Monte Carlo simulation of kinetics and chain-length distribution in radical polymerization

In this paper, the Monte Carlo method for numerically simulating the kinetics and chain-length distribution in radical polymerization is described. Because the Monte Carlo method is not subject to the assumption of steady-state, it is particularly suitable for studying the kinetic behaviour before the steady-state has been reached and for systems in which the steady-state assumption may be violated. Illustrative applications of the algorithm given in this paper not only demonstrate convincingly both the feasibility and usefulness of the algorithm, but also provide some new insight into the illustrative examples. For the case of pseudostationary radical polymerization such as rotating-sector and pulsed-laser initiations, we have found that the pseudostationary radical concentration can be reached after two or three initiation periods. However, the number-average chain-length x̄_n reaches the pseudostationary value much slower than the radical concentration. It is oscillatively reaching the pseudostationary value, and the amplitudes of the oscillations are decreasing with time. We have also found that the chain-length distribution of the resulting polymer in the case of pseudostationary radical polymerization with termination by combination has stronger periodic modulation. Hence, it should be easier to locate the points of inflection in practice. Therefore, the rate constant of propagation, k_p, can be determined precisely for systems which are dominated by a combination-type of termination.     

Monte Carlo simulation of chain length distribution in radical polymerization with transfer reaction

In this paper, the basic principle and a Monte Carlo method are described for numerically simulating the chain-length distribution in radical polymerization with transfer reaction to monomer. The agreement between the simulated and analytical results shows that our algorithm is suitable for systems with transfer reaction. With the simulation algorithm, we confirm that transfer reaction has a similar effect as disproportionation on the molecular weight distribution in radical polymerization with continuous initiation. In the pulsed laser (PL) initiated radical polymerization with transfer reaction, the ‘waves’ on the chain-length distribution profile become weaker as the ratio of transfer reaction rate constant, k_tr, to the propagation rate constant, k_p, is increased in the case with either combination-type or disproportionation-type termination. Moreover, it seems that the combination termination has a broadening effect on the waves. Therefore, k_p can also be determined by precisely locating the inflection point L_o on the chain-length distribution profile for radical polymerization with transfer reaction, unless k_tr is large enough to smear out the waves on the chain-length distribution.     

New aspects of pseudostationary polymerization and their application

Contrary to the stationary state little thought has been given so far to the general principles of the pseudostationary state. In this discourse an attempt is made to demonstrate that — within wide limits — arbitrary initiation profiles may be used to determine k_p/k_t (k_p = rate constant of chain propagation, k_t = rate constant of chain termination) from the frequency dependence of rate of polymerization (in analogy to the rotating-sector technique) as well as to evaluate k_p from the chain-length distribution (CLD) of samples prepared under pseudostationary conditions. Adverse factors like nonspontaneous transformation of absorbed photons into primary radicals do not invalidate this result. The existence of a universal relationship (independent of the initiation profile) is proved to exist for the second moment of the CLD of samples prepared under pseudostationary initiation conditions for constant (chain-length independent) k_t. Pseudostationarity, however, might be also achieved if not the initiation but the termination is periodically varied. In this case the CLD has a completely different shape but allows determination of k_p likewise. Finally, the case of chain-length dependent k_t is shortly discussed in connection with pulsed-laser initiation. Although the general equation for the second moment of the CLD does not apply any longer for this case some generality appears to exist under these conditions, too.     

