5764
J. Phys. Chem. B 2010, 114, 5764–5768
Grand Canonical Monte Carlo Studies of CO2 and CH4 Adsorption in p-tert-Butylcalix[4]Arene John L. Daschbach, Xiuquan Sun, Praveen K. Thallapally, B. Peter McGrail, and Liem X. Dang* Pacific Northwest National Laboratory, Richland, Washington 99352 ReceiVed: October 23, 2009; ReVised Manuscript ReceiVed: March 11, 2010
Grand Canonical Monte Carlo simulations were performed for single component isotherms of CO2 and CH4 in the p-tert-butylcalix[4]arene structure. Comparison with literature data for adsorption used the Peng-Robinson equation of state to map simulated fugacities to experimentally determined pressures. CO2 binding in the high-pressure structure of TBC4 (TBC4-H) occurs in two distinct waves. The cage sites in TBC4 completely fill up, followed by the filling of interstitial sites, resulting in the sum of two Langmuir isotherms being the best way to describe the total absorption isotherms. Our simulation results capture the essential experimental feature that the cage sites are the major contributor to the absorption isotherms, and the contribution of interstitial sites are significantly less. We found that CH4 does not exhibit the same two-site binding characteristic and has a smaller temperature dependence, which arises from a smaller negative entropy change upon absorption compared with the case for CO2. Our calculations give higher binding than observed experimentally for the cage site but lower binding for the interstitial site. We also demonstrate that by rescaling the interaction between CO2 and the lattice, the results can reproduce the experimental data well at low loadings. The rescaled potentials are within the range found in other studies. This makes the discrepancy between experiment and simulation at high loadings greater, which is unexpected for this system. It is postulated that the simulation points to structural changes or defects being partially responsible for the relatively higher absorption found experimentally. I. Introduction The current understanding of global warming indicates that CO2 accumulation in the atmosphere plays an important role, and a significant source of atmospheric CO2 over recent decades is the combustion of carbon based fuels. In addition to hydrocarbon combustion, CO2 is generated in the production of some other fuels such as biomethane, green synfuel, and hydrogen. One important approach to minimizing CO2 emission into the atmosphere is carbon capture and sequestration. Capture of CO2 from flue gases, or during fuel production, is a key component in this strategy. The CO2 capture phase of the sequestration process is estimated to cost up to 75% of the complete process based on the current widespread use of amine scrubbing. There is a strong economic incentive to develop alternative capture processes based on other materials, which would be less expensive but have high relative capacity, be able to be regenerated at reasonable cost, and have good selectivity. Many materials are under investigation, and their development is proceeding toward this goal, including activated carbons,1,2 zeolites,3,4 metal-organic frameworks (MOF),5-10 periodic mesoporous silica,11 covalentorganic frameworks,12 zeolitic imidazole frameworks (ZIF),13,14 nanoporous material-supported polymer sorbents,15,16 and organic molecular solids.17-21 Different classes of materials have advantages in separate functional requirements for a commercially viable material, including cost, mass, volume, reversibility, robustness, and safety, and no distinct class appears to possess all requisite properties, which may vary by application. A better understanding of structure-function relationships across a wide range of materials will facilitate the development of better CO2 capture materials.
