Biomedical Engineering Reference
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which is the general multilayer adsorption isotherm. It is applicable to multiadsorption site
chemisorptions (strong adsorbent e adsorbate molecular interactions) as well as physisorp-
tions. In general, the multilayer adsorption isotherm is written as
N
1
½
1
þ Nð
1
K A C A ÞðK A C A Þ
n As;N ¼ n s1 cK A C A
(9.72)
1
ð
1
K A C A Þ½
1
ð
1
cÞK A C A cðK A C A Þ
Because of interaction with adsorbent surface is the key for the adsorption to occur, the
number of layers of adsorption is thus restricted. Most commonly held belief is that chemi-
sorptions has to be monolayer, which stems from this notion. Correctly so, adsorption without
adsorbent surface e adsorbate molecule interaction would be meaningless. Molecules can be
more compact when adsorbed actually than in their solid state due to the geometric confine-
ment and interactions with the adsorbent surface. Therefore, at this point, Eqn (9.73) is general
although only two levels of interactions were allowed in deriving this equation.
9.1.4.3. BET Isotherm and Physisorption
We next turn our attention to physisorption only. At this point, Eqns (9.72) and (9.73) are
applicable to both chemisorption and physisorption. Because of the weak adsorbate e
adsorbate and adsorbate e adsorbent interactions in physisorption, we can further simplify
Eqns (9.72) and (9.73) . While chemisorptions can only be modeled with finite number of
layers, physisorptions could actually occur on multiple layers where the adsorbate e
adsorbent interactions are nearly negligible. Therefore, it is unique to physisorption that
1) an infinite number of layers could take place if the geometric restriction is absent and
2) the adsorbate molecules could not be differentiated with the liquid or solid adsorbate
molecules. When the partial pressure of the adsorbate in the bulk gas phase reaches the vapor
pressure of the “liquefied” or “solidified” adsorbate, the adsorption reaches maximum as
there is no difference between the molecules in the liquid phase and the adsorbed molecules.
That is to say, when p A ¼ p A , n As / N
. Based Eqn (9.72) , we have
p A
p A
ap A ¼ b ¼
(9.74)
Therefore, Eqn (9.72) is reduced to
1
þ N 1
p A
p A
N
p A
p A
1
n As;N ¼ n s1 c p A
(9.75)
1
1
p A c p A
Nþ1
p A
p A
p A
p A
ð
1
p A
which is applicable only for physisorptions.
Eqns (9.72) and (9.75) can describe all the cases or types of adsorption shown in Fig. 9.11 .
When N
¼
1, Eqn (9.72) is reduced to
c p A
p A
n As;1 ¼ n s1
(9.76)
þ c p A
p A
1
for which we have recovered the form of the Langmuir adsorption isotherm. Eqn (9.76)
describes the monolayer coverage and is identical to Langmuir isotherm.
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