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Termination, Transfer, and Propagation Kinetics of Trimethylaminoethyl Acrylate Chloride Radical Polymerization in Aqueous Solution Hendrik Kattner and Michael Buback* Institut für Physikalische Chemie, Georg-August-Universität Göttingen, Tammannstr. 6, D-37077 Göttingen, Germany S Supporting Information *

ABSTRACT: The SP−PLP−EPR (single pulse−pulsed laser polymerization−electron paramagnetic resonance) method has been used to measure the rate coefficients of termination, intramolecular transfer, and propagation for the radical polymerization of 20 wt % trimethylaminoethyl acrylate chloride (TMAEA) in the temperature range 0−90 °C. The high complexity of this acrylate system is due to water being the solvent, to the monomer being a strong electrolyte, and to both secondary chain-end radicals and tertiary midchain radicals being simultaneously present. The termination kinetics, which was analyzed by a chain-length-dependent scheme, largely differs from the situation met with nonionized radicals. The reliability of the rate coefficients obtained from the SP−PLP−EPR experiments has been demonstrated by the almost perfect agreement of TMAEA conversion vs time data from simulation, on the basis of these coefficients, and from the chemically initiated TMAEA polymerization experiment at 70 °C.

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termination of two radicals of chain length i.1,14 kt(i,i) decreases toward larger chain lengths with this dependency being described by the composite model introduced by Smith, Russell, and Heuts (eq 3).15

INTRODUCTION Pulsed laser polymerization (PLP) with single pulse (SP) initiation carried out in conjunction with electron paramagnetic resonance (EPR) spectroscopy, SP−PLP−EPR, has emerged as a perfect method for detailed investigations into the termination,1−4 intramolecular transfer,4−10 and even propagation kinetics.4,11,12 Via online EPR spectroscopy, the type and the concentration of radicals produced by applying a laser pulse are measured with a time resolution of microseconds.4 In the case of nonoverlapping bands in the EPR spectrum, the SP−PLP−EPR technique even allows for monitoring the time evolution of more than one radical species.9,10,13 Within SP experiments, the radical chain length, i, increases linearly with time, t, after applying the laser pulse at t = 0. Unless transfer reactions come into play, eqs 1 and 2 represent this correlation with monomer concentration, cM, and propagation rate coefficient, kp. i = k pc Mt (1) i = k pc Mt + 1

k t(i,i) = k t(1,1)i−αS

k t(i,i) = k t(1,1)ic−αS+ αli−αl = k t0i−αl

i > ic

(3)

Toward larger radical size, kt(i,i) decreases with the power-law exponents αs and αl in the short-chain and long-chain regions, respectively. Both regimes are separated by the crossover chain length, ic. The decay of kt(i,i) is more pronounced at small chain lengths, below ic, i.e., αs > αl, than for larger radicals, which get entangled and undergo segmental diffusion prior to reaction. Theory predicts αs to be in the range 0.5−1.0,1,16−18 depending on the shape of the radicals, random coil or rodlike, whereas α l is predicted to be around 0.16 for large macroradicals with the radical functionality at the chain end.19−21 The fourth composite-model parameter is the rate coefficient for termination of two radicals both of chain length unity, kt(1,1), which may be correlated with the hydrodynamic radius, r1, the self-diffusion coefficients of the monomeric radical species, DA1 and DB1, the Avogadro number, NA, the spin factor, Pspin = 0.25, and the capture radius, Rc, according to the Smoluchowski equation:22

(2)

The additional term in eq 2 accounts for the photoinitiatorderived primary fragment which is already present at t = 0. Hence, the term (+1) provides a better description of the chain-length dependence at small i.14 In the absence of chain transfer, termination at time, t, after pulsing occurs between two macroradicals of almost identical size. The analysis of radical concentration as a function of time thus allows for investigations into chain-length-dependent termination (CLDT) kinetics and yields rate coefficients, kt(i,i), for © XXXX American Chemical Society

i ≤ ic

Received: February 13, 2017 Revised: April 24, 2017

A

DOI: 10.1021/acs.macromol.7b00328 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules k t(1,1) = 2πPspinNA(DA1 + DB1)R c

kps, is not available from an independent experiment, which is due to the high backbiting and low termination rate of this monomer.28 The present study thus aims at the kinetic analysis of termination, transfer (backbiting), and propagation being carried out exclusively via the SP−PLP−EPR method. The validity of the so-obtained values will be checked by PREDICI modeling of chemically initiated TMAEA polymerization based on the entire set of rate coefficients deduced from SP−PLP− EPR.

