Thermodynamics of the Carbon DioxideâEpoxide Copolymerization

Article pubs.acs.org/Macromolecules

Thermodynamics of the Carbon Dioxide−Epoxide Copolymerization and Kinetics of the Metal-Free Degradation: A Computational Study Donald J. Darensbourg* and Andrew D. Yeung Department of Chemistry, Texas A&M University, 3255 TAMU, College Station, Texas 77843, United States S Supporting Information *

ABSTRACT: The copolymerization reactions of carbon dioxide and epoxides to give polycarbonates were examined by density functional theory (DFT), and chemically accurate thermochemical data (benchmarked to experimental values) were obtained via composite ab initio methods. All of the examples studied, i.e., formation of poly(ethylene carbonate), poly(propylene carbonate), poly(chloropropylene carbonate), poly(styrene carbonate), poly(cyclohexene carbonate), and poly(indene carbonate), exhibited enthalpies of polymerization of 21−23 kcal/mol, with the exception of poly(cyclopentene carbonate) (15.8 kcal/mol) which suffers both ring strain and intramolecular steric repulsion caused by the cyclopentane ring fused to the polymer chain. The metal-free carbonate backbiting reaction by a free anionic polycarbonate strand is inhibited by bulky groups at the methine carbon but is accelerated by resonance stabilization of the pentavalent transition state in the case involving poly(styrene carbonate). Nucleophilic attack at the methylene carbon of a substituted epoxide has a lower barrier than for the corresponding reaction involving ethylene oxide due to charges being distributed onto the pendant groups. The undesired backbiting reaction to afford cyclic organic carbonates observed under polymerization conditions for many systems due to the low activation barrier (ΔG‡ = 18−25 kcal/mol) was negligible for poly(cyclohexene carbonate) because, in this instance, it must overcome an additional endergonic conformational change (ΔG = 4.7 kcal/mol) before traversing the activation barrier (ΔG‡ = 21.1 kcal/mol) to cyclization. Backbiting from an alkoxide chain end is proposed to proceed via a tetrahedral alkoxide intermediate, where formation of this intermediate is barrierless. Further reaction of this intermediate to the cyclic carbonate has a free energy barrier 10 kcal/mol less than the carbonate chain end backbiting reaction.

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INTRODUCTION The ever-increasing levels of atmospheric carbon dioxide as a result of anthropogenic emissions primarily from carbon-based fossil fuels is currently a major environmental concern. This worldwide problem will become even more heightened by population increases along with the emerging economics of several countries. Because of the enormity of CO2 emissions generated by humans (∼35 Gt per year), numerous technologies will need to be put in place to effectively reduce its accumulation in the atmosphere.1 One such method which has received major consideration involves carbon dioxide capture and storage (CCS).2 Carbon capture and storage technologies have experienced notable gains during the past decade. Among these are the utilization of metal−organic frameworks (MOFs) which provide a solid-state method for CO2 adsorption and separation and therefore represent potential replacement technology for aqueous alkanolamine absorbents widely used for CO2 scrubbing.3 These processes implicating the large-scale separation of CO2 from power and industrial plants flue gases will lead to the isolation of large volumes of CO2. The fate of the recovered CO2 would be either disposal in natural fields, e.g., aquifers or deep underground wells, or its utilization. Although the former method leads to long-term sequestration of the majority of the © XXXX American Chemical Society

recovered CO2, it involves significant energy and economic costs. On the other hand, utilization adds value to the waste CO2, thereby offsetting the cost of capture and storage. With regard to CO2 utilization, conversion of CO2 into viable economic products is currently rather limited.4 The presently employed industrial processes consuming sizable quantities of carbon dioxide are the synthesis of urea, salicylic acid, methanol, and inorganic carbonates (Scheme 1), with urea accounting for about 50% of the consumption. Recently, production of BPA polycarbonate via diphenyl carbonate derived from CO2 has accounted for a significant increase in organic chemicals from carbon dioxide.5 The reactions of CO2 with three-membered cyclic ethers to afford either linear polycarbonates or five-membered cyclic carbonates represent promising technologies for CO2 utilization to contribute to a sustainable chemical industry (eq 1).6 Importantly, there is a need to integrate large-scale utilization of CO2 into large-scale recovery processes. Indeed, recently North and co-workers have successfully integrated an aluminum catalyst system for the production of cyclic carbonates from CO2 produced by the Received: October 18, 2012 Revised: November 27, 2012