The molecular solid p-tert-butylcalix[4]arene (TBC4) is one well-studied example of an organic molecular solid with reversible gas sorption properties. Each TBC4 molecule possesses a cage composed of four phenyl rings (more like a bowl shape), which depending on the crystal phase may be open or filled with a tert-butyl group from the opposing layer. More than one open structure is known, depending on guest inclusion, temperature, and method of growth.19,20 A study by Udachin et al.21 reported CO2 uptake in TBC4 up to 1.6 CO2/TBC4 at 298 K and 3400 kPa with data showing cages filled with single CO2 molecules along with CO2 molecules in interstitial sites, a sorptive capacity of 109 mg of CO2/g of sorb, with an uptake around 25 mg of CO2/g of sorb at 100 kPa. This is lower than some of the state of the art materials under milder conditions, such as the “molecular basket” sorbent MBS-2 at 140 mg of CO2/g of sorb at 448 K and 15 kPa and the zeolitic imidazolate framework-78 (ZIF-78) around 52 mg of CO2/g of sorb at 298 K and 15 kPa and about 200 mg CO2/g sorb at 106 kPa, but only by about an order of magnitude under similar conditions. Comparisons with ZIFs synthesized to date show that TBC4 has a smaller cage, ∼70 Å3 vs 358 Å3 for ZIF-78, which may enhance desired selectivity under certain conditions. II. Computational Approach Methane and carbon dioxide absorption in TBC4 were calculated using the MUSIC simulation package from Gupta and co-workers.22 Two structures of the TBC4 lattice were considered for CO2 absorption with coordinates for both the high and low CO2 pressure structures taken from the work of Ripmeester and co-workers.21 The low pressure structure is the same as the empty low density structure of TBC4 (P21/n) and
10.1021/jp9101465 2010 American Chemical Society Published on Web 04/13/2010
CO2 and CH4 Adsorption in p-tert-Butylcalix[4]arene it absorbs CO2 up to a 1:1 CO2:TBC4 loading ratio with CO2 located in the calix cage (TBC4-L). The high pressure structure has the same space group as the 1:1 compounds formed when TBC4 is crystallized from fluorobenzene23 or toluene24 and absorbs CO2 in two crystalographically distinct locations, one in the calix cage and the other in an interstitial site between two calixarene molecules (TBC4-H). The TBC4 lattice was considered rigid with methane treated in the united atom model with potential parameters from Jorgensen et al.25 and carbon dioxide as a three-atom rigid linear molecule with potential parameters and partial charges from the AMBER 99EP potential set.26 These CO2 and CH4 parameters are widely used, including some of our earlier reports.27,28 The TBC4 lattice parameters and partial charges used the values for identical atoms and bond conjugations from the Amber molecular dynamics package and were the same as in our earlier reports on the TBC4 system. The simulation configuration consisted of 16 TBC4 molecules with 1664 atoms and the dimension of the system is about 25.4 × 25.4 × 25.2 Å3. The same Lenard-Jones parameters from the Amber package were used by other workers in MD simulations of the TBC4 system29,30 with small differences in the atomic partial charges. Molecular behavior in this system will be dominated by the Lenard-Jones potentials, and only small differences in energetics are expected with small perturbations to the partial charges. Another report on TBC4 used LenardJones parameters from the MM3 force fields.31 Reported Lennard-Jones parameters for a variety of carbon based structures span a range of values within the Amber parameters used here and are near the deeper end of well depths found in recent literature.32-35 Therefore we also explored reducing the well depth by scaling the lattice carbon LJ well depth for both types of carbon atoms by the same amount in one set of calculations retaining the parameters for the CH4 and CO2 while using the Lorentz-Berthlot mixing rules. In future studies, nonadditive polarizable potential models (i.e., many body effects) will be employed to describe the interaction between host-guest complexes. Grand Canonical Monte Carlo (GCMC) simulations were performed for single component isotherms of CO2 and CH4 in the TBC4 structure computed on a log spaced grid in fugacity. Comparison with literature data for adsorption used the Peng-Robinson equation of state to map simulated fugacities to experimental pressures. The GCMC steps included insertion and deletion of the absorbate with equal trial probabilities, and translational and rotational trial probabilities equal to each other, but 10 times lower than the insertion/deletion probabilities. Isotherms were computed sequentially with the input configuration for each pressure coming from the final configuration of the prior pressure. To check convergence, a few isotherms were calculated in both directions, from high to low and low to high pressures. Most of the reported calculation data were from high to low pressure with an initial configuration calculated at 100 K and 10 GPa. All calculations were run for a minimum of 20 million steps with the first 10 million used for equilibration. At high loadings the successful insertion probability decreased to around 10-4, and longer runs were required to achieve consistent statistics. III. Results and Discussion A. CO2 in TBC4. The high pressure TBC4-H structure can take up to one CO2 per cage and one CO2 per interstitial site, and the two distinct waves in the isotherm correspond to filling the cages at lower pressure and the interstitial site at higher pressure, as shown in Figure 1. In all of our simulations, the
J. Phys. Chem. B, Vol. 114, No. 17, 2010 5765
Figure 1. Distribution of CO2 in TBC4. Red spheres represent the atoms in TBC4 molecules. Blue and green spheres represent the carbon and oxygen atoms in CO2 molecules.
