Models Based On Classical Theories; Surface Energy; Pore Size - Micromeritics ASAP 2020 Confirm Operator's Manual

ASAP 2020 Confirm

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 cal-
culations appendix. Be aware that the deconvolution method only provides a fitting
mechanism; it does not overcome 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 mono-
layer 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 pressures somewhat below the prevailing saturated vapor pressure of the adsorptive. When
combined with a correlating function that relates pore size with a critical condensation pres-
sure, 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 further 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 methods 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 frequently leads to inconsistencies
when carried to small mesopore sizes. If the thickness curve used is too steep, it finally will
predict a larger increment of adsorptive for a given pressure increment than is actually
observed; since a negative pore volume is non-physical, the algorithm must stop. Conversely,
if the thickness curve used underestimates film thinning, accumulated error results in the cal-
culation of an overly large volume of (possibly nonexistent) small pores.
The use of equation (1) represents an improvement over the traditional algorithm. Kernel
functions corresponding to various classical Kelvin-based methods have been calculated for
differing geometries and included in the list of models.
02-42811-01 - Mar 2011
Appendix F
F-13