Theoretical Study of Intermolecular Chain Transfer to Polymer Reactions of Alkyl Acrylates

18 Pages·2015·2.22 MB·English

Article
pubs.acs.org/IECR
Theoretical Study of Intermolecular Chain Transfer to Polymer
Reactions of Alkyl Acrylates
† ‡ § # ‡
Nazanin Moghadam, Shi Liu, 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: Mechanisms of intermolecular chain transfer to polymer (CTP) reactions in monomer self-initiated
polymerization of alkyl acrylates, such as methyl acrylate, ethyl acrylate, and n-butyl acrylate, are studied using density
functional theory calculations. Dead polymer chains with three different structures are considered, and three types of hybrid
density functionals and four basis sets are used. The energy barrier and rate constant of each reaction are calculated using the
transitionstatetheoryandtherigidrotorharmonicoscillatorapproximation.Thestudyindicatesthattertiaryhydrogensofdead
polymersformedbydisproportionationreactionsaremostlikelytobetransferredtolivepolymerchainsinCTPreactions.The
length of the polymer chain has little effect on the calculated activation energies and transition-state geometries in all CTP
mechanismsexploredinthisstudy.Moreover,CTPreactionsofmethyl,ethyl,andbutylacrylateshavesimilarenergybarriersand
rate constants. The application of the integral equation formalism-polarizable continuum model results in higher CTP energy
barriers. This increase in the predicted CTP energy barriers is larger in n-butanolthan in p-xylene. However, the application of
the conductor-like screening model does not affect the predicted CTP kinetic parameters.
1. INTRODUCTION experimentally that hydrogen bonding has a disruptive effect
on acrylate backbiting mechanisms, and the level of branching
Acrylic binder resins are used in paint and coating formula-
can be reduced by choosing an appropriate solvent.27 The
tions.1 Environmental regulations, which require the volatile
contributionofCTPtothelevelofbranchingwasexploredfor
organic content of resins to be less than 300 ppm, have caused
controlled radical polymerization (CRP)28 and conventional
changesinthebasicdesignofresinsusedinautomobilecoating
free radical polymerization (FRP) of butyl acrylate (BA), and
formulations.2 High temperature (>100 °C) free-radical
the level of branches as a function of transient lifetime was
polymerization allows production of low-molecular-weight high-
polymer-content acrylic resins that have low viscosity.3−5 How- reported.23,26 The role of midchain radicals, formed through
inter- and intramolecular CTP reactions during BA polymer-
ever, in high temperature polymerization, secondary reactions6
such as β-scission,7 monomer self-initiation,8−10 and intra- and iczoamtiopnareadt hwiigthh-ttehmatpeorfatsuerceos,ndwaarsysrtauddicieadls.2e9xpTerhiemseenmtalildychaanind
isntrtoernmgloyleacffuelcatrpcrhoapinerttireasnosfferthteoppoolylmymererpr(oCdTucPt)s.6r,7e,a13c−ti1o8ns11,12 rtaald1i9c,3a0ls−4u1nadnedrgotheβo-rsectisicsaiol1n5,4r2e−a4c8tioinnvse.stNiguamtioenrosuhsaveexpeproiminteend-
There are two types of CTP reactions: intramolecular and
out that CTP reactions can strongly impact the overall rate of
intermolecular.Inanintramolecularchaintransfer(backbiting) polymerization.AsCTPreactionsaffectthemolecularstructure
reaction, a secondary radical (live chain) abstracts a hydrogen of the final polymer,19,49 a better understanding of CTP
atom from its backbone, producing a midchain radical.11,19−21
reactions will enable optimizing polymerization processes and
In an intermolecular chain transfer reaction, however, a live producing desired polymers.15,50,51
polymer chain abstracts a hydrogen atom from a dead poly- CTP and β-scission reactions in thermal polymerization of
mer.15,19 Prior to this work, it was inconclusive which dead
n-BA and n-butyl methacrylate (BMA) have been studied
polymer structure was most likely to provide the hydrogen using nuclear magnetic resonance (NMR) spectroscopy and
atom during CTP reactions. Although at low polymer electrospray ionization/Fourier transform mass spectroscopy
concentrationsintramolecularCTPisdominant,19athighpoly-
mer concentrations intermolecular CTP is dominant.15,19,22−26
Special Issue: Scott Fogler Festschrift
The new radicals generated by CTP reactions propagate to
formbranchesorterminatebycouplingwithotherpropagating Received: October 18, 2014
radicals.15 The kinetic parameters of backbiting reactions of Revised: December 18, 2014
chain-end and midchain radicals were investigated by applying Accepted: December 29, 2014
the density functional theory (DFT) approach.20 It was found
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(ESI/FTMS).15,49,52NMRanalysisofthesepolymersindicated andpropagationreactionsofalkenes,62,71MA,78andMMA81in
thepresenceofendgroupsfromCTPreactionsattemperatures thegasphase.Chaintransfertomonomer(CTM)82andchain
lower than 70 °C.19,33,49 Experimental studies have shown the transfer to solvent (CTS)83 reactions have also been studied.
