Theoretical Study of Chain Transfer to Solvent Reactions of Alkyl

Article pubs.acs.org/JPCA

Theoretical Study of Chain Transfer to Solvent Reactions of Alkyl Acrylates Nazanin Moghadam,† Sriraj Srinivasan,§ Michael C. Grady,# Andrew M. Rappe,‡ and Masoud Soroush*,† †

Department of Chemical and Biological Engineering, Drexel University, Philadelphia, Pennsylvania 19104, United States The Makineni Theoretical Laboratories, Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323, United States § Arkema Inc., 900 First Avenue, King of Prussia, Pennsylvania 19406, United States # DuPont Experimental Station, Wilmington, Delaware 19898, United States ‡

S Supporting Information *

ABSTRACT: This computational and theoretical study deals with chain transfer to solvent (CTS) reactions of methyl acrylate (MA), ethyl acrylate (EA), and n-butyl acrylate (n-BA) self-initiated homopolymerization in solvents such as butanol (polar, protic), methyl ethyl ketone (MEK) (polar, aprotic), and p-xylene (nonpolar). The results indicate that abstraction of a hydrogen atom from the methylene group next to the oxygen atom in n-butanol, from the methylene group in MEK, and from a methyl group in p-xylene by a live polymer chain are the most likely mechanisms of CTS reactions in MA, EA, and n-BA. Energy barriers and molecular geometries of reactants, products, and transition states are predicted. The sensitivity of the predictions to three hybrid functionals (B3LYP, X3LYP, and M06-2X) and three different basis sets (6-31G(d,p), 6-311G(d), and 6-311G(d,p)) is investigated. Among n-butanol, sec-butanol, and tertbutanol, tert-butanol has the highest CTS energy barrier and the lowest rate constant. Although the application of the conductorlike screening model (COSMO) does not affect the predicted CTS kinetic parameter values, the application of the polarizable continuum model (PCM) results in higher CTS energy barriers. This increase in the predicted CTS energy barriers is larger for butanol and MEK than for p-xylene. The higher rate constants of chain transfer to n-butanol reactions compared to those of chain transfer to MEK and p-xylene reactions suggest the higher CTS reactivity of n-butanol.

1. INTRODUCTION There has been continuing interest in the physical properties of poly(n-alkyl acrylates) since their first investigation by Rehberg and Fisher in the 1940s.1 Acrylates are principal monomers in the production of coatings, adhesives, and polymers, which are used in medical and pharmaceutical applications due to their transparency and resistance to breakage.2 The basic design of resins used in automobile coatings has been changed, due to environmental limitations on allowable volatile organic contents (VOCs) of resins.3 Although environmental regulations and consumer awareness have led to the production of greener acrylic resins, solution polymerization is still widely used. Production of resins with lower solvent contents and molecular weights has been achieved via high temperature (>100 °C) free-radical polymerization.4−6 It has been reported7−10 that at high temperatures, propagating free radicals undergo secondary reactions such as β-scission and chain transfer to monomer (CTM), polymer, and solvent reactions. Midchain radicals (MCRs) formed via chain transfer reactions cause the production of low molecular weight and branched polymers.11,12 A better understanding of the solvent effects in high temperature free-radical polymerization will improve process efficiency and the quality of acrylic resins. Secondary reactions (such as β-scission, CTS, and radical transfer to solvent from initiator radical) in high-temperature © XXXX American Chemical Society

polymerization of n-butyl acrylate (n-BA) have been observed using liquid chromatography-electrospray ionization-tandem mass spectrometry (LC-ESI-MS).13 In thermal polymerization of ethyl acrylate (EA), methyl acrylate (MA), and ethyl methacrylate (EMA), chain transfer to solvent rate constants for various solvents, such as hydrocarbons, alcohols, ketones, acids, and esters, have been estimated from polymer sample measurements.14,15 Moreover, the effect of solvent in homopolymerization of n-BA has been investigated.16 These experimental studies reported kp/kt0.5 values. They also indicated that as the solvent concentration increases, the rate of CTS reactions and the rate of formation of shorter chains increase, and these shorter chains terminate faster than longer chains. Although the influence of different solvent concentrations on the overall rate of polymerization (Rp) has been reported,16 investigation of solvent effects on the individual rate constants (kp and kt) is still challenging. Including chain transfer agents (CTAs) during controlled radical polymerization processes (such as nitroxides for nitroxidemediated polymerization) has enabled atom transfer radical polymerization (ATRP) and reversible addition−fragmentation Received: February 27, 2014 Revised: June 25, 2014

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dx.doi.org/10.1021/jp5020669 | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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chain transfer (RAFT).17−22 CTAs control the growth of propagating chains and lead to the formation of uniform chainlength polymers. However, self-regulation and polymers with uniform chain lengths have been observed in thermal polymerization of alkyl acrylates, in the absence of these agents.23 These observations can be attributed to the self-regulatory capability of chain transfer mechanisms. Therefore, a fundamental understanding of these capabilities can help the control, design, and optimization of thermal polymerization processes. Previous studies report polymer chains with end groups formed by chain transfer reactions using electrospray ionization-Fourier transform mass spectrometry9 and matrix-assisted laser desorption ionization mass spectrometry24 in self-initiated polymerization of MA, EA, and n-BA (100−180 °C). The presence of these end groups was confirmed using nuclear magnetic resonance analysis of the polymers.9 Chain transfer and radical propagation rate coefficients of acrylates25−27 have been determined using pulsedlaser polymerization/size exclusion chromatography at various temperatures below 30 °C,28−30 the upper limit of this approach. Although useful overall understanding of chain transfer reactions can be gained from experimental studies, the investigation of individual reaction mechanisms and reacting species is best handled with quantum chemical calculations. Polymerization reaction rate constants have been estimated in thermal polymerization of acrylates by fitting macroscopic kinetic models of polymerization reactors to experimental measurements, including initiation, propagation, termination, and chain transfer reactions.7,31,32 The reliability of this approach depends on the accuracy of the measurements and the reactor model (which is based on a set of postulated reactions). Furthermore, this approach is unable to conclusively suggest the most likely mechanism of individual reactions. Computational quantum chemistry can be applied to identify mechanisms, reacting species, energy barriers, and rate constants of polymerization reactions. Although kinetics of various polymerization reactions have been studied experimentally,27,33−40 determination of individual reaction mechanisms without taking advantage of quantum chemical calculations is not feasible. Density functional theory (DFT) and wave function based quantum chemical methods have been extensively used to explore different reaction mechanisms, such as self-initiation and propagation in thermal polymerization of alkyl acrylates.41−45 DFT is computationally less expensive and it requires less memory storage in comparison to MP2 and MCSCF approaches.46,47 Another computational advantage of DFT is the availability of parallel and linear-scaling algorithms.48,49 However, the DFT functionals are known to inaccurately predict kinetic parameters, which can be overcome by screening and benchmarking numerous pure and hybrid functionals as carried out for the propagation reactions of MA and MMA,44 self-initiation of styrene,50 MA, EA, n-BA,41,42 and MMA,43 and cyclohexanone-monomer co-initiation mechanism in thermal homopolymerization of MA and MMA.51 The geometries of the intermediate molecular species can be identified through these calculations. Previous studies have shown the most likely monomer self-initiation mechanism in spontaneous thermal polymerization of alkyl acrylates.41,42 The monoradicals generated by the self-initiation are shown in Figure 1. Despite the high accuracy of quantum chemistry for isolated molecules, there are major difficulties in dealing with transition states and molecules in different solvent environments.52 Solvents can increase the stability of transition state geometries in solution polymerization.24 Different solvent

