J. Phys. Chem. B 2009, 113, 1877–1882
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Multiscale Modeling Catalytic Decomposition of Hydrocarbons during Carbon Nanotube Growth A. V. Vasenkov,*,† D. Sengupta,† and M. Frenklach‡ CFD Research Corporation, 215 Wynn DriVe, HuntsVille, Alabama 35805, and Department of Mechanical Engineering, UniVersity of California, Berkeley, California 94720-1740 ReceiVed: September 19, 2008; ReVised Manuscript ReceiVed: December 17, 2008
A molecular dynamics simulator coupled to a quantum semiempirical Hamiltonian model was applied to multiscale modeling of the catalytic decomposition of hydrocarbons during carbon nanotube (CNT) and carbon nanofiber (CNF) growth. It was found that catalytic decomposition of acetylene is accompanied by a large energy release and its rate weakly depends on temperature in the range from 20 to 700 °C. In contrast, the methane decomposition rate substantially decreases as the iron temperature drops. A comparative analysis of acetylene decomposition on a clean surface and on an oxidized Fe(100) surface showed that the presence of oxygen reduces the decomposition rate by an order of magnitude, but has very little influence on the amount of heat released by the reaction. We also found that oxygen absorbed on the surface of catalyst does not easily diffuse into the catalyst or desorb from the surface. This implies that the surface of the catalyst is quickly covered by oxygen during CNT/CNF growth even at low oxygen flow rates. 1. Introduction Computational design has the potential to accelerate the development of nanotechnology by guiding and focusing experiments and by providing better understanding of highly coupled processes occurring on disparate scales. Significant progress has been achieved during the past decade in the development of atomistic models with different levels of detail.1,2 Ab initio methods are typically used to simulate interactions between a few hundred atoms on the tiny length scales of a few angstroms. For example, the first-principles density functional theory (DFT) method is very efficient for electronic structure calculations of molecules and solids,3 while the quantum molecular dynamics (QMD) method is successfully used for modeling the dynamic evolution of a molecular system over time scales of a few picoseconds or for determining reaction pathways.4 Classical molecular dynamics (CMD) models with empirical force fields are capable of modeling large systems with up to a few hundred thousand atoms over time scales of a few nanoseconds.5,6 CMD models typically use empirical potentials that ignore quantum mechanical effects, or attempt to capture quantum effects in a limited way through entirely empirical equations. Parameters in these potentials are fitted against known physical properties of the simulated atoms such as elastic constants and lattice parameters.7 One of the major drawbacks with CMD is its inability to model chemical reactions resulting in breaking or making bonds. This drawback was recently addressed, for example, in ref 8, where a reactive CMD model was introduced to account for chemical reactions during thermal degradation of polymers. MD with a quantum semiempirical Hamiltonian (MD-QSH) bridges the gap between QMD and CMD. The MD-QSH method makes use of the semiempirical Hamiltonian computed through empirical formulas via estimating the degree of overlap of specific atomic orbitals. * To whom correspondence should be addressed. † CFD Research Corporation. ‡ University of California.
MD methods are particularly suited to study chemical transformations during the synthesis of nanomaterials such as carbon nanotubes (CNTs) and carbon nanofibers (CNFs). For example, a reactive force field was developed by Zhao et al.9 to account for bond-breaking and bond-forming processes. The CMD with this reactive force field was used to illustrate how carbon atoms dissolved into the metal cluster and then precipitated on its surface, forming various carbon structures. A CMD model with another empirical potential energy surface was used by Ding et al.10 to study the nucleation of bamboo-like CNTs. The simulations revealed that the inner walls of the bamboo structures nucleated at the junction between the outer wall and the catalyst particle. Also, it was found that bamboo-like CNTs nucleated at higher dissolved carbon concentrations than those where non-bamboo-like CNTs were nucleated. First-principles methods were used by Esfarjani et al.11 to construct a classical force field accounting for the interactions of a carbon atom and a nickel surface. The developed force field was used to investigate the growth mechanism of CNT on the surface of a nickel nanoparticle. Results of the CMD simulations suggested that the growth of an armchair CNT took place via attachment of dimers to its end which is in contact with the nickel surface. It was also found that the radius of the nickel nanoparticle affected the attachment barrier during this process. A tightbinding MD-QSH model was used by Andriotis et al.12 to investigate the dynamic interaction between a catalyst and a CNT in the presence of nonbonded C atoms. The above-listed examples highlight the critical role of the force field in MD modeling. Ideally, high-level ab initio molecular orbital or density functional calculations should be used to eliminate any need for parameters. The primary drawback of such an approach is the large amount of computational time which would limit the MD method to studying only small molecules. MD-QSH offers a compromise between high-level quantum description and computational speed. Over the past 50 years, QSH techniques have been extensively developed as computationally more efficient alternatives to ab initio methods.13 Recently, QSH methods such as the PM6
10.1021/jp808346h CCC: $40.75 2009 American Chemical Society Published on Web 01/27/2009
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Figure 1. Example of the surface model at constant Y (left panel) and constant Z (right panel), for coupled MD-QSH simulations. It was constructed by truncating the (100) surface of the body centered cubic (bcc) Fe crystal. Large and small spheres depict quantum and empirical atoms, respectively.
