Investigation of Free-Radical Copolymerization Propagation Kinetics

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J. Phys. Chem. B 2010, 114, 4213–4222

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Investigation of Free-Radical Copolymerization Propagation Kinetics of Vinyl Acetate and Methyl Methacrylate Marco Dossi,† Kun Liang,‡ Robin A. Hutchinson,‡ and Davide Moscatelli*,† Dipartimento di Chimica, Materiali e Ingegneria Chimica “Giulio Natta”, Politecnico di Milano, 20131 Milano, Italy, and Department of Chemical Engineering, Dupuis Hall, Queen’s UniVersity, Kingston, Ontario K7L 3N6, Canada ReceiVed: January 26, 2010; ReVised Manuscript ReceiVed: February 22, 2010

The free-radical copolymerization propagation kinetics of vinyl acetate (VAc) and methyl methacrylate (MMA) at 50 °C were investigated through an experimental study combined with a computational analysis based on quantum chemistry. Copolymer composition data, obtained using pulsed laser polymerization followed by size exclusion chromatography (PLP-SEC) and proton nuclear magnetic resonance (NMR), were well represented by the terminal model using monomer reactivity ratios obtained with the computational approach (rVAc ) 0.001 and rMMA ) 27.9). Concerning the composition-averaged copolymerization propagation rate coefficient kp,cop, the differences between the terminal model and the implicit penultimate unit effect (IPUE) model (sMMA ) 0.544 and sVAc ) 0.173) are small for VAc/MMA, with the terminal model sufficient to describe the experimental kp,cop data measured by PLP-SEC. Monomer and radical charge distributions determined computationally are used to explain the reactivity exhibited by the VAc/MMA system. Introduction

(

kp [L · mol-1 · s-1] ) 107.16 exp -

It is well-known that pulsed laser polymerization combined with size exclusion chromatography (PLP-SEC) represents the most recommended and modern technique to provide reliable and accurate information about the kinetics of polymerization reactions.1-7 Unfortunately, contrary to styrene and methacrylate systems, vinyl esters have proven to be difficult systems to study with this technique. Vinyl acetate (VAc) is an important industrial monomer used to produce homo- and copolymers with a wide range of applications, primarily in the field of adhesives or paints. Thus, better knowledge of its polymerization kinetics is required to aid in process and product development. The difficulties in measuring propagation rate coefficients (kp) for VAc homopolymerization by PLP-SEC have been previously explored in literature. In our previous work8 a mathematical model was developed to gain a better understanding about the relative importance of propagation, termination, and transfer events on the laser generated molecular weight distributions (MWDs) for VAc laser induced polymerizations. This study led to the conclusion that, under typical PLP experimental conditions, an insufficient fraction of radicals survive in the time between two pulses in succession, because the termination rate is very fast, as later shown in a full study of VAc termination kinetics.9 As a consequence, successful PLP experiments on VAc require low photoinitiator concentrations and/or high repetition rates.10,11 A subsequent study conducted with a 100 Hz laser proposed the following Arrhenius relationship to describe VAc homopolymerization kinetics.10 * Corresponding author. E-mail: [email protected]. † Politecnico di Milano. ‡ Queen’s University.

20.7 [kJ · mol-1] RT

)

(1)