Figure 1. Two types of monoradical generated by monomer selfinitiation.42

continuum models have been applied to explore the solvent effects on the solute.53,54 In the continuum model, solvent is treated as a dielectric continuum mean field polarized by the solute that is placed in this continuum. Although the selfconsistent reaction field method places the solute in a spherical cavity,55 the polarizable continuum model (PCM) introduces molecular shape for the cavity.56,57 PCM has been applied to predict the propagation rate coefficient of acrylic acid in the presence of toluene.54 However, microscopic structure of the solvent−solute interaction cannot be described through these models. The conductor-like screening model (COSMO), originally developed by Klamt and Schuurman,58 is another approach for polarized continuum calculations in which the surrounding medium (solvent) is assumed to be a conductor rather than a dielectric to simplify the electrostatic interactions between solvent and solute. The effect of solvents with different dielectric constants on the propagation rate coefficients in freeradical polymerization of acrylonitrile and vinyl chloride has been investigated.59 Also, COSMO has been applied to predict nonequilibrium solvation energies of biphenyl−cyclohexane− naphthalene.60 The conductor-like screening model for real solvents (COSMO-RS) is another solvation model, which was used by Klamt61 and Deglmann et at.62 to explore solvent effects on propagation reactions in free-radical polymerization and estimate rate coefficients of propagation reactions in freeradical solution polymerization of acrylates. In this work we compare performances of PCM and COSMO. Different CTM mechanisms for MA, EA, and n-BA have been explored using quantum chemical calculations.63 Bimolecular hydrogen abstraction reactions between a growing polymer chain and a monomer as well as different dead polymers, copolymers, and chain transfer agents have been explored using quantum chemical calculations.64,65 These studies showed that hydrogen abstraction from species that have a weaker electron-donor group close to the abstracted hydrogen is the most likely mechanism for hydrogen abstraction in homo- and copolymerization of n-butyl acrylate.64,65 Although the existence of CTS reactions has been known for many decades,66,67 prior to the studies,65,68 no specific CTS reaction mechanisms had been reported. A portion of results included in this paper were presented at the meeting.68 This paper presents a computational and theoretical study of CTS reactions of MA, EA, and n-BA homopolymerizations in butanol (polar, protic), methyl ethyl ketone (MEK) (polar, aprotic), and p-xylene (nonpolar). Energy barriers and molecular geometries of reactants, products, and transition states are calculated using DFT. We explore the abstraction of a hydrogen from n-butanol, MEK, and p-xylene by a live polymer chain to identify the most likely mechanisms of CTS reactions in MA, EA, and n-BA homopolymerizations. The activation energy and rate constants of CTS mechanisms are calculated using transition state theory. PCM and COSMO solvation models are B



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Figure 2. End-chain transfer to solvent reactions involving a two-monomer-unit live chain initiated by M2• shown in Figure 1. CTB = chain transfer to n-butanol, CTM = chain transfer to methyl ethyl ketone, CTX = chain transfer to p-xylene.

Table 1. H−R Bond-Dissociation Energies (kJ mol−1) at 298 K CTB1-2 CTB2-2 CTB3-2 CTB4-2 CTB5-2 CTM12 CTM2-2 CTM3-2 CTX1-2 CTX2-2

B3LYP 6-31G(d,p)

B3LYP 6-311G(d)

B3LYP 6-311G(d,p)

M06-2X 6-31G(d,p)

M06-2X 6-311G(d)

M06-2X 6-311G(d,p)

4.05 × 1002 4.27 × 1002 4.21 × 1002 4.20 × 1002 4.37 × 1002 3.89 × 1002 4.12 × 1002 4.41 × 1002 3.88 × 1002 4.67 × 1002

4.01 × 1002 4.16 × 1002 4.17 × 1002 4.16 × 1002 4.33 × 1002 3.86 × 1002 4.10 × 1002 4.36 × 1002 3.84 × 1002 4.72 × 1002

4.02 × 1002 4.34 × 1002 4.18 × 1002 4.19 × 1002 4.35 × 1002 3.90 × 1002 4.13 × 1002 4.38 × 1002 3.87 × 1002 4.76 × 1002

4.14 × 1002 4.42 × 1002 4.30 × 1002 4.29 × 1002 4.42 × 1002 4.01 × 1002 4.21 × 1002 4.51 × 1002 4.03 × 1002 4.80 × 1002

4.11 × 1002 4.30 × 1002 4.24 × 1002 4.25 × 1002 4.38 × 1002 3.97 × 1002 4.18 × 1002 4.47 × 1002 3.99 × 1002 4.75 × 1002

4.12 × 1002 4.39 × 1002 4.27 × 1002 4.26 × 1002 4.47 × 1002 4.00 × 1002 4.19 × 1002 4.47 × 1002 4.00 × 1002 4.79 × 1002

applied to explore chain transfer to n-butanol, MEK, and p-xylene from polymer chains of MA, EA, and n-BA. The effect of selfinitiating monoradicals on CTS is also investigated. In this study, we consider CTS reactions in monomer-self-initiated polymerization of alkyl acrylates. Because of the higher computational cost of simulating chain transfer from longer live chains to a solvent, we limited our CTS studies to monomer-self-initiated live polymer chains with two monomer units.