(4)

The SP−PLP−EPR technique has been applied to the detailed study of termination kinetics of a series of monomers, e.g., to bulk homopolymerizations of methyl methacrylate,23 vinyl acetate,3 and styrene.2 With these systems, the excellent applicability of the composite model for describing CLDT has been demonstrated. The four composite-model parameters αs, αl, ic, and kt(1,1) exhibit the expected behavior also with butyl acrylate polymerization in bulk and in an organic solvent as well as in aqueous solutions of acrylamide, where two types of radicals are occurring, secondary propagating and midchain radicals. A different situation applies with fully ionized monomers and thus fully ionized radicals, as has been shown by SP−PLP−EPR studies into sodium methacrylate (NaMAA) and trimethylaminoethyl methacrylate chloride (TMAEMA) homopolymerizations in aqueous solution. Whereas the numbers for αs, αl, and ic are close to the ones measured in bulk and in organic solution and for nonionized monomers in aqueous solution, the rate parameter kt(1,1) is by orders of magnitude below the value estimated for encounter control according to the Smoluchowski equation (eq 4). Other than with sterically highly hindered monomers, such as dibutyl itaconate,11,24 where kt(1,1) is also far below the number estimated from eq 4, the fully ionized monomers NaMAA and TMAEMA exhibit an activation energy of kt(1,1) which is significantly below the one of fluidity.25−27 This unusual type of behavior has been assigned to the mediating action of counterions, which may be understood as some kind of ion pair formation associated with a higher termination rate. An increase in temperature enhances both fluidity (diffusivity) and the amount of ionic (i.e., noncomplexed) species, resulting in opposing effects on termination rate. Thus, the activation energy for termination, in particular of kt(1,1), should be below the separately measurable activation energy of fluidity. The present investigation into trimethylaminoethyl acrylate chloride (TMAEA, Scheme 1) adds complexity with respect to

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EXPERIMENTAL PART

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RESULTS AND DISCUSSION

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). In the 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 3 G modulation amplitude in conjunction with a modulation frequency of 100 kHz, a receiver gain of 84, and an attenuation of 13 dB. Temperature was controlled by an ER 4131VT unit (Bruker). Experimental details, including the calibration procedure, are given elsewhere.29,30 The fluidities (presented as Supporting Information) and the solution densities were determined by a viscosity meter AMVn (Anton Paar, 1569) and a DPR 2000 instrument (Anton Paar), respectively. Overall monomer conversion per pulse was measured via near-infrared (NIR) spectroscopy on an FTIR instrument (Bruker, IFS 88) equipped with a tungsten halogen lamp (Gilway Technical Lamp, L7417A, 12 V, 50 W), a silicon-coated calcium difluoride beam splitter (model T8401), and a liquid-nitrogen-cooled InSb detector (InfraRed Associates, model D413). The procedure applied for determination of the monomer-to-polymer conversion either in the stationary or in the SP−PLP experiments is described in detail elsewhere.12,27 A flat cell (Suprasil TE102 aqueous cell, sample volume 100 μL) was used for the EPR experiments. The monomer trimethylaminoethyl acrylate chloride (TMAEA, IUPAC: 2-(acryloyloxy)-N,N,N-trimethylethan-1-aminium chloride, 80 wt % in H2O, Sigma-Aldrich) stabilized with 600 ppm monomethyl ether hydroquinone (MEHQ, Sigma-Aldrich) and the solvent deuterium oxide (D2O, Euriso-Top, 99.90% D) were degassed by several pump−freeze−thaw cycles. The photoinitiator Darocur 1173 (2-hydroxy-2-methyl-1-phenylpropan-1-one, Aldrich, 97%) was used as received and added to the solutions of 20 wt % TMAEA in D2O under an argon atmosphere. The initial Darocur concentration was 1.1 × 10−2 mol L−1. A sample volume of 100 μL was filled into the EPR flat cell and used immediately after preparation under the exclusion of visible light. The analysis of the radical concentration vs time curves from SP−PLP−EPR and of the monomer conversion vs time data from NIR monitoring of chemically initiated polymerization was carried out via the software packages PREDICI (see Supporting Information) and Origin. Full EPR spectra were fitted and simulated via MATLAB in conjunction with the software package Easyspin For the chemically initiated polymerization, VA-086 (2,2′-azobis[2methyl-N-(2-hydroxyethyl)propionamide], Wako) was used as the thermal initiator without further purification and was dissolved in the degassed aqueous monomer solution under an argon atmosphere as described elsewhere.27 The IUPAC-recommended termination rate law, dcR/dt = −2 < kt> cR2, was used for kinetic analysis.31,32

Scheme 1. Top: Chemical Structure of TMAEA; Bottom: Backbiting by a [1,5]-H-Shift Reaction via a Six-Membered Transition State (Tagged by ‡) Transfers a Secondary Propagating Chain-End Radical (SPR) into a Tertiary Midchain Radical (MCR)a

a

The side group is denoted by R, which is COOC2H4N(CH3)3 in the case of TMAEA.

