- Email: [email protected]
On the role of surface migration in the growth and structure of graphene layers
Carbon 42 (2004) 1209–1212 www.elsevier.com/locate/carbon
On the role of surface migration in the growth and structure of graphene layers Michael Frenklach b
a,*
, Jonathan Ping
b
a Department of Mechanical Engineering, University of California, Berkeley, CA 94720-1740, USA Environmental Energy Technologies Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
Received 10 July 2003; accepted 28 December 2003 Available online 18 February 2004
Abstract The principle of chemical similarity, postulating analogy of chemical reactions taking place on a graphene edge to those of aromatic species, has lead to the formulation of detailed reaction models for the growth of carbonaceous surfaces. While meeting a reasonable success, for instance in the areas of soot and carbon-black formation, such an analogy-based approach cannot be expected to provide a truly realistic description of surface processes. The primary cause of the possible dissimilarity is the difference in steric confinements of reactive sites. A recent quantum chemical study of possible reaction steps led to a proposed phenomenon of surface migration of five-member rings along an edge of a graphene layer. The migrating ring can either desorb or convert to a sixmember ring upon an encounter with another six-member ring or a reaction with a gaseous species. All these processes––migration, desorption, and transformation reactions––are mediated by reactions with gaseous hydrogen atoms. The subject of the present communication is analysis of this coupled phenomenon. We will report the results of new Monte Carlo simulations that examine the interplay among surface migration, gas–surface reactions, desorption, and surface transformation reactions of the five-member rings, focusing on emergent morphologies of graphene layers. 2004 Elsevier Ltd. All rights reserved. Keywords: A. Carbon black; C. Molecular simulation; D. Reaction kinetics
1. Introduction There are a variety of carbonaceous materials whose growth is envisioned through extension of aromatic edges; familiar examples may include pyrolytic graphite, carbon black, combustion soot, interstellar ‘‘dust’’, fullerenes, and nanotubes. Experimental studies with laminar premixed flames concluded that surface growth rate of soot particles is proportional to the acetylene concentration in the gas phase [1,2]. These observations have been interpreted in terms of the hydrogen-abstraction-C2 H2 -addition (HACA) mechanism, a repetitive reaction sequence of two principal steps: abstraction of a hydrogen atom from the aromatic-edge C–H bond by a gaseous hydrogen atom, followed by addition of a gaseous acetylene molecule to the formed surface radical site *
Corresponding author. Tel.: +1-510-643-1676; fax: +1-510-6426163. E-mail address: [email protected] (M. Frenklach). 0008-6223/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.carbon.2004.01.025
[3]. That early analysis [4], leading to identification of the HACA mechanism, was based on the hypothesis of chemical similarity [5], which postulated that chemical reactions taking place on soot particle surface are analogous to those of large polycyclic aromatic hydrocarbons (PAHs). The postulate of chemical similarity provided a natural extension of the gas-phase chemistry of aromatics, enabling a description of surface processes in terms of elementary chemical steps. The postulate of chemical similarity, however, is only an assumption. In reality, there could be substantial differences between gaseous and surface reactions, even in cases of seemingly analogous molecular interactions. The primary cause of the possible dissimilarity is the difference in steric confinements of reactive sites. In other words, a reaction of a gaseous species with a surface radical may have a ‘‘sticking probability’’ and equilibrium constant varying with the nature of neighboring sites and their occupancy. Furthermore, while the localized steric factors may affect the surface kinetics in it own right,
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M. Frenklach, J. Ping / Carbon 42 (2004) 1209–1212
sometimes it leads to substantially different global kinetic patterns, like in the case of surface migration. Extensive theoretical analysis of diamond surface chemistry has led to a conclusion that surface migration of CH2 bridges on diamond (1 0 0)–(2 · 1) surfaces must play the governing role in the growth of diamond films [6]. The newly identified migration of the five-member rings [7] opens a similar possibility to the growth of graphene layers. Here we explore further this phenomenon.
atom the cyclopenta ring opens even faster reaction channels; this direction is presently under investigation. 3. Computational model 3.1. Surface model The initial graphene edge was modeled by a onedimensional zigzag substrate, ...