states in the gas phase. Optimized reactants and transition states are confirmed by Hessian calculations. The rigid rotor harmonic oscillator (RRHO) approximation69 is used to calculate energy barriers relative to the energy of reactants. A rate constant k(T) is calculated using transition state theory70 with

2. COMPUTATIONAL METHODS The functionals B3LYP, X3LYP, and M06-2X with the basis sets 6-31G(d,p), 6-311G(d), and 6-311G(d,p) are used to optimize the molecular geometries of reactants, products, and transition

where κ is a transmission coefficient, co is the inverse of the reference volume assumed in the translational partition function calculation, kB is the Boltzmann constant, T is temperature, h is Planck’s constant, R is the universal gas constant, m is the

k(T ) = κ(c o)1 − m

C

⎛ ΔH ‡ − T ΔS‡ ⎞ kBT exp⎜ − ⎟ h RT ⎝ ⎠

(1)



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Table 2. Activation Energy (Ea), Enthalpy of Activation (ΔH‡), and Gibb’s Free Energy of Activation (ΔG‡) in kJ mol−1; Tunneling Factor (κw for Wigner Correction); and Frequency Factor (A) and Rate Constant (k, without Tunneling; kw, with Tunneling) in M−1 s−1, for CTB1-2, CTM1-2, and CTX1-2 Mechanisms of MA at 298 K B3LYP 6-31G(d,p)

B3LYP 6-311G(d)

B3LYP 6-311G(d,p)

X3LYP 6-31G(d,p)

Ea ΔH‡ ΔG‡ loge A k κw kw

45.50 40.60 95.10 12.65 3.30 × 10−03 3.27 1.07 × 10−02

52.70 47.70 102.60 12.52 1.60 × 10−04 3.50 5.60 × 10−04

50.50 44.60 100.00 12.29 3.07 × 10−04 3.49 1.07 × 10−03

42.30 37.10 90.70 13.01 1.73 × 10−02 3.28 5.67 × 10−02


68.20 63.30 107.40 16.85 2.26 × 10−05 3.61 8.15 × 10−05

75.30 70.30 114.00 17.15 1.80 × 10−06 3.83 6.89 × 10−06

72.00 67.20 110.40 17.23 7.24 × 10−06 3.78 2.73 × 10−05

63.30 57.90 101.70 16.98 1.90 × 10−04 3.63 6.89 × 10−04


65.90 61.00 107.50 15.89 2.19 × 10−05 3.57 7.81 × 10−05

71.60 66.60 113.00 16.04 2.60 × 10−06 3.77 9.80 × 10−06

70.50 65.00 111.80 15.78 3.13 × 10−06 3.76 1.18 × 10−05

63.40 58.20 104.40 16.02 7.00 × 10−05 3.58 2.50 × 10−04

X3LYP 6-311G(d) CTB1-2 51.00 45.70 100.20 12.65 3.60 × 10−04 3.48 1.25 × 10−03 CTM1-2 71.20 66.20 109.10 17.35 1.13 × 10−05 3.81 4.30 × 10−05 CTX1-2 70.20 65.50 111.40 16.14 5.07 × 10−06 3.75 1.90 × 10−05

X3LYP 6-311G(d,p)

M06-2X 6-31G(d,p)

M06-2X 6-311G(d)

M06-2X 6-311G(d,p)

48.10 43.30 96.60 13.14 1.90 × 10−03 3.49 6.63 × 10−03

22.90 17.90 78.40 10.25 2.78 × 1000 3.41 9.48 × 1000

27.10 22.10 79.60 11.47 1.72 × 1000 3.50 6.02 × 1000

25.20 20.10 80.00 10.49 1.38 × 1000 3.40 4.70 × 1000

69.10 64.20 106.50 17.59 3.35 × 10−05 3.79 1.27 × 10−04

50.30 45.40 100.50 12.40 3.60 × 10−04 3.17 1.14 × 10−03

52.10 47.10 107.80 10.17 1.90 × 10−05 3.27 6.21 × 10−05

51.50 46.20 101.90 12.17 1.80 × 10−04 3.15 5.67 × 10−04

68.30 62.70 107.70 16.50 1.57 × 10−05 3.77 5.90 × 10−05

54.70 49.70 100.60 14.14 3.60 × 10−04 3.32 1.19 × 10−03

56.00 51.00 107.40 11.90 2.30 × 10−05 3.42 7.86 × 10−05

55.20 50.50 102.40 13.74 1.95 × 10−04 3.33 6.49 × 10−04

Figure 3. Transition state geometry of the CTB1-2 mechanisms for (a) MA, (b) EA, and (c) n- BA. Color key: large gray = carbon; small gray = hydrogen; red = oxygen. D



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Figure 4. Transition state geometry of the CTM1-2 mechanisms for (a) MA, (b) EA, and (c) n- BA. Color key: large gray = carbon; small gray = hydrogen; red = oxygen.

molecularity of the reaction, and ΔS‡ and ΔH‡ are the entropy and enthalpy of activation, respectively. ΔH‡ is given by ΔH ‡ = (E0 + ZPVE + ΔΔH )TS − R

where ν‡ is the imaginary frequency of the transition state. All calculations are performed using GAMESS.74 PCM and COSMO are applied to include solvent effects. These two continuum solvation methods are applied to each particular solvent by setting physical properties such as the dielectric constant and the solvent molecule radius.

(2)

where ΔΔH is the difference in enthalpy between the transition state and the reactants, ZPVE is the difference in zero-point vibrational energy between the transition state and the reactants, and E0 is the difference in electronic energy between the transition state and the reactants. The activation energy Ea is calculated using Ea = ΔH ‡ + mRT

3. RESULTS AND DISCUSSIONS 3.1. Most Likely CTS Mechanisms for MA, EA, and n-BA. Different mechanisms of CTS reactions for n-butanol, MEK, and p-xylene are shown in Figure 2. The hydrogen atom is abstracted via various mechanisms (Figure 2). The bond-dissociation energies of these hydrogen atoms are given in Table 1. Bonddissociation energy is defined as the energy difference between a solvent molecule and bond cleavage products (hydrogen radical and solvent radical):75

(3)

and the frequency factor A by A = κ(c o)1 − m

⎛ mR + ΔS‡ ⎞ kBT exp⎜ ⎟ h R ⎝ ⎠

(4)

bond‐dissociation energy = E(bond cleavage products) − E(solvent)