Simulation of pseudostationary radical polymerization, 1. Chain-length distributions for arbitrary initiation profiles

A procedure is developed which allows to treat arbitrary periodic initiation profiles (asymmetric and symmetric triangle profiles, sinusoidal profiles, Gaussian profiles etc.) in pseudostationary radical polymerization. Using an iterative method these profiles are transformed into the (likewise periodic) radical profiles and into the chain-length distributions of the resulting polymer in case of termination by disproportionation. These distributions are analysed for the position of their inflection points which may be used for experimental determination of the elementary rate constant of chain propagation k_p. It turned out that for all profiles that have at least one discontinuity (e.g. asymmetric triangle profiles) the position of the point of inflection is a correct measure of k_p for a conveniently wide range of experimental parameters. In case of profiles without discontinuity (symmetric triangle profiles, sinusoidal and Gaussian profiles) the position of the inflection point is shifted to lower values which means that the k_p values determined on this basis will be a little too small. In most cases, however, the error introduced by this fact will not exceed the overall error of the experiment so that in practice the method of determining k_p in pseudostationary polymerization is not restricted to those profiles which exhibit discontinuities.     

The incorporation of side reactions into pseudostationary polymerization, 1. The closed solution of a kinetic scheme comprising chain-transfer to monomer or solvent

A procedure is developed that allows the calculation of chain length distributions of polymers prepared by periodic modulation of the initiation process, considering termination by disproportionation and chain transfer. For the case of a (pseudostationary) laserpulse initiated polymerization process a closed solution can be derived for the chain length distribution (cld) of dead polymer and its O^th, 1^st and 2^nd moments. By analysis of the detectability of the “extra-peaks” appearing in the cld (which represent the key for the determination of propagation constants) as a function of the parameters chosen the optimum conditions can be predicted for experiments.     

Synthesis and polymerization studies of N-cyanomethanimine monomers

New imine monomers containing C-aryl and N-cyano substituents were synthesized and polymerized by both radical and anionic initiation. Homopolymerization yielded low molecular weight polymers (M_n < 2100). Higher yields were obtained with anionic initiation rather than radical initiation. Radical initiated copolymerization with p-methoxystyrene gave low yields of low molecular weight copolymers. Radical initiated copolymerization with methyl acrylate gave copolymers of 15,000–,32,000 molecular weight in moderate yields, but with rather low incorporation of the imine monomer. The C-substituent affected the anionic and free radical reactivity similarly. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35 : 2703–2710, 1997     

Chain-length dependent termination in pulsed-laser polymerization, 2. On the prospects of determining the bimolecular termination constant kt from the second moment of the chain-length distribution

The correct (event weighted) average of k_t, 〈k_t〉, has been calculated for pseudostationary laser-induced polymerization for a kinetic scheme with chain-length dependent termination and compared to the average k̄_t obtained by formally solving for k_t the expression for the second moment of the chain-length distribution valid for chain-length independent termination (represented by the product of rate of polymerization ν_p and weight average degree of polymerization P̄_w). It is shown that there is a fair agreement between the two quantities. This may be used to recover experimentally the power-law governing the dependence of k_t on chain-length, especially its exponent.     

Chain‐length dependent termination in rotating sector polymerization, 1. The evaluation of the rate constant of chain propagation kp

The chain‐length distributions (CLDs) of polymers prepared by rotating‐sector (RS) techniques under pseudostationary conditions were simulated for the case of chain‐length dependent termination and analysed for their suitability of determining the rate constant of chain propagation k_p from the positions of their points of inflection. The tendency to underestimate k_p is a little more pronounced than in pulsed‐laser polymerization (PLP) but, interestingly, the situation improves in the presence of chain‐length dependent termination. The estimates also were found to be more precise a) for smaller rates of initiation, b) for higher order points of inflection, c) if termination is by combination, d) if the role played by the shorter one of the two chains becomes less dominant. Taken in all, the determination of k_p from the points of inflection in the CLD of RS‐prepared polymers may well compete with the more famous PLP method, especially if some care is taken with respect to the choice of experimental conditions.     