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dx.doi.org/10.1021/ma3021823 | Macromolecules XXXX, XXX, XXX−XXX

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Scheme 1

Scheme 3

(Figure 1). It should be noted that the undesirable consequence of cyclic carbonate formation is twofold: they consume

combustion of methane.7 Of course, the real breakthrough will come when CO2 can be effectively converted to fuels for transportation using a renewable solar energy source. Nevertheless, as petroleum resources are depleted, biomass and CO2 will be the main sources of chemical carbon for the chemical industry.1,8 The current mechanistic model for the synthesis of polycarbonates from epoxides and CO2 catalyzed by the wellstudied five-coordinate (salen)MIIIX (M = Cr, Co, or Al) complexes in the presence of an anionic initiator (Nuc−) consists of the individual steps outlined in Scheme 2. In a side

Figure 1. Cobalt complex used for epoxide/CO2 copolymerization.

monomer and necessitate product separation and block the metal center from binding epoxide monomers since they are the better ligands.12 Our previous experimental studies have examined the reaction sequence in eq 1 from both synthetic and mechanistic viewpoints. We have also studied the azide-catalyzed alkoxide backbiting reactions of several polycarbonates.13 While some specific reactions between epoxides and CO2 have been described computationally,14,15 no systematic investigations have been carried out for a variety epoxides relevant to observed copolymerization processes. In particular, aside from one calorimetric investigation,16 the thermodynamics of polycarbonate chain growth is not well described. The important questions we wish to address herein with theoretical computations are (a) the thermodynamics of the alternating copolymerization of CO2 and epoxide (ΔH per repeat unit) for various epoxides, (b) analogous thermodynamics of cyclic carbonate formation, and (c) kinetic barriers for the free polymer chain backbiting process involving either carbonate or alkoxide end groups. That is, this article reports our theoretical calculations of the thermodynamics of this CO2/epoxide coupling process and evaluates the kinetics of the depolymerization reaction to cyclic carbonates via a backbiting process.

Scheme 2

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reaction during the ring-opening step of the activated epoxide, the anionic growing polymer chain is displaced by the incoming epoxide monomer from the metal center. As a free polymer chain, it can rapidly backbite upon itself to yield the cyclic carbonate product (Scheme 3). Second-generation bifunctional (salen)MX catalysts, where the salen ligand has a covalently tethered onium salt, have greatly aided in curtailing this behavior.9−11 In these instances, the positive charge of the onium salts help to maintain close contact between the dissociated anionic polymer chain and the metal complex

RESULTS AND DISCUSSION Benchmarking of Computational Methods. The four reactions described in Scheme 4 were modeled for a variety of cyclic and acyclic carbonates, and the calculated enthalpies were compared to gas phase data.17 For this test set, the G4,18 CBS4M,19,20 and CBS-QB319,21 composite methods gave the best all-round performance (∼1 kcal/mol deviations), while G3(MP2)22 occasionally gave large deviations (3−4 kcal/mol). The good agreement found is consistent with previous work.23 B


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effects. While several iterations are required for the enthalpies of polymerization to converge, the difference is expected to be small ( anionic 1‐mer ≈ methyl carbonate > chloride ≈ bromide

This ranking shows a good correlation between the ability of each anion to act as a leaving group and the ease at which carbonate backbiting occurs to give the cyclic carbonate. It was also encouraging to note that carbonate anion approximates the electronics of the polycarbonate chain well. The results are also consistent with a previous computational study by Rieger and co-workers that reported an electronic energy barrier of 23 kcal/mol for X = acetate.35 These backbiting reactions are all exergonic.