Scaling factors of 0.961, 0.966, and 0.967 are used for the B3LYP functional with the 6-31G(d,p), 6-311G(d), and 6-311G(d,p) basis sets, respectively, to calculate activation entropies, temperature corrections, and zero point vibrational energies. These factors are from the National Institute of Standards and Technology (NIST) scientific and technical database.71 Quantum tunneling should be considered in the reactions involving the transfer of a hydrogen atom.72,73 The Wigner tunneling73 correction is calculated using 2 1 ⎛ hν ‡ ⎞ κ≈1+ ⎟ ⎜ 24 ⎝ kBT ⎠

(6)

According to Table 1, C−H breaking bonds in CTB1-2, CTM1-2, and CTX1-2 mechanisms are weaker than those in other mechanisms. Cleavage of methylene group C−H bonds forms radicals that are more stable than those formed through methyl group C−H bond cleavage. This suggests that hydrogen abstraction from the methylene groups is favored over the methyl group in n-butanol. Mulliken charge analysis also shows that the methylene carbon atom (0.047) next to the oxygen atom is much more positive than the oxygen atom (−0.573), making the methylene carbon more likely to release a hydrogen atom. The same conclusion can also be obtained for MEK simply by

(5) E



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Figure 5. Transition state geometry of the CTX1-2 mechanisms for (a) MA, (b) EA, and (c) n- BA. Color key: large gray = carbon; small gray = hydrogen; red = oxygen.

polymerization.8 However, the theoretically estimated rate constant is 4 orders of magnitude smaller than the experimentally estimated one. This difference is very likely due to the underestimation of the solvent-based entropic effects and frequency factor. It indicates that hybrid meta-GGA functionals such as M06-2X can better account for van der Waals interactions76,77 and provide more accurate predictions of barrier heights relative to B3LYP, but they do not accurately account for all solvent interactions. 3.2. Chain Transfer to n-Butanol, sec-Butanol, and tertButanol. Several mechanisms of chain transfer to n-butanol, secbutanol, and tert-butanol are shown in Figure 6. A live polymer chain can abstract a hydrogen atom from several locations in these solvents. We calculated bond-dissociation energies of all available hydrogen atoms in these solvents (Figure 6), and the calculated dissociation energies are given in Table 5. The results indicate that the weakest C−H bond is the one that is broken in the CTBsec1-2 mechanism, which shows the higher capability of methylene carbon atoms to release a hydrogen atom, relative to methyl carbon atoms and oxygen. The methylene carbon atom next to the oxygen in sec-butanol with a Mulliken charge of 0.152 is likely to release a hydrogen than the other methylene carbon atom that has a Mulliken charge of −0.228. Because bond-dissociation energies calculated for CTBtert1-1 and CTBtert1-2 mechanisms are not very different, these mechanisms are equally likely mechanisms for chain transfer to tert-butanol. The calculated kinetic parameters of CTB1-2, CTBsec1-2 and CTBtert1-2 mechanisms of MA are given in Table 6; among n-butanol, sec-butanol, and tert-butanol, tert-butanol has the lowest and sec-butanol has the highest

comparing the Mulliken charge of methylene carbon atom (−0.309) and the two methyl carbon atoms (−0.351 and −0.435). However, due to the presence of delocalized molecular orbitals (stable ring) in p-xylene, abstraction of a methyl group hydrogen is more favorable. We calculated the thermodynamic and kinetic parameters (activation energies, enthalpies of reaction, Gibb’s free energies, frequency factors, and rate constants) of the most likely mechanisms of CTS reactions of MA, EA, and n-BA. Table 2 presents the kinetic parameters of the most likely mechanisms of chain transfer to n-butanol, MEK and p-xylene for MA. The transition-state geometries for CTB1-2, CTM1-2, and CTX1-2 are shown in Figures 3, 4, and 5, respectively. It was found that the activation energy of chain transfer to n-butanol is lower than that of MEK and p-xylene reactions (Table 2), and the rate constant for chain transfer to n-butanol is higher than that of MEK and p-xylene. We attribute this to the polar and protic nature of n-butanol, which can readily donate a hydrogen atom to the polymer chain to facilitate chain transfer. p-Xylene and MEK lack a labile hydrogen atom to transfer. It was determined that M06-2X, a hybrid meta-GGA functional, gives lower activation energies and higher rate constants than B3LYP and X3LYP. This agrees with the findings for CTM reactions of alkyl acrylates.63 The calculated kinetic parameters for chain transfer to n-butanol, MEK, and p-xylene for EA and n-BA are given in Tables 3 and 4, respectively. The similarities in the predicted results for MA, EA, and n-BA show little effect of the end substituent groups of the live chains. The activation energy of chain transfer to p-xylene calculated using M06-2X/6-31G(d,p) functional is in agreement with those estimated from measurements taken in high-temperature n-BA F



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Table 3. Activation Energy (Ea), Enthalpy of Activation (ΔH‡), and Gibb’s Free Energy of Activation (ΔG‡) in kJ mol−1; Tunneling Factor (κw for Wigner Correction); and Frequency Factor (A) and Rate Constant (k, without Tunneling; kw, with Tunneling) in M−1 s−1, for CTB1-2, CTM1-2, and CTX1-2 Mechanisms of EA at 298 K B3LYP 6-31G(d,p)

B3LYP 6-311G(d)

B3LYP 6-311G(d,p)

X3LYP 6-31G(d,p)


45.60 40.60 94.30 13.00 4.50 × 10−03 3.29 1.48 × 10−02

53.30 48.30 102.00 13.08 2.20 × 10−04 3.51 7.72 × 10−04

50.30 44.70 98.30 13.02 6.90 × 10−04 3.48 2.40 × 10−03

40.60 35.70 88.70 13.26 4.40 × 10−02 3.28 1.44 × 10−01


68.20 63.30 105.10 17.80 5.90 × 10−05 3.60 2.12 × 10−04

75.60 70.60 111.30 18.24 4.70 × 10−06 3.82 1.79 × 10−05

72.30 66.90 109.20 17.59 9.20 × 10−06 3.80 3.49 × 10−05

61.20 56.50 98.20 17.83 1.03 × 10−03 3.61 3.71 × 10−03


66.10 61.20 103.30 17.67 1.20 × 10−04 3.59 4.30 × 10−04

72.90 68.00 113.00 16.51 2.40 × 10−06 3.79 9.09 × 10−06

70.30 64.80 106.50 17.83 2.63 × 10−05 3.84 1.00 × 10−04

62.00 57.40 100.30 17.35 4.60 × 10−04 3.57 1.64 × 10−03

X3LYP 6-311G(d) CTB1-2 49.00 43.60 96.90 13.14 1.30 × 10−03 3.52 4.57 × 10−03 CTM1-2 70.20 65.30 107.90 17.47 1.90 × 10−05 3.85 7.30 × 10−05 CTX1-2 69.30 64.10 105.80 17.83 3.93 × 10−05 3.82 1.50 × 10−04