This estimate was in reasonable agreement with previous estimates obtained with different techniques.12,13 More recently, the system has been studied via PLP-SEC with a 500 Hz laser setup.11 While the reported activation energy is in reasonable agreement, the absolute kp values were found to be as much as 50% higher. Further experimentation is required to resolve this discrepancy. In this study, we focus on the copolymerization behavior of vinyl acetate. Dating back to the 1940s, Mayo et al. investigated the copolymerization of vinyl acetate with eight representative monomers and found that vinyl acetate is one of the least reactive of any common monomers toward free radical attack.14 Later the Q-e scheme proposed by Price and Alfrey15 was used to investigate the relative reactivity of VAc radical and monomer with other compounds.16 In particular, Nikolayev et al.17 studied the copolymerization of VAc and butyl acrylate (BA) in bulk and in solution, clearly showing that VAc radicals are extremely reactive toward other vinyl compounds compared to its own less active monomer. The same findings were more recently confirmed and extended by Dube´ and Penlidis, who report monomer reactivity ratios of rBA ) 5.9 and rVAc ) 0.026 for the VAc/BA system.18 These values are in reasonable agreement with ratios estimated by Kulkarni et al.19 for bulk copolymerization of methyl acrylate (MA) with VAc at 60 °C (rMA ) 6.3 ( 0.4 and rVAc ) 0.031 ( 0.006) and other VAc/MA studies.20,21 Though it is well-known that uncertainties in the values of reactivity ratios are large when the two values are very different,22 other works concerning the reactivity of VAc with butyl methacrylate (BMA)23 and VAc with ethyl methacrylate (EMA)24 found that the difference between the two reactivity ratios is even larger for VAc/methacrylate systems than for VAc/ acrylate copolymerization.

10.1021/jp1007686  2010 American Chemical Society Published on Web 03/05/2010

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Focusing the attention on the VAc/MMA system, in 1993 Ma et al.12 performed a bulk copolymerization study of VAc and MMA at 40 °C using the rotating sector method and determining the compositions of VAc/MMA copolymers through 1 H NMR. According to this work the composition curve conformed with the terminal model25 (rMMA ) 27.8 and rVAc ) 0.014), even if a moderate penultimate-unit effect was observed in conformity to the prediction of the implicit penultimate-unit effect IPUE model.26 In the same year Brar and Charan27 also used 1H NMR spectroscopy to study VAc/MMA copolymerization in benzene at 60 °C, reporting reactivity ratios in general agreement with those of Ma et al. Most recently, Scorah et al.28 performed a series of batch, bulk, and solution (in toluene) copolymerizations of VAc and MMA under various reaction conditions to high monomer conversions as well as low conversion bulk experiments to estimate monomer reactivity ratios. A combination of the low and high conversion data with results from previous studies yielded reactivity ratio estimates of rMMA ) 27.5 and rVAc ) 0.0102. These various estimates for VAc/MMA monomer reactivity ratios are in remarkable agreement, considering the difficulty in studying a system with such disparate relative reactivities. However, the copolymerization propagation kinetics of the system has not yet been studied using the PLP-SEC technique, to verify the mild penultimate unit effect reported by Ma et al.12 from rotating sector experimentation. Thus, the aim of the study is to clarify which model (terminal or IPUE) better describes the VAc/MMA system and to analyze and explain the VAc monomer and radical reactivity in this copolymerization process. Moreover, a computational study based on quantum mechanics is done in parallel with the experimental activity to support and enrich the findings pointed out in the work. Ab initio methods utilized to study free radical polymerizations,29-32 have been recently applied to study acrylate and methacrylate systems with good success,33-35 and the density functional theory (DFT) techniques have also been used to investigate copolymerization reactions.36,37 In this work the computational approach is extended to the study of a vinyl ester compound (VAc) and to the analysis of its reactivity in the copolymerization with MMA. Experimental Section MMA (99% purity, containing 10-100 ppm monomethyl ether hydroquinone as inhibitor), VAc (99% purity, containing 3-20 ppm hydroquinone as inhibitor), photoinitiator DMPA (2,2-dimethoxy-2-phenylacetophenone, 99% purity), and chloroform-d (containing 99.9 atom % D) were all obtained from Sigma Aldrich and used as received. Low conversion polymerizations were conducted in a pulsed laser setup consisting of a Spectra-Physics Quanta-Ray 100 Hz Nd:YAG laser that is capable of producing a 355 nm laser pulse of duration 7-10 ns and energy of 1-50 mJ per pulse. The laser beam is reflected twice (180°) to shine into a Hellma QS165 0.8 mL jacketed optical sample cell used as the PLP reactor. A digital delay generator (DDG, Stanford Instruments) is used to regulate the pulse output repetition rate at a value between 10 and 100 Hz. Monomer mixtures in solvents with about 5 mmol · L-1 DMPA photoinitiator were added to the cylindrical quartz cell and exposed to laser energy, with temperature controlled by a circulating oil bath. Experiments were run at 40 and 50 °C, with the MMA fraction in the monomer mixture varied between 0 and 100%. Most work was done at 50 °C, with some experiments conducted at 40 °C to allow direct comparison to the rotating sector data of Ma et al.12 Monomer conversions

