Penultimate Model Research Articles

Radical copolymerization behaviors of styrene and coumarin

The radical copolymerizations of styrene (M1) with coumarin (M2) (and 7-acetoxycoumarin) have been first carried out in benzene (and in DMF) at 60° C using AIBN as initiator. The terminal model monomer reactivity ratios (MRR) were determined by Fineman-Ross method, Kelen-Tudos method and nonlinear method. The respective estimated values are r1 = 43.08, r2 = 0.63; r1 = 39.17, r2 = 0.43; and r1 = 49.94, r2 = 1.04 for styrene-coumarin (S-C) system. For styrene-7-acetoxycoumarin (S-AC) system, the values are r1 = 51.44, r2 = 1.24; r1 = 50.56, r2 = 1.20 and r1 = 56.23, r2 = 1.48, respectively. The penultimate model MRRs are determined by Fenn-Barson method and nonlinear method to be r1= 49.18, r1′ = 2.01, r2 = r2′ = 0.43 and r1 = 51.21, r1′ = 0.86, r2= r2′ =0, respectively, for S-C system; r1 = 64.76, r1′= 3.46, r2 = r2′= 1.20 and r1 = 59.90, r1 = 0.57, r2 = r2′ = 0. respectively, for S-AC system. It is found that coumarin is about 1.2 times more reactive toward styrene-terminated radical than 7-acetoxycoumarin for steric reasons. The penultimate model of Fenn-Barson is fairly adequate in describing the copolymerization mechanism of styrene-coumarin system, while the terminal model is more suitable for styrene-7-acetoxycoumarin system.

A novel mechanistic study of the radical copolymerization of styrene with citraconic anhydride via 13C n.m.r. spectroscopy

The composition and monomer unit sequence distributions of copolymers of styrene with citraconic (α-methylmaleic) anhydride (CA) prepared in methyl ethyl ketone at 50.0±0.1°C have been determined over a range of comonomer feed mole fractions using 13C n.m.r. spectroscopy. The monomer units in these copolymers were found to display an increasingly strong tendency to alternate as the mole fraction of CA in the feed increased. The terminal, penultimate, complex-participation and complex-dissociation models were each tested for applicability to the mechanism of copolymerization for this comonomer system by applying reactivity ratio related test functions to the experimental sequence distribution data, enabling a direct visual assessment of the applicability of each model to be made. On the basis of these test functions, the terminal, penultimate and complex-dissociation models were each found to provide inadequate descriptions of this copolymerization system.

A high-field 13C-NMR study of the aqueous copolymerizations of acrylonitrile and vinyl acetate. Determination of comonomer reactivity ratios

The radical initiated aqueous “slurry” copolymerization of acrylonitrile and vinyl acetate has been investigated. High field 13C-NMR spectra have been recorded for samples prepared employing both batch and starve-fed (semi-continuous) techniques. Copolymer composition and A-centred triad fractions have been obtained from the NMR spectra for a range of different feed compositions and give terminal model reactivity ratios of r V and r A of 2.7 and 0.05, respectively. However, the penultimate model gives a superior fit to the experimental A-centred triad fraction data. A comparison is made with data obtained for the same system employing the spin-trapping technique in conjunction with ESR spectroscopy.

Tacticities of Copoly(vinyl ester)s Obtained by Radical Polymerization

Tacticity simulations of poly(vinyl acetate-co-vinyl propionate) [poly(VAc-co-VPr)], poly(vinyl acetate-co-vinyl decanoate) [poly(VAc-co-VD)] and poly(vinyl acetate-co-vinyl pivalate) [poly(VAc-co-VP)] were tried by a terminal model. Cotacticities for vinyl acetate (VAc)/vinyl pivalate (VPr) and vinyl acetate (VAc)/vinyl decanoate (VD) were well simulated and coisotactic parameters for these systems could be estimated. But the tacticities of poly(VAc-co-VP) could not be well simulated by the terminal model indicating penulutimate effect and simulation by penultimate model was tried.

