ARTICLE pubs.acs.org/JPCC
Simulation of Steady-State Methanol Flux through a Model Carbon Nanotube Catalyst Support Jacob Goldsmith and Bruce J. Hinds* Department of Chemical and Materials Engineering, University of Kentucky, Lexington, Kentucky 40506-0046, United States ABSTRACT: Nonequilibrium molecular dynamic (MD) simulations were performed to show transport of a watermethanol solution through a novel catalysis membrane, constructed from single-walled carbon nanotubes (CNTs) with a Pt monolayer catalyst at the membrane’s exit. These calculations are directed toward understanding methanol transport dynamics in the CNT core, past the Pt coating, and to find the conditions for optimal efficiency as a function of both CNT diameter and pressure. Probability density function calculations for various methanol observables show that methanol primarily travels along the pore wall, which is ideal for methanol to interact efficiently with a catalyst at the exit. From the percent of methanol that passed through the pores within the minimum of the Lennard-Jones potential (21/6σPtO), we estimate the residence time of methanol flux past the Pt monolayer in the range of 26 ps. The mass transport percent efficiency of the methanol flowing past the catalyst site is as high as 86% for (10,10) CNTs at flow velocities near 100 cm/s. Optimal diameters are ca. 1 nm, and flow rates should be 1 ps
0.05
86
50
0.10
71
43
0.15
61
39
0.01 0.05
77
100 57
0.10
54
41
0.15
42
33
0.05
56
49
0.10
42
36
0.15
30
27
0.01
92
0.01
79
Figure 2. Probability density function for the radial position of methanol’s carbon (fi = 0.15, Pt charged). Zero is the center of the CNT pore. Analysis was done on methanol molecules in the CNT and 7 Å from the Pt in this plot.
Table 7. Uncharged Pt Simulation with the Mass Transport Efficiency % and Values That Use Residence Times That Are Greater than 1 ps CNT index (10,10)
(14,14)
(18,18)
fi
% efficiency
0.01
% > 1 ps 50
0.05
70
45
0.10
57
40
0.15
62
42
0.01
83
0.05 0.10
66 49
48 39
0.15
39
32
0.01
84
0.05
68
60
0.10
38
33
0.15
33
29
Lennard-Jones potential, that is, 21/6*σPtO (abbreviated σ = 3.3 Å). This assumption allows us to estimate residence time of methanol on the Pt monolayer as follows. When the methanol’s oxygen was within one σ from a Pt, we started counting. If the methanol drifted two σ away, then the residence time was output and the counter was reset. The efficiency was calculated from a purely geometrical manner: the number of methanol molecules that passed within our criterion (σ = 3.3 Å) divided by the total number of the methanol molecules that passed through the membrane. This data is found in Tables 6 and 7, and we feel that this value is an appropriate gauge of how likely any reaction might occur at a given flow rate. We calculated the flux of water and methanol through the nanopore if and only if water started from one side of the membrane and traveled to the other side past the plane of Pt atoms. However, for the methanol case, we counted any that passed through the pore. For low pressures, a moderate back flux of water by diffusion was observed, but a negligible amount of methanol (one to five molecules) was due to the 30:1 dilution. The flux reported in Tables 4 and 5 is the difference between forward and back flux values the net flux. For higher pressures, no molecules flowed in the opposite direction of the applied
Figure 3. Probability density function for the radial position of the oxygen on the methanol. Analysis was done on methanol molecules in the CNT and 7 Å from the Pt in this plot. Methanol spends the majority of its time near the walls of the CNT. The second peak is attributed to a methanol hydrogen bonding to a water molecule in the CNT.
