Chain-Length-Dependent Termination of Styrene Bulk

Article pubs.acs.org/Macromolecules

Chain-Length-Dependent Termination of Styrene Bulk Homopolymerization Studied by SP−PLP−EPR Hendrik Kattner and Michael Buback* Institut für Physikalische Chemie, Georg-August-Universität Göttingen, Tammannstr. 6, D-37077 Göttingen, Germany S Supporting Information *

ABSTRACT: Single-pulse pulsed-laser polymerization in conjunction with time-resolved quantitative EPR detection of radicals, SP−PLP−EPR, has been carried out in the early period of styrene polymerizations between 73 and 135 °C using dicumyl peroxide as the photoinitiator. To enhance signal-to-noise quality, in addition to styrene-H8, the fully deuterated monomer, Sty-d8, has been investigated. The chain-length dependence of the rate coefficient for termination of two radicals of chain length i, ki,it , is adequately represented by the composite model. The power-law exponents for short-chain and long-chain radicals are obtained as αs = 0.51 ± 0.05 and αl = 0.16 ± 0.05, respectively, with the two ranges being separated by the crossover chain length, ic = 30 ± 10. The termination rate coefficient for two radicals of chain length unity, k1,1 t , scales with temperature as does monomer fluidity. From ki,it deduced via SP−PLP−EPR, chain-length-averaged termination rate coefficients, ⟨kt⟩, have been estimated, which are close to the reported experimental values.

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INTRODUCTION Actual work into radical polymerization (RP) mostly addresses reversible-deactivation radical polymerization (RDRP). Studies into the individual steps of conventional RP however continue to be of significant interest, as the wide majority of industrial RPs are carried out by conventional RP, which require kinetic simulation to model technical processes and to identify optimum reaction conditions. Moreover, conventional RP kinetics constitutes a core part also of RDRP. With the advent of pulsed-laser techniques, the accuracy and reliability by which RP rate coefficients may be determined have enormously improved. This is particularly true for propagation rate coefficients, kp, which are nowadays determined by the IUPAC-recommended pulsed-laser polymerization−size-exclusion chromatography (PLP−SEC) technique.1 Simulation of RP however requires further accurately known rate coefficients, e.g., the one for termination, kt. For the special situation of RDRP, termination rate coefficients as a function of chain length i, ki,it , should be available because the distribution of radicals is narrow throughout an RDRP, with the length i steadily increasing during polymerization to higher degrees of monomer conversion. The past decade has seen an enormous progress in studying termination kinetics,2−9 as detailed in the excellent review provided by Barner-Kowollik and Russell.4 These authors emphasize a couple of methods, such as SP−PLP−NIR, SP−PLP−MMD, RAFT−CLD−T, and SP−PLP−RAFT, which are of proven suitability for measuring chain-lengthdependent termination (CLDT). SP stands for a laser single pulse and RAFT for reversible addition−fragmentation (chain) transfer. The review further addresses steady-state and © XXXX American Chemical Society

pseudostationary polymerization experiments. It is beyond the scope of the present paper to reiterate the pros and cons of these techniques for CLDT analysis as detailed in ref 4. The disadvantages of the above-mentioned methods are partly due to the need for making simplifying assumptions. Moreover, the information about CLDT is indirect in that monomer conversion or polymer molecular mass distribution (MMD) are measured. The SP−PLP−EPR method developed in our laboratory directly probes radical concentration as a function of time via electron paramagnetic resonance (EPR) spectroscopy, thereby enabling CLDT measurements in unprecedented detail.10−18 Pulsed-laser polymerization is induced by a single pulse which almost instantaneously decomposes a photoinitiator. The subsequent time evolution of radical concentration is monitored via highly time-resolved EPR spectroscopy. With both the type and the concentration of radicals being accessible, the SP−PLP−EPR experiment may, in addition, provide backbiting rate coefficients, which refer to the 1,5-hydrogen shift reaction of chain-end radicals to yield midchain radicals.19−22 Moreover, the addition rate coefficient of monomer to midchain radicals may be deduced from SP−PLP−EPR.11,23,24 The technique has also been successfully used for resolving kinetic issues in reversible addition− fragmentation (RAFT)25,26 or atom transfer radical polymerization (ATRP).27 The success of using SP−PLP−EPR results from the almost instantaneous production of an intense burst of Received: November 14, 2014 Revised: December 19, 2014

A

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Because of the rapid consumption of radicals, high signal-tonoise quality of the EPR analysis is of key importance. Thus, the favorable effect already used in our preceding study into vinyl acetate18 has been applied, and the fully deuterated monomer, Sty-d8, has been subjected to EPR analysis, which allows to reach radical chain lengths beyond ic under acceptable conditions for quantitative EPR analysis. We selected dicumyl peroxide as the photoinitiator,34,35 the fragments of which rapidly add to electron-rich double bonds. Our study aims at measuring chain-length-dependent termination rate coefficients of styrene bulk homopolymerization up to 9% monomer conversion. The resulting ki,it values will be compared with chain-averaged ⟨kt⟩ from stationary styrene polymerization.

