Application To Surface Energy Distribution; Application To Pore Size Distribution - Micromeritics ASAP 2020 Confirm Operator's Manual

Appendix C

Application to Surface Energy Distribution

Under certain conditions, an energetically heterogeneous surface may be characterized by a
distribution of adsorptive energies. The conditions are that the sample is not microporous, i.e.,
that adsorption is taking place on essentially a free surface with no pore filling processes at
least to about 0.2 relative pressure. Secondly, that each energetically distinct patch contributes
independently to the total adsorption isotherm in proportion to the fraction of the total surface
that it represents. This condition is satisfied if the patches are relatively large compared to an
adsorptive molecule, or if the energy gradient along the surface is not steep. In mathematical
terms, this concept is expressed by the integral equation of adsorption in the following form.
Qp
where
Q(p)
q(p,e)
f(e)
The exact form of the energy-dependent term depends on the form of the model isotherms
expressed in the kernel function and is provided in the library model description in Chapter 5.

Application to Pore Size Distribution

Similarly, a sample of porous material may be characterized by its distribution of pore sizes.
It is assumed in this case that each pore acts independently. Each pore size present then con-
tributes to the total adsorption isotherm in proportion to the fraction of the total area of the
sample that it represents. Mathematically, this relation is expressed by
Q p  
where
Q(p)
q(p,H)
f(H)
Numerical values for the kernel functions in the form of model isotherms can be derived from
modern statistical mechanics such as density functional theory or molecular simulations, or
can be calculated from one of various classical theories based on the Kelvin equation. Several
types are found in the models library.
202-42811-01 - Mar 2011
 q p     f   

= d
= the experimental quantity adsorbed per gram at pressure p,
= the quantity adsorbed per unit area at the same pressure, p, on
an ideal free surface of energy e, and
= the total area of surface of energy e in the sample
   f H  

= d H q p H
= the experimental quantity adsorbed at pressure p,
= the quantity adsorbed per unit area at the same pressure, p, in
an ideal pore of size H, and
= the total area of pores of size H in the sample.
ASAP 2020 Confirm
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C-41