pressure gradient. Because we did not exclude the methanols that entered from the opposite direction, for the smallest applied force, back-flux is possible, and our estimate of the efficiency was overestimated. That is, because the flux of methanol is so low for this simulation, reservoir methanol meets the distance criterion, and the calculation is error prone for low flux rates and is thus omitted. Fickian diffusion of methanol and water dominates at the lowest applied pressures. Probability density functions (PDFs) are calculated from the radial positions of the methanol’s oxygen and carbon (Figures 2 and 3) and the angle the CO bond makes with the axis (z B) of the pore. (See Figure 4.) The angle is calculated via standard linear algebra techniques as the arcos() of the normalized dot ! product of the CO vector dotted with the unit vector ^z. Bin sizes for the radial PDF are 0.1 Å, whereas 1° bins are used for the angle PDF. We also calculate the methanol makes ! ! the angle with the Pt (the angle the PtO and the H3 CO vectors make) in the area around the monolayer (Figure 5) of Pt, similar distance criterion to the residence time calculations. PDF data are similar for both varied pressure and CNT diameter; all calculations are over the entire 6 ns simulation. The Pt angle calculation also 19161
dx.doi.org/10.1021/jp201467y |J. Phys. Chem. C 2011, 115, 19158–19164
The Journal of Physical Chemistry C
Figure 4. Probability density function ((18,18) CNT and fi = 0.01) of the angle the CO bond makes with the pore axis, with the O as the head of the vector (system in this Figure: (18,18) CNT and fi = 0.01). Analysis was done on methanol molecules in the CNT and 7 Å from the Pt in this plot. The molecule rarely leads with the CO bond pointing perfectly forward or backward.
Figure 5. Probability density function of the angle the COPt makes, with the O as the apex of the angle (system in this Figure: (system in this figure: (14,14) CNT and fi = 0.01). In this Figure, we focused on the region near Pt. We show the probability density function for the angle created by PtOC, where the O is the vertex of the angle. The plot is for the charged Pt system and is nearly identical to the uncharged system.
ignores methanol in the bulk solution and focuses only on the methanol that passes through the membrane. All angle histograms are plotted from 0 to 180°, whereas the radial histograms are cut off at the maximal sampled position of the methanol. Both radial and angle PDFs are properly normalized to unity.
’ RESULTS First, it is necessary to compare the charged and uncharged Pt systems to determine if the observed dynamics of methanol past the catalytic sites are affected by this basic assumption. The key calculations as described above include the residence times and flux to estimate the efficiency of the model eletrocatalyst. PDFs show the statistical behavior of the methanol as it passes through the CNT and as methanol passes the Pt sites. In synthetic homogeneous/heterogeneous catalysis, the approach angle is random, resulting in very low turnover frequency. There is potential for preferential methanol orientation along the CNT wall that affects the approach angle to the catalytic site, potentially increasing catalytic activity. Residence Times and Efficiency. The residence time (Tables 2 and 3) for methanol range from 1 to 6 ps but show a
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Figure 6. Extrapolation of the velocity versus pressure that we derived from the net flux of molecules through the CNT pore. (See the text.) We assume an intercept of (0,0) and fit the velocity to y = mx. The slopes (m) for each CNT diameter are 0.86, 0.91, and 0.52 for the (10,10), (14,14), and (18,18) CNT, respectively, with units cm/s 3 atm. The results shown are for the charged Pt CNT tip.
large variation, as can be seen from the standard deviation of all times calculated. From a mechanistic point of view, the larger CNT system allows longer residence times because spatially there are more Pt surface sites on the larger circumference. The small CNT, however, has a constant stream pushing the methanol past the opening and gives lower residence times. In general, there is very little difference in the residence times between the charged Pt and the uncharged Pt simulations. The uncertainty in this data is approximately equal to the output frequency of the coordinates (500 fs) and is also related to the interaction distance assumptions we make in our calculations. For example, if we used a larger Pt interaction distance, then we would get a proportionately larger residence time. We calculate the effective velocity to compare with experimental flux rates. If one had a total flux rate of 100 molecules during the 6 ns simulation, then flow velocity would be 100 molecules/6 ns as flux/(F*ACNT), where F is the density of water and ACNT is the area of the pore. At that representative flux, the flows range from 15, 29, to 70 cm/s for the (10,10), (14,14), and (18,18) CNTs, respectively. Our flux