Vasenkov et al. were saturated with “ghost” hydrogen atoms as shown in Figure 2. The distance between the ghost hydrogen atoms and the quantum cluster was determined by scaling distances between boundary atoms from the quantum and empirical regions. 2.2. MD-QSH Model. The present MD-QSH model uses a numerical solution of the many-body problem of classical mechanics in conjunction with the results of the semiempirical Hamiltonian. For an isolated system containing a fixed number of atoms N in the fixed volume V, the atomic motion is given by Newton’s equations:
b Fi(t) ) m
Figure 2. Quantum atoms passivated with hydrogen atoms at the boundaries for computing the QSH potential. The left and right panels are for constant Y and constant Z, respectively. 13
Hamiltonian have been parametrized for transition metals. This creates an opportunity to provide insight into the dynamics of catalytic reactions during CNT/CNF synthesis. In this article, we used the MD-QSH method for computing pathways of catalytic decomposition of hydrocarbons during CNT/CNF growth. The advantage of our method is its ability to model breaking and making bonds within the quantum chemical framework with orders of magnitude faster than ab initio methods. As a test case, we computed the dynamics of methane and acetylene decomposition on a clean surface and on an oxidized surface of iron which is proposed to be a major mechanism for carbon supply to growing CNT/CNF.14,15 The paper is arranged as follows. The MD-QSH model is outlined in section 2. The results of hydrocarbon decomposition on an iron surface are presented in section 3. The effect of oxygen on catalytic decomposition of hydrocarbons during CNT/CNF growth is discussed in section 4. Our concluding remarks are in section 5. 2. MD-QSH Modeling In this section we outline the MD-QSH method for modeling elementary reaction pathways on a complex potential energy surface at a finite temperature. This method couples classical MD simulation with QSH modeling. The details of the method have previously been described,16-18 so only brief outlines are given here. 2.1. Surface Model. In the present method, the surface model is constructed by truncating an infinite solid system of interest to a size that is computationally tractable. A typical example of the surface model is shown in Figure 1. Periodic conditions were used to account for the artificial boundaries resulting from truncation. Existing QSH models either are not capable of computing gradients for periodic systems or do it extremely slowly.19 To address this problem, we introduced empirical and quantum atoms as shown in Figure 2. Interactions between empirical atoms and between empirical atoms and the quantum cluster were simulated using an analytical (empirical) Morse potential.20 Forces acting on quantum atoms were computed using the QSH model at the end of each dynamic time step. In the QSH calculations, the boundaries of the quantum cluster
d2b ri 2
)-
dt
∂U(b r 1, b r 2, ..., b r N) ∂b ri
(1)
where b Fi is the force acting on the atom i caused by the N - l other atoms and U is the potential energy depending on the positions of atoms in the system. By iteratively integrating eq 1, one can obtain trajectories for each atom. Beeman’s third order predictor algorithm was used to integrate Newton’s equations of motion. This algorithm is written as21
1 b r n+1 ) b rn + b V n+1∆t + (4a a n-1)(∆t)2 bn - b 6
(2)
1 b V n+1 ) b V n + (2a bn - b a n-1)(∆t) bn+1 + 5a 6
(3)
where b rn is the position, b Vn is the velocity, and b an is the acceleration on the nth time step, and ∆t is the time step. A time step of 0.5 fs was typically used in the MD-QSH computations to maintain constant total energy with a relative accuracy of about 10-6. An effective temperature control in MD-QSH simulations was achieved by scaling atomic velocities after each dynamic time step by a factor η, which is defined as22
[
η) 1+
(
∆t To -1 τ T
)]
1/2
(4)
where τ is the adjustable parameter, To is the desired temperature to be maintained, and T is the instantaneous temperature of the system. Chemical reactions were modeled in the present work only for quantum atoms. Bonds between these atoms were not kept fixed as in conventional CMD simulations. In contrast, the quantum atoms were able to break or to form different bonds during the MD-QSH modeling due to the coupling between the MD and the QSH modules.16-18 The algorithm of this coupling can be outlined as follows. At the end of each dynamic step in the MD module, coordinates of atoms constituting the quantum cluster were saturated with hydrogen atoms and transferred to the QSH module. Here, instantaneous potential energy and interatomic forces were computed and fed back to the MD module. The contributions from the ghost hydrogen atoms were zeroed, and forces acting on quantum atoms were combined with the Morse-type forces computed for empirical atoms. In the first iteration between the MD and QSH modules, a default guess of molecular orbital coefficients was used. At subsequent iterations, the set of molecular orbital coefficients describing the electronic structure at the previous time step was used to reduce the time needed to reach selfconsistent field (SCF) convergence. At the end of each iteration in
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C2H-Fen f CH-Fen + C-Fen
Figure 3. Computational results illustrating dissociation of C2H2 on the surface of Fe at 700 °C. Some H atoms are hidden by the front Fe atoms.