Figure 6. The carbonate anion can occur at the methine (left) or methylene (right) positions. E


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Table 3a (b) X = methyl carbonate (CH3OC(O)O−)

(a) X = chloride no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

EC-X PC-1X PC-2X ClPC-1X ClPC-2X SC-1X SC-2X cis-CPC-X cis-CHC-X cis-CHC-relaxedb trans-CHC-X EC-Br EC-N3 EC-PEC1 TMC-X

open chain

transition state

cyclic carbonate + X

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

14.4 16.4 10.8 18.2 12.8 14.0 12.2 13.7 13.5 8.0 31.0 15.3 24.7 20.8 17.8

−16.0 −16.3 −19.2 −15.5 −16.7 −14.5 −18.2 −23.6 −21.4

−

open chain

transition state

cyclic carbonate + X−

0 0 0 0 0 0 0 0 0 0 0

20.4 24.0 18.5 25.5 19.7 19.5 20.2 20.3 21.1 4.7 40.5

−2.2 −3.4 −6.0 −2.0 −4.1 −3.6 −2.6 −5.3 −8.2

0

26.1

2.9

−12.5 −14.6 −1.8 −4.0 −12.0

3.1

Free energies for the backbiting of an anionic 1-mer to give the cyclic carbonate and an X− anion, calculated at the CBS-QB3 level with solvation. Electronic energies and enthalpies are included in Supporting Information (Tables S3 and S4). -Cl = chloride, -Br = bromide, -N3 = azide, -PEC1 = −OCO2CH2CH3 (poly(ethylene carbonate) 1-mer). -1 and -2 denote attack at the methine and methylene carbons, respectively. bEnergy difference between the relaxed chair conformation and the boat conformation required for cyclohexene carbonate to backbite. a

barely perturbed O−CH−CH2 angles of 109°−112°, ruling out angular compression as a major reason for the lowered activation barriers in these systems (Table 4). In low-lying molecular orbitals, the electrons on the pendant groups delocalize into the p orbitals on the methylene carbons undergoing reaction (Figure 8). This in-phase interaction is believed to contribute to the lower energy of the transitionstate structure. The reactions with styrene carbonate, propylene carbonate, and chloropropylene carbonate at the methine positions were examined (Table 3, entries 2, 4, and 6). At the transition state, the phenyl substituent was better able to stabilize the partial positive charge on the methine carbon (Mulliken charge of +0.335) than the methyl (Mulliken charge of +0.445) and the chloromethyl substituents (Mulliken charge of +0.702). In the language of valence bond theory, the superior electronic stabilization is due to the ability of the phenyl pπ electrons to delocalize with the p orbitals on the sp2 methine carbon. This stabilization is not possible with the methyl and chloromethyl substituents; the calculated molecular orbital of the transition state structure clearly show the favorable interactions between the phenyl substituent and the methine center (Figure 9). The free energy barrier for reaction at the methine carbon is thus lower for styrene carbonate than for propylene carbonate and chloropropylene carbonate (14.0 kcal/mol vs 16.4 and 18.2 kcal/mol). When the carbonate attacks the methylene carbon, the lack of resonance stabilization leads to qualitatively similar

Figure 7. Profile of the potential energy surface connecting the openchain 1-mer to the cyclic carbonate associated with the chloride anion. In this and subsequent figures, standard CPK colors are used: gray = carbon, white = hydrogen, red = oxygen, green = chlorine.

The nature of the R substituent on the epoxide precursor for the cycloaddition reaction in Figure 6 was also investigated. Pendant groups on short chains have been observed to favor ring closure, including for cyclic carbonates.36,37 Many rationalizations have been offered,38 but those that involve conformational flexibility or entropic effects are not relevant to the present discussion of an elementary reaction. Structures of the open chain and the backbiting transition states of propylene, chloropropylene, and styrene carbonates show Table 4a

open chain no. 1 2 3 4

EC-Cl ClPC-2Cl PC-2Cl SC-2Cl

transition state

ΔG‡ (kcal/mol)

R−C−H (deg)

O−CH−CH2 (deg)

R−C−H (deg)

O−CH−CH2 (deg)

14.4 12.8 10.8 12.2

109.5 108.2 108.5 106.8

109.3 110.9 111.3 112.1

108.7 109.5 109.8 108.6

112.1 111.0 110.6 109.5

a B3LYP/6-311++G(2d,p) bond angles of the aliphatic carbonates do not show significant perturbation, suggesting a weak Thorpe−Ingold effect if any.

