Molecular simulation of multi-component adsorption

processes related to carbon capture in a high surface area,

disordered activated carbon

Emanuela Di Biase and Lev Sarkisov *

1 Institute for Materials and Processes, School of Engineering, The University of

Edinburgh, EH9 3JL, UK

We employ a previously developed model of a high surface area activated carbon,

based on a random packing of small fragments of a carbon sheet, functionalized with

hydroxyl surface groups, to explore adsorption of water and multicomponent mixtures

under conditions representing typical carbon capture processes. Adsorption of water is

initialized and proceeds through the growth of clusters around the surface groups, in a

process predominantly governed by hydrogen bond interactions. In contrast,

energetically favorable locations for carbon dioxide molecules are different from that

for water, with the main contribution coming from the Lennard-Jones interactions

with the extended surfaces of the fragments. This explains why over a broad range of

conditions small amounts of water do not have any substantial impact on adsorption

of carbon dioxide and other species in activated carbons. From the studies of various

carbon capture processes, the model material shows promising properties for pre-

combustion capture due to large capacity at high pressures and other favorable

characteristics.

* Corresponding author: e-mail address: Lev.Sarkisov@ed.ac.uk

SI1

Supplemental Data

Contents

1. Simulation details SI3

2. Details of the molecular forcefield SI4

3. Comparison of the Ewald summation and Fennell-Gezelter methods

for fluid-fluid electrostatic interactionsSI6

4. On the consistency of the micropore volume obtained from the

computational Helium porosimetry and from a nitrogen adsorption

isotherm at 77K using the Dubinin-Radushkevich (DR) method

SI7

5. Comparison of the nitrogen adsorption isotherms at 77K for a sample

of Maxsorb MSC-30 in this work and SAC31 by Miyawaki et alSI10

6. Full sets of isotherms for all the separations not involving water

presented in the workSI11

7. Application of alternative carbon-hydrogen potentials to the

simulation of the binary mixture CO2/H2

SI15

8. Application of Ideal Adsorbed Solution Theory (IAST) on the binary

mixturesSI17

9. Dew pressure at 313 K as a function of water content in gaseous

mixturesSI20

10. Geometric pore size distribution SI21

11. References SI23

SI2

1. Simulation details

Grand Canonical Monte Carlo (GCMC) simulations were carried using the MuSiC

simulation package [1]. Lennard-Jones (LJ) interactions between different atoms were

evaluated through the standard Lorentz-Berthelot mixing rules. Coulombic

interactions between partial charges were calculated using the Ewald summation

method in the case of the solid-fluid interactions [2] and the Fennell-Gezelter (FG)

method based on a spherically truncated summation [3] in the case of the fluid-fluid

interactions. Further details are summarized in table S1.

Table S1. Details of the GCMC simulations.

Iterations (mixtures) 20·106 - 40·106

Iterations (single component water) 300·106 - 900·106

Cut-off (Å) 13 (no tail corrections)

Type of moves

Insertion, deletion,

translation, rotation (for

non-spherical species)

Weight of each type of move 0.25, 0.25, 0.25, 0.25

Iterations used for equilibration 50%

Iterations used for statistical sampling 50%

α and shield parameters for the FG method 0.1, 1.0

KMAX (number of unit cell images in the reciprocal space), κ

(parameter related to the width of the Gaussian function, see

http://www.iec.northwestern.edu/Music/electrostatic/electrostatic.htm)

for the Ewald method

15, 6.7

xyz dimensions of the unit cell in the platelet models (Å) 60.0, 60.0, 60.0

Angles of the unit cell (º) 90.0, 90.0, 90.0

SI3

2. Details of the molecular forcefield

Atom types involved in the construction of a platelet fragment and the corresponding

Lennard-Jones parameters are summarized in table S2. Partial charges have been

calculated using the B3LYP Density Functional Theory method [4], with 6-31g basis

set and CHELPG charge analysis [5] with the Gaussian 09 software package [6].

Table S2. Atom types associated with the platelet, and the corresponding Lennard-

Jones parameters from Tenney and Lastoskie [7].

