Electronic Supplementary Material
The influence of geometric heterogeneity of
closed carbon nanotube bundles on benzene
adsorption from the gaseous phase - Monte
Carlo simulations
Piotr A. Gauden(*)1, Sylwester Furmaniak1, Jerzy Włoch2, Artur P. Terzyk1,
Wojciech Zieliński1, Piotr Kowalczyk3, Justyna Kurzawa1
(1) Faculty of Chemistry, Physicochemistry of Carbon Materials Research Group, Nicolaus
Copernicus University in Toruń, Gagarin Street 7, 87-100 Toruń, Poland
(2) Faculty of Chemistry, Synthesis and Modification of Carbon Materials Research Group,
Nicolaus Copernicus University in Toruń, Gagarin Street 7, 87-100 Toruń, Poland
(3) School of Engineering and Information Technology, Murdoch University, Murdoch 6150
WA, Australia.
Number of pages: 9
Number of Figures: 4
Number of Tables: 1
1
The separation of monolayer
In order to discuss the position and orientation of benzene molecules towards to the
CNT surface, the monolayer should be separated from total adsorption. Thus, C 6H6 molecule
is in the monolayer if the distance between its center and carbon atoms of CNT is smaller than
the critical value, crit,mono. In the current studies this value is obtained from the analysis of
45 000 representative equilibrium configurations simulated using the hyper parallel tempering
Monte Carlo method for each point of the adsorption isotherm. The investigations are limited
only to the exposed space of the peripheral tubes (Fig. S1(a)). This assumption is adopted to
avoid the influence of two neighboring CNTs on the properties of the adsorbed phase of the
selected nanotube. For arbitrarily chosen but representative points of adsorption isotherms
(Table S1) molecular densities (ρN) are calculated as the function of the distance of the center
of the ring plane to the center of nanotube axis, r. The respective curves are compared in Fig.
6. As it is expected the results show that all studied systems are characterized by essentially
the same external solvation structures for the exposed space regardless of the separation
distance between tubes. For all the systems, ρN(r) vs. r curves exhibit distinctive cylindrical
shell-like distributions, of which the first minimum is located at ~ 0.6 nm from the exterior
wall (or ~ 1.15 nm from the tube axis). It should be noted that crit,mono = 0.6 nm is
comparable with empirically value estimated by us previously from the observation of special
animations of adsorption with marked atoms in the monolayer, however, for significantly
wider nanotubes and graphite structure (Furmaniak et al. 2009).
The division in adsorption space
It is evident, that concentration of benzene molecules changes with the distance from the
center of any particular nanotube. Concentration inside the system (between CNTs) is
different than that outside the bundle, however, in contact with the tube wall. In the other
words in the exposed space of the system the behavior of benzene particles seems to be
independent on the distance between nanotubes in a bundle. Moreover, the properties of these
C6H6 molecules will be probably similar to those for isolated nanotubes. In order to separate
the mentioned above two regions for each nanotube some arbitrary assumptions should be
used. There is clear borderline between internal and exposed space due to Lbox,x   Lbox,y
(Table 1). First of all it is easy to divide radial matrixes into three separated parts taking into
account the half distance between the centers of two neighboring tubes (see Fig. S1(b) - dark
2
green lines). Additionally, in this figure bright green dashed circles represent the range of the
monolayer for crit,mono = 0.6 nm. After the intersection of dark green lines, the first origin of a
line segment is obtained. The second origin is the center of the given tube. Connection of
these points determines the intertubular space (red lines). In that way we obtain two regions pink area (exposed, interbundle) from the center of nanotube projection to the bulk and
yellow region (space between nanotubes surfaces (intertubular)) remaining “inner” part as
shown in Fig. S1(b). Consequently, the internal pore volume of the bundle comprises
interstitial channel and grooves (sites (ii) and (iii) in Fig. S1(a), respectively). Site (iv) in Fig.
S1(a), i.e. the external surface of the bundle, can be attributed to the exposed space of the
peripheral tubes.