CO2 molecules are absorbed in the cage sites first, and then the interstitial sites are filled for the high pressure structure (TBC4H) or CO2 pairs are formed with the existing CO2 molecules in the cage sites for low pressure structure (TBC4-L) after all the cage sites are fully occupied. Thus it is reasonable to consider the overall adsorption as a process with two independent steps. This observation is consistent with the free energy calculation for different loadings in our earlier work.28 For the high-pressure 2:1 structure, the data are well represented by the sum of two Langmuir isotherms
θ)
R1P R 2P + 1 + R1P 1 + R2P
(1)
The constant R in eq 1 can be expressed in terms of a temperature independent entropy term and a temperature dependent enthalpy term36
R)
1 exp(A/R) exp(-B/RT) P0
(2)
In the absence of intercage interactions, and with identical cage configurations, the Langmuir model exactly fits the current system when the absorbate is treated as an ideal gas. The inset of Figure 2 shows isotherms calculated for TBC4-H at 300 K with pressure calculated from the Peng-Robbinson equation of state with the sum of two isotherms fit to experimental data of Udachin et al.21 The two components of the sum of isotherm fits for both simulation and experiment are shown in Figure 2. The results clearly demonstrate that our simulation results capture the essential experimental features in that the cage sites are the major contributor to the absorption isotherms and the interstitial sites contribute significantly less. We note that our calculations give a slightly higher binding energy than that observed experimentally for the cage site but lower binding for the interstitial site. Udachin et al.21 interpreted their data at loadings up to 0.6 CO2/TBC4 as appearing to arise from a Langmuir adsorption isotherm with a 1:1 composition at full loading. Our simulation data are fully consistent with this view. However, they note
5766
J. Phys. Chem. B, Vol. 114, No. 17, 2010
Figure 2. Calculated isotherm at 300 K for CO2 for cage sites (red circles) and interstitial sites (blue circles) in structure TBC4-H with the pressure calculated from the Peng-Robinson equation of state and the corresponding cage (red squares) and interstitial (blue squares) sites isotherms fit to experimental data reported at 298 K by Udachin et al.21 Also shown are the combined isotherms (inset).
that at higher loadings the data were inconsistent but then converged at the highest loadings to a common set of values. They chose to represent their data fit with a single Langmuir isotherm for the entire range of data. This single Langmuir isotherm does not fit the experimental results very well. In this work, we refit the experimental results with a sum of two Langmuir isotherms model, and the fit is improved significantly. The reason is that the two CO2 adsorption sites for TBC4 molecules are very energetically different. Our fit at the low pressure region is mainly contributed from one term of the two Langmuir isotherms, which means a single Langmuir isotherm feature of the adsorption of CO2 molecules at low pressure. Although the simulation results capture the essential features of the experimental one, the large quantitative discrepancy between the experimental and simulation results is unexpected. It is possible the experimental data are influenced by the metastable nature of the TBC4-H structure. It is noted that initial loading is slow, but after full loading and CO2 release, subsequent reloading is rapid, and it is postulated that the phase change is not reversed upon unloading and this facilitates more rapid reloading, or that there is a reduction in particle size. This combined with the inconsistent data at intermediate loadings introduces the possibility that the system is substantially altered upon full loading. The simulations are performed with the ideal crystal structure of the TBC4. This may not be true in the real experimental systems, which more likely contains a mixture of TBC-L and TBC4-H or other phases in the system due to the metastable nature of