F


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free energy barriers (12.2 kcal/mol vs 10.8 and 12.8 kcal/mol, respectively). Trends in free energy barriers discussed for X = Cl are also observed for X = methyl carbonate. Although steric bulk increases the barrier for reaction at the methine carbon, any pendant group adjacent to the carbon undergoing substitution decreases the barrier by helping to disperse the positive charge there. Styrene carbonate reacts easily at both methine and methylene positions due to resonance stabilization of the transition state when reaction occurs at the methine position and by aiding in dispersing the positive charge when reaction occurs at the methylene position.32 Relative Stabilities of Alicyclic Carbonates. As an extension of the benchmarking section of this contribution, the enthalpies of cyclic carbonate formation from carbon dioxide and epoxide at the CBS-4M level are presented in Figure 10. In the lower energy chair conformation, cis-

Figure 8. HOMO-15 and HOMO-17 of PC-2Cl (left) and ClPC-2Cl (right) at their respective transition states. These two molecular orbitals indicate some interactions between the pendant group and the methylene carbon undergoing reaction.

Figure 10. Enthalpy of the reaction between carbon dioxide and an epoxide to give the corresponding cyclic carbonate(s). The uncertainty of the experimental values presented are denoted by the error bars. See Supporting Information, Table S1.

cyclohexene carbonate is more stable than trans-cyclohexene carbonate by 4 kcal/mol (enthalpy). Intuitively, the reverse order is expected because the cis-isomer bears substituents at the axial and equatorial positions, whereas the trans-isomer’s substituents occupy only equatorial positions (Figure 11). However, the O−CH−CH2 angles for the trans- and cis-isomers are 108.3° and 118.0°, respectively. In this instance, angle strain

Figure 9. HOMO-8 (left) of the styrene carbonate transition state to carbonate backbiting and the equivalent HOMO-6 (right) for propylene carbonate. The transition state for styrene carbonate shows delocalization of the aromatic pπ electrons into the carbon p orbital. Stabilization of the transition state species reduces the activation barrier to carbonate “backbiting”. The molecular orbitals for propylene carbonate show no such substituent participation.

Figure 11. The carbonate group is attached to trans-cyclohexene carbonate (right) at equatorial positions, whereas for the cis-isomer (left), it is attached at one equatorial and one apical position. However, the O−CH−CH2 angles are 108.3° and 118.0°, respectively; angle strain is more significant than steric repulsion here, and the cisisomer is more stable by 4 kcal/mol (enthalpy, CBS-4M). G


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appears to outweigh the steric repulsion suffered by axial substituents. Cyclopentene carbonate and indene carbonate are lower in enthalpy as the cis-isomer than the trans-isomer by 17 and 22 kcal/mol due to the extreme angle strain found at its tetrahedral bridgehead carbon (O−CH−CH2 trans-: 126.2°, cis-: 109.3° for CPC, trans-: 129.3°, cis-:111.8° for IC; see Figure 12).

Figure 13. Relaxed poly(cyclohexene carbonate) 1-mer (left), twistboat conformation (ΔH = +8.6 kcal/mol), transition state to carbonate backbiting (ΔH = +9.4 kcal/mol from the twist-boat conformation).

poly(cis-cyclohexene carbonate) to give trans-cyclohexene carbonate has an extremely high barrier (Table 3, entries 9 vs 11) and is unlikely to proceed. Indeed, the usual cyclic carbonate byproduct is the trans-isomer rather than the cisisomer that must result from metal-bound or metal-free alkoxide backbiting (Figure 14).

