Chain-Length-Dependent Termination of Styrene Bulk Polymerization

Jul 14, 2017 - Polymerization up to High Degrees of Monomer Conversion. Hendrik Kattner and ... A constant value of the power-law exponent for small-...
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Chain-Length-Dependent Termination of Styrene Bulk Polymerization up to High Degrees of Monomer Conversion Hendrik Kattner and Michael Buback* Institut für Physikalische Chemie, Georg-August-Universität Göttingen, Tammannstr. 6, D-37077 Göttingen, Germany ABSTRACT: Single pulse−pulsed laser polymerization in conjunction with the highly time-resolved detection of radical concentration by electron paramagnetic resonance (SP-PLP-EPR) was applied for the first time toward measuring termination kinetics up to high degrees of monomer conversion with styrene bulk polymerization up to 80% conversion taken as an example. Monomer conversion was mimicked by the addition of polystyrene. The composite model turns out to provide an adequate representation of the termination kinetics. A constant value of the power-law exponent for smallchain radicals, αs, holds up to about 50% conversion, in which region the model parameter kt(1,1), the rate coefficient for termination of two radicals of size unity, exhibits a minor decay. Above 50% polymer content, both αs and kt(1,1) decrease significantly. Above 80% polymer, the chain-length dependence almost disappears, and termination runs under reaction-diffusion control. As the region of large radicals is not accessible at higher monomer conversion, the knowledge from the composite model has been used to represent the chain-length dependence of large radicals. To check for the quality of the measured and predicted rate parameters, PREDICI estimates on the basis of this data have been compared to experimental results for chemically initiated bulk styrene polymerizations up to almost full conversion. The satisfactory comparison suggests that the data obtained by the SP-PLP-EPR studies are suitable for kinetic simulations of styrene bulk polymerization over the entire conversion range.

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INTRODUCTION The advent of pulsed-laser techniques has enormously improved the accuracy and reliability by which the relevant rate coefficients of conventional and reversible-deactivation radical polymerizations may be determined.1 This is particularly true for termination rate coefficients, k t , which were demonstrated to significantly vary with chain length i.2 The SP-PLP-EPR method developed in our laboratory is perfectly suited for this kind of experiment by directly probing, via electron paramagnetic resonance (EPR) spectroscopy, radical concentration in pulsed-laser polymerization (PLP) after applying a laser single pulse (SP).3 Suitable selection of the photoinitiator ensures instantaneous decomposition and fast addition of monomer to the primary radical species.4,5 The resulting very narrow size distribution of growing radicals allows for studying chain-length-dependent termination (CLDT) in unprecedented detail.5−13 Time evolution of radical concentration after firing a laser pulse is monitored via EPR spectroscopy on a microsecond time scale. With both, the type and the concentration of radicals, being accessible, the SP-PLPEPR experiment may also provide backbiting rate coefficients, which refer to the [1,5]-hydrogen shift reaction of chain-end radicals, e.g., with acrylates, to yield midchain radicals.14−17 The SP-PLP-EPR technique has also been successfully used for solving kinetic issues in reversible addition−fragmentation (RAFT)18,19 or atom transfer radical polymerization (ATRP)20 and even provides kp data, i.e., propagation rate coefficients.21,22 The success of using SP-PLP-EPR is due to the instantaneous © XXXX American Chemical Society

production of an intense burst of radicals in conjunction with the high sensitivity of quantitative time-resolved detection of these radicals. Unless chain transfer comes into play, radical chain length increases linearly with time t after laser pulsing at t = 0, according to eq 1, with cM being monomer concentration and kp the propagation rate coefficient. i = k pc Mt

(1)

i = k pc Mt + 1

(2)

At very early times t, eq 1 has to be replaced by eq 2, which additionally takes the photoinitiator-derived primary radical species into account.3 At low degrees of monomer conversion, CLDT of two radicals of identical chain length, kt(i,i), has been found to be well represented by the composite model (eq 3), introduced by Smith et al.:10,23 kt(i ,i) = kt(1,1)i−αs

i ≤ ic

kt(i ,i) = kt(1,1)ic−αs + αli−αl = kt0i−αl i [[mml:gt]] ic

(3)