2. Graphene edge migration Recent theoretical investigations [7,8] revealed new reaction pathways for aromatic ring growth, such as enhanced formation of five-member aromatic rings •
•
H
3.2. Gas-phase composition
H
H
C2 H2
H
ð1Þ
H
H
•
(-H)
conversion of five- to six-member rings •
•
C 2H 2
ð2Þ
•
and migration of the cyclopenta ring along zigzag aromatic edges •
ð3Þ
•
All of these pathways have one critical mechanistic feature in common: the reaction pathway is induced or assisted by hydrogen atom migration. The theoretical analysis [7,8] indicated that these reactions should be sufficiently fast to play a critical role in the growth of graphene layers. Specifically, the following mechanistic picture was envisioned [8]. The fivemember ring formed in reaction (1) will migrate along the zigzag edge, reaction (3), until it is either desorbed, converted to a six-member ring at the edge corner according to reaction (2), or converted to a six-member ring if encountered by another six-member ring, e.g., via reaction (4): •
•
• •
The simulations were performed without imposing periodic boundary conditions, thus allowing reaction (2) to occur at the substrate corners.
•
•
•
ð4Þ In this way, the migrating five-member rings will propagate the zipper filling of the zigzag graphene edge. A ‘‘collision’’ of these propagating fronts may create a site that cannot be filled by ring cyclization and thus cannot support further growth, again reminiscent of the diamond case. Formation of such surface defects may be responsible for the loss of reactivity of soot particle surface to growth [7,9]. Another possibility for this may be a ‘‘collision’’ of two migrating cyclopenta groups. While reactions (2)–(4) are already estimated to be sufficiently fast [7,8], it is also feasible that addition of H
The gas contacting the substrate was assumed to have the same temperature as the surface and to be composed of H, H2 , and C2 H2 ––the principal gaseous species of the HACA mechanism [3]. The gas-phase species concentrations and temperature were maintained unchanged during an individual simulation, however they differ from run to run. For the ‘‘base’’ case the pressure was chosen to be 1 atm, temperatures from 1000 to 2500 K, and the mole fractions of the respective species xH ¼ 0:01, xH2 ¼ 0:1, and xC2 H2 ¼ 0:1, typical of laminar premixed flame simulations of the past studies [9]. 3.3. Reaction model The reaction scheme included 10 individual steps, those describing reactions (2)–(4) along with homogeneous nucleation of six-member rings and their desorption reactions. The rate coefficients were taken from the literature or estimated on the basis of quantum chemical calculations. The details of the reaction mechanism will be reported elsewhere. 3.4. Solution procedures The process of growth is modeled as a Markovian sequence of reaction events. There are two types of reactions that comprise the present model: bimolecular reactions between the gaseous species and graphene sites, and unimolecular decompositions of graphene species. All stochastic events were treated as first-order processes, with respective per-site rates, k, determined from elementary sets of reactions. The solution algorithm followed that of Gillespie [10]. Given tn , the instant of a current reaction event, we calculate the time for next reaction event at each substrate site i as tnþ1;i ¼ tn ðln xÞ=ktotal;i , where x is a random number distributed uniformly from 0 to 1 and ktotal;i is the sum of per-site rates of reactions possible at site i. The smallest among the values of tnþ1;i becomes the
M. Frenklach, J. Ping / Carbon 42 (2004) 1209–1212
Fig. 1. A snapshot obtained in a Monte Carlo run at 1600 K and about 0.5 ms reaction time.
time instant of the next reaction event, and the specific reaction that takes place at that time is chosen according to pj;i ¼ kj;i =ktotal;i . Once the reaction event is implemented, the process repeats itself. 4. Numerical results A series of Monte Carlo simulations were performed at conditions described in Section 3.2. The simulations produce either smooth, completely filled surfaces or those interrupted with ring-size holes; a typical snapshot of the latter is shown in Fig. 1. 5. Conclusions The sterically resolved Monte Carlo simulations provide further support to the critical role of five-ring migration in the growth of graphene layers. An important implication of this phenomenon is that while fivemember rings are being constantly formed on the growing edge, they do not accumulate but rather converted to six-member rings.
Acknowledgements The research was supported by the Director, Office of Science, Office of Basic Energy Sciences, Chemical Sciences Division of the U.S. Department of Energy, under the contract number DE-AC03-76SF00098.
