BASIC CONCEPTS AND AN OVERVIEW - Foundations of Nanotechnology: Pore Size in Carbon-Based Nano-Adsorbents - page 79

1.2.2 BASIC MODELS FOR PSD CALCULATING FROM DATA OF
SIMULATED ADSORPTION ISOTHERMS

1.2.2.1 THEORETICAL MODELS FOR MAIN TYPES OF
COMPARATIVE PLOTS THAT CALCULATING PSD
Physical adsorption of gases and vapors on a non-porous surface or on the meso-
pore surface occurs via layer-by-layer mechanism, whereas adsorption in micro-
pores resembles the volume filling mechanism. In the case of porous solids con-
taining both micropores and mesopores, active carbons, ordered microporous and
mesoporous carbons and active carbon fibers, the volume filling of micropores
occurs first at low pressures and it is followed by the formation of a multilayer
film on the mesopore walls, and finally, the remaining empty space inside meso-
pores is filled via capillary condensation. Thus, the dependence of the amount
adsorbed on a porous solid plotted (compared) against the amount adsorbed on
reference non-porous solids is linear at higher pressures because the layer-by-
layer adsorption occurs on both solid surfaces. However, at low pressures the
adsorption mechanisms on the solid studied and on the reference adsorbent can
be the same or different, resulting in linear or non-linear behavior of the initial
segment of the comparative plot. It should be noted that the linear segment of
the comparative plot at higher pressures is rather insensitive on the choice of the
reference solid because after all micropores are filled and the first adsorbed layer
is completed, the surface effects are negligible and the film formation is mostly
controlled by adsorbate-adsorbate interactions. The slope of the linear segment
at the low pressures is proportional to the total surface area and the slope of the
linear segment at high pressures is proportional to the external surface area of
mesopores, whereas its intercept determines the maximum amount adsorbed in
micropores, which can be converted to the micropore volume. There are several
types of comparative plots such as the t-plot, -plot and -plot, which differ only in
the way of presenting the standard adsorption isotherm measured on the refer-
ence solid. In the case of the-plot, the standard isotherm isexpressed in terms of
the surface coverage, which is the ratio of the amount adsorbed to the monolayer
capacity. The thickness of the surface film on the reference solid,, whichis ob-
tained by multiplication of the surface coverage by the monolayer thickness, is
used toconstruct the t-plot. In the-method the amount adsorbed on a porous solid
is plotted against the reduced standard adsorption. The -method was proposed.
A brief description of this method is provided below. The total amount adsorbed
at relative pressure is the sum of the amount adsorbed in the micropores and the
amount adsorbed on the mesopore surface:

p p p

� � � � � �

a =q +q a

0

a

0

„

(30)

p p p

ƒ „ ƒ „ ƒ

mi mi me

0 0 0