Toward increasing time and chain length, kt(i,i) decreases with the power-law exponent αs and, above the crossover chain Received: April 10, 2017 Revised: June 14, 2017

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Macromolecules length, ic, with the power-law exponent αl which is clearly below αs. Depending on the shape of the macroradicals, e.g., random coil vs a rodlike species, αs values are expected to be in the range 0.5−1.0,10,24−26 whereas theory predicts αl = 0.16 for two long macroradicals with radical functionality at the chainend.27−29 The composite-model parameters are obtained by fitting the radical concentrations from SP-PLP-EPR to eq 4 for αl and ic as well as to eq 5 for αs and kt(1,1)c0R, with c0R being the primary laser-pulse-induced radical concentration at t = 0. The time required for a single propagation step is denoted by tp = (kpcM)−1. According to Clouet and Chaffanjon,30 kp of fully deuterated styrene is by a factor of 1.2 above kp(Sty-H8), i.e., kp = 1900 L mol−1 s−1 at 110 °C, as used in the present study. ⎛ 2k 0c 0 t αl ⎞ ⎛ c0 ⎞ t R p ⎟ + (1 − αl) log(t ) log⎜ R − 1⎟ = log⎜⎜ ⎟ 1 ⎠ ⎝ c R (t ) ⎝ − αl ⎠

MMA termination rate coefficient exhibits a weaker decrease with conversion than is expected from viscosity. Termination in this region is assigned to reaction diffusion (RD), i.e., to the approach of radical sites by propagation. The decrease at very high monomer conversion is due to RD diffusion being reduced at very low monomer contents with additional contributions by diffusion-controlled propagation. As has been shown elsewhere,34 the relative impact of the contributions from SD, TD, and RD may result in rather different correlations of overall ⟨kt⟩ vs monomer conversion. Bulk styrene polymerization has been chosen for this study. Beyond being the archetype monomer, an important argument for selecting styrene was that due to its nonpolar nature, high EPR signal intensity may be achieved which, in addition, stays constant over the entire range of monomer conversion.37,38 Thus, the calibration for radical concentration7 carried out for monomer solutions may be used up to high degrees of monomer conversion. The Russell group39 has reported on styrene termination at low conversion. Zetterlund et al. have investigated styrene polymerization to high conversion.40−44 Within earlier work by our group, the general framework for conversion-dependent termination has been applied to styrene. It is common to these earlier attempts that only chain-length-averaged termination kinetics has been considered.34,36,45 So far, CLDT kinetics of styrene homopolymerization has only been investigated at low conversion, by SP-PLP-EPR from 73 to 135 °C. The difficulties of using the powerful SP-PLPEPR method with styrene are due to the unfavorable combination of low propagation and high termination rates. Under such conditions, termination results in a strong decay of radical concentration prior to reaching larger radical size. To ensure high EPR signal quality with styrene, the SP-PLP-EPR experiments were carried out on the perdeuterated monomer, Sty-d8, where the EPR signal intensity is condensed into a singlet upon full deuteration.5,9,31,46 For Sty-H8, no EPR detection at similar signal-to-noise quality is within reach. The Sty-d8 termination rate data are also valid for Sty-H8, as demonstrated elsewhere.31 Within the present study, kt(i,i) of styrene bulk polymerization has been studied as a function of the degree of monomer conversion at 110 °C, where propagation is sufficiently fast to reach larger chain lengths. At higher temperature, self-initiation of styrene comes into play which unfavorably affects the SP-PLP-EPR experiment in that eqs 1 and 2 are no longer valid. In order to precisely reach preselected degrees of conversion, polystyrene was mixed with the monomer−photoinitiator solution prior to the SP-PLPEPR experiment.