(R2)
Reactions R1 and R2 were investigated at three different temperatures: 700 °C (typical temperature of CNT/CNF growth), 400 °C (desirable temperature for enabling direct growth of CNTs/CNFs on electronic devices), and 20 °C (room temperature). Time-dependent profiles of bond orders computed for different temperatures are given in Figure 4. At the beginning of the simulations, when C2H2 was 5 Å above the Fe surface, the C-C bond order was slightly less than 3 due to the strain resulting from the Fe cluster. Starting at t < 3 × 10-2 ps, the C-C bond order slowly decreased with time. We observed a sharp minimum for the C-C bond order at about 0.08 ps (see Figure 3 for the corresponding structure). This minimum resulted in breaking the C-C bond at 400 °C. The C-C bond at 700 and 20 °C recovered from the minimum at 0.08 ps and was broken at a later time. The differences in breaking of the C-C bond at different temperatures were attributed to the different reaction pathways that result in the formation of a dissociative configuration. The common feature of results obtained at
the QSH module, bond orders, charge densities, and other quantum mechanics properties were calculated from the density matrix elements. This information is useful in the visualization of chemical reactions and surface motion as demonstrated in section 3. It was previously shown16-18 that the SCF convergence must be high enough during the MD-QSH modeling that electronic energy at successive SCF iterations differs by less than 5 × 10-8 kcal/mol. Such a high degree of precision is necessary to achieve sufficient accuracy in the calculations of the trajectories since the precision of quantum forces scales as the square root of the precision of the potential energy. In the current implementation, the MOPAC 7.2 quantum chemical package with the PM6 Hamiltonian was used because of its ability to account for transition metal elements via d orbitals.13 The lowest electronic state of this cluster was determined by the SCF method. We tested both unrestricted Hartree-Fock (UHF) and configuration interaction (CI) techniques for modeling catalytic decomposition of hydrocarbons, and found that the CI model gives better accuracy. This is because the single configuration description of the UHF wave function is not appropriate for atoms with d orbitals.13 3. Catalytic Decomposition of Hydrocarbons As a test case, we considered the catalytic decomposition of hydrocarbons, which is supposed to be the major mechanism for carbon supply to the growing CNT/CNF.14,15 The simulations were conducted for acetylene (C2H2) and methane (CH4), which are typical processing gases. At the end of the section, the effect of different precursors on CNT/CNF deposition is discussed. 3.1. C2H2. C2H2 was initially positioned 5 Å above the (100) Fe surface as shown in the top panel of Figure 3. In all simulation cases, positions of empirical Fe atoms bordering the quantum cluster were fixed. It was found that the major path for dissociation of C2H2 involves the formation of a C2H-Fen complex (see the bottom panel in Figure 3) due to the following hydrogen removal reaction:
C2H2 + Fen f C2H-Fen + H-Fen
(R1)
The C2H-Fen complex was not stable and quickly dissociated, producing atomic carbon, which was capable of diffusing into the metal surface:
Figure 4. Time-dependent bond order profiles for the dissociation of C2H2 on iron surface at different temperatures: 700 °C (typical temperature of CNT/CNF growth), 400 °C (desirable temperature for the direct synthesis of CNT/CNF on electronics devices), and 20 °C (room temperature).
