Micromeritics Gemini VII 2390a, Operator'S Manual

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Q p
 
q p
   
f
  
d

=

Gemini VII Appendix C
239-42828-01 - Dec 2012 C-37
Application to Surface Energy Distribution
Under certain conditions, an energetically heterogeneous surface may be characterized by a distribu-
tion 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 adsorp-
tion 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 gradi-
ent along the surface is not steep. In mathematical terms, this concept is expressed by the integral
equation of adsorption in the following form.
(2)
Q p
 
H q p H
  
f H
 
d

=
where
Q(
p
) = the experimental quantity adsorbed per gram at pressure
p
,
q(
p
, ε ) = the quantity adsorbed per unit area at the same pressure,
p
, on an ideal free
surface of energy e, and
ƒ( ε ) = the total area of surface of energy e in the sample.

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 model description.
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 contributes 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
(3)
where
Q(p)
= the experimental quantity adsorbed at pressure p,
q(p,H)
= the quantity adsorbed per unit area at the same pressure,
p
, in an ideal pore of
size
H
, and
f(H)
= the total area of pores of size
H
in the sample.

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.