ATOM σ (Å) ε/kB (K)

C (aromatic) 3.4 28.0

C (aromatic, C-H) 3.4 28.0

C (aromatic, C-OH) 3.4 28.0

C (aromatic, C-COOH) 3.4 28.0

H (H-C) 2.4 12.0

O (hydroxylic) 3.1 79.0

H (hydroxylic) 1.3 30.0

All adsorbate species are treated in this work as either simple fluids (represented with

one Lennard-Jones particle) or rigid molecules. Table S3 reports structural parameters

of rigid molecular species. Table S4 reports Lennard-Jones parameters and charges

for adsorbate models.

SI4

Table S3. Bond lengths and bond angles for the molecular models of adsorbate

species. Here and throughout the SI file, F stands for a fictitious particle bearing a

partial charge but no mass.

Molecule Bond length (Å) Bond angle (°) Reference

CO2 (C-O) 1.16 (O-C-O) 180 [8]N2 (N-N) 1.1 (N-F-N) 180 [8]O2 (O-O) 1.21 (O-F-O) 180 [9]H2S (H-S) 1.34 (H-S-H) 92.5 [10]CO (C-O) 1.12 - [11]H2O (TIP4P) (H-O) 0.9572 (H-O-H) 104.52 [12]H2O (TIP4P) (F-O) 0.15 - [12]

Table S4. Lennard-Jones parameters and charges associated with the models of

adsorbate species.

Site σ (Å) ε/kB (K) Charge (e) Reference

C (CO2) 2.800 27.00 0.7000 [8]

O (CO2) 3.050 79.00 -0.3500 [8]

CH4 3.730 148.00 0.0000 [13]

N (N2) 3.310 36.00 -0.4820 [8]

F (N2) 0.000 0.00 0.9640 [8]

H2 2.960 34.20 0.0000 [14]

O (O2) 3.020 49.00 -0.1130 [9]

F (O2) 0.000 0.00 0.2260 [9]

S (H2S) 3.720 232.00 -0.3800 [10]

H (H2S) 0.000 0.00 0.1900 [10]

C (CO) 3.490 22.80 0.0203 [11]

O (CO) 3.130 63.50 -0.0203 [11]

O (H2O) 3.154 78.00 0.0000 [12]

SI5

H (H2O) 0.000 0.00 0.5200 [12]

F (H2O) 0.000 0.00 -1.0400 [12]

3. Comparison of the Ewald summation and Fennell-Gezelter methods for fluid-

fluid electrostatic interactions

Here we assess the effect of using the approximate Fennell-Gezelter method for

electrostatic fluid-fluid interactions on the accuracy of the adsorption isotherms. The

reference results are obtained using the Ewald summation method. Solid-fluid

electrostatic interactions are pre-calculated using the Ewald summation in all cases.

As a case study, we consider adsorption of water at 298K, since any inaccuracy in

treating polar interactions should strongly manifest itself in this system.

SI6

Fig. S1. TIP4P water adsorption isotherms in Maxsorb MSC-30 model (number of

molecules per simulation cell as a function of fugacity, kPa) at 298K. White squares

are for the Fennell-Gezelter method and black squares are from the reference

simulation based on the Ewald summation.

As can be seen from Fig. S1 above, there are some differences in loading density

between the two methods, particularly near the capillary condensation transition. In

both cases substantial equilibration times were required (up to 900·106 Monte Carlo

moves). Within the current implementation of MuSiC, the FG method performed

better from the computational efficiency perspective (in some cases reaching up 30

times speed up). Given a substantial computational cost associated with the currently

available Ewald code, the differences of the magnitude shown in Fig. S1 were deemed

acceptable and all fluid-fluid calculations the FG method was used. We note here, that

our previous comparisons of the two methods for polar species such as carbon dioxide

showed very good agreement.

