A method for determining reactivity ratios whenn copolymerizations are influenced by penultimate group effects

A novel kinetic treatment is proposed for the copolymerization of two monomers M₁ and M₂ when terminal −M₂· groups are susceptible to penultimate group effects. If [M₁] ⪢ [M₂], as is possible experimentally when M₂ is radioactively labelled, a value of the reactivity ratio r₁ which is independent of penultimate group effects can be obtained. This value is then used to find values for the other reactivity ratios. The method involves a solution for reactivity ratios by means of intersecting curves, each curve representing a given monomer feed ratio and copolymer composition ratio.     

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.     

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.     

Monomer reactivity ratios for acrylonitrile–methyl acrylate free‐radical copolymerization

Nonlinear monomer reactivity ratios for the homogeneous free‐radical copolymerization of acrylonitrile and methyl acrylate were determined from ¹H NMR and real‐time Fourier transform infrared (FTIR) analyses. All ¹H NMR data were obtained on polymers isolated at low conversions (<10%), whereas the FTIR data were collected in situ. The copolymerizations were conducted in N,N‐dimethylformamide at 62 °C and were initiated with azobisisobutyronitrile. The real‐time FTIR technique allowed for many data points to be collected for each feed composition, which enabled the calculation of copolymer compositions (dM₁/dM₂) with better accuracy. Monomer reactivity ratios were estimated with the Mayo–Lewis method and then were refined via a nonlinear least‐squares analysis first suggested by Mortimer and Tidwell. Thus, monomer reactivity ratios at the 95% confidence level were determined to be 1.29 ± 0.2 and 0.96 ± 0.2 for acrylonitrile and methyl acrylate, respectively, which were valid under the specific system conditions (i.e., solvent and temperature) studied. The results are useful for the development of acrylonitrile (<90%) and methyl acrylate, melt‐processable copolymer fibers and films, including precursors for carbon fibers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2994–3001, 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.     

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.     

Copolymerization of styrene and methyl methacrylate. Reactivity ratios from conversion–composition data

A method for the determination of reactivity ratios from conversion–composition data has been outlined. The conversion–composition changes during the copolymerization of styrene (M₁) and methyl methacrylate (M₂) have been studied at 60°C. By a method of graphical intersection, the integrated form of Skeist's equation has been used to determine the reactivity ratios (r₁ = 0.54 ± 0.02 and r₂ = 0.50 ± 0.06) in reasonably good agreement with values reported in the literature. The area of intersection was used as a measure of the precision of the data.     

Kinetic Study of Radical Polymerization VIII. A Comprehensive Study of Solution Copolymerization of Vinyl Acetate and Methyl Acrylate by 1H‐NMR Spectroscopy

Radical copolymerization reaction of vinyl acetate (VA) and methyl acrylate (MA) was performed in a solution of benzene‐d₆ using benzoyl peroxide (BPO) as the initiator at 60°C. Kinetic studies of this copolymerization reaction were investigated by on‐line ¹H‐NMR spectroscopy. Individual monomer conversions vs. reaction time, which was followed by this technique, were used to calculate the overall monomer conversion, as well as the monomer mixture and the copolymer compositions as a function of time. Monomer reactivity ratios were calculated by various linear and nonlinear terminal models and also by simplified penultimate model with r _2(VA)=0 at low and medium/high conversions. Overall rate coefficient of copolymerization was calculated from the overall monomer conversion vs. time data and k _p  . k _t ^?0.5 was then estimated. It was observed that k _p  . k _t ^?0.5 increases with increasing the mole fraction of MA in the initial feed, indicating the increase in the polymerization rate with increasing MA concentration in the initial monomer mixture. The effect of mole fraction of MA in the initial monomer mixture on the drifts in the monomer mixture and copolymer compositions with reaction progress was also evaluated experimentally and theoretically.     