Dossi et al. were kept below 5% to avoid significant composition drift. The polymers produced by PLP were also used for composition analysis by proton NMR, using procedures described previously.12 Polymers produced by PLP were used to determine kp,cop from analysis of polymer molecular weight distributions (MWDs) measured by SEC. The resulting samples of low concentration of VAc from PLP were precipitated in methanol, while the samples of high content of VAc were precipitated in hexane. The detailed precipitation and drying procedures are reported in a previous work.37 Molecular weight distributions were measured with a Waters 2960 separation module connected to a Waters 410 differential refractometer (DRI) and a Wyatt Instruments Dawn EOS 690 nm laser photometer multiangle light scattering (LS) detector. Tethahydrofuran (THF) was used to carry polymers at a flow rate of 1 mL · min-1 through the four Styragel columns (HR 0.5, 1, 3, 4) maintained at 35 °C. The DRI detector was calibrated by 10 molecular weight polystyrene standards with narrow polydispersities (870-355 000 Da), and the LS detector was calibrated by toluene, as recommended by the manufacturer. MW results were converted to absolute values for MMA/VAc copolymers using the principle of universal calibration for data from the DRI detector and polymer refractive indices for data from the LS detector, as detailed later. Computational Details Density functional theory (DFT) was adopted to study the VAc/MMA system through a theoretical approach in parallel with the experimental activity. In particular, the Becke 3 parameter and Lee-Yang-Parr functional (B3LYP) were adopted in the DFT calculations to evaluate exchange and correlation energy.38,39 All quantum chemical calculations of radicals were performed with a spin multiplicity of 2 and using an unrestricted wave function to avoid spin contamination (UB3LYP). The triple ζ all electron 6-311 basis set with added polarization and diffuse functions (6-311+G(d,p))40 was used as the basis set. Even if this method is less accurate in the prediction of the electronic energies than other new different hybrid density functionals,33,34,41 it is generally accepted that B3LYP methods provide excellent low-cost performance, especially concerning the structure optimizations and frequency calculations.29,42-44 Moreover, successful results were recently obtained by applying this functional to the study of copolymeric systems.37 All geometries were fully optimized with the Berny algorithm and were followed by frequency calculations. The geometry of each molecular structure was considered stable only after vibrational frequencies and force constants were calculated and if no imaginary vibrational frequencies were found. Transition state structures were located by adopting the synchronous transitguided quasi Newton method and were characterized by a single imaginary vibrational frequency.45 In the evaluation of reactivity ratios, the kinetic rate coefficients were determined by adopting the conventional transition state theory (TST) according to eq 2.

k(T) ) A · e-Ea/kbT )

k bT · h

rot vib el q* q* q*

∏

rot vib el

· e-Ea/kbT

q q q

reactants

(2) In particular kb is the Boltzmann constant, h is the Plank constant, T is the temperature, Ea indicates the activation energy