all preceding investigations due to the simultaneous occurrence of water being the solvent, of fully ionized species being present, and of the monomer undergoing backbiting, thus resulting in both secondary chain-end radicals (SPRs) and tertiary midchain radicals (MCRs), also depicted in Scheme 1. An additional problem results from the fact that the propagation rate coefficient of TMAEA chain-end radicals,

Shown in Figure 1 are EPR spectra measured during TMAEA polymerizations (20 wt %) in aqueous solution at 21 and 95 °C under pseudostationary laser irradiation at a pulse repetition rate (p.r.r.) of 20 Hz. The spectra provide the first evidence for the occurrence of backbiting which transforms a propagating B


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Figure 1. EPR spectra recorded during aqueous-solution polymerizations of TMAEA (20 wt %) at 21 and 95 °C under pseudostationary laser irradiation with a pulse repetition rate of p.r.r. = 20 Hz and with Darocur (1.9 × 10−2 mol L−1) acting as the photoinitiator. The magnetic field positions of SPRs (red, left part) reflect the applied p.r.r. (framed area). Because of the low SPR content at higher temperature, the oscillations are not seen in the EPR spectrum at 95 °C (right part). The sweep time for each full EPR spectrum was 5.12 s.

Figure 2. EPR spectra recorded during polymerization of 20 wt % TMAEA in aqueous solution at 0 and 80 °C (black lines). The spectra refer to a sweep time of 5.12 s and to stationary UV irradiation with Darocur (1.9 × 10−2 mol L−1) acting as the photoinitiator. Fitting of the experimental spectra by the red lines allows for the determination of the relative amounts of SPRs and MCRs. The indicated MCR fraction, xMCR, refers to the sum of both conformers, MCR3 and MCR5.

insensitive toward temperature throughout the entire experimental range, from −5 to 95 °C, whereas the hfc pattern of the MCR5 conformer changes with temperature and has been adjusted for each temperature (see Figure 4 and Table S2). Under otherwise identical experimental conditions, no variation in composition occurs in the EPR spectra recorded at higher or lower sweep time, corresponding to different degrees of monomer conversion. Thus, the impact of conversion on the EPR spectra may be ignored for the spectra under investigation. The close agreement of measured and fitted EPR spectra allows for the reliable determination of molar MCR fractions, xMCR (Figure 3). The numbers obtained for xMCR are

secondary chain-end radical, SPR, into a tertiary midchain radical, MCR, via a six-membered transition-state structure (Scheme 1). Bands due to SPRs are clearly identified at 21 °C (left-hand side of Figure 1) by the oscillations of the associated EPR components. The SPR intensity rapidly decays on a millisecond time scale and is recovered by the subsequent pulse, which instantaneously produces a large amount of SPRs again. The termination rate of the MCRs is too small to induce a significant decay in MCR concentration between two laser pulses at a p.r.r. of 20 Hz, i.e., at a time delay of 50 ms.33 The oscillation of the SPR components is not detected at the higher temperature of 95 °C (right-hand side of Figure 1), as the fraction of SPRs is too small at this elevated temperature. The positions assigned to SPRs correspond to the typical quartet pattern of a(3H) = 20.6 G as observed for other acrylates (see Supporting Information). This hyperfine coupling constant was used for simulation of the contribution of SPRs to the overall EPR spectra measured in the entire temperature range under investigation.34 The right-hand-side spectrum essentially refers to the EPR spectrum of MCRs. The adequate assignment and simulation of the measured EPR spectra are important for kinetic analysis. To monitor individual SPR and MCR concentrations by time-resolved SP− PLP−EPR experiments, EPR field positions have to be identified, which are exclusively due to individual radical species, i.e., are not overlapped by another radical species. Presented in Figure 2 are experimental and simulated EPR spectra measured under stationary UV irradiation at 0 and 80 °C. The experimental spectra were fitted by a single SPR component and by two MCR conformers, MCR3 and MCR5, which are represented by a characteristic triplet (MCR3) and a quintet (MCR5) EPR spectrum.35−40 The deconvolution of the overall EPR band has been performed via a two-step procedure: First, the contribution of SPRs has been determined via fitting the spectrum in the region where only SPRs are contributing. Second, the remaining signal, which is entirely due to MCR3 and MCR5 species, has been analyzed on the basis of the associated hyperfine coupling constants listed in Table S2. The presence of two such coexisting MCR conformers is in agreement with literature data and constitutes a general feature of MCRs in acrylate polymerizations.34,39,41 Hyperfine coupling constants (hfc’s) deduced from the experimental spectra are listed in Table S2. The hfc’s of the SPR and MCR3 species are

