Figure 7.10(b), adsorption seems to continue indefinitely as a function of
bulk concentration. Adsorption in this case does not stop after a
saturated monolayer has formed; instead, adsorption continues and
multilayers are formed on the surface. In Figure 7.10(c), adsorption seems
to increase exponentially with bulk concentration. This situation occurs if
the presence of the adsorbate at the surface promotes further adsorption
due to favorable intermolecular interactions. This kind of adsorption is
known as cooperative adsorption. It may or may not eventually level off at
very high bulk concentrations.
If the bulk phase is a gas, then the adsorption isotherm can be represented by a plot of surface coverage as a function of gas pressure at a
constant temperature. Adsorption isotherms allow us to determine some
important characteristics of the adsorption process such as equilibrium
constants, the number of adsorption sites available for adsorption on the
substrate, and the enthalpy of adsorption.
The Langmuir adsorption isotherm, presented by Langmuir in 1918, is
the simplest adsorption isotherm. The Langmuir adsorption isotherm
assumes that there are a finite number of identical adsorption sites on
the solid substrate and that each site is taken up by a single adsorbate
molecule. During the adsorption processes, these sites are taken up until
a point of saturation is reached in which all sites have been taken up
by adsorbate molecules. This point represents complete monolayer
coverage, at which further adsorption ceases. Furthermore, the Langmuir
adsorption isotherm assumes that there are no interactions between the
adsorbate molecules during the adsorption process and that the enthalpy
of adsorption is independent of surface coverage. Figure 7.10(a) represents a Langmuir adsorption profile.
By representing the solid surface by S(s) and the adsorbate molecules in a
gas phase by A(g), we can write the following equilibrium between the
adsorbate and the substrate:
A g
ð Þ + S s
ð Þ⇌
k a
k d
AS s
ð Þ
(7.5)
The constants k a and k d are the rate constants for the adsorption and
desorption process, respectively. At equilibrium, the forward and reverse
rates are the same, and so from basic kinetics,
k a ½A½S = k d ½AS
(7.6)
CHAPTER 7: Fundamentals of Surface Nanoscience
236
bulk concentration. Adsorption in this case does not stop after a
saturated monolayer has formed; instead, adsorption continues and
multilayers are formed on the surface. In Figure 7.10(c), adsorption seems
to increase exponentially with bulk concentration. This situation occurs if
the presence of the adsorbate at the surface promotes further adsorption
due to favorable intermolecular interactions. This kind of adsorption is
known as cooperative adsorption. It may or may not eventually level off at
very high bulk concentrations.
If the bulk phase is a gas, then the adsorption isotherm can be represented by a plot of surface coverage as a function of gas pressure at a
constant temperature. Adsorption isotherms allow us to determine some
important characteristics of the adsorption process such as equilibrium
constants, the number of adsorption sites available for adsorption on the
substrate, and the enthalpy of adsorption.
The Langmuir adsorption isotherm, presented by Langmuir in 1918, is
the simplest adsorption isotherm. The Langmuir adsorption isotherm
assumes that there are a finite number of identical adsorption sites on
the solid substrate and that each site is taken up by a single adsorbate
molecule. During the adsorption processes, these sites are taken up until
a point of saturation is reached in which all sites have been taken up
by adsorbate molecules. This point represents complete monolayer
coverage, at which further adsorption ceases. Furthermore, the Langmuir
adsorption isotherm assumes that there are no interactions between the
adsorbate molecules during the adsorption process and that the enthalpy
of adsorption is independent of surface coverage. Figure 7.10(a) represents a Langmuir adsorption profile.
By representing the solid surface by S(s) and the adsorbate molecules in a
gas phase by A(g), we can write the following equilibrium between the
adsorbate and the substrate:
A g
ð Þ + S s
ð Þ⇌
k a
k d
AS s
ð Þ
(7.5)
The constants k a and k d are the rate constants for the adsorption and
desorption process, respectively. At equilibrium, the forward and reverse
rates are the same, and so from basic kinetics,
k a ½A½S = k d ½AS
(7.6)
CHAPTER 7: Fundamentals of Surface Nanoscience
236