TBC4-H. In our simulations, the energy surface of the system is well-defined as two separated wells, corresponding to two CO2 binding sites, with a large energetic difference. However, the energy surface is predicted to be composed of lots of local minimum with a much smaller energetic difference in experiments. Such an energy surface will give a lower binding of CO2 at low pressure and higher binding at high pressure for TBC4. This hypothesis explains the quantitative discrepancy between experimental and simulation results. Because the simulation uses identical cages, the entropy contribution to adsorption must be more negative than for the real molecular system, so the binding enthalpy difference will be smaller also. The experimental data do not exhibit a plateau, as seen in the simulation results. Using a simple model in which fully loading the higher binding cage sites takes place before
Daschbach et al. the interstitial sites are loaded, a much smaller difference in site-dependent binding energy than found in the simulation would explain the differences with experiment. It was noted that the experimental kinetics of CO2 sorption in TBC4 was initially very slow, but after degassing, repeated loadings were more rapid, and the uptake kinetics were temperature dependent with equilibration taking on the order of 20 h at room temperature and 2-3 h at 373 K.21 Because there are no channels in TBC4, the mechanism of absorption and the nature of CO2 diffusion are unclear. It is possible that diffusion is facilitated differently in defects. Our use of classical potentials developed for other systems is certain to lead to discrepancies between what would be the best pairwise potentials, and those used here. A recent simulation study by Jiang and Sandler34 calculated adsorption isotherms for CO2 in C168 Schwarzite, a hypothetical periodic carbon framework with well-defined pores and channels, with two types of pores with average diameters of 7 and 9 Å, larger than the 4 Å cage diameter in TBC4. Two sets of potentials for the C168-CO2 system were investigated, one based on the empirical Steele potential developed for gas adsorption on graphite, and the other on a series of ab initio calculations with different basis sets for CO2 interaction with a section of the C168 structure. The ab initio well depth for the C-C(CO2) interaction was similar to that found in the Amber potentials, 35.92 K compared with 39.55 and 35.33 K for the two types of framework carbons in TBC4, while the Steele potential for the same interaction was 27.0 K. The C-O(CO2) interaction was 55.18 K in the ab initio derived pairwise potential and 45.6 K for the Steele potential, compared to the Amber values of 67.4 and 59.8 K for the two framework carbon atom types. Another simulation study using the MUSIC code investigated CO2 absorption in C168 with well depths 2.0 and 2.4 K deeper than the Steele potential for C-C and C-O, respectively.35 The Amber potentials have stronger interactions than either of the parameter sets used in the C168 studies. The isoteric heats of adsorption for CO2 in C168 were 10.39 and 7.76 kcal mol-1 for the ab initio and Steele potentials, respectively, in the first study,34 and 8.52 kcal mol-1 in the second study,35 while we calculate a ∆Hads value of 8.55 kcal mol-1. With a smaller cage size in TBC4, well suited to CO2, it is surprising the results here are not larger on the basis of the comparison of potentials, but the absorption energetics appear similar to other CO2-carbon cage systems. It is interesting to estimate what reduction in potentials or lower binding energies would better fit the experimental data. Given the relatively simple nature of the physisorption in this system, the use of classical MD should qualitatively capture the behavior of the system. Tuning the potentials to match a portion of the experimental data, either the low or high loading regime, would increase the discrepancy between simulation and experiment of the other regime. However, it is still interesting to see the sensitivity of the potential parameters affecting