4. On the consistency of the micropore volume obtained from the computational

Helium porosimetry and from a nitrogen adsorption isotherm at 77K using the

Dubinin-Radushkevich (DR) method

The current philosophy of building molecular models of high surface area activated

carbons is based on capturing their key structural characteristics, such as surface area

and pore volume. To calculate the pore volume, here we use computational Helium

porosimetry, as described by Talu and Myers [15]. The experimental micro and

mesopore volume are however more often obtained from the nitrogen adsorption

isotherm at 77K. Here we show that for models of microporous structures the

SI7

computational Helium porosimetry and the Dubunin-Radishkevich method applied to

the simulated nitrogen adsorption isotherm give consistent results for the micropore

volume.

The systems we are now considering are based on packings of respectively coronene

(CR) platelets, considered in our previous work [16] and with properties summarized

in Table S5, and corannulene platelets featuring two hydroxilic groups (CRNL(OH)2)

(current model).

Table S5. Characteristics of the model structure based on coronene platelets (CR)

[16], compared to the experimentally measured properties of Maxsorb MSC-30

(MSC-30). In this table, S.A. is the surface area, Vmicro is the micropore volume, kH is

the Henry’s constant of adsorption and C/O is the carbon to oxygen ratio (in weight)

in the material.

SYSTEM S.A. Vmicro, 298 K kH CH4, 298 K kH CO2, 298 K C/O

m2/g cm3/g mol/kg/Bar mol/kg/Bar

CR 3428.8 1.24 0.51 2.00 -

MSC-30 3000 - 3500 1.3 – 1.7 1.3 – 1.9 2.4 7.8

These systems are here considered as representative of all systems based on non-

curved platelets (CR model) and systems based on structural elements featuring

curvature respectively. Figure S2 shows the DR plots for CR (graph (a)) and CRNL

(OH)2 models (graph (b)).

SI8

0 1 2 30.03

0.06

0.09lo

g V

log2(p0/p) (a)0 1 2 3 4 5

0.00

0.03

0.06

0.09

log

V

log2(p0/p) (b)

Figure S2. DR plots for the systems (a): CR and (b): CRNL-(OH)2. V here is the

adsorbed amount in cm3/g.

In the case of CR model the application of the DR method gives a value of micropore

volume of 1.21 cm3/g, which is very close to the value of 1.24 cm3/g, calculated using

He as a probe. In the case of CRNL(OH)2 (current model of Maxsorb) the micropore

volume calculated using the DR method is 1.19 cm3/g, while from the computational

Helium porosimetry it is 1.28 cm3/g. In this case, given the curvature of the elements,

the graphitic carbon-He ε parameter has been scaled by a factor 1.23, according to the

protocol adopted for all non-polar adsorptive species when simulating adsorption

using CRNL(OH)2 model. The agreement between the two values of micropore

volume can still be considered reasonable. Without applying any scaling factor to the

solid-fluid interaction, the result becomes 1.18 cm3/g from the Helium porosimetry,

which is much closer to the value calculated using the DR method. This might suggest

that in the case of Helium a scaling factor may not be required. Nevertheless, the

problem would need to be further investigated. The difference between the two

different values calculated for the micropore volume has proved not to be sufficient to

cause any noticeable difference in the excess adsorption isotherms.

SI9

5. Comparison of the nitrogen adsorption isotherms at 77K for a sample of

Maxsorb MSC-30 in this work and SAC31 by Miyawaki et al [17]

0.0 0.2 0.4 0.6 0.8 1.00

10

20

30

40

50

60

Ads

orpt

ion

(mm

ol/g

)

Relative pressure p/po

Fig. S3. Experimental excess adsorption isotherms for nitrogen at 77K for Maxsorb

MSC-30 material (this work, black triangles) and for SAC31 sample from Miyawaki

et al [17] (white triangles).

From figure S3 it is clear that nitrogen adsorption isotherms for two samples of

Maxsorb material (MSC-30 in this work and SAC31 from Miyawaki and co-workers)

are slightly different. This can be due to the actual material property variations from

sample to sample, sample degassing protocol, differences in the equilibration time.