Chain-length dependent termination in pulsed-laser polymerization, 3. On the prospects of determining the bimolecular termination constant kt from rate data

The correct (event-weighted) average of k_t, 〈k_t〉, has been calculated from simulation data for pseudostationary laser-induced polymerization for a kinetic scheme with chain-length dependent termination and compared to the average k̄_t which is obtained by employing the formal procedures, originally designed for the evaluation of individual rate constants from rate data in the case of chain-length independent termination. Satisfactory (and in fact excellent) results are obtained only if the complete equation for the conversion per laser pulse is solved for k̄_t. This leads to an almost perfect recovery of the power-law governing the dependence of k_t on chain-length, especially the exponent.     

Arenesulfonyl bromides: The second universal class of functional initiators for the metal‐catalyzed living radical polymerization of methacrylates,acrylates, and styrenes

The metal‐catalyzed living radical polymerization of methyl methacrylate, n‐butyl acrylate, and styrene, initiated with p‐toluenesulfonyl bromide and phenoxybenzene‐4,4′‐disulfonyl bromide and catalyzed with CuBr/2,2′‐bipyridine (bpy) and various self‐regulated Cu‐based catalytic systems such as Cu₂O/bpy, Cu₂S/bpy, Cu₂Se/bpy, and Cu₂Te/bpy, is reported. Similarities and differences between the arenesulfonyl chloride and arenesulfonyl bromide initiators are discussed. The arenesulfonyl bromide initiators require reduced reaction times to produce polymers in high conversions under milder reaction conditions than the corresponding arenesulfonyl chloride initiators. At the same time, they exhibit 100% initiator efficiency and generate polymers with narrow molecular weight distributions and functional chain ends. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 319–330, 2005     

Polymerization and crosslinking of epoxides: Base-catalyzed polymerization of phenyl glycidyl ether

The anionic polymerization of 2,3-epoxypropyl phenyl ether initiated by sodium methoxide and dimsyl sodium in dioxane and in dimethyl sulfoxide has been studied. Kinetic and dielectric constant measurements have been recorded, and a mechanism for the initiation reaction with dimsyl sodium has been put forward. Polymerization initiated with dimsyl sodium revealed almost total absence of sulfur in the polymer by endgroup analysis. The reaction was shown to be inhibited by oxygen. Molecular weight determinations have indicated a reaction involving transfer to give polymers of lower than calculated M?_n and a ratio of k_p/k_tr ratio of approximately 73. Gel-permeation chromatography suggests a narrow molecular weight distribution in the polymers prepared.     

9‐Bromoanthracene photodimers as initiators in controlled radical polymerization: Silane radical atom abstraction coupled with nitroxide mediated polymerization

Slow initiation relative to propagation has previously prevented photodimers of 9‐bromoanthracene or 9‐chloroanthracene, formed by [4 + 4] photocyclization reactions of the analogous 9‐haloanthracene, from being viable initiators in atom transfer radical polymerization (ATRP) reactions. The resulting polymers were found to possess high polydispersity index (PDI) values, much higher than expected number average molecular weight (M_n) values, with the reaction displaying a nonlinear relationship between monomer conversion and M_n. We report here the use of silane radical atom abstraction (SRAA) to create initiating bridgehead radicals in the presence of 2,2,6,6‐tetramethylpiperidine‐1‐oxyl (TEMPO) to mediate the polymerization. When using SRAA coupled with nitroxide mediated polymerization, a dramatic decrease in PDI values was observed compared with analogous ATRP reactions, with M_n values much closer to those anticipated based on monomer‐to‐initiator ratios. Analysis using UV‐Vis spectroscopy indicated only partial anthracene labeling (～ 25%) on the polymers, consistent with thermolysis of the anthracene photodimer coupled with competition between initiation from the bridgehead photodimer radical and silane‐based radical. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 6016–6022, 2008     

Novel substituted epoxide initiators for the carbocationic polymerization of isobutylene

