Theoretical Study of Chain Transfer to Solvent Reactions of AlkylAcrylatesNazanin 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, Pennsylvania19104-6323, 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 tosolvent (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 resultsindicate that abstraction of a hydrogen atom from the methylene group next to the oxygenatom in n-butanol, from the methylene group in MEK, and from a methyl group inp-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, andtransition states are predicted. The sensitivity of the predictions to three hybridfunctionals (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 tert-butanol, tert-butanol has the highest CTS energy barrier and the lowest rate constant. Although the application of the conductor-like screening model (COSMO) does not affect the predicted CTS kinetic parameter values, the application of the polarizablecontinuum model (PCM) results in higher CTS energy barriers. This increase in the predicted CTS energy barriers is larger forbutanol and MEK than for p-xylene. The higher rate constants of chain transfer to n-butanol reactions compared to those ofchain 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 ofpoly(n-alkyl acrylates) since their first investigation by Rehbergand Fisher in the 1940s.1 Acrylates are principal monomers in theproduction of coatings, adhesives, and polymers, which are used inmedical and pharmaceutical applications due to their transparencyand resistance to breakage.2 The basic design of resins used inautomobile coatings has been changed, due to environmentallimitations on allowable volatile organic contents (VOCs) ofresins.3 Although environmental regulations and consumerawareness have led to the production of greener acrylic resins,solution polymerization is still widely used. Production of resinswith lower solvent contents and molecular weights has beenachieved via high temperature (>100 °C) free-radical polymer-ization.4−6 It has been reported7−10 that at high temperatures,propagating free radicals undergo secondary reactions such asβ-scission and chain transfer to monomer (CTM), polymer, andsolvent reactions. Midchain radicals (MCRs) formed via chaintransfer reactions cause the production of low molecular weightand branched polymers.11,12 A better understanding of the solventeffects in high temperature free-radical polymerization willimprove 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

polymerization of n-butyl acrylate (n-BA) have been observedusing liquid chromatography-electrospray ionization-tandemmass spectrometry (LC-ESI-MS).13 In thermal polymeriza-tion of ethyl acrylate (EA), methyl acrylate (MA), and ethylmethacrylate (EMA), chain transfer to solvent rate constants forvarious solvents, such as hydrocarbons, alcohols, ketones, acids,and esters, have been estimated from polymer sample measure-ments.14,15 Moreover, the effect of solvent in homopolymeriza-tion of n-BA has been investigated.16 These experimental studiesreported kp/kt

0.5 values. They also indicated that as the solventconcentration increases, the rate of CTS reactions and the rate offormation of shorter chains increase, and these shorter chainsterminate faster than longer chains. Although the influence ofdifferent solvent concentrations on the overall rate of polymer-ization (Rp) has been reported,16 investigation of solvent effectson the individual rate constants (kp and kt) is still challenging.Including chain transfer agents (CTAs) during controlled radicalpolymerization processes (such as nitroxides for nitroxide-mediated polymerization) has enabled atom transfer radicalpolymerization (ATRP) and reversible addition−fragmentation

Received: February 27, 2014Revised: June 25, 2014Published: June 27, 2014

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chain transfer (RAFT).17−22 CTAs control the growth ofpropagating chains and lead to the formation of uniform chain-length polymers. However, self-regulation and polymers withuniform chain lengths have been observed in thermal polymer-ization of alkyl acrylates, in the absence of these agents.23 Theseobservations can be attributed to the self-regulatory capability ofchain transfer mechanisms. Therefore, a fundamental under-standing of these capabilities can help the control, design, andoptimization of thermal polymerization processes.Previous studies report polymer chains with end groups formed

by chain transfer reactions using electrospray ionization-Fouriertransformmass spectrometry9 andmatrix-assisted laser desorptionionization mass spectrometry24 in self-initiated polymerizationof MA, EA, and n-BA (100−180 °C). The presence of these endgroups was confirmed using nuclear magnetic resonance analysisof the polymers.9 Chain transfer and radical propagation ratecoefficients of acrylates25−27 have been determined using pulsed-laser polymerization/size exclusion chromatography at varioustemperatures below 30 °C,28−30 the upper limit of this approach.Although useful overall understanding of chain transfer reactionscan be gained from experimental studies, the investigation ofindividual reaction mechanisms and reacting species is besthandled with quantum chemical calculations.Polymerization reaction rate constants have been estimated

in thermal polymerization of acrylates by fitting macroscopickinetic models of polymerization reactors to experimentalmeasurements, including initiation, propagation, termination,and chain transfer reactions.7,31,32 The reliability of this approachdepends on the accuracy of the measurements and the reactormodel (which is based on a set of postulated reactions).Furthermore, this approach is unable to conclusively suggest themost likely mechanism of individual reactions.Computational quantum chemistry can be applied to identify

mechanisms, reacting species, energy barriers, and rate constantsof polymerization reactions. Although kinetics of variouspolymerization reactions have been studied experimen-tally,27,33−40 determination of individual reaction mechanismswithout taking advantage of quantum chemical calculations is notfeasible. Density functional theory (DFT) and wave functionbased quantum chemical methods have been extensively used toexplore different reaction mechanisms, such as self-initiation andpropagation in thermal polymerization of alkyl acrylates.41−45

DFT is computationally less expensive and it requires less memorystorage in comparison to MP2 and MCSCF approaches.46,47