i ≫ ic (4)

c R0 c R (t )

−1=

2kt(1,

1 ≤ i [[mml:lt]] ic

1)c R0 ((k pcMt

1 − αs

+ 1)

− 1)

k pcM(1 − αs) (5)

A range of homotermination rate coefficients, kt(i,i), has been determined so far, e.g., for acrylates,10,14 itaconates,13,22 methacrylates,8,9 styrene,31 vinyl esters,5 acrylamide,32 and methacrylic acid11 in aqueous solution and for fully ionized monomers, e.g., sodium methacrylate in aqueous solution.33 These studies have exclusively been carried out in the initial polymerization period. The present study provides the first SPPLP-EPR investigation into CLDT kinetics up to high degrees of monomer conversion. A qualitative picture of the variation of termination rate up to high conversion has already been presented.34,35 This description which is illustrated for methyl methacrylate bulk polymerization in Figure 1 refers to chain-length-averaged kt,

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Figure 1. Variation of the chain-length-averaged termination rate coefficient, ⟨kt⟩, with the degree of monomer conversion. The example refers to methyl methacrylate bulk polymerization. The plot has been constructed from literature data for the individual contributions to diffusion-controlled termination. For details see text as well as refs 34 and 36 where several types of ⟨kt⟩ vs monomer conversion are presented.

EXPERIMENTAL SECTION

The EPR measurements were performed on a Bruker EPR CW/ transient spectrometer system Elexsys-II 500T equipped with an ER 41122SHQE-LC cavity (Bruker). For the single-pulse experiments, a Quantum Composers 9314 pulse generator (Scientific Instruments) was used to synchronize the XeF laser (LPX 210 iCC, Lambda Physik) with the EPR spectrometer. Good signal-to-noise quality was achieved by using a 5 G modulation amplitude in conjunction with a modulation frequency of 100 kHz, a receiver gain of 60, and an attenuation of 20 dB. Temperature control was achieved by an ER 4131VT unit (Bruker). Experimental details, including the calibration procedure, are given elsewhere.7,47 In a glovebox under argon, perdeuterated styrene (Sty-d8, ≥98 atom % D, Sigma-Aldrich, stabilized, received in a vial) was purified by passing through a column filled with aluminum oxide (Brockmann

⟨kt⟩, with the chain lengths being mostly above ic. An initial plateau region, which is assigned to segmental-diffusion (SD) control of entangled radicals and to translational diffusion control of radicals with sizes below ic, is followed by a steep decrease in ⟨kt⟩, which is due to termination running under translational-diffusion (TD) control at significantly enhanced solution viscosity. From moderately high conversions on, the B

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Macromolecules Number 1, grade 507-C-I, neutral). The photoinitiator dicumyl peroxide (DCP, 98%, Sigma-Aldrich) was used as received and added to the purified monomer. The initial DCP concentration was chosen to be 9.0 × 10−2 mol L−1. To mimic different degrees of monomer-topolymer conversion, nondeuterated “dead” poly(styrene) from conventional radical polymerization (MW = 35 000 g/mol, as reported by the supplier: Sigma-Aldrich) was added to the monomer−initiator solution contained in EPR quartz tubes (Wilmad) of 5 mm o.d. and 4 mm i.d. The so-prepared mixtures, which correspond to initial conversions of 20, 35, 50, 65, 70, 75, and 80%, were stored in sealed EPR tubes under the exclusion of light and under argon for several days at −5 °C in order to achieve homogeneity of the mixtures, which was checked by visual inspection. The online Fourier transform (FT)-NIR measurement of monomer conversion vs time during chemically initiated polymerizations has been described elsewhere.48 Nondeuterated styrene (Sty-H8, ≥99%, p.a., Sigma-Aldrich) used in these polymerizations was degassed by several pump−freeze−thaw cycles. The chemical initiator di-tert-butyl peroxide (tBPO, 98%, Luperox DI, Sigma-Aldrich) was used as received and dissolved in Sty-H8 under an argon atmosphere.