important role of intramolecular chain transfer and scission Before this study, there was no report on the optimal level of
reactions in the reduction of dead-polymer average molecular theory needed to explore CTP reactions or dead polymer
weights and the enhancement of the overall rate of polymer- structuresthatmostlikelyreleaseahydrogenatomduringCTP
ization.7,12,15,42NMRandESI/FTMSanalysesofsamplesfrom reactions in high temperature polymerization ofalkyl acrylates.
spontaneous (no thermal initiator added) high-temperature Solvent molecules are known to affect the stability of
homopolymerization of ethyl acrylate (EA) and n-BA have transition-state structures of reactions in solution free-radical
shown that different branch points are generated during the polymerization.84 The solvent stabilization of transition-state
polymerization.25 The pulsed-laser polymerization/size exclu- structures can cause significant differences between gas-phase
sion chromatography (PLP/SEC) method was used to study rate constants calculated using computational quantum
the kinetics of CTP reactions in the polymerization of alkyl chemistry and rate constants obtained experimentally in
acrylate.42,53Whilepulsed-laserpolymerization(PLP)hasbeen solution polymerization.85,86 The polarizable continuum
used to estimate the rate constants of propagation reactions model (PCM)87,88 was applied to estimate the propagation
(k ) of monomers such as styrene54 and methyl methacrylate ratecoefficient ofacrylic acidinthepresence oftoluene,89and
p
(MMA),55 and chain transfer reactions of n-butyl methacrylate smalldifferencesbetweengas-phaseandliquid-phaseactivation
(BMA),56areproduciblevalueofthepropagationrateconstant energies and rate constants were observed. Another solvation
obtained using low laser pulse-repetition rates (<100 Hz) has model, the conductor-like screening model (COSMO),90 was
not been reported for alkyl acrylates at temperatures above appliedtoexploretheeffectofsolventswithdifferentdielectric
30 °C. The molecular-weight distributions of PLP-generated constants on the propagation rate coefficients in free-radical
polymers showed peak broadening at temperatures above polymerizationofacrylonitrileandvinylchloride.91Inaddition,
30 °C, which was attributed to the occurrence of both inter- COSMO was applied to predict nonequilibrium solvation
and intramolecular CTP reactions.33,57 However, high repeti- energies of biphenyl-cyclohexane-naphthalene.92 The perfor-
tion rates have been applied to overcome the temperature mances of PCM and COSMO in predicting solvent effects on
restrictions.58 At temperatures above 30 °C, intermolecular kinetic parameters of CTS reactions have also been com-
CTP reactions in free-radical polymerization of n-BA15,19 and pared.83 Integral equation formalism (IEF),93,94 which is a
2-ethylhexyl acrylate49 have also been studied using NMR version of PCM, was used to study polar interaction effects
spectroscopy. Whiletheseanalyticaltechniqueshavebeenvery on barriers of chain transfer to several agents in free-radical
useful in characterizing acrylate polymers generated from polymerization of ethylene, MMA, and acrylamide based on
thermal free-radical polymerizations, their use has not led to integral operators.95 In this work we apply IEF-PCM and
a conclusive determination of specific reaction mechanisms or COSMOtoCTPreactions,comparetheperformances ofIEF-
estimation of individual reaction kinetic parameters. PCM and COSMO, and determine the effects of several
Macroscopic kinetic models have been used extensively59 to solvents on the reactions.
