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Thermal decomposition of graphene armchair oxyradicals
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Proceedings of the Combustion Institute 34 (2013) 1759–1766
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Thermal decomposition of graphene armchair oxyradicals David E. Edwards a,b,⇑, Xiaoqing You a,1, Dmitry Yu. Zubarev c, William A. Lester Jr. c,d, Michael Frenklach a,b a Department of Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94720-1740, USA Environmental Energy Technologies Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA c Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, CA 94720-1460, USA d Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA b
Available online 19 June 2012
Abstract Energetics and kinetics of the thermal decomposition of oxyradicals with oxygen bonded to a graphene armchair edge were investigated. Phenanthrene, benzoperylene, and an 11-ring polycyclic aromatic hydrocarbon (PAH) were selected as substrates to model the armchair edge, with a total of five different oxyradicals studied. The elementary steps of the reaction pathways were analyzed using density functional theory. Rate coefficients over the ranges of 1500–2500 K and 0.01–10 atm were obtained by solving the master equations. The computed rate coefficients were found to be temperature, pressure, and substrate-size dependent. The results revealed that the decomposition rate of an oxyradical with oxygen positioned on the outside of a corner armchair edge is faster than the rate with oxygen positioned to the inside of the edge. The trends in the computed oxyradical decomposition rates could be rationalized by the structural characteristics of the substrates. The decomposition rates computed for the armchair edge oxyradicals are shown to be similar to those previously obtained for corner zigzag edge oxyradicals. This implies that given an arbitrary shaped PAH, oxidation should preferentially occur at armchair and corner-zigzag sites, leaving resistant to oxidation inner zigzag sites essentially intact. Considering that growth of both armchair and zigzag edges proceeds at effectively the same rate, we expect to find proliferation of zigzag-edge surfaces on soot particles formed in flame environments. Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Soot; Graphene; PAH; Oxidation; Reaction mechanisms
⇑ Corresponding author. Address: 244 Hesse Hall, Department of Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94720, USA. E-mail address: [email protected] (D.E. Edwards). 1 Current address: Center for Combustion Energy, Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China.
1. Introduction Chemical evolution of graphene edges is one of the key processes in the formation, growth, and oxidation of soot and its aromatic precursors [1– 3]. Assuming that the soot particle surface is comprised of molecular aromatic sites (i.e., graphene
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edges) and invoking chemical similarity, it was postulated that soot surface reactions can be thought of as chemically analogous reactions of polycyclic aromatic hydrocarbons (PAHs) [4,5]. Growth reactions, those increasing PAH size by reactions with gaseous species, primarily acetylene, received immediate and continuing attention (see, e.g., [1–3] and references therein). However, it was also recognized that the chemical analogy was not sufficient to describe reactions taking place at the surface and steric effects, neighboring sites, and substrate size must also be considered [6]. The latter realization increased substantially the number of possible elementary reactions [7– 13]; for instance, the latest detailed graphene-edge growth mechanism is composed of 42 elementary reactions [14]. The oxidation of PAHs and soot surfaces has received lesser attention. The initial detailed models of soot oxidation invoked two principal steps: an elementary reaction of a surface radical with O2 and an atomistically-unresolved attack of OH on a generic surface site [5,15]. Both reactions were assumed to remove one C atom per O atom of the gaseous reactant and both assumed to form a “pristine” surface site (CsurfaceH or Csurface ) as the substrate product of oxidation. The former reaction was modeled following the postulate of chemical similarity by phenyl + O2 [16]. The oxidation by OH was described using the collision efficiency determined in flame studies [17]. This oxidation model has been widely adopted in modeling studies recently with different values of the rate coefficients [18]. Considering the knowledge gained with growth reactions, where the reaction chemistry of larger aromatic edges turned out to be much richer than that of the analogous smaller aromatic species, there is clearly a need for similar exploration of possible pathways for oxidation. We began this process with the examination of the thermodynamic stability of the key intermediates, graphene-edge oxyradicals, located at both zigzag and armchair sites [19,20]. It turns out that thermodynamic stability varies substantially at different O chemisorbed sites, and this variability can be explained and correlated with substrate aromaticity. We then turned to our next objective, the kinetics of graphene oxyradical decomposition. In a just-completed study [21], we examined the decomposition of oxyradicals on a zigzag edge of graphene. The results indicated that the rate of decomposition varies with the location of the O chemisorbed site on the zigzag edge. The principal conclusion, combining the thermodynamic [19,20] and kinetic results [21], is that only the outer rings of a zigzag edge are able to undergo oxidation, similar to phenoxy decomposition [22–24], whereas the inner rings resist oxidation in combustion environments.
In the present study, we compute decomposition rates of graphene oxyradicals whose oxygen atom is located at armchair sites, compare these rates to those at zigzag sites [21], and show that kinetic stability of oxyradicals, similar to their thermodynamic stability, is correlated with substrate aromaticity. We conclude with the implications of these findings for soot oxidation. 2. Computational methodology The computational methodology follows that of our previous studies [8–11,21]. Briefly, potential energy surfaces (PES) of all stable species and transition states for the oxyradical systems were calculated using density functional theory (DFT). Geometry optimization and vibrational frequency calculations were performed to identify all stationary points on the reaction pathways using the B3LYP hybrid functional [25,26] and a 6–311G(d,p) basis set [27]. All the quantum-chemical calculations were carried out using the Gaussian 03 [28] and the Gaussian 09 [29] program packages. Further details are reported in Section 1 of the Supplemental Data. We note that the rather large size of aromatic systems of the present study limits the choice of possible methods. Our objective of exploring unknown armchair pathways is met by comparing the order of magnitude of their rates rather than precise values. The chosen level of theory should suffice for this purpose. Also, this theoretical approach was shown to match closely the experimental rates of phenoxy decomposition [21] (see also Section 1.3 of the Supplemental Data). Using the quantum-chemical results described above, we calculated the rate coefficients of the thermally activated reaction systems. These calculations were performed using the MultiWell suite of codes [30–32] for temperatures ranging from 1500 to 2500 K and pressures from 0.01 to 10 atm. As in our previous studies [8–11,21], the exponential-down model with hDEidown = 260 cm1 was used to describe the collisional energy transfer [33]. We prefer to use a constant value of hDEidown rather than a temperature-dependent hDEidown expression as suggested by a reviewer. Our preference is based on the analysis of phenoxy decomposition, detailed in Section 1.3 of the Supplementary Data. Still, we performed calculations with both a constant and temperature-dependent hDEidown as reported in Section 3.3 below. For each set of initial conditions, the number of stochastic trials was varied from 4 104 to 1 109 to keep statistical error below 5%. This approach is estimated to produce rate coefficients to within an order-of-magnitude accuracy [8–11]. Further details on the computational methodology are included in Section 1 of the Supplemental Data.
