Micromeritics TRISTAR II PLUS Operator's Manual page 277

M C M
ONTE ARLO
In the Monte Carlo method, determination of the system equilibrium distribution begins with an
assumption (which may be only approximate) about the initial configuration of particles in the
system. The system is "equilibrated" through a process of randomly selecting one particle and
conditionally moving it a random distance in a random direction.
If the move results in a configuration of lower total energy, then the move is completed and
another particle is randomly selected to be moved.
If the move results in a configuration of higher energy, a probability for that event is calculated,
and a random number between zero and one is generated. If the generated number is smaller
than the probability of the event, then the move is accepted; otherwise, another particle is selected
and the process is repeated. This process continues until the average total energy of the system
no longer decreases; at this point, average configuration data are accumulated to yield the mean
density distribution of particles in the system.
Monte Carlo simulations require considerably less computation time than molecular dynamic
simulations and can yield the same results; however, neither method provides a really practical
way to calculate complete isotherms.
D F
ENSITY UNCTIONAL
Density functional theory offers a practical alternative to both molecular dynamic and Monte Carlo
simulations. When compared to reference methods based on molecular simulation, this theory
provides an accurate method of describing inhomogeneous systems yet requires fewer
calculations. Because the density functional theory provides accuracy and a reduced number of
calculations, it is the basis embodied in the DFT models.
The system being modeled consists of a single pore represented by two parallel walls separated
by a distance H. The pore is open and immersed in a single component fluid (adsorptive) at a fixed
temperature and pressure. Under such conditions, the fluid responds to the walls and reaches an
equilibrium distribution. In this condition (by the definition of equilibrium), the chemical potential at
every point equals the chemical potential of the bulk fluid. The bulk fluid is a homogenous system
of constant density; its chemical potential
well-known equations. The fluid near the walls is not of constant density; its chemical potential is
composed of several position-dependent contributions that must total at every point to the same
value as the chemical potential of the bulk fluid.
1 )
Chemical potential may be thought of as the energy change felt by a probe particle when it is
inserted into the system from a reference point outside the system. It can also be defined as the
partial derivative of the grand potential energy with respect to density (or concentration).
TriStar II Plus Operator Manual
303-42800-01 (Rev M ) — Sep 2023
ETHOD
F
ORMULATION
1 )
is determined by the pressure of the system using
Models Based on Statistical Thermodynamics
B - 3