Dft Models; Models Based On Statistical Thermodynamics; Theoretical Background - Micromeritics ASAP 2020 Confirm Operator's Manual

ASAP 2020 Confirm
Theories are developed by scientists in an attempt to explain a class of observed behavior. In
the experimental physical sciences, theories are often expressed in terms of a model that can
be visualized and described mathematically. Early models of physical adsorption were quite
simple, both conceptually and mathematically, for very practical reasons — hand computa-
tions were required. Today we can explore complex models that describe adsorption systems
on the atomic scale of size and sub-picosecond time frame. This is not because scientists are
smarter, but because of available tools. The DFT models are created by classical approaches
to adsorption as well as models based on modern statistical thermodynamics.

Models Based on Statistical Thermodynamics

Included in this group are methods that model the adsorption system in terms of forces acting
between individual molecules.

Theoretical Background

Traditional adsorption theories attempt to describe experimental adsorption isotherms with an
isotherm equation containing a small number of parameters. At a minimum, these parameters
include the extent of the surface, such as the monolayer capacity (Vm), and the molar inten-
sity of the gas-surface interaction, such as the Langmuir "K" constant or the BET "C"
constant. In some equations, additional parameters take into account the lateral interaction of
adsorbed molecules with each other. Other theories, such as the Dubinin-Astakhov approach,
also include parameters for the effect of adsorbent porosity.
Instead of this classical kinetic or phenomenological approach, we can use a molecular-based
statistical thermodynamic theory that allows us to relate the adsorption isotherm to the micro-
scopic properties of the system: the fluid-fluid and fluid-solid interaction energy parameters,
the pore size, the pore geometry, and the temperature.
The following example is given so that you may understand how such a theory is constructed.
A clean sample of a solid material containing slit-shaped pores of a single width is placed in
an evacuated space. It is kept at a fixed temperature as a known quantity of pure argon gas is
admitted into the space surrounding the sample. The pressure within the space is recorded
over time. In this situation, the pressure falls rapidly from its initial value and gradually
approaches a steady reading, called the equilibrium pressure. The amount adsorbed corre-
sponds to the quantity of gas effectively removed from the gas phase by the solid surface. A
graph that plots amount adsorbed versus equilibrium pressure is called an adsorption
isotherm.
Under such conditions, the argon atoms that randomly enter the pore space feel the presence
of the solid surface as the action of an external attractive force (the dispersion forces or Van
der Waal's forces) and spend more time near the surface. As a result, the space near the sur-
face acquires a greater average density of argon atoms than regions farther removed.
02-42811-01 - Mar 2011
F. DFT MODELS
Appendix F
F-1