Kinetics of Vinyl Acetate and Methyl Methacrylate

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Figure 1. Copolymer composition data for low-conversion vinyl acetate/methyl methacrylate bulk copolymerization at 50 °C ([), plotting mole fraction MMA in copolymer (F1) as a function of MMA mole fraction in the monomer phase (f1). The dashed curve is the prediction of the terminal copolymerization model with the monomer reactivity ratio determined with the computational approach. The solid curve is the prediction of the terminal copolymerization model with literature12 monomer reactivity ratios rMMA ) 27.8 and rVAc ) 0.014. rot el vib rot el of the reactive step investigated. qvib * , q* , q* and q , q , q are the vibrational, rotational, and electronic partition functions, respectively, for the transition state and reactants. The partition functions are constructed using the independent harmonic-oscillator (HO) approximation. Analyzing the low vibrational modes of the molecules, it is possible to identify some motions that correspond to internal rotations. The importance of considering the low vibrational frequencies as internal rotations is well documented in the literature and represents an improvement in the computational accuracy.34,44,46-48 Despite this, simulations have been performed without considering the low vibrational frequencies as internal rotations. The approximation adopted can be considered satisfactory for reasonable order of magnitude estimates of the rate coefficients and to obtain realistic information about the relative reactivity of a system, as previously discussed in the literature.37,49 All quantum chemistry calculations were performed with the Gaussian 03 suite of programs and all structures drawn with PyMol 1.3.50,51

Results and Discussion Monomer Reactivity Ratio. Low conversion PLP experiments were carried out at 40 and 50 °C on VAc/MMA samples, with the resulting polymer compositions determined by proton NMR. The full set of experimental conditions and results is summarized in Table S1 in the Supporting Information. A plot of MMA mole fraction in the copolymer (F1) as a function of MMA mole fraction in the monomer phase (f1) is reported in Figure 1. Monomer mixtures contained at least 10 mol % MMA in this PLP study; thus these new results have been combined with the experimental data reported in previous studies.12,27,28 The solid line in Figure 1 is the prediction of the Mayo-Lewis terminal copolymerization model (eq 3)25 calculated using literature monomer reactivity ratios, r1 ) 27.8 and r2 ) 0.014,12

f1 )

r1 f12 + f1 f2 r1 f12 + 2f1 f2 + r2 f22

(3)

where r1 ) kp11/kp12, r2 ) kp22/kp21, and kpij is the propagation rate coefficient for addition of monomer-j to radical-i.

TABLE 1: Arrhenius Parameters for the Determination of Monomer Reactivity Ratios in Methyl Methacrylate (1)/ Vinyl Acetate (2) Copolymerizations Theoretically Determineda data

kp11

kp12

kp22

kp21

log10(Ap) Ep

7.49 8.76

7.49 10.90

7.35 6.64

8.24 3.48

a Activation energies in kcal · mol-1, Ap in L · mol-1 · s-1. kpij ) Ap exp(-Ep/RT). Ep is considered independent of temperature while Ap is calculated at 50 °C.

The dashed curve in Figure 1 is the prediction of the Mayo-Lewis terminal copolymerization model with monomer reactivity ratio determined with the computational approach, r1 ) 27.9 and r2 ) 0.001; the Arrhenius parameters for the monomer reactivity ratios theoretically determined are summarized in Table 1. As in past studies,37,52 monomeric radicals were adopted in the computational simulations, disregarding as a first approximation any chain length effect on radical selectivity. Complete information regarding optimized molecular structures of reactants, products, and transition states involved in the reactions is available as Table S2 in the Supporting Information. The shape of the composition curve is conditioned by the monomer reactivity ratio values and in particular is related to the low reactivity of VAc monomer in comparison with MMA monomer. An extensive study about the charge distributions on these molecules was done to explore these reactivity differences, as presented later. The prediction of the terminal copolymerization model with the monomer reactivity ratios determined with the computational approach, reproduces with good confidence the experimental results, especially for f1 > 0.1. In particular, the values of r1 obtained with DFT are in perfect agreement with the value proposed in the literature,12,27 while the computational r2 value of 0.001 differs from the value of 0.014 proposed by Ma et al. This discrepancy, mainly due to an underestimation of k22, results in a higher initial slope for the low f1 region (f1 < 0.1), even if the general shape of the composition curve is not substantially influenced. The effect of temperature on the monomer reactivity ratio values was also considered. The computational results show an