Figure 3. Molar fraction of midchain radicals, xMCR, deduced from fitting the experimental EPR spectra recorded during polymerization of TMAEA in aqueous solution between −5 and +95 °C. Experimental values of xMCR for BA polymerization (16.8 wt % in toluene)34 and AAm (10 wt % in H2O)10 are included for comparison.

significantly above the ones measured for butyl acrylate (BA) in toluene and acrylamide (AAm) in aqueous solution which are included in Figure 3. Fitting the experimental spectra by the SPR and MCR contributions also allows for identifying magnetic field positions where the EPR spectrum is entirely due to a single radical species which thus enables the time-resolved detection of this particular species by SP−PLP−EPR. The individual SPR and MCR components of the measured EPR spectra for 20 wt % TMAEA in aqueous solution at 0 and 80 °C are shown in Figure 4. The arrows indicate the field positions at which the SPR and MCR components do not overlap. At these positions, the individual SPR and MCR concentrations may be separately monitored by SP−PLP−EPR experiments. The insensitivity of C


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conversion amounts to 51% at 50 °C. The measured decay of monomer concentration up to 125 s after applying the laser pulse has been implemented into PREDICI to deduce the rate coefficient for propagation of secondary radicals, kps, as outlined in the Supporting Information. During SP data analysis by PREDICI, no indication has been found for MCR homotermination as well as β-scission and depropagation having a measurable impact on the TMAEA polymerizations under investigation. Thus, these side reactions have been neglected in the PREDICI scheme for deducing the rate coefficients presented below. This is not saying that MCRMCR termination does not occur. PREDICI modeling with MCR-MCR termination being included with the rate coefficient kttt = 0.01ktss, however, tells that homotermination of MCRs does not affect the radical concentration vs time profiles and thus may be ignored within the present study. By simultaneous fitting of the SP−PLP−EPR traces for SPRs and MCRs, the following rate coefficients have been determined: for backbiting, kbb, for propagation from an MCR, kpt, as well as for chain-length-dependent termination of two SPRs and of an SPR with an MCR, ktss(1,1) and ktst(1,1), respectively. The composite-model parameters αs, αl, and ic have been adopted from SP−PLP−EPR studies into the methylated derivative of TMAEA, i.e., TMAEMA (see Supporting Information). This strategy appears to be justified as these three parameters show little variation within a broad range of monomers. The composite-model parameters for SPRs cannot be determined via SP−PLP−EPR, as the high backbiting rate requires temperatures which are below the freezing point of the aqueous system. Adopting the parameters measured for the methylated analogue appears to be no critical assumption, as full ionization plays a far more important role than replacing an H atom at the backbone by a methyl group.

Figure 4. Simulated SPR and MCR spectra for 0 and 80 °C as deduced from fitting the experimental spectra in Figure 2 with the hfc’s listed in Table S2. The positions used for monitoring the SPR and MCR concentrations are labeled by the arrows. The baseline indicated by the dashed horizontal line illustrates the negligible contribution of MCR intensity at the magnetic field position used for SPR monitoring in the SP−PLP−EPR studies. The MCR simulation refers exclusively to the MCR5 conformer, which is present in large excess. There is no EPR contribution of MCR3s at the field position used for SPR monitoring.

the magnetic field position for the SPRs toward temperature facilitates the determination of SPR concentration. The EPR spectrum of the MCRs changes slightly with temperature, but neither the MCR3 nor the MCR5 band contributes to the EPR spectrum at the specific SPR field position indicated by the arrow. The analysis of the SPR and MCR concentration vs time profiles rests on modeling via PREDICI, as detailed elsewhere.10 The individual reaction steps as well as the fitting procedure are described in the Supporting Information (Figure S1 and Table S1). The SP−PLP−EPR investigations were performed on 20 wt % TMAEA dissolved in D2O between 0 and 90 °C. In Figure 5, representative examples of SPR and

Figure 6. Arrhenius plot of the backbiting rate coefficient, kbb, for 20 wt % TMAEA between 0 and 90 °C. The rate coefficients were determined by simultaneous PREDICI fitting of the measured SPR and MCR concentration vs time profiles (see Supporting Information).

Figure 5. Measured and fitted SPR (left) and MCR (right) concentration vs time profiles after applying a laser single pulse at t = 0 during TMAEA polymerization (20 wt %/D2O) at 50 °C. The baseline for the SPR trace is indicated by the dashed line. The rapid decay of SPR intensity (left) accounts for the oscillation in SPR intensity in between two pulses applied at a pulse repetition rate of 20 Hz. The higher noise level with the SPR signal compared to the MCR one results from the difference in time resolution, which is only 10 μs for the SPR signal but is 100 μs for the MCR signal.