estimate the rate constants of initiation, propagation, chain DFT has been applied to calculate the entropy change of
transfer, and termination reactions in free-radical polymer- various organic reactions, giving entropies that are in good
ization of acrylates, from polymer-sample measurements of agreement with experimental values.96 This good agreement
monomer conversions and average molecular weights.59,60 has also been reported for systems with high molecular
However, the accuracy of these estimated kinetic parameters weights.96 However, large differences between the entropies of
depends on the accuracy of the assumed mechanistic model bimolecular and unimolecular reactions have been observed.97
and measurements used in the estimation. Also, these models These differences have been blamed on the different degrees-
are incapable of conclusively determining mechanisms and of-freedom lost in these reactions.97 In the unimolecular re-
molecular species involved. actions,thenetchangeinthenumberofdegreesoftranslation,
Computational quantum chemistry methods have been used rotation, and vibration is zero. However, in bimolecular re-
successfully to explore the mechanisms of free-radical actions,thereisalossofthreetranslationalandthreerotational
reactions.61−76 Specifically, DFT has been widely applied to degrees of freedom (a gain of six new vibrational modes).97 In
calculate the rate constants of initiation, propagation, chain bimolecular reactions, in which two species are interacting, the
transfer, and termination reactions in free-radical polymer- total entropy of the system is approximately the entropy of
ization of various monomers.61−75 The forward and reverse oneofthespeciesduetothelargecontributionoftranslational
reaction rate coefficients have been calculated for a series of frequencies to the total entropy of the system.11,96,97 The
reversible addition−fragmentation chain-transfer (RAFT) translational entropy of most molecules depends on the space
reactions using high-level wavefunction-based quantum chem- availabletothemolecule(ratherthanmassofthemolecule).97
istry calculations.77 DFT-based methods are computationally Temperature, moment of inertia, and the symmetry of a
less intensive than wavefunction-based methods,78,79 and are molecule play a major role in the calculation of the rotational
therefore preferred for studying chain transfer reactions in the entropy.97 The vibrational entropy is proportional to the
polymerization of alkyl acrylates given the large size of the frequency of vibration and temperature.97 Activation entropies
polymer system. Molecular geometries and rate constants of ofvariousbimolecularreactionshavebeenreported20,53,56,57,81,98
variousreactionsinthepolymerizationofalkenesandacrylates to be about −150 to −170 J mol−1 K−1, which is higher (more
have been predicted accurately using DFT-based methods.62,69 negative) than those of unimolecular reactions.97 Although
The B3LYP/6-31G(d) level of theory has been applied to entropiesoftransitionstatesandreactantsarelowerinsolution,
explore self-initiation mechanisms of styrene,68 MA, EA, the entropy change of dimerization of cyclopentadiene reaction
n-BA,8,9 and MMA,10 cyclohexanone-monomer co-initiation insolutionisonlyslightlydifferent(13Jmol−1K−1)fromthatin
reaction in thermal homopolymerization of MA and MMA,80 the gas phase.97 This has been attributed to the higher boiling
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ptroainnstitiaonndstcaotnestehqaunenthtleyrleaarcgtearntesn.9t7r,9o9py of vaporization of the ΔH⧧= E0 + (ZPVE + ΔΔH)TS−R (2)
Inthiswork,mechanismsofCTPreactionsinmonomerself- whereΔΔHisthedifferenceinenthalpyofthetransitionstate
initiated polymerization of alkyl acrylates are studied using (TS) and the reactants (R), ZPVE is the difference in zero-
DFTcalculations.Themechanismsareinvestigatedusingthree point vibrational energy between the transition state and the
types of hybrid functionals (B3LYP, X3LYP, and M06-2X) reactants, and E0 is the barrier (the difference in electronic
and four basis sets (6-31G(d), 6-31G(d, p), 6-311G(d), and energy of the transition state and the reactants). In this work,
6-311G(d, p)). Dead polymer chains with three different the RRHO approximation66,81 is used when estimating ZPVE,
structuresareconsidered.TheCTPreactivitiesofMA,EA,and ΔΔH, and ΔS⧧ due to its simplicity and reasonable accuracy
n-BA are calculated using these levels of theory, and the shown in previous studies.10,68,81 The activation energy (Ea) is
calculated values are compared with each other and experi- calculated using
amnednCtaOlrSeMsuOlts,.hTawveobdeieffnereexnptloimrepdl.icTithseollevveenltomfothdeeolsr,yIEadFe-qPuCaMte Ea = ΔH⧧+ mRT (3)
forstudyingCTPreactionsandpropersolventmodelstoapply and the frequency factor (A) using
are investigated. The energy barrier and rate constant of each
⎛ ⎞
reaction are calculated using transition state theory and the A = (c0)1−mkBT exp⎜mR + ΔS⧧⎟
rigid rotor harmonic oscillator (RRHO) approximation. h ⎝ R ⎠
(4)
The rest of this paper is organized as follows. Section 2 dis-
cusses the applied computational methods. Section 3 provides Quantumtunnelingshouldbeconsideredinreactionsinvolving
results and discussion. Finally, section 4 presents concluding thetransferofahydrogenatom.17,48,106,107TheWignertunnel-
remarks. ing107 correction is calculated in this work using
⎛ ⎞2
1 hν⧧
2. COMPUTATIONAL METHODS κ ≈ 1 + ⎜ ⎟
The thermodynamic and kinetic parameters (activation ener- 24⎝kBT⎠ (5)
gies, enthalpies of reaction, Gibbs free energies, frequency ⧧
where v is the imaginary frequency of the transition state.