Another computational advantage of DFT is the availability ofparallel and linear-scaling algorithms.48,49 However, the DFTfunctionals are known to inaccurately predict kinetic parameters,which can be overcome by screening and benchmarking numerouspure and hybrid functionals as carried out for the propagationreactions of MA and MMA,44 self-initiation of styrene,50 MA,EA, n-BA,41,42 and MMA,43 and cyclohexanone-monomerco-initiation mechanism in thermal homopolymerization of MAand MMA.51 The geometries of the intermediate molecularspecies can be identified through these calculations. Previousstudies have shown the most likely monomer self-initiationmechanism in spontaneous thermal polymerization of alkylacrylates.41,42 The monoradicals generated by the self-initiationare shown in Figure 1. Despite the high accuracy of quantumchemistry for isolated molecules, there are major difficulties indealing with transition states and molecules in different solventenvironments.52

Solvents can increase the stability of transition stategeometries in solution polymerization.24 Different solvent

continuum models have been applied to explore the solventeffects on the solute.53,54 In the continuum model, solvent istreated as a dielectric continuum mean field polarized by thesolute that is placed in this continuum. Although the self-consistent reaction field method places the solute in a sphericalcavity,55 the polarizable continuum model (PCM) introducesmolecular shape for the cavity.56,57 PCM has been applied topredict the propagation rate coefficient of acrylic acid in thepresence of toluene.54 However, microscopic structure of thesolvent−solute interaction cannot be described through thesemodels. The conductor-like screening model (COSMO),originally developed by Klamt and Schuurman,58 is anotherapproach for polarized continuum calculations in which thesurrounding medium (solvent) is assumed to be a conductorrather than a dielectric to simplify the electrostatic interactionsbetween solvent and solute. The effect of solvents with differentdielectric constants on the propagation rate coefficients in free-radical polymerization of acrylonitrile and vinyl chloride hasbeen investigated.59 Also, COSMO has been applied to predictnonequilibrium solvation energies of biphenyl−cyclohexane−naphthalene.60 The conductor-like screening model for realsolvents (COSMO-RS) is another solvation model, whichwas used by Klamt61 and Deglmann et at.62 to explore solventeffects on propagation reactions in free-radical polymerizationand estimate rate coefficients of propagation reactions in free-radical solution polymerization of acrylates. In this work wecompare performances of PCM and COSMO.Different CTM mechanisms for MA, EA, and n-BA have been

explored using quantum chemical calculations.63 Bimolecularhydrogen abstraction reactions between a growing polymer chainand a monomer as well as different dead polymers, copolymers,and chain transfer agents have been explored using quantumchemical calculations.64,65 These studies showed that hydrogenabstraction from species that have a weaker electron-donor groupclose to the abstracted hydrogen is the most likely mechanismfor hydrogen abstraction in homo- and copolymerization ofn-butyl acrylate.64,65 Although the existence of CTS reactionshas 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 atthe meeting.68

This paper presents a computational and theoretical studyof CTS reactions of MA, EA, and n-BA homopolymerizationsin butanol (polar, protic), methyl ethyl ketone (MEK) (polar,aprotic), and p-xylene (nonpolar). Energy barriers and moleculargeometries of reactants, products, and transition states arecalculated using DFT. We explore the abstraction of a hydrogenfrom n-butanol, MEK, and p-xylene by a live polymer chainto identify the most likely mechanisms of CTS reactions in MA,EA, and n-BA homopolymerizations. The activation energyand rate constants of CTS mechanisms are calculated usingtransition state theory. PCM and COSMO solvation models are

Figure 1. Two types of monoradical generated by monomer self-initiation.42

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

2. COMPUTATIONAL METHODS

The functionals B3LYP, X3LYP, and M06-2X with the basis sets6-31G(d,p), 6-311G(d), and 6-311G(d,p) are used to optimizethe molecular geometries of reactants, products, and transition

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

κ= − Δ − Δ−‡ ‡⎛

⎝⎜⎞⎠⎟k T c

k Th

H T SRT

( ) ( ) expmo 1 B

(1)

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

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

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)

CTB1-2 4.05 × 1002 4.01 × 1002 4.02 × 1002 4.14 × 1002 4.11 × 1002 4.12 × 1002

CTB2-2 4.27 × 1002 4.16 × 1002 4.34 × 1002 4.42 × 1002 4.30 × 1002 4.39 × 1002

CTB3-2 4.21 × 1002 4.17 × 1002 4.18 × 1002 4.30 × 1002 4.24 × 1002 4.27 × 1002

CTB4-2 4.20 × 1002 4.16 × 1002 4.19 × 1002 4.29 × 1002 4.25 × 1002 4.26 × 1002

CTB5-2 4.37 × 1002 4.33 × 1002 4.35 × 1002 4.42 × 1002 4.38 × 1002 4.47 × 1002

CTM12 3.89 × 1002 3.86 × 1002 3.90 × 1002 4.01 × 1002 3.97 × 1002 4.00 × 1002

CTM2-2 4.12 × 1002 4.10 × 1002 4.13 × 1002 4.21 × 1002 4.18 × 1002 4.19 × 1002

CTM3-2 4.41 × 1002 4.36 × 1002 4.38 × 1002 4.51 × 1002 4.47 × 1002 4.47 × 1002

CTX1-2 3.88 × 1002 3.84 × 1002 3.87 × 1002 4.03 × 1002 3.99 × 1002 4.00 × 1002

CTX2-2 4.67 × 1002 4.72 × 1002 4.76 × 1002 4.80 × 1002 4.75 × 1002 4.79 × 1002

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

B3LYP6-31G(d,p)