The so-obtained numbers for kbb between 0 and 90 °C are presented in Figure 6. The associated Arrhenius expression reads k bb/s−1 = 7.1 × 109 exp(− 5846(T −1/K−1))

MCR concentration vs time profiles measured at 50 °C are shown together with the associated PREDICI fits. The traces in Figure 5 refer to a “true” single pulse experiments without averaging over multiple successive single pulse measurements. The final monomer-to-polymer conversion induced by a single laser pulse has been measured by FT-NIR spectroscopy after the complete decay of SPR and MCR concentrations. This final

(20 wt % TMAEA in aqueous solution)

The Arrhenius parameters, EA(kbb) = 48 ± 2 kJ mol−1 and A(kbb) = (7.1 ± 0.7) × 109 s−1, are close to the data for 10 wt % AAm in aqueous solution but are distinctly different from the values measured for BA in solution of toluene (Table 1). As can D


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Macromolecules be seen from absolute kbb, also listed in Table 1, the relatively high MCR fractions with TMAEA illustrated in Figure 3 are not due to a high kbb.

the probability for propagation, i.e., for the reaction of two equally charged species, and thus counteracts the general rate enhancement with temperature and results in a smaller than expected activation energy, EA(kp). The entropy-motivated pre-exponential factor, A(kpt), reflects the mobility within the transition state structure, which may be reduced for ionized monomers due to the strong electrostatic inter- and intramolecular interactions.43,44 This argument is in line with kps studies for nonionized and fully ionized methacrylic acid where A(kps) is reduced upon ionization.42 As both kps and kpt refer to propagation steps, it appears reasonable to assume that A(kpt) and A(kps) for TMAEA exhibit similar changes. The lower absolute kpt for TMAEA listed in Table 2 may, at least partly, explain the higher MCR fraction seen in Figure 3. Shown in Figure 8 are the rate coefficients of SPR homotermination and of cross-termination for TMAEA radicals

Table 1. Comparison of the Rate Coefficients for Backbiting, kbb, at 50 °C and of the Arrhenius Parameters for kbb of TMAEA, BA, and AAm (in Different Solvent Environments) kbb TMAEA (20 wt %/D2O) AAm (10 wt %, 20 wt %/H2O) BA (1.5 M/toluene)

EA(kbb)/ kJ mol−1

A(kbb)/ 108 s−1

kbb (50 °C)/s−1

48 ± 2

71 ± 7

97

49 ± 2

37 ± 7

44

35 ± 2

0.48 ± 0.07

393

ref present study 10 9

The second quantity deduced from the radical concentration vs time profiles is the rate coefficient for MCR propagation, kpt. According to the plot in Figure 7, kpt is given by the Arrhenius expression: k p t /(L mol−1 s−1) = 6.8 × 104 exp(− 3127(T −1/K−1)) (20 wt % TMAEA in aqueous solution)

Figure 8. Arrhenius plot of the rate coefficients for SPR homotermination and for MCR-SPR cross-termination, ktss(1,1) and ktst(1,1), respectively, of radicals of chain length unity between 0 and 90 °C. The rate coefficients were determined by PREDICI fitting of the SPR and MCR concentration vs time traces from SP−PLP−EPR experiments (see Supporting Information). The dashed line represents the diffusion limit as estimated via the separately measured viscosities, η, which are associated with an activation energy of fluidity: EA(η−1) = 17 ± 1 kJ mol−1.

Figure 7. Arrhenius plot of the rate coefficient for MCR propagation, kpt, of 20 wt % TMAEA in D2O between 0 and 90 °C.

The activation energy of kpt for 20 wt % TMAEA, EA(kpt) = 26 ± 2 kJ mol−1, is slightly below the one for BA in toluene solution and for the one of AAm in aqueous solution, whereas the pre-exponential factor, A(kpt) = (6.8 ± 2.0) × 104 L mol−1 s−1, is by more than 1 order of magnitude below A(kpt) of the nonionized monomers BA and AAm (Table 2). That the activation energy for propagation of ionized monomers is below the one of corresponding nonionized monomers has already been recognized upon comparison of the propagation rate of fully ionized sodium methacrylate with kp of nonionized methacrylates.42 This effect has been assigned to a lowering of ion-pair formation toward higher temperature, which reduces

of chain length unity, ktss(1,1) and ktst(1,1), which were deduced from simultaneous PREDICI fitting of the experimental SP−PLP−EPR traces for SPRs and MCRs with the composite-model parameters αs, αl, and ic being adopted from the methylated analogue, TMAEMA.26 The temperature dependence associated with the Arrhenius fits in Figure 8 is given by the relations: k t ss(1,1)/(L mol−1 s−1) = 2.6 × 108 exp(− 998(T −1/K−1)) (for 20 wt % TMAEA in aq solution) k t st(1,1)/(L mol−1 s−1) = 3.8 × 107 exp(− 1276(T −1/K−1)) (for 20 wt % TMAEA in aq solution)

