Effects of chain length dependence of termination rate constant on the kinetics of free-radical polymerization. 1. Evaluation of an analytical expression relating the apparent rate constant of termination to the number-average degree of polymerization

Mahabadi, H. K.

doi:10.1021/ma00148a048

Cited by 85 publications

(90 citation statements)

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“…For STY the situation is largely the same, although admittedly the short-chain behavior is not as well studied experimentally: [6] α S • 0.5 and i c • 50, [15,16,20] , again in accord with expectation, [21] with oligomer diffusion coefficients, [48] and with measurements on methacrylates with more spherical pendant groups; [9,11] and α L • 0.16, [15,16,20,[44][45][46]49] as predicted by theory. [47] While all this amounts to a highly pleasing chapter of scientific work, unfortunately it does not easily lead to prediction of the overall termination rate coefficient, k t , as measured in the present work, because Equation (8) cannot yield a closed expression for k t .…”

Section: Introductionmentioning

confidence: 68%

Termination Rate Coefficients for Radical Homopolymerization of Methyl Methacrylate and Styrene at Low Conversion

Taylor

Berkel

Alghamdi

et al. 2010

Macro Chemistry & Physics

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A comprehensive and systematic study of overall termination rate coefficients, k t , in low-conversion radical (homo)polymerization of methyl methacrylate and styrene is presented. Values of k t were determined by gravimetric analysis of steady-state experiments, employing 2,2'-azoisobutyronitrile as initiator. The values delivered by this simple method were found to be in qualitative and quantitative agreement with those from more modern and sophisticated techniques for measuring k t . Accordingly, correlations for bulk, low-conversion k t as a function of temperature are given for each monomer. The effects of initiator concentration, c I , and temperature on bulk k t were studied in a controlled way for both monomers. Additionally, ethyl benzene was used as solvent in order to investigate rigorously the effect of monomer concentration, c M , on styrene k t . The trends found by these systematic studies were considered in the light of what is known about the chain-length dependence of 2 termination. Styrene's behavior was always found to be qualitatively in accord with expectation, although the variations of k t with c I and c M were not as strong as should be the case. However its activation energy, 15 kJ·mol -1 , is shown to be almost perfectly in agreement with theory. Methyl methacrylate, on the other hand, is recalcitrant in that its overall k t does not make manifest the chain-length dependent termination that has been directly measured by other techniques. Possible reasons for these discrepancies are discussed, as are reasons for the difference in values between k t for the two monomers. On the latter topic it is concluded likely that the chain-length dependence of termination at short chain lengths is primarily responsible for styrene having k t that is higher by a factor of about 3, with there also being a contribution that arises from styrene's slower propagation.

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Section: Introductionmentioning

confidence: 68%

Termination Rate Coefficients for Radical Homopolymerization of Methyl Methacrylate and Styrene at Low Conversion

Taylor

Berkel

Alghamdi

et al. 2010

Macro Chemistry & Physics

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“…In the numerical approach, [17][18][19][20][21][22][23][24] which has become available with the increasing speed of computers, these simplifications are not made and all possible termination events between macroradicals of different sizes are accounted for. Although this approach is physically more correct, one still needs to assume a chain-length-dependent termination model, among them the harmonic mean model, 14 the geometric mean model, [14][15][16]25,26 and the Smoluchowski model 27 with chain-length-dependent diffusion coefficients. 17,20 (In the numerical approach only the latter two have been used, [17][18][19][20][21][22][23][24] sometimes in combination with a chain-length-independent residual termination model.…”

Section: Chain-length Dependence Of Bimolecular Free-radical Terminationmentioning

confidence: 99%

“…36 In the Smoluchowski model 27 chain-length-dependent diffusion coefficients 17,20 were included, according to in which p spin is the probability of reaction upon encounter of two radicals (as a result of spin multiplicity), 37 D i is the diffusion coefficient for macroradicals of chain length i, σ is the capture radius of the reaction, D mon is the diffusion coefficient of a monomer unit, a and b are the parameters that control the degree of chain-length dependence, and X c represents a critical chain length at which the modeling of the diffusion coefficient of a macroradical is changed from a smallchain to a large-chain approach. Finally, the geometric mean model [14][15][16]25,26 was used, according to in which k t 1,1 is the termination rate coefficient for a termination reaction between two primary radicals and R is the parameter that controls the degree of the chainlength dependence. The numerical values used in the simulations can be found in Table 1.…”

