Termination, Propagation, and Transfer Kinetics of Midchain Radicals

Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

Termination, Propagation, and Transfer Kinetics of Midchain Radicals in Methyl Acrylate and Dodecyl Acrylate Homopolymerization Hendrik Kattner and Michael Buback* Institut für Physikalische Chemie, Georg-August-Universität Göttingen, Tammannstr. 6, D-37077 Göttingen, Germany ABSTRACT: Methyl acrylate (MA) and dodecyl acrylate (DA) homopolymerizations (1.5 M in toluene) were investigated via single pulse−pulsed laser polymerization in conjunction with detection of the type and of the concentration of radicals by electron paramagnetic resonance spectroscopy (SP−PLP−EPR). The evolution of secondary propagating (SPR) and midchain (MCR) radicals, after instantaneous laser-induced production of an intense burst of primary radicals, was measured with a time resolution of microseconds from 0 to 60 °C. With the kinetics of chain-length-dependent termination and of propagation for SPRs being already known from experiments at subzero temperature, the rate coefficients for the formation of MCRs from SPRs by backbiting, kbb, of propagation from MCRs, kpt, and of cross-termination between an SPR and an MCR, ktst, were deduced. The present paper aims at elucidating the impact of the size of the ester side chain on kbb, kpt, and ktst. In passing from MA to DA (in 1.5 M solution of toluene), the rate coefficients are lowered by factors of about 1.5 for kbb, 3.7 for kpt, and 8 for ktst, depending on polymerization temperature. Together with the earlier results for SPRs, the reported data provide a comprehensive set of rate coefficients for the simulation of MA and DA homopolymerizations in solution. The data may be used for estimating, by interpolation, the rate coefficients of acrylates with intermediate sizes of the alkyl side chain.

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As first shown for methacrylate polymerization, the composite model (eq 1) adequately represents the homotermination of SPRs.5,6 Power-law expressions describe the dependence of kt(i,i) on chain length i, with kt(i,i) being the termination rate coefficient of two radicals of identical chain length. Among the four composite-model parameters, kt(1,1) is the termination rate coefficient for two radicals of chain length unity. The exponents αs for the dependence on chain length of short-chain and αl for long-chain radicals are clearly different. The transition between the two regimes occurs at the crossover chain length, ic, which is the fourth composite-model parameter.

INTRODUCTION Acrylates are widely used as monomers for radical polymerization. The complexity of acrylate polymerizations results from the fact that two types of radicals, secondary propagating (chain-end) radicals (SPRs) and midchain radicals (MCRs), are present which largely differ in reactivity.1,2 These two radical species may undergo propagation and termination reactions as well as cross-termination. MCRs are produced from SPRs by backbiting, i.e., via an intramolecular hydrogen transfer reaction (Scheme 1), whereas addition of a monomer molecule transforms an MCR into an SPR. With the advent of the single pulse−pulsed laser polymerization−electron paramagnetic resonance (SP−PLP−EPR) technique, the concentration of SPRs and MCRs may be monitored via highly time-resolved EPR after instantaneous production of an intense burst of primary small radicals.3,4 The method has been successfully used in a stepwise fashion for deducing the relevant rate coefficients for BA polymerization (1.5 M in toluene).1 Within the first step, experiments were carried out at low temperature (−40 °C), where backbiting is too slow to produce a significant fraction of MCRs. Thus, the chain-length-dependent termination kinetics of SPRs may be mapped out. This information is implemented into the second step where the concentrations of both SPRs and MCRs are measured at higher temperature. The so-obtained SP−PLP− EPR traces for both radical species were subjected to PREDICI analysis to deduce the individual rate coefficients of backbiting, kbb, of propagation from midchain radicals, kpt, and of crosstermination, ktst. © XXXX American Chemical Society

k t(i,i) = k t(1,1)i−αs i ≤ ic = k t(1,1)ic−αs + αli−αl i > ic

(1)

Unless chain transfer comes into play, the size of radicals in pulse-laser-induced experiments is proportional to the time t after firing the laser pulse, i = kpcMt, where kp is the propagation rate coefficient and cM is monomer concentration.7 The exponent αs is expected to be in the range 0.5−1.0 with the lower and upper limits being associated with center-of-mass diffusion of random coils and rodlike chains, respectively.8−14 Mean-field theory predicts αl = 0.16 for long-chain radicals in good solvents.15−17 Received: October 20, 2017 Revised: December 1, 2017

A

DOI: 10.1021/acs.macromol.7b02241 Macromolecules XXXX, XXX, XXX−XXX

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Scheme 1. Backbiting by a [1,5]-H-Shift Reaction, via a Six-Membered Transition State (Tagged by ‡), Transforms a Secondary Propagating Chain-End Radical (SPR) into a Tertiary Midchain Radical (MCR)a

a

The side group is denoted by R, which is an ester moiety in the case of acrylates.