radicals in conjunction with the high sensitivity of quantitative time-resolved detection of the fate of these radicals. Absolute radical concentrations as a function of time are determined from EPR intensities measured at a characteristic magnetic field position after calibration of the EPR setup with stable radicals, as detailed in ref 11. Suitable selection of the photoinitiator ensures fast addition of monomer to the primary radical species, which results in a close-to-monodisperse size distribution of growing radicals during polymerization. Unless chain transfer comes into play, radical chain length increases linearly with time t after laser pulsing, according to eqs 1 and 2, respectively, with cM being monomer concentration. i = k pc Mt

■

(1)

i = k pc Mt + 1

(2)

Equation 1 fails for t → 0, i.e., in the very early time t period, and has to be replaced for analysis into the short chain length region by eq 2.28 At low degrees of monomer-to-polymer conversion, the chain-length dependence for termination of two radicals of identical chain length, ki,it , has been found to be well represented by the so-called composite model (eq 3), introduced by Smith et al.3,28 k ti , i = k t1,1i−αs k ti , i

=

k t1,1ic −αs + α1i−α1

i ≤ ic =

k t0i−α1

i > ic

EXPERIMENTAL PART

The EPR measurements were performed on a Bruker EPR CW/ transient spectrometer system Elexsys-II 500T equipped with an ER 41122SHQE-LC cavity (Bruker) and synchronized with a XeF laser (LPX 210 iCC, Lambda Physik) by a Quantum Composers 9314 pulse generator (Scientific Instruments). Typical EPR parameters for styrene were a 3 G modulation amplitude with a modulation frequency of 100 kHz, a receiver gain of 60, and an attenuation of 26 dB. In the range under investigation, from 73 to 135 °C, temperature was controlled by an ER 4131VT unit (Bruker). Stationary photopolymerizations were carried out using a mercury-arc lamp (LAX 1450/SH2/5, 500 W, Müller). Further experimental details are given elsewhere.11,18 Nondeuterated (Sty-H8, ≥99%, p.a., Aldrich) and fully deuterated styrene (Sty-d8, 99.5 atom % D, over molecular sieve 3 Å, ABCR) were purified by passing through a column filled with aluminum oxide (Brockmann Number 1, grade 507-C-I, neutral). Dicumyl peroxide (DCP, 98%, Aldrich) was used as received and added to the degassed monomer in a glovebox under an argon atmosphere. Initial DCP concentration was selected to be 9.0 × 10−2 mol L−1. Samples of 0.35 mL volume were filled into EPR quartz tubes (Wilmad) of 3 mm o.d. and 2 mm i.d., sealed with Parafilm, and used immediately after preparation under the exclusion of light. A density meter DPR 2000 (Anton Paar) and a viscosity meter AMVn (Anton Paar, 1569) were used to measure bulk density and viscosity, respectively, of Sty-H8/ DCP mixtures as the ones subjected to PLP.

(3)

The highest kt value is associated with termination of two radicals of chain length unity, k1,1 t . Toward increasing time t and thus chain length, ki,it initially decreases according to the powerlaw exponent αs. Above the crossover chain length, ic, ki,it decreases to a weaker extent, with the power-law exponent αl. Below ic, termination is assumed to occur under center-of-mass diffusion control. Above ic, termination is assigned to segmental diffusion of two larger entangled chains. Depending on the shape of the macroradicals, e.g., random coil vs rodlike coil, αs values are expected to be in the range 0.5−1.0,14,23,29,30 whereas theory predicts αl = 0.16 for two long macroradical coils with radical functionality at the chain end.24,31,32 It appears to be a matter of priority to accurately determine ki,it for styrene, which is the archetype monomer. In view of the importance of styrene radical polymerization, the knowledge about the termination kinetics of this monomer is scarce. The Russell group33 has provided the most recent report on styrene termination, in which the existing literature has been reviewed. When applied to styrene, even the SP−PLP−EPR technique runs into problems, which are associated with the unfavorable combination of low propagation and high termination rate. Under such conditions, studies into CLDT become difficult, as the laser-pulse-induced radical concentration decays to a low level before larger chain lengths have been reached. At 25 °C, the propagation rate coefficient of styrene is below kp of methyl acrylate, vinyl acetate, and methyl methacrylate by a factor of 154, 40, and 3.8, respectively. In order to reach a reasonable chain size within the short time window of 0.01 s, which has to be selected for time-resolved EPR detection of the rapidly terminating radicals, SP−PLP−EPR experiments on bulk styrene have been carried at temperatures up to 135 °C, where a maximum chain length of imax ≈ 236 may be reached within 0.01 s. Measurements at further enhanced temperature run into difficulties because of significant styrene self-initiation.