This article presents the first detailed account of the discovery that substituted epoxides can initiate the carbocationic polymerization of isobutylene. α‐Methylstyrene epoxide (MSE), 2,4,4‐trimethyl‐pentyl‐epoxide‐1,2 (TMPO‐1), 2,4,4‐trimethyl‐pentyl‐epoxide‐2,3 (TMPO‐2), and hexaepoxi squalene (HES) initiated isobutylene polymerization in conjunction with TiCl₄. MSE, TMPO‐2, and HES initiated living polymerizations. A competitive reaction mechanism is proposed for the initiation and propagation. According to the proposed mechanism, initiator efficiency is defined by the competition between the S_N1 and S_N2 reaction paths. A controlled initiation with external epoxides such as MSE should yield a primary hydroxyl head group and a tert‐chloride end‐group. The presence of tert‐chloride end‐groups was verified by NMR spectroscopy, whereas the presence of primary hydroxyl groups was implied by model experiments. Multiple initiation by HES was verified by diphenyl ethylene end‐capping and NMR analysis; the resulting star polymer had an average of 5.2 arms per molecule. A detailed investigation of the reaction mechanism and the characterization of the polymers are in progress. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 444–452, 2000     

Simulation of pseudostationary radical polymerization, 3. Periodic modulation of the termination process for termination by disproportionation

A procedure is developed that allows the calculation of chain-length distributions of polymers prepared by periodic modulation of the termination rate constant, considering termination by disproportionation. Applying some (hypothetical) field which suppresses — or at least diminishes — the termination rate constant periodically, results in step-function-like chain-length distributions. In principle, the same information may be obtained as in the case of periodical variation of the rate of initiation.     

Azobenzene‐based initiator for atom transfer radical polymerization of methyl methacrylate

2‐Bromopropionic acid 2‐(4‐phenylazophenyl)ethyl ester, 2‐bromopropionic acid 6‐(4‐phenylazophenoxy)hexyl ester (BPA₆), 2‐bromopropionic acid‐(4‐phenylazoanilide), and 2‐bromopropionic acid 4‐[4‐(2‐bromopropionyloxy)phenylazo]phenyl ester (BPPE) were used as initiators with monofunctional or difunctional azobenzene for the heterogeneous atom transfer radical polymerization of methyl methacrylate with a copper(I) chloride/N,N,N′,N″,N″‐pentamethyldiethylenetriamine catalytic system. The rates of polymerizations exhibited first‐order kinetics with respect to the monomer, and a linear increase in the number‐average molecular weight with increasing monomer conversion was observed for these initiation systems. The polydispersity indices of the polymer were relatively low (1.15–1.44) up to high conversions in all cases. The fastest rate of polymerization and the highest initiation efficiency were achieved with BPA₆, and this could be explained by the longer distance between the halogen and azobenzene groups and the better solubility of the BPA₆ initiator. The redshifting of the UV absorptions of the polymers only occurred for the BPPE‐initiated system. The intensity of the UV absorptions of the polymers were weaker than those of the corresponding initiators in chloroform and decreased with the increasing molecular weights of the polymers in all cases. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 2358–2367, 2005     

Evidence for chain transfer in the atom transfer radical polymerization of butyl acrylate

Poly(butyl acrylate) (PBuA) of high molecular weight was synthesized by atom transfer radical polymerization (ATRP) in ethyl acetate. Whereas for low molecular weight polymers, a linear increase of the number‐average molecular weight, M_n, versus conversion and narrow molecular weight distributions indicate the suppression of side reactions, a downward curvature in the plot of M_n versus conversion was observed for high molecular weights (M_n > 50 000). This effect is explained by chain transfer reactions, leading to branched polymers. GPC measurements with a viscosity detector give evidence for the branched structure of high molecular weight polymers obtained in ATRP. In addition, transfer to solvent or monomer is likely to occur.     

