BASIC CONCEPTS AND AN OVERVIEW - Foundations of Nanotechnology: Pore Size in Carbon-Based Nano-Adsorbents - page 150

“available” pore width w. This quantity is assumed to be related to H, the distance
separating the planes through the centers of the first layer of C atoms on opposing
walls, N =integral 0-infinity f(w) N(w) d(w),where f(w) is the PSD and N(w) is
the amount adsorbed in the pores of width w at the given pressure. In principle,
it is possible to calculate N by carrying out simulations to determine N(w) for
a large number of fixed pore widths H covering the range of widths shown by
the experimentally determined PSD. The total adsorption can then be determined
from above integral, using the experimentally determined PSD, f(w). At low pres-
sures a few pore widths suffice for such a scheme, since the isotherm changes
slowly with pressure. For higher pressures a much larger number of pore widths
is needed since pore filling occurs, and the adsorption changes rapidly. Since the
simulations are lengthy, even on the fastest supercomputers, it is not feasible at
present to carry out such calculations for a large number of pore widths.
In addition, in this molecular simulation method Calculations were carried
out using the grand canonical Monte Carlo (GCMC) method. This method is con-
venient for adsorption studies, since the chemical potential í, temperature T, and
volume V are specified and kept fixed in the simulation. Since í and T are the
same in the bulk and adsorbed phases at equilibrium, the thermodynamic state of
the bulk phase is known in such simulations. Three types of molecular moves are
attempted: molecular creation, molecular destruction, and the usual Monte Carlo
translation/rotation moves. Each of these three moves is attempted with equal fre-
quency. The type of move is chosen randomly to maintain microscopic reversibil-
ity. The probability of successful creations or destructions is strongly dependent
on the density of the system. The maximum allowable rotation and displacement
of a molecule are adjusted so that the combined move has an acceptance probabil-
ity of about 40%. This value should ensure the most efficient probing of the phase
space distribution. It is noteworthy that the values of the maximum displacement
and rotation are very small compared to values encountered for non-bonding sys-
tems. In these simulations the number of adsorbed molecules fluctuates during
the simulation. Calculation of the average of this number for a range of chemical
potential enables the adsorption isotherm to be constructed. The walls of the slit
pores lie in the x - y plane. Normal periodic boundary conditions, together with the
minimum image convention, are applied in these two directions. For low pres-
sures, P/P 0 below 0.02, the length of the simulation cell in the two directions par-
allel to the walls was maintained at 10 nm for each of the pore widths studied, to
maintain a sufficient number of adsorbed molecules. For higher pressures where
more water molecules were present, the minimum cell length in the x and y direc-
tions was 4 nm. While this value is not high enough to require biased sampling
methods, long runs are needed to ensure ergodicity. Associating water molecules
tend to remain in energetically favorable configurations for many MC steps, and
the system thus requires many steps to reach a true equilibrium state. In our runs
500 million MC steps were used for equilibration, followed by a further 500 million