Environmental Engineering Reference
In-Depth Information
Ta b l e 1 Geometrical properties of the three cavities studied
Confinement
Number of particles at the wall
Relevant parameter ( ˃ units)
Circle
200
Radius
=
31
.
83
Square
228
Side
=
57
Triangle
258
Side = 86
Ta b l e 2 Number of particles (density) inside the three cavities studied
ˁ
Circular
Square
Triangular
0.1
318
324
320
0.25
795
812
800
0.5
1,521
1,624
1,601
0.75
2,387
2,436
2,401
U ij . Confinement is built with a fixed number of spherical particles in such a way
that the order of magnitude for the cavities is around nanometers. Table 1 shows
detailed geometrical properties of the three cavities studied in this work.
In our simulations we vary the number of particles inside the cavities (density
ˁ ), while keeping a reduced temperature T =
kT
=
1
,
here k is the Boltzmann
constant. The reduced density ˁ = ˁ˃
3 was varied from 0
.
.
1to0
75 at intervals of
.
0
25. A detailed description of the number of particles for each studied density is
shown in Table 2 .
For the integration of the governing equations (Eqs. 1 and 2 ) we use a Velocity-
Verlet scheme with a step size of
To s t ar t
the simulations, particles are randomly distributed. For high densities, overlapped
particles were relocated using a Monte Carlo algorithm. The simulations were per-
formed in a canonical ensemble using 3
Δ
t
=
0
.
003 (20ns in the Argon scale)
.
10 6 steps
for the reported averages that characterize diffusion. To maintain thermodynamic
equilibrium a classic (Berendsen et al. 1984 ) thermostat was used. To speed up the
code a force decomposition MPI formalism plus neighbor list was used.
10 6
×
integration steps and 6
×
3 Results
In this section, we study the effect of confinement and interaction on particle diffusion
based onMolecular Dynamics simulations. By focusing on three prototypical cavities
(triangular, square and circular) we simulate four scenarios (varying ˁ from 0
.
1to
0
for each cavity, and for the three mentioned interaction
potentials. Figure 3 shows three representative density scenarios (0
.
75 at intervals of 0
.
25
)
75)
and we plot in each column, the mean-square displacement as a function of cavity
shape for the three analyzed potentials (CLJ, SLJ and HLJ). At low densities ( ˁ =
.
1, 0
.
5 and 0
.
 
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