factors,andrateconstants)ofintermolecularCTPreactionsfor
MA, EA, and n-BA are calculated using DFT. Since there is 3. RESULTS AND DISCUSSIONS
exactly one unpaired spin in our systems, we use restricted
Weconsiderthreedeadpolymerstructuresformedbythethree
open-shellwavefunctionsinourcalculations.B3LYPisselected
terminationreactionsshowninFigure1.Twomonoradicalscan
to calculate energy barriers and optimize the molecular geo-
undergo termination by coupling reaction to form a dead poly-
metriesofreactants,products,andtransitionstates.X3LYPand
M06-2X100−102functionalsareappliedtovalidatethecalculated mer (D1) [Figure 1a]. A monoradical (M1 shown in Figure 2)
results. Four different basis sets (6-31G(d), 6-31G(d, p), after one propagation step, can be terminated by hydrogen
abstraction, leading to the formation of the dead polymer D2
6-311G(d), and 6-311G(d, p)) are used with each of these
[Figure 1b]. A monoradical with two monomer units can also
functionals. Reactants and transition states are validated by
react with a monoradicalwithone monomerunittoforma D3
performing Hessian calculations. NMR spectra of dead poly-
dead polymer [Figure 1c].
mers generated by CTP mechanisms are calculated using sev-
3.1. Mechanisms of Chain Transfer to D1 Dead
eralfunctionals(B3LYP,andX3LYP)andbasissets(6-31G(d),
Polymer. Possible mechanisms of chain transfer to the D1
6-31G(d, p), 6-311G(d), and 6-311G(d, p)). These calculated
deadpolymerforMA,EA,andn-BA,areshowninFigures3,4
spectra are compared with experimental spectra reported
for EA and n-BA polymers.19,25 Implicit solvent models, IEF- and 5, respectively. The energy differences of optimized re-
PCM and COSMO, are applied to account for solvent effects. actantsandproductsinvolvedineachofthesemechanismsare
calculated by applying B3LYP and X3LYP functionals and
Minimum-energy pathways for several reactions of interest are
6-31G(d), 6-31G(d,p), 6-311G(d), and 6-311G(d,p) basis
determined using intrinsic reaction coordinated (IRC) cal-
sets. The results are reported in the Supporting Information
culations. Vibrational frequency scaling factors 0.960, 0.961,
(TablesS1,S2,andS3,respectively).Theseresultsindicatethat
0.966, and 0.967 are used for the B3LYP method with
MA2-D1-1, EA2-D1-1, and n-BA2-D1-1 mechanisms are exo-
6-31G(d), 6-31G(d,p), 6-311G(d), and 6-311G(d,p) basis sets,
thermic, while the other mechanisms are endothermic. Since
respectively. These scaling factors are from the National
Institute of Standards and Technology (NIST) scientific and tertiary radicals are more stable than secondary radicals,108,109
technical database.103 We use GAMESS for all calculations.104 the likelihood of the occurrence of the MA2-D1-1, EA2-D1-1,
and n-BA2-D1-1 mechanisms is higher.
A rate constant k(T) is calculated using the transition state
theory105 with Thesamefunctionalsandbasissetsareusedtocalculatethe
bond-dissociation energies of hydrogen atoms involved in the
⎛ ⎞ proposedmechanisms.Thesedissociationenergiesaregivenin
k(T) = (c0)1−mkBT exp⎜−ΔH⧧− TΔS⧧⎟ Table 1. While in agreement with previous results,102 they
h ⎝ RT ⎠ (1) indicatethatthebond-dissociationenergiesofhydrogenatoms
attached tothe tertiary carbon atoms (whichareabstracted via
where c0is the inverse ofthe reference volume assumed in the MA2-D1-1, EA2-D1-1, and n-BA2-D1-1 mechanisms) are
translational partition functioncalculation, k is theBoltzmann about 50 kJ/mol lower than those of other hydrogen atoms
B
constant, T is temperature, h is Planck’s constant, R is the ofthedeadpolymers. Thissuggests thatsuchatertiary carbon
universal gas constant, m is the molecularity of the reaction, atom has a higher tendency to release a hydrogen atom.
and ΔS⧧ and ΔH⧧ are the entropy and enthalpy of activation, 3.1.1.EffectoftheTypeoftheRadicalthatInitiatedaLive
respectively. ΔH⧧ is given by MA-PolymerChain.Ithaspreviouslybeenreported8,9thattwo
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Figure 1. Dead polymer chains formed from (a) termination by coupling of two monoradicals, (b) termination by hydrogen abstraction, and
(c)termination by coupling of alive chain anda monoradical.