B3LYP6-311G(d)

B3LYP6-311G(d,p)

X3LYP6-31G(d,p)

X3LYP6-311G(d)

X3LYP6-311G(d,p)

M06-2X6-31G(d,p)

M06-2X6-311G(d)

M06-2X6-311G(d,p)

CTB1-2Ea 45.50 52.70 50.50 42.30 51.00 48.10 22.90 27.10 25.20ΔH‡ 40.60 47.70 44.60 37.10 45.70 43.30 17.90 22.10 20.10ΔG‡ 95.10 102.60 100.00 90.70 100.20 96.60 78.40 79.60 80.00loge A 12.65 12.52 12.29 13.01 12.65 13.14 10.25 11.47 10.49k 3.30 × 10−03 1.60 × 10−04 3.07 × 10−04 1.73 × 10−02 3.60 × 10−04 1.90 × 10−03 2.78 × 1000 1.72 × 1000 1.38 × 1000

κw 3.27 3.50 3.49 3.28 3.48 3.49 3.41 3.50 3.40kw 1.07 × 10−02 5.60 × 10−04 1.07 × 10−03 5.67 × 10−02 1.25 × 10−03 6.63 × 10−03 9.48 × 1000 6.02 × 1000 4.70 × 1000

CTM1-2Ea 68.20 75.30 72.00 63.30 71.20 69.10 50.30 52.10 51.50ΔH‡ 63.30 70.30 67.20 57.90 66.20 64.20 45.40 47.10 46.20ΔG‡ 107.40 114.00 110.40 101.70 109.10 106.50 100.50 107.80 101.90loge A 16.85 17.15 17.23 16.98 17.35 17.59 12.40 10.17 12.17k 2.26 × 10−05 1.80 × 10−06 7.24 × 10−06 1.90 × 10−04 1.13 × 10−05 3.35 × 10−05 3.60 × 10−04 1.90 × 10−05 1.80 × 10−04

κw 3.61 3.83 3.78 3.63 3.81 3.79 3.17 3.27 3.15kw 8.15 × 10−05 6.89 × 10−06 2.73 × 10−05 6.89 × 10−04 4.30 × 10−05 1.27 × 10−04 1.14 × 10−03 6.21 × 10−05 5.67 × 10−04

CTX1-2Ea 65.90 71.60 70.50 63.40 70.20 68.30 54.70 56.00 55.20ΔH‡ 61.00 66.60 65.00 58.20 65.50 62.70 49.70 51.00 50.50ΔG‡ 107.50 113.00 111.80 104.40 111.40 107.70 100.60 107.40 102.40loge A 15.89 16.04 15.78 16.02 16.14 16.50 14.14 11.90 13.74k 2.19 × 10−05 2.60 × 10−06 3.13 × 10−06 7.00 × 10−05 5.07 × 10−06 1.57 × 10−05 3.60 × 10−04 2.30 × 10−05 1.95 × 10−04

κw 3.57 3.77 3.76 3.58 3.75 3.77 3.32 3.42 3.33kw 7.81 × 10−05 9.80 × 10−06 1.18 × 10−05 2.50 × 10−04 1.90 × 10−05 5.90 × 10−05 1.19 × 10−03 7.86 × 10−05 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.

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molecularity of the reaction, and ΔS‡ and ΔH‡ are the entropyand enthalpy of activation, respectively. ΔH‡ is given by

Δ = + + ΔΔ‡−H E H( ZPVE )0 TS R (2)

where ΔΔH is the difference in enthalpy between the transitionstate and the reactants, ZPVE is the difference in zero-pointvibrational energy between the transition state and the reactants,and E0 is the difference in electronic energy between thetransition state and the reactants. The activation energy Ea iscalculated using

= Δ +‡E H mRTa (3)

and the frequency factor A by

κ= + Δ−‡⎛

⎝⎜⎞⎠⎟A c

k Th

mR SR

( ) expmo 1 B

(4)

Scaling factors of 0.961, 0.966, and 0.967 are used forthe B3LYP functional with the 6-31G(d,p), 6-311G(d), and6-311G(d,p) basis sets, respectively, to calculate activationentropies, temperature corrections, and zero point vibrationalenergies. These factors are from the National Institute ofStandards and Technology (NIST) scientific and technicaldatabase.71 Quantum tunneling should be considered in thereactions involving the transfer of a hydrogen atom.72,73 TheWigner tunneling73 correction is calculated using

κ ν≈ +‡⎛

⎝⎜⎞⎠⎟

hk T

11

24 B

2

(5)

where ν‡ is the imaginary frequency of the transition state.All calculations are performed using GAMESS.74 PCM andCOSMO are applied to include solvent effects. These twocontinuum solvation methods are applied to each particularsolvent by setting physical properties such as the dielectricconstant and the solvent molecule radius.

3. RESULTS AND DISCUSSIONS3.1. Most Likely CTSMechanisms for MA, EA, and n-BA.

Different mechanisms of CTS reactions for n-butanol, MEK, andp-xylene are shown in Figure 2. The hydrogen atom is abstractedvia various mechanisms (Figure 2). The bond-dissociationenergies of these hydrogen atoms are given in Table 1. Bond-dissociation energy is defined as the energy difference between asolvent molecule and bond cleavage products (hydrogen radicaland solvent radical):75

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

(6)

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

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.