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TABLE 2: Parameters for Calculation of kp,cop from SEC Analysis of PLP-Generated Copolymer Samples of Vinyl Acetate (VAc) with Methyl Methacrylate (MMA)8,10 Mark-Houwink parameters monomer

density F (g · mL-1)

dn/dc (mL · g-1)

K (dL · g-1) × 10-4

a

VAc MMA

0.9584-0.0013276T/°C 0.9569-0.001219T/°C

0.058 0.089

2.24 2.39

0.674 0.537

absence of changes in r2 values for temperatures between 20 and 50 °C. On the contrary, r1 decreases noticeably in the same temperature range, moving from 39 to 27. This evidence must be confirmed by experimental work. Copolymerization Propagation Kinetics. The application of the PLP-SEC technique to study the propagation kinetics in copolymerization systems is demonstrated in the literature37,53-56 but has not yet been applied to copolymer systems with VAc. The copolymer-averaged propagation rate coefficient kp,cop can be deduced from eq 4, knowing the total monomer concentration [M] and the flash interval t0. L0 represents the length of dead chains initiated by a laser flash that propagate, survive the dark period between two pulses, and terminate with the next flash.

L0 ) kp,cop[M]t0

(4)

In particular, if well-structured MWDs are formed, kp,cop values can be calculated from the first inflection point of the MWD according to eq 5, where MW0 is the polymer molecular weight at the first inflection point and F (g · mL-1) is the density of monomer mixture calculated assuming volume additivity.

kp,cop (L · mol

-1

MW0 ·s )) 1000Ft0 -1

mental kp,cop value measured with f1 ) 0.1 is about 150 L · mol-1 · s-1, more than 40 times lower than the VAc homopolymer value, and then increases linearly with increasing f1 to the MMA homopolymer rate coefficient value. The same general behavior is observable at 40 °C (Figure 3a), although there is a discrepancy as much as 50% between the current PLPSEC study and the earlier rotating sector results.12 Despite this difference, which can be attributed to the assumptions required to analyze rotating sector data,4,12 both techniques clearly capture the inhibitory effect of adding MMA to a VAc system. This kp,cop behavior combines with the unequal monomer reactivity ratios to give interesting dynamics in a batch MMA/VAc copolymerization taken to high conversion, as shown by Scorah et al.;28 MMA-rich copolymer is produced at a moderate rate until the MMA is largely depleted from the monomer phase, at which point the production of what is essentially VAc homopolymer occurs at a much higher reaction rate. To define which model, terminal25 or penultimate,26 is able to better describe the behavior of the VAc/MMA copolymer system, the curves reproducing the two models are plotted in the same Figure 3. The curve standing for the terminal model is obtained by plotting eq 6 and the curve standing for the penultimate model (implicit penultimate unit effect, IPUE)26 is obtained by plotting eq 7.

kp,cop )

kp,cop

(5)