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3. Results and discussion 3.1. Armchair oxyradicals To study the decomposition of armchair edge oxyradicals, five molecules were selected; their structures are displayed as reactant 1 in panels a–e of Fig. 1. Figure 1f explicates zigzag and armchair edges. Phenanthrene oxyradicals I and II
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were selected to examine the differences in decomposition rate between the two principal armchair sites. Phenanthrene oxyradical III was included to provide comparison with the previously studied zigzag site decomposition [21]. Benzoperylene oxyradical and the extended-armchair oxyradical have oxygen located on an armchair site that is the same as in phenanthrene II, but part of a larger substrate. The intent of including these larger
Fig. 1. (a–e) Minimum potential energy paths for the thermal decomposition of phenanthrene I, II, III, benzoperylene, and extended armchair oxyradicals, respectively, at the B3LYP/6311G(d,p) level. Energies are in kcal/mol at 0 K relative to the reactant of each respective PES. (f) Description of armchair and zigzag edges—atoms 1,2, and 3 forming a zigzag edge and atoms 4,5,6 and 7 forming an armchair edge.
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substrates is to examine if and by how much the decomposition rate for the same edge site changes with substrate size. 3.2. Minimum energy paths Phenanthrene oxyradicals I, II, and III decompose via similar pathways and intermediates (Fig. 1a–c). The three pathways contain a cyclic intermediate 2, and all have at least one ringopening intermediate 5. For phenanthrene oxyradical I, two five-member rings with attached CO, intermediates 3 and 7, were found. For phenanthrene oxyradicals II and III, only one such intermediate, 3, was discovered. An additional channel was found for phenanthrene oxyradical II, namely TS 2-4, which connects intermediate 2 directly to product 4. These pathways are similar to those computed for the decomposition of pentacene corner oxyradicals [21], which included the cyclic (2), attached-CO (3), and ring-opening (5) intermediates. Furthermore, the products of decomposition are also comparable in that all contain a fivemember ring. Barrier energies of the corner-pentacene and phenanthrene oxyradical decomposition pathways are also very close to each other, often within 3-4 kcal/mol. Such parallels in the reaction pathways indicate that the armchair-edge and corner zigzag-edge decompositions are comparable and could be classified as equivalent types of oxidation reactions. Phenanthrene oxyradicals I, II, and III are all single row structures. To test the influence of substrate size on decomposition kinetics, the benzoperylene and extended-armchair oxyradicals were studied; both have oxygen on a site similar to that in phenanthrene II. The phenanthrene II and benzoperylene decomposition pathways, shown in Fig. 1b and d, respectively, contain the same intermediates, but the energy of the highest transition state barrier along the lowest potential energy path (TS 1-2) is larger by 7 kcal/mol for benzoperylene. Furthermore, the benzoperylene ringopening barrier (TS 1-5) is 13.5 kcal/mol higher than the phenanthrene II barrier. As shown in the next section, these higher barriers lead to an almost 10-fold slower decomposition rate for benzoperylene oxyradical relative to phenanthrene II oxyradical. The extended-armchair decomposition pathway differs from the phenanthrene II and benzoperylene pathways. The extended-armchair pathway, shown in Fig. 1e, does not contain the cyclic intermediate 2, but it does have the ring-opening intermediate 5. In this case, rather than proceeding from 1 to 2 to 3 as with the other structures, the extended-armchair oxyradical goes directly from 1 to 3. The difference in potential energy between the highest barrier on the lowest energy path of the extendedarmchair (TS 1-3) and that of benzoperylene
(TS 1-2) is 2.8 kcal/mol. This difference is counteracted by a 11.7 kcal/mol higher ring-opening barrier (TS 1-5) of benzoperylene compared to that of the extended-armchair. These opposing trends nearly cancel and, as shown in the next section, the extended-armchair and benzoperylene oxyradicals decompose at similar rates. For all molecular structures, Table S23 reports all zero-point energies, expectation values of the S2 operator, vibrational frequencies and rotational constants. Table S24 lists the Cartesian coordinates for all optimized structures. 3.3. Reaction rate coefficients The main results of the present study are reaction rates calculated for the following five reactions,
The principal products of oxyradical decompositions were the attached (embedded) five-member ring and CO. The accumulation of other species was negligible for the conditions studied.