On the polymerization reactivity of fluorinated vinyl monomers

The polymerization reactivities of α,β,β‐trifluorovinyl compounds (CF₂=CF—R) and α‐trifluoromethylvinyl compounds (CH₂=C(CF₃)—R) are discussed since these monomers have scarcely been investigated and hardly yielded corresponding homopolymers, although tetrafluoroethylene and chlorotrifluoroethylene have been studied under radical polymerization conditions. In the case of α,β,β‐trifluorostyrene, a homopolymer is obtained in low yields by anionic polymerization and it is concluded that the reaction takes place without any side reactions once the reaction has started, since simple addition polymerization is observed and the molecular weight distribution is very narrow. Anionic polymerization of hexafluorobuta‐1,3‐diene is successfully achieved by the addition reaction of living end to the 2‐carbon of hexafluorobuta‐1,3‐diene followed by isomerization to produce excellently high thermostable polymers. ω‐Trifluorovinyloxyfluoroalkyl alcohol produces a polyether via a polyaddition reaction under anionic conditions. The homopolymers of α‐trifluoromethylacrylates are quantitatively obtained under anionic polymerization conditions. α‐Trifluoromethylstyrene derivatives are likely to polymerize under radical conditions, but are not well‐studied. The radical polyaddition reaction of perfluoroisopropenyl esters in 1,4‐dioxane, diethyl ether or 1,2‐dimethoxyethane yields the polymers possessing the solvent moiety in the polymer main chain, respectively. It is clearly demonstrated that each fluorinated vinyl monomer discussed in this article demands its own reaction conditions. Therefore, more experimental data on the polymerization of these individual monomers is needed, including research on developing the reactions discovered in the organofluorine chemistry field to the preparation of polymers.     

Atom transfer radical polymerization of styrene using the novel initiator ethyl 2‐N,N‐(diethylamino)dithiocarbamoyl‐butyrate

The atom transfer radical polymerizations (ATRPs) of styrene initiated by a novel initiator, ethyl 2‐N,N‐(diethylamino)dithiocarbamoyl‐butyrate (EDDCB), in both bulk and solution were successfully carried out in the presence of copper(I) bromide (CuBr) and N,N,N′,N″,N″‐pentamethyldiethylenetriamine at 115 °C. The polymerization rate was first‐order with respect to the monomer concentration, and the molecular weights of the obtained polymers increased linearly with the monomer conversions with very narrow molecular weight distributions (as low as 1.17) up to higher conversions in both bulk and solution. The polymerization rate was influenced by various solvents in different degrees in the order of cyclohexanone > dimethylformamide > toluene. The molecular weight distributions of the produced polymers in cyclohexanone were higher than those in dimethylformamide and toluene. The results of ¹H NMR analysis and chain extension confirmed that well‐defined polystyrene bearing a photo‐labile N,N‐(diethylamino)dithiocarbamoyl group was obtained via ATRP of styrene with EDDCB as an initiator. The polymerization mechanism for this novel initiation system is a common ATRP process. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 32–41, 2006     

Electrochemical and chemical polymerization of acrylamide

The electrochemical and chemical polymerization of acrylamide (AA) has been studied. The electrolysis of the monomer in N,N-dimethylformamide (DMF) containing (C₄H₉)₄NClO₄ as the supporting electrolyte leads to polymer formation in both anode and cathode compartments. The cathodic polymer dissolves in the reaction mixture and the anodic polymer precipitates during the course of polymerization. A plausible mechanism for the anodic and cathodic initiation reaction has been given. The chemical polymerization of acrylamide that has been initiated by HClO₄ is analogous to its anodic polymerization. The polymer yield increases with an increase in concentration of the monomer and HClO₄. Raising the reaction temperature also enhances the polymerization rate. The overall apparent activation energy of the polymerization was determined to be ca. 19 kcal/mole. The copolymerization of acrylamide was carried out with methyl methacrylate (MMA) in a solution of HClO₄ in DMF. The reactivity ratios are r₁ (AA) = 0.25 and r₂ = 2.50. The polymerization with HClO₄ appears to be by a free radical mechanism. When the polymerization of acrylamide is carried out with HClO₄ in H₂O, a crosslinked water-insoluble gel formation takes place.