potential energy surface with C1−H2 and H2−C3 bond
lengths ranging from 1.19 to 1.59 Å. Figure 7a shows the
transition-state geometry for the MA2-D1-1 mechanism with
C1−H2 and H2−C3 bond lengths of 1.37 and 1.35 Å, respec-
tively.Theactivationenergies,enthalpiesofactivation,frequency
factors, and rate constants of the MA2-D1-1 mechanism are
provided in Table 2. These results show that the activation
Figure 2. Two types of monoradicals generated by monomer self- energies and rate constants calculated using different basis sets
initiation.8,9 varyby±10kJ/moland2ordersofmagnitude.Thekineticand
thermodynamic parameters predicted using the M06-2X func-
types of monoradicals (M (cid:129) and M (cid:129)) are produced in the tional are different from those obtained with B3LYP and
1 2
monomer self-initiation of alkyl acrylates (Figure 2). The X3LYP (Table 2). It is important to note that the M06-2X
hydrogen atom abstraction from a tertiary carbon atom of a functionalismoreaccuratethantheotherfunctionalsbecauseit
dead polymer chain initiated by M (cid:129) (MA1-D1-1, shown in accountsforvanderWaals(vdW)interactions.110,111B3LYP,as
Figure6)andM (cid:129)(MA2-D1-1,show1ninFigure3)areinvesti- a hybrid GGA functional, depends on ρ(r) and |∇ρ(r)|, where
2
gatedinthisstudy.Threedifferentfunctionals,B3LYP,X3LYP, ρ(r) is charge density at that point r. However, M06-2X is a
andM06-2X,andseveralbasissetsareapplied.TheMA1-D1-1 hybrid meta-GGA functionalanddependson ρ(r),|∇ρ(r)|, and
and MA2-D1-1 mechanisms are explored by sampling the kinetic energy density. The rate constant estimates calculated
Figure 3. Possiblechain transfer topolymer mechanisms for MA: Ri(i = 1,2, and 3) is the radical formed through the MA2-D1-imechanism.
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Figure 4.Possible chain transfer to polymer mechanisms for EA: Ri(i= 1,2, 3,and 4) is the radical formed through the EA2-D1-imechanism.
Figure 5. Possible chain transfer to polymer mechanisms for n-BA; Ri (i = 1, 2, 3, 4, 5, and 6) is the radical formed through the n-BA2-D1-i
mechanism.
Table 1. H−R Bond Dissociation Energies (kJ mol−1) at 298 K
B3LYP B3LYP B3LYP B3LYP X3LYP X3LYP X3LYP X3LYP
mechanism 6-31G(d) 6-31G(d,p) 6-311G(d) 6-311G(d,p) 6-31G(d) 6-31G(d,p) 6-311G(d) 6-311G(d,p)
MA2-D1-1 387 390 383 385 385 387 384 387
MA2-D1-2 446 448 440 441 447 450 441 443
MA2-D1-3 435 436 428 429 435 437 429 431
EA2-D1-1 387 390 383 385 388 391 385 387
EA2-D1-2 445 448 440 441 447 450 441 443
EA2-D1-3 422 424 417 419 423 425 418 420
EA2-D1-4 451 453 445 447 452 455 446 448
n-BA2-D1-1 387 390 383 385 388 392 385 387
n-BA2-D1-2 446 449 440 442 447 450 441 443
n-BA2-D1-3 422 424 417 418 423 426 418 419
n-BA2-D1-4 433 436 429 430 435 438 425 432
n-BA2-D1-5 429 432 424 426 431 434 425 427
n-BA2-D1-6 447 449 440 442 448 451 441 443
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Figure 6. Mostprobable CTP mechanisms involving two-MA-unit live chain initiatedby M(cid:129).
1
Figure 7. Transition state geometry for the MA2-D1-1 (a),EA2-D1-1 (b), and n-BA2-D1-1 (c)mechanisms.
using M06-2X are in good agreement with experimental values EA and n-BA we study hydrogen abstraction by a live polymer
reported for CTM reactions of MA, EA, and n-BA.82 No chain initiated by M(cid:129).
2
significant change in activation energies or rate constants was 3.1.2.CTPMechanismsforEAandn-BA.EA2-D1-1(Figure4)
observed with different basis sets. The transition-state structure and n-BA2-D1-1 (Figure 5) CTP mechanisms are examined.
of the MA1-D1-1 mechanism has C1−H2 and H2−C3 bond The abstraction of a hydrogen atom from a tertiary carbon by
(cid:129)
lengthsof1.37and1.36Å,respectively(SupportingInformation, a live polymer chain initiated by M is studied by choosing
2
FigureS1).Table2givesthekineticparametersfortheMA1-D1- C1−H2 and H2−C3 bond lengths as reaction coordinates.