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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 molecularorbitals (stable ring) in p-xylene, abstraction of a methyl grouphydrogen is more favorable. We calculated the thermodynamicand kinetic parameters (activation energies, enthalpies of reaction,Gibb’s free energies, frequency factors, and rate constants) of themost likely mechanisms of CTS reactions of MA, EA, and n-BA.Table 2 presents the kinetic parameters of the most likelymechanisms of chain transfer to n-butanol, MEK and p-xylene forMA. The transition-state geometries for CTB1-2, CTM1-2, andCTX1-2 are shown in Figures 3, 4, and 5, respectively. It was foundthat the activation energy of chain transfer to n-butanol is lowerthan that of MEK and p-xylene reactions (Table 2), and the rateconstant for chain transfer to n-butanol is higher than that ofMEKand p-xylene. We attribute this to the polar and protic nature ofn-butanol, which can readily donate a hydrogen atom to thepolymer chain to facilitate chain transfer. p-Xylene andMEK lack alabile hydrogen atom to transfer. It was determined that M06-2X,a hybrid meta-GGA functional, gives lower activation energies andhigher rate constants than B3LYP and X3LYP. This agrees withthe findings for CTM reactions of alkyl acrylates.63 The calculatedkinetic parameters for chain transfer to n-butanol, MEK, andp-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-BAshow little effect of the end substituent groups of the live chains.The activation energy of chain transfer to p-xylene calculatedusing M06-2X/6-31G(d,p) functional is in agreement with thoseestimated from measurements taken in high-temperature n-BA

polymerization.8 However, the theoretically estimated rateconstant is 4 orders of magnitude smaller than the experimentallyestimated one. This difference is very likely due to the under-estimation of the solvent-based entropic effects and frequency factor.It indicates that hybrid meta-GGA functionals such as M06-2X canbetter account for van der Waals interactions76,77 and provide moreaccurate predictions of barrier heights relative to B3LYP, but they donot accurately account for all solvent interactions.

3.2. Chain Transfer to n-Butanol, sec-Butanol, and tert-Butanol. Several mechanisms of chain transfer to n-butanol, sec-butanol, and tert-butanol are shown in Figure 6. A live polymerchain can abstract a hydrogen atom from several locations inthese solvents. We calculated bond-dissociation energies of allavailable hydrogen atoms in these solvents (Figure 6), andthe calculated dissociation energies are given in Table 5. Theresults indicate that the weakest C−H bond is the one that isbroken in the CTBsec1-2 mechanism, which shows the highercapability of methylene carbon atoms to release a hydrogenatom, relative to methyl carbon atoms and oxygen. Themethylene carbon atom next to the oxygen in sec-butanol witha Mulliken charge of 0.152 is likely to release a hydrogen thanthe other methylene carbon atom that has a Mulliken charge of−0.228. Because bond-dissociation energies calculated forCTBtert1-1 and CTBtert1-2 mechanisms are not very different,these mechanisms are equally likely mechanisms for chaintransfer to tert-butanol. The calculated kinetic parameters ofCTB1-2, CTBsec1-2 and CTBtert1-2 mechanisms of MA aregiven in Table 6; among n-butanol, sec-butanol, and tert-butanol,tert-butanol has the lowest and sec-butanol has the highest

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.

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

B3LYP6-31G(d,p)

B3LYP6-311G(d)

B3LYP6-311G(d,p)

X3LYP6-31G(d,p)

X3LYP6-311G(d)

X3LYP6-311G(d,p)

M06-2X6-31G(d,p)

M06-2X6-311G(d)

M06-2X6-311G(d,p)

CTB1-2

Ea 45.60 53.30 50.30 40.60 49.00 48.40 19.40 23.80 21.20

ΔH‡ 40.60 48.30 44.70 35.70 43.60 43.40 14.50 18.90 16.40

ΔG‡ 94.30 102.00 98.30 88.70 96.90 95.60 74.20 79.10 76.90

loge A 13.00 13.08 13.02 13.26 13.14 13.62 10.56 10.36 10.25

k 4.50 × 10−03 2.20 × 10−04 6.90 × 10−04 4.40 × 10−02 1.30 × 10−03 2.70 × 10−03 1.53 × 1001 2.11 × 1000 5.43 × 1000

κw 3.29 3.51 3.48 3.28 3.52 3.51 3.49 3.59 3.49

kw 1.48 × 10−02 7.72 × 10−04 2.40 × 10−03 1.44 × 10−01 4.57 × 10−03 9.47 × 10−03 5.34 × 1001 7.57 × 1000 1.89 × 1001

CTM1-2

Ea 68.20 75.60 72.30 61.20 70.20 68.50 45.50 49.90 48.30

ΔH‡ 63.30 70.60 66.90 56.50 65.30 62.70 40.60 44.90 42.80

ΔG‡ 105.10 111.30 109.20 98.20 107.90 104.40 98.10 103.90 100.90

loge A 17.80 18.24 17.59 17.83 17.47 17.83 11.45 10.85 11.21

k 5.90 × 10−05 4.70 × 10−06 9.20 × 10−06 1.03 × 10−03 1.90 × 10−05 5.40 × 10−05 9.90 × 10−04 9.30 × 10−05 2.50 × 10−04

κw 3.60 3.82 3.80 3.61 3.85 3.81 3.17 3.27 3.20

kw 2.12 × 10−04 1.79 × 10−05 3.49 × 10−05 3.71 × 10−03 7.30 × 10−05 2.06 × 10−04 3.13 × 10−03 3.04 × 10−04 8.00 × 10−04