References [1] Harris SJ, Weiner AM. Chemical kinetics of soot particle growth. Annu Rev Phys Chem 1985;36:31–52. [2] Xu F, Sunderland PB, Faeth GM. Soot formation in laminar premixed ethylene/air flames at atmospheric pressures. Combust Flame 1997;108:471–93. [3] Frenklach M. Reaction mechanism of soot formation in flames. Phys Chem Chem Phys 2001;4:2028–37. [4] Frenklach M, Wang H. Detailed modeling of soot particle nucleation and growth. Proc Combust Inst 1991;23:1559– 66. [5] Frenklach M. A unifying picture of gas phase formation and growth of PAH, soot, diamond and graphite. In: Tarter JC, Chang S, DeFrees DJ, editors, Carbon in the galaxy: studies from Earth and space. NASA Conference Publication 3061, 1990. p. 259–73.
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[6] Frenklach M, Skokov S. Surface migration in diamond growth. J Phys Chem 1997;101:3025–36. [7] Frenklach M, Moriarty NW, Brown NJ. Hydrogen migration in polyaromatic growth. Proc Combust Inst 1998;27:1655–61. [8] Moriarty NW, Brown NJ, Frenklach M. Hydrogen migration in the phynylethen-2-yl radical. J Phys Chem A 1999;103:7127– 35. [9] Frenklach M. On surface growth mechanism of soot particles. Proc Combust Inst 1996;26:2285–93. [10] Gillespie DT. Exact stochastic simulation of coupled chemical reactions. J Phys Chem 1977;81:2340–61.
QUESTIONS AND COMMENTS Peter Harris, University of Reading, UK. ([email protected]) We know that soot particles are spheroidal in shape. Is this anything to do with pentagons? Michael Frenklach It could but it does not have to be. The possible explanation of the spheroidal shape of primary soot particles by pentagon formation, first offered by Kroto, has received our attention [Q1,Q2]. Briefly, there are two factors that need to be considered. The first is the reaction kinetics: assuming that the curvature comes entirely from surface reactions, some of which may form pentagons and hence start the curvature, cannot explain the time scale of particle size growth; i.e., the surface growth alone is too slow to explain the appearance of tens-of-nanometers size of primary soot particles. The second phenomenon that needs to be considered is particle coagulation. In fact, the particle size is primarily the result of particle-particle ‘‘sticky’’ collisions. It turns out that the spheroidal shape of particles is essentially a geometric phenomenon, controlled by the competition among nucleation, coagulation, and surface growth [Q3,Q4]. In summary, while the kinetics of pentagon formation is not prohibitive, and has been considered in many studies including the present one, the presence of pentagons does not need to be invoked to explain the spheroidal shape of primary particles. This conclusion is consistent with experiments performed on diesel soot samples that showed no pentagon signatures present in those soot particles [Q1]. References [Q1] Frenklach M, Ebert LB. Comment on the proposed role of spheroidal carbon clusters in soot formation. J Phys Chem 1988;92:561–3. [Q2] Frenklach M, Wang H. Detailed modeling of soot particle nucleation and growth. Proc Combust Inst 1991;23:1559–66. [Q3] Mitchell P, Frenklach M. Particle aggregation with simultaneous surface growth. Phys Rev E 2003;67: 061407.
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M. Frenklach, J. Ping / Carbon 42 (2004) 1209–1212
[Q4] Mitchell P, Frenklach M. Monte Carlo simulation of soot aggregation with simultaneous surface growth – Why primary particles appear spherical; Proc Combust Inst 1998;27:1507–14. Francisco G. Emmerich, Universidade Federal do Espirito Santo, Brazil. ([email protected]) Could the movement of the atoms be regarded as a penetration through a quantum potential barrier? Michael Frenklach Perhaps in qualitative terms, but the more accurate description of this phenomenon is as follows. Atoms move as a result of a series of chemical reactions, a sequence of surface transformations mediated by gassurface attacks by hydrogen atoms. Many of the ele-
mentary steps involved have potential energy barrier, and the hydrogen-atom reactions ‘‘enable’’ surmounting these barriers. John B. Paine III, Philip Morris, USA ([email protected]) A nitrogen analogue of your mechanism (e.g. hydrogen cyanide, HC B N) versus acetylene (HC B CN), can be calculated to determine whether N atoms like to accumulate in the ‘‘pockets’’ that tend to form, which may help explain route to metal-nitrogen active sites in carbons. Michael Frenklach This is an interesting suggestion.
