Chemical Reactions on Solid Surfaces - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 463

If the available adsorption sites are linearly distributed about the excess interaction energy
between 0 and E max , then the adsorption isotherm becomes

þ P N m¼1 K m C m e E max RTK j C j

E max P N s

ln 1

RT

q j ¼ (9.39)

þ P N s
m¼ 1 K m C m

1

1 K m C m m¼

For single species adsorption, Eqn (9.39) is reduced to

þ K A C A e E max RT

E max

ln 1

RT

q A ¼ (9.40)

1 þ K A C A

which is also known as the UniLan ( uni form distribution Lan gmuir) model.
In the intermediate coverage region,

<< K A C A e Emax 1 and 1 >> K A C A

RT

Eqn (9.40) may be approximated by

RT
E max ln

ðK A C A e Emax

q A z Þ (9.42)

RT

which is the Temkin isotherm.
Nonideal surfaces can also be modeled with multilayer adsorptions as the adsorbate e
adsorbate molecular interactions and steric interactions can be introduced via multilayer
adsorption concept. True multilayer adsorption is common in physisorptions. Assuming
that 1) on the first layer, the interaction is only between adsorbate and adsorbent
surface, and this interaction is uniform; 2) the interactions among adsorbate e adsorbate
and adsorbate e adsorbent are uniform and identical for all other layers; we obtain for single
species N -layer adsorptions,

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 (9.73)

Nþ 1

ð 1 K A C A Þ½ 1 ð 1 cÞK A C A cðK A C A Þ

or

N

1 ½ 1 þ Nð 1 K A C A ÞðK A C A Þ

C As;N ¼ C As1 N cK A C A (9.73a)

Nþ 1

ð 1 K A C A Þ½ 1 ð 1 cÞK A C A cðK A C A Þ

In terms of partial pressure in the bulk phase,

N

1 ½ 1 þ Nð 1 ap A Þðap A Þ

n As;N ¼ n s1 cap A (9.72)

Nþ 1

ð 1 ap A Þ½ 1 ð 1 cÞap A cðap A Þ

When N ¼ 1, the Langmuir adsorption isotherm, Eqn (9.9) , is recovered. If N ¼ 2, Eqn (9.73) is

reduced to

cK A C A ð 1 þ 2K A C A Þ

n As;2 ¼ n s1 (9.55)

1 þ cK A C A ð 1 þ K A C A Þ

which is the bilayer adsorption isotherm.