Table 2. Comparison of the Rate Coefficients for MCR Propagation, kpt, at 50 °C, and of the Arrhenius Parameters for kpt of TMAEA, BA, and AAm (in Different Solvent Environments) kpt TMAEA (20 wt % /D2O) AAm (10 wt %, 20 wt %/H2O) BA (1.5 M/ toluene)

EA(kpt)/ kJ mol−1

A(kpt)/106 s−1

kpt (50 °C)/ L mol−1 s−1

26 ± 2

0.068 ± 0.02

4

30 ± 2

1.4 ± 0.2

20

present study 10

28 ± 2

0.9 ± 0.2

25

9

The activation energies, EA(ktss(1,1)) = 8.3 ± 0.9 kJ mol−1 and EA(ktst(1,1)) = 10.6 ± 0.8 kJ mol−1, respectively, are close to each other but are significantly below the measured activation energy of fluidity for 20 wt % TMAEA in D2O: EA(η−1) = 17 ± 1 kJ mol−1. The latter value was used for estimating the diffusion limiting behavior illustrated in Figure 8. As with NaMAA, the small activation energies, EA(kt), may be assigned to counterion mediated termination.25 Toward higher temperature, counterion condensation and thus complexation become weaker, which lowers the termination rate for two equally charged radicals and results in EA(ktss(1,1)) and EA(ktst(1,1))

ref

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Macromolecules being below the activation energy of fluidity, EA(η−1). As a consequence, the empirical relation kt(1,1)η = constant breaks down, which holds for the entire set of nonionized monomers/ radicals studied so far. The termination process with ionized monomers thus differs in that the diffusion control in the Smoluchowski sense of encounter control is not applicable.25,45,46 The absolute values of kt(1,1) are well below the diffusion limiting values estimated from eq 4 due to the shielding of radical functionality by electrostatic repulsion. Within the temperature range under investigation, the ratio of SPR-MCR cross-termination to SPR homotermination rate coefficients is found to be ktst(1,1)/ktss(1,1) = 0.06 ± 0.02 for 20 wt % TMAEA in aqueous solution at 50 °C. This ratio is by a factor of about 3.6 and 10 below the associated numbers for AAm polymerization in aqueous solution (ktst(1,1)/ktss(1,1) = 0.22 ± 0.05) and for BA polymerization in toluene (ktst(1,1)/ ktss(1,1) = 0.6 ± 0.04), respectively.9,10 The above-mentioned ratios of ktst(1,1)/ktss(1,1) indicate that ionization lowers ktst(1,1) to a larger extent than ktss(1,1), which is most likely due to the fact that the approach of an SPR experiences the repulsive action of two (identical) charges sitting on either side of the midchain radical functionality. Table 3 demonstrates that the ktss(1,1) values for fully ionized monomers are by 1−2 orders of magnitude below

varies with temperature for NaMAA and TMAEA according to EA(kt(1,1)) < EA(η−1). k t(1,1) =

TMAEA (20 wt % in D2O) TMAEMA (20 wt % in D2O) NaMAA (10 wt % in H2O) NaMAA (5 wt % in H2O) AAm (10 wt % in H2O) sty (bulk) VAc (bulk) MMA (bulk) BA (1.5 M in toluene)

ktss(1,1)/107 L mol−1 s−1 1.3 1.2 3.1 1.0 63 69 123 90 62

(5)

The expression for f associated with ktss(1,1) of 20 wt % TMAEA in D2O reads ln(f ) = 8.7 − 1345(T −1/K−1)

for k t ss(1,1)

The numbers for f (Table 4) are not affected by differences in initial viscosity. They highlight the massive deviations from Table 4. Comparison of Microfriction, f, According to Eq 5, for Fully Ionized SPRs of NaMAA and TMAEA in Aqueous Solution at 60 °Ca f NaMAA (5 wt %/H2O) NaMAA (10 wt %/H2O) TMAEA (20 wt %/D2O) AAm (10 wt %/H2O)

170 45.8 105 2.5

a

The situation with nonionized monomer is represented by the entry for 10 wt % AAm.

encounter control (eq 4) in the case of charged species. Microfriction in aqueous solution is enhanced along the series: f (10 wt % NaMAA) < f (20 wt % TMAEA) < f (5 wt % NaMAA). Since the polymerizations of 20 wt % TMAEA and of 10 wt % NaMAA refer to almost the same molar concentration, the direct comparison of f indicates that the longer side chain with TMAEA radicals may provide additional hindrance for termination. The difference may however also be due to retardation of two cationic species following other trends than anion−anion repulsion. The comparison of f for the two NaMAA concentrations listed in Table 4 is most likely due to countercation condensation being weaker at 5 wt %, resulting in a smaller termination rate coefficient and thus in higher f at the lower NaMAA concentration.25 As found for ktss(1,1), also ktst(1,1) for 20 wt % TMAEA in aqueous solution (Table 5) is by 1−2 orders of magnitude

Table 3. Comparison of Homotermination Rate Coefficients, ktss(1,1), for Several Monomers in Organic and in Aqueous Solution at 60 °Ca 60 °C

RT 1 3η f

ref present study 26 25 25 10 2 3 23 9

a

The empty row separates the ionized systems from the nonionized ones.