CTX1-2

Ea 66.10 72.90 70.30 62.00 69.30 67.50 53.20 55.50 51.10

ΔH‡ 61.20 68.00 64.80 57.40 64.10 62.20 48.30 50.60 45.90

ΔG‡ 103.30 113.00 106.50 100.30 105.80 103.30 102.00 104.10 102.20

loge A 17.67 16.51 17.83 17.35 17.83 18.06 13.02 12.89 11.93

k 1.20 × 10−04 2.40 × 10−06 2.63 × 10−05 4.60 × 10−04 3.93 × 10−05 1.03 × 10−04 2.10 × 10−04 7.40 × 10−05 1.68 × 10−04

κw 3.59 3.79 3.84 3.57 3.82 3.83 3.30 3.40 3.28

kw 4.30 × 10−04 9.09 × 10−06 1.00 × 10−04 1.64 × 10−03 1.50 × 10−04 3.94 × 10−04 6.93 × 10−04 2.52 × 10−04 5.50 × 10−04

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

B3LYP6-31G(d,p)

B3LYP6-311G(d)

B3LYP6-311G(d,p)

X3LYP6-31G(d,p)

X3LYP6-311G(d)

X3LYP6-311G(d,p)

M06-2X6-31G(d,p)

M06-2X6-311G(d)

M06-2X6-311G(d,p)

CTB1-2

Ea 45.10 53.30 52.40 40.30 46.60 46.10 20.40 21.00 20.30

ΔH‡ 40.20 48.20 46.60 34.70 41.80 41.40 15.40 16.50 15.00

ΔG‡ 94.10 101.50 101.10 86.60 95.40 94.40 76.50 77.00 76.70

loge A 12.89 13.14 12.65 13.74 13.02 13.26 10.00 10.25 9.77

k 5.00 × 10−03 2.30 × 10−04 2.10 × 10−04 8.00 × 10−02 3.00 × 10−03 4.70 × 10−03 5.90 × 1000 5.90 × 1000 4.83 × 1000

κw 3.28 3.52 3.34 3.32 3.54 3.36 3.50 3.60 3.49

kw 1.64 × 10−02 8.09 × 10−04 7.01 × 10−04 2.65 × 10−01 1.06 × 10−02 1.58 × 10−02 2.06 × 1001 2.12 × 1001 1.68 × 1001

CTM1-2

Ea 63.10 69.20 69.60 60.00 67.30 66.60 41.00 45.50 43.10

ΔH‡ 58.20 63.80 65.20 55.50 62.00 61.90 36.10 40.40 38.50

ΔG‡ 99.90 106.40 106.60 98.40 103.40 103.60 95.10 98.50 97.20

loge A 17.83 17.47 17.95 17.35 17.95 17.83 10.85 11.21 10.97

k 4.80 × 10−04 2.85 × 10−05 3.93 × 10−05 1.04 × 10−03 9.94 × 10−05 1.20 × 10−04 3.40 × 10−03 7.80 × 10−04 1.60 × 10−03

κw 3.59 3.82 3.62 3.58 3.86 3.66 3.17 3.29 3.19

kw 1.72 × 10−03 1.09 × 10−04 1.42 × 10−04 3.72 × 10−03 3.83 × 10−04 4.39 × 10−04 1.07 × 10−02 2.56 × 10−03 5.10 × 10−03

CTX1-2

Ea 64.30 67.50 70.40 58.50 65.20 65.20 54.70 57.00 59.10

ΔH‡ 58.90 61.70 65.30 53.50 60.50 60.30 49.70 51.60 53.60

ΔG‡ 99.10 104.90 107.90 94.90 103.40 102.30 100.10 104.90 107.20

loge A 18.43 17.23 17.47 17.95 17.35 17.71 14.34 13.14 13.02

k 5.40 × 10−04 4.45 × 10−05 1.76 × 10−05 3.40 × 10−03 1.30 × 10−04 1.80 × 10−04 4.40 × 10−04 5.17 × 10−05 1.96 × 10−05

κw 3.58 3.78 3.59 3.62 3.82 3.63 3.34 3.42 3.35

kw 1.93 × 10−03 1.68 × 10−04 6.31 × 10−05 1.23 × 10−02 4.96 × 10−04 6.53 × 10−04 1.47 × 10−03 1.76 × 10−04 6.57 × 10−05

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chain-transfer rate constant. These findings are in agreementwith the experimentally estimated chain transfer to n-butanol,sec-butanol, and tert-butanol rate constants in MA polymer-ization 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 polymer-ization at 80 °C, given in Table 6, indicates that (a) the

M06-2X-estimated values are closer to the experimentallyestimated ones, (b) the M06-2X-estimated values of chaintransfer to n-butanol and sec-butanol rate constants are very closeto the experimentally estimated ones, and (c) the values of chaintransfer to tert-butanol rate constant estimated by M06-2Xand B3LYP are, respectively, approximately four and six orders ofmagnitude smaller than the experimentally estimated value.