of the Langmuir isotherms in the simulations. Figure 3 shows isotherms calculated with the Amber potentials at 300 K and when the interaction between the framework carbon and the CO2 atoms is scaled down by a factor of 0.63. The simulations with other factors, 0.89 and 0.77, were also performed. The experimental data at low CO2 loading ratios lie between the adjusted potentials scaled by 0.77 and 0.63, somewhat closer to the latter. To match the experimental data appears to require potential parameters with weaker interactions than for other similar systems, in some cases where the parameters have been chosen to match experimental data. Heuchel et al. used a twosite LJ + point quadrupole to model CO2 absorption in activated
CO2 and CH4 Adsorption in p-tert-Butylcalix[4]arene
J. Phys. Chem. B, Vol. 114, No. 17, 2010 5767
Figure 3. Calculated isotherms at 300 K for CO2 in structure TBC4-H using the Lennard-Jones potential parameter for the lattice carbons rescaled by a factor of 0.63 with pressure calculated from the Peng-Robinson equation of state (open circles) along with experimental data reported at 298 K by Udachin et al.21
carbon with the interaction between the two CO2 sites and the carbon ε/kB ) 59 K, which fit experimental absorption data well.1 Direct comparison with the more common three-site model used here is not possible, but simply summing the sites with the Heuchel potential parameters gives a total interaction of 118 K while the Steele potential parameters developed for O2 adsorption on planar graphite and used in the simulation of CO2 absorption in Schwarzite34 would sum to 103 K, and ab initio derived parameters for CO2 absorption in Schwarzite sum to 146 K. Similar treatment of the unscaled parameters here gives 165 K with the scaled potentials at 147, 127, and 103 K. Although comparison between the two-site and three-site models is dependent upon specific geometry, the unperturbed threesite model here has a stronger interaction with the framework carbons than the comparable potentials developed for graphite. The first perturbation of the Amber potentials is close to the ab initio derived Lennard-Jones parameters, but simulations based on this set of potentials are not a good fit to the experimental data. The best fit to the experimental data is from potentials close to those developed by Steele for absorption on planar graphite. Figure 4a shows isotherms at various temperatures for the high pressure TBC4-H structure. The sum of two Langmuir models fits very well for the adsorption at both cage and interstitial sites at all temperatures. The adsorption sites in TBC4-H are well separated, little interaction is observed between the cage-cage and interstitial-interstitial site CO2 molecules. The absorptions of CO2 for the low-pressure structure TBC4-L are studied as well (Figure 4b). Since there is no interstitial site in this structure, the second CO2 molecule adsorbed by each TBC4 molecule is stabilized as a CO2 pair formed with the first adsorbed CO2 molecule at the cage sites. The Langmuir model does not fit the second CO2 molecule adsorption for the lowpressure TBC4-L structure. While the pressure-loading conditions for this adsorption are not found in nature, as the TBC4 lattice undergoes a phase transformation to accommodate the increased loading, the Langmuir model should still fit the simulation data if the second CO2 molecules adsorbed in all 16 TBC4 molecules are identical and these CO2 molecules are not interacting. The inability of the Langmuir equation to fit the simulation data, especially evident at 200 K, indicates there is some CO2-CO2 interaction for this physically fictitious structure. The shape of the 200 K isotherm, with loading relative to a Langmuir isotherm that decreases at higher loading (and this
Figure 4. Calculated isotherms (solid circles) at various temperatures for CO2 in structure TBC4-H (a) and TBC4-L (b). The lines are fitted to the sum of two Langmuir isotherm models.
Figure 5. Calculated isotherms at 200 (red circles) and 300 (red squares) K for CO2 in structure TBC4-H and for a united atom representation of CH4 at 200 (blue circles) and 300 (blue squares) K.38