On the role of surface migration in the growth and structure of graphene layers Michael Frenklach b
a,*
, Jonathan Ping
b
a Department of Mechanical Engineering, University of California, Berkeley, CA 94720-1740, USA Environmental Energy Technologies Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
Received 10 July 2003; accepted 28 December 2003 Available online 18 February 2004
Abstract The principle of chemical similarity, postulating analogy of chemical reactions taking place on a graphene edge to those of aromatic species, has lead to the formulation of detailed reaction models for the growth of carbonaceous surfaces. While meeting a reasonable success, for instance in the areas of soot and carbon-black formation, such an analogy-based approach cannot be expected to provide a truly realistic description of surface processes. The primary cause of the possible dissimilarity is the difference in steric confinements of reactive sites. A recent quantum chemical study of possible reaction steps led to a proposed phenomenon of surface migration of five-member rings along an edge of a graphene layer. The migrating ring can either desorb or convert to a sixmember ring upon an encounter with another six-member ring or a reaction with a gaseous species. All these processes––migration, desorption, and transformation reactions––are mediated by reactions with gaseous hydrogen atoms. The subject of the present communication is analysis of this coupled phenomenon. We will report the results of new Monte Carlo simulations that examine the interplay among surface migration, gas–surface reactions, desorption, and surface transformation reactions of the five-member rings, focusing on emergent morphologies of graphene layers. 2004 Elsevier Ltd. All rights reserved. Keywords: A. Carbon black; C. Molecular simulation; D. Reaction kinetics
1. Introduction There are a variety of carbonaceous materials whose growth is envisioned through extension of aromatic edges; familiar examples may include pyrolytic graphite, carbon black, combustion soot, interstellar ‘‘dust’’, fullerenes, and nanotubes. Experimental studies with laminar premixed flames concluded that surface growth rate of soot particles is proportional to the acetylene concentration in the gas phase [1,2]. These observations have been interpreted in terms of the hydrogen-abstraction-C2 H2 -addition (HACA) mechanism, a repetitive reaction sequence of two principal steps: abstraction of a hydrogen atom from the aromatic-edge C–H bond by a gaseous hydrogen atom, followed by addition of a gaseous acetylene molecule to the formed surface radical site *
Corresponding author. Tel.: +1-510-643-1676; fax: +1-510-6426163. E-mail address: [email protected] (M. Frenklach). 0008-6223/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.carbon.2004.01.025
[3]. That early analysis [4], leading to identification of the HACA mechanism, was based on the hypothesis of chemical similarity [5], which postulated that chemical reactions taking place on soot particle surface are analogous to those of large polycyclic aromatic hydrocarbons (PAHs). The postulate of chemical similarity provided a natural extension of the gas-phase chemistry of aromatics, enabling a description of surface processes in terms of elementary chemical steps. The postulate of chemical similarity, however, is only an assumption. In reality, there could be substantial differences between gaseous and surface reactions, even in cases of seemingly analogous molecular interactions. The primary cause of the possible dissimilarity is the difference in steric confinements of reactive sites. In other words, a reaction of a gaseous species with a surface radical may have a ‘‘sticking probability’’ and equilibrium constant varying with the nature of neighboring sites and their occupancy. Furthermore, while the localized steric factors may affect the surface kinetics in it own right,
1210
M. Frenklach, J. Ping / Carbon 42 (2004) 1209–1212
sometimes it leads to substantially different global kinetic patterns, like in the case of surface migration. Extensive theoretical analysis of diamond surface chemistry has led to a conclusion that surface migration of CH2 bridges on diamond (1 0 0)–(2 · 1) surfaces must play the governing role in the growth of diamond films [6]. The newly identified migration of the five-member rings [7] opens a similar possibility to the growth of graphene layers. Here we explore further this phenomenon.
atom the cyclopenta ring opens even faster reaction channels; this direction is presently under investigation. 3. Computational model 3.1. Surface model The initial graphene edge was modeled by a onedimensional zigzag substrate, ...