X3LYP 6-311G(d,p)

M06-2X 6-31G(d,p)

M06-2X 6-311G(d)

M06-2X 6-311G(d,p)

48.40 43.40 95.60 13.62 2.70 × 10−03 3.51 9.47 × 10−03

19.40 14.50 74.20 10.56 1.53 × 1001 3.49 5.34 × 1001

23.80 18.90 79.10 10.36 2.11 × 1000 3.59 7.57 × 1000

21.20 16.40 76.90 10.25 5.43 × 1000 3.49 1.89 × 1001

68.50 62.70 104.40 17.83 5.40 × 10−05 3.81 2.06 × 10−04

45.50 40.60 98.10 11.45 9.90 × 10−04 3.17 3.13 × 10−03

49.90 44.90 103.90 10.85 9.30 × 10−05 3.27 3.04 × 10−04

48.30 42.80 100.90 11.21 2.50 × 10−04 3.20 8.00 × 10−04

67.50 62.20 103.30 18.06 1.03 × 10−04 3.83 3.94 × 10−04

53.20 48.30 102.00 13.02 2.10 × 10−04 3.30 6.93 × 10−04

55.50 50.60 104.10 12.89 7.40 × 10−05 3.40 2.52 × 10−04

51.10 45.90 102.20 11.93 1.68 × 10−04 3.28 5.50 × 10−04

Table 4. Activation Energy (Ea), Enthalpy of Activation (ΔH‡), and Gibb’s Free Energy of Activation (ΔG‡) in kJ mol−1; Tunneling Factor (κw for Wigner Correction); and Frequency Factor (A) and Rate Constant (k, without Tunneling; kw, with Tunneling) in M−1 s−1, for CTB1-2, CTM1-2, and CTX1-2 Mechanisms of n-BA at 298 K B3LYP 6-31G(d,p)

B3LYP 6-311G(d)

B3LYP 6-311G(d,p)

X3LYP 6-31G(d,p)


45.10 40.20 94.10 12.89 5.00 × 10−03 3.28 1.64 × 10−02

53.30 48.20 101.50 13.14 2.30 × 10−04 3.52 8.09 × 10−04

52.40 46.60 101.10 12.65 2.10 × 10−04 3.34 7.01 × 10−04

40.30 34.70 86.60 13.74 8.00 × 10−02 3.32 2.65 × 10−01


63.10 58.20 99.90 17.83 4.80 × 10−04 3.59 1.72 × 10−03

69.20 63.80 106.40 17.47 2.85 × 10−05 3.82 1.09 × 10−04

69.60 65.20 106.60 17.95 3.93 × 10−05 3.62 1.42 × 10−04

60.00 55.50 98.40 17.35 1.04 × 10−03 3.58 3.72 × 10−03


64.30 58.90 99.10 18.43 5.40 × 10−04 3.58 1.93 × 10−03

67.50 61.70 104.90 17.23 4.45 × 10−05 3.78 1.68 × 10−04

70.40 65.30 107.90 17.47 1.76 × 10−05 3.59 6.31 × 10−05

58.50 53.50 94.90 17.95 3.40 × 10−03 3.62 1.23 × 10−02

X3LYP 6-311G(d) CTB1-2 46.60 41.80 95.40 13.02 3.00 × 10−03 3.54 1.06 × 10−02 CTM1-2 67.30 62.00 103.40 17.95 9.94 × 10−05 3.86 3.83 × 10−04 CTX1-2 65.20 60.50 103.40 17.35 1.30 × 10−04 3.82 4.96 × 10−04 G

X3LYP 6-311G(d,p)

M06-2X 6-31G(d,p)

M06-2X 6-311G(d)

M06-2X 6-311G(d,p)

46.10 41.40 94.40 13.26 4.70 × 10−03 3.36 1.58 × 10−02

20.40 15.40 76.50 10.00 5.90 × 1000 3.50 2.06 × 1001

21.00 16.50 77.00 10.25 5.90 × 1000 3.60 2.12 × 1001

20.30 15.00 76.70 9.77 4.83 × 1000 3.49 1.68 × 1001

66.60 61.90 103.60 17.83 1.20 × 10−04 3.66 4.39 × 10−04

41.00 36.10 95.10 10.85 3.40 × 10−03 3.17 1.07 × 10−02

45.50 40.40 98.50 11.21 7.80 × 10−04 3.29 2.56 × 10−03

43.10 38.50 97.20 10.97 1.60 × 10−03 3.19 5.10 × 10−03

65.20 60.30 102.30 17.71 1.80 × 10−04 3.63 6.53 × 10−04

54.70 49.70 100.10 14.34 4.40 × 10−04 3.34 1.47 × 10−03

57.00 51.60 104.90 13.14 5.17 × 10−05 3.42 1.76 × 10−04

59.10 53.60 107.20 13.02 1.96 × 10−05 3.35 6.57 × 10−05



Article

Figure 6. End-chain transfer to sec-butanol and tert-butanol reactions for MA involving a two-monomer-unit live chain initiated by M2• shown in Figure 1.