data extrapolate to roughly ca. 1 cm/s 3 atm for the (10,10), (14,14), and (18,18) CNTs (Figure 6), consistent with experimental reports of 3 cm/s 3 atm at lower pressures.22,29 The atomistically calculated residence time of Tables 2 and 3 are significantly shorter than a macroscopic average flow-velocitybased residence time (flow velocity divided by the 0.6 nm Pt interaction length). This is because other solvent molecules (i.e., water) can come between the methanol and Pt, thus temporarily forcing methanol out of the weak Lennard-Jones (LJ) Pt interaction volume, whereas the ensemble flows out the exit. This work identifies windows of two time scales for catalytic membranes to operate within (1) atomistic time to form a bond stronger than a simple LJ potential (50% even for fast flow rates, indicating that a catalysis membrane (of a similar diameter) would be small enough to optimize the reactants touching the catalysis while exiting. For the zero Pt partial charge case, the efficiency dropped slightly. Although the drop was generally only a few percent, partial charge is an important parameter that justifies further examination. It should be noted that although the (10,10) nanopore has the largest efficiency, the larger pores have flux rates nearly an order of magnitude greater, roughly proportional to the area increase within the core of the CNT. It is a trade off between high efficiency (high methanol-to-catalyst contact area) versus a large flux. We conclude that both diameter and flux rate are equally important to optimize an electrocatalytic membrane, where the ideal is a high proportion of 1 nm diameter CNTs. Probability Density Functions. PDFs describe the statistically preferred location of methanol in the CNT. Importantly, we found that the alkane side of the methanol is most likely found near the wall of the CNT (Figure 2), whereas the hydrophilic side is hydrogen bonding with waters in the pore, similar to the work of Shao et al.33 This can be seen from the radial PDF of the methanol’s oxygen in Figure 3. The carbon PDF shows that the carbon acts as a hydrophobic tail and clings to the pore wall. One broad side peak is observed in both Figures 2 and 3, but the peak is small in comparison with the main peak. The error in the PDFs is approximately equal to the noise shown in the graphs. Similar behavior is also seen experimentally in the work of Burghaus et al., who showed methanol adsorbed to surface CNT sites,47 and seen theoretically in MD work by Zheng et al.31 The affect of concentrating the methanol to flow along the CNT wall clearly maximizes the methanol’s interaction with the catalyst monolayer at the CNT’s exit. We expect in the experimentally feasible longer CNT (i.e., 5 μm) to have even stronger portioning along the walls and a correspondingly higher mass transport efficiency to catalysis sites. If this is a generalization of how other hydrocarbons flow in CNT membranes, then it would be advantageous for membrane catalysts. In the mechanism of methanol oxidation, water must be present in the final stages of the decomposition. Clearly, a membrane with water and methanol solution constantly flowing (as well as water from the reservoir side) would make water available at the last step of the catalytic oxidation process. In catalysis, the orientation of the reactant molecule with respect to the catalyst is important. Figures 4 and 5 show that the methanol has a visible preference to have the OH group normal to the CNT wall. Each Figure shows the corresponding geometric construct. The probability for a particular angle range is calculated via the integral of the PDF. For the charged system, there is a probability of 0.66 that a methanol is within (45° of the vector normal to Bz . Similarly, Figure 5 shows larger probabilities for methanol to be perpendicular to the Pt; there is a probability
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of 0.72 that a methanol-Pt vector is within (45° from 90°. As the methanol approaches the Pt, the distribution narrows slightly (for both cases studied). That is, the oxygen is more likely to point toward the Pt. It is known that the oxygen is thermodynamically favored to chemisorb to the Pt; therefore, the dynamics we sampled demonstrate the first step in the methanol reduction reaction. It can also be noted that the methanol undergoes rotation as it leaves the pore. This is true for both the charged simulation and the uncharged simulation, which indicates that the methanol dynamics are more likely influenced by the bulk reservoir hydrogen bonding, whereas the charges on the Pt play only a small role in influencing the methanol as it leaves the pore. Controlling the orientation of the reactant molecule can have a profound influence on catalytic activity, as in the basis of natural enzyme systems, but is not perfect in this case. Charge on the Pt was not enough to enhance this effect, and more elaborate catalytic sites to direct the orientation of methanol to the catalyst site would have to be explored.