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RESULTS AND DISCUSSION In contrast to chain-end radicals of vinylic monomers, such as acrylates,19,22 vinyl esters,18,36−38 and itaconates,17 styryl-H8 radicals exhibit a relatively complicated hyperfine coupling pattern due to the delocalization of radical functionality over the aromatic ring (Figure 1). The measured spectrum is in close agreement with literature and is adequately fitted via the hyperfine coupling constants listed in Table 1.39,40 The quality of the single-pulsed measurements is impaired, as overall EPR intensity is spread over a multitude of peaks with Sty-H8. Therefore, fully deuterated styrene, Sty-d8, has been studied, where the EPR intensity of the styryl radical is more or less condensed into a singlet band (Figure 1). The reason behind this simplification is the lower, by a factor of 0.154, gyromagnetic ratio, γ, of deuterium compared to hydrogen.18,41 With respect to termination kinetics, Sty-d8 is expected to behave as does Sty-H8 because the impact of deuteration on diffusion-controlled termination should be negligible.42 Although no clear dynamic isotope effect has been observed for MMA and VAc bulk homopolymerizations,13,18 the assumption of a negligible isotope effect on termination will be experimentally verified for styrene (see below). Single-pulse measurements were performed at the magnetic field positions indicated by the arrows in Figure 1. To enhance the signal-to-noise ratio of the radical concentration vs time B

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are of smaller size within the identical time interval because of lower kp. The EPR signal intensity is converted into absolute radical concentration, cR, by calibration with TEMPO, according to the procedure detailed elsewhere.11 The composite-model parameters ic and αl were deduced from the linear log(c0R/cR − 1) vs log t correlation according to eq 4, where c0R refers to the initial radical concentration at t = 0. The time required for a single propagation step to occur is referred to as tp = (kpcM)−1. Equation 4 is derived on the basis of assuming i to be given by i = kpcMt. The regimes of short-chain and long-chain radicals, associated with short and long times after applying the laser pulse, exhibit different slopes: (1 − αs) and (1 − αl), respectively, with αs > αl (Figure 4). The transition between the two regimes occurs at the crossover chain length ic.

Figure 1. EPR spectra of Sty-H8 and of Sty-d8 at 85 °C with DCP (9.0 × 10−2 mol L−1) acting as the photoinitiator under continuous irradiation with a mercury-arc lamp. The fitting (gray line) of the StyH8 spectrum was achieved under the assumption of a delocalized unpaired electron. Radical concentration was close to 3 × 10−7 mol L−1 in both cases. The magnetic field positions used within the timeresolved SP−PLP−EPR experiments are indicated by the arrows (↑).

2k t1,1c R0 t pαs 1 − α c R0 −1= t s 1 ≪ i ≤ ic c R (t ) 1 − αs 2k t0c R0 t pαl 1 − α c R0 −1= t l 1 − αl c R (t )

Table 1. Hyperfine Coupling Constants a for Sty-H8 Radicals in Styrene Bulk Homopolymerization As Obtained from Fitting of the Experimental Spectra, e.g., of the One in Figure 1 no. and position of nuclei

a/G

no. and position of nuclei

a/G

1Hα 2Hβ 2Hortho

17.6 16.3 5.2

2Hmeta 1Hpara

1.7 5.3

i ≫ ic

(4)

No absolute radical concentrations and thus no calibration are required for this double-log analysis, as c0R/cR, which is given by the ratio of the associated EPR intensities. Bulk monomer concentration, cM, and kp at the experimental temperature are available from the literature.1,33,43,44 Because of the enhanced signal-to-noise ratio (Figure 3), ic has exclusively been deduced from Sty-d8 experiments.

traces, about 10 individual traces were coadded. Monomer-topolymer conversion was checked gravimetrically to ensure that polymerization occurs in the initial range up to 9% monomer conversion. The radical concentration vs time traces at the lowest and highest experimental temperature are close to each other (Figure 2). This surprising result is due to some compensation of the effect of temperature on kp and kt: The decay of radical concentration by termination is reduced toward lower temperature but is enhanced as the terminating radicals

Figure 3. Relative radical concentration vs time traces for Sty-H8 (gray line) and Sty-d8 (black line) at 100 °C with DCP (9.0 × 10−2 mol L−1) acting as the photoinitiator. Both traces have been deduced from coadding the same number of (19) pulses. Initial radical concentration was close to 3.5 × 10−4 mol L−1 in both cases.

According to Clouet and Chaffanjon,45 the propagation rate coefficient of fully deuterated styrene is by a factor of 1.2 above kp(Sty-H8). The bulk density of Sty-d8 at 100 °C is by 7% above the one of Sty-H8. Both effects were included into our analysis. The resulting impact on the composite-model parameters of styrene is however small and occurs within the limits of experimental accuracy, as is indicated by the close agreement of the relative radical concentration vs time profiles in Figure 3. The intercept of the two straight lines may be identified at ic(Sty-d8) = 30 ± 10 for 120 and 135 °C. This value slightly exceeds ic ≈ 18 reported by Johnston-Hall and Monteiro29 but is in perfect agreement with the value of ic ≈ 30 subsequently published by the same authors.30 These two literature values