a slight decrease, by a factor of about 1.3, occurs for kps in toluene solution upon passing from MA to DA.28,29 The reason behind these different trends is the impact of the molecular environment, which differently affects the internal degrees of hindered rotational motion of the transition state for propagation.30 This genuine physicochemical effect is pronounced in an aqueous environment, e.g., of (meth)acrylic acid, where kps in dilute aqueous solution may be by about 1 order of magnitude above the associated bulk value. The effect is weaker with less polar monomers and in less polar solvents but has to be taken into account with accurate kinetic studies. The enhancement of kps from bulk MA to bulk DA reflects the shielding of the polar moieties by the long alkyl side chains, which act as solubilizer and enhance rotational mobility and thus the entropic pre-exponential, A(kps). In dilute solution of toluene the molecular environment is mostly toluene, irrespective of the acrylate under investigation. The weak reduction of kps from MA to DA in toluene is probably due to a slightly enhanced shielding of the reaction site by the larger alkyl ester moiety. Within the present study, kps of DA in toluene has been used, which was extrapolated from studies into acrylates up to nonyl acrylate in toluene solution.28,29

The principle of the SP−PLP−EPR method has been outlined elsewhere.3,4,18 Initiation occurs by a laser single pulse (SP) which almost instantaneously decomposes the photoinitiator. The evolution of SPR and MCR concentrations is monitored by EPR with a time resolution of microseconds. The SP−PLP−EPR technique provides an easy and unrivaled access to chain-length-dependent rate coefficients, kt(i,i). The method has already been applied toward measuring the termination kinetics of chain-end radicals for the bulk homopolymerizations of dodecyl methacrylate,6 cyclohexyl methacrylate,6 benzyl methacrylate,6 and dibutyl itaconate19,20 and for the more rapidly terminating monomers MMA,21 styrene,22 vinyl acetate, and vinyl pivalate23 as well as for acrylamide in aqueous solution.2 Moreover, the chain-length-dependent termination kinetics of SPRs in methyl acrylate (MA), butyl acrylate (BA), and dodecyl acrylate (DA) homopolymerizations in toluene solution has been investigated at temperatures well below 0 °C.8 With the exception of fully ionized radicals, e.g., with sodium methacrylate,24 where the composite-model parameter kt(1,1) has been found to be significantly below the number expected from fluidity and to exhibit a clearly weaker temperature dependence than fluidity, the composite model provides a very satisfactory representation of chain-length-dependent termination rate coefficients for chain-end radicals at the low degrees of monomer conversion investigated so far. The present study addresses the midchain-related kinetics of acrylates in an attempt to identify the dependence of the rate coefficients kbb, kpt, and ktst on the size of the alkyl side chain. In order to cover a wide range of side-chain lengths, MA and DA have been selected for this study. To reduce polarity, the SP− PLP−EPR experiments were carried out in toluene solution.8 As is typical for acrylates, MA and DA undergo backbiting reactions and thus, at moderate and high temperatures, exhibit SPRs and MCRs. In what follows, the second of the abovementioned two steps for detailed SP−PLP−EPR analysis has been addressed, i.e., the simultaneous analysis of SP−PLP− EPR traces measured for SPRs and MCRs at higher temperatures. The results for MA and DA should enable estimates of SPR and MCR rate coefficients of other acrylates by interpolation between the numbers measured for MA and DA. Kinetic analysis including chain-length-dependent termination requires the propagation rate coefficient of SPRs, kps, to be accurately known. The difficulties of measuring kps, which are due to the occurrence of backbiting, have been detailed elsewhere.25 For MA bulk polymerization, IUPAC-recommended kps values have been compiled.26,27 As discussed in refs 28 and 29, kps of bulk MA may be used to adequately represent propagation in solution of toluene. The same is not true for long-chain acrylates. Whereas bulk kps increases toward larger alkyl acrylate side chain, e.g., by a factor of 1.5 from MA to DA,

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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) containing a sample volume of 0.35 mL in a quartz tube (4 mm o.d. and 5 mm i.d.). In the single-pulsed experiments, a Quantum Composers 9314 pulse generator (Scientific Instruments) was used to synchronize the XeF laser (LPX 210 iCC, Lambda Physik). In stationary measurements, a mercury-arc lamp (LAX 1450/SH2/5,500W, Müller) was used for photoinitiation. 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.3,18 The monomers methyl acrylate (MA, 99%, Sigma-Aldrich) and dodecyl acrylate (DA, 90%, Sigma-Aldrich) were purified by passing through a column filled with inhibitor remover (Sigma-Aldrich). The solvent toluene (analytic standard, 99.9%, Sigma-Aldrich) was used as received. Solutions of 1.5 mol L−1 MA and of 1.5 mol L−1 DA were degassed by several pump−freeze−thaw cycles. The photoinitiator αmethyl-4(methylmercapto)-α-morpholinopropiophenone (MMMP, 98%, Aldrich) was used as received at initial concentrations of about 3 × 10−2 mol L−1 and added to the monomer solutions under an argon atmosphere. EPR spectra recorded under stationary UV irradiation at 0, 21, 40, and 60 °C were simulated and fitted via the Matlab-related EPR package Easyspin while PREDICI was used for analyzing the instationary SP−PLP−EPR experiments. The viscosity of a 1.5 M solution of BA in toluene at 50 °C has been measured on a viscosity meter AMVn (Anton Paar, 1569). B