Kinetic and electron paramagnetic resonance studies on radical polymerization. Radical copolymerization of p‐tert‐butoxy‐styrene and dibutyl fumarate in benzene

AbstractThe copolymerization of p‐tert‐butoxystyrene (1) (M1) and dibutyl fumarate (2) (M2) initiated with dimethyl 2,2′‐azobisisobutyrate (3) was studied in benzene at 60°C kinetically and by means of electron paramagnetic resonance (EPR) spectroscopy. The monomer reactivity ratios were determined to be r1 = 0,18 and r2 = 0,01, indicating that homopropagation of M2 is almost negligible in the copolymerization. The copolymerization system was revealed to involve EPR‐observable propagating polymer radicals under practical copolymerization conditions. The apparent rate constants of propagation (kp) and termination (kt) determined by EPR show a rapid increase in the range from 0,9 to 1,0 of feed composition (f1 = {[M1]/([M1] + [M2])}) of M1. From the relationship between kp and f1 based on Fukuda's penultimate model, the rate constants of propagation of copolymerization were evaluated; k111 = 140 L · mol−1 · s−1, k211 = 4,3 L · mol−1 · s−1, k112 = 778 L · mol−1 · s−1, k212 = 24 L · mol−1 s−1 and k121 = 19 L · mol−1 · s−1, suggesting a pronounced penultimate effect.

Model discrimination via designed experiments: discriminating between the terminal and penultimate models on the basis of composition data

Computer simulations have been used to study the application of statistical model discrimination methods to the modeling of copolymerizations. Statistical model discrimination methods describe how experiments should be designed and analyzed to obtain the maximum possible information on the strengths of competing models. The potential benefits of applying model discrimination methods are described by contrasting them with pest work on the modeling of copolymerizations. Three model discrimination techniques (Buzzi-Fenaris and Forzetti, 15 effect entropy, 14 and Hsiang end Reilly 21 ) have been applied to the systems styrene-acrylonitrile, styrene-methyl methacrylate, and styrene-butyl acrylate

Microstructural analysis of methacrylonitrile‐styrene copolymers to obtain reactivity ratios

AbstractThe copolymerization of methacrylonitrile (M) and Styrene (S) at 60°C in bulk has been studied at low conversion by the use of 1H‐ and 13C‐NMR to examine the copolymer microstructure for copolymer composition and sequence distribution. The penultimate model was found to provide the best description of the polymerization with rMM = 0.220, rSM = 0.519, rSS = 0.241, rMS = 0.570. These results have been compared with those found for the corresponding acrylonitrile‐styrene copolymerization. © 1993 John Wiley & Sons, Inc.

Revisiting the design of experiments for copolymer reactivity ratio estimation

AbstractTidwell 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 r̂1, and one which in a function of r̂2. 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.

A mechanistic study of the radical copolymerisation of p‐methoxystyrene with citraconic anhydride via 13C NMR spectroscopy

AbstractThe composition and monomer unit sequence distribution of copolymers of p‐methoxystyrene (p‐MST) with citraconic anhydride (CA) prepared in methyl ethyl ketone (MEK) at 50,0 ± 0,1°C were determined over a range of comonomer feed mole fractions using 13C NMR spectroscopy. The monomer units in these copolymers were found to display an increasingly strong tendency to alternate as the mole fraction of CA in the feed increases. The existence of a 1:1 charge‐transfer complex formed between p‐MST and CA in the feed was confirmed via UV spectroscopy and the equilibrium constant for complex formation was determined. The terminal, penultimate and complex‐participation models were tested for applicability to the mechanism of copolymerisation for this comonomer system. On the basis of copolymer composition data, the penultimate and complex‐participation models were found to provide each an adequate description of the mechanism of copolymerisation in the comonomer system via non‐linear least squares methods. The inadequacies of the terminal and penultimate models in describing the copolymers were exposed more explicitly through an analysis of their comonomer unit sequence distributions using reactivity ratio related test functions.

