Cross-propagation Rate Constants Research Articles

Design, Synthesis, and Self-Assembly of Polymers with Tailored Graft Distributions.

Grafting density and graft distribution impact the chain dimensions and physical properties of polymers. However, achieving precise control over these structural parameters presents long-standing synthetic challenges. In this report, we introduce a versatile strategy to synthesize polymers with tailored architectures via grafting-through ring-opening metathesis polymerization (ROMP). One-pot copolymerization of an ω-norbornenyl macromonomer and a discrete norbornenyl comonomer (diluent) provides opportunities to control the backbone sequence and therefore the side chain distribution. Toward sequence control, the homopolymerization kinetics of 23 diluents were studied, representing diverse variations in the stereochemistry, anchor groups, and substituents. These modifications tuned the homopolymerization rate constants over 2 orders of magnitude (0.36 M-1 s-1 < khomo < 82 M-1 s-1). Rate trends were identified and elucidated by complementary mechanistic and density functional theory (DFT) studies. Building on this foundation, complex architectures were achieved through copolymerizations of selected diluents with a poly(d,l-lactide) (PLA), polydimethylsiloxane (PDMS), or polystyrene (PS) macromonomer. The cross-propagation rate constants were obtained by nonlinear least-squares fitting of the instantaneous comonomer concentrations according to the Mayo-Lewis terminal model. In-depth kinetic analyses indicate a wide range of accessible macromonomer/diluent reactivity ratios (0.08 < r1/r2 < 20), corresponding to blocky, gradient, or random backbone sequences. We further demonstrated the versatility of this copolymerization approach by synthesizing AB graft diblock polymers with tapered, uniform, and inverse-tapered molecular "shapes." Small-angle X-ray scattering analysis of the self-assembled structures illustrates effects of the graft distribution on the domain spacing and backbone conformation. Collectively, the insights provided herein into the ROMP mechanism, monomer design, and homo- and copolymerization rate trends offer a general strategy for the design and synthesis of graft polymers with arbitrary architectures. Controlled copolymerization therefore expands the parameter space for molecular and materials design.

Control of Grafting Density and Distribution in Graft Polymers by Living Ring-Opening Metathesis Copolymerization.

Control over polymer sequence and architecture is crucial to both understanding structure-property relationships and designing functional materials. In pursuit of these goals, we developed a new synthetic approach that enables facile manipulation of the density and distribution of grafts in polymers via living ring-opening metathesis polymerization (ROMP). Discrete endo,exo-norbornenyl dialkylesters (dimethyl DME, diethyl DEE, di-n-butyl DBE) were strategically designed to copolymerize with a norbornene-functionalized polystyrene (PS), polylactide (PLA), or polydimethylsiloxane (PDMS) macromonomer mediated by the third-generation metathesis catalyst (G3). The small-molecule diesters act as diluents that increase the average distance between grafted side chains, generating polymers with variable grafting density. The grafting density (number of side chains/number of norbornene backbone repeats) could be straightforwardly controlled by the macromonomer/diluent feed ratio. To gain insight into the copolymer sequence and architecture, self-propagation and cross-propagation rate constants were determined according to a terminal copolymerization model. These kinetic analyses suggest that copolymerizing a macromonomer/diluent pair with evenly matched self-propagation rate constants favors randomly distributed side chains. As the disparity between macromonomer and diluent homopolymerization rates increases, the reactivity ratios depart from unity, leading to an increase in gradient tendency. To demonstrate the effectiveness of our method, an array of monodisperse polymers (PLAx-ran-DME1-x)n bearing variable grafting densities (x = 1.0, 0.75, 0.5, 0.25) and total backbone degrees of polymerization (n = 167, 133, 100, 67, 33) were synthesized. The approach disclosed in this work therefore constitutes a powerful strategy for the synthesis of polymers spanning the linear-to-bottlebrush regimes with controlled grafting density and side chain distribution, molecular attributes that dictate micro- and macroscopic properties.

Quantifying the Copolymerization Kinetics of Ethylene and 1-Octene Catalyzed with rac-Et(Ind)2ZrCl2 in a Solution Reactor

We developed a new methodology to estimate the cross-propagation rate constants and their confidence regions for the copolymerization of ethylene and 1-olefins using single site catalysts. We applied the method to a series of ethylene/1-octene copolymers made with rac-Et(Ind)2ZrCl2/MAO in a solution reactor operated in semibatch mode. The method estimates the reactivity ratios using the Mayo–Lewis equation and the cross-propagation rate constants with combination of the Mayo–Lewis equation and a polymerization kinetics model based on monomer uptake curves. More importantly, our strict statistical treatment of the data allows us to estimate the joint confidence regions for these parameters, which is essential to establish the reliability of these estimates.

