Micromeritics Gemini VII 2390a, Operator'S Manual

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Gemini VII Appendix F
239-42828-01 - Dec 2012 F-1
F. DFT MODELS
Theories are developed by scientists in an attempt to explain a class of observed behavior. In the exper-
imental 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 computations were required. Today we can
explore complex models that describe adsorption systems on the atomic scale of size and sub-picosec-
ond 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 (Q
m
), and the molar intensity of the gas-surface interac-
tion, 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 theo-
ries, 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 statisti-
cal thermodynamic theory that allows us to relate the adsorption isotherm to the microscopic
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 evacu-
ated 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 corresponds to the quantity of gas effectively removed
from the gas phase by the solid surface. A graph that plots amount adsorbed versus equilibrium pres-
sure 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 surface acquires a greater
average density of argon atoms than regions farther removed.