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

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)

CTBsec1-2 3.97 × 1002 3.99 × 1002 3.98 × 1002 4.08 × 1002 4.04 × 1002 4.06 × 1002

CTBsec2-2 4.34 × 1002 4.37 × 1002 4.35 × 1002 4.50 × 1002 4.47 × 1002 4.49 × 1002

CTBsec3-2 4.21 × 1002 4.23 × 1002 4.20 × 1002 4.34 × 1002 4.33 × 1002 4.34 × 1002

CTBtert1-2 4.34 × 1002 4.36 × 1002 4.35 × 1002 4.50 × 1002 4.48 × 1002 4.46 × 1002

CTBtert2-2 4.45 × 1002 4.49 × 1002 4.46 × 1002 4.52 × 1002 4.47 × 1002 4.46 × 1002

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

n-butanol sec-butanol tert-butanol

B3LYP 6-31G(d,p) Ea 45.50 45.30 79.50ΔH‡ 40.60 40.30 74.00ΔG‡ 95.10 93.90 127.00loge A 12.65 13.02 13.26k 3.30 × 10−03 5.20 × 10−03 6.63 × 10−09

κw 3.27 3.25 3.15kw 1.07 × 10−02 1.69 × 10−02 2.10 × 10−08

M06-2X 6-31G(d,p) Ea 22.90 24.10 64.30ΔH‡ 17.90 19.20 59.40ΔG‡ 78.40 77.20 109.70loge A 10.25 11.27 14.34k 2.78 × 1000 4.60 × 1000 9.00 × 10−06

κw 3.41 3.37 3.28kw 9.48 × 1000 1.55 × 1001 2.95 × 10−05

experimental14,78 k (353 K) 1.10 × 1001 5.50 × 1001 1.50 × 1000

B3LYP 6-31G(d,p) k (353 K) 5.76 × 10−02 8.93 × 10−02 9.87 × 10−07

M06-2X 6-31G(d,p) k (353 K) 1.16 × 1001 2.10 × 1001 5.20 × 10−04

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

for n-butanol is higher than those obtained via gas phasecalculations, so the PCM-calculated rate constant for n-butanolis lower. p-Xylene is nonpolar, so applying PCM does notsignificantly affect the stability of reactants or the transitionstates. n-Butanol and MEK are both polar solvents, so thestability of reactants and transition states individually are eachstrongly affected. Because the polarity and dipole moment ofMEK are higher than those of n-butanol, the inclusion of PCMstabilizes the transition state of CTM1-2 more than that of

Table 7. Activation Energy (Ea), Enthalpy of Activation (ΔH‡), andGibb’s Free Energy of Activation (ΔG‡) in kJmol−1; FrequencyFactor (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 CTM1-2 CTX1-2

COSMO PCM COSMO PCM COSMO PCM

MAEa 23.50 38.10 51.00 48.40 51.60 56.50ΔH‡ 18.40 33.20 46.20 43.40 46.60 51.50ΔG‡ 78.50 84.70 96.60 103.50 96.30 105.60loge A 10.49 13.86 14.22 10.60 14.82 13.02k 2.73 × 1000 2.20 × 10−01 1.72 × 10−03 1.31 × 10−04 2.46 × 10−03 5.63 × 10−05

EAEa 20.30 34.40 47.10 46.30 51.30 59.50ΔH‡ 15.30 28.60 42.20 40.70 46.50 54.20ΔG‡ 73.50 80.20 97.10 98.40 94.10 105.60loge A 11.09 14.21 12.41 11.57 15.42 13.62k 1.81 × 1001 1.38 × 1000 1.36 × 10−03 8.11 × 10−04 5.10 × 10−03 3.10 × 10−05

BAEa 18.00 35.50 39.10 45.40 54.20 57.20ΔH‡ 13.50 30.40 34.20 40.40 49.10 51.60ΔG‡ 75.30 82.60 88.40 98.30 98.50 106.00loge A 9.53 13.26 13.01 11.21 14.82 13.01k 9.63 × 1000 3.43 × 10−01 6.26 × 10−02 8.13 × 10−04 8.62 × 10−04 4.20 × 10−05

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

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CTB1-2. In the case of MEK, the change in the stability ofCTM1-2 transition state is nearly the same as that of thereactants. PCM calculations are also carried out to studyCTB1-2, CTM1-2, and CTX1-2 mechanisms for EA and n-BA.Again, although PCM has a strong effect on the activationenergies and rate constants of chain transfer to n-butanol

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

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

CTB1-1 CTM1-1 CTX1-1

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

MAEa 48.40 23.00 67.40 52.20 66.40 56.10ΔH‡ 42.60 18.30 61.60 47.40 61.20 51.30ΔG‡ 93.70 75.80 111.30 102.10 110.50 107.50loge A 14.21 11.45 14.82 12.41 14.82 12.05k 4.87 × 10−03 8.73 × 1000 4.92 × 10−06 1.70 × 10−04 6.27 × 10−06 2.51 × 10−05

κw 3.27 3.41 3.62 3.19 3.59 3.33kw 1.59 × 10−02 2.97 × 1001 1.78 × 10−05 5.42 × 10−04 2.25 × 10−05 8.35 × 10−05

EAEa 46.30 22.30 69.50 48.10 67.00 53.40ΔH‡ 41.20 17.20 63.60 43.50 62.10 48.40ΔG‡ 97.00 75.40 107.70 94.30 105.50 102.00loge A 12.05 10.85 15.42 12.05 16.02 14.22k 1.30 × 10−03 6.36 × 1000 4.18 × 10−06 6.30 × 10−04 1.63 × 10−05 6.50 × 10−04

κw 3.28 3.50 3.63 3.17 3.56 3.30kw 4.26 × 10−03 2.22 × 1001 1.52 × 10−05 1.99 × 10−03 5.80 × 10−05 2.15 × 10−03