Figure 12. trans- and cis- cyclopentene carbonate (top left and right) and indene carbonate (bottom left and right). The cis-isomers of cyclopentene and indene carbonates are more stable by 17 and 22 kcal/mol, respectively (enthalpy, CBS-4M), due to the lack of appreciable O−CH−CH2 angle strain (trans: 126.2°, cis: 109.3° for cyclopentene carbonate; trans: 129.3°, cis: 111.8° for indene carbonate). The boat-like conformation was chosen for cyclopentene carbonate because it is more stable than the chair-like conformation by 2 kcal/mol (enthalpy).

The relative stabilities of cyclohexene carbonate’s conformations are important because they directly influence the enthalpy of cyclic carbonate formation via the backbiting mechanism. The backbiting mechanism can only lead to the cis-cyclohexene carbonate isomer (poly(cis-cyclohexene carbonate) is not present in the polymer). Many research groups including our own have previously reported that cyclohexene oxide readily copolymerizes with carbon dioxide to give poly(trans-cyclohexene carbonate) upon catalysis and that very little cyclic carbonate is produced as an undesired byproduct. In particular, when catalyzed by a (salen)chromium(III)X complexes, enchainment and cyclic carbonate formation have activation energies of 11.2 and 31.8 kcal/mol, respectively.30 In the present computational study, the free energy of activation for the carbonate of an anionic 1-mer to backbite to lose a chloride anion was 13.5 kcal/mol, but the transition state required for this reaction had a cyclohexane backbone in a boatlike conformation (a chair-like transition state could not be found). The relaxed chair conformation is 8.0 kcal/mol lower in free energy, establishing 21.5 kcal/mol as the floor for the overall activation barrier. Degradation of this copolymer thus occurs by the polymer first undergoing an energetically demanding chair to boat conversion, before the carbonate backbiting mechanism is able to continue (Figure 13). We thus independently arrived at the same conclusion as a study by Rieger et al.15 Where more accessible pathways such as chain growth (Ea = 11.2 kcal/mol when catalyzed by a (salen)chromium(III)X complex30) exist, they predominate over the degradation of poly(cyclohexene carbonate), and cyclic carbonate formation is low. Tangentially, the carbonate backbiting of a hypothetical

Figure 14. (a) Copolymerization of cyclohexene oxide with carbon dioxide leads to the cyclohexane’s two substituents being mutually trans. (b) Carbonate backbiting causes inversion at the site of substitution, yielding cis-cyclohexene carbonate. (c) Alkoxide backbiting causes no inversion at the cyclohexane carbons, and the substituents’ mutual trans geometry is maintained in the final cyclic carbonate. This explanation is applicable for all alicyclic polycarbonates and for both metal-bound and metal-free backbiting reactions.

Backbiting of Metal-Free Alkoxides. While the carbonate backbiting degradation of polycarbonates operates under polymerization conditions (i.e., in a carbon dioxide environment), the alkoxide backbiting degradation is of greater relevance in the absence of carbon dioxide. Since the alkoxide anion is a strong base, this reaction is not expected to occur under ambient conditions since the alkoxide will be protonated by moisture in the air. Rather, polymers may be deliberately recycled to cyclic carbonates for purification and eventual reuse, e.g., as a high-temperature solvent. To the best of our knowledge, the mechanism of the base transesterification of organic carbonate esters has not been studied computationally. In this study, we drew inspiration from the base hydrolysis of organic carbonates39 and carboxylate esters.40 In our proposed mechanism, the alkoxide−carbonate reactant complex eventually forms a tetrahedral intermediate with four oxygen substituents. This intermediate can eliminate either of the alkoxide ligands to H


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revert to the starting material or to proceed to the product (Scheme 6).