Figure 3. Normalized radical concentration vs time profiles from SPPLP-EPR experiments on Sty-d8 bulk polymerizations at 110 °C. The curves refer to different degrees of monomer conversion brought upon by the addition of polystyrene prior to the PLP experiment.

For monomer conversions up to 50%, the cR/c0R vs t profiles sit on top of each other. Toward higher conversion, the decay of cR/cR0 with t is much weaker, which indicates slower termination. The reduction in termination rate is very pronounced in passing from 70 to 75% monomer conversion. Toward even higher conversion, the decay of cR shows little variation. To deduce composite-model parameters, the normalized radical concentration profiles have to be analyzed via eqs 4 and 5. Because of the unfavorable combination of high kt and low kp, larger concentrations of long-chain radicals, with i ≫ ic, as required for the data treatment via eq 4, are not reached. Thus, ic and αl could not be reliably derived from the data of the present study. In the earlier SP-PLP-EPR experiments on CLDT with styrene, ic = 30 was determined at low degrees of monomer conversion for 135 °C. Within the present study, we restricted ourselves to measurements below 120 °C in order to avoid undesirable interference by styrene self-initiation. As imax decreases upon the addition of polystyrene, i.e., upon lowering monomer concentration, the occurrence of long chains and thus the opportunity for measuring αl and ic are further reduced. The analysis was thus restricted to short-chain radicals, up to ic. The associated analysis via eq 5 is shown in Figure 4 for the limiting situations of 20 and 80% monomer conversion brought upon by addition of the respective amounts of polystyrene.

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RESULTS AND DISCUSSION Shown in Figure 2 is the EPR spectrum of growing radicals in styrene-d8 polymerization measured at 110 °C under laser-

Figure 2. EPR spectrum of Sty-d8 recorded at 110 °C under pseudostationary laser initiation with a pulse repetition rate of 20 Hz. To mimic a monomer conversion of 20%, an equivalent amount of polystyrene has been added to the monomer. The magnetic field position used for monitoring the time-resolved concentration of Styd8 radicals is indicated by the arrow.

pulse initiation at a repetition rate of 20 Hz. To mimic 20% monomer conversion, the corresponding amount of polystyrene has been added to the monomer−photoinitiator (dicumyl peroxide, DCP) mixture. The spectrum is in perfect agreement with the one reported for styrene polymerization at very low conversion 31 with the shape being insensitive toward conversion in the extended range under investigation. The spectral position at which the radical concentration vs time profiles were monitored during the SP-PLP-EPR experiment is indicated by the arrow. Radical concentration vs time profiles obtained from the SPPLP-EPR experiments are displayed in Figure 3 on a normalized scale for different amounts of added polystyrene corresponding to different degrees of monomer conversion. The signals in Figure 3 are obtained by coaddition of up to 10 individual single-pulse measurements. It has been checked that the radical concentration vs time profiles do not change during applying this number of laser pulses. As the conversion induced by a single pulse is below 0.1%, the resulting kinetic data have been assigned to the degree of monomer conversion prepared by adding the precisely known amount of polystyrene.

Figure 4. Analysis of SP-PLP-EPR data by fitting to eq 5 in order to deduce αs and kt(1,1)c0R for Sty-d8 homopolymerizations at 110 °C with polystyrene contents of 20% (left) and 80% (right), respectively. The lines represent the best fits associated with the indicated αs values and with kt(1,1) = 1.0 × 109 L mol−1 s−1 and kt(1,1) = 3.3 × 107 L mol−1 s−1 for 20 and 80% monomer conversion, respectively. These kt(1,1) values are obtained from the actual fit parameter kt(1,1)c0R via the separately measured primary radical concentration, c0R. C