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The rate coefficients at specific values of pressure and temperature were computed by solving the master equations using the MultiWell suite of codes. The computed values of the rate coefficients of reactions R1–R5 for a matrix of temperatures and pressures are reported in Tables S1–S5 and in graphical form in Figs. S3–S7 of the Supplemental Data. These are computed employing a constant hDEidown. For the purpose of comparison, the rate coefficients were also calculated using the temperature-dependent hDEidown expression; these values are reported in Tables S6–S10 of the Supplemental Data. The average difference between the rate coefficients calculated using the two approaches, a constant hDEidown and temperature-dependent hDEidown, was a factor of 2 and the maximum difference was a factor of 3.3. All of these reactions displayed similar pressure and temperature dependence. In observing the pressure dependence, it was desirable to calculate the high-pressure-limit rate coefficients for each of the overall reactions R1– R5. To accomplish this aim, we assumed that all intermediates of an individual reaction system are in steady state. The rate expressions derived in this manner are reported in Table S22 and the MultiWell high-pressure-limit rates of the individual reactions steps are summarized in Tables S16– S20 of the Supplemental Data. The fitted Arrhenius expressions for the high-pressure-limit rate coefficients of reactions R1–R5 are presented in Table 1. In addition, for completeness, Table S21 lists the equilibrium constants for the respective reactions R1–R5. Inspection of rate coefficients computed for the three phenanthrene oxyradicals, displayed in Fig. 2, indicates that phenanthrene I, with oxygen farthest to the outside, decomposes faster than phenanthrene II, whereas the latter decomposes about as fast as phenanthrene III. The correlation of these rates with the molecular structure of the three phenanthrene oxyradicals can be rationalized by counting “free edges”, a concept introduced in our earlier study [21]. A “free edge” classifies the connectivity of the C–O site in the context of the multi-ring aromatic structure. For example, in phenanthrene I, C–O is connected, on both sides, to carbon atoms that are members of only one ring; we classify each of these edges as free edges. On the other hand, C–O in phenanthrenes II and III is connected on one side to a Table 1 High-pressure-limit rate coefficients. Reaction
Rate coefficient (s1)
R1 R2 R3 R4 R5
1:08 102 T 3:28 expð21866=T Þ 4:00 102 T 4:38 expð243624=T Þ 6:42 1010 T 1:00 expð29183=T Þ 3:78 104 T 2:59 expð30151=T Þ 4:47 1012 T 0:39 expð33796=T Þ
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Fig. 2. Rate coefficients of the decomposition of phenanthrene oxyradicals I, II and III. The solid lines are the high-pressure-limit values and the dashed lines are the rate coefficients at 1 atm.
C atom that is a member of two rings, and on the other side to a C atom that is a member of one ring. Therefore, phenanthrenes II and III contain only one free edge, with the non-free edge connected to the carbon atom that is a member of two rings. Using this simple structural classification enables us to rationalize the relative ordering of the decomposition rates among phenanthrene oxyradicals I, II, and III. Phenanthrene I has two free edges and decomposes fastest, whereas II and III, each having just one free edge, decompose slower than I and at nearly comparable rates. In Fig. 3 we compare the decomposition rates of phenanthrene II, benzoperylene, and the extended-armchair oxyradicals. Inspection of these findings indicates that the increase in substrate size, from phenanthrene to benzoperylene, substantially reduces the computed reaction rate, whereas the rate seems to level off with further increase in size, from benzoperylene to the extended-armchair oxyradical. The benzoperylene oxyradical decomposes nearly an order of magnitude slower than the phenanthrene II oxyradical. This is primarily due to the higher potential energy of TS 1-2 and TS 1-5 in the benzoperylene pathway compared to those in the phenanthrene II pathway. Comparing the extended-armchair energetics to that of benzoperylene indicates that although the lowest energy path for the extended-armchair has a higher barrier (TS 1-3) than benzoperylene (TS 1-2), it has a substantially lower barrier to ring-opening, thus making its decomposition rate competitive with that of benzoperylene oxyradical decomposition. These results indicate that benzoperylene may be sufficiently large to represent an armchair-edge reaction for an arbitrarily large graphene substrate.
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Fig. 3. Rate coefficients of the decomposition of phenanthrene oxyradical II (black lines), benzoperylene oxyradical (black lines), and the extended-armchair oxyradical (gray lines). The solid lines are the highpressure-limit values and the dashed lines are the rate coefficients at 1 atm.
Finally, comparing the decomposition rates of the armchair-edge and zigzag-edge oxyradicals highlights the resemblance between the decomposition rates of the armchair and corner zigzag edges. Figure 4 displays the decomposition rates of phenanthrene I and II as well as those of pentacene I and II from the previous study [21]. Focusing first on the 1 atm results displayed in Fig. 4,
we see strong correlation between the phenanthrene and pentacene decomposition rates, namely phenanthrene I and pentacene I decomposition rates are very close to one another, as are the decomposition rates of phenanthrene II and pentacene II. Structurally, phenanthrene I is similar to pentacene I—both have free edges on each side of the C–O bond. Likewise, phenanthrene II structurally resembles pentacene II, with a free edge on only one side of the C–O bond. Again, the structures with the same number of free edges decompose at similar rates, and the structures with two free edges decompose faster than those with one free edge. However, at the high-pressure limit the correlation between the pentacene and phenanthrene oxyradical decomposition rates is weaker (Fig. 4). The general trend within the different types of molecules still holds, as oxyradical structures with more free edges decompose at a faster rate than those with just one free edge. This “free-edge” analysis rationalizes one of the key results of the present study, namely, that phenanthrene oxyradicals and corner pentacene oxyradicals decompose at similar rates. We also calculated branching ratios of the ring-opening and cyclic pathway rates for reactions R1–R5, i.e., k1!2/k1!5 for R1–R4 and k1!3/k1!5 for R5. They are reported in Tables S11–S15 of the Supplemental Data for a range of temperatures and pressures. The ring-opening pathway generally dominates for reactions R2, R3, and R5, and the cyclic pathway dominates for reactions R1 and R4. The competitiveness of the ring-opening pathway is due to the higher entropy of the ring-opening transition structure compared to the cyclic one. 3.4. Correlation with aromaticity
Fig. 4. Rate coefficients of the decomposition of phenanthrene oxyradicals I and II (black lines) and pentacene oxyradicals I and II (gray lines) [21]. The solid lines are the high-pressure-limit values and the dashed lines are the rate coefficients at 1 atm.