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Figure 1. (a) Experimental and fitted EPR spectra for a 1.5 M solution of MA in toluene at 60 °C under stationary UV irradiation with MMMP acting as the photoinitiator. (b) Simulated EPR spectra for the MCR 5 and for the SPR component, which have been used for fitting the experimental spectrum in (a). The component spectra were obtained via the reported hyperfine coupling constants for the SPR, MCR 5 and MCR 3 components (see text and Figure 2b, below).32 The magnetic field positions for monitoring the SPR and MCR concentrations (in two separate SP− PLP−EPR experiments) are denoted by the arrows.

Figure 2. (a) Experimental and fitted EPR spectra for a 1.5 M solution of DA in toluene measured at 60 °C under stationary UV irradiation with MMMP acting as the photoinitiator. The overall spectrum has been fitted by coadding the individual SPR, MCR 3, and MCR 5 species obtained from the reported hyperfine coupling constants.31,33 The fitting procedure reveals that the content of SPRs amounts to only 5% of the total radical concentration. (b) Relative amounts of MCR 3 and MCR 5 species contained in the overall spectrum (a). The arrow for MCRs indicates the magnetic field position at which the concentrations of both MCR species, MCR 3 and MCR 5, were monitored in the SP−PLP−EPR experiment. The position used for the time-resolved measurement of SPRs is represented by the dashed arrow in (b) to illustrate that this component (not included in (b)) is not overlapped by EPR bands of the midchain radicals.

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RESULTS AND DISCUSSION Prior to each SP−PLP−EPR experiment, the full EPR spectrum was recorded under stationary photoinitiation with a mercuryarc lamp. Shown in Figure 1a is the so-obtained EPR spectrum for MA (1.5 M in toluene), which is similar to the one reported for BA in toluene solution.31 The MA spectrum may be fitted by the four-line EPR spectrum for SPRs and the five-line spectrum for MCRs shown in Figure 1b. Actually, the five-line MCR component, MCR 5, consists of seven lines which, because of band broadening, reduce to a five-line spectrum. The EPR components in Figure 1b were constructed from the reported hyperfine coupling constants.32 The simulation of the experimental EPR spectra by the individual SPR and MCR spectra additionally serves the purpose of identifying suitable magnetic field positions for single-pulse experiments, where no significant band overlap of these individual species occurs. These positions are indicated by the arrows in Figure 1b. Fitting the experimental curve in Figure 1a for 60 °C results in fractions of 17% SPRs and a total of 83% MCRs with the majority of 93% MCR 5 species (see below). Shown in Figure 2a is the EPR spectrum obtained during photopolymerization of DA in toluene solution under stationary irradiation. The spectrum differs from the one recorded for MA (Figure 1a), as has already been reported.31,33 The overall spectrum for DA at 60 °C is represented by the four-line component for SPRs, with however contributes to only 5%, by the five-line spectrum of midchain radicals, MCR 5, and by a second MCR component, MCR 3, which consists of three lines.

The necessity of including a second midchain component has already been outlined.31 Whether the EPR components MCR 3 and MCR 5 refer to two different conformers or to a single hindered species is not yet firmly decided but plays no major role for the kinetic analysis presented here, as the sum of both signals is monitored at the position indicated by the arrow in Figure 2b.31,34−36 The MCR 3 and MCR 5 components contributing to the EPR spectrum of DA in Figure 2a are depicted in Figure 2b. The MCR 3 component is indicative of a lower degree of internal rotational mobility of DA midchain radicals as compared to MCR 5 species, which dominate at smaller alkyl side chains, e.g., with MA.32,37−39 The ratio of the MCR 3 to MCR 5 contributions decreases toward higher temperature and varies with the type of monomer, e.g., the fraction of MCR 3 species at 60 °C in toluene solution, MCR3/ (MCR3 + MCR5), is 7.9% and 42.8% for MA and DA, respectively. The dashed arrow in Figure 2b indicates the peak position of the magnetic field, at which the fraction of SPRs has been monitored. The associated EPR contribution is not included in Figure 1b, as this figure just serves the purpose of demonstrating that the EPR maximum of SPRs is not overlapped by the MCR components. The SPR spectrum of DA radicals is close to the one shown for the MA in Figure 1b. Shown in Figure 3 are the measured radical concentration vs time profiles for SPRs and MCRs in MA (1.5 M in toluene) polymerization at three temperatures, as obtained from the SP−PLP−EPR experiments at the characteristic magnetic field C