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kt(1,1) values exhibit a slight decrease up to 50% monomer conversion. This change appears to be due to the reduction in diffusivity of the small radical species, of chain length unity, toward higher polymer content. Measurements of the selfdiffusion coefficient, Ds, for small molecules in styrene− polystyrene (PS) mixtures have not been reported for polymer with molar masses as the ones of our SP-PLP-EPR experiments. Pickup and Blum studied Ds of toluene in PS solutions containing up to 90 wt % PS.49 Whereas the diffusivity of toluene should afford for a reasonable representation of the diffusion of small styrene radicals, the weight-average molar mass of PS was about 10 times larger in the Pickup and Blum study, which poses problems toward the quantitative estimate of self-diffusion coefficients for the situation met in our experiments. The Pickup and Blum results, however, clearly demonstrate the qualitative trend of a decrease in Ds which is relatively mild in the region of moderate polymer contents and rapidly decays toward high PS contents. The reported decrease in Ds up to about 35% PS is by about 4 times larger than the decrease in kt(1,1) associated with the lowest kt(1,1) data point for 35% PS in Figure 6. Because of the huge difference in PS molar mass, it cannot be decided whether the slight initial decrease in kt(1,1), illustrated in Figure 6, is entirely due to a reduction in diffusivity of the small styryl radicals. Above 50% conversion, kt(1,1) decreases by about 2 orders of magnitude up to 80%. This variation reflects the reduction in termination rate shown in Figure 3. The reason behind the enormous drop in kt(1,1) above 50% conversion is most likely due to the exponential increase in viscosity associated with a major reduction in diffusivity. As a consequence, a transition from translational-diffusion-controlled termination to reaction diffusion (RD) control occurs with RD providing faster termination at very high viscosity. As RD exhibits no chainlength dependence, i.e., αs = 0, it is pleasing to see that αs decreases toward the highest degrees of monomer conversion. It should be noted that this finding refers to data analysis via the composite model. Alternatively, one may state that at high degrees of monomer conversion, the composite model should be replaced by the far simpler RD model with just a single parameter. As the model parameter kt(1,1) is the highest rate coefficient of the composite model and as ktRD refers to the fastest mode of motion under RD conditions, we used the RD constant to estimate a number for kt(1,1). Reaction diffusion (RD) differs from segmental and translational diffusion in that ktRD is expected to be independent of chain length, as the radical sites approach each other by propagation with kp being constant and independent of radical size unless the glassy state is reached. With bulk polymerizations, reaction diffusion is considered to be the dominant termination mechanism at the highest degrees of monomer conversion, where center-of-mass diffusion of radicals is no longer effective.34 The reaction diffusion constant, CRD, specified by ktRD = CRDkp(1 − X) has been reported to be CRD = 800 for styrene.36,45 The kt(1,1) values estimated for at 85, 90, and 95% polymer content (monomer conversion) via this CRD value are included in Figure 6 as gray circles. The fit of the entire set of kt(1,1) values at 110 °C in Figure 6 is represented by eq 7.

Comparison of the data sets in Figure 4 reveals that the curvature of the cR/c0R − 1 data is significantly reduced upon passing from 20 to 80% monomer conversion, which says that the power-law exponent for short chains, αs, is reduced toward higher monomer conversion. The entire set of αs values deduced from the experimental SP-PLP-EPR data for Sty-d8 homopolymerizations at 110 °C, via eq 5, is plotted in Figure 5. Up to 50% conversion, the

Figure 5. Dependence on fractional monomer conversion of the shortchain power-law exponent, αs, as deduced from SP-PLP-EPR data for the Sty-d8 homopolymerizations at 110 °C presented in Figure 4. The solid gray line illustrates the best fit, via eq 6, up to a fractional conversion of 0.8.

exponent αs stays constant at the value measured for negligible conversion31 and subsequently decreases steeply. Fitting the entire data set including the literature value for zero conversion yields αs as a function of fractional conversion, X, as represented by the full line and by eq 6. ⎛ X − 0.29 ⎞ ⎟ αs = 0.51 − 0.003 exp⎜ ⎝ 0.10 ⎠