Table 5. H−R Bond-Dissociation Energies (kJ mol−1) at 298 K CTBsec1-2 CTBsec2-2 CTBsec3-2 CTBtert1-2 CTBtert2-2

B3LYP 6-31G(d,p)

B3LYP 6-311G(d)

B3LYP 6-311G(d,p)

M06-2X 6-31G(d,p)

M06-2X 6-311G(d)

M06-2X 6-311G(d,p)

3.97 × 10 4.34 × 1002 4.21 × 1002 4.34 × 1002 4.45 × 1002

3.99 × 10 4.37 × 1002 4.23 × 1002 4.36 × 1002 4.49 × 1002

3.98 × 10 4.35 × 1002 4.20 × 1002 4.35 × 1002 4.46 × 1002

4.08 × 10 4.50 × 1002 4.34 × 1002 4.50 × 1002 4.52 × 1002

4.04 × 10 4.47 × 1002 4.33 × 1002 4.48 × 1002 4.47 × 1002

4.06 × 1002 4.49 × 1002 4.34 × 1002 4.46 × 1002 4.46 × 1002

02

02

02

02

02

Table 6. Activation Energy (Ea), Enthalpy of Activation (ΔH‡), and Gibb’s Free Energy of Activation (ΔG‡) in kJ mol−1; Tunneling Factor (κw for Wigner Correction); and Frequency Factor (A) and Rate Constant (k, without Tunneling; kw, with Tunneling) in M−1 s−1, for CTB1-2, CTBsec1-2, and CTBtert1-2 Mechanisms of MA at 298 K B3LYP 6-31G(d,p)

M06-2X 6-31G(d,p)

experimental14,78 B3LYP 6-31G(d,p) M06-2X 6-31G(d,p)

Ea ΔH‡ ΔG‡ loge A k κw kw Ea ΔH‡ ΔG‡ loge A k κw kw k (353 K) k (353 K) k (353 K)

n-butanol

sec-butanol

tert-butanol

45.50 40.60 95.10 12.65 3.30 × 10−03 3.27 1.07 × 10−02 22.90 17.90 78.40 10.25 2.78 × 1000 3.41 9.48 × 1000 1.10 × 1001 5.76 × 10−02 1.16 × 1001

45.30 40.30 93.90 13.02 5.20 × 10−03 3.25 1.69 × 10−02 24.10 19.20 77.20 11.27 4.60 × 1000 3.37 1.55 × 1001 5.50 × 1001 8.93 × 10−02 2.10 × 1001

79.50 74.00 127.00 13.26 6.63 × 10−09 3.15 2.10 × 10−08 64.30 59.40 109.70 14.34 9.00 × 10−06 3.28 2.95 × 10−05 1.50 × 1000 9.87 × 10−07 5.20 × 10−04

chain-transfer rate constant. These findings are in agreement with the experimentally estimated chain transfer to n-butanol, sec-butanol, and tert-butanol rate constants in MA polymerization at 80 °C.14 A comparison of experimentally estimated14,78 and theoretically estimated values of chain transfer to n-butanol, sec-butanol, and tert-butanol rate constants in MA polymerization at 80 °C, given in Table 6, indicates that (a) the

M06-2X-estimated values are closer to the experimentally estimated ones, (b) the M06-2X-estimated values of chain transfer to n-butanol and sec-butanol rate constants are very close to the experimentally estimated ones, and (c) the values of chain transfer to tert-butanol rate constant estimated by M06-2X and B3LYP are, respectively, approximately four and six orders of magnitude smaller than the experimentally estimated value. H



Article

Table 7. Activation Energy (Ea), Enthalpy of Activation (ΔH‡), and Gibb’s Free Energy of Activation (ΔG‡) in kJ mol−1; Frequency Factor (A) and Rate Constant (k) in M−1 s−1, for CTB1-2, CTM1-2, and CTX1-2 Mechanisms of MA, EA, and n-BA at 298 K, Using PCM and COSMO M06-2X 6-31G(d,p) CTB1-2 COSMO

CTM1-2 PCM

COSMO

CTX1-2 PCM

COSMO

PCM

48.40 43.40 103.50 10.60 1.31 × 10−04

51.60 46.60 96.30 14.82 2.46 × 10−03

56.50 51.50 105.60 13.02 5.63 × 10−05

46.30 40.70 98.40 11.57 8.11 × 10−04

51.30 46.50 94.10 15.42 5.10 × 10−03

59.50 54.20 105.60 13.62 3.10 × 10−05

45.40 40.40 98.30 11.21 8.13 × 10−04

54.20 49.10 98.50 14.82 8.62 × 10−04

57.20 51.60 106.00 13.01 4.20 × 10−05

MA Ea ΔH‡ ΔG‡ loge A k

23.50 18.40 78.50 10.49 2.73 × 1000

38.10 33.20 84.70 13.86 2.20 × 10−01

Ea ΔH‡ ΔG‡ loge A k

20.30 15.30 73.50 11.09 1.81 × 1001

34.40 28.60 80.20 14.21 1.38 × 1000


18.00 13.50 75.30 9.53 9.63 × 1000

35.50 30.40 82.60 13.26 3.43 × 10−01

51.00 46.20 96.60 14.22 1.72 × 10−03 EA 47.10 42.20 97.10 12.41 1.36 × 10−03 BA 39.10 34.20 88.40 13.01 6.26 × 10−02

Figure 7. Mechanisms for CTS reactions involving a two-monomer-unit live chain initiated by M1• shown in Figure 1.

3.3. Continuum Solvation Models: PCM and COSMO. The kinetics of CTS reactions is explored using two different solvation models, PCM and COSMO to predict the kinetic parameters of the most likely CTS reaction mechanisms (CTB1-2, CTM1-2, and CTX1-2) in solutions of n-butanol, MEK, and p-xylene. As shown in Table 7, the use of PCM strongly affects the activation energy and rate constant of chain transfer to n-butanol but weakly affects those of chain transfer to MEK and p-xylene. We found that the PCM-calculated activation energy

for n-butanol is higher than those obtained via gas phase calculations, so the PCM-calculated rate constant for n-butanol is lower. p-Xylene is nonpolar, so applying PCM does not significantly affect the stability of reactants or the transition states. n-Butanol and MEK are both polar solvents, so the stability of reactants and transition states individually are each strongly affected. Because the polarity and dipole moment of MEK are higher than those of n-butanol, the inclusion of PCM stabilizes the transition state of CTM1-2 more than that of I



Article

Table 8. Activation Energy (Ea), Enthalpy of Activation (ΔH‡), and Gibb’s Free Energy of Activation (ΔG‡) in kJ mol−1; Tunneling Factor (κw for Wigner Correction); and Frequency Factor (A) and Rate Constant (k, without Tunneling; kw, with Tunneling) in M−1 s−1, for CTB1-1, CTM1-1, and CTX1-1 Mechanisms of MA, EA, and n-BA at 298 K CTB1-1 B3LYP 6-31G(d,p)

CTM1-1

M06-2X 6-31G(d,p)

B3LYP 6-31G(d,p)

CTX1-1

M06-2X 6-31G(d,p)