Table 5. Comparison of Cross-Termination Rate Coefficients, ktst(1,1), for Ionized TMAEA and Nonionized BA and AAm at 50 °C

ktss(1,1) for nonionized monomers in organic and aqueous solution which highlights the significant impact of ionization on termination rate and indicates low termination to be a characteristic feature of polymerization with ionized monomers. The ktss(1,1) values for fully ionized monomers are by 1−2 orders of magnitude below ktss(1,1) for nonionized monomers in organic and aqueous solution, as is shown by the entries in Table 3. To afford for a comparison of kt values in the low conversion region, but with different initial viscosities at zero conversion, the Smoluchowski−Stokes−Einstein relation for kt(1,1) has been modified by using the quantity f, which has been referred to as microfriction in ref 47 and has been applied in ref 48 without however explicitly mentioning the term microfriction. The so-obtained eq 5 captures the deviation of the experimental kt(1,1) from the encounter-controlled diffusion limiting value given by the Smoluchowski expression (eq 4). The limiting case of f = 1 refers to spherical radicals which react upon each (statistical) encounter. For nonionized but sterically “hindered” species, f clearly exceeds unity but remains independent of temperature, whereas f is large and

60 °C

ktst(1,1)/107 L mol−1 s−1

ref

TMAEA (20 wt %/D2O) AAm (10 wt %/H2O) AAm (20 wt %/H2O) BA (1.5 M/toluene)

0.082 14 9 3.8

this paper 10 10 9

below the associated numbers for AAm and BA polymerization. This result supports the neglect of MCR homotermination in the aqueous-solution polymerization of 20 wt % TMAEA. The rate coefficients measured at 20 wt % TMAEA allow for estimating the molar MCR fractions via eq 6.49 The so-obtained data (red line in Figure 9) is in full agreement with the xMCR data deduced from stationary experiments (Figure 3). For the estimates via eq 6, the rate coefficient of cross-termination, ⟨ktst⟩, has been implemented as a chain-length-averaged quantity. The mean value, ⟨ktst⟩, was estimated on the basis of the composite-model parameters for ktss(1,1) and an average chain length of i = 1000. The SPR concentration, cSPR, was F


Article

Macromolecules

the values obtained for kps are considered to be accurate only within a factor of 2. Monomer conversion induced by a single laser pulse is significantly higher than with other systems, which is due to kt being very low, whereas typical photoinitiator and thus primary radical concentrations have been used. The high conversion per pulse is favorable in that the rate coefficient kps may be determined with better accuracy. The decay of monomer concentration during the single pulse experiment is taken into account by using PREDICI for data treatment. A reduction of photoinitiator concentration would provide access to rate coefficients for narrower initial conversion ranges, but on the expense of a lower signal-to-noise quality of the radical concentration vs time profiles and thus of the deduced rate coefficients. Moreover, the assumption of kt(1,1) staying constant across 50% monomer conversion appears to be a reasonable one. Assuming rate coefficients such as kp and kt(1,1) to be insensitive toward monomer conversion is supported by recent investigations into fully ionized monomers which strongly suggest that the counterion concentration primarily matters. This quantity does not change during polymerization up to high degrees of monomer conversion.12,25,27 The values for kps of 20 wt % TMAEA are represented by the Arrhenius plot in Figure 10 and by the following equation:

Figure 9. Comparison of molar fractions of midchain radicals, xMCR. The individual data points (star symbols) were deduced from fitting of the experimental EPR spectra, whereas the full line was estimated via eq 6 on the basis of the rate coefficients deduced from the SP−PLP− EPR experiments on 20 wt % TMAEA in aqueous solution between 0 and 95 °C.

adopted to be 1.5 × 10−3 mol L−1, which value has been measured for 50 °C. xMCR =

k bb +

k bb + ⟨k tst⟩cSPR

k ptc M

(6)

The satisfying agreement of experimental and estimated numbers in Figure 9 demonstrates the quality of the data obtained by the two independent experimental methods. The comparison in Table 6 of the rate coefficients which determine the fraction of MCRs, xMCR, reveals that the low

k ps/(L mol−1 s−1) = 1.7 × 106 exp(− 1239(T −1/K−1)) (for 20 wt % TMAEA in aq solution)

