Biomedical Engineering Reference
In-Depth Information
8.3.3 Monte Carlo Sampling Techniques in the Grand
Canonical Ensemble
Since the Metropolis algorithm was introduced in a seminal paper
in 1953 [71], the Monte Carlo method has been applied for sampling
the configurations space of
-particle systems within different
thermodynamic conditions. Different statistical ensembles can
be sampled by Metropolis Monte Carlo algorithms such as the
ones suitable for gas physisorption in nanostructured or porous
materials.
For an accurate sampling of the configuration space, many
particles are required and thus classical atomistic interaction
potentials designed appropriately are needed. The grand canonical
statistical ensemble, that is appropriate for gas adsorption studies,
can be sampled easily with the Metropolis algorithm [33], and thus
large scale simulations of gas adsorption can be performed, provided
that the chemical events, such as bonding, bond breaking, reactions,
etc., are excluded; the key factor affecting the reliability of GCMC
simulation is the choice of the atomistic interaction potential used
to calculate the configuration energy of the system. Still nowadays,
the simple Lennard-Jones (LJ) potential (and the ones derived from
it) is a popular choice [93].
Quantum effects are considered mainly through Path Integral
Monte Carlo (PIMC) schemes where each quantum particle is
replaced by a classical polymeric ring containing a variable number
of “beads” that is increased until the equilibrium properties of
the polymer ring converge. It is demonstrated that the statistical
equilibrium properties of such a classical system return the statistical
properties of the quantum system under consideration [19, 31, 108].
N
8.4
Gas Physical Adsorption in Carbon
Nanostructures
A great deal of the scientific literature over the past 20 years has been
devoted to hydrogen physical adsorption in carbon nanostructures
of different allotropic forms due to the strategic potential importance
of nanotechnology to solve this challenging problem that is still
preventing the hydrogen economy from the success.
Thus we have dedicated the following subsection to the hydrogen
storage in carbon nanostructures while we have grouped together
the other gaseous species.