effect decreases with temperature), would arise in the periodic simulation lattice from entropic effects, indicating that at higher loadings there is some increased order in the CO2 structure coming from CO2-CO2 interactions. B. CH4 in TBC4. Figure 5 shows calculated isotherms for CO2 and a united atom representation of CH4 in TBC4-H at 200 and 300 K. The selectivity for CO2 is apparent and expected given the excellent fit in the TBC4 cage and the strong interaction of the oxygen in CO2 with the framework carbons. The entropy change upon adsorption is, as expected, much smaller for the spherical CH4 molecule compared with CO2, as
5768
J. Phys. Chem. B, Vol. 114, No. 17, 2010
evidenced in the smaller temperature shift for adsorption for CH4 compared with CO2. The CO2 absorption in the TBC4 cage has an entropy change >95% of the limit for going from the gas phase to totally immobilized. This would result in the largest possible temperature dependence for physisorption, and therefore a relatively lower energy for cycling the absorption process. The simulation results for the selectivity are consistent within the Gibbs free energies of adsorption in an earlier work.37 The calculated free energies for CO2 adsorption at cage sites are -7.1 and -5.4 kcal/mol at 200 and 300 K, respectively, and the corresponding values for CH4 adsorption are -5.8 and -4.4 kcal/mol. The free energy difference decreases with increasing temperature. The equilibrium CO2/CH4 ratios computed from the free energies are 5.6 and 26 at 300 and 200 K, respectively. Thus, the noninteracting gas assumption is a good approximation. The higher selectivity for CO2 over CH4 is predicted at low temperature and pressure. IV. Conclusion A rigid lattice simulation of CO2 absorption in TBC4-H can be modeled as the sum of two independent Langmuir processes. The higher binding energy cage sites fill completely before the interstitial sites begin to fill. Interaction between CO2 in different sites is minimal. The small cage size in TBC4 makes the configurational space for the absorbed molecule small, resulting in a very large negative entropy change upon absorption. Such a system therefore has a high degree of temperature dependence for absorption, which could be advantageous in some applications to reversibly sorb gases. The use of the interaction potentials from the AMBER package yields simulated absorption with higher binding than found experimentally at low pressure. Rescaling the well depth for the interaction between the absorbate and the framework carbons between 0.63 and 0.77 of the original potential brings the simulated absorption for loadings below 1:1 close to that found experimentally. However, even the original potentials dramatically underestimate binding for loadings greater than 1:1. On the basis of comparison with potentials used in other absorption systems with carbon based systems, the rescaling of the potentials based on the low loading experimental data appears justified, the process being consistent with how classical pair potentials are tuned in most systems. But the sign change and even larger discrepancy at high loadings that results from this tuning is inconsistent with the expected behavior of using classical potentials for simulating simple physisorption systems. This suggests that changes in the system studied volumetrically by Udachin et al.21 may be responsible for different behavior observed for loading in addition to the changes in absorption kinetics noted in that study. The simulation data suggest a reexamination of the experimental system may be illuminating. CH4 has a lower binding energy than CO2 in TBC4, and the entropy change upon absorption is less negative. The entropy change upon absorption increases selectivity at lower temperatures. The large negative entropy change for CO2 absorption is attractive for temperature driven absorption-desorption cycling. Acknowledgment. This work was performed at the Pacific Northwest National Laboratory (PNNL) and was supported by the Division of Chemical Sciences, Geosciences and Bio-