(6)

The kt(1,1) values, which were also deduced from the cR/c0R − 1 vs t data via eq 5, are shown in Figure 6. The mean value of kt(1,1) for 20% monomer conversion is slightly below the value reported for zero conversion.31 Other than seen for αs, the

Figure 6. Dependence on fractional monomer conversion of the rate coefficient for termination of two monomeric radicals, kt(1,1), as deduced from the SP-PLP-EPR data for Sty-d8 homopolymerization at 110 °C via eq 5. The data from the present study are represented by triangles, whereas the data above 80% conversion (circles) were estimated from the reported CRD value, which refers to termination under reaction-diffusion control (see text).36 The kt(1,1) value for zero conversion (star symbol) was taken from the earlier SP-PLP-EPR investigation.31 The solid line has been fitted to the data from the three sources.

k t(1, 1)/L mol−1 s−1 =

D

1.05 − 0.11X − 0.65 ( X 0.04 )

1 + exp

(7)

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Macromolecules To check for the quality of the CLDT kinetics from SP-PLPEPR, the monomer conversion vs time profile of a thermally initiated Sty-H8 polymerization has been compared to the associated PREDICI-simulated profile based of the classical kinetic scheme comprising initiation, propagation, and termination. The IUPAC-recommended expression dcR/dt = −2kt·cR2 has been used as the termination rate law.50,51The Arrhenius parameters of the rate coefficient for the effective decay of di-tert-butyl peroxide, kd f, as well as of kp(Sty-H8) were taken from the literature.52,53 The measured increase in reaction temperature during polymerization from 110 °C, which was the initial temperature, to a maximum value of 125 °C in the conversion range X = 0.5−0.8 was implemented into the simulation. The termination-related kinetics was taken from the present study as follows: Up to X = 0.8, eqs 6 and 7 were used for estimates of the variation with monomer conversion of the two composite-model parameters kt(1,1) and αs. The crossover chain length ic = 30 was adopted from the earlier SPPLP-EPR investigation31 and was assumed to be independent of monomer conversion. The conversion dependence of the long-chain power-law exponent, αl, was obtained from αs by assuming αl(X) = 0.16/0.51·αs(X), i.e., by multiplication of αs with the ratio αl/αs = 0.16/0.51 measured for the two powerlaw exponents at very low conversion.31 At fractional conversions above 0.8, where no experiments could be carried out, αs has been assumed to decrease linearly with conversion from 0.05 to 0 at X = 1. The comparison of experimental and simulated monomer conversion vs time curves is considered to be satisfactory in view of (a) trace amounts of inhibitor being present in the monomer, which are not taken into account within the simulation, of (b) uncertainties resulting from including the temperature profile during polymerization which has only been measured at a single position in the sample cell, and of (c) the limited accuracy of initiation efficiency and of kp. Figure 7 may be taken as an indication of the quality of SPPLP-EPR-derived termination rate data from the present study. The variation of chain-length-averaged termination rate coefficient, ⟨kt⟩, with polymer content is illustrated in Figure 8 for a stationary styrene bulk polymerization with 0.16 mol/L di-tert-butyl peroxide as the thermal initiator. The ⟨kt⟩ values have been calculated on the basis of the PREDICI model as applied for the simulation in Figure 7, i.e., using the entire set of

Figure 8. Dependence on fractional monomer conversion of the chain-length-averaged termination rate coefficient, ⟨kt⟩, as estimated by PREDICI simulation (see text) for stationary styrene bulk polymerization at 110 °C with 0.16 mol/L di-tert-butyl peroxide as the thermal initiator. The red dashed lines illustrate deviations from the mean value by ±25%, respectively. Included as circles are literature values for chain-length-averaged ⟨kt⟩, which however depend on the particular polymerization conditions, e.g., on initiator type and concentration.31,54