1 mechanism. A comparison of the activation energies and rate The C1−H2 and H2−C3 bond lengths of the transition-state
constants calculated for the MA2-D1-1 and MA1-D1-1 structure for the EA2-D1-1 mechanism are 1.38 and 1.35 Å,
mechanisms indicates that the type of radical that initiated the respectively (Figure 7b). The activation energies, enthalpies of
livechainhaslittleornoeffectonthecapabilityofthelivechain reaction,frequencyfactors,andrateconstantsoftheEA2-D1-1
toparticipateinaCTPreaction.However,asTable2showsthat mechanism are given in Table 3. The activation energies and
(cid:129) (cid:129)
M isalittlemorereactiveinMACTPreactionsthanM ;for rateconstantscalculatedusingthemethodsB3LYPandX3LYP
2 1
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e
ction);andRat M06-2X11G(d,p) 67−×11074×110 −×2108−×1310×010
rreK; 6-3 29248410.3.43.01.01.9 2924879.18.93.12.83.5
o
C8
9
r2
forWigneorMAat M06-2X6-311G(d) 31268510.97−×11.9103.19−×16.0610×18.110 33288810.49−×26.2103.23−×12.0010×03.110
f
w
κ(ms
gFactorMechanis M06-2X6-31G(d,p) 2823859.56−×11.9103.08−×15.8510×11.110 2823879.11−×29.6103.11−×12.9910×04.710
n
eliTP
−1ol;TunnrobableC M06-2X6-31G(d) 3025889.29−×25.8103.11−×11.810×02.0810 34298412.35−×12.7103.15−×18.510×01.910
mP
Jst
⧧ΔG)inkortheMo X3LYP6-311G(d,p) 544910412.39−×57.8103.78−×42.9510−×33.710 575210612.7−×53.3103.79−×41.2510−×32.610
(f
on−1, 1 1
ofActivati−1)inMs X3LYP6-311G(d) viaMA2-D1-595410514.17−×55.5103.98−×42.1910−×32.610viaMA1-D1-635810913.97−×69.9103.94−×53.910−×42.510
’),andGibbsFreeEnergykng;and,withTunnelingw X3LYPX3LYP6-31G(d)6-31G(d,p) HydrogenAbstraction5247474210810610.168.76−−××552.0104.1103.833.73−−××547.66101.5310−−××331.3103.210HydrogenAbstraction5653514911110710.4911.15−−××656.2102.9103.843.75−−××542.38101.0910−−××432.8102.010
⧧H eli
ΔActivation(withoutTunn B3LYP6-311G(d,p) 605511112.16−×65.9103.6−×52.1210−×43.510 645911811.15−×73.8103.73−×61.4210−×51.610
EnthalpyofkConstant(,k13K()413 B3LYP6-311G(d) 635811711.17−×75.4103.64−×61.9710−×53.310 686312310.52−×84.9103.93−×71.9310−×62.210
EEnergy(),aA)andRateunnelingat4 B3LYP6-31G(d,p) 555010811.32−×51.6103.49−×55.5810−×31.610 615611510.84−×61.1103.70−×64.0710−×57.510
ActivationyFactor(withoutT B3LYP6-31G(d) 575210812.08−×51.6103.58−×55.7310−×49.910 625711610.99−×77.2103.79−×62.7310−×53.710
ct
2.enan
TableFrequConst Ea⧧ΔH⧧ΔGlogAekκwkwk413 Ea⧧ΔH⧧ΔGlogAekκwkwk413
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d and the basis sets (6-31G(d), 6-31G(d,p), 6-311G(d), and
Correction);)at298K;an M06-2X6-311G(d,p) 2319838.7−×14.5103.161.42×15.310 6oswme-fi3attmsgh1ni1iansiGgtunm(d3idtoeu,pr.dek)eTJ)c./hoamTernheosetildsratpieffnaennesrtirfdt:oeionrtmhnrtae-aatsnettdacimtffeeceooorssnfettnsrMbtucayce0nt61uti-ns3r2eXakwcoJtwi/ftimvhitatihhontielodani1nffn-eedBrnoeA2ernd2rotg-eDirbredas1eso-rii1sssf
orWigner(EA2-D1-1 M06-2X6-311G(d) 2419848.6−×13.2103.231.03×14.610 Tmvaaelubcehlesana4ir.semAgcivtisievnsahtiinoownTnaEbinnleerF4g.iygOu(ruEer)fi7,cn,Ediannntghdathltphayetnok-fiBnAAetc2itc-iDvpa1at-ri1oamnisettheer
κfwEA (ΔH⧧), and Gibb’s Free Energay of Activation (ΔG⧧) in kJ
(r mol−1; Tunneling Factor (κ for Wigner Correction);
nelingFactorMechanismfo M06-2X6-31G(d,p) 2116818.71.13.123.43×21.310 nwTF-ruiBetnhqAnou2eue-ltnDincT1gy-u;1FnanaMncedteloicnkrhwga(,nAawti)si4tmah1n3aTdtuKR2wna9(nt8kee4l1KiCn3);go)annsitdnanRMta−(t1ek,sC−wo1i,nthfsootarunttthe
−1ol;TunbleCTP M06-2X6-31G(d) 2419838.714.23.15×11.3210×17.110 EΔaH⧧ B3L5561YP/6-31G(d) B3L54Y38P/6-31G(d,p)
mba ΔG⧧ 114 110
o
⧧ΔGFreeEnergyofActivation()inkJ−−11Tunneling)inMs,fortheMostPr X3LYPX3LYPX3LYP6-31G(d,p)6-311G(d)6-311G(d,p) 49625944575410210410111.3515.6115.51−−−×××4541.9108.5102.7103.764.003.80−−−×××4437.14103.4101.0310−−−×××2223.3101.4102.710 mratBrmpraedr3atpaoeeenLgovsqsntYiruikκklkocottiw4wPatoeuig1pout3d/nseredn6Asoeet-sbtaxs.3ot4atnpu12abetdtGalrTeeici(e(mhc7ssduit.m.e4s,r4rp2nuaei)ttcnc×a,etOhdluly19361airuivc1.....nse72733ara0psi07570ltsu−ream×××cbe0esba6du)111lootitc000hcoufu−−−tniaft663s2ltoa9ttthClt2eohkedt0TweJh/PmeelmakrecekJvoitc/ibesinlhvml,y4eaa2iottnonaiifcailobssntntoa93724hidhouc.....ge76475ifrte18020oogepnuhtr×××e4hayeremter111rhcgao000eawpryr−−−nletd,p653cathaeulyciaureltwnassdiatoiinnetonidhdgasf.