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The laser-induced decomposition of the photoinitiator MMMP was assumed to occur instantaneously, i.e., at a much faster rate than the first propagation step.40 The rate coefficient for addition of a monomer molecule to the photoinitiatorderived primary radical, ki, was estimated via ki = 104kps to ensure rapid initiation and to exclude an impact of initiation on the radical concentration vs t profile.40 The SPR propagation rate coefficient, kps, for MA in toluene was adopted from bulk polymerization,26 as no significant difference between kps in solution and in bulk has been found.28,29 As mentioned above, the situation is different with DA, where bulk kps exceeds the associated value in toluene solution. The pre-exponential for DA in toluene was estimated from solution experiments for several acrylates from MA to nonyl acrylate to be A(kps) = 8.0 × 108 L mol−1 s−1.8 Within the simulations for 50 °C, the following propagation rate coefficients for secondary (chainend) radicals in toluene solution have been used: kps(MA) = 25 563 L mol−1 s−1, kps(DA) = 14 297 L mol−1 s−1, and (for the estimates in Table 1) kps(BA) = 21 400 L mol−1 s−1. The decrease of kp in dilute toluene solution upon increasing alkyl ester size is consistent with the data tabulated in ref 41 for MA, BA, and DA. The IUPAC-recommended termination rate law, dcR/dt = −2⟨kt⟩cR2, was used for kinetic analysis.42,43 PREDICI modeling has been carried out for chain-length-dependent termination. The composite-model parameters ktss(1,1), αs, αl, and ic, which adequately describe the chain-length dependence of SPR termination in MA and in DA homopolymerization, were adopted from the literature.8 These reported parameters were deduced via the above-mentioned kps values of DA, i.e., were corrected for the impact of molecular environment. Thus, consistent kps data were used. Backbiting was assumed to be independent of (backbone) chain length i. The rate coefficient of MCR propagation, kpt, was obtained from the fitting procedure as an independent parameter, whereas the MCRSPR cross-termination rate coefficient was introduced via ktst(1,1) = aktss(1,1) with a being the actual fit parameter and with the chain-length dependence being contained in ktss(1,1). Homo- and cross-termination thus refer to an identical set of composite-model parameters αs, αl, and ic. According to Fröhlich et al., the composite-model parameters αs, αl, and ic may differ for SPRs and MCRs.44 Our PREDICI simulations on the basis of reasonably varied composite-model parameters for MCRs, however, revealed no significant impact on the fitted data. Moreover, PREDICI simulations showed that even extensive variation of the MCR homotermination rate coefficient, kttt(1,1), has only a negligible impact on the MCR concentration vs t traces at the polymerization conditions under investigation. A similar conclusion had already been reached for BA homopolymerization.1 Hence, the experimental MCR vs t traces were fitted for kbb, kpt, and ktst(1,1) upon neglecting MCR homotermination. The fitting procedure was simultaneously applied to the SPR and MCR concentration vs time profiles measured in separate experiments, but under identical conditions. The kbb data for MA and DA in Figure 5 are close to each other with the values for DA being slightly but systematically below the ones for MA. It should be noted that the values obtained for kbb of DA by adopting either the bulk kp value or the lower solution-in-toluene value differ only by 7%, which is within the limits of experimental error. The dashed line in Figure 5 represents literature data for BA (also in 1.5 M toluene), which are almost identical to the kbb values for DA.

Figure 3. Radical concentration vs time profiles for SPRs and MCRs in MA polymerization at different temperatures as obtained from the SP−PLP−EPR experiments. The radical species were recorded at the magnetic field position indicated in Figure 1b. The profile measured for 40 °C is not shown for reasons of clarity.

positions indicated in Figure 1b. The SPR concentrations decrease on a microsecond time scale with the decay rate increasing toward higher temperature. The right-hand side of Figure 3 illustrates the time dependence of MCR concentration after applying the laser pulse at t = 0. The concentration (of the MCR components) passes through a maximum and subsequently decays on a time scale which is by about 2 orders of magnitude above the one with SPRs. The shape of the MCR vs t curve demonstrates that the MCRs are produced from SPRs. The intermediate maximum of MCR concentration increases with temperature but stays significantly below the initial SPR concentration. The highest SPR decay rate is associated with the highest intermediate MCR concentration. The SP−PLP−EPR data for DA in toluene solution follow similar trends. Figure 4 shows EPR-derived radical concen-

Figure 4. Comparison of the experimental SPR and MCR concentration vs time profiles with the associated PREDICI fits for DA polymerization at 21 °C.

trations for DA (1.5 M in toluene) at 21 °C. Again, the SPR concentration rapidly decays, while the MCR concentration passes through a maximum followed by a far slower decay than seen for the SPRs. Also included in Figure 4 are the PREDICI fits for the evolution of SPR and MCR concentrations at 21 °C. The relevant reaction steps which have been implemented into PREDICI are shown in Scheme 2. D


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Scheme 2. Reaction Steps Implemented into the PREDICI Model for Fitting SPR and MCR Concentration vs Time Profiles from the SP−PLP−EPR Experiments between 0 and 60 °C