’ CONCLUSIONS In this work, we have shown nonequilibrium MD simulations of water and methanol flowing through CNT membranes with catalyst sites at the end. There is a large partitioning of methanol to the CNT walls as the solution flows through the membrane that enables efficient transport to catalytic sites. We have show that for small pore diameters the likelihood of a methanol touching a catalyst particle is greater than that for larger pore diameters. Efficiences are as high as 86% for the (10,10) CNTs at flow velocities near 100 cm/s. Although in this work we focus only on one concentration, which is a standard case for fuel cell experiments,5 we would expect similar results for modest concentrations; we would expect lower efficiencies and broader side peaks in the radial PDFs for higher concentrations. Furthermore, we show that a charge on the Pt did not dramatically affect the dynamics of the methanol near the catalytic site. This system overcomes initial hurdles for membrane catalysis, as described by Armor,48 such as choosing a system with high flux and orientational selectivity. Future work focuses on improving the force field for metal and CNT interactions as well as quantum MD simulations of similar systems. These MD-derived trajectories can be used as a starting point for quantum mechanical simulations, which aim to explore the kinetics (i.e., bond breaking) and thermodynamic pathways of catalytic steps in similar membranes. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT This work was financially supported by DARPA (W911NF09-1-0267). ’ REFERENCES (1) Bond, G. C. Catal. Rev. 2008, 50, 532–567. (2) Zhong, C.; Lou, J.; Fang, B.; Wanjala, B. N.; Njoki, P. N.; Loukrakpam, R.; Yin, J. Nanotechnology 2010, 21, 062001. (3) Greeley, J.; Nørskov, J. K.; Mavrikakis, M. Annu. Rev. Phys. Chem. 2002, 53, 319–348. 19163
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The Journal of Physical Chemistry C (4) Shao, Y.; Liu, J.; Wang, Y.; Lin, Y. J. Mater. Chem. 2009, 19, 46–59. (5) Iwasita, T. Electrochim. Acta 2002, 47, 3663–3674. (6) Wang, D.; Lu, S.; Jiang, S. P. Electrochim. Acta 2010, 55, 2964–2971. (7) Razmi, H.; Habibi, E.; Heidari, H. Electrochim. Acta 2008, 53, 8178–8185. (8) Ye, F.; Wang, T.; Li, J.; Wang, Y.; Li, J.; Wang, X. J. Electrochem. Soc. 2009, 156, B981–B985. (9) Su, X.; Hinds, B. J. Carbon 2011, 49, 1145–1150. (10) Meng, H.; Shen, P. K. Electrochem. Commun. 2006, 8, 588–594. (11) Mitchell, P. C. H.; Wolohan, P.; Thompsett, D.; Cooper, S. J. J. Mol. Catal. A 1997, 119, 223–233. (12) Berezhkovskii, A.; Hummer, G. Phys. Rev. Lett. 2002, 89, 064503–1. (13) Hanasaki, I.; Nakatani, A. J. Chem. Phys. 2006, 124, 144708. (14) Whitby, M.; Quirke, N. Nat. Nanotechnol. 2007, 12, 87. (15) Takaiwa, D.; Hatano, I.; Koga, K.; Tanaka, H. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 39–43. (16) Zang, J.; Konduri, S.; Nair, S.; Sholl, D. S. ACS Nano 2009, 3, 1548–1556. (17) Goldsmith, J.; Martens, C. C. J. Phys. Chem. Lett. 2010, 1, 528–535. (18) Majumder, M.; Chopra, N.; Andrews, R.; Hinds, B. Nature 2005, 438, 44. (19) Majumder, M.; Chopra, N.; Hinds, B. J. Am. Chem. Soc. 2005, 127, 9062–9070. (20) Byl, O.; Liu, J.; Wang, Y.; Yim, W.; Johnson, J. K.; Yates, J. T. J. Am. Chem. Soc. 2006, 128, 12090–12097. (21) Kim, S.; Jinschek, J. R.; Chen, H.; Sholl, D. S.; Marand, E. Nano Lett. 2007, 7, 2806–2811. (22) Majumder, M.; Chopra, N.; Hinds, B. J. Am. Chem. Soc. 2005, 127, 9062–9070. (23) Majumder, M.; Zhan, X.; Andrews, R.; Hinds, B. J. Langmuir 2007, 23, 8624–8631. (24) Houk, K.; Cheong, P. Nature 2008, 455. (25) Kua, J.; Goddard, W. A., III. J. Am. Chem. Soc. 1999, 121, 10928–10941. (26) Sholl, D. S. Acc. Chem. Res. 2006, 39, 403–411. (27) Maginn, E. J.; Elliott, J. R. Ind. Eng. Chem. Res. 2010, 49, 3059–3078. (28) Harting, C.; Vassilev, P.; Koper, M. T. Electrochim. Acta 2003, 48, 3751–3758. (29) Holt, J.; Park, H.; Wang, Y.; Stadermann, M.; Artyukhin, A.; Grigoropoulos, C.; Noy, A.; Bakajin, O. Science 2006, 312, 1034. (30) Joseph, S.; Aluru, N. Nano Lett. 2008, 8, 452–458. (31) Zheng, J.; Lennon, E. M.; Tsao, H.; Sheng, Y.; Jiang, S. J. Chem. Phys. 2005, 122, 214702. (32) Zhang, Q.; Zheng, J.; Shevade, A.; Zhang, L.; Gehrke, S.; Heffelfinger, G.; Jiang, S. J. Chem. Phys. 2002, 117, 808–818. (33) Shao, Q.; Huang, L.; Zhou, J.; Lu, L.; Zhang, L.; Lu, X.; Jiang, S.; Gubbins, K.; Zhu, Y.; Shen, W. J. Phys. Chem. C 2007, 111, 15677–15685. (34) Adzic, R. R.; Zhang, J.; Sasaki, K.; Vukmirovic, M.; Shao, M.; Wang, J. X.; Nilekar, A. U.; Mavrikakis, M.; Valerio, J. A.; Uribe, F. Top. Catal. 2007, 46, 249–262. (35) Humphrey, W.; Dalke, A.; Schulten, K. J. Mol. Graphics 1996, 14, 33–38. (36) Kale, L.; Skeel, R.; Bhandarkar, M.; Brunner, R.; Gursoy, A.; Krawetz, N.; Philips, J.; Shinozaki, A.; Varadarajan, K.; Schulten, K. J. Comput. Phys. 1999, 151, 283. (37) Phillips, J.; Braun, R.; Wang, W.; Gumbart, J.; Tajkhorshid, E.; Villa, E.; Chipot, C.; Skeel, R.; Kale, L.; Schulten, K. J. Comput. Chem. 2005, 26, 1781–1802. (38) Pollack, M.; Fair, R. B.; Shenderov, A. D. Appl. Phys. Lett. 2000, 77, 1725–1726. (39) Hu, L.; Gruner, G.; Gong, J.; Kim, C.; Hornbostel, B. Appl. Phys. Lett. 2007, 90, 093124. (40) Selvarani, G.; Selvaganesh, S. V.; Krishnamurthy, S.; Kiruthika, G.; Sridhar, P.; Pitchumani, S.; Shukla, A. K. J. Phys. Chem. C 2009, 113, 7461–7468.
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(41) Mink, J.; Goggin, P. Can. J. Chem. 1991, 69, 1857–1863. (42) Tarmyshov, K. B.; M€uller-Plathe, F. J. Chem. Phys. 2007, 126, 074702. (43) Jorgensen, W.; Chandrasekhar, J.; Maduura, J. J. Chem. Phys. 1983, 79, 926. (44) Leung, K.; Rempe, S. B. J. Comput. Theor. Nanosci. 2009, 6, 1948–1955. (45) Zhu, F.; Tajkhorshid, E.; Schulten, K. Biophys. J. 2002, 83, 154–160. (46) Lu, L.; Shao, Q.; Huang, L.; Lu, X. Fluid Phase Equilib. 2007, 261, 191–198. (47) Burghaus, U.; Bye, D.; Cosert, K.; Goering, J.; Guerard, A.; Kdossov, E.; Lee, E.; Nadoyama, Y.; Richter, N.; Shaefer, E.; Smith, J.; Ulness, D. Chem. Phys. Lett. 2007, 442, 344–347. (48) Armor, J. N. Appl. Catal., A 2001, 222, 91–99.
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