Table 5. Free Energies (kcal/mol) of the Various Species Involved in the Alkoxide Backbiting Reaction Relative to the Tetrahedral Intermediate

Scheme 6 no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

The working model of the alkoxide backbiting process is depicted in Scheme 7. The polymer chain is represented by a methoxide anion for computational economy. The alkoxide nucleophile can be on the methylene or the methine carbon of the future cyclic carbonate, and the substituent can be syn- or anti- with the carbonyl oxygen (“up” and “down”), respectively. While B3LYP/6-311G(2d,d,p) predefined in the CBS-QB3 composite method was suitable for the carbonate backbiting study, it was inadequate for describing loosely bound transition states involved in the alkoxide backbiting process due to the lack of diffuse functions. The CBS-QB3(+) composite method that uses B3LYP/6-311+G(2d,d,p) reference geometries was used instead,24 and the results are summarized in Table 5. Despite various attempts, the transition state between the tetrahedral intermediate and the open chain form of cyclohexene carbonate (where the pendant groups are anti to the carbonyl oxygen) could not be located (entry 15). With the exception of trans-cyclopentene carbonate, the free energy barrier required for the polymeric alkoxide to reach the tetrahedral intermediate is very small (Table 5 and Figure 15). The electronic energy barriers for these reactions are small (Supporting Information, Table S3). After vibrational corrections are taken into account, some of these barriers may be inundated by the height of the first vibrational mode. Consequently, there is little to no barrier for the alkoxide to backbite to give the tetrahedral intermediate. By the same reasoning, there is a negligible energy barrier for an alkoxide polymer chain to attack a cyclic carbonate unit, leading to chain growth. However, this pathway is entropically disfavored at high temperature. Furthermore, the ring-opened cyclic carbonate readily reverts to the tetrahedral intermediate because the alkoxide anion is tethered to the new carbonate group. This “chelate effect” helps ensure that the alkoxide ringopened product is disfavored.

EC PC-up-1 PC-up-2 PC-down-1 PC-down-2 ClPC-up-1 ClPC-up-2 ClPC-down-1 ClPC-down-2 SC-up-1 SC-up-2 SC-down-1 SC-down-2 cis-CHC-up cis-CHC-down trans-CHC cis-CPC-up cis-CPC-down trans-CPC

open chain

TS1

9.4 10.6 10.0 7.5 7.6 7.9 9.7 5.7 10.3 7.9 9.2 4.9 8.0 9.8

9.5 10.4 10.0 8.8 10.1 8.8 10.0 5.8 12.1 8.0 9.3 6.2 7.5 10.3

6.2 10.2 5.6 −3.4

6.8 9.6 7.9 4.3

tetrahedral intermediate

TS2

cyclic carbonate + methoxide

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

11.6 12.7 12.7 11.8 11.8 14.1 14.1 12.4 12.4 13.0 13.0 10.7 10.7 11.5 14.8 14.6 12.3 9.9 16.5

8.9 9.0 9.0 9.5 9.5 11.5 11.5 11.5 11.5 10.5 10.5 8.9 8.9 6.4 11.6 11.0 8.7 8.6 13.0

Generally, the alkoxide backbiting intermediate is less stable (by 0.2−3.3 kcal/mol, free energy) when the pendant group is anti to the carbonyl oxygen (“down”) than when the pendant group is syn (“up”). The energy differences between the synand anti-conformers at the second transition state are small (0.1−1.5 kcal/mol). The difference in activation barriers to backbiting is attributed to the energies of the intermediate, rather than the energies of the second transition states. Poly(ethylene carbonate) has no pendant groups, and the substituents for poly(cyclopentene carbonate) and poly(cyclohexene carbonate) are required to be “up” and “down” at the same time due to their trans conformation. Of the aliphatic polycarbonates, poly(styrene carbonate) has the lowest free energy barrier to give cyclic carbonate. Extending the ground-state argument, HOMO-2 of the poly(styrene carbonate) tetrahedral intermediate shows an out-of-phase interaction between the pπ orbitals on the phenyl

Scheme 7

I


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Figure 15. Free energy diagram for the alkoxide backbiting to eventually yield propylene carbonate and an alkoxide polymer chain (represented by methoxide). See entry 4 of Table 5.

pendant group and the orbitals on the five-membered cyclic carbonate ring. Such pendant group interactions are not observed for ethylene, propylene, and chloropropylene polycarbonates (Figure 16).