Table 1. Arrhenius Parameters of kbb as Well as Absolute kbb at 50 °C for MA and DA Polymerizations (1.5 M in Toluene) Obtained by PREDICI Fitting of the EPRDeduced SPR and MCR Concentrations Measured as a Function of Time after Pulsing between 0 and 60 °Ca kbb

A(kbb)/s−1 108

EA(kbb)/kJ mol−1

kbb (50 °C)/s−1

ref

MA BA DA

1.5 ± 0.2 1.60 2.1 ± 0.3

33.2 ± 0.3 34.7 35.2 ± 0.3

645 393 429

this study 1 this study

Toward increasing size of the alkyl ester group, from MA to DA, both the pre-exponential A(kbb) and the activation energy, EA(kbb), are weakly enhanced. In view of the scatter on the MA and DA kbb data, it appears justified to present a single expression for an averaged kbb of acrylates in dilute solution of toluene. This Arrhenius expression (eq 2) has been obtained by fitting the entire set of MA and DA data: ln(k bb/s−1) = 19.0 − 4113(T /K)−1

(2)

Equation 2 should be helpful for estimating the backbiting rate coefficients for the entire family of linear alkyl acrylates in dilute solution of toluene. Illustrated in Figure 6 is the temperature dependence of the propagation rate coefficient from midchain radicals, kpt, as

a

The reported numbers for BA (1.5 M in toluene) are included (in italics).1

Figure 5. Arrhenius plot of kbb for MA and DA polymerizations (1.5 M in toluene) between 0 and 60 °C as deduced from simultaneous PREDICI fitting of the SPR and MCR concentration vs time profiles. The dashed line represents kbb data reported for BA polymerization.1

Figure 6. Arrhenius plot of the propagation rate coefficient from midchain radicals, kpt, for MA and DA homopolymerizations in solution of toluene between 0 and 60 °C as deduced from simultaneous PREDICI fitting of SPR and MCR concentration vs t profiles. The dashed line represents the reported BA data.1

Although one would expect the literature kbb data to be slightly higher, by about 25%, to be in between the MA and DA values, the comparison of the BA data from 2010 is considered to be very satisfactory. The common plot of the kbb data for MA, BA, and DA constitutes a critical testing of the quality of these rate coefficients. The Arrhenius parameters of kbb for MA, BA, and DA are summarized in Table 1, with the older BA data being presented in italics. As both kbb and kp are reduced toward larger size of the alkyl ester moiety, the ratio kbb/(kpscM) for MA and DA differs to a lesser extent than does kbb. At 50 °C, kbb/ (kpscM) in toluene solution is 1.6 × 10−2 and 2.0 × 10−2 for MA and DA, respectively. These ratios significantly vary, in absolute and in relative size, depending on polymerization temperature. The numbers for 50 °C indicate similar branching levels for the two acrylates.

deduced by PREDICI fitting of the EPR traces for MA and DA in toluene. The associated literature data for BA are represented by the dashed line.1 The numbers for MA are by about a factor of 3.7 above the DA data. The observed trend of kpt decreasing toward larger alkyl acrylate side chain suggests that steric effects play a role. The literature BA values, also measured in toluene solution, are found to be about halfway in between the MA and DA kpt data. The Arrhenius parameters of kpt are summarized in Table 2. Interestingly, the ratio of the pre-exponentials for SPR propagation over MCR propagation, A(kps)/A(kpt), also given in Table 2, is about the same within the acrylate family, which indicates that the relative hindrance toward internal rotational mobility, that affects the ratio of pre-exponentials, is primarily E


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Table 2. Arrhenius Parameters for MA and DA Polymerization (1.5 M in Toluene) As Obtained by PREDICI Fitting of the EPR-Deduced SPR and MCR Concentration vs t Profiles between 0 and 60 °Ca

a

kpt

A(kpt)/L mol−1 s−1 105

EA(kpt)/kJ mol−1

kpt (50 °C)/L mol−1 s−1

A(kps)/A(kpt)

ref

MA BA DA

8.9 ± 0.5 9.2 4.5 ± 0.8

26.8 ± 1.5 28.3 28.5 ± 1.4

41 24 11

18.7 19.7 17.8

this study 1 this study

Given in italics are the numbers for BA (1.5 M in toluene) from ref 1. The pre-exponentials, A(kps), are from ref 26.