BAEa 45.60 21.20 65.50 43.10 64.20 56.10ΔH‡ 41.10 16.50 60.40 38.50 59.10 51.50ΔG‡ 95.70 74.30 106.30 94.50 107.20 103.00loge A 12.41 11.21 16.02 12.17 15.42 13.62k 2.50 × 10−03 1.42 × 1001 2.99 × 10−05 5.40 × 10−03 2.77 × 10−05 1.20 × 10−04

κw 3.31 3.48 3.57 3.16 3.61 3.36kw 8.27 × 10−03 4.94 × 1001 1.07 × 10−04 1.70 × 10−02 1.00 × 10−04 4.03 × 10−04

Table 9. Activation Energy (Ea), Enthalpy of Activation (ΔH‡), andGibb’s Free Energy of Activation (ΔG‡) in kJmol−1; FrequencyFactor (A) and Rate Constant (k) inM−1 s−1, for CTB1-1, CTM1-1, and CTX1-1Mechanisms ofMA, EA, and n-BA at 298 K, UsingPCM and COSMO

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

CTB1-1 CTM1-1 CTX1-1

COSMO PCM COSMO PCM COSMO PCM

MAEa 24.50 39.30 50.50 50.10 53.20 57.50ΔH‡ 19.10 33.90 45.30 45.40 48.30 51.60ΔG‡ 79.50 86.10 97.20 102.00 102.40 104.800loge A 10.49 13.62 13.50 11.57 12.78 13.26k 1.82 × 1000 1.10 × 10−01 1.00 × 10−03 1.80 × 10−04 1.70 × 10−04 4.75 × 10−05

EAEa 23.40 35.50 48.20 48.60 50.30 58.40ΔH‡ 17.60 30.30 42.60 44.00 44.60 53.40ΔG‡ 77.50 80.80 97.30 102.70 93.50 108.70loge A 10.73 13.98 13.02 10.85 15.30 12.05k 3.60 × 1000 7.10 × 10−01 1.60 × 10−03 1.60 × 10−04 6.70 × 10−03 9.90 × 10−06

BAEa 23.50 37.20 45.40 48.10 58.10 57.00ΔH‡ 18.20 31.70 40.30 43.40 53.40 52.50ΔG‡ 78.60 82.00 91.80 100.10 102.20 104.00loge A 10.13 14.46 13.62 11.69 14.94 13.50k 1.90 × 1000 5.70 × 10−01 9.00 × 10−03 4.40 × 10−04 2.00 × 10−04 7.44 × 10−05

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reduces the rate of formation of branch-points along the polymerbackbone during polymerization of n-BA and increases theaverage 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 relativestability of the reactants to the transition states. These resultsseem to indicate that COSMO is not able to represent the effects

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

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, withTunneling) 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′ CTM1-2′ CTX1-2′

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

MAEa 47.30 24.40 68.10 52.20 67.00 54.70ΔH‡ 41.70 18.60 63.30 47.50 62.30 50.40ΔG‡ 99.40 81.20 114.60 103.80 112.00 107.30loge A 11.45 9.53 13.73 11.57 14.46 11.69k 4.80 × 10−04 7.30 × 10−01 1.06 × 10−06 7.49 × 10−05 3.43 × 10−06 3.08 × 10−05

κw 3.39 3.57 3.88 3.31 3.84 3.55kw 1.63 × 10−03 2.60 × 1000 4.11 × 10−06 2.48 × 10−04 1.32 × 10−05 1.09 × 10−04

EAEa 46.60 23.40 70.10 50.20 68.00 58.30ΔH‡ 42.20 18.10 65.20 45.20 63.50 52.70ΔG‡ 98.10 81.30 115.00 104.80 106.90 110.30loge A 12.05 9.05 14.46 10.37 16.74 11.81k 1.20 × 10−03 6.70 × 10−01 9.82 × 10−07 5.06 × 10−05 2.24 × 10−05 8.12 × 10−06

κw 3.48 3.61 3.92 3.37 3.90 3.55kw 4.17 × 10−03 2.41 × 1000 3.85 × 10−06 1.70 × 10−04 8.73 × 10−05 2.88 × 10−05

BAEa 48.10 28.30 67.50 48.30 66.20 61.00ΔH‡ 43.10 23.50 61.70 43.40 60.90 56.40ΔG‡ 105.60 92.90 121.40 111.30 119.20 119.60loge A 9.41 6.40 10.97 7.24 11.33 8.69k 4.52 × 10−05 6.60 × 10−03 8.55 × 10−08 4.76 × 10−06 2.07 × 10−07 1.21 × 10−07

κw 3.49 3.76 3.94 3.37 3.88 3.70kw 1.58 × 10−04 2.48 × 10−02 3.37 × 10−07 1.60 × 10−05 8.03 × 10−07 4.47 × 10−07

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3.4. Effect of the Type of Initiating Radical on CTS. Twotypes of monoradicals generated via monomer self-initiation41,42

are shown in Figure 1. In the previous sections, the most likelyCTS reaction mechanisms of a two-monomer-unit live polymerchain initiated via M2

• were investigated. Figure 7 shows themost likely CTS reaction mechanisms of a two-monomer-unitlive polymer chain initiated via M1

•. The kinetic parameters ofthe CTB1-1, CTM1-1, and CTX1-1 reactions in the gas phase arecalculated (Table 8). We found that the calculated rates arecomparable to that of two-monomer-unit live polymer chaininitiated via M2