The parameters necessary to estimate kp,cop from SEC data are summarized in Table 2, with monomer densities calculated as a function of temperature, the refractive index (dn/dc) values required for interpretation of LS results, and Mark-Houwink parameters required to analyze the output from the RI detector. The copolymer MW is calculated as a composition-weighted average of the homopolymer values, as done previously.37 A systematic PLP-SEC study with experiments at 40 and 50 °C, and pulse repetition rates of 33 and 20 Hz, was carried out. Complete experimental conditions and results are summarized in Table S1 in the Supporting Information. Figure 2 shows a plot of copolymer MWDs measured by the two detectors for comonomer mixtures of varying composition pulsed at 50 °C with a laser repetition rate of 33 Hz, and the corresponding firstderivative plots used to identify inflection points. The MWDs shift to the left and the corresponding MW0 values decrease as the mole fraction of MMA in the comonomer mixture decreases from 1.0 to 0.1. The kp,cop data obtained with PLP-SEC are plotted at 40 and 50 °C in Figure 3a,b, respectively, as a function of MMA composition in the monomer phase (f1). The agreement between experiments run at 20 and 33 Hz at 50 °C (Figure 3b) is good over the entire composition range, while the kp,cop values estimated from LS and RI detectors shows some minor discrepancy ( kVAc-VAc > kMMA-MMA > kMMA-VAc. The difference in reactivity is reflected by the transition state geometry for each radicalmonomer reaction, shown in Figure 4. The distance d between the two carbon atoms involved in the reaction decreases in the same order as the corresponding rate coefficients: dVAc-MMA > dVAc-VAc > dMMA-MMA > dMMA-VAc. Generally speaking, a greater distance d indicates higher reactivity, as radical and monomer are able to react requiring less energy to approach each other. To explain these differences in reactivity, it is possible to analyze the chemical structures of monomers and radicals

J. Phys. Chem. B, Vol. 114, No. 12, 2010 4219 considered. The resonance structures of MMA and VAc monomers are reported in Figure 5. Considering the MMA monomer (Figure 5a), the presence of the electron attractor carbonyl group, bound to carbon atom 2, leads to the formation of a positive charge on the carbon atom 1 in the limit resonance structure. In contrast, for the VAc monomer (Figure 5b), the oxygen atom, bound to the carbon atom 2′, leads to the formation of a negative charge on the carbon atom 1′. According to this, a generic radical can attack the double bond on MMA monomer easier than the double bond on VAc monomer, and for this reason the MMA monomer is more reactive. To support these theoretical considerations, simulations were performed to determine the charge of each atom in the monomer and radical molecules. The procedure adopted is called restrained electrostatic potential (RESP), and it is usually applied for the determination of charges in molecular dynamics (MD). Following this procedure the electrostatic potentials were calculated at the B3LYP/6-311+g(d,p) level, and charges were fit using the RESP formalism. ESP values were determined on a grid of 1 point/Å2 at 1.4, 1.6, 1.8, and 2.0 times the van der Waals radii and then fit through a two-step procedure to atomic charges.61 The charge distributions for VAc and MMA monomer are collected in Table 5. As expected, the negative charge on the carbon atom C(1) of MMA monomer is lower than the negative charge on carbon atom C(1) of VAc monomer, consistent with its higher reactivity. Finally, another supplementary observation to explain the differences in the reactivity showed by MMA and VAc can be made by taking into consideration the IR spectra obtained from

TABLE 5: Charge Distributions for VAc Monomer and MMA Monomer

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Figure 6. Simulated IR spectra for (a) vinyl acetate and (b) methyl methacrylate. The frequencies of the carbonyl group are pointed out.

TABLE 6: Charge Distribution for VAc Radical and MMA Radical

the quantum mechanics simulations and in particular pointing out the frequencies of the carbonyl group for each monomer (Figure 6). In the literature, it has been reported that the differences in reactivity between different compounds can be correlated to a shift in the carbonyl IR peak. In particular, a shift to a lower wavelength can indicate an higher reactivity.37,56,62,63 Even in this case, it is possible to point out for the carbonyl IR peak a substantial shift (10 cm-1) to a lower wavelength in favor of MMA monomer. As for the monomers, the reactivity of MMA and VAc monomeric radicals can also be studied starting from the molecular structures reported in Figure 7. The carbonyl group is an electron attractor substituent and, because of its presence, the radical on the carbon atom 1 belonged to MMA (Figure

7a) is partially impoverished. On the contrary in the VAc monomeric radical (Figure 7b), the electronic concentration is centralized on the carbon atom 1′, due to the presence of the oxygen atom with electron donor properties. This analysis is

Figure 7. Molecular structures of (a) MMA monomeric radical and (b) VAc monomeric radical.