Entropy of the adsorbed phase
It is well known that the difference in Gibbs free energy between the adsorbed phase
(at the given equilibrium pressure – p) and the gaseous phase at standard pressure (po) is given
by the basic thermodynamic equation (Ross and Olivier 1964):
G  RT ln
p
po
(S1)
On the other hand, there are two factors whose balance determines the changes in free energy:
enthalpy (ΔH) and entropy (ΔS):
G  H  T S
(S2)
The difference in enthalpy between the adsorbed and bulk phases is related to the isosteric
enthalpy of adsorption:
H  q st
(S3)
3
The negative sign is a consequence of the generally accepted signing convention. The
combining of Eqs. (S1) - (S3) allows calculating the difference in entropy between the
adsorbed phase and the gaseous one:
S  
q st
p
 R ln o
T
p
(S4)
Since
S  Sa  S go
(S5)
where Sa and S go are the entropies of the adsorbed and gaseous phase, respectively, entropy of
benzene adsorbed at the given pressure may be calculated from the formula:
S a  S go 
q st
p
 R ln o
T
p
(S6)
4
Fig. S1. (a) Different adsorption sites in an homogeneous bundle of SWCNTs:
(i) intratubular, (ii) interstitial (interbundle) channel, (iii) external groove, and (iv) external
rounded surface (exposed space). r is the distance to the center of nanotube and  is the angle
around any particular nanotube. The solid bold black lines locate the centers of the carbon
atoms on the nanotube walls of b3 system. (b) Schematic representation of the separation of
exposed surfaces of the tubes (interbundle region - pink area) and space between nanotubes
(intertubular region - yellow region). Light green dashed lines indicate the presence of
monolayer. For additional details see text.
Fig. S2. Schematic representation of an angle defining the benzene ring orientation against
the nanotube surfaces.
5
Fig. S3. The comparison of benzene adsorption (a, red line), enthalpy (qst, open black circles),
and entropy (Sa, closed blue circles) of C6H6 adsorption at 298 K for three studied carbon
nanotube bundles, i.e. b1 - b3.
6
Fig. S4. The same as Fig. S3 but the results correspond b4 - b6 systems (a - red line, qst - open
black circles, and Sa - closed blue circles). Additionally, the data related to isolated tubes (b0)
are presented (a - red dashed line, qst - black dashed line, and Sa - blue dashed line) - this data
is treated as the reference one.
7
Table S1. Parameters characterising the arbitrarily chosen nine points of adsorption isotherms (Fig. 1), i.e. relative pressures and corresponding
average numbers of adsorbed molecules. Molecular concentration of benzene molecules calculated as the function of r (distance to the center of
nanotube) and orientation of C6H6 molecules against the wall as the function of  (the angle around any particular nanotube) are calculated from
45 000 representative equilibrium configurations for the selected points of adsorption isotherms.
1
2
3
4
5
6
7
8
9
b0
b1
b2
b3
b4
b5
b6
p/ps
6.92·10-3
0.0133
0.0207
0.0316
0.0562
0.100
0.200
0.400
1.000
<N>
24.8
50.1
74.4
94.9
111.9
126.2
139.1
152.3
179.0
p/ps
2.57·10-5
1.00·10-3
5.14·10-3
0.0122
0.0277
0.0562
0.117
0.333
1.000
<N>
24.5
54.6
101.0
151.4
201.1
229.8
254.3
294.4
381.4
p/ps
9.00·10-8
4.00·10-6
1.00·10-4
1.00·10-3
3.98·10-3
8.78·10-3
0.0145
0.0316
1.000
<N>
24.6
53.1
74.6
102.4
155.0
205.0
250.9
302.0
498.4
p/ps
8.11·10-4
8.32·10-4
8.68·10-4
2.00·10-3
5.00·10-3
0.0156
0.0237
0.0562
1.000
<N>
31.1
67.1
112.7
149.2
202.5
309.0
346.4
405.7
625.7
p/ps
2.50·10-3
4.50·10-3
7.00·10-3
0.0110
0.0147
0.0189
0.0300
0.100
1.000
<N>
25.9
49.4
83.9
145.0
206.2
317.9
397.6
500.3
743.0
p/ps
2.51·10-3
5.15·10-3
9.38·10-3
0.0133
0.0237
0.0369
0.0750
0.180
1.000
<N>
24.7
53.6
103.8
154.0
249.7
303.9
364.1
425.6
858.4
p/ps
2.51·10-3
4.76·10-3
9.38·10-3
0.0133
0.0237
0.0369
0.0750
0.160
1.000
<N>
24.5
48.2
102.2
148.4
244.2
299.7
364.5
407.5
948.6
8
References
Furmaniak, S., Terzyk, A.P., Gauden, P.A., Wesołowski, R.P., Kowalczyk, P.: Ar, CCl4, and
C6H6 adsorption outside and inside of the bundles of multi-walled carbon nanotubes simulation study. Phys. Chem. Chem. Phys. 11, 4982-4995 (2009)
Ross, S., Olivier, J.P.: On Physical Adsorption. John Wiley & Sons Inc., New York (1964)
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