Note that only entries 16 and 19 of Table 5 are germane to the formation of cyclic carbonates from alicyclic polycarbonates that are of a trans configuration, whereas the remaining entries are included for completeness. Alkoxide backbiting by these poly(trans-cycloalkene carbonates) yield the trans-cycloalkene carbonate with retention of configuration (Figure 14). The free energy barrier to trans-cyclohexene carbonate is one of the highest, and that is again consistent with the lack of cyclic carbonate byproduct as poly(cyclohexene carbonate) is prepared. Comparing Tables 3 and 5, the most important conclusion to be drawn is that the metal-free carbonate backbiting reactions have free energy barriers 10 kcal/mol higher than the equivalent alkoxide backbiting reactions. This alkoxide backbiting reaction has been investigated experimentally by our group as well.13 In that study, azide was used as a base to deprotonate purified, metal-free polymers bearing hydroxy end groups, and the rates of reaction were monitored by in situ infrared spectroscopy (Scheme 8). Unlike the present computational study, the experimental rate constants take into account the equilibria between the alcohol and alkoxide forms of the polymer chains. Even so, the computationally derived results agree qualitatively with that previously reported: the activation barriers for alkoxide backbiting are lowest for poly(SC), and the activation barriers for poly(PC) and poly(ClPC) are similar and higher.

Figure 16. From left to right: HOMO-6 of the ethylene carbonate alkoxide backbiting intermediate and the corresponding HOMO-2s for propylene carbonate, chloropropylene carbonate, and styrene carbonate backbiting intermediates. For styrene carbonate, the outof-phase interaction between the pπ orbitals on the pendant benzene ring and the orbitals on the base of the cyclic carbonate destabilize the intermediate, effectively lowering the barrier to eliminate styrene carbonate.

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CONCLUDING REMARKS The enthalpies of polymerization of several aliphatic polycarbonates and poly(cyclohexene carbonate) were found by computational methods to be essentially the same (21−23 kcal/mol), and the polymerization reactions are all more exothermic than cyclic carbonate formation. On the other hand, the enthalpy of polymerization for poly(cyclopentene carbonate) formation because of ring strain was found to be significantly lower at 15.8 kcal/mol. It is apparent that cyclic carbonate formation is more entropically favored than polymer

trans-Cyclopentene carbonate is anomalous because the open chain species has less angle strain than both the transition state and the tetrahedral intermediate (Figure 17). As a result, poly(trans-cyclopentene carbonate) has a 7.7 kcal/mol free energy barrier for the open-chain alkoxide to backbite onto the carbonate to give the tetrahedral intermediate. J


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Figure 17. Free energies and the O−CH−CH2 bond angles for the trans-cyclopentene carbonate alkoxide backbiting process. This carbonate has a very high effective free energy barrier of 19.9 kcal/mol to cyclize via alkoxide backbiting compared to the other carbonates.

In the absence of a CO2 atmosphere, the polymer chain end will be in the form of a free alkoxide anion. Metal-free alkoxide backbiting is proposed to occur via a tetrahedral intermediate. Alkoxide attack of the carbonate to give the tetrahedral intermediate is generally barrierless. The rate-determining step to alkoxide backbiting is therefore the activation barrier to the second transition state which leads to cyclic carbonate formation. The free energy barrier for this process is more favorable than the carbonate backbiting process by about 10 kcal/mol. Chain extension through alkoxide attack is not likely because the ring-closing reaction is much more favorable because of the “chelate effect”. In closing, the CBS-QB3 composite ab initio method was successfully used to determine the enthalpies of polymerization and cyclic carbonate formation and the energy barriers for carbonate and alkoxide backbiting reactions. The energies determined are expected to be “chemically accurate” (±1 kcal/ mol), and we have shown this to be true for a set of benchmark reactions. The importance of validating DFT calculated reaction enthalpies with experimental data and/or high level ab initio calculations cannot be overemphasized.41

