Environmental Engineering Reference
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configurations of a system by integrating Newton's law of motion. Using MD
simulations, various diffusion coefficients can be measured from the trajectories
showing how the positions and velocities of the particles vary with time in the
system. Several different types of gas diffusion coefficients and the methods to
measure them will be addressed in the next section in details. In accessing the gas
diffusion in nanoporous materials, equilibrium MD simulations, which model the
behavior of the system in equilibrium, have been very widely used. In equilibrium
MD simulations, first a short grand canonical Monte Carlo (GCMC) simulation is
applied to generate the initial configurations of the atoms in the nanopores. Initial
velocities are generally randomly assigned to each particle (atom) based on Max-
well-Boltzmann velocity distribution. An initial NVT-MD (NVT: constant num-
ber of molecules, constant volume, constant temperature) simulation is performed
to equilibrate the system. After the equilibration, Newton's equation is integrated
and the positions of each particle in the system are recorded at a prespecified rate.
Nosé-Ho over thermostat is very widely applied to keep the desired temperature
and the integration of the system dynamics is based on the explicit N-V-T chain
integrator by keeping temperature constant, Newton's equations are integrated in
a canonical ensemble (NVT) instead of a microcanonical ensemble. To describe
the dynamics of rigid-linear molecules such as carbon dioxide the MD algorithm
is widely used. The so-called order N algorithm is implemented to calculate the
diffusivities from the saved trajectories. In order to perform classical MD simula-
tions to measure gas diffusion in MOFs' pores, force fields defining interactions
between gas molecules-gas molecules and gas molecules-MOF's atoms are re-
quired. Once these force fields are specified, dynamical properties of the gases
in the simulated material can be probed. These force fields will be studied in two
parts: models for gas molecules (adsorbates) and models for MOFs (adsorbents).
1.3.2.7.2
MODELS FOR GASES
Diffusion of hydrogen, methane, argon, carbon dioxide and nitrogen are very
widely studied in MOFs. For H 2 , three different types of fluid-fluid potential mod-
els have been used. In most of the MD simulations, spherical 12-6 Lennard-Jones
(LJ) model has been used for H 2 . The Buch potential is known to reproduce the
experimental bulk equation of state accurately for H 2 . Two-site LJ models have
also been used in the literature. The potential model of many researchers has been
used to account for the quadrupole moment of H 2 molecules. This potential con-
sists of a LJ core placed at the center of mass of the molecule and point charges at
the position of the two protons and the center of mass.
1.3.2.7.3
MODELS FOR MOFS
When the first MD simulations were performed to examine gas diffusion in MOFs
at the beginning of 2004, there was no experimental data to validate the accuracy of
 
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