2. Graphene edge migration Recent theoretical investigations [7,8] revealed new reaction pathways for aromatic ring growth, such as enhanced formation of five-member aromatic rings •
•
H
3.2. Gas-phase composition
H
H
C2 H2
H
ð1Þ
H
H
•
(-H)
conversion of five- to six-member rings •
•
C 2H 2
ð2Þ
•
and migration of the cyclopenta ring along zigzag aromatic edges •
ð3Þ
•
All of these pathways have one critical mechanistic feature in common: the reaction pathway is induced or assisted by hydrogen atom migration. The theoretical analysis [7,8] indicated that these reactions should be sufficiently fast to play a critical role in the growth of graphene layers. Specifically, the following mechanistic picture was envisioned [8]. The fivemember ring formed in reaction (1) will migrate along the zigzag edge, reaction (3), until it is either desorbed, converted to a six-member ring at the edge corner according to reaction (2), or converted to a six-member ring if encountered by another six-member ring, e.g., via reaction (4): •
•
• •
The simulations were performed without imposing periodic boundary conditions, thus allowing reaction (2) to occur at the substrate corners.
•
•
•
ð4Þ In this way, the migrating five-member rings will propagate the zipper filling of the zigzag graphene edge. A ‘‘collision’’ of these propagating fronts may create a site that cannot be filled by ring cyclization and thus cannot support further growth, again reminiscent of the diamond case. Formation of such surface defects may be responsible for the loss of reactivity of soot particle surface to growth [7,9]. Another possibility for this may be a ‘‘collision’’ of two migrating cyclopenta groups. While reactions (2)–(4) are already estimated to be sufficiently fast [7,8], it is also feasible that addition of H
The gas contacting the substrate was assumed to have the same temperature as the surface and to be composed of H, H2 , and C2 H2 ––the principal gaseous species of the HACA mechanism [3]. The gas-phase species concentrations and temperature were maintained unchanged during an individual simulation, however they differ from run to run. For the ‘‘base’’ case the pressure was chosen to be 1 atm, temperatures from 1000 to 2500 K, and the mole fractions of the respective species xH ¼ 0:01, xH2 ¼ 0:1, and xC2 H2 ¼ 0:1, typical of laminar premixed flame simulations of the past studies [9]. 3.3. Reaction model The reaction scheme included 10 individual steps, those describing reactions (2)–(4) along with homogeneous nucleation of six-member rings and their desorption reactions. The rate coefficients were taken from the literature or estimated on the basis of quantum chemical calculations. The details of the reaction mechanism will be reported elsewhere. 3.4. Solution procedures The process of growth is modeled as a Markovian sequence of reaction events. There are two types of reactions that comprise the present model: bimolecular reactions between the gaseous species and graphene sites, and unimolecular decompositions of graphene species. All stochastic events were treated as first-order processes, with respective per-site rates, k, determined from elementary sets of reactions. The solution algorithm followed that of Gillespie [10]. Given tn , the instant of a current reaction event, we calculate the time for next reaction event at each substrate site i as tnþ1;i ¼ tn ðln xÞ=ktotal;i , where x is a random number distributed uniformly from 0 to 1 and ktotal;i is the sum of per-site rates of reactions possible at site i. The smallest among the values of tnþ1;i becomes the
M. Frenklach, J. Ping / Carbon 42 (2004) 1209–1212
Fig. 1. A snapshot obtained in a Monte Carlo run at 1600 K and about 0.5 ms reaction time.
time instant of the next reaction event, and the specific reaction that takes place at that time is chosen according to pj;i ¼ kj;i =ktotal;i . Once the reaction event is implemented, the process repeats itself. 4. Numerical results A series of Monte Carlo simulations were performed at conditions described in Section 3.2. The simulations produce either smooth, completely filled surfaces or those interrupted with ring-size holes; a typical snapshot of the latter is shown in Fig. 1. 5. Conclusions The sterically resolved Monte Carlo simulations provide further support to the critical role of five-ring migration in the growth of graphene layers. An important implication of this phenomenon is that while fivemember rings are being constantly formed on the growing edge, they do not accumulate but rather converted to six-member rings.
Acknowledgements The research was supported by the Director, Office of Science, Office of Basic Energy Sciences, Chemical Sciences Division of the U.S. Department of Energy, under the contract number DE-AC03-76SF00098.