Application of the monomer reactivity ratios to the kinetic‐model discrimination and the solvent‐effect determination for the styrene/acrylonitrile monomer system

The impact of reactivity ratios determined with the Nelder and Mead simplex method on the kinetic‐model discrimination and the solvent‐effect determination for the styrene/acrylonitrile monomer system was investigated. For the monomer system, the penultimate unit effect was inversely proportional to the polarity of the solvent: acetonitrile < N,N‐dimethylformamide < methyl ethyl ketone < toluene. Quantitatively, the penultimate unit effect could be correlated with an absolute value of the difference between the standard deviation of the reactivity ratios determined for the terminal and penultimate models. By application of the F test, the penultimate model was justified for copolymerization in toluene. The conclusion was less certain for polymerization in methyl ethyl ketone. With a scanning procedure based on the simplex method, it was found that an equivalent representation of the copolymer‐composition data could be achieved with multiple sets of penultimate‐model reactivity ratios. However, the relationship between the triad‐sequence distribution and copolymer composition depended on the reactivity‐ratio set chosen for the microstructure determination. The microstructure calculated with the penultimate‐model reactivity ratios determined with the simplex method from the initial guess (r₁₁ = r₁, r₂₁ = 1/r₂, r₂₂ = r₂, r₁₂ = 1/r₁) did not obey the general “bootstrap effect” rule. This observation still requires some theoretical interpretation. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 846–854, 2000     

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).     

Penultimate effects in methyl methacrylate-4-vinyl pyridine copolymers

From the ¹H-NMR spectra of methyl methacrylate (M₁)-4-vinyl pyridine (M₂) radical copolymers with various monomer ratios, the reactivity ratios have been found using the penultimate model (r₁₁ = 1.51 r₂₁ = 0.10 r₂ = 0.24) and the co-isotactic alternating addition probability (σ = 0.5) as the best fit of the pentad distribution between the three parts of the methoxy signal.     

The use of the radiotracer method to circumvent penultimate group and ceiling temperature effects in copolymerisation

The radiotracer method can be used to study copolymerisations of M₁ and M₂ under conditions where [M₁]?[M₂]. In these circumstances, the probability of two M₂ units becoming adjacent in the polymer chain during propagation is negligible. Experimentally derived reactivity ratios, obtained by a simple graphical solution of composition data, are realistic measures of relative reactivities even with systems where penultimate group effects or depropagation effects due to M₂M₂ diads are normally significant.     

Kinetic and ESR studies on radical copolymerization of p-tert-butoxystyrene and di-n-butyl maleate in benzene

The copolymerization of p-tert-butoxystyrene (TBOSt) (M₁) and di-n-butyl maleate (DBM) (M₂) with dimethyl 2,2′-azobisisobutyrate (MAIB) in benzene at 60°C was studied kinetically and by means of ESR spectroscopy. The monomer reactivity ratios were determined to be r₁ = 2.3 and r₂ = 0 by a curve-fitting method. The copolymerization system was found to involve ESR-observable propagating polymer radicals under practical copolymerization conditions. The apparent rate constants of propagation (k_p) and termination (k_t) at different feed compositions were determined by ESR. From the relationship of k_p and f₁ (f₁ = [M₁]/([M₁] + [M₂])) based on a penultimate model, the rate constants of five propagations of copolymerization were evaluated as follows; k₁₁₁ = 140 L/mol s, k₂₁₁ = 3.5 L/mol s, k₁₁₂ = 61 L/mol s, k₂₁₂ = 1.5 L/mol s, and k₁₂₁ = 69 L/mol s. Thus, a pronounced penultimate effect was predicted in the copolymerization. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 1449–1455, 1998     

Comprehensive Study of Free Radical Copolymerization Using a Monte Carlo Simulation Method, 1

Summary: In order to investigate the influence of reactivity ratios and initial feed composition on the microstructure of macromolecules in free radical copolymerization, a comprehensive study was carried out using a Monte Carlo simulation method. As a result, a new procedure was introduced to modify the works of others on the initiation step. The variation of the copolymer composition and the fashion of the arrangement of monomers in simulated chains were evaluated as a function of copolymerization parameters. The model was capable of monitoring any change in azeotropy as well as the magnitude and direction of composition drift from the azeotrope point. The maximum reachable conversion (MRC) was predicted for different combinations of initial feed compositions and reactivity ratios. According to the simulation results, a critical conversion where the macromolecules produced inherited the maximum allowed alternation was obtained for the reactivity ratios given.

Change of sequence distribution of simulated copolymer chains with conversion for various initial feed compositions on a triangular graph (r_A = 0.5, r_B = 0.9).     