Kinetics of Vinyl Acetate and Methyl Methacrylate also confirmed by the study of charge distributions on the two radicals. The data calculated using the RESP technique61 are collected in Table 6. In particular, it is observed that the influence of the carbonyl group on the carbon atom C(1) belonging to the MMA radical produces a partial positive charge, despite the presence of the two methyl groups that are electron donor substituent groups. The carbon atom C(1) on the VAc radical shows instead a negative charge due to the action of the oxygen atom directly bound. These observations explain the high reactivity of the VAc radical toward unsaturated bonds. Conclusions An experimental PLP-SEC study was combined with a computational analysis to investigate the free-radical copolymerization propagation kinetics of VAc and MMA at 50 °C. New copolymer composition data were combined with literature data and shown to be well represented by the terminal model using monomer reactivity ratios obtained by use of ab initio method based on DFT. An explanation of the highly different reactivity exhibited by VAc and MMA monomer and VAc and MMA radicals was provided through an analysis based on the computational determination of monomer and radical charge distributions. VAc/MMA composition-averaged copolymer propagation rate coefficients (kp,cop) were measured for the first time using the PLP-SEC technique. The addition of only 10 mol % MMA to VAc reduces kp,cop by more than a factor of 40 from the literature VAc homopolymer kp value, a finding in good agreement with the rotating sector data of Ma et al.12 This kinetic behavior is described reasonably well by both terminal and penultimate chain-growth models, using the monomer (rVAc ) 0.001 and rMMA ) 27.9) and radical (sVAc ) 0.173 and sMMA ) 0.544) reactivity ratios determined computationally. This agreement demonstrates that computational techniques can be used to reliably estimate relative reactivity in free-radical polymerization systems, reducing the amount of experimentation required. Supporting Information Available: Full set of experimental conditions and results for low conversion PLP experiments carried out at 40 and 50 °C. Complete information regarding optimized molecular structures of reactants, products, and transition states involved in the reactions. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Olaj, O. F.; Bitai, I.; Hinkelmann, F. Makromol. Chem. 1987, 188, 1689–1702. (2) Olaj, O. F.; Schnollbitai, I. Eur. Polym. J. 1989, 25, 635–641. (3) Buback, M.; Gilbert, R. G.; Hutchinson, R. A.; Klumpermann, B.; Kuchta, F. D.; O’Driscoll, K. F.; Russell, G. T.; Schweer, J. Macromol. Chem. Phys. 1995, 196, 3267–3280. (4) 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. Macromol. Chem. Phys. 1997, 198, 1545–1560. (5) Beuermann, S.; Buback, M.; Davis, T. P.; Gilbert, R. G.; Hutchinson, R. A.; Kajiwara, A.; Klumpermann, B.; Russell, G. T. Macromol. Chem. Phys. 2000, 201, 1355–1364. (6) Beuermann, S.; Buback, M.; Davis, T. P.; Garcia, N.; Gilbert, R. G.; Hutchinson, R. A.; Kajiwara, A.; Kamachi, M.; Lacik, I.; Russell, G. T. Macromol. Chem. Phys. 2003, 204, 1338–1350. (7) Asua, J. M.; Beuermann, S.; Buback, M.; Castignolles, P.; Charleux, B.; Gilbert, R. G.; Hutchinson, R. A.; Leiza, J. R.; Nikitin, A. N.; Vairon, J.-P.; van Herk, A. M. Macromol. Chem. Phys. 2004, 205, 2151–2160. (8) Hutchinson, R. A.; Richards, J. R.; Aronson, M. T. Macromolecules 1994, 27, 4530–4537. (9) Theis, A.; Davis, T. P.; Stenzel, M. H.; Barner-Kowollik, C. Polymer 2006, 47, 999–1010. (10) Hutchinson, R. A.; Paquet, D. A.; McMinn, J. H.; Beuermann, S.; Fuller, R. E.; Jackson, C. DECHEMA Monogr. 1995, 131, 467–492.

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