rate coefficients, with the only one difference of temperature being held constant at 110 °C. The so-obtained ⟨kt⟩ differs from the behavior of kt(1,1) plotted in Figure 6 in that kt(1,1) decays with degree of monomer conversion in the early polymerization period, whereas ⟨kt⟩ is more or less insensitive toward polymer content and even exhibits a slight maximum at around X = 0.6 before rapidly decaying. The initial almost constant ⟨kt⟩ value reflects compensation of the lowering in both diffusivity and average chain length. In the region 0.6 < X < 0.8, the drop in diffusivity controls both ⟨kt⟩ and kt(1,1) and indicates a change in termination mechanism. Initial ⟨kt⟩ is in satisfactory agreement with reported data, although the chainlength-averaged values depend on the particular polymerization conditions, e.g., on initiator type and concentration.31,54

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CONCLUSIONS SP-PLP-EPR investigations into styrene radical polymerization up to high degrees of monomer conversion (up to high polystyrene contents) revealed that the termination kinetics may be adequately represented by the composite model. Up to about 50% conversion, the power-law exponent for termination of small radicals with chain lengths below the crossover size, ic, remains constant at a typical value slightly above αs = 0.5, whereas the rate coefficient for termination of two radicals of size unity, kt(1,1), weakly decays. It would be interesting to measure the diffusivity of small species for polystyrene solutions with polymer molar masses as close as possible to the ones of the SP-PLP-EPR studies. This data would allow for checking, whether the initial decay of kt(1,1) may be mostly or even entirely assigned to changes in diffusivity. Toward higher polystyrene contents, both αs and kt(1,1) are significantly reduced, by more than 1 order of magnitude, which suggests a transition to a different mode of termination rate control. At the highest polymer contents, the chain-length dependence vanishes at rather low absolute kt(1,1). This behavior is indicative of termination running under reaction diffusion control. It goes without saying that the SP-PLP-EPR studies should be expanded to added polystyrenes of different molar masses and dispersities as well as to polymerizations in solution. Moreover, the termination kinetics of further monomers should

Figure 7. Comparison of the simulated monomer conversion vs time profile (black line) with the experimental profile (gray line) referring to an initial temperature of 110 °C and to 0.16 mol/L di-tert-butyl peroxide acting as the thermal initiator. Simulation with ⟨kt⟩ being assumed to remain constant over the entire conversion range, i.e., in the absence of any gel effect, would result in significantly lower conversions at longer reaction times, e.g., monomer conversion would be below 70% after 240 min. E