N-vinylpyrrolidone and 4-vinyl Benzylchloride Copolymers: Synthesis,Characterization and Reactivity Ratios

The copolymers prepared in this study by free radical copolymerization of N-vinylpyrrolidone (M ₂) with 4-vinylbenzylchloride (M ₁) using 2,2′-azobisisobutyronotrile (AIBN) initiator in 1,4-dioxane solvent at 70°C were characterized by FTIR, ¹H-NMR and ¹³C-NMR techniques. Polymer solubility was tested in both polar and nonpolar solvents. The thermal properties were studied by thermogravimetric analysis (TGA) and differential scanning calorimeter (DSC). Copolymer compositions were established by H¹-NMR spectra, while reactivity ratios of the monomers were computed using the linearization methods viz., Fineman-Ross (FR) (r ₁ = 1.67 and r ₂ = 0.67), Kelen-Tudos (KT) (r ₁ = 1.77 and r ₂ = 0.65) and extended Kelen-Tudos (EK-T) (r ₁ = 1.72 and r ₂ = 0.63) methods at lower conversion. Furthermore, reactivity ratios in nonlinear error-in-variables method (RREVM) also compute the reactivity ratios (r ₁ = 1.76 and r ₂ = 0.66); these are found to be in good agreement with each other. The distribution of monomer sequence along the copolymer chain was calculated using a statistical method based on the calculated reactivity ratios.     

Living carbocationic copolymerization of isobutylene with styrene

The carbocationic copolymerization of isobutylene (IB) and styrene (St), initiated by 2‐chloro‐2,4,4‐trimethylpentane/TiCl₄ in 60/40 (v/v) methyl chloride/hexane at ?90 °C, was investigated. At a low total concentration (0.5 mol/L), slow initiation and rapid monomer conversion were observed. At a high total comonomer concentration (3 mol/L), living conditions (a linear semilogarithmic rate and M_n–conversion plots) were found, provided that the St concentration was above a critical value ([St]₀ ～ 0.6 mol/L). The breadth of the molecular weight distribution decreased with increasing IB concentration in the feed, reaching M_w/M_n ～ 1.1. St homopolymerization was also living at a high total concentration, yielding polystyrene with M_n = 82,000 g/mol, the highest molecular weight ever achieved in carbocationic St polymerization. An analysis of this system by both the traditional gravimetric–NMR copolymer composition method and FTIR demonstrated penultimate effects. IB enrichment was found in the copolymers at all feed compositions, with very little drift at a high total concentration and above the critical St concentration. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1778–1787, 2007     

Radical copolymerization behavior of a highly fluorinated cyclic olefin with vinyl ether

The copolymerization of a highly fluorinated cyclic monomer, octafluorocyclopentene (OFCPE, M₁), with ethyl vinyl ether (EVE, M₂) was investigated with a radical initiator in bulk. Despite the poor homopolymerizability of each monomer, the copolymerization proceeded successfully, and the molecular weights of the copolymers reached up to more than 10,000. Incorporation of the OFCPE units into the copolymer led to an increase in the glass‐transition point. The copolymer composition was determined from ¹H NMR spectra and elemental analysis data. The molar fraction of the OFCPE unit in the copolymer increased and approached but did not exceed 0.5. The monomer reactivity ratios were estimated by the Yamada–Itahashi–Otsu nonlinear least‐squares procedure as r_1,OFCPE = ?0.008 ± 0.010 and r_2,EVE = 0.192 ± 0.015. The reactivity ratios clearly suggest that the copolymerization proceeds alternatively in the case of an excessive feed of OFCPE. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 1151–1156, 2002     

Revisiting the design of experiments for copolymer reactivity ratio estimation

Tidwell and Mortimer used the D-optimal criterion to design terminal model reactivity ratio estimation experiments. In this paper, two problems are investigated which were not addressed by Tidwell and Mortimer. The first problem is the design of reactivity ratio estimation experiments subject to composition constraints. It is shown that all the key information contained in the D-optimal criterion can be summarized in two equations: one which is a function of r?₁, and one which in a function of r?₂. These two equations can be used to design reactivity ratio estimation experiments under composition constraints which are within 3 mol % of the D-optimal feed compositions. The second problem is the design of penultimate reactivity ratio estimation experiments. The D-optimal criterion for the penultimate model was derived and optimized for two existing systems as well as a large number of hypothetical systems. The D-optimal criterion for the penultimate model was found to be much more complicated than the terminal model criterion. For this reason, the optimal penultimate reactivity ratio estimation experiments can not be approximated by simple equations. Anyone interested in designing such experiments must derive and optimize the D-optimal criterion. © 1993 John Wiley & Sons, Inc.