Interestingly, according to the figure S3, the total pore volume of the SAC31 sample

should be about 15% lower compared to MSC-30 in this work; however, water

adsorption isotherms presented in the main article follow the reverse trend, with the

isotherm published by Miyawaki et al [17] reaching the plateau at higher loadings

compared to the simulation predictions for MSC-30 in this work.

SI10

6. Full sets of isotherms for all the separations not involving water presented in

the work

In this section we present the full set of adsorption isotherms involved in the CO2

separation from the mixtures examined in this study and not containing water.

6.1 Post-combustion case

0.0 0.2 0.4 0.6 0.8 1.0 1.20.00

0.05

0.10

0.15

0.20

Total pressure (Bar)

A

dsor

ptio

n (m

mol

/g)

(b)0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Total pressure (Bar)

Ads

orpt

ion

(mm

ol/g

)

(a)

Fig. S4. Simulated adsorption isotherms for the binary mixtures of molar composition

CO2/N2=50/50 (graph (a)) and CO2/N2=10/90 (graph (b)) at 323 K. Circles: carbon

dioxide; triangles: nitrogen.

SI11

0.00

0.05

0.10

0.15

0.20

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Ads

orpt

ion

(mm

ol/g

)

Total pressure (Bar)Fig. S5. Simulated adsorption isotherms for the ternary mixture of molar composition

CO2/N2/O2=15/80/5 at 323 K. Circles: carbon dioxide, triangles: nitrogen; crosses:

oxygen.

6.2 Pre-combustion case

0 10 20 30 40 50 60-202468

1012141618

Total pressure (Bar) (a)

A

dsor

ptio

n (m

mol

/g)

0 10 20 30 40 50 60-202468

1012141618

Total pressure (Bar)

A

dsor

ptio

n (m

mol

/g)

(b)

SI12

Fig. S6. Simulated excess adsorption isotherms for the binary mixtures of molar

composition CO2/H2=50/50 (graph (a)) and CO2/H2=40/60 (graph (b)) at 313 K.

Circles: carbon dioxide; diamonds: hydrogen.

0 10 20 30 40 50 60

0

4

8

12

16

Ads

orpt

ion

(mm

ol/g

)

Total pressure (Bar) (a)0 10 20 30 40 50 60

0

4

8

12

16

Ads

orpt

ion

(mm

ol/g

)

Total pressure (Bar) (b)

Fig. S7. Simulated adsorption isotherms for the ternary mixture of molar composition

CO2/H2/H2S=39/60/1 (graph (a)) and CO2/H2/H2S/CO=38/60/1/1 at 313 K. Circles:

carbon dioxide; diamonds: hydrogen; empty squares: hydrogen sulphide; stars: carbon

monoxide.

0 10 20 30 40 50 60-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

Ads

orpt

ion

(mm

ol/g

)

Total pressure (Bar) (a)0 10 20 30 40 50 60

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

Total pressure (Bar)

Ads

orpt

ion

(mm

ol/g

)

(b)

Fig. S7_exp. Expanded version of figure S7 with a focus on minor components.

Simulated adsorption isotherms for the ternary mixture of molar composition

SI13

CO2/H2/H2S=39/60/1 (graph (a)) and CO2/H2/H2S/CO=38/60/1/1 at 313 K. Diamonds:

hydrogen; empty squares: hydrogen sulphide; stars: carbon monoxide.

0 10 20 30 400

4

8

12

16

Total pressure (Bar)

Ads

orpt

ion

(mm

ol/g

)

(a)-0.35

0.00

0.35

0.70

0 10 20 30 40A

dsor

ptio

n (m

mol

/g)

(b)Total pressure (Bar)

Fig. S8. (a) Excess adsorption isotherms for the mixture

CO2/H2/CO/H2S/H2O=38.8/59/1/1/0.2 at 313 K. Filled circles are for CO2, diamonds

are for H2, stars are for CO, empty squares are for H2S, empty circles are for H2O

(figure 14 in the main text). (b) Expanded version of graph (a) (carbon dioxide data is

not shown)

6.3 Sweetening of sour natural gas

0 20 40 60 8002468

1012141618

Total pressure (Bar)

A

dsor

ptio

n (m

mol

/g)

(a)0 20 40 60 80

02468

1012141618

Ads

orpt

ion

(mm

ol/g

)

Total pressure (Bar) (b)

SI14

Fig. S9. Simulated adsorption isotherms for the binary mixtures of molar composition

CO2/CH4=50/50 (graph (a)) and CO2/CH4=15/85 (graph (b)) at 288 K. Circles: carbon

dioxide, squares: methane.

