Environmental Engineering Reference
In-Depth Information
could be expressed in terms of the characteristic adsorption curve and the adsorp-
tion potential distribution:
( )
( )
��
A
q
A
Ä
S
=
−a
ƒ„
(13)
T
XA
q
This function provides quantitative information about the distribution of the
Gibbs free energy for a heterogeneous porous solid and through Eq. (13) it allows
one to estimate the entropy and enthalpy [1, 2, 16, 24, 37].
1.2.1.2.1
LENARD-JONES POTENTIAL FUNCTION
In this work, all of the particles include hydrogen molecules, carbon monoxide
molecules and carbon atoms are treated as structure less spheres. Particle-particle
interactions between them are modeled with Lenard-Jones potential located at the
mass-center of the particles. For a pair of particles i and j separated by the distance
r, the interaction between them is given by:
12
6
s
s
����
( )
ij
ij
φ =e
r
4
 
-
€‚€‚
ij
ij
ƒ„ƒ„
r
r
 
-
(14)
where i and j donate hydrogen, or carbon monoxide, or carbon particles, ε and
σ are the energy and size potential parameters, which are 36.7K and 0.296 nm
for hydrogen, 100.2K and 0.3763 nm for carbon monoxide, and 28.2Kand 0.335
nm for carbon, respectively. Lorentz-Berthelot rules are used to calculate the pa-
rameters of interaction between different kinds of particles. The general potential
between a gas molecule and the nanotube is calculated by summing up pair inter-
actions between individual carbon atoms and the gas molecules:
( )
Vr
=φ−
(
r r
)
(15)
ij
i
j
j
where r i is the position of hydrogen or carbon monoxide molecule, ri j is that of a
carbon atom and φij (r) is the pair potential between a certain gas molecule and
a carbon atom, while the sum is over all of the atoms on the tube. Assuming that
the atoms of the solid are distributed continuously up and on a sequence of paral-
lel surfaces that form the pore wall, the interaction potential of the fluid molecule
with one of these surfaces of area A and number density θ is given by:
12
6
s
s
( )
( )
FC
FC
V r
= q
vrd
a= e q
4
d
a
 
-
FC
ƒ
ƒ
r
r
(16)
 
-
A
A
where θ = 38 nm −2 , ε FC and σ FC are Lenard-Jones parameters of the interaction
between fluid molecule and carbon atom. The fluids include hydrogen and carbon
monoxide. Integrating over the whole nanotube, the following expression can be
obtained:
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