References [1] Harris SJ, Weiner AM. Chemical kinetics of soot particle growth. Annu Rev Phys Chem 1985;36:31–52. [2] Xu F, Sunderland PB, Faeth GM. Soot formation in laminar premixed ethylene/air flames at atmospheric pressures. Combust Flame 1997;108:471–93. [3] Frenklach M. Reaction mechanism of soot formation in flames. Phys Chem Chem Phys 2001;4:2028–37. [4] Frenklach M, Wang H. Detailed modeling of soot particle nucleation and growth. Proc Combust Inst 1991;23:1559– 66. [5] Frenklach M. A unifying picture of gas phase formation and growth of PAH, soot, diamond and graphite. In: Tarter JC, Chang S, DeFrees DJ, editors, Carbon in the galaxy: studies from Earth and space. NASA Conference Publication 3061, 1990. p. 259–73.
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[6] Frenklach M, Skokov S. Surface migration in diamond growth. J Phys Chem 1997;101:3025–36. [7] Frenklach M, Moriarty NW, Brown NJ. Hydrogen migration in polyaromatic growth. Proc Combust Inst 1998;27:1655–61. [8] Moriarty NW, Brown NJ, Frenklach M. Hydrogen migration in the phynylethen-2-yl radical. J Phys Chem A 1999;103:7127– 35. [9] Frenklach M. On surface growth mechanism of soot particles. Proc Combust Inst 1996;26:2285–93. [10] Gillespie DT. Exact stochastic simulation of coupled chemical reactions. J Phys Chem 1977;81:2340–61.
QUESTIONS AND COMMENTS Peter Harris, University of Reading, UK. ([email protected]) We know that soot particles are spheroidal in shape. Is this anything to do with pentagons? Michael Frenklach It could but it does not have to be. The possible explanation of the spheroidal shape of primary soot particles by pentagon formation, first offered by Kroto, has received our attention [Q1,Q2]. Briefly, there are two factors that need to be considered. The first is the reaction kinetics: assuming that the curvature comes entirely from surface reactions, some of which may form pentagons and hence start the curvature, cannot explain the time scale of particle size growth; i.e., the surface growth alone is too slow to explain the appearance of tens-of-nanometers size of primary soot particles. The second phenomenon that needs to be considered is particle coagulation. In fact, the particle size is primarily the result of particle-particle ‘‘sticky’’ collisions. It turns out that the spheroidal shape of particles is essentially a geometric phenomenon, controlled by the competition among nucleation, coagulation, and surface growth [Q3,Q4]. In summary, while the kinetics of pentagon formation is not prohibitive, and has been considered in many studies including the present one, the presence of pentagons does not need to be invoked to explain the spheroidal shape of primary particles. This conclusion is consistent with experiments performed on diesel soot samples that showed no pentagon signatures present in those soot particles [Q1]. References [Q1] Frenklach M, Ebert LB. Comment on the proposed role of spheroidal carbon clusters in soot formation. J Phys Chem 1988;92:561–3. [Q2] Frenklach M, Wang H. Detailed modeling of soot particle nucleation and growth. Proc Combust Inst 1991;23:1559–66. [Q3] Mitchell P, Frenklach M. Particle aggregation with simultaneous surface growth. Phys Rev E 2003;67: 061407.
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M. Frenklach, J. Ping / Carbon 42 (2004) 1209–1212
[Q4] Mitchell P, Frenklach M. Monte Carlo simulation of soot aggregation with simultaneous surface growth – Why primary particles appear spherical; Proc Combust Inst 1998;27:1507–14. Francisco G. Emmerich, Universidade Federal do Espirito Santo, Brazil. ([email protected]) Could the movement of the atoms be regarded as a penetration through a quantum potential barrier? Michael Frenklach Perhaps in qualitative terms, but the more accurate description of this phenomenon is as follows. Atoms move as a result of a series of chemical reactions, a sequence of surface transformations mediated by gassurface attacks by hydrogen atoms. Many of the ele-
mentary steps involved have potential energy barrier, and the hydrogen-atom reactions ‘‘enable’’ surmounting these barriers. John B. Paine III, Philip Morris, USA ([email protected]) A nitrogen analogue of your mechanism (e.g. hydrogen cyanide, HC B N) versus acetylene (HC B CN), can be calculated to determine whether N atoms like to accumulate in the ‘‘pockets’’ that tend to form, which may help explain route to metal-nitrogen active sites in carbons. Michael Frenklach This is an interesting suggestion.