EA(η−1) = 11.5 kJ mol−1 for DA.8 The close similarity of each of the EA(η−1) values with the associated EA(ktst(1,1) indicates that termination occurs under diffusion control. Such close agreement has already been reported for EA(η−1) and for the activation energy of SPR homotermination, EA(ktss(1,1)).8,19,22,23 With the activation energies of SPR homotermination and SPR-MCR cross-termination thus being both close to EA(η−1) and thus being more or less identical, the difference between ktss(1,1) and ktst(1,1) results from the preexponential, with ktss(1,1) being higher by about a factor of 3 (A(ktss(1,1)/A(ktst(1,1) in Table 3). As shown elsewhere,2,4,19 diffusion control of termination leads to almost identical values of ktss(1,1)η, the product of ktss(1,1) and of viscosity, for radicals of similar size. This product amounts to (3.4 ± 0.3) × 105 L Pa mol−1 for small radicals, such as methyl acrylate, methyl methacrylate, and vinyl acetate, and is 1.3 × 105 L Pa mol−1 for monomers with tertbutyl side groups. An attractive feature of these product terms relates to their insensitivity toward temperature, as the effects of temperature on η and on diffusion-controlled ktss(1,1) compensate each other. With ktss(1,1)η being known for a particular monomer system, the measurement of solution viscosity prior to polymerization allows for an estimate of ktss(1,1) in the early polymerization period at reaction conditions as in the viscosity experiment. In case of acrylates, division of ktss(1,1) by the factor of 3 (see Table 3) yields an estimate of ktst(1,1). In order to check for the quality of the rate coefficients from SP−PLP−EPR, the mole fractions of midchain radicals, xMCR, have been estimated via eq 3,45 which includes the entire set of rate coefficients deduced within the present study (Figure 8). An approximation contained in eq 3 relates to the rate coefficient of cross-termination, ⟨ktst⟩, being implemented as a chain-length-averaged quantity. For the calculations of xMCR via eq 3, ⟨ktst⟩ has been estimated via the reported compositemodel parameters for chain lengths of 300 for MA and of 800 for DA, as predicted from PREDICI simulation for stationary conditions on the basis of the entire set of rate coefficients.8 The initial SPR concentration was assumed to be 3.1 × 10−6 mol L−1 for MA and 4.3 × 10−6 mol L−1 for DA as measured for the stationary UV-initiated MA and DA polymerizations at 40 °C.

due to the type of radical but is insensitive toward the size of the alkyl side group. The activation energies, EA(kpt), within the acrylate family are close to each other, as has been found for the propagation rate coefficient of SPRs, kps.26 The change with the size of the alkyl ester side group (in dilute solution of toluene) occurs into the same direction for both kps and kpt. This effect is however about 2 times larger for kpt, which may be understood as a consequence of the radical functionality within an MCR experiencing steric hindrance by alkyl ester moieties from both sides, other than with SPRs. As the third parameter from PREDICI fitting, the crosstermination rate coefficient of two radicals of chain length unity, ktst(1,1), is plotted in Figure 7 as a function of

Figure 7. Arrhenius plot of the rate coefficients of MCR-SPR crosstermination, ktst(1,1), for MA and DA homopolymerizations (1.5 M in toluene) between 0 and 60 °C. The value for BA (1.5 M in toluene) at 50 °C (star symbol) is from ref 1.

temperature for both MA and DA. The ktst(1,1) data for MA and DA are significantly different, by about a factor of 8. The associated Arrhenius parameters are listed in Table 3. The literature value for ktst(1,1) of BA (star symbol) in toluene solution is in between the MA and DA data but is closer to the numbers for MA.1 The dependence of the composite-model parameter ktst(1,1) on temperature, quantified by EA(ktst(1,1)), is almost identical to the associated activation energies of fluidity, η−1, determined via the viscosity of the MA and DA reaction mixtures prior to polymerization.8 The so-obtained viscosities for zero conversion should be a suitable measure for the fluidity and thus diffusivity of the polymerizing mixture at the low degrees of monomer conversion under investigation. The activation energies of fluidity are EA(η−1) = 9.1 kJ mol−1 for MA and

xMCR =

k bb k bb + k p tc M + ⟨k t st⟩cSPR

(3)

Table 3. Arrhenius Parameters for MA and DA Polymerization (1.5 M in Toluene) As Deduced by PREDICI Fitting from the Measured SPR and MCR Concentration vs t Profiles between 0 and 60 °Ca

a

ktst(1,1)

A(ktst(1,1))/L mol−1 s−1 109

EA(ktst(1,1)/kJ mol−1

ktst(1,1) (50 °C)/L mol−1 s−1 108

A(ktss(1,1)/A(ktst(1,1)

ref

MA DA

8.7 ± 0.5 4.1 ± 0.2

8±1 11 ± 1

4.4 0.6

2.6 3.1

this study this study

The numbers for A(ktss(1,1)) were taken from ref 8. F


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Figure 9. Dependence on the square root of the number of carbon atoms, nC, in the alkyl side chain of the rate coefficient for MCR propagation, kpt, and of the product ktst(1,1)η, i.e., of crosstermination, ktst(1,1), and viscosity for MA, BA, and DA. The kpt data have been measured in toluene solution at 50 °C, whereas ktst(1,1)η has been obtained from experiments at −40 °C for MA and DA and at 50 °C for BA (in toluene). The common fit of the ktst(1,1)η data from experiments at rather different temperatures demonstrates that this product is not sensitive toward temperature.