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(15) Barth, J.; Meiser, W.; Buback, M. SP-PLP-EPR Study into Termination and Transfer Kinetics of Non-Ionized Acrylic Acid Polymerized in Aqueous Solution. Macromolecules 2012, 45 (3), 1339−1345. (16) Liang, K.; Hutchinson, R. A.; Barth, J.; Samrock, S.; Buback, M. Reduced Branching in Poly (Butyl Acrylate) via Solution Radical Polymerization in N -Butanol. Macromolecules 2011, 44, 5843−5845. (17) Barth, J.; Buback, M.; Hesse, P.; Sergeeva, T. EPR Analysis of NButyl Acrylate Radical Polymerization. Macromol. Rapid Commun. 2009, 30 (23), 1969−1974. (18) Meiser, W.; Barth, J.; Buback, M.; Kattner, H.; Vana, P. EPR Measurement of Fragmentation Kinetics in Dithiobenzoate-Mediated RAFT Polymerization. Macromolecules 2011, 44 (8), 2474−2480. (19) Barth, J.; Buback, M.; Meiser, W.; Vana, P. Easy Access to the RAFT Equilibrium Constant. Macromolecules 2010, 43 (1), 51−54. (20) Soerensen, N.; Barth, J.; Buback, M.; Morick, J.; Schroeder, H.; Matyjaszewski, K. SP-PLP-EPR Measurement of ATRP Deactivation Rate. Macromolecules 2012, 45 (9), 3797−3801. (21) Kattner, H.; Drawe, P.; Buback, M. Novel Access to Propagation Rate Coefficients of Radical Polymerization by the SP-PLP-EPR Method. Macromol. Chem. Phys. 2015, 216 (16), 1737−1745. (22) Kattner, H.; Buback, M. Propagation and Chain-LengthDependent Termination Rate Coefficients Deduced from a Single SP−PLP−EPR Experiment. Macromolecules 2016, 49 (10), 3716− 3722. (23) Smith, G. B.; Russell, G. T.; Heuts, J. P. A. Termination in Dilute-Solution Free-Radical Polymerization: A Composite Model. Macromol. Theory Simul. 2003, 12 (5), 299−314. (24) Johnston-Hall, G.; Monteiro, M. J. Diffusion Controlled Termination of Linear Polystyrene Radicals in Linear, 4-Arm, and 6Arm Star Polymer Matrices in Dilute, Semidilute, and Concentrated Solution Conditions. Macromolecules 2008, 41 (3), 727−736. (25) Johnston-Hall, G.; Monteiro, M. J. Bimolecular Radical Termination: New Perspectives and Insights. J. Polym. Sci., Part A: Polym. Chem. 2008, 46, 3155−3173. (26) Johnston-Hall, G.; Theis, A.; Monteiro, M. J.; Davis, T. P.; Stenzel, M. H.; Barner-Kowollik, C. Accessing Chain Length Dependent Termination Rate Coefficients of Methyl Methacrylate (MMA) via the Reversible Addition Fragmentation Chain Transfer (RAFT) Process. Macromol. Chem. Phys. 2005, 206 (20), 2047−2053. (27) Friedman, B.; O’Shaughnessy, B. Theory of Intramolecular Reactions in Polymeric Liquids. Macromolecules 1993, 26 (18), 4888− 4898. (28) Friedman, B.; O’Shaughnessy, B. Kinetics of Intermolecular Reactions in Dilute Polymer Solutions and Unentangled Melts. Macromolecules 1993, 26 (21), 5726−5739. (29) Khokhlov, A. R. Influence of Excluded Volume Effect on the Rates of Chemically Controlled Polymery-Polymer Reactions. Makromol. Chem., Rapid Commun. 1981, 2, 633−636. (30) Clouet, G.; Chaffanjon, P. Rate Constants in the Free-Radical Polymerization of Perdeuterated Styrene. J. Macromol. Sci., Part A: Pure Appl.Chem. 1990, 27 (2), 193−212. (31) Kattner, H.; Buback, M. Chain-Length-Dependent Termination of Styrene Bulk Homopolymerization Studied by SP − PLP − EPR. Macromolecules 2015, 48 (2), 309−315. (32) Kattner, H.; Buback, M. Termination and Transfer Kinetics of Acrylamide Homopolymerization in Aqueous Solution. Macromolecules 2015, 48 (20), 7410−7419. (33) Kattner, H.; Drawe, P.; Buback, M. Chain-Length-Dependent Termination of Sodium Methacrylate Polymerization in Aqueous Solution Studied by SP−PLP−EPR. Macromolecules 2017, 50, 1386. (34) Buback, M. Free-Radical Polymerization up to High Conversion. A General Kinetic Treatment. Makromol. Chem. 1990, 191 (7), 1575−1587. (35) Achilias, D. S. A Review of Modeling of Diffusion Controlled Polymerization Reactions. Macromol. Theory Simul. 2007, 16 (4), 319−347.

be investigated via SP-PLP-EPR to check for the applicability of the composite model at high degrees of monomer conversion.

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AUTHOR INFORMATION

Corresponding Author

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

Michael Buback: 0000-0002-8617-919X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful to BASF SE for support of this study. H.K. gratefully acknowledges a postdoc fellowship granted by the Deutsche Forschungsgemeinschaft.

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REFERENCES

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DOI: 10.1021/acs.macromol.7b00745 Macromolecules XXXX, XXX, XXX−XXX