Polyaromatic hydrocarbons are structurally related to the benzene molecule. This connection implies strong similarity in electronic structure that characterizes aromatic systems, namely, that of delocalized bonding. However, in the analysis of chemical properties of large PAHs studied as models of extended systems, such as soot and graphene, this connection is rarely exploited. It is reasonable to examine thermodynamic and kinetic aspects of reactivity of large PAHs on the basis of their local and global aromaticity. Such a connection can lead to formulation of simple quantitative or semi-quantitative predictive models that appeal to chemical intuition and help to rationalize structure-property relationships of the target systems—soot and graphene. Aromaticity can be defined as the extra stabilization of a system featuring delocalized bonds with respect to a fictitious system with completely localized bonds. In practice, assessment of the resonance energy is a difficult task, especially for molecules that require multiple Kekule structures
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in the resonance description. Multiple measures of aromaticity have been proposed in order to simplify the task and connect the analysis to observable properties [34–36]. Considering the computational challenges associated with theoretical treatment of large PAHs it appears reasonable to choose the simplest model of aromaticity that utilizes the observation that aromatic bonding is strongly associated with equalization of bond lengths due to formation of a delocalized bonding framework. In the Harmonic Oscillator Model of Aromaticity (HOMA) [37], one evaluates the mean deviation of bond lengths in a system under consideration with respect to bond lengths in benzene. It is further scaled such that HOMA = 0 for the Kekule form of benzene and HOMA = 1 for the aromatic form. Previous studies of our group [19,20] demonstrated that a simple correlation exists between cumulative HOMA of oxyradicals and their relative thermodynamic stability. The origin of this relationship is fragmentation of the delocalized p-bonding framework due to its disruption upon chemisorption of an O atom at a graphene radical site. It is reasonable to assume that the same reasoning applies to energetic characteristics of oxyradical decomposition. In the present case, HOMA can be used for reactivity analysis for reaction kinetics. Considering the diversity of factors controlling reaction kinetics, for example, the multiple intermediates and transition states, we narrowed the range of analyzed characteristics down to a single one, namely the relative energy of the first transition state. Barrier height is a relative value, so it is logical to consider its relationship to a relative descriptor of aromatic bonding, that can be defined as the difference between HOMA of the benzene-like ring undergoing CO expulsion of the reactant and HOMA of the transition state, i.e., HOMArel = HOMATS HOMAreactant. A simple correlation in the data
Fig. 5. First barrier heights of oxyradical decompositions against relative HOMA of respective transition states (TS 1-2). Phenoxy and pentacene structures are from [21].
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can be seen by plotting (Fig. 5) the results obtained in the present and previous [21] studies. The smallest barrier height is associated with the smallest absolute HOMA change, thus suggesting that CO expulsion should proceed via the route that involves the smallest rearrangement of the conjugated bonding framework. The correlation is not perfect; for instance, the benzoperylene point falls from this general trend. A possible explanation is that benzoperylene is the only two row structure, while the other points are all single row structures. Further analysis requires a larger data set. 4. Conclusions The energetics and kinetics of the thermal decomposition of five graphene armchair-edge oxyradicals were investigated. In all cases studied, the computed decomposition rates are both temperature and pressure dependent. The extent of the pressure dependence, especially at higher temperatures, turned out to be substantial even for the largest molecular substrate studied, an 11-ring PAH. Also noteworthy is the influence of substrate size on computed rates; the effect was clearly pronounced in going from 3 to 6-ring aromatics, yet seemed to level off for larger systems as found for 6 to 11-ring aromatics. Applying the previously introduced concept of “free edges” for polycyclic aromatics [21], the trends obtained here for computed decomposition rates with substrate molecular structure are rationalized. Oxyradicals with more free edges decompose at faster rates than those with a fewer number of free edges. This relationship holds strongest within oxyradicals of similar structures (e.g., different phenanthrene oxyradicals), and is weaker in explaining the relative rates between different structures (e.g., phenanthrene versus pentacene oxyradicals). The kinetic stability of graphene-edge oxyradicals, both armchair studied here and zigzag of the previous study [21], was shown to be correlated with change in aromaticity during the initial, typically rate-controlling, step of oxyradical decomposition. This correlation, together with a recently-established similar scaling for thermodynamic stability [19,20], could lead to practical rules for predicting oxidation rate coefficients for arbitrary size and shape aromatics, thereby supplementing and enhancing models of soot oxidation. The potential energy pathways and overall decomposition rates computed in the present study for armchair edge oxyradicals are very similar to those obtained in our previous study [21] for corner zigzag edge oxyradicals. This finding implies that for an arbitrary shaped PAH, oxidation should predominantly remove armchair and corner-zigzag
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sites, leaving resistant-to-oxidation [21] inner zigzag sites essentially intact. Considering that the growth of both armchair and zigzag edges proceed at effectively the same rate [7,14], we expect to find proliferation of zigzag-edge surfaces on soot particles formed in flame environments.
Acknowledgments XY and MF were supported by the US Army Corps of Engineers, Humphreys Engineering Center Support Activity, under Contract No. W912HQ-07-C-0044. DYZ was supported by the National Science Foundation under grant NSF CHE-0809969. DEE, WAL, and MF were supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences, Geosciences and Biosciences Division of the US Department of Energy, under Contract No. DE-AC03-76F00098. This research used computational resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the US Department of Energy under Contract No. DEAC02-05CH11231. The authors are indebted to Professors David Golden and John Barker for their help with the use of the MultiWell code. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http:// dx.doi.org/10.1016/j.proci.2012.05.031. References [1] M. Frenklach, Phys. Chem. Chem. Phys. 4 (11) (2002) 2028–2037. [2] H. Bockhorn, A. D’Anna, A.F. Sarofim, H. Wang (Eds.), Combustion Generated Fine Carbonaceous Particles, KIT Scientific, Karlsruhe, Germany, 2009. [3] H. Wang, Proc. Combust. Inst. 33 (2011) 41–67. [4] M. Frenklach, in: J.C. Tarter, S. Chang, D.J. DeFrees (Eds.), A Unifying Picture Of Gas Phase Formation And Growth Of Pah, Soot, Diamond And Graphite Carbon In The Galaxy: Studies From Earth And Space, NASA Conference Publication 3061, 1990, pp. 259–273. [5] M. Frenklach, H. Wang, Proc. Combust. Inst. 23 (1991) 1559–1566. [6] M. Frenklach, Proc. Combust. Inst. 26 (2) (1996) 2285–2293. [7] M. Frenklach, C.A. Schuetz, J. Ping, Proc. Combust. Inst. 30 (2005) 1389–1396. [8] R. Whitesides, A.C. Kollias, D. Domin, et al., Proc. Combust. Inst. 31 (1) (2007) 539–546.