Figure 8. Experimental midchain radical fractions, xMCR (triangles), obtained under stationary UV irradiation for MA and DA (1.5 M in toluene) from fitting full EPR spectra as in Figures 1a and 2a by the individual SPR and MCR components in Figures 1b and 2b. The solid lines refer to estimates of xMCR via eq 3 using the rate coefficients from the present study. The initial SPR concentration, cSPR, was 3 × 10−6 mol L−1 for MA and 4.3 × 10−6 mol L−1 for DA, as measured at 40 °C.

ln(k p t(50 °C)/L mol−1 s−1) = 4.2 − 0.53nc 0.5

(in 1.5 M toluene)

(4)

As shown in Figure 8, the mole fractions estimated from eq 3 are in very satisfactory agreement with the xMCR values determined independently from fitting the EPR spectra for MA and DA (Figures 1a and 2a) by the individual SPR and MCR components shown in Figures 1b and 2b. That xMCR for acrylates in toluene solution decreases toward smaller alkyl ester side chain results from the fact that the second and third term in the denominator on the right-hand side of eq 3 are enhanced from DA to MA. The close comparison of simulated and experimental xMCR data for both MA and DA in solution of toluene provides strong support for the reliability of the EPR technique toward measuring the individual SPR and MCR concentrations. In conjunction with the literature values for the SPR kinetics, which are also accessible from laser-assisted techniques, in particular from SP−PLP−EPR, the MCR-related rate coefficients of the present study allow for the comprehensive representation of the kinetics of MA and of DA radical polymerizations in toluene solution over an extended temperature range. To avoid SP−PLP−EPR experiments for each member of the acrylate family, it appears rewarding to check for interpolation strategies by which kpt and ktst(1,1) for acrylates of intermediate size may be deduced from the data for the limiting MA and DA systems. The two rate coefficients are assumed to reflect steric hindrance. The square root of the number of carbon atoms on the linear alkyl side chain, nc, should be a suitable measure of spatial and thus of steric demand. As ktst(1,1) is affected by both steric effects and diffusivity, the correlation with nc0.5 has been tested for ktst(1,1)η rather than for ktst(1,1) because diffusivity is eliminated by the product term. ktst(1,1)η is known for MA and DA (in 1.5 M toluene) from the individually measured quantities ktst(1,1) and η at −40 °C and is accessible for BA from ktst(1,1) measured at 50 °C and from the viscosity determined for 1.5 M BA in toluene to be η(50 °C) = 0.46 mPa·s. As ktst(1,1)η should be insensitive toward temperature, the product terms for different temperatures may be represented by a common fit. Plotted in Figure 9 are kpt and ktst(1,1)η values as a function of nc0.5. It is gratifying to note that the data points for MA, BA, and DA closely fit to straight lines for both kpt and for ktst(1,1)η with these correlations being represented by eqs 4 and 5, respectively.

ln(k t st(1,1)η/L mPa mol−1) = 19.9 − 0.54nc 0.5

(in 1.5 M toluene)

(5)

Equations 4 and 5 should be helpful for estimating the two rate coefficients for linear alkyl acrylates with sizes in between nc = 1 (MA) and nc = 12 (DA), as is suggested by the close fit in Figure 9 of the BA data to the straight lines connecting the MA and DA data. Whereas kpt(50 °C) is directly obtained from eq 4 for acrylates with a linear side chain of nc carbon atoms, deducing ktst from eq 5 requires an additional experiment in case that the viscosity of the monomer solution in toluene is not known. In principle, a plot as in Figure 9 could also be prepared for kbb. The backbiting rate coefficients for MA and DA are however very close to each other such that it may be sufficient to use eq 2 for estimating kbb of alkyl acrylates. Once the kinetics of SPR radicals is known, the rate coefficients of the present study allow for the simulation of the radical polymerization kinetics of linear alkyl acrylates at higher temperatures where both SPRs and MCRs are simultaneously occurring. Most likely, the SPR rate coefficients may also be estimated from simple correlations as the ones in Figure 9, and ktss(1,1) may additionally be estimated from measured viscosities, as indicated for BA above.

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CONCLUSIONS The favorable application of the SP−PLP−EPR technique toward the detailed analysis of radical homopolymerization of monomers which undergo backbiting and thus exhibit two types of radicals, secondary chain-end propagating radicals (SPRs) and tertiary midchain radicals (MCRs), has been demonstrated for methyl acrylate (MA) and dodecyl acrylate (DA). The experiments have been carried out on 1.5 M solutions in toluene at temperatures from 0 to 60 °C. The MCR-related rate coefficients of backbiting, kbb, of propagation from MCRs, kpt, and of cross-termination between an SPR and an MCR, ktst, were deduced. Together with the rate coefficients for SPRs which are available from literature, also based on PLP experiments, the rate coefficients of the present study allow for the comprehensive analysis and simulation of the kinetics of the G