Can Propagation Reaction in Carbocationic Polymerization and Copolymerization of Styrene be Diffusion Controlled ?

AbstractSummary: The reactivity ratios r1 and r2 in copolymerizations of styrene and parasubstituted styrenes, for which r1 = 1/r2, are in contradiction with diffusion control for their propagation reactions. The cross propagation rate constants k12copol in copolymerization of styrene with p‐chlorostyrene, p‐methylstyrene and p‐methoxystyrene have been shown to increase with their nucleophilicity parameter N. This is also not compatible with diffusion controlled cross propagation and propagation, but agrees with similar rate constants of propagation for these monomers. The capping rate constants k12capp of reactions of poly(p‐methylstyrene)± and poly(p‐methoxystyrene)± with π‐nucleophiles also increase with N, but with a much larger selectivity. This shows that k12copol and k12capp are not identical. The k, from 109 to 6 109 L mol−1 s−1, obtained with p‐chlorostyrene, styrene and p‐methylstyrene by the Diffusion Clock (DC) method are not consistent with those derived from the ionic species concentration (ISC method) for indene, 2,4,6‐trimethylstyrene and p‐methoxystyrene of the order of 104 – 105 L mol−1 s−1, also measured for living polymerization. These last values are in agreement with those measured previously in nonliving systems, and with an approximate compensation between the reactivity of a monomer and that of the corresponding carbocation.

Reactivities of carbocations and monomers in carbocationic polymerization and copolymerization

In carbocationic polymerization and copolymerization, a recent publication concluded that the substituent effect on carbocation reactivity is much larger than its effect on monomer reactivity, and this by a factor 106 in the case of the rate constant k12capp for p-methylstyrene addition (monomer M2) on, respectively, poly(p-methoxystyrene)± or poly(p-methylstyrene)± (M). This conclusion is disputed, as well as the assumption that the rate constants of capping (k12capp) obtained in deactivation reactions of poly(p-methoxystyrene)± are identical with cross propagation rate constants in copolymerization (k12copol). It is shown that the large calculated k12capp are based on propagation constant values for p-methylstyrene (k ≈ 109) obtained by the diffusion-clock method. They are 104 times smaller as found for all styrenes, that is, between 104 and 105 when they are based on the ionic species concentrations. In such a case, the available data are still in agreement with an approximate compensation between the reactivities of a monomer and of the corresponding carbocation. It is also shown that copolymerization data for styrenes are not compatible with k values near to diffusion control, and that variations of log k12capp and log k12copol with the nucleophilicity parameter N of the monomers indicate a much lower selectivity of the monomers in the case of copolymerization. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 2666–2680, 2010

On the determination of the ratios of the propagation rate constants on the basis of the MWD of copolymer chains: A new Monte Carlo algorithm

AbstractPossibility of determination of the relations among homo- and crosspropagation rate constants on the basis of analysis of the detailed distribution of copolymer chain lengths is presented. Importance of application of correct computation algorithms in Monte Carlo modelling of copolymerization is indicated. A new algorithm for Monte Carlo modelling of polymerization processes is proposed.

Evident solvent effect on propagation reactions during radical copolymerization of maleimide and alkene

The radical copolymerization of N-(2,6-dimethylphenyl)maleimide (DMPhMI) and 2,4,4-trimethylpentene (TP) was investigated in several solvents at 60°C. The copolymerization rate and the molecular weight of the resulting copolymers were dependent on the kind of solvent used. It was also revealed that the monomer reactivity ratios depended on the solvent; r 1 = 0.086 and r 2 = 0 in chloroform and r 1 = 0.25 and r 2 = 0 in benzene, where DMPhMI and TP are M 1 and M 2 , respectively. The propagation rate constants were determined for the homopolymerization and copolymerization in chloroform and benzene using electron spin resonance spectroscopy. The homo- and crosspropagation rate constants (k 11 and k 12 , respectively) were revealed to depend on the solvent: k 11 is 20 and 37 L/mol.s and k 12 is 230 and 150 L/mol.s in chloroform and in benzene, respectively. The interaction between the maleimide moiety and the solvent molecules was discussed based on the acceptivity of the solvents.

Effect of N-substituents on polymerization reactivity of N-alkylitaconimides in radical polymerization

Radical polymerization and copolymerization of N-alkyl-substituted itaconimides were kinetically investigated in benzene at 60 °C. The rate constants of propagation and termination were determined using the ESR method during the homopolymerization. The cross-propagation rate constants were also evaluated from monomer reactivity ratios during the copolymerization with styrene or methyl methacrylate. The effects of the N-substituents on the polymerization rates, propagation rate constants, cross-propagation rate constants, and termination rate constants were discussed. The polymerization reactivity of the itaconimides was compared with those of other related monomers that had been previously reported, i.e. dialkyl itaconates, dialkyl fumarates, N-substituted maleimides, and alkyl methacrylates.