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Proceedings of the Combustion Institute 34 (2013) 1759–1766
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Thermal decomposition of graphene armchair oxyradicals David E. Edwards a,b,⇑, Xiaoqing You a,1, Dmitry Yu. Zubarev c, William A. Lester Jr. c,d, Michael Frenklach a,b a Department of Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94720-1740, USA Environmental Energy Technologies Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA c Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, CA 94720-1460, USA d Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA b
Available online 19 June 2012
Abstract Energetics and kinetics of the thermal decomposition of oxyradicals with oxygen bonded to a graphene armchair edge were investigated. Phenanthrene, benzoperylene, and an 11-ring polycyclic aromatic hydrocarbon (PAH) were selected as substrates to model the armchair edge, with a total of five different oxyradicals studied. The elementary steps of the reaction pathways were analyzed using density functional theory. Rate coefficients over the ranges of 1500–2500 K and 0.01–10 atm were obtained by solving the master equations. The computed rate coefficients were found to be temperature, pressure, and substrate-size dependent. The results revealed that the decomposition rate of an oxyradical with oxygen positioned on the outside of a corner armchair edge is faster than the rate with oxygen positioned to the inside of the edge. The trends in the computed oxyradical decomposition rates could be rationalized by the structural characteristics of the substrates. The decomposition rates computed for the armchair edge oxyradicals are shown to be similar to those previously obtained for corner zigzag edge oxyradicals. This implies that given an arbitrary shaped PAH, oxidation should preferentially occur at armchair and corner-zigzag sites, leaving resistant to oxidation inner zigzag sites essentially intact. Considering that growth of both armchair and zigzag edges proceeds at effectively the same rate, we expect to find proliferation of zigzag-edge surfaces on soot particles formed in flame environments. Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Soot; Graphene; PAH; Oxidation; Reaction mechanisms
⇑ Corresponding author. Address: 244 Hesse Hall, Department of Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94720, USA. E-mail address: [email protected] (D.E. Edwards). 1 Current address: Center for Combustion Energy, Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China.
1. Introduction Chemical evolution of graphene edges is one of the key processes in the formation, growth, and oxidation of soot and its aromatic precursors [1– 3]. Assuming that the soot particle surface is comprised of molecular aromatic sites (i.e., graphene
1540-7489/$ - see front matter Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.proci.2012.05.031
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edges) and invoking chemical similarity, it was postulated that soot surface reactions can be thought of as chemically analogous reactions of polycyclic aromatic hydrocarbons (PAHs) [4,5]. Growth reactions, those increasing PAH size by reactions with gaseous species, primarily acetylene, received immediate and continuing attention (see, e.g., [1–3] and references therein). However, it was also recognized that the chemical analogy was not sufficient to describe reactions taking place at the surface and steric effects, neighboring sites, and substrate size must also be considered [6]. The latter realization increased substantially the number of possible elementary reactions [7– 13]; for instance, the latest detailed graphene-edge growth mechanism is composed of 42 elementary reactions [14]. The oxidation of PAHs and soot surfaces has received lesser attention. The initial detailed models of soot oxidation invoked two principal steps: an elementary reaction of a surface radical with O2 and an atomistically-unresolved attack of OH on a generic surface site [5,15]. Both reactions were assumed to remove one C atom per O atom of the gaseous reactant and both assumed to form a “pristine” surface site (CsurfaceH or Csurface ) as the substrate product of oxidation. The former reaction was modeled following the postulate of chemical similarity by phenyl + O2 [16]. The oxidation by OH was described using the collision efficiency determined in flame studies [17]. This oxidation model has been widely adopted in modeling studies recently with different values of the rate coefficients [18]. Considering the knowledge gained with growth reactions, where the reaction chemistry of larger aromatic edges turned out to be much richer than that of the analogous smaller aromatic species, there is clearly a need for similar exploration of possible pathways for oxidation. We began this process with the examination of the thermodynamic stability of the key intermediates, graphene-edge oxyradicals, located at both zigzag and armchair sites [19,20]. It turns out that thermodynamic stability varies substantially at different O chemisorbed sites, and this variability can be explained and correlated with substrate aromaticity. We then turned to our next objective, the kinetics of graphene oxyradical decomposition. In a just-completed study [21], we examined the decomposition of oxyradicals on a zigzag edge of graphene. The results indicated that the rate of decomposition varies with the location of the O chemisorbed site on the zigzag edge. The principal conclusion, combining the thermodynamic [19,20] and kinetic results [21], is that only the outer rings of a zigzag edge are able to undergo oxidation, similar to phenoxy decomposition [22–24], whereas the inner rings resist oxidation in combustion environments.
In the present study, we compute decomposition rates of graphene oxyradicals whose oxygen atom is located at armchair sites, compare these rates to those at zigzag sites [21], and show that kinetic stability of oxyradicals, similar to their thermodynamic stability, is correlated with substrate aromaticity. We conclude with the implications of these findings for soot oxidation. 2. Computational methodology The computational methodology follows that of our previous studies [8–11,21]. Briefly, potential energy surfaces (PES) of all stable species and transition states for the oxyradical systems were calculated using density functional theory (DFT). Geometry optimization and vibrational frequency calculations were performed to identify all stationary points on the reaction pathways using the B3LYP hybrid functional [25,26] and a 6–311G(d,p) basis set [27]. All the quantum-chemical calculations were carried out using the Gaussian 03 [28] and the Gaussian 09 [29] program packages. Further details are reported in Section 1 of the Supplemental Data. We note that the rather large size of aromatic systems of the present study limits the choice of possible methods. Our objective of exploring unknown armchair pathways is met by comparing the order of magnitude of their rates rather than precise values. The chosen level of theory should suffice for this purpose. Also, this theoretical approach was shown to match closely the experimental rates of phenoxy decomposition [21] (see also Section 1.3 of the Supplemental Data). Using the quantum-chemical results described above, we calculated the rate coefficients of the thermally activated reaction systems. These calculations were performed using the MultiWell suite of codes [30–32] for temperatures ranging from 1500 to 2500 K and pressures from 0.01 to 10 atm. As in our previous studies [8–11,21], the exponential-down model with hDEidown = 260 cm1 was used to describe the collisional energy transfer [33]. We prefer to use a constant value of hDEidown rather than a temperature-dependent hDEidown expression as suggested by a reviewer. Our preference is based on the analysis of phenoxy decomposition, detailed in Section 1.3 of the Supplementary Data. Still, we performed calculations with both a constant and temperature-dependent hDEidown as reported in Section 3.3 below. For each set of initial conditions, the number of stochastic trials was varied from 4 104 to 1 109 to keep statistical error below 5%. This approach is estimated to produce rate coefficients to within an order-of-magnitude accuracy [8–11]. Further details on the computational methodology are included in Section 1 of the Supplemental Data.