Article

Macromolecules

(12) Mahabadi, H. K.; O’Driscoll, K. F. Concentration Dependence of the Termination Rate Constant During the Initial Stages of Free Radical Polymerization. Macromolecules 1977, 10, 55−58. (13) Mahabadi, H. K.; O’Driscoll, K. F. Termination Rate Constant in Free-Radical Polymerization. J. Polym. Sci., Polym. Chem. Ed. 1977, 15 (2), 283−300. (14) Kirkwood, J. G.; Riseman, J. The Intrinsic Viscosities and Diffusion Constants of Flexible Macromolecules in Solution. J. Chem. Phys. 1948, 16 (6), 565−573. (15) Friedman, B.; O’Shaughnessy, B. Theory of Intramolecular Reactions in Polymeric Liquids. Macromolecules 1993, 26 (18), 4888− 4898. (16) Friedman, B.; O’Shaughnessy, B. Kinetics of Intermolecular Reactions in Dilute Polymer Solutions and Unentangled Melts. Macromolecules 1993, 26 (21), 5726−5739. (17) Khokhlov, A. R. Influence of Excluded Volume Effect on the Rates of Chemically Controlled Polymer-Polymer Reactions. Makromol. Chem., Rapid Commun. 1981, 2, 633−636. (18) Barth, J.; Buback, M. SP-PLP-EPR − A Novel Method for Detailed Studies into the Termination Kinetics of Radical Polymerization. Macromol. React. Eng. 2010, 4 (5), 288−301. (19) 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. (20) Buback, M.; Egorov, M.; Junkers, T.; Panchenko, E. Termination Kinetics of Dibutyl Itaconate Free-Radical Polymerization Studied via the SP-PLP-ESR Technique. Macromol. Chem. Phys. 2005, 206 (3), 333−341. (21) Barth, J.; Buback, M. SP−PLP−EPR Investigations into the Chain-Length-Dependent Termination of Methyl Methacrylate Bulk Polymerization. Macromol. Rapid Commun. 2009, 30 (21), 1805− 1811. (22) Kattner, H.; Buback, M. Chain-Length-Dependent Termination of Styrene Bulk Homopolymerization Studied by SP−PLP−EPR. Macromolecules 2015, 48 (2), 309−315. (23) Kattner, H.; Buback, M. Chain-Length-Dependent Termination of Vinyl Acetate and Vinyl Pivalate Bulk Homopolymerizations Studied by SP-PLP-EPR. Macromol. Chem. Phys. 2014, 215 (12), 1180−1191. (24) 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. (25) Drawe, P.; Buback, M. The PLP-SEC Method: Perspectives and Limitations. Macromol. Theory Simul. 2016, 25 (1), 74−84. (26) Beuermann, S.; Buback, M. Rate Coefficients of Free-Radical Polymerization Deduced from Pulsed Laser Experiments. Prog. Polym. Sci. 2002, 27, 191−254. (27) Beuermann, S.; Buback, M.; Davis, T. P.; Gilbert, R. G.; Hutchinson, R. A.; Olaj, O. F.; Russell, G. T.; Schweer, J.; van Herk, A. M.; Kajiwara, A.; Klumperman, B.; Russell, G. T. Critically Evaluated Rate Coefficients for Free-Radical Polymerization. 2. Propagation Rate Coefficients for Methyl Methacrylate. Macromol. Chem. Phys. 1997, 198 (5), 1545−1560. (28) Couvreur, L.; Piteau, G.; Castignolles, P.; Tonge, M.; Coutin, B.; Charleux, B.; Vairon, J.-P. Pulsed-Laser Radical Polymerization and Propagation Kinetic Parameters of Some Alkyl Acrylates. Macromol. Symp. 2001, 174 (1), 197−208. (29) Buback, M. Propagation Kinetics in Radical Polymerization Studied via Pulsed Laser Techniques. Macromol. Symp. 2009, 275−276 (1), 90−101. (30) Beuermann, S. Solvent Influence on Propagation Kinetics in Radical Polymerizations Studied by Pulsed Laser Initiated Polymerizations. Macromol. Rapid Commun. 2009, 30 (13), 1066−1088. (31) Barth, J.; Buback, M.; Hesse, P.; Sergeeva, T. EPR Analysis of NButyl Acrylate Radical Polymerization. Macromol. Rapid Commun. 2009, 30 (23), 1969−1974. (32) Kajiwara, A.; Nanda, A. K.; Matyjaszewski, K. Electron Spin Resonance Study of Monomeric, Dimeric, and Polymeric Acrylate

two monomers. The so-obtained kinetic data also provide estimates of the fraction of MCRs as a function of polymerization temperature. Kinetic information about other acrylates may be deduced by interpolation of the data for the two limiting systems, i.e., for MA and DA. Such interpolations may be carried out by correlations via the square root of the size of the alkyl ester side group, with the size being expressed by the number of carbon atoms within the alkyl moiety. The SP−PLP−EPR technique should be well suited also for the kinetic analysis of acrylates in solvents other than toluene and for acrylate bulk polymerizations.

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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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Termination, Propagation, and Transfer Kinetics of Midchain Radicals

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