Radical Polymerization Behavior of N-Acryloyl-2,2-dimethyl-5(R)-phenyl-1,3-oxazolidine

The radical polymerization of N-acryloyl-2,2-dimethyl-5(R)-phenyl-1,3-oxazolidine (ADPO) was investigated kinetically and by means of ESR spectroscopy. The polymerization of ADPO was carried out in benzene with dimethyl 2,2'-azobis(isobutyrate) (MAIB) as an initiator in the temperature range of 50-70°C. From the Arrhenius plot of the initial polymerization rate (R p ), the overall activation energy of the polymerization was calculated to be 82 kJ mol -l . R p at 60 °C was expressed by R p = k[MAIB] 0.5 [ADPO] I .°. Thus the polymerization of ADPO was found to show the usual kinetic behavior. An ESR spectrum was observed in the actual polymerization, which was ascribed to the propagating poly(ADPO) radical. Using the spectrum, the concentration of the propagating polymer radical was determined and the rate constants of propagation (k p ) and termination (k t ) of ADPO were estimated at 50, 60, and 70 °C. From the Arrhenius plots of k p and k t , the activation energies of propagation and termination were estimated. Furthermore the copolymerization of ADPO (M1) with styrene (M 2 ) was also examined at 60 °C, and the following copolymerization parameters were obtained using a curve-fitting method ; r 1 = 0.22, r 2 = 0.76 (SD = 0.01), Q 1 = 0.45, e 1 = +0.53. The rate constants of cross-propagations of copolymerization were also estimated.

Synthesis and radical polymerization of α‐ethyl β‐hexafluoroisopropyl itaconate

AbstractThe synthesis of α‐ethyl β‐hexafluoroisopropyl itaconate (EFiPI) was performed. The polymerization of EFiPI initiated with dimethyl 2,2′‐azobisisobutyrate (MAIB) was investigated kinetically in benzene. The polymerization rate (Rp) was expressed by Rp = k[MAIB]0.5[EFiPI]2.0 at 50°C. The overall activation energy of the polymerization was calculated to be a low value of 57.38 kJ/mol. Rate constants of propagation (kp) and termination (kt) were estimated under different polymerization conditions, using the ESR‐determined concentrations of the propagating polymer radical. The increase in kp value (3.3‐6.0 L/mol s) and the decrease in kt value (0.94‐3.7 × 105 L/mol s) with monomer concentration are mainly responsible for the high dependence of Rp on the monomer concentration. Activation energies of initiation (Ei), propagation (Ep), and termination (Et) were also determined: Ei = 130.7 kJ/mol, Ep = 18.0 kJ/mol, Et = 57.4 kJ/mol. The large apparent activation energy of termination is a main origin of low overall activation energy of the polymerization. Thermal behavior of the resulting poly(EFiPI) was investigated by differential scanning calorimetry (DSC) and dynamic thermogravimetry (TG). Copolymerization of EFiPI (M1) with St (M2) was also examined at 50°C in benzene. The following copolymerization parameters were obtained according to the curve‐fitting method: r1 = 0.05, r2 = 0.46, Q = 0.46, e = +1.14. Using these results, the rate constants of cross propagations in the copolymerization were estimated. © 1995 John Wiley &amp; Sons, Inc.

Kinetic and ESR studies on radical polymerization. Radical polymerization of diisopropyl itaconate

The polymerization of diisopropyl itaconate (DIPI) initiated with dimethyl 2,2′-azobisisobutyrate(MAIB) was investigated kinetically in benzene. The polymerization rate ( R p) was expressed by R p = k[MAIB] 0.46[DIPI] 1.6 at 50°. The overall activation energy of the polymerization was calculated to be a low value of 60.2 kJ/mol. Rate constants of propagation ( k p) and termination ( k 1) were estimated different polymerization conditions, using the ESR-determined concentrations of the propagating polymer radical. The k p value (2.4–2.9 1/mol · sec) at 50° shows a little increase with monomer concentration. The k 1 value (1.8–4.9 × 10 4 1/mol · sec) was fairly dependent on the chain-length of the propagating polymer radical, which is mainly responsible for the high dependence of R p on the monomer concentration. Activation energies of initiation ( E i), propagation ( E p) and termination ( E t) were also determined; E i = 129.1 kJ/mol, E p = 28.5 kJ/mol, E t, = 66.1 kJ/mol. The large apparent activation energy of termination is a main origin of the low overall activation energy of the polymerization. Copolymerization of DIPI ( M 1) with St ( M 2) was also examined at 50° in benzene. The following copolymerization parameters were obtained according to the Kelen-Tüdős method; r 1 = 0.11, r 2 = 0.56, Q = 0.47, e = + 0.87. Using the above results, the rate constants of cross-propagations in the copolymerization were estimated.

