Dioxide Is Facilitated In Narrow Carbon. Nanopores

Transcription

1 Displacement of Methane by Coadsorbed Carbon Dioxide Is Facilitated In Narrow Carbon Nanopores Piotr Kowalczyk *1, Piotr A. Gauden 2, Artur P. Terzyk 2, Sylwester Furmaniak 2, and Peter J.F. Harris 3 [1] Nanochemistry Research Institute, Department of Chemistry, Curtin University of Technology, P.O. Box U1987, Perth, 6845 Western Australia, Australia [2] Department of Chemistry, Physicochemistry of Carbon Materials Research Group, N. Copernicus University, Gagarin St. 7, Torun, Poland [3] Centre for Advanced Microscopy, University of Reading, Whiteknights, Reading RG6 6AF, UK Corresponding author footnote (*To whom correspondence should be addressed): Dr Piotr Kowalczyk Tel: Piotr.Kowalczyk@curtin.edu.au 1

2 Number of pages: 9 Number of Figures: 3 2

3 IS. CO 2 -CH 4 force field and Lorentz-Berthelot mixing rules The interactions between CO 2 and CH 4 (i.e., cross-interaction parameters) were calculated using the Lorentz-Berthelot (LB) mixing rules: σ 12 = (σ 11 + σ 22 )/2 ε 12 = (ε 11 ε 22 ) 1/2 (1S) (2S) For example, the (12,6) Lennard-Jones potential parameters describing dispersion interactions between O(in CO 2 ) and H(in CH 4 ) are give by: σ 12 = ( )/2 = (Å) (3S) ε 12 = ( ) 1/2 = (K) (4S) Similarly, LB mixing rule was used for the computation of the CO 2 -C and CH 4 - C interactions. As previously, for carbon atoms, we used (12,6) Lennard-Jones parameters from Steele s work: σ = 3.4 (Å), ε / k B = 28.0 (K). Note that these parameters were optimized for graphite flat surface. It is expected that ε / k B is higher for curved graphite sheets because of the polarization of adsorbed molecules. However, we would like to stress, that for studied adsorbates this effect should be negligible (CH 4 and CO 2 are nonpolar molecules). Notice that the LB mixing rule is not perfect method to compute the intermolecular interactions between CO 2 -CH 4 /CH 4 -C/CO 2 -C. Clearly, the best way to get accurate intermolecular forces is to combine various experimental data with the first-principle calculations. We argue that the methods of quantum mechanics without the extensive experimental data cannot correctly describe the CO 2 -CH 4 /CH 4 -C/CO 2 -C intermolecular interactions at studied operating conditions (i.e., for dense adsorbed phases). First, to get an accurate force field 3

4 between pair of studied molecules we need to have the first-principle method that treat the weak van der Waals interactions with high accuracy. Therefore, density functional methods (DFT) are not good candidates. Møller Plesset perturbation theory (MP-like methods) or coupled cluster calculations seem to be good candidates, but they are expensive. Second, the accurate potential surface between pair of molecules (i.e., for dilute gas phase) is not enough to correctly describe dense fluids. In condensed phases, we need to add multi-body interactions that are very difficult to compute. That is why we need the set of experimental data in condensed phases. Third, the properties of adsorbed molecules, here CO 2 and CH 4, more precisely the mutual interactions between them, may be affected by the presence of the solid atoms. Simply, the third body always affects the geometry of the adsorbed molecules. The question is whatever this effect can be neglected. Therefore, the used LB mixing rule is a compromise between the lack of the experimental data and the high computational cost of quantum calculations. Nevertheless, we would like to point out that LB mixing rule is not a sole of the studied phenomenon. The interactions between CO 2 -CH 4 /CH 4 -C/CO 2 -C are attractive. The question is only about their strength. They can be lower/higher than that computed from the LB mixing rule. Fluid-fluid and solid-fluid intermolecular forces scale the amount of coadsorbed fluid. Therefore, the studied phenomenon is qualitatively the same for stronger/weaker intermolecular interactions. 4

5 IIS. Virtual Porous Carbons Virtual porous carbons (VPCs) are computer-generated structures of real porous carbons. Their internal structures were elucidated from extensive experimental observations and experiments. Opposed to classical slit-shaped model of porous carbons, VPCs consist of curved graphene fragments arranged in threedimensional carbon network. Type and number of curved graphene fragments controls the porosity of VPCs. By providing more realistic representation of porous structures, VPCs allow to elucidate the fundamentals of fluids or fluid mixtures adsorbed in nano-scale confinement. In the current work we studied two samples of Harris s VPCs (see Fig. 1S and 2S). The nitrogen adsorption isotherms on S00 and S24 carbon samples computed from GCMC method at 77 K are presented in Fig. 3S. 5

6 Fig. 1S. The S00 Harris virtual porous carbon sample studied in the current work. The average pore size computed from the method of Bhattacharya and Gubbins 1 (see Fig. 10 in the main article) is 1.25 nm, whereas the carbon density is 1.28 g cm -3. The method of construction of the S00 carbon sample is described in Reference 2,3. 6

7 Fig. 2S. The S24 Harris virtual porous carbon sample studied in the current work. The average pore size computed from the method of Bhattacharya and Gubbins (see Fig. 10 in the main article) is 0.7 nm, whereas the carbon density is 1.25 g cm -3. The method of construction of the S24 carbon sample is described in Reference 2,3. 7

8 Fig. 3S. Nitrogen (N 2 ) adsorption isotherm on S00 and S24 carbon sample simulated from GCMC algorithm at 77 K (top panel). The bottom panel presents the variation of the molar enthalpy of N 2 adsorption with the absolute value of N 2 adsorption at 77 K computed from GCMC algorithm. Note the reduction of the adsorption capacity and the enhanced molar enthalpy of N 2 adsorption for sample S24 as compared to S00 one. The presence of smaller micropores in sample S24 is responsible for the observed regularities (see Figure 10 in the main article). 8

9 References (1) Bhattacharya, S.; Gubbins, K. E. Langmuir 2006, 22, (2) Terzyk, A.P.; Furmaniak, S.; Harris, P. J. Gauden, P. A.; Wloch, J.; Kowalczyk, P.; Rychlicki, G. Phys. Chem. Chem. Phys. 2007, 9, (3) Terzyk, A. P.; Furmaniak, S.; Gauden, P. A.; Harris, P. J. F.; Wloch, J.; Kowalczyk, P. J. Phys.: Condens. Matter 2007, 19,