Micromeritics Gemini VII 2390a, Operator'S Manual

Page: 359 / 426

Gemini VII Appendix F
239-42828-01 - Dec 2012 F-13
Ar - Zeolites Me-Form by NLDFT
Model isotherms were calculated using the prescriptions of Tarazona for density dependent weighting
functions and cylindrical pore geometry. The pore wall potential is described by the Lennard-Jones
potential of interaction between a gas molecule and the oxide surface of an infinitely long cylinder.
This model is similar to the model above, but it more appropriate is for characterizing alkali metal
exchanged zeolites. The reported pore size range is from 3.5 to 300 Å.
Models Based on Classical Theories
Both surface energy distribution and pore size distribution may be evaluated using classical
approaches to model kernel functions for use with equation (1) of the DFT Theory in the calculations
appendix. Be aware that the deconvolution method only provides a fitting mechanism; it does not over-
come any inherent shortcomings in the underlying theory.
Surface Energy
The use of classical theories to extract adsorptive potential distribution is mostly of historical interest.
At a minimum, the equation must contain a parameter dependent on adsorption energy and another
dependent on monolayer capacity or surface area. This is sufficient to permit the calculation of the set
of model isotherms that is used to create a library model. The Langmuir equation has been used in the
past, as have the Hill-de Boer equation and the Fowler-Guggenheim equation. All of these suffer from
the fact that they only describe monolayer adsorption, whereas the data may include contributions
from multilayer formation.
Pore Size
It is well established that the pore space of a mesoporous solid fills with condensed adsorbate at pres-
sures somewhat below the prevailing saturated vapor pressure of the adsorptive. When combined with
a correlating function that relates pore size with a critical condensation pressure, this knowledge can be
used to characterize the mesopore size distribution of the adsorbent. The correlating function most
commonly used is the Kelvin equation. Refinements make allowance for the reduction of the physical
pore size by the thickness of the adsorbed film existing at the critical condensation pressure. Still fur-
ther refinements adjust the film thickness for the curvature of the pore wall.
The commonly used practical methods of extracting mesopore distribution from isotherm data using
Kelvin-based theories, such as the BJH method, were for the most part developed decades ago and
were designed for hand computation using relatively few experimental points. In general, these meth-
ods visualize the incremental decomposition of an experimental isotherm, starting at the highest
relative pressure or pore size. At each step, the quantity of adsorptive involved is divided between pore
emptying and film thinning processes and exactly is accounted for. This computational algorithm fre-
Geometry
Cylinder
Substrate
Zeolite
Category:
Porosity
Method:
Argon at 77 K