Figure 2. Normalized EPR intensity vs time traces measured for nondeuterated styrene, Sty-H8, at the lowest (gray line) and the highest temperature of the present study (black line) with DCP (9.0 × 10−2 mol L−1) being used as the photoinitiator. About 10 individual traces were coadded to enhance the SP−PLP−EPR signal-to-noise ratio. EPR intensity vs time traces were recorded at the magnetic field position indicated in Figure 1. The initial radical concentrations were close to 6.7 × 10−6 mol L−1 in both cases. C

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concentration needs not to be known for this determination of αs.

were determined by the RAFT-CLDT-technique. The crossover chain length of styrene is significantly below the ones of methyl methacrylate, ic(MMA) = 100,23 and vinyl pivalate, ic(VPi) = 110 ± 30,18 but is close to the numbers for vinyl acetate,18 ic(VAc) = 20 ± 10, and methyl acrylate,14 ic(MA) = 35 ± 10, and is not too far off the number for butyl acrylate,14 ic(BA) = 65 ± 20. No detailed understanding of the dependence of crossover chain length on monomer structure has emerged so far. Chain flexibility obviously plays a role, as higher flexibility favors the entanglement of two macroradical chains, which is considered to be the rate-determining step for termination of longer radicals. Interestingly, the size of the alkyl side chain has an opposite effect on ic in the acrylate and methacrylate families. Toward larger size of the alkyl side chain, the crossover chain length increases for acrylates14 and vinyl esters 18 but decreases (from a higher i c level) for methacrylates.13,46 A tentative explanation of this finding may be that long alkyl side chains solubilize the stiffer methacrylate backbone structure and thus lower ic, whereas they reduce the mobility of the flexible acrylate structure and thus enhance ic. Unless a mechanistic understanding and thus a prediction of ic has been reached, ic needs to be experimentally determined.13,14,16,19 The power-law exponent associated with the straight-line fit (Figure 4) for long-chain radicals, αl = 0.16 ± 0.05, is in perfect

2k t1,1c R0 ((k pc Mt + 1)1 − αs − 1) c R0 −1= c R (t ) k pc M(1 − αs)

1 ≤ i < ic (5)

Shown in Figure 5 are the results of the least-squares fitting of the time-resolved EPR traces for Sty-d8 at 85 °C. The

Figure 5. Least-squares fitting of SP−PLP−EPR data to deduce αs and 0 k1,1 t cR for Sty-d8 homopolymerization at 85 °C. The solid line represents the best fit according to eq 5 with αs = 0.47 and k1,1 t = 9.0 × 108 L mol−1 s−1. The dashed lines, which were estimated for identical k1,1 t , may be considered as lower and upper bounds for αs.

analysis was restricted to EPR data taken at chain lengths below ic. Neither for Sty-H8 nor for Sty-d8 does individual αs exhibit any systematic variation with temperature. Moreover, the arithmetic mean values αs = 0.53 ± 0.05 for Sty-H8 and αs = 0.49 ± 0.05 for Sty-d8 agree within the limits of experimental accuracy. The mean value of αs = 0.51 ± 0.05, represented by the dashed line in Figure 6, is deduced as the temperatureindependent power-law exponent for termination of shortchain radicals, i < ic, in styrene homopolymerization. The αs value is not affected by deuteration, as demonstrated in Figure 6 by the αs values obtained via least-squares fitting to eq 5 of the SP−PLP−EPR data measured on both Sty-H8 and Sty-d8. The insensitivity of αs toward both deuteration and temperature has also been found for MMA and VAc.13,18 Figure 6 is not indicative of any need for using deuterated styrene, however, as Figure 3 tells, deuteration is required to reach high signal-to-noise quality at large t, which corresponds to long radical chain lengths. The αs value for styrene is in close agreement with the number from RAFT−CLDT investigations, αs = 0.53,29 and agrees with the power-law exponent measured for the chain-length dependency of the styrene self-diffusion coefficient Di, αD = 0.51 ± 0.13.48 The power-law exponent for short-chain styryl radicals is below the associated numbers for MMA, αs = 0.65,13 for VPi, αs = 0.67,18 and for MA, αs = 0.8014 but agrees within experimental accuracy with the αs values reported for VAc, αs = 0.57,18 and for dibutyl itaconate, αs = 0.50.17 This finding is consistent with the statement in the Barner-Kowollik and Russell review,4 in which styrene is listed among the monomers with lowest αs.