Penultimate model description of the propagation kinetics for the free radical copolymerization of styrene and methyl methacrylate

AbstractRecently experimental data on the free radical copolymerization of styrene and methyl methacrylate in bulk were shown to obey penultimate model kinetics. These data were now reevaluated with respect to copolymerization parameters by means of a simultaneous fit of the penultimate model both to the copolymer composition and to the overall propagation rate coefficient, and in dependence on the monomer feed composition. Different simultaneous fit procedures were used and compared. The following parameters are finally suggested: r11 = 0,498; r21 = 0,589; r22 = 0,463; r12 = 0,547; s1 = 0,478 and s2 = 0,256.

The applicability of copolymer composition and sequence distribution data to the mechanistic study of the alternating copolymerisation of maleic anhydride with substituted styrene derivatives

AbstractThe composition and sequence distribution of copolymers of maleic anhydride (MA) with p‐methoxystyrene (p‐MST) and p‐chlorostyrene (p‐CST) prepared in ethyl methyl ketone at 50 ± 0,1°C were analysed using 13C DEPT NMR techniques, in order to compare the applicability of composition and sequence distribution data to the study of the mechanism of copolymerisation using the terminal, penultimate and complex‐participation models. In the case of the strongly alternating copolymerisation of p‐MST with MA, the comparison of models on the basis of sequence distribution data was found to be better at separating each model in terms of its applicability, with the complex‐participation model providing the best fit to the data. In the case of the less strongly alternating copolymerisation of p‐CST with MA, neither method of comparison could clearly distinguish between the penultimate and complex‐participation models.

Free radical copolymerization: an NMR investigation of current kinetic models

The ability of terminal model kinetics to predict copolymer microstructure was tested for the styrene-Me methacrylate system copolymd. at 40 Deg at various fractions of monomers. 13C NMR studies (in the accompanying paper) showed that previous peak assignments of statistical styrene-Me methacrylate copolymers were incorrect. The peak areas obtained for all copolymers were described in terms of triad sequences and were also adequately predicted by the terminal model utilizing reactivity ratios calcd. from a nonlinear least squares fit to the copolymer compn. data detd. by 1H NMR spectra. The nonterminal model behavior of the kinetics of polymn. described elsewhere could be successfully modeled by the restricted penultimate model of T. Fukuda et al (1985, 1987). All current data could also be explained by various bootstrap or monomer-polymer complex models

Copolymérisation du dicyanure de propène‐1 ylidène‐1 avec l'acétate de vinyle et des styrènes substitutés. Calcul des taux de réactivité et étude de l'effet pénultième

Abstract1‐Propen‐1‐ylidene dicyanide was copolymerized in bulk with vinyl acetate and five substituted styrenes. The reactivity ratios of these copolymerizations were calculated by the Fineman‐Ross or the Kelen‐T¨︁udős method. The penultimate model describes satisfactorily the deviation from the terminal model in the copolymerization reactions between 1‐propene‐1‐ylidene dicyanide and the substituted styrenes.

Analysis of the linear methods of determining copolymerization reactivity ratios, 13. A critical application of penultimate model (r2 = 0) to radical copolymerization data of styrene

AbstractIn an until now widest study of the penultimate effect the reactivity ratios of 66 published styrene copolymerization systems showing a non‐classical behaviour have been reviewed. For the alternating systems a simplified two‐parameter penultimate model with r2 = r′ = 0 was applied. The systems were classified into 2 groups: 1. alternating and 2. non‐alternating systems. 32 systems of the first group have been reevaluated. r‐Values, together with their 95% confidence limits have been calculated. The confidence parameter δ′ and the “efficiency factor” of planning Q, suitable for classification of the systems, have been applied. In this number 23 (72%) systems yielded linear Kelen‐Tüdős‐plots (13 belong to class I, 10 to class I!). 5 (16%) systems were assigned to class II (non‐adequacy of the penultimate model possible) and 4 (12%) to class III, where the experimental data are inconsistent and the r‐values meaningless.