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3. Results and discussion 3.1. Armchair oxyradicals To study the decomposition of armchair edge oxyradicals, five molecules were selected; their structures are displayed as reactant 1 in panels a–e of Fig. 1. Figure 1f explicates zigzag and armchair edges. Phenanthrene oxyradicals I and II
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were selected to examine the differences in decomposition rate between the two principal armchair sites. Phenanthrene oxyradical III was included to provide comparison with the previously studied zigzag site decomposition [21]. Benzoperylene oxyradical and the extended-armchair oxyradical have oxygen located on an armchair site that is the same as in phenanthrene II, but part of a larger substrate. The intent of including these larger
Fig. 1. (a–e) Minimum potential energy paths for the thermal decomposition of phenanthrene I, II, III, benzoperylene, and extended armchair oxyradicals, respectively, at the B3LYP/6311G(d,p) level. Energies are in kcal/mol at 0 K relative to the reactant of each respective PES. (f) Description of armchair and zigzag edges—atoms 1,2, and 3 forming a zigzag edge and atoms 4,5,6 and 7 forming an armchair edge.
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substrates is to examine if and by how much the decomposition rate for the same edge site changes with substrate size. 3.2. Minimum energy paths Phenanthrene oxyradicals I, II, and III decompose via similar pathways and intermediates (Fig. 1a–c). The three pathways contain a cyclic intermediate 2, and all have at least one ringopening intermediate 5. For phenanthrene oxyradical I, two five-member rings with attached CO, intermediates 3 and 7, were found. For phenanthrene oxyradicals II and III, only one such intermediate, 3, was discovered. An additional channel was found for phenanthrene oxyradical II, namely TS 2-4, which connects intermediate 2 directly to product 4. These pathways are similar to those computed for the decomposition of pentacene corner oxyradicals [21], which included the cyclic (2), attached-CO (3), and ring-opening (5) intermediates. Furthermore, the products of decomposition are also comparable in that all contain a fivemember ring. Barrier energies of the corner-pentacene and phenanthrene oxyradical decomposition pathways are also very close to each other, often within 3-4 kcal/mol. Such parallels in the reaction pathways indicate that the armchair-edge and corner zigzag-edge decompositions are comparable and could be classified as equivalent types of oxidation reactions. Phenanthrene oxyradicals I, II, and III are all single row structures. To test the influence of substrate size on decomposition kinetics, the benzoperylene and extended-armchair oxyradicals were studied; both have oxygen on a site similar to that in phenanthrene II. The phenanthrene II and benzoperylene decomposition pathways, shown in Fig. 1b and d, respectively, contain the same intermediates, but the energy of the highest transition state barrier along the lowest potential energy path (TS 1-2) is larger by 7 kcal/mol for benzoperylene. Furthermore, the benzoperylene ringopening barrier (TS 1-5) is 13.5 kcal/mol higher than the phenanthrene II barrier. As shown in the next section, these higher barriers lead to an almost 10-fold slower decomposition rate for benzoperylene oxyradical relative to phenanthrene II oxyradical. The extended-armchair decomposition pathway differs from the phenanthrene II and benzoperylene pathways. The extended-armchair pathway, shown in Fig. 1e, does not contain the cyclic intermediate 2, but it does have the ring-opening intermediate 5. In this case, rather than proceeding from 1 to 2 to 3 as with the other structures, the extended-armchair oxyradical goes directly from 1 to 3. The difference in potential energy between the highest barrier on the lowest energy path of the extendedarmchair (TS 1-3) and that of benzoperylene
(TS 1-2) is 2.8 kcal/mol. This difference is counteracted by a 11.7 kcal/mol higher ring-opening barrier (TS 1-5) of benzoperylene compared to that of the extended-armchair. These opposing trends nearly cancel and, as shown in the next section, the extended-armchair and benzoperylene oxyradicals decompose at similar rates. For all molecular structures, Table S23 reports all zero-point energies, expectation values of the S2 operator, vibrational frequencies and rotational constants. Table S24 lists the Cartesian coordinates for all optimized structures. 3.3. Reaction rate coefficients The main results of the present study are reaction rates calculated for the following five reactions,
The principal products of oxyradical decompositions were the attached (embedded) five-member ring and CO. The accumulation of other species was negligible for the conditions studied.