Figure 4. Double-log plot of the SP−PLP−EPR data measured for Sty-d8 at 120 °C according to eq 2. Analysis of the long-chain regime at high t yields αl. ic is obtained from the intersection of the straight lines fitted to the data at low and high radical chain length (or time elapsed after laser pulsing).

agreement with the experimental values reported for other monomers29,30 and with the exponent which theory predicts for termination of two long chain-end radicals.24,31,32,47 The insensitivity of ic and αl toward temperature, which is evidenced by our experiments, has also been found for other monomers.13,18,46 The correlation i = kpcMt, underlying eq 2, is not valid in the very early time period after applying the laser pulse. As an adequate expression for the region t → 0, Smith and Russell28 introduced i = kpcMt + 1 which, after integration, results in eq 5. Least-squares fitting of the EPR data taken at t < t(ic) to eq 5 0 yields αs together with the product k1,1 t cR. As the initial radical 0 concentration, cR, is known from calibration, k1,1 is directly t 0 accessible from k1,1 t cR. It should be noted that absolute radical D

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Figure 7. Arrhenius-type plot of the rate coefficient for termination of two monomeric radicals, k1,1 t , for Sty-H8 and Sty-d8 homopolymerizations at low degrees of monomer conversion. The dashed line represents the diffusion limit of k1,1 t for styrene as estimated from eqs 6 and 7 via the separately measured value of EA(η−1) = 10.4 ± 0.1 kJ mol−1.

Figure 6. Individual values (symbols) deduced for the short-chain exponent, αs, by least-squares fitting according to eq 5 for Sty-H8 and Sty-d8 at polymerization temperatures from 73 to 135 °C. The symbol X indicates that two data points are sitting exactly on top of each other.

as used in the SP−LP−EPR experiments (see Supporting Information). As is illustrated by the upper four entries in Table 2, almost the same value of k1,1 t η is obtained for styrene, vinyl acetate, and for the “first” (methyl ester) members of the acrylate and methacrylate families. The data refer to 80 °C and thus include some extrapolation, as the SP-PLP-EPR measurements have not been carried out at a common temperature. The close agreement of the four entries suggests that, with these small radicals, most of the diffusional encounters result in reaction. As the activation energies of k1,1 t and of fluidity are close to each other, the product k1,1 η should not be sensitive toward t temperature. Toward larger size and thus larger unreactive surface of the radicals, k1,1 t η should decrease due to an enhancement of both hydrodynamic radius and shielding of the radical site. This is indeed what the entries 5 and 6 in Table 2 suggest. It is interesting to note that the replacement of a methyl group by a tert-butyl moiety, i.e., passing from vinyl acetate to vinyl pivalate (VPi) and from MMA to tert-butyl methacrylate (tert-BMA), results in almost the same decrease in k1,1 t η. It comes as no surprise that further strong shielding as in the case of dibutyl itaconate gives rise to an even more pronounced reduction of k1,1 t η. This can be seen from entry 7 in Table 2. The relevance of taking chain-length-dependent termination into account may be illustrated by a comparison of SP−PLP−EPR results with data from both chemically initiated polymerization and from SP−PLP experiments carried out in conjunction with the time-resolved measurement of monomer consumption by near-infrared spectroscopy (SP−PLP−NIR). Chain length averaged kt values, ⟨kt⟩, from SP−PLP−NIR yield ⟨kt⟩(Sty)/⟨kt⟩(MMA) = 2.0 for 90 °C and ambient pressure, assuming an activation volume of 14.5 cm3 mol−1 for both monomers.1,49,50 In contrast, the SP−PLP−EPR measurements 1,1 result in k1,1 t (Sty)/kt (MMA) = 0.7. This seeming contradiction may be resolved by considering the average chain length associated with the SP−PLP−NIR data for the two monomers, deduced from the same time interval (0.15 s) after laser pulsing. Within 0.15 s,1,49 chain growth at 90 °C occurs up to a maximum chain length of imax(Sty) = 1092 and of imax (MMA) = 2120. Based on estimated average chain lengths of ⟨i⟩(Sty) = 500 and ⟨i⟩(MMA) = 1000 and on the composite-model parameters

Assuming termination of short chains (i < ic) to be dominated by center-of-mass diffusion, the rate coefficient for termination of two radicals both of chain length unity, k1,1 t , may be correlated via the Smoluchowski expression (eq 6) to the capture radius, Rc, of the macroradical, the spin factor, Pspin, and to the self-diffusion coefficient of the monomeric radical, D1, with NA being Avogadro’s constant. k t1,1 = 4πPspinNA(DA1 + DB1)R c

(6)

1

With D obeying the Stokes−Einstein equation (eq 7) and ri 1,1 being the hydrodynamic radius, k1,1 t scales with fluidity, kt (T) −1 ∝ η(T) . The activation energy for termination of two monomeric radicals, EA(k1,1 t ), should thus be essentially given by the activation energy of fluidity, EA(η−1). Di =

kBT 6πriη

(7)

Molecular mobility is reduced by deuteration, as the associated increase in viscosity results in a lower diffusion coefficient. Holz et al.42 showed that this dynamic isotope effect is small for molecules of relatively high molar mass, such as benzene and dimethylformamide. From the molar mass ratio of M(Sty-H8)/M(Sty-d8), the lowering of k1,1 t is estimated to be below 6%, i.e., occurs within the limits of accuracy of our k1,1 t measurement. The results of corresponding estimates for fully deuterated and nondeuterated VAc and VPi are in line with the results from the associated SP−PLP−EPR experiments.18 From 1,1 the experimental k1,1 t (Sty-d8) and kt (Sty-H8) values, which are in close agreement (Figure 7), the following Arrhenius relation is obtained: ln(k t1,1(Sty)/L mol−1 s−1) = 23.7 − 1117/(T /K)

