Displacement of Methane by Coadsorbed Carbon
Dioxide Is Facilitated In Narrow Carbon
Nanopores
Piotr Kowalczyk*1, Piotr A. Gauden2, Artur P. Terzyk2, Sylwester Furmaniak2,
and Peter J.F. Harris3
[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, 87-100 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: +61 8 9266 7800
E-mail: [email protected]
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Number of pages: 9
Number of Figures: 3
2
IS. CO2-CH4 force field and Lorentz-Berthelot mixing rules
The interactions between CO2 and CH4 (i.e., cross-interaction parameters) were
calculated using the Lorentz-Berthelot (LB) mixing rules:
σ 12 = ( σ 11 + σ 22 )/2
ε12 = ( ε11 ⋅ ε22 )
(1S)
1/2
(2S)
For example, the (12,6) Lennard-Jones potential parameters describing
dispersion interactions between O(in CO2) and H(in CH4) are give by:
σ 12 = ( 3.026 + 2.65)/2 = 2.838 (Å)
(3S)
1/2
(4S)
ε12 = ( 82.0 ⋅ 7.901 )
= 25.4535
(K)
Similarly, LB mixing rule was used for the computation of the CO2-C and CH4C interactions. As previously, for carbon atoms, we used (12,6) Lennard-Jones
parameters from Steele’s work: σ = 3.4 (Å), ε / kB = 28.0 (K). Note that these
parameters were optimized for graphite flat surface. It is expected that ε / kB 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 (CH4 and CO2 are nonpolar molecules).
Notice that the LB mixing rule is not perfect method to compute the
intermolecular interactions between CO2-CH4/CH4-C/CO2-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
CO2-CH4/CH4-C/CO2-C intermolecular interactions at studied operating
conditions (i.e., for dense adsorbed phases). First, to get an accurate force field
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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 CO2 and CH4, 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 CO2-CH4/CH4-C/CO2-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
intermolecular interactions.
4
the
same
for
stronger/weaker
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.
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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
Gubbins1 (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.
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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.
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Fig. 3S. Nitrogen (N2) 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 N2 adsorption with the absolute value of
N2 adsorption at 77 K computed from GCMC algorithm. Note the reduction of
the adsorption capacity and the enhanced molar enthalpy of N2 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).
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References
(1) Bhattacharya, S.; Gubbins, K. E. Langmuir 2006, 22, 7726-7731.
(2) Terzyk, A.P.; Furmaniak, S.; Harris, P. J. Gauden, P. A.; Wloch, J.;
Kowalczyk, P.; Rychlicki, G. Phys. Chem. Chem. Phys. 2007, 9,
5919-5927.
(3) Terzyk, A. P.; Furmaniak, S.; Gauden, P. A.; Harris, P. J. F.; Wloch,
J.; Kowalczyk, P. J. Phys.: Condens. Matter 2007, 19, 406208406224.
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