7. Application of alternative carbon-hydrogen potentials to the simulation of the

binary mixture CO2/H2

Following the results presented in our last publication [16] we now apply two

different carbon-hydrogen potentials to the simulation of the carbon dioxide/hydrogen

mixture with molar composition 40/60 at 313 K and pressures up to 55 Bar (pre-

combustion conditions). The two potentials, called here respectively Potential 1 and

Potential 2, are described below and have already been explored in our last

publication [16], following the work by Nguyen and co-workers [18].

Potential 1: this is the potential applied in the article. Hydrogen is represented using

the spherical model by Buch [14], while for graphitic carbon the parameters listed in

Table S2 are applied. The solid-fluid ε (epsilon) calculated using the standard

Lorentz-Berthelot mixing rules is scaled by the factor 1.23 adopted in the present

work [16].

Potential 2: hydrogen is represented using a spherical model with the Lennard-Jones

parameters taken from Levesque et al. (σH-H = 2.958 Å and εH-H/kB = 36.7 K) [19],

which provide an excellent agreement between the simulated bulk isotherms and

corresponding reference data at or above 77 K. The carbon-hydrogen interaction is

estimated from the solid-fluid parameters determined by Wang et al. [20] for the

graphite-H2 interaction (σC-H = 2.97 Å and εc-H/kB = 42.75 K) based on the fit of the

SI15

theoretical quantum mechanical energy spectrum of hydrogen on graphite with its

experimental counterpart measured by scattering methods. Nguyen et al. [18] further

scale this epsilon by 1.134 (and the same scaling is applied to all other solid-fluid

epsilon parameters to take the curvature of surfaces into account). We scale the

parameters of Wang et al. [20] by 1.23 adopted throughout this work. A list of the

carbon-hydrogen parameters used for the two different types of potential is presented

in Table S6.

Table S6. Parameters for carbon-hydrogen Lennard-Jones interaction used in the

present study.

σC-H (Å) εC-H/kB (K) Type of potential

3.18 38.06 Potential 1

2.97 52.58 Potential 2

The results of the simulations are presented in Fig. S10.

SI16

0 10 20 30 40 50 60-202468

10121416

Total pressure (Bar)

Ads

orpt

ion

(mm

ol/g

)

Fig. S10. Simulated adsorption isotherms for the binary mixture of molar composition

CO2/H2=40/60 at 313 K (pre combustion conditions) on the model for Maxsorb MSC-

30. The solid-fluid potentials which have been applied are respectively Potential 1

(black symbols) and Potential 2 (white symbols) as described earlier in this section.

It is clear from the figure above that the two different solid-fluid potentials give very

similar results. In particular, negative adsorption for hydrogen is observed in both

cases, and therefore it is not related to the particular model adopted for hydrogen.

8. Application of Ideal Adsorbed Solution Theory (IAST) on the binary mixtures

Here present the results of the application of IAST to the main separations involved in

the CO2 capture processes and compare them with the results of the direct simulation

of the mixtures. In all cases the results of IAST are represented using empty symbols,

while the results of the direct simulations are shown as filled symbols.

SI17

Fig. S11 shows data for the equimolar binary mixture CO2/N2 (graph (a)) and for the

mixture of molar composition 10/90 (graph (b)), both in post-combustion conditions.

Fig. S12 and Fig. S13 show results for pre-combustion and sweetening of sour natural

gas conditions respectively. Similarly to Fig. S11, in both cases graphs (a) show

results for the equimolar mixture, while graphs (b) show results for a more realistic

composition: for Fig. S12 this is CO2/H2 = 40/60 and for Fig. S13 this is CO2/CH4 =

15/85.