Depending on temperature, experimental k1,1 t is between 20% and 50% below the diffusion-limited value estimated from eq 6 upon assuming Rc = 2r1, PSpin = 0.25, and the Stokes−Einstein equation (eq 7) to hold for D1. The activation energy, EA(k1,1 t ) = 9 ± 1 kJ mol−1, is close to EA(η−1) = 10.4 ± 0.1 kJ mol−1, which value has been determined from independent viscosity measurements on styrene containing DCP of the concentration E

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Macromolecules a Table 2. Comparison of k1,1 t η for Bulk Polymerizations of Several Monomers −1 −1 k1,1 s ) × 109 t (80 °C) (L mol

1 2 3 4 5 6 7

VAc MMA MA Sty VPi tert-BMA DBI

(1.5 (1.1 (1.2 (0.83 (0.41 (0.3 (0.09

± ± ± ± ± ± ±

0.3) 0.3) 0.3)b 0.05) 0.05) 0.1) 0.01)d

η(80 °C) (mPa s)

−1 8 k1,1 t (80 °C)η(80 °C) (L mPa mol ) × 10

ref

0.24 0.3451 0.31c 0.39 0.33 0.4516,52 1.32e

3.6 3.7 3.7 3.2 1.4 1.3 0.12

18 13 14 this work 18 16 17

The activation energies required for extrapolation to 80 °C were taken from the cited literature. The k1,1 t values are exclusively from SP−PLP−EPR investigations. bExtrapolated from −40 °C via EA(η−1). cFrom Supporting Information to ref 14. dExtrapolated from the reported k0t value at 45 °C via EA(k0t ) = 27.6 kJ mol−1 and estimated with ic = 100, αs = 0.5, and αl = 0.16 from ref 17. eMeasured for 80 °C. a

for both monomers, with αs = 0.65, ic = 100, and αl = 0.16 for MMA,13,30 a chain-length-adjusted ratio of about k500,500 (Sty)/ t k1000,1000 (MMA) = 2.2 is found, which number is in close t agreement with the above-cited ratio of ⟨kt⟩(Sty)/⟨kt⟩(MMA) from SP−PLP−NIR experiments averaged over the same time period, i.e., of 0.15 s. The detailed analysis of termination behavior thus requires propagation rate and chain-length dependence of termination, as given by the composite-model parameters, to be properly taken into account. The higher kp value of MMA results in longer radicals which, in conjunction with higher ic and αs, reduce termination rate and contribute to bulk polymerization rate of MMA being above the one of styrene under stationary conditions at 80 °C.33 Taylor et al. measured ⟨kt⟩ for chemically initiated bulk polymerization of styrene33 under steady-state conditions, i.e., in the presence of a broad distribution of chain lengths. Important kinetic quantities such as ⟨kt⟩ and the numberaverage degree of polymerization, DPn, have been correlated with the power-law expression for chain-length-dependent kt by Mahabadi53and by Olaj and his group54,55 On the basis of this early work, eq 8 has been proposed for deducing chain-length averaged ⟨kt⟩ from chain-length-dependent ki,it = k0t i−α1 with kt0 being defined in eq 3.3,4,33 The symbol Γ in eq 8 denotes the gamma function. The efficiency of initiation, f, the rate coefficient for decomposition of the thermal initiator, kd, and the initiator concentration, cI, are available from ref 33.

Figure 8. Arrhenius-type plot of experimental ⟨ktexp⟩ and calculated chain-length averaged ⟨ktCLDT⟩ for chemically initiated styrene homopolymerization at 90 °C; ⟨ktCLDT⟩ has been deduced from the EPR-derived composite-model parameters for long-chain radicals via eq 8, whereas the ⟨ktPredici⟩ data are from Predici simulation including the entire set of four composite-model parameters. The experimental values, ⟨ktexp⟩, are from ref 33.

energy resulting from the estimate via eq 8, EA(⟨ktCLDT⟩) = 15.3 kJ mol−1, is significantly above EA(k1,1 t ) but is close to the experimental value: EA(⟨ktexp⟩) = 14.3 kJ mol−1. The activation energy associated with the Predici-based estimate, EA(⟨ktPredici⟩) = 14.8 kJ mol−1, is in very satisfying agreement with EA(⟨ktexp⟩). The close agreement of ⟨ktCLDT⟩ and ⟨ktexp⟩ suggests that the data from the SP−PLP−EPR experiments and the ones from conventional steady-state polymerization are both reliable. It appears recommendable to use the ki,it data from EPR whenever CLDT needs to be explicitly taken into account, whereas ⟨ktexp⟩ provides an adequate description of conventional chain-lengthaveraged termination kinetics. Obviously, ki,it constitutes the suitable set of rate coefficients for representation of termination with reversible deactivation polymerization of styrene, where growing radicals of more or less identical size react with each other.