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Figure 5. Computational results illustrating dissociation of CH4 on the surface of Fe at 700 °C. Some H atoms are hidden by the front Fe atoms.
Vasenkov et al.
Figure 7. C-C bond order and released energy versus time during C2H2 decomposition on a clean iron surface at 500 °C.
was broken at 0.3 ps. In contrast, at 700 °C, the first C-H bond was broken at 0.1 ps, the second at 0.2 ps, and the third at 0.6 ps. 3.3. Effect of Precursors on CNT/CNF Deposition. C2H2 and CH4 are both processing gases and key deposition precursors in the catalytic synthesis of CNTs/CNFs when the gas-phase reactions are suppressed in favor of surface reactions. However, often many other hydrocarbon species including C2H and CH3 can form in the gas phase during the synthesis.14 The abundance of these hydrocarbons in plasma-assisted chemical vapor depostion (CVD) synthesis was well established24 and was linked to the preferable growth of CNFs rather than CNTs.23 C2H and CH3, once absorbed on the surface of a catalyst, can rapidly produce CH and CH2 surface species via catalytic dissociation reactions as discussed above. These dissociation reactions may be especially important in the plasma-assisted CVD process typically operated at a temperature lower than that maintained during the thermal CVD process.14 Results in Figures 4 and 6 indicate that the surface reactions starting with C2H and CH3 can produce CH and CH2 substantially faster at lower temperatures in comparison to reactions starting with C2H2 and CH4, respectively. CH and CH2 surface species, in their turn, can efficiently produce surface carbon via hydrogenabstraction reactions.25 One can hypothesize that the abovedescribed reaction path can compete with the direct catalytic dissociation of processing gases in the case of plasma-assisted CNF growth.
Figure 6. Time-dependent bond order profiles for the dissociation of CH4 on an iron surface at 700 °C (typical temperature of CNT/CNF growth) and 20 °C.
4. Effect of Catalytic Oxidation on Decomposition of Hydrocarbons
different temperatures is that the C-H bond was broken either just before the elimination of the C-C bond or immediately after this event. Also, the obtained results indicate that carbon supply for catalytically growing CNT/CNF can be successfully generated even at room temperature since C2H2 can be efficiently broken at 20 °C. 3.2. CH4. CH4 was introduced 5 Å above the (100) Fe surface as shown in the top panel of Figure 5. It was found that decomposition of CH4 involved the formation of an unstable CH3-Fen complex which quickly dissociated to form a more stable CH2-Fen complex. A comparison of time-dependent bond orders, given in Figure 6, indicates that the decomposition of CH4 is a temperature-dependent process. At 20 °C the first C-H bond was broken at about 0.25 ps and the second C-H bond
One of the recent trends in the growth of CNTs/CNFs is the use of oxygen.26,27 To provide insight into the role of oxygen in the catalytic decomposition of hydrocarbons during CNT/ CNF growth, we performed comparative analysis of C2H2 decomposition on a clean surface and on an oxidized surface of catalyst. MD-QSH simulations at constant total energy were performed to determine both time-dependent bond orders and energy released during the decomposition. Prior to running the simulations with reactions, an oxidized surface or a clean (100) Fe surface was relaxed during a 0.5 ps MD-QSH simulation at a constant temperature. Computed C-C bond order and energy released during C2H2 decomposition on a clean (100) Fe surface are presented in Figure 7. The C-C bond breaks faster in this case in comparison to results obtained at constant temperatures, presented in Figure 4, owing to different reaction pathways in the formation of a dissociative configuration. Based on the results in Figures 4 and
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Figure 8. O-O bond order and released energy versus time during O2 decomposition on the surface of iron.
Figure 9. Computational results illustrating dissociation of C2H2 on oxidized surface of Fe at 700 °C.
7, we estimated that the decomposition rate of acetylene on the (100) surface of iron is in the range 5 × 1012 - 1 × 1013 1/s. The large amount of released energy demonstrates that this reaction is an exothermic process with a peak of 110 kcal/mol as shown in Figure 7. This is in agreement with the literature binding energy of 135 kcal/mol for the dissociated C2H2 with CH fragments in two adjacent positions.28 Next, we computed the decomposition of molecular oxygen on the (100) Fe surface. Prior to running the simulations with reactions, the Fe surface was relaxed during 0.5 ps at a constant temperature of 500 °C. An oxygen molecule with zero kinetic energy was placed 5 Å above an Fe dimer to initiate the reaction. The initial O-O bond order was equal to 1 because of the iron surface presence. This initial bond order is in agreement with that obtained for the chemisorptions of molecular oxygen onto a reconstructed (100) diamond surface in ref 18. We found, as illustrated in Figure 8, that molecular oxygen easily dissociates and produces a substantial amount of heat with a peak of 150 kcal/mol. This is in good agreement with DFT calculations of the maximum heat of dissociative absorption of O2 on Fe, which is in the range 134-154 kcal/mol.29 The longer (a few picoseconds) runs showed that oxygen, absorbed on the surface of catalyst, does not diffuse inside the catalyst or easily desorb from the surface. This implies that the oxygen quickly covers the surface of catalyst during CNT/CNF growth even at low oxygen flow rates.