0.0 0.2 0.4 0.6 0.8 1.0 1.20

2

4

6

8

10

12

Mol

ecul

es/u

nit c

ell

Total pressure (Bar) (b)0.0 0.2 0.4 0.6 0.8 1.0 1.20

10

20

30

40

Mol

ecul

es/u

nit c

ell

Total pressure (Bar) (a)

Fig. S11. Comparison between the results of IAST (empty symbols) and the results of

the direct simulation (filled symbols) of the binary mixtures CO2/N2=50/50 (graph (a))

and CO2/N2 = 10/90 (graph (b)) at 323 K. Circles represent carbon dioxide and

triangles represent nitrogen.

SI18

0 10 20 30 40 50 600

260

520

780

1040

1300

Total pressure (Bar)

Mol

ecul

es/u

nit c

ell

(a)0 10 20 30 40 50 60

0

260

520

780

1040

1300

Mol

ecul

es/u

nit c

ell

Total pressure (Bar) (b)

Fig. S12. Comparison between the results of IAST (empty symbols) and the results of

the direct simulation (filled symbols) of the binary mixtures CO2/H2=50/50 (graph (a))

and CO2/H2 = 40/60 (graph (b)) at 313 K. Circles represent carbon dioxide and

diamonds represent hydrogen.

0 20 40 60 800

260

520

780

1040

1300

Total pressure (Bar)

Mol

ecul

es/u

nit c

ell

(a)0

200

400

600

800

1000

0 20 40 60 80

Mol

ecul

es/u

nit c

ell

Total pressure (Bar) (b)Fig. S13. Comparison between the results of IAST (empty symbols) and the results of

the direct simulation (filled symbols) of the binary mixtures CO2/CH4=50/50 (graph

(a)) and CO2/CH4 = 15/85 (graph (b)) at 288 K. Circles represent carbon dioxide and

squares represent methane.

From the figures above it is clear that for the separations under consideration IAST

agrees very well with the direct simulations of the mixtures. We can only notice a

SI19

slight deterioration in the accuracy at the highest pressures, at which the

dissimilarities of the adsorbate molecules may have a more important effect.

In the case of the binary mixtures containing water IAST cannot be successfully

applied, because in the ranges of pressure under consideration water as a single

component would condense.

9. Dew pressure at 313 K as a function of water content in gaseous mixtures.

Table S7.

Water molar %Dew point of

the mixture (Bar) at 313 K

0.1 73.3

0.2 36.6

0.5 14.6

0.75 9.8

1 7.3

10. Geometric pore size distribution

SI20

The geometric pore size distribution has been determined using the package

Poreblazer 1.2 (15). The parameters involved in the calculation are presented in Table

S9.

Table S8. Parameters involved in the determination of the geometric pore size

distribution.

Smallest probe diameter (Å) 0.2

Probe diameter increment (Å) 0.2

Maximum probe diameter (Å) 30.0

The geometric pore size distribution determined for the final model for Maxsorb

developed in this work is presented in Fig. S3.

0 5 10 15 20 25 300.00

0.05

0.10

0.15

0.20

0.25

Pore diameter, d (Å)

dV(d

)/dd

(cc/

Å/g

)

Fig. S14. Geometric pore size distribution for the model for Maxsorb MSC-30

activated carbon developed in the present work.

SI21

The pore size distribution appears to be centered around values of pore diameters of

about 5 – 7.5 Å. This value is smaller than the typical values of ~20 Å experimentally

determined through the adsorption of nitrogen at 77 K (16), (17).

This result is not surprising as the model developed in this work does not take into

account the mesoporosity of the sample. In principle, the model can be further

modified to introduce the actual mesopores in the structure. One way of doing it

would be to enlarge the system in one dimension without adding any graphitic

fragments in the extra space. In periodic boundary conditions, this would introduce

slit-like pores of certain width in the model, and this may result in the reconciliation

of the pore size distributions. Preliminary calculations have shown that this would

have only a minor effect on the simulated adsorption isotherms for methane and

carbon dioxide at ambient temperatures.

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11. References

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