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The rate coefficients at specific values of pressure and temperature were computed by solving the master equations using the MultiWell suite of codes. The computed values of the rate coefficients of reactions R1–R5 for a matrix of temperatures and pressures are reported in Tables S1–S5 and in graphical form in Figs. S3–S7 of the Supplemental Data. These are computed employing a constant hDEidown. For the purpose of comparison, the rate coefficients were also calculated using the temperature-dependent hDEidown expression; these values are reported in Tables S6–S10 of the Supplemental Data. The average difference between the rate coefficients calculated using the two approaches, a constant hDEidown and temperature-dependent hDEidown, was a factor of 2 and the maximum difference was a factor of 3.3. All of these reactions displayed similar pressure and temperature dependence. In observing the pressure dependence, it was desirable to calculate the high-pressure-limit rate coefficients for each of the overall reactions R1– R5. To accomplish this aim, we assumed that all intermediates of an individual reaction system are in steady state. The rate expressions derived in this manner are reported in Table S22 and the MultiWell high-pressure-limit rates of the individual reactions steps are summarized in Tables S16– S20 of the Supplemental Data. The fitted Arrhenius expressions for the high-pressure-limit rate coefficients of reactions R1–R5 are presented in Table 1. In addition, for completeness, Table S21 lists the equilibrium constants for the respective reactions R1–R5. Inspection of rate coefficients computed for the three phenanthrene oxyradicals, displayed in Fig. 2, indicates that phenanthrene I, with oxygen farthest to the outside, decomposes faster than phenanthrene II, whereas the latter decomposes about as fast as phenanthrene III. The correlation of these rates with the molecular structure of the three phenanthrene oxyradicals can be rationalized by counting “free edges”, a concept introduced in our earlier study [21]. A “free edge” classifies the connectivity of the C–O site in the context of the multi-ring aromatic structure. For example, in phenanthrene I, C–O is connected, on both sides, to carbon atoms that are members of only one ring; we classify each of these edges as free edges. On the other hand, C–O in phenanthrenes II and III is connected on one side to a Table 1 High-pressure-limit rate coefficients. Reaction
Rate coefficient (s1)
R1 R2 R3 R4 R5
1:08 102 T 3:28 expð21866=T Þ 4:00 102 T 4:38 expð243624=T Þ 6:42 1010 T 1:00 expð29183=T Þ 3:78 104 T 2:59 expð30151=T Þ 4:47 1012 T 0:39 expð33796=T Þ
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Fig. 2. Rate coefficients of the decomposition of phenanthrene oxyradicals I, II and III. The solid lines are the high-pressure-limit values and the dashed lines are the rate coefficients at 1 atm.
C atom that is a member of two rings, and on the other side to a C atom that is a member of one ring. Therefore, phenanthrenes II and III contain only one free edge, with the non-free edge connected to the carbon atom that is a member of two rings. Using this simple structural classification enables us to rationalize the relative ordering of the decomposition rates among phenanthrene oxyradicals I, II, and III. Phenanthrene I has two free edges and decomposes fastest, whereas II and III, each having just one free edge, decompose slower than I and at nearly comparable rates. In Fig. 3 we compare the decomposition rates of phenanthrene II, benzoperylene, and the extended-armchair oxyradicals. Inspection of these findings indicates that the increase in substrate size, from phenanthrene to benzoperylene, substantially reduces the computed reaction rate, whereas the rate seems to level off with further increase in size, from benzoperylene to the extended-armchair oxyradical. The benzoperylene oxyradical decomposes nearly an order of magnitude slower than the phenanthrene II oxyradical. This is primarily due to the higher potential energy of TS 1-2 and TS 1-5 in the benzoperylene pathway compared to those in the phenanthrene II pathway. Comparing the extended-armchair energetics to that of benzoperylene indicates that although the lowest energy path for the extended-armchair has a higher barrier (TS 1-3) than benzoperylene (TS 1-2), it has a substantially lower barrier to ring-opening, thus making its decomposition rate competitive with that of benzoperylene oxyradical decomposition. These results indicate that benzoperylene may be sufficiently large to represent an armchair-edge reaction for an arbitrarily large graphene substrate.
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Fig. 3. Rate coefficients of the decomposition of phenanthrene oxyradical II (black lines), benzoperylene oxyradical (black lines), and the extended-armchair oxyradical (gray lines). The solid lines are the highpressure-limit values and the dashed lines are the rate coefficients at 1 atm.
Finally, comparing the decomposition rates of the armchair-edge and zigzag-edge oxyradicals highlights the resemblance between the decomposition rates of the armchair and corner zigzag edges. Figure 4 displays the decomposition rates of phenanthrene I and II as well as those of pentacene I and II from the previous study [21]. Focusing first on the 1 atm results displayed in Fig. 4,
we see strong correlation between the phenanthrene and pentacene decomposition rates, namely phenanthrene I and pentacene I decomposition rates are very close to one another, as are the decomposition rates of phenanthrene II and pentacene II. Structurally, phenanthrene I is similar to pentacene I—both have free edges on each side of the C–O bond. Likewise, phenanthrene II structurally resembles pentacene II, with a free edge on only one side of the C–O bond. Again, the structures with the same number of free edges decompose at similar rates, and the structures with two free edges decompose faster than those with one free edge. However, at the high-pressure limit the correlation between the pentacene and phenanthrene oxyradical decomposition rates is weaker (Fig. 4). The general trend within the different types of molecules still holds, as oxyradical structures with more free edges decompose at a faster rate than those with just one free edge. This “free-edge” analysis rationalizes one of the key results of the present study, namely, that phenanthrene oxyradicals and corner pentacene oxyradicals decompose at similar rates. We also calculated branching ratios of the ring-opening and cyclic pathway rates for reactions R1–R5, i.e., k1!2/k1!5 for R1–R4 and k1!3/k1!5 for R5. They are reported in Tables S11–S15 of the Supplemental Data for a range of temperatures and pressures. The ring-opening pathway generally dominates for reactions R2, R3, and R5, and the cyclic pathway dominates for reactions R1 and R4. The competitiveness of the ring-opening pathway is due to the higher entropy of the ring-opening transition structure compared to the cyclic one. 3.4. Correlation with aromaticity
Fig. 4. Rate coefficients of the decomposition of phenanthrene oxyradicals I and II (black lines) and pentacene oxyradicals I and II (gray lines) [21]. The solid lines are the high-pressure-limit values and the dashed lines are the rate coefficients at 1 atm.