Figure 10. C-C bond orders and released energy versus time during C2H2 decomposition on oxidized surface of iron. A comparison of results in this figure and in Figure 7 indicates that the presence of oxygen on the surface of catalyst reduces the C2H2 decomposition rate by an order of magnitude.
Figure 11. Computational results illustrating dissociation of C2H2 at 700 °C on Fe surface when only half of surface sites are passivated with oxygen atoms. Some H atoms are hidden by the front Fe atoms.
Our simulation results illustrate how catalytic surface oxidation affects the decomposition of hydrocarbons. As shown in Figure 9, C2H2 diffuses between two oxygen atoms before decomposing on the catalyst material. The time-dependent variations of bond orders and released energy during the decomposition of C2H2 on the oxidized Fe surface are shown in Figure 10 at two temperatures: 700 °C, a typical temperature of CNT/CNF growth, and 500 °C, a typical temperature below
1882 J. Phys. Chem. B, Vol. 113, No. 7, 2009 which deterministic growth of well-graphitized CNTs/CNFs is not established yet.30 (It should be noted here that direct growth of CNTs/CNFs on electronic devices requires reducing the growth temperature to 400 °C.) A comparison of results in Figure 10 and in Figure 7 indicates that the presence of oxygen on the surface of the catalyst increases the time necessary for breaking the C-C bond by an order of magnitude and, consequently, reduces the C2H2 decomposition rate by an order of magnitude. Finally, we modeled C2H2 decomposition in the case when oxygen occupies only half the iron surface sites. Computational results given in Figure 11 imply that the C2H2 decomposition rate in this case is 5 times faster than that for the fully oxidized iron surface (Figure 10), but approximately half as fast as that for a clean Fe surface (Figure 7). The demonstrated ability of the MD-QSH model to monitor in real time spatial positions of reacting atoms and their actual bond orders are unique features, contrasting the MD-QSH method with the DFT method. Although conventional CMD models utilizing empirical reactive force fields were also used for modeling chemical reactions,8-11 the results of these models heavily depend on empirical parameters. 5. Summary A method that couples a molecular dynamics model to a quantum semiempirical Hamiltonian model was applied to modeling catalytic decomposition of hydrocarbons. In contrast to conventional classical molecular dynamics models with empirical force fields, the present model can “naturally” account for chemical bond-making and bond-breaking events, as well as for heat consumption and heat production during complex catalytic reactions without prior assumptions. For example, it was found that the decomposition of acetylene on the surface of iron has a weak dependence on temperature. In contrast, the methane decomposition rate substantially decreases as the iron temperature drops. The decomposition rate of acetylene on Fe(100) was estimated to be 5 × 1012 - 1 × 1013 1/s with a peak energy release of 110 kcal/mol. This is in in agreement with the literature binding energy of 135 kcal/mol for the dissociated C2H2 with CH fragments in two adjacent positions. A comparative analysis of acetylene decomposition on an oxidized surface and on a clean surface of iron revealed that the presence of oxygen reduces the decomposition rate by an order of magnitude, but has very little influence on the amount of heat released during the decomposition reaction. We also found that the oxygen absorbed on the surface of catalyst does not easily diffuse inside the catalyst or desorb from the surface. This implies that the oxygen quickly covers the surface of the catalyst during CNT/CNF growth even at low oxygen flow rates. The catalytic decomposition rate of oxygen was found to be 2 × 1013 1/s with a peak energy release of 150 kcal/mol. This is in good agreement with the literature value for the heat of dissociative absorption of O2 on Fe, which is in the range 134-154 kcal/mol.