⎡ ⎛ 2 ⎞⎤ ⟨k tCLDT⟩ = k t0⎢Γ⎜ ⎟⎥ ⎢⎣ ⎝ 2 − αl ⎠ ⎥⎦

−2

⎡ 4fkdc Ik t0 ×⎢ ⎢ k pc M ⎣

⎛ 2 ⎞⎤ ⎟⎥ ⎜ ⎝ 2 − αl ⎠⎥⎦

2αl /(2 − αl)

(8)

Figure 8 illustrates the remarkable agreement of ⟨ktCLDT⟩ deduced via eq 8 with experimental ⟨ktexp⟩ from stationary polymerization. ⟨ktCLDT⟩ is only by about 18% below ⟨ktexp⟩ in the temperature range 40−90 °C with the experiments covering the range up to 15% monomer conversion. This minor discrepancy may in part be due to the calculation via eq 8 being entirely based on parameters for the long-chain regime, but neglect small radicals of i < ic, for which ki,it is higher than predicted by the specific power-law expression underlying eq 8. Thus, ⟨ktCLDT⟩ may slightly underestimate ⟨kt⟩. Via Predici simulation, the composite model may be used with all four parameters: k1,1 t , αs, ic, and αl for an estimate of a compositemodel kt average, ⟨ktPredici⟩, which turns out (Figure 8) to be very close to ⟨ktCLDT⟩. The Predici procedure is specified in the Supporting Information. It should be noted that the activation

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CONCLUSION With dicumyl peroxide as the photoinitiator, the chain-length dependence of the termination rate coefficient of styrene bulk polymerization has been measured via SP−PLP−EPR experiments at degrees of monomer conversion up to 9%. The quality of the EPR-derived data has been enhanced by carrying out part of the experiments on fully deuterated styrene, which allows for measurements up to larger chain lengths. Diffusion control of termination is adequately described by the composite model. The temperature dependence of the composite-model parameter k1,1 t , which represents termination of two radicals of chain F

DOI: 10.1021/ma5022665 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

(24) Friedman, B.; O’Shaughnessy, B. Macromolecules 1993, 26, 5726−5739. (25) Meiser, W.; Barth, J.; Buback, M.; Kattner, H.; Vana, P. Macromolecules 2011, 44, 2474−2480. (26) Barth, J.; Buback, M.; Meiser, W.; Vana, P. Macromolecules 2010, 43, 51−54. (27) Soerensen, N.; Barth, J.; Buback, M.; Morick, J.; Schroeder, H.; Matyjaszewski, K. Macromolecules 2012, 45, 3797−3801. (28) Smith, G. B.; Russell, G. T. Z. Phys. Chem. 2005, 219, 295−323. (29) Johnston-Hall, G.; Monteiro, M. J. Macromolecules 2008, 41, 727−736. (30) Johnston-Hall, G.; Monteiro, M. J. J. Macromol. Sci., Part A: Polym. Rev. 2008, 46, 3155−3173. (31) Friedman, B.; O’Shaughnessy, B. Macromolecules 1993, 26, 4888−4898. (32) Khokhlov, A. Makromol. Chem., Rapid Commun. 1981, 2, 633− 636. (33) Taylor, D. R.; van Berkel, K. Y.; Alghamdi, M. M.; Russell, G. T. Macromol. Chem. Phys. 2010, 211, 563−579. (34) Buback, M.; Kuelpmann, A. Macromol. Chem. Phys. 2003, 204, 632−637. (35) Vana, P.; Davis, T. P.; Barner-Kowollik, C. Aust. J. Chem. 2002, 55, 315−318. (36) Kamachi, M. J. Polym. Sci., Part A: Polym. Chem. 2002, 40, 269− 285. (37) Kamachi, M.; Kuwae, Y.; Kohno, M.; Nozakura, S. Polym. J. 1985, 17, 541−543. (38) Kubota, N.; Kajiwara, A.; Zetterlund, P. B.; Kamachi, M.; Treurnicht, J.; Tonge, M. P.; Gilbert, R. G.; Yamada, B. Macromol. Chem. Phys. 2007, 208, 2403−2411. (39) Yamada, B.; Kageoka, M.; Otsu, T. Macromolecules 1992, 25, 4828−4831. (40) Yamada, B.; Tagashira, S.; Sakamoto, K.; Nagano, Y.; Miura, Y. Polym. Bull. 1997, 346, 339−346. (41) Fairhurst, S. A.; Pilkington, R. S.; Sutcliffe, L. H. J. Chem. Soc., Faraday Trans. 1 1983, 79, 925−940. (42) Holz, M.; Mao, X.; Seiferling, D.; Sacco, A. J. Chem. Phys. 1996, 104, 669−679. (43) Russell, G. T. Macromol. Theory Simul. 1995, 4, 549−576. (44) Matheson, M. S.; Auer, E. E.; Bevilacqua, E. B.; Hart, E. J. J. Am. Chem. Soc. 1951, 73, 1700−1706. (45) Clouet, G.; Chaffanjon, P. J. Macromol. Sci., Part A: Chem. 1990, 37−41. (46) Buback, M.; Müller, E.; Russell, G. T. J. Phys. Chem. A 2006, 110, 3222−3230. (47) Olaj, O. F.; Zifferer, G. Macromolecules 1987, 20, 850−861. (48) Piton, M. C.; Gilbert, R. G.; Kuchel, P. W. Macromolecules 2003, 26, 4472−4477. (49) Buback, M.; Kowollik, C. Macromol. Chem. Phys. 2000, 201, 464−469. (50) Buback, M.; Kowollik, C. Macromolecules 1998, 31, 3211−3215. (51) Fan, W.; Zhou, Q.; Sun, J.; Zhang, S. J. Chem. Eng. Data 2009, 54, 2307−2311. (52) Buback, M.; Junkers, T. Macromol. Chem. Phys. 2006, 207, 1640−1650. (53) Mahabadi, H. K. H. Macromolecules 1985, 1324, 1319−1324. (54) Olaj, O.; Zifferer, G.; Gleixner, G. Macromolecules 1987, 20, 839−850. (55) Olaj, O. F.; Zifferer, G.; Gleixner, G. G. Makromol. Chem., Rapid Commun. 1985, 6, 773−784.