Scheme 8

growth, since cyclic carbonate formation is the thermodynamically more favored product in all cases. Metal-free carbonate backbiting is believed to be the main pathway to cyclic carbonate coproduction under polymerization conditions where there is an excess of carbon dioxide, as the metal-bound carbonates backbiting has a much higher activation barrier than backbiting via the free carbonate chain end. The barrier is increased by steric bulk at the carbon undergoing reaction regardless of the pendant group’s electrondonating or -withdrawing ability, except where the transition state is stabilized by pπ−p delocalization. Two special cases merit reiteration: The reaction of styrene oxide and carbon dioxide gives rise to large amounts of cyclic carbonate byproduct despite the formation of the latter being less exothermic by 8.0 kcal/mol. This is due to the low activation barrier for carbonate backbiting. Conversely, preparation of poly(cyclohexene carbonate) yields little cyclic carbonate byproduct because (i) cis-cyclohexene carbonate is 5.9 kcal/mol less stable (enthalpy) than the polymer, (ii) the growing polymer chain must undergo an 4.7 kcal/mol chairboat conformational change and then overcome a 21.1 kcal/ mol free energy barrier to undergo carbonate backbiting, and (iii) the barrier for the polymer to undergo backbiting to yield trans-cyclohexene carbonate is 14.6 kcal/mol, 3 kcal/mol higher than for aliphatic polycarbonates.

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COMPUTATIONAL METHODS All calculations were performed using the Gaussian 09 suite.42 The ab initio and DFT methods chosen were used primarily with Pople-style basis sets.43 All local minima and saddle points were confirmed by their calculated vibrational frequencies (zero and one imaginary frequencies, respectively). The saddle points found were confirmed to be the correct ones by visualizing the imaginary vibrational modes with AGUI44 and Avogadro.45 Where solvation was applied, tetrahydrofuran was the prototypical solvent used, and the integral equation formalism polarization continuum model (IEFPCM) calculation with radii and nonelectrostatic terms for Truhlar and co-workers’ SMD solvation model was used.46 K


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Benchmarking. Geometries and frequencies of all species were calculated at the B3LYP/6-31+G(d′) level. Single-point energies were obtained using other methods and basis sets, and the previously obtained thermodynamic corrections were applied. The B3LYP/6-31+G(d′) structures were also used as the starting geometries for the composite methods (CBS4M,19,20 CBS-QB3,19,21 G3(MP2),22 and G4 18). These calculated gas-phase enthalpies were compared to critically evaluated thermodynamic data published by the NIST.17 Enthalpies of Polymerization. B3LYP/6-31G(d′) geometries of the polycarbonate oligomers were found, and they served as starting points for the CBS-4M calculations in the gas phase. Carbonate and Alkoxide Backbiting. For the carbonate backbiting calculations, gas phase B3LYP/6-311++G(2d,p) optimized geometries with single-point solvation energy corrections were used, whereas geometries were optimized at the B3LYP/6-311+G(2d,d,p) level with solvation throughout for the alkoxide backbiting calculations. Molecular orbitals were visualized at the same levels of theory. Unmodified CBS-QB3 calculations with solvation were performed for the carbonate backbiting reaction, whereas the CBS-QB3(+) model as modified by Martin and co-workers24 with solvation was used for the alkoxide backbiting reaction. B3LYP/6-311+G(2d,d,p) reference geometries and frequencies were read-in, and the CBS-QB3 calculation proceeded directly to the third step (CCSD(T)/6-31+G(d′)) using the CBS-QB3(StartMP2) keyword in Gaussian 09. The scale factor for the zero-point energies was not changed from the 0.99 predefined by CBSQB3.

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ASSOCIATED CONTENT

* Supporting Information S

Benchmarking study: computational methods vs experimental data, optimized geometries of selected oligomers, and electronic energies of the alkoxide backbiting process. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful to the National Science Foundation (CHE1057743) and the Robert A. Welch Foundation (A0923) for financial support for this work. We also thank Dr. Lisa M. Pérez for valuable discussions and the Laboratory for Molecular Simulation and the Supercomputing Facility at Texas A&M University for providing computing resources.

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REFERENCES

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