Kinetic Studies on the Radical Polymerization of Butadiene Derivatives

A kinetic study on the radical polymerization of diene compounds was carried out at 25±0.001°C. The diene compounds were ethyl pentadienoate and its derivatives CH2=CX–CH=CHCOOCH2CH3 (EP:X=H, EMP:X=CH3, and EEP:X=OCH3) and 1-acetoxybutadiene (AB). Elementary rate constants of these diene compounds were determined by the rotating sector method; the values of kp and kt for EP, EMP, EEP, and AB were 30.9 and 1.9×107, 29.7 and 2.3×107, 9.9 and 0.93×107, and 18.0 and 28.1×107 M−1 s−1, respectively. These kp values are lower than those reported for styrene, MMA, methyl acrylate, and vinyl acetate. Cross-propagation rate constants (k12 and k21) were estimated from the kp values and monomer reactivity ratios in the copolymerizations of these dienes (M2) with styrene (M1). Reactivity of the monomers and the propagating radicals was compared with vinyl compounds and other dienes by using k12 and k21, respectively. Lower kp values of these dienes are primarily ascribed to the fact that the decrease in the reactivity of the propagating radical is larger than the increase in that of monomer. Change in radical reactivity among dienes is larger than that in their monomer reactivity. Effects of the resonance stabilization of the propagating radicals on kt were not clearly evident in these radical polymerizations which are discussed on the basis of the preexponential factor.

Determination of Absolute Rate Constants for Radical Polymerization and Copolymerization of Ethyl α-Chloroacrylate: Effects of Substituents on Reaction Rates of Monomer and Polymer Radical

Abstract The propagation and termination rate constants (kp and kt) for the radical polymerization of ethyl a-chloroacrylate (ECA) were determined by the rotating sector method kp = 1660 and kt = 3.33 × 108 L/mol•s at 30° C. The absolute rate constants for cross-propagations in copolymerization were evaluated from the kp determined for ECA or those for common monomers and the monomer reactivity ratios. The reactivities of ECA and poly-(ECA) radicals estimated as the rate constants of cross-propagations were accounted for by using equations relating these rate constants to the polar and resonance effects of the substituents. ECA was highly reactive toward various polymer radicals as expected from the resonance effects of the carbethoxy and chloro substituents. The poly(ECA) radical was found to be more reactive than common polymer radicals. The reactivity of a polymer radical in cross-propagation seemed to increase with increasing electron-accepting power by facilitating electron transfer from a monomer required for the new C-C bond formation.

Kinetic Features and Mechanism of Alternating Copolymerization of lndene with Maleic Anhydride

Abstract The radical copolymerization of indene (IN) with maleic anhydride (MA) was investigated. The charge-transfer complexes (CT complexes) between comonomers were studied by means of spectrophotometric measurements. It was found that the maximum copolymerization rate occurred at a comonomer feed ratio that did not correspond to the composition of the CT complex and the composition of copolymer. It was shown that rate maximum was displaced towards an excess of IN in the solvents with strong donicity. The Acceptor Number of solvent influences neither the initial rate nor the position of the rate maximum. Some kinetic calculations were made to assess values of the cross-propagation rate constants and to elucidate the mechanism of propagation of macromolecular chains.

Determination of the cross propagation rate constants in the autoxidation of hydrocarbons by the electron spin resonance technique

Determination of the cross propagation rate constants in the autoxidation of hydrocarbons by the electron spin resonance technique

ChemInform Abstract: ON THE ACCURACY OF THE HYDROPEROXIDE METHOD OF DETERMINING ABSOLUTE RATE CONSTANTS FOR HYDROGEN ATOM ABSTRACTION BY THE TERT.‐BUTYLPEROXY RADICAL

Measurements of rates of oxygen absorption and steady-state peroxy radical concentrations for the autoxidation of tetralin in the presence of tert-butyl hydroperoxide have shown that the rate constant for reaction of the tert-butylperoxy radical with tetralin at 60°C is approximately 11.0 M−1s−1. This rate constant is about a factor of 4 larger than the value recently reported by Niki, Okayasu, and Kamiya for this reaction. The present work emphasizes that great care should be taken when the hydroperoxide method is used to estimate cross-propagation rate constants for a substrate as reactive as tetralin at a temperature as high as 60°C.