Section: Characteristics Of Computer Simulations: Models and Parametersmentioning

confidence: 99%

A Theoretical Description of a Method for Model-Independent Determination of Bimolecular Chain-Length-Dependent Free-Radical-Termination Rate Coefficients

et al. 1997

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. (1997). A theoretical description of a method for model-independent determination of bimolecular chain-length-dependent free-radical-termination rate coefficients. Macromolecules, 30(22), 6743-6753. DOI: 10.1021/ma970288l General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. ABSTRACT: A theoretical description is given of a method for model-independent determination of bimolecular chain-length-dependent free-radical-termination rate coefficients. By on-line determination of the monomer concentration versus time in a time-resolved pulsed laser polymerization, the value of the termination rate coefficient kt i,i of the termination reaction between species of identical chain length can be determined in a very simple fashion. The key assumption in this kt determination is that the radical chain-length distribution that is generated with a laser pulse is extremely narrow, such that all chains can be considered as being identical in chain length. With computer simulations the effects of several processes which could undermine this key assumption were investigated. For the monomer methyl methacrylate (MMA) the effects of (i) a Poisson distribution of the polymerization events, (ii) chain transfer to monomer, and (iii) the presence of a background initiation process were investigated. For MMA, none of these processes interfere with the model-independent determination of the termination rate coefficients, as long as suitable experimental conditions are chosen, which follow from the simulations.

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“…The basis of this theory is the assumption that termination rate constants k t (and the propagation rate constants k p ) are independent of living chain lengths and dead chain concentration. Flory theory has been very successful in predicting kinetics of FRP at high dilution 3 ("low conversion"), although there is convincing experimental evidence [9][10][11][30][31][32] that, even at low conversions k t depends on chain length. We will see below how the predictions of the Flory-Schulz theory are modified 27 when one considers the dependence of k t on chain length at low conversions.…”

Section: Flory-schulz Theory and Beyondmentioning

confidence: 99%

“…1,2 Consequently, intense research efforts have focused in understanding the mechanisms underlying FRP since its early developments in the 1930s. [3][4][5][6][7][8][9][10][11][12][13][14][15][16] Despite this, many fundamental issues in FRP remain poorly understood today. Most notably it remains a subject of controversy as to what mechanisms underlie the "gel effect" 3 of FRP, during which polymerization rates "autoaccelerate" and molecular weights of dead chains being produced are observed to increase by up to an order of magnitude.…”

Section: Introductionmentioning

confidence: 99%

Photocopying Living Chains. 1. Steady-State

et al. 2001

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We present the first ever measurements of living chain molecular weight distributions (MWDs), ψ o (N), in free radical polymerization (FRP), using a new technique, the "photocopy method". Though living chains are the fundamental objects in FRP, their MWDs have eluded measurement until now, principally due to their very short lifetimes (j1 s). In the photocopy method, the living population is converted, essentially instantaneously, to a labeled inert one by "photoinhibitor" molecules activated by a short laser pulse. This floods the FRP with photoinhibitor radicals, which ideally (i) are extremely slow to initiate new living chains yet (ii) couple with existing living chains (and each other) at near diffusion-controlled rates and (iii) carry a fluorescent label. Thus, the living chains are "frozen" and labeled. They are subsequently detected selectively using GPC equipped with a fluorescence detector (a second detector simultaneously detects unlabeled chains). We applied the photocopy method to low conversion methyl methacrylate FRP. Our measured MWDs are exponential as predicted by the classical FlorySchulz theory (which ignores the chain length dependence of the termination rate constant, k t), but only for chains longer than the mean living chain length N h o. For N < N h o, our data are consistent with a stretched exponential as predicted by modern FRP theories accounting for N dependence of kt. However, the small N data may also be accounted for by nonideal effects, initiation of new living chains by photoinhibitors, which lead to power law behavior. Another complication is that thermal initiation persists during the photocopying process in its present form. Thus, post-laser-pulse initiated living chains react with photoinhibitor radicals, distorting the measured MWDs from that of the steady-state living chains. From the measured living and dead MWDs, we infer living and dead chain concentrations and mean lengths and the fraction of living chains terminating via coupling. Finally, using reported values of propagation rate constants, we estimate mean living chain lifetime, polymerization rate, and the average termination rate constant.

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Effects of chain length dependence of termination rate constant on the kinetics of free-radical polymerization. 1. Evaluation of an analytical expression relating the apparent rate constant of termination to the number-average degree of polymerization

Cited by 85 publications

References 3 publications

Termination Rate Coefficients for Radical Homopolymerization of Methyl Methacrylate and Styrene at Low Conversion

Termination Rate Coefficients for Radical Homopolymerization of Methyl Methacrylate and Styrene at Low Conversion

A Theoretical Description of a Method for Model-Independent Determination of Bimolecular Chain-Length-Dependent Free-Radical-Termination Rate Coefficients

Photocopying Living Chains. 1. Steady-State

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