length unity, meets the predictions by the Smoluchowski equation and may be correlated to viscosities measured as a function of temperature. The ki,it data from SP−PLP−EPR experiments provide a detailed understanding of termination in the initial period of styrene homopolymerization. It appears to be a matter of priority to perform SP−PLP−EPR experiments for styrene bulk polymerizations up to higher degrees of monomer conversion.

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ASSOCIATED CONTENT

S Supporting Information *

Figures S1 and S2. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (M.B.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful to the Deutsche Forschungsgemeinschaft (DFG) for financial support of this study. REFERENCES

(1) Beuermann, S.; Buback, M. Prog. Polym. Sci. 2002, 27, 191−254. (2) Buback, M. Makromol. Chem. 1990, 191, 1575−1587. (3) Smith, G. B.; Russell, G. T.; Heuts, J. P. A. Macromol. Theory Simul. 2003, 12, 299−314. (4) Barner-Kowollik, C.; Russell, G. T. Prog. Polym. Sci. 2009, 34, 1211−1259. (5) Achilias, D.; Kiparissides, C. Macromolecules 1992, 3739−3750. (6) Achilias, D. S. Macromol. Theory Simul. 2007, 16, 319−347. (7) Benson, S. W.; North, A. M. J. Am. Chem. Soc. 1959, 81, 1339− 1345. (8) Benson, S. W.; North, A. M. J. Am. Chem. Soc. 1962, 84, 935− 940. (9) De Kock, J. B. L.; Van Herk, A. M.; German, A. L. J. Macromol. Sci., Part C: Polym. Rev. 2001, 41, 199−252. (10) Buback, M.; Egorov, M.; Junkers, T.; Panchenko, E. Macromol. Rapid Commun. 2004, 25, 1004−1009. (11) Kattner, H.; Buback, M. Macromol. Symp. 2013, 333, 11−23. (12) Barth, J.; Siegmann, R.; Beuermann, S.; Russell, G. T.; Buback, M. Macromol. Chem. Phys. 2012, 213, 19−28. (13) Barth, J.; Buback, M. Macromol. Rapid Commun. 2009, 30, 1805−1811. (14) Barth, J.; Buback, M.; Russell, G. T.; Smolne, S. Macromol. Chem. Phys. 2011, 212, 1366−1378. (15) Barth, J.; Buback, M. Macromolecules 2011, 44, 1292−1297. (16) Barth, J.; Buback, M.; Hesse, P.; Sergeeva, T. Macromolecules 2009, 42, 481−488. (17) Buback, M.; Egorov, M.; Junkers, T.; Panchenko, E. Macromol. Chem. Phys. 2005, 206, 333−341. (18) Kattner, H.; Buback, M. Macromol. Chem. Phys. 2014, 215, 1180−1191. (19) Barth, J.; Buback, M.; Hesse, P.; Sergeeva, T. Macromolecules 2010, 43, 4023−4031. (20) Barth, J.; Meiser, W.; Buback, M. Macromolecules 2012, 45, 1339−1345. (21) Liang, K.; Hutchinson, R. A.; Barth, J.; Samrock, S.; Buback, M. Macromolecules 2011, 44, 5843−5845. (22) Barth, J.; Buback, M.; Hesse, P.; Sergeeva, T. Macromol. Rapid Commun. 2009, 30, 1969−1974. (23) Johnston-Hall, G.; Theis, A.; Monteiro, M. J.; Davis, T. P.; Stenzel, M. H.; Barner-Kowollik, C. Macromol. Chem. Phys. 2005, 206, 2047−2053. G

DOI: 10.1021/ma5022665 Macromolecules XXXX, XXX, XXX−XXX