process and, what is more, they may mislead researchers as to the choice of the copolymerization mechanism. The latter unexpected result is further illustrated with experimental data from the literature. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 2319–2332, 2000     

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     

The comppen model: A combined complex-participation/penultimate effect model for free-radical copolymerization

The Comppen model for the mechanism of free-radical copolymerization has been developed to account for both penultimate effects and the participation of 1:1 electron donor-acceptor complexes during chain propagation. This was achieved by incorporating penultimate effects into the existing complex participation model of Cais, Farmer, Hill, and O'Donnell, using probability theory to derive new copolymer composition and sequence distribution equations that are solely functions of the reactivity ratios, the composition of the comonomer feed, and the equilibrium constant for 1:1 electron donor-acceptor complex formation. The model was applied to experimental data from styrene/maleic anhydride copolymers prepared in methyl ethyl ketone at 50°C over a wide range of comonomer feed compositions, using nonlinear least-squares curve fitting techniques to determine best estimates of the reactivity ratios. Copolymer compositions and sequence distributions for copolymers in this comonomer system were then predicted using the Comppen model and compared to those determined experimentally via ¹³C-NMR spectroscopy. © 1994 John Wiley & Sons, Inc.     

Free‐radical copolymerization of styrene with butyl acrylate. II. Elemental kinetic copolymerization step predictions from homopolymerization data

The free‐radical copolymerization of styrene and butyl acrylate has been carried out in benzene at 50 °C. The lumped k _p/k parameter (where k _p and k _t are the average copolymerization propagation and termination rate constants, respectively) has been determined. Applying the implicit penultimate unit model for the overall copolymerization propagation rate coefficient and the terminal unit effect for the overall copolymerization termination rate coefficient and using the homopolymerization kinetic coefficients, we have found good qualitative agreement between the experimental and theoretical k _p/k values. The variation of the copolymerization rate in solution with respect to the values previously found in bulk has been ascribed to a chain length effect on the copolymerization termination rate coefficient. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 130–136, 2004     

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.     

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     

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     

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.     

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     

Molecular ordering of a cyano compound at a displacive transition temperature: a statistical analysis based on quantum mechanics and computer simulations

A statistical analysis has been carried out to determine the configurational preference of a pair of 4-cyanophenyl 4-n-pentylbenzoate (CPPB) molecules with respect to translatory and orientational motions. The CNDO/2 method has been employed to evaluate the net atomic charge and atomic dipole components at each atomic centre of the molecule. Configurational energy has been computed using the Rayleigh—Schodinger perturbation method. The total interaction energy values obtained through these computations were used to calculate the probability of each configuration at the phase transition temperature using the Maxwell—Boltzmann formula. An attempt has been made to identify the most probable configuration at the phase transition temperature. Further, the flexibility of various configurations has been studied in terms of variation of probability due to small departures from the most probable configuration. On the basis of stacking, in-plane and terminal interaction energy calculations, all possible geometrical arrangements of the molecular pair have been considered. The results are discussed in the light of experimental as well as theoretical observations. The nature of the mesophase has been correlated with the parameter introduced in this paper.     

Molecular ordering of a cyano compound at a displacive transition temperature: a statistical analysis based on quantum mechanics and computer simulations

A statistical analysis has been carried out to determine the configurational preference of a pair of 4-cyanophenyl 4- n -pentylbenzoate (CPPB) molecules with respect to translatory and orientational motions. The CNDO/2 method has been employed to evaluate the net atomic charge and atomic dipole components at each atomic centre of the molecule. Configurational energy has been computed using the Rayleigh-Schodinger perturbation method. The total interaction energy values obtained through these computations were used to calculate the probability of each configuration at the phase transition temperature using the Maxwell-Boltzmann formula. An attempt has been made to identify the most probable configuration at the phase transition temperature. Further, the flexibility of various configurations has been studied in terms of variation of probability due to small departures from the most probable configuration. On the basis of stacking, in-plane and terminal interaction energy calculations, all possible geometrical arrangements of the molecular pair have been considered. The results are discussed in the light of experimental as well as theoretical observations. The nature of the mesophase has been correlated with the parameter introduced in this paper.