Analysis of the linear methods of determining copolymerization reactivity ratios, 11. Copolymerization of styrene with methyl α‐cyanocinnamate and fumaroyldipyrrolidone

AbstractThe composition of copolymers was determined as a function of the monomer feed for two systems: styrene/methyl a‐cyanocinnamate in toluene and styrene/fumaroyldipyrrolidone in dimethyl sulfoxide both at 60°C with 2,2′‐azoisobutyronitrile (AIBN) as initiator. To ascertain the accuracy of reaction modelling in terms of the classical and the penultimate model, the extended linearized forms of both models were applied. The styrene/methyl a‐cyanocinnamate system was found to copolymerize non‐classically; the two‐parameter penultimate model described properly the experimental data yielding r'1/r1 ≈ 3–6. The styrene/fumaroyldipyrrolidone system showed only a slight penultimate effect. However, in this case, the terminal model gave a better fit of experimental data.

Analysis of the linear methods of determining copolymerization reactivity ratios, 12. Copolymerization of styrene or methyl methacrylate with N‐p‐tolylcitraconimide or fumarodinitrile

AbstractFor copolymerization of styrene or methyl methacrylate with N‐p‐tolylcitraconimide (in toluene) or fumarodinitrile (in benzene) at 60°C with 2,2′‐azoisobutyronitrile (AIBN) as initiator, the composition of the resulting copolymers was measured as a function of the monomer feed composition. To provide good accuracy of reaction modelling in terms of the terminal and penultimate models, the linearized forms of both models were applied assuring high sensitivity of the evaluation. Among the systems considered the styrene/fumarodinitrile system with r′1/r′1 ≈ 10 was found to copolymerize according to the penultimate mechanism to a significant degree.

Radical copolymerization of citraconic anhydride with styrene and terpolymerization of citraconic anhydride and maleic anhydride with styrene

Existence of a 1:1 charge transfer complexe between citraconic anhydride (CAn) and styrene (St) in the copolymerization system was confirmed. The penultimate model was shown to be the relatively adequate description of the mechanism of the copolymerization of CAn with St. The relative reactivity of maleic anhydride toward a poly(St) radical was found to be about 6.8 times higher than that of CAn. The alternating copolymer of dialkyl citraconate with St having a relatively high thermal stability was prepared by esterification of the St-CAn copolymer.

Copolymerization of acrylonitrile and methacrylic acid. An assessment of the copolymerization mechanism

The free-radical copolymerization of acrylonitrile and methacrylic acid has been investigated in bulk at 60 °C with the aim of elucidating the best model for the polymerization. Quantitative measurements of the copolymerization compositions and diad, triad, and tetrad fractions in the comonomer sequence distribution have been determined by using elemental analysis and H, C, and C DEPT NMR. This microstructural information was found to be consistent with a terminal polymerization mechanism with r= 3.7 and r = 0.19. The penultimate model was not found to provide a statistically significant improvement over the terminal model.

The study of the copolymerization of styrene and acrylonitrile to high conversion. application of low conversion reactivity ratios

The copolymerization of styrene and acrylonitrile has been investigated with the purpose of predicting the changes in copolymer composition and comonomer sequence distribution with increasing conversion. Toluene was used as the solvent and the copolymerization was examined initially under low conversion conditions to determine whether the terminal or the penultimate model best described the polymerization. The penultimate model was found to provide the best fit to both the experimental composition and triad fraction data. The reactivity ratios (for the penultimate model) were then used to predict the changes in copolymer composition and triad fractions with conversion. The results show that the penultimate model provides an excellent prediction for the polymerization across the complete conversion range for all comonomer feed compositions.

Kinetics of free-radical copolymerization: the pseudo-kinetic rate constant method

The pseudo-kinetic rate constant method in which the kinetic treatment of a multicomponent polymerization reduces to that of a homopolymerization is a useful tool to analyse the kinetics of copolymerization. This method is applicable not only for the systems described by the terminal model for copolymerization but also for those described by the higher order Markov chain statistics such as the penultimate model. It has also been clarified that this method can practically be applicable even when the effect of the chain length dependent bimolecular termination reaction is significant.