•. This indicates that the choice of initiatingradical 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 energiesand rate constants of the CTB1-1, CTM1-1, and CTX1-1reactions are listed in Table 9. The energy and rate constants oflive polymer chains initiated by M1

• vary by ±3 kJ/mol and1 order of magnitude from that of live polymer chains initiated byM2

• (Table 7). The≈16 kJ/mol increase in activation energy andthe 2 orders of magnitude decrease in the rate constant calculatedusing PCM in comparison with those calculated in the gas phase(reported in Table 8) show the significant effect of PCM on thekinetic parameters of the CTB1-1mechanism. COSMO (Table 9)was found to have negligible effect on the rate comparisonbetween 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 thoseobtained for the CTB1-2, CTM1-2, CTX1-2 mechanisms(Table 7). The kinetic parameters using this solvation modeldo 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 witha three-monomer-unit live chain initiated by M2

• (Figure 8) areinvestigated. Table 10 shows that an increase in the length of thelive chain polymer does not affect the kinetics of CTS reactions ofMA, EA, and n-BA. The geometries of the transition states of theCTB1-2′, CTM1-2′, and CTX1-2′ mechanisms are quite similarto those of the CTB1-2, CTM1-2, and CTX1-2 mechanismsin which the two-monomer-unit live chain initiated by M2

• wasconsidered as the reactant (Figures 3−5). It can be concludedthat live polymer chain length does not affect the geometry ofthe reaction center significantly. These findings are in agree-ment with CTM studies63 and propagation reactions of alkylacrylates.44 The same studies are performed using PCM toidentify the impacts of live polymer chain length on the kineticsof the CTS reactions in the presence of solvents. The resultsreported in the Supporting Information confirm our earlierfindings that the length of a live polymer chain does not affect thekinetics of the CTS reactions significantly. Comparing theseresults with those given in Table 7, we can conclude that PCMhas no significant differential effect on the kinetics of CTSreactions involving live polymer chains with different lengths.

4. CONCLUDING REMARKSThe mechanisms for chain transfer to n-butanol, MEK, andp-xylene in self-initiated high-temperature polymerization ofthree alkyl acrylates were studied using first-principles quantum-chemical calculations. Abstraction of a hydrogen from themethylene group next to the oxygen atom in n-butanol, fromthe methylene group in MEK, and from a methyl group inp-xylene by a live polymer chain were found to be the mostlikely mechanisms of CTS reactions in MA, EA, and n-BA.

Among n-butanol, sec-butanol, and tert-butanol, tert-butanol hasthe highest CTS energy barrier and the lowest rate constant.Chain transfer to n-butanol and sec-butanol reactions havecomparable kinetic parameter values. The activation energy ofthe most likely chain transfer to p-xylene mechanism of a two-monomer-unit live n-BA polymer chain initiated by M2

•

calculated using M06-2X/6-31G(d,p) was found to be close tothose estimated from polymer sample measurements. Applica-tion of PCM resulted in remarkable changes in the kineticparameters of the chain transfer to n-butanol. However, it hadvery little effect on the stability of the reactants and the transitionstates in chain transfer to MEK and p-xylene. COSMO showedno solvent effect on the kinetics of CTS reactions of MA, EA, andn-BA. It was found that the live polymer chain length has verylittle effect on the activation energies and rate constants of CTSreactions. MA, EA, and n-BA live chains initiated by M2

• andM1•

showed similar hydrogen abstraction abilities, indicating that thetype of monoradical generated via self-initiation has little or noeffect on the capability of MA, EA, and n-BA live polymer chainsto undergo CTS reactions.

■ ASSOCIATED CONTENT*S Supporting InformationFive tables of activation energies, enthalpies of activation, Gibb’sfree energies of activation, frequency factors, and rate constants.This material is available free of charge via the Internet athttp://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*M. Soroush. Phone: (215) 895-1710. E-mail: ms1@drexel.edu.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis material is based upon work partially supported by theNational Science Foundation under Grants CBET-0932882,CBET-1160169, and CBET-1159736. Any opinions, findings,and conclusions or recommendations expressed in this materialare those of the authors and do not necessarily reflect the views ofthe National Science Foundation. Acknowledgment is also madeto the Donors of the American Chemical Society PetroleumResearch 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 wasprovided by the High-Performance Computing ModernizationOffice of the U.S. Department of Defense.

■ REFERENCES(1) Rehberg, C. E.; Fisher, C. H. Preparation and properties of the n-alkyl acrylates. J. Am. Chem. Soc. 1944, 66, 1203−1207.(2) Okor, R. S. Drug release on certain acrylate methacrylate salicylic-acid coacervated systems. J. Controlled Release 1990, 12 (3), 195−200.(3) VOC’s Directive, EU Committee of the American Chamber ofCommerce in Belgium, ASBL/VZw, Brussels, July 8. 1996.(4) Grady, M. C.; Simonsick, W. J.; Hutchinson, R. A. Studies of highertemperature polymerization of n-butyl methacrylate and n-butylacrylate. Macromol. Symp. 2002, 182, 149−168.(5) Chiefari, J.; Jeffery, J.; Mayadunne, R. T. A.; Moad, G.; Rizzardo, E.;Thang, S. H. Chain transfer to polymer: A convenient route tomacromonomers. Macromolecules 1999, 32 (22), 7700−7702.(6) Buback, M.; Klingbeil, S.; Sandmann, J.; Sderra, M. B.; Vogele, H.P.; Wackerbarth, H.; Wittkowski, L. Pressure and temperature

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