Polyaromatic hydrocarbons are structurally related to the benzene molecule. This connection implies strong similarity in electronic structure that characterizes aromatic systems, namely, that of delocalized bonding. However, in the analysis of chemical properties of large PAHs studied as models of extended systems, such as soot and graphene, this connection is rarely exploited. It is reasonable to examine thermodynamic and kinetic aspects of reactivity of large PAHs on the basis of their local and global aromaticity. Such a connection can lead to formulation of simple quantitative or semi-quantitative predictive models that appeal to chemical intuition and help to rationalize structure-property relationships of the target systems—soot and graphene. Aromaticity can be defined as the extra stabilization of a system featuring delocalized bonds with respect to a fictitious system with completely localized bonds. In practice, assessment of the resonance energy is a difficult task, especially for molecules that require multiple Kekule structures
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in the resonance description. Multiple measures of aromaticity have been proposed in order to simplify the task and connect the analysis to observable properties [34–36]. Considering the computational challenges associated with theoretical treatment of large PAHs it appears reasonable to choose the simplest model of aromaticity that utilizes the observation that aromatic bonding is strongly associated with equalization of bond lengths due to formation of a delocalized bonding framework. In the Harmonic Oscillator Model of Aromaticity (HOMA) [37], one evaluates the mean deviation of bond lengths in a system under consideration with respect to bond lengths in benzene. It is further scaled such that HOMA = 0 for the Kekule form of benzene and HOMA = 1 for the aromatic form. Previous studies of our group [19,20] demonstrated that a simple correlation exists between cumulative HOMA of oxyradicals and their relative thermodynamic stability. The origin of this relationship is fragmentation of the delocalized p-bonding framework due to its disruption upon chemisorption of an O atom at a graphene radical site. It is reasonable to assume that the same reasoning applies to energetic characteristics of oxyradical decomposition. In the present case, HOMA can be used for reactivity analysis for reaction kinetics. Considering the diversity of factors controlling reaction kinetics, for example, the multiple intermediates and transition states, we narrowed the range of analyzed characteristics down to a single one, namely the relative energy of the first transition state. Barrier height is a relative value, so it is logical to consider its relationship to a relative descriptor of aromatic bonding, that can be defined as the difference between HOMA of the benzene-like ring undergoing CO expulsion of the reactant and HOMA of the transition state, i.e., HOMArel = HOMATS HOMAreactant. A simple correlation in the data
Fig. 5. First barrier heights of oxyradical decompositions against relative HOMA of respective transition states (TS 1-2). Phenoxy and pentacene structures are from [21].
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can be seen by plotting (Fig. 5) the results obtained in the present and previous [21] studies. The smallest barrier height is associated with the smallest absolute HOMA change, thus suggesting that CO expulsion should proceed via the route that involves the smallest rearrangement of the conjugated bonding framework. The correlation is not perfect; for instance, the benzoperylene point falls from this general trend. A possible explanation is that benzoperylene is the only two row structure, while the other points are all single row structures. Further analysis requires a larger data set. 4. Conclusions The energetics and kinetics of the thermal decomposition of five graphene armchair-edge oxyradicals were investigated. In all cases studied, the computed decomposition rates are both temperature and pressure dependent. The extent of the pressure dependence, especially at higher temperatures, turned out to be substantial even for the largest molecular substrate studied, an 11-ring PAH. Also noteworthy is the influence of substrate size on computed rates; the effect was clearly pronounced in going from 3 to 6-ring aromatics, yet seemed to level off for larger systems as found for 6 to 11-ring aromatics. Applying the previously introduced concept of “free edges” for polycyclic aromatics [21], the trends obtained here for computed decomposition rates with substrate molecular structure are rationalized. Oxyradicals with more free edges decompose at faster rates than those with a fewer number of free edges. This relationship holds strongest within oxyradicals of similar structures (e.g., different phenanthrene oxyradicals), and is weaker in explaining the relative rates between different structures (e.g., phenanthrene versus pentacene oxyradicals). The kinetic stability of graphene-edge oxyradicals, both armchair studied here and zigzag of the previous study [21], was shown to be correlated with change in aromaticity during the initial, typically rate-controlling, step of oxyradical decomposition. This correlation, together with a recently-established similar scaling for thermodynamic stability [19,20], could lead to practical rules for predicting oxidation rate coefficients for arbitrary size and shape aromatics, thereby supplementing and enhancing models of soot oxidation. The potential energy pathways and overall decomposition rates computed in the present study for armchair edge oxyradicals are very similar to those obtained in our previous study [21] for corner zigzag edge oxyradicals. This finding implies that for an arbitrary shaped PAH, oxidation should predominantly remove armchair and corner-zigzag
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sites, leaving resistant-to-oxidation [21] inner zigzag sites essentially intact. Considering that the growth of both armchair and zigzag edges proceed at effectively the same rate [7,14], we expect to find proliferation of zigzag-edge surfaces on soot particles formed in flame environments.
Acknowledgments XY and MF were supported by the US Army Corps of Engineers, Humphreys Engineering Center Support Activity, under Contract No. W912HQ-07-C-0044. DYZ was supported by the National Science Foundation under grant NSF CHE-0809969. DEE, WAL, and MF were supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences, Geosciences and Biosciences Division of the US Department of Energy, under Contract No. DE-AC03-76F00098. This research used computational resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the US Department of Energy under Contract No. DEAC02-05CH11231. The authors are indebted to Professors David Golden and John Barker for their help with the use of the MultiWell code. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http:// dx.doi.org/10.1016/j.proci.2012.05.031. References [1] M. Frenklach, Phys. Chem. Chem. Phys. 4 (11) (2002) 2028–2037. [2] H. Bockhorn, A. D’Anna, A.F. Sarofim, H. Wang (Eds.), Combustion Generated Fine Carbonaceous Particles, KIT Scientific, Karlsruhe, Germany, 2009. [3] H. Wang, Proc. Combust. Inst. 33 (2011) 41–67. [4] M. Frenklach, in: J.C. Tarter, S. Chang, D.J. DeFrees (Eds.), A Unifying Picture Of Gas Phase Formation And Growth Of Pah, Soot, Diamond And Graphite Carbon In The Galaxy: Studies From Earth And Space, NASA Conference Publication 3061, 1990, pp. 259–273. [5] M. Frenklach, H. Wang, Proc. Combust. Inst. 23 (1991) 1559–1566. [6] M. Frenklach, Proc. Combust. Inst. 26 (2) (1996) 2285–2293. [7] M. Frenklach, C.A. Schuetz, J. Ping, Proc. Combust. Inst. 30 (2005) 1389–1396. [8] R. Whitesides, A.C. Kollias, D. Domin, et al., Proc. Combust. Inst. 31 (1) (2007) 539–546.
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