B3LYP 6-31G(d,p)

M06-2X 6-31G(d,p)

52.20 47.40 102.10 12.41 1.70 × 10−04 3.19 5.42 × 10−04

66.40 61.20 110.50 14.82 6.27 × 10−06 3.59 2.25 × 10−05

56.10 51.30 107.50 12.05 2.51 × 10−05 3.33 8.35 × 10−05

48.10 43.50 94.30 12.05 6.30 × 10−04 3.17 1.99 × 10−03

67.00 62.10 105.50 16.02 1.63 × 10−05 3.56 5.80 × 10−05

53.40 48.40 102.00 14.22 6.50 × 10−04 3.30 2.15 × 10−03

43.10 38.50 94.50 12.17 5.40 × 10−03 3.16 1.70 × 10−02

64.20 59.10 107.20 15.42 2.77 × 10−05 3.61 1.00 × 10−04

56.10 51.50 103.00 13.62 1.20 × 10−04 3.36 4.03 × 10−04

MA Ea ΔH‡ ΔG‡ loge A k κw kw

48.40 42.60 93.70 14.21 4.87 × 10−03 3.27 1.59 × 10−02

23.00 18.30 75.80 11.45 8.73 × 1000 3.41 2.97 × 1001


46.30 41.20 97.00 12.05 1.30 × 10−03 3.28 4.26 × 10−03

22.30 17.20 75.40 10.85 6.36 × 1000 3.50 2.22 × 1001


45.60 41.10 95.70 12.41 2.50 × 10−03 3.31 8.27 × 10−03

21.20 16.50 74.30 11.21 1.42 × 1001 3.48 4.94 × 1001

67.40 61.60 111.30 14.82 4.92 × 10−06 3.62 1.78 × 10−05 EA 69.50 63.60 107.70 15.42 4.18 × 10−06 3.63 1.52 × 10−05 BA 65.50 60.40 106.30 16.02 2.99 × 10−05 3.57 1.07 × 10−04

Table 9. Activation Energy (Ea), Enthalpy of Activation (ΔH‡), and Gibb’s Free Energy of Activation (ΔG‡) in kJ mol−1; Frequency Factor (A) and Rate Constant (k) in M−1 s−1, for CTB1-1, CTM1-1, and CTX1-1 Mechanisms of MA, EA, and n-BA at 298 K, Using PCM and COSMO M06-2X 6-31G(d,p) CTB1-1 COSMO

CTM1-1 PCM

COSMO

CTX1-1 PCM

COSMO

PCM

50.10 45.40 102.00 11.57 1.80 × 10−04

53.20 48.30 102.40 12.78 1.70 × 10−04

57.50 51.60 104.800 13.26 4.75 × 10−05

48.60 44.00 102.70 10.85 1.60 × 10−04

50.30 44.60 93.50 15.30 6.70 × 10−03

58.40 53.40 108.70 12.05 9.90 × 10−06

48.10 43.40 100.10 11.69 4.40 × 10−04

58.10 53.40 102.20 14.94 2.00 × 10−04

57.00 52.50 104.00 13.50 7.44 × 10−05

MA Ea ΔH‡ ΔG‡ loge A k

24.50 19.10 79.50 10.49 1.82 × 1000

39.30 33.90 86.10 13.62 1.10 × 10−01


23.40 17.60 77.50 10.73 3.60 × 1000

35.50 30.30 80.80 13.98 7.10 × 10−01


23.50 18.20 78.60 10.13 1.90 × 1000

37.20 31.70 82.00 14.46 5.70 × 10−01

50.50 45.30 97.20 13.50 1.00 × 10−03 EA 48.20 42.60 97.30 13.02 1.60 × 10−03 BA 45.40 40.30 91.80 13.62 9.00 × 10−03

reactions, its impact on the kinetic parameters of chain transfer to MEK and p-xylene are negligible. Moreover, Table 7 shows that the effect of PCM does not depend on the end substituent group. Liang et al.79 investigated the effect of n-butanol on the rate of intramolecular chain transfer to polymer reactions. They found that n-butanol inhibits backbiting reactions and consequently

CTB1-2. In the case of MEK, the change in the stability of CTM1-2 transition state is nearly the same as that of the reactants. PCM calculations are also carried out to study CTB1-2, CTM1-2, and CTX1-2 mechanisms for EA and n-BA. Again, although PCM has a strong effect on the activation energies and rate constants of chain transfer to n-butanol J



Article

Figure 8. Mechanisms for CTS reactions involving a three-monomer-unit live chain initiated by M2• shown in Figure 1.

Table 10. Activation Energy (Ea), Enthalpy of Activation (ΔH‡), and Gibb’s Free Energy of Activation (ΔG‡) in kJ mol−1; Tunneling Factor (κw for Wigner Correction); and Frequency Factor (A) and Rate Constant (k, without Tunneling; kw, with Tunneling) in M−1 s−1, for CTB1-2′, CTM1-2′, and CTX1-2′ Mechanisms of MA, EA, and n-BA at 298 K CTB1-2′ B3LYP 6-31G(d,p)

CTM1-2′

M06-2X 6-31G(d,p)

B3LYP 6-31G(d,p)

CTX1-2′

M06-2X 6-31G(d,p)

B3LYP 6-31G(d,p)

M06-2X 6-31G(d,p)

52.20 47.50 103.80 11.57 7.49 × 10−05 3.31 2.48 × 10−04

67.00 62.30 112.00 14.46 3.43 × 10−06 3.84 1.32 × 10−05

54.70 50.40 107.30 11.69 3.08 × 10−05 3.55 1.09 × 10−04

50.20 45.20 104.80 10.37 5.06 × 10−05 3.37 1.70 × 10−04

68.00 63.50 106.90 16.74 2.24 × 10−05 3.90 8.73 × 10−05

58.30 52.70 110.30 11.81 8.12 × 10−06 3.55 2.88 × 10−05

48.30 43.40 111.30 7.24 4.76 × 10−06 3.37 1.60 × 10−05

66.20 60.90 119.20 11.33 2.07 × 10−07 3.88 8.03 × 10−07

61.00 56.40 119.60 8.69 1.21 × 10−07 3.70 4.47 × 10−07

MA Ea ΔH‡ ΔG‡ loge A k κw kw

47.30 41.70 99.40 11.45 4.80 × 10−04 3.39 1.63 × 10−03

24.40 18.60 81.20 9.53 7.30 × 10−01 3.57 2.60 × 1000


46.60 42.20 98.10 12.05 1.20 × 10−03 3.48 4.17 × 10−03

23.40 18.10 81.30 9.05 6.70 × 10−01 3.61 2.41 × 1000


48.10 43.10 105.60 9.41 4.52 × 10−05 3.49 1.58 × 10−04

28.30 23.50 92.90 6.40 6.60 × 10−03 3.76 2.48 × 10−02

68.10 63.30 114.60 13.73 1.06 × 10−06 3.88 4.11 × 10−06 EA 70.10 65.20 115.00 14.46 9.82 × 10−07 3.92 3.85 × 10−06 BA 67.50 61.70 121.40 10.97 8.55 × 10−08 3.94 3.37 × 10−07