sh This inadequacy is attributed to the limitation of the hybrid
⧧H’),andGibbkng;and,witw X3LYP6-31G(d) 544910113.81−×43.2103.86−×31.2410−×25.110 fopeAuanolntcwlhycheotiruoafigusnnshladultsmiovdoieaidslnscudtraoethlptedhaienrrenceauicoecstnslteyrioeboslneatfuttiwRdvinyieRsetHtnihcfOreeDS.emcF-FhreTiarcro-dshctdiaa-cipnlnacrilgusinmelacrptieopaednllqeydsumaaknDetidinroFieznTteaixctipitssoheonarat-f.
Δvation(utTunneli B3LYP6-311G(d,p) 635811312.39−×62.5103.78−×69.4510−×47.010 ihrpmeoalvlieyaenmbtblaeeelrleiyaznpadtprieeortponeoa,r1mcr1ht,2ein0d,f2eo,1drp,8r2aee,1csv1tt2iiiovmdautuasiteoisnnttugoedneriearerstroeghriaeccvosaennascsnthedalolnawfttrsienoqnitnuheianfntrceeDyele-FcfraTtarcdotiioncsraicasl
Energy(),EnthalpyofActiakandRateConstant(,withoktTunnelingat413K()413 B3LYPB3LYP6-31G(d,p)6-311G(d) 5666516110711612.2212.31−−××572.8106.4103.593.80−−××461.0102.4310−−××355.9109.610 |gaocscast∇ittunnaenorunnlddρunadetc(tabyhirtr|loief∇aus)enrnl|reic,gρ(ezsaqlde(aplua((reidspqne)usapirun|dcnefi)gotic,dnredixyvadedki-aadmpriintnn-bihfieadaoegaoantcstnisrtiteoomec-odnaoenrrepnvleoetypeoeaannlrrrfe-coeeogGtatrsenyixhdgotGx)iieiymncmcniAharhsgaa.nada1fttund1rifeiougot3ngnonenneecTsnc-tidctihto(tsoyioerGeefo)nornlnbGrfapas-ealociccyAltlcfaatasyohu)nnt(irrfcρ(omrta(edhe(nbcdler.qeiye1e)npuf1puago4eeaec−cnnfnttno1cdicDe1dvmttyirhi6naiFornbtaogLfnTitgaiornoacsnoplecdt)osonoadenelripwnnw)fρeuwρehthn(crn(iierracgdtrc))nlhhy)s--,,
EA)ou Hartree−Fock exchange functionals to increase accuracy (which
ActivationcyFactor(nstantwith B3LYP6-31G(d) 595411011.96−×68.4103.66−×53.0710−×31.410 aiimtsrseeataakt-htnGryaobGcwrtAiinvdefauGspnGechrtAfyioobrnrfmuiadnlasncftsuciueonc-ncthtoail-oa,cnsohasMaltss)0r.ab6teF-i2oeoXn.r8,9puexrsMoaemdveitdpaee-lxeGt,aeGnBmAs3iovLaerYenlyPda,cdhcwuyuehbriarctitodhe
3.enCo prediction of barrier heights, as they can adequately account for
TableFrequRate Ea⧧ΔH⧧ΔGlogAekκwkwk413 hvaignhdeerrleWvealaslsoifntthereaocrtyiosnusc.1h00a−s10G2,4110is,11n1eFeudretdh.erinvestigationwith
H DOI:10.1021/ie504110n
Ind.Eng.Chem.Res.XXXX,XXX,XXX−XXX
Industrial & Engineering Chemistry Research Article
n-BA2-D1-1) indicate that the end-substituent groups (methyl,
ethyl, and butyl acrylate side chains) do not affect the kinetics
of CTP reaction in the alkyl acrylates. This can be explained
through the similarity of the reactive sites involved in the
CTP reaction of MA, EA, andn-BA.82,83 The pathways for the
CTPmechanismsinthealkylacrylates(MA2-D1-1,EA2-D1-1,
and n-BA2-D1-1) are determined through IRC calculations
(Figure 8). The presence of concerted pathways can be ob-
served through these calculations in the forward and backward
directions starting from transition-state structures for MA, EA,
and n-BA.