Vasenkov et al. Acknowledgment. This work was supported by the National Science Foundation (SBIR Award No. 0724878). References and Notes (1) Dollet, A. Surf. Coat. Technol. 2004, 177-178, 245. (2) Cavallotti, C.; Pantano, E.; Veneroni, A.; Masi, M. Cryst. Res. Technol. 2005, 40, 958. (3) Kohanoff, J. Electronic Structure Calculations for Solids and Molecules: Theory and Computational Methods; Cambridge University Press: Cambridge, U.K., 2006. (4) Marx, D.; Hutter, J. Ab Initio Molecular Dynamics: Theory and Implementation. In Modern Methods and Algorithms of Quantum Chemistry, Proceedings; Grotendorst, J., Ed.; John von Neumann Institute for Computing: Juelich, Germany, 2000; pp 149. (5) Leach, A. R. Molecular Modelling: Principles and Applications; Prentice Hall: New York, 2001. (6) Bolton, K.; Ding, F.; Rosen, A. J. Nanosci. Nanotechnol. 2006, 6, 1211. (7) Rappe, A. K.; Casewit, C. J.; Colwell, K. S.; Goddard, W. A., III; Skiff, W. M. J. Am. Chem. Soc. 1992, 114, 10024. (8) Stoliarov, S. I.; Westmoreland, P. R.; Nyden, M. R.; Forneyb, G. P. Polymer 2003, 44, 883. (9) Zhao, J.; Martinez-Limia, A.; Balbuena, P. B. Nanotechnology 2005, 16, 575. (10) Ding, F.; Bolton, K.; Rosen, A. J. Electron. Mater. 2006, 35, 207. (11) Esfarjani, K.; Gorjizadeh, N.; Nasrollahi, Z. Comput. Mater. Sci. 2006, 36, 117. (12) Andriotis, A. N.; Menon, M.; Froudakis, G. Phys. ReV. Lett. 2000, 85, 3193. (13) Stewart, J. J. P. J. Mol. Mod. 2007, 13, 1173. (14) Melechko, A. V.; Merkulov, V. I.; McKnight, T. E.; Guillorn, M. A.; Klein, K. L.; Lowndes, D. H.; Simpson, M. L. J. Appl. Phys. 2005, 97, 041301. (15) Chhowalla, M.; Teo, K. B. K.; Ducati, C.; Rupesinghe, N. L.; Amaratunga, G. A. J.; Ferrari, A. C.; Roy, D.; Robertson, J.; Milne, W. I. J. Appl. Phys. 2001, 90, 5308. (16) Frenklach, M.; Carmer, C. S. AdV. Classical Trajectory Methods 1999, 4, 27. (17) Frenklach, M.; Skokov, S.; Weiner, B. Nature 1994, 372, 535. (18) Skokov, S.; Carmer, C. S.; Weiner, B.; Frenklach, M. Phys. ReV. B 1994, 49, 5662. (19) Stewart, J. J. P. Semiempirical Molecular Orbital Methods. In ReViews in Computational Chemistry; Lipkowitz, K. B., Boyd, D. B., Eds.; VCH Publishers: New York, 1990; Vol. 1; p 45. (20) Pamur, H. T. H. Phys. Status Solidi A 1976, 37, 695. (21) Beeman, J. J. Comput. Phys. 1976, 20, 130. (22) Berendsen, H. J. C.; Postma, J. P. M.; Gunsteren, W. F. v.; DiNola, A.; Haak, J. R. J. Chem. Phys. 1984, 81, 3684. (23) Hash, D. B.; Meyyappan, M. J. Appl. Phys. 2003, 93, 750. (24) Meyyappan, M.; Delzeit, L.; Cassell, A.; Hash, D. Plasma Sources Sci. Technol. 2003, 12, 205. (25) Battaile, C. C.; Srolovitz, D. J. Annu. ReV. Mater. Res. 2002, 32, 297. (26) Rummeli, M. H.; Palen, E. B.; Gemming, T.; Pichler, T.; Knupfer, M.; Kalbac, M.; Dunsch, L.; Jost, O.; Silva, S. R. P.; Pompe, W.; Buchner, B. Nano Lett. 2005, 5, 1209. (27) Vasenkov, A. V.; Carnahan, D.; Sengupta, D.; Frenklach, M. Technical Proceedings of the 2008 Nanotechnology Conference and Trade Show, 2008, Boston, MA, Vol. 1, P 159. (28) Anderson, A. B. J. Am. Chem. Soc. 1977, 99, 696. (29) Jenkins, S. J. Surf. Sci. 2006, 600, 1431. (30) Vasenkov, A. V. J. Comput. Theor. Nanosci. 2008, 5, 48.
JP808346H