of solvent molecules on the kinetic parameters of CTS reactions. In COSMO, nonelectrostatic solute−solvent interactions, such as dispersion, repulsion, and cavitation are considered as well as electrostatic interactions. Because the contribution of nonelectrostatic interactions in COSMO are included in a simple form, large errors for molecules with specific interactions, such as hydrogen bonding, can be obtained. The insignificant effect of COSMO on CTS reactions is in agreement with that reported for propagation reactions of acrylonitrile and vinyl chloride.59

reduces the rate of formation of branch-points along the polymer backbone during polymerization of n-BA and increases the average molecular weights of the polymer. The solvation model COSMO is applied to investigate solvent effects on the rates and barriers of CTB1-2, CTM1-2, and CTX1-2 reactions for MA, EA, and n-BA. As Table 7 shows, unlike PCM, COSMO does not affect appreciably the relative stability of the reactants to the transition states. These results seem to indicate that COSMO is not able to represent the effects K



Article

3.4. Effect of the Type of Initiating Radical on CTS. Two types of monoradicals generated via monomer self-initiation41,42 are shown in Figure 1. In the previous sections, the most likely CTS reaction mechanisms of a two-monomer-unit live polymer chain initiated via M2• were investigated. Figure 7 shows the most likely CTS reaction mechanisms of a two-monomer-unit live polymer chain initiated via M1•. The kinetic parameters of the CTB1-1, CTM1-1, and CTX1-1 reactions in the gas phase are calculated (Table 8). We found that the calculated rates are comparable to that of two-monomer-unit live polymer chain initiated via M2•. This indicates that the choice of initiating radical has little role in the rate of CTS reaction. PCM was applied to understand the influence of initiating radicals on CTS in solution. The calculated activation energies and rate constants of the CTB1-1, CTM1-1, and CTX1-1 reactions are listed in Table 9. The energy and rate constants of live polymer chains initiated by M1• vary by ±3 kJ/mol and 1 order of magnitude from that of live polymer chains initiated by M2• (Table 7). The ≈16 kJ/mol increase in activation energy and the 2 orders of magnitude decrease in the rate constant calculated using PCM in comparison with those calculated in the gas phase (reported in Table 8) show the significant effect of PCM on the kinetic parameters of the CTB1-1 mechanism. COSMO (Table 9) was found to have negligible effect on the rate comparison between types of live chain polymer initiating radical for MA, EA, and n-BA. The activation energies are at most 6 kJ/mol higher (and the rate constants 1 order of magnitude lower) than those obtained for the CTB1-2, CTM1-2, CTX1-2 mechanisms (Table 7). The kinetic parameters using this solvation model do not differ from those estimated via gas phase calculations (Table 8). 3.5. Effect of Live Polymer Chain Length. The CTB1-2′, CTM1-2′, and CTX1-2′ mechanisms for MA, EA, and n-BA with a three-monomer-unit live chain initiated by M2• (Figure 8) are investigated. Table 10 shows that an increase in the length of the live chain polymer does not affect the kinetics of CTS reactions of MA, EA, and n-BA. The geometries of the transition states of the CTB1-2′, CTM1-2′, and CTX1-2′ mechanisms are quite similar to those of the CTB1-2, CTM1-2, and CTX1-2 mechanisms in which the two-monomer-unit live chain initiated by M2• was considered as the reactant (Figures 3−5). It can be concluded that live polymer chain length does not affect the geometry of the reaction center significantly. These findings are in agreement with CTM studies63 and propagation reactions of alkyl acrylates.44 The same studies are performed using PCM to identify the impacts of live polymer chain length on the kinetics of the CTS reactions in the presence of solvents. The results reported in the Supporting Information confirm our earlier findings that the length of a live polymer chain does not affect the kinetics of the CTS reactions significantly. Comparing these results with those given in Table 7, we can conclude that PCM has no significant differential effect on the kinetics of CTS reactions involving live polymer chains with different lengths.

Among n-butanol, sec-butanol, and tert-butanol, tert-butanol has the highest CTS energy barrier and the lowest rate constant. Chain transfer to n-butanol and sec-butanol reactions have comparable kinetic parameter values. The activation energy of the most likely chain transfer to p-xylene mechanism of a twomonomer-unit live n-BA polymer chain initiated by M2• calculated using M06-2X/6-31G(d,p) was found to be close to those estimated from polymer sample measurements. Application of PCM resulted in remarkable changes in the kinetic parameters of the chain transfer to n-butanol. However, it had very little effect on the stability of the reactants and the transition states in chain transfer to MEK and p-xylene. COSMO showed no solvent effect on the kinetics of CTS reactions of MA, EA, and n-BA. It was found that the live polymer chain length has very little effect on the activation energies and rate constants of CTS reactions. MA, EA, and n-BA live chains initiated by M2• and M1• showed similar hydrogen abstraction abilities, indicating that the type of monoradical generated via self-initiation has little or no effect on the capability of MA, EA, and n-BA live polymer chains to undergo CTS reactions.

■

ASSOCIATED CONTENT

S Supporting Information *

Five tables of activation energies, enthalpies of activation, Gibb’s free energies of activation, frequency factors, and rate constants. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*M. Soroush. Phone: (215) 895-1710. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This material is based upon work partially supported by the National Science Foundation under Grants CBET-0932882, CBET-1160169, and CBET-1159736. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. Acknowledgment is also made to the Donors of the American Chemical Society Petroleum Research Fund for partial support of this research. A.M.R. acknowledges the Air Force Office of Scientific Research, through grant FA9550-10-1-0248. Computational support was provided by the High-Performance Computing Modernization Office of the U.S. Department of Defense.

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REFERENCES

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