3.1.3.EffectoftheLivePolymerChainLength.Theeffects
ofthelengthofalivepolymerchainontheactivationenergies
andthegeometriesoftransitionstatesareexploredforMAand
EA. The abstraction a hydrogen atom from a dead polymer
(cid:129)
chain by a live chain, which is initiated by M and has 3 or 4
2
monomer units, is investigated for MA (Figure 9). The acti-
Figure8.Intrinsicreactioncoordinate(IRC)pathsfortheMA2-D1-1, vation energies and rate constants of these mechanisms are
EA2-D1-1, and n-BA2-D1-1 mechanisms (energies are relative to given in Table 5. They indicate that the rate constants change
reactants). at most 2 orders of magnitude, as the length of the live chain
changes. The activation energies of these reactions nearly do
The kinetic parameters estimated for the most likely CTP not change (at most 4 kJ/mol) by increasing the length of the
mechanismsofMA,EA,andn-BA(MA2-D1-1,EA2-D1-1,and live chain.
Figure 9. Mostprobable CTP mechanism involving a three [MA2-D1-1(a)] or four [MA2-D1-1(b)] MA-unitlive chain initiated by M(cid:129).
2
Table 5. Bond Length in Å, Activation Energy (E), Enthalpy (ΔH⧧), and Free Energy (ΔG⧧) in kJ mol−1; Tunneling Factor
a
(κ for WignerCorrection); and Frequency Factor (A) and Rate Constant (k, without Tunneling; and k : with Tunneling) in
w w
M−1 s−1 by Considering the Radicals with Different Monomer Units for MA and EA, Using B3LYP/6-31G(d,p)
(C1−H2)Å (C3−H2)Å E ΔH⧧ ΔG⧧ log A k κ k
a e w w
MA2-D1-1ThreeMonomerUnits
1.37 1.35 59 54 114 10.63 1.70×10−6 3.76 6.39×10−6
MA2-D1-1FourMonomerUnits
1.39 1.36 56 51 118 7.56 3.00×10−7 3.86 1.16×10−6
EA2-D1-1ThreeMonomerUnits
1.37 1.36 54 49 123 4.52 3.80×10−8 3.79 1.44×10−7
I DOI:10.1021/ie504110n
Ind.Eng.Chem.Res.XXXX,XXX,XXX−XXX
Industrial & Engineering Chemistry Research Article
Figure 10. Mostprobable CTP mechanism involving a three EA-unitlive chain initiated by M(cid:129).
2
Figure11.PossiblechaintransfertotheD2andD3deadpolymersmechanismsforMA,EA,andn-BA;Ri(i=1,2,and3)andRˈi(i=1,2,3,
and 4) are the radicals formed through the Y-D2-iand Y-D3-imechanisms, respectively; Y= MA, EA, andn-BA.
Table6.H−RBondDissociationEnergies(kJmol−1)forD2 three monomer units. The activation energy and rate constant
and D3 Dead Polymers at 298 K, Using B3LYP/6-31G(d,p) of EA2-D1-1 (including two monomer units) mechanism do not
change significantly, as the length of the live polymer chain
H−Rbond-dissociationenergy increases (Table 5). This agrees with previous theoretical studies
Y-D2-1 Y-D2-2 Y-D2-3 Y-D3-1 Y-D3-2 Y-D3-3 Y-D3-4 thatthepropagationrateconstantsofMAandMMAareinsensitive
363 417 387 357 364 366 405 to the chain length after the first propagating step.81 Such chain-
lengthinsensitivityhasalsobeenreportedforhomoterminationrate
coefficients in free-radical polymerization of acrylates.117 These
The mechanism of CTP for EA (EA2-D1-1(a)) is explored findingsindicatethatitisappropriatetouseadimer(trimer)model
as shown in Figure 10. In this mechanism the live chain has system to study the chain transfer to polymer reaction.
J DOI:10.1021/ie504110n
Ind.Eng.Chem.Res.XXXX,XXX,XXX−XXX