Daschbach et al. sciences, Office of Basic Energy Sciences, U.S. Department of Energy (DOE). PNNL is operated by Battelle for the DOE. We also gratefully acknowledge support received from the National Energy Technology Laboratory of DOE’s Office of Fossil Energy. References and Notes (1) Heuchel, M.; Davies, G. M.; Buss, E.; Seaton, N. A. Langmuir 1999, 15, 8695. (2) He, Y. F.; Seaton, N. A. Langmuir 2005, 21, 8297. (3) Goj, A.; Sholl, D. S.; Akten, E. D.; Kohen, D. J. Phys. Chem. B 2002, 106, 8367. (4) Jaramillo, E.; Chandross, M. J. Phys. Chem. B 2004, 108, 20155. (5) Eddaoudi, M.; Kim, J.; Rosi, N.; Vodak, D.; Wachter, J.; O’Keeffe, M.; Yaghi, O. M. Science 2002, 295, 469. (6) Yang, Q. Y.; Xue, C. Y.; Zhong, C. L.; Chen, J. F. AIChE J. 2007, 53, 2832. (7) Bae, Y. S.; Farha, O. K.; Spokoyny, A. M.; Mirkin, C. A.; Hupp, J. T.; Snurr, R. Q. Chem. Commun. 2008, 4135. (8) Bae, Y. S.; Mulfort, K. L.; Frost, H.; Ryan, P.; Punnathanam, S.; Broadbelt, L. J.; Hupp, J. T.; Snurr, R. Q. Langmuir 2008, 24, 8592. (9) Thallapally, P. K.; Tian, J.; Kishan, M. R.; Fernandez, C. A.; Dalgarno, S. J.; McGrail, P. B.; Warren, J. E.; Atwood, J. L. J. Am. Chem. Soc. 2008, 130, 16842. (10) Yang, Q. Y.; Zhong, C. L.; Chen, J. F. J. Phys. Chem. C 2008, 112, 1562. (11) He, Y. F.; Seaton, N. A. Langmuir 2006, 22, 1150. (12) Babarao, R.; Jiang, J. W. Energy EnViron. Sci. 2008, 1, 139. (13) Banerjee, R.; Phan, A.; Wang, B.; Knobler, C.; Furukawa, H.; O’Keeffe, M.; Yaghi, O. M. Science 2008, 319, 939. (14) Banerjee, R.; Furukawa, H.; Britt, D.; Knobler, C.; O’Keeffe, M.; Yaghi, O. M. J. Am. Chem. Soc. 2009, 131, 3875. (15) Ma, X. L.; Wang, X. X.; Song, C. S. J. Am. Chem. Soc. 2009, 131, 5777. (16) Wang, X. X.; Schwartz, V.; Clark, J. C.; Ma, X. L.; Overbury, S. H.; Xu, X. C.; Song, C. S. J. Phys. Chem. C 2009, 113, 7260. (17) Atwood, J. L.; Barbour, L. J.; Jerga, A.; Schottel, B. L. Science 2002, 298, 1000. (18) Thallapally, P. K.; McGrail, B. P.; Atwood, J. L.; Gaeta, C.; Tedesco, C.; Neri, P. Chem. Mater. 2007, 19, 3355. (19) Thallapally, P. K.; McGrail, B. P.; Dalgarno, S. J.; Schaef, H. T.; Tian, J.; Atwood, J. L. Nat. Mater. 2008, 7, 146. (20) Thallapally, P. K.; McGrail, P. B.; Dalgarno, S. J.; Atwood, J. L. Cryst. Growth Des. 2008, 8, 2090. (21) Udachin, K. A.; Moudrakovski, I. L.; Enright, G. D.; Ratcliffe, C. I.; Ripmeester, J. A. Phys. Chem. Chem. Phys. 2008, 10, 4636. (22) Gupta, A.; Chempath, S.; Sanborn, M. J.; Clark, L. A.; Snurr, R. Q. Mol. Simul. 2003, 29, 29. (23) Brouwer, D. H.; Moudrakovski, I. L.; Udachin, K. A.; Enright, G. D.; Ripmeester, J. A. Cryst. Growth Des. 2008, 8, 1878. (24) Enright, G. D.; Brouwer, E. B.; Udachin, K. A.; Ratcliffe, C. I.; Ripmeester, J. A. Acta Crystallogr., Sect. B: Struct. Sci. 2002, 58, 1032. (25) Jorgensen, W. L.; Buckner, J. K.; Boudon, S.; Tiradorives, J. J. Chem. Phys. 1988, 89, 3742. (26) Wang, J. M.; Wolf, R. M.; Caldwell, J. W.; Kollman, P. A.; Case, D. A. J. Comput. Chem. 2004, 25, 1157. (27) Daschbach, J. L.; Thallapally, P. K.; Atwood, J. L.; McGrail, B. P.; Dang, L. X. J. Chem. Phys. 2007, 127. (28) Daschbach, J. L.; Sun, X. Q.; Chang, T. M.; Thallapally, P. K.; McGrail, B. P.; Dang, L. X. J. Phys. Chem. A 2009, 113, 3369. (29) Alavi, S.; Afagh, N. A.; Ripmeester, J. A.; Thompson, D. L. Chem.sEur. J. 2006, 12, 5231. (30) Alavi, S.; Ripmeester, J. A. Chem.sEur. J. 2008, 14, 1965. (31) Gu, X.; Zhang, L.; Gong, X. A.; Lau, W. M.; Liu, Z. F. J. Phys. Chem. B 2008, 112, 14851. (32) Bojan, M. J.; Steele, W. A. Langmuir 1987, 3, 116. (33) Bojan, M. J.; Steele, W. A. Langmuir 1987, 3, 1123. (34) Jiang, J. W.; Sandler, S. I. J. Am. Chem. Soc. 2005, 127, 11989. (35) Babarao, R.; Hu, Z. Q.; Jiang, J. W.; Chempath, S.; Sandler, S. I. Langmuir 2007, 23, 659. (36) Myers, A. L.; Monson, P. A. Langmuir 2002, 18, 10261. (37) Daschbach, J. L.; Thallapally, P. K.; McGrail, B. P.; Dang, L. X. Chem. Phys. Lett. 2008, 453, 123. (38) Dalgarno, S. J.; Thallapally, P. K.; Barbour, L. J.; Atwood, J. L. Chem. Soc. ReV. 2007, 36, 236.
JP9101465