Table 6. Comparison of the Rate Coefficients for Backbiting, kbb, for MCR Propagation, kpt, and for SPR-MCR CrossTermination, ktst(1,1), at 50 °C of TMAEA, AAm, and BA in Aqueous and in Organic Solution 50 °C

kbb/ s−1

kpt/ L mol−1 s−1

ktst(1,1)/ 108 L mol−1 s−1

TMAEA (20 wt % /D2O) AAm (10 wt % /H2O) BA (1.5 M/toluene)

98 44 394

4.2 22 25

0.007 1.2 3.6

numbers for kpt and in particular for ktst(1,1) are responsible for the high xMCR with TMAEA. The higher xMCR for BA compared to AAm results from the higher backbiting rate. The numbers for the monomer-to-polymer conversion, X, measured after applying a single laser pulse, are listed in Table 7. These values were implemented into PREDICI for

Figure 10. Arrhenius fit of the propagation rate coefficient for chainend TMAEA radicals, kps, at 20 wt % monomer for temperatures from 0 to 90 °C.

The Arrhenius correlation yields kps = 42 500 L mol−1 s−1 for 60 °C, which is by about a factor of 12 above kps = 3500 L mol−1 s−1, the number for TMAEMA at otherwise identical conditions. Differences of about the same size have been measured for associated acrylates and methacrylates as well as for nonionized methacrylic acid and acrylic acid, where the two kps differ by a factor of 13 at 5 wt % and 60 °C. The activation energy of kps, EA(kps) = 10.3 kJ mol−1, is slightly below the one of nonionized species, e.g., acrylic acid,50 acrylamide,51 or methacrylic acid52 in aqueous solution, but is very similar to the numbers measured for ionized systems such as sodium methacrylate42 and sulfobetaines.53 This similarity suggests that the novel procedure outlined in more detail in the Supporting Information provides reasonable kps. The rate coefficients obtained exclusively via the SP−PLP− EPR technique, with the additional measurement only of monomer conversion brought upon by applying a single laser pulse, comprises termination, transfer, and propagation kinetics. To check for the reliability of this data set, chemically initiated

Table 7. Measured Fractional Monomer-to-Polymer Conversion, X, and Rate Coefficients for SPR Propagation, kps, for 20 wt % TMAEA in D2O Resulting from PREDICI Fitting (See Text) ϑ/°C 0 20 50 90

kps/104 L mol−1 s−1

X 0.42 0.44 0.51 0.60

± ± ± ±

0.05 0.07 0.04 0.02

1.8 2.5 3.7 5.7

± ± ± ±

0.4 0.3 0.2 0.3

estimating kps as the only remaining unknown (see Supporting Information). It has been carefully checked by EPR spectroscopy that the radical concentration has completely decayed prior to the measurement of X. The procedure yields kps via iterative fitting. As the experimental uncertainties of the individual rate coefficient measurements accumulate in kps, G


Macromolecules

■

polymerizations have been carried out for 20 wt % TMAEA in aqueous solution (Figure 11).27 The measured conversion vs

Article

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.

■

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

■ Figure 11. Comparison of experimental and simulated fractional monomer conversion, X, vs time traces for chemically initiated TMAEA (20 wt % in D2O) polymerization at 50 °C with VA-086 (2.9 mmol L−1), acting as the thermal initiator. The simulation is based on the kinetic scheme in Table S1 (see Supporting Information) with the rate coefficients taken from the SP−PLP−EPR experiment presented above. The experimental data were taken from ref 27.

time trace at 70 °C is compared to the data simulated via PREDICI on the basis of the rate coefficients deduced from the SP−PLP−EPR experiments on both radical species (see Supporting Information). The rate coefficient of initiator decomposition, kd, and the initiator efficiency, f *, for the chemical initiator VA-86 were taken from literature with f * being assumed to be independent of monomer conversion.54,55 Figure 11 shows the favorable comparison of experiment and simulation, which demonstrates the quality of the measured rate coefficients.

■

CONCLUSION The SP−PLP−EPR technique allows for the detailed and comprehensive study of the relevant rate coefficients for radical polymerization of 20 wt % TMAEA in aqueous solution at temperatures up to 90 °C. The enormous complexity of this system arises from water being the solvent, from the occurrence of two types of radicals, and from the reacting species being strong electrolytes. Rate coefficients were deduced for backbiting, for propagation of tertiary midchain and secondary propagating radicals, and for termination, in particular for the composite-model parameter, kt(1,1), referring to the termination of two radicals both of chain length unity. The termination rate coefficient of the fully ionized radicals differs largely from the situation with nonionized radicals both in absolute value and in the dependence on temperature. The SP−PLP−EPR technique, which allows for an extended kinetic analysis without any additional time-dependent experiment being required, should be applicable toward the detailed study into a wide range of monomers, including complicated systems.

■

REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.7b00328. Figures S1−S3 and Tables S1, S2 (PDF) H


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