3 THEORETICAL BACKGROUND
3.2 Adsorption of Aqueous Organic Substrates on TiO
In order to successfully represent the dynamic adsorptive behaviour of any substance from the fluid to the solid phase, it is important to have a satisfactory description of the equilibrium state between the two phases of the adsorption system.
3.2.1 Sorption Equilibrium
Adsorption of molecules can be represented as a chemical reaction (Eq. 3.15):
THEORETICAL BACKGROUND
B A B
A + ⇔ ⋅ Eq. 3.15
where A is the adsorbate, B is the adsorbent, and A·B is the adsorbed compound. Sorbates are held on the surface by various types of chemical forces such as hydrogen bonds, dipole-dipole interactions, and van der Waals forces. If the reaction is reversible, molecules continue to accumulate on the surface until the rate of the forward reaction (adsorption) equals the rate of the reverse reaction (desorption). If this condition exists, equilibrium has been reached and no further accumulation will occur.
One of the most important characteristics of an adsorbent is the quantity of adsorbate that it can accumulate. The state of equilibrium is described by means of adsorption isotherms. The relationship can be based on two general approaches, theoretical and empirical models.
Theoretical models seek to describe a system based on the thermodynamic principles.
Empirical models provide a mathematical description of observed experimental data by measuring the concentrations and loadings.
3.2.2 Experimental determination of sorption isotherms
The state of equilibrium of the sorption of a single component can be derived from experimental data by means of mass balances. In batch methods the equilibrium is determined by contacting a solution of a given composition with a sorbent material of known solid-phase composition.
In the case of a binary system the mass balance of the system is described by Eq. 3.16, where VL is a volume of liquid phase with an initial concentration of sorptive C0 and with a sorbent mass m is placed in contact.
C V q m C V q
m⋅ 0 + L⋅ 0 = ⋅ + L⋅ Eq. 3.16
If the initial loading is zero (q0=0), one obtains from Eq. 3.16
(
C C)
m
q = VL 0 − Eq. 3.17
This equation describes the so-called operation line from the initial state of the system (c0, qo=0) to the state of equilibrium.
By varying either the initial concentration or the mass of sorbent added to the constant volume of solution, several points of the isotherm may be obtained.
THEORETICAL BACKGROUND
Numerous studies have shown that the adsorption of organic compounds on the surface of semiconductors can be described by means of a Langmuir relationship (Fox and Dulay 1993;
Hoffmann, Martin et al. 1995; Mills and Le Hunte 1997).
3.2.3 Langmuir isotherm
Langmuir developed the adsorption theory to describe adsorption of gases on solid surfaces (Langmuir 1918). The derivation of the Langmuir adsorption isotherm involves some implicit assumptions: a) the adsorption is at a fixed number of localized sites; b) there is only a monolayer of adsorbed molecules; c) the surface is homogeneous, that mean, all the adsorption sites are equivalent; d) there is no lateral interaction between adsorbate molecules;
e) the equilibrium is characterized by the fact that the rates of adsorption and desorption are equal. The Langmuir isotherm describes the relationship between the amount adsorbed at equilibrium (qe) and its equilibrium concentration (Ce) by the equation Eq. 3.18
e L
e L
e K C
C q K
q = +
max1 Eq. 3.18
where qmax and KL are the Langmuir constants which are related to the adsorption capacity and adsorption energy, respectively. There are two limiting cases for the Langmuir relationship:
At small sorbate concentrations, the denominator of Eq. 3.18 tends to 1 and the equation simplifies to:
e L
e q K C
q = max Eq. 3.19
This relationship corresponds to the Henry´s law, which gives a linear adsorption isotherm expressed by the product of KL and qmax.
At large concentrations, the equation simplifies to:
qmax
qe = Eq. 3.20
This means that the adsorbent loading is independent of the concentration. This is partly due to the filling up of a significant number of the total possible adsorption sites. This results in a smaller chance of an ion from the solution to find a vacant site, and therefore being adsorbed.
The Langmuir adsorption isotherm has the simplest form, an equally simple physical picture, and shows reasonable agreement with a large number of experimental isotherms. Therefore,
THEORETICAL BACKGROUND
the Langmuir adsorption model is probably the most useful one among all isotherms describing adsorption, and often serves as a basis for more detailed developments (Snoeyink and Summers 1999).
The Langmuir constants (qmax and KL) can be deduced from experimental values by means of linearization methods. There are three different possibilities to linearize the Langmuir relationship, Eq. 3.18 and to deduce the numerical values of the parameters. These are shown in Table 3.2.
3.2.4 Freundlich isotherm
The Freundlich isotherm is one of the earliest empirical equations used to describe equilibria data (Freundlich 1906). The Freundlich adsorption isotherm has often been found to fit liquid-phase adsorption data quite well, provided that the adsorption sites are not identical, and the total adsorbed amount is the same over all types of sites. The Freundlich isotherm is expressed as:
( )
e nFF
e K C
q = 1 Eq. 3.21
where KF and nF are the Freundlich constants related to the capacity and intensity of adsorption, respectively (Snoeyink and Summers 1999).
The Freundlich equation gives an expression encompassing the surface heterogeneity and the exponential distribution of active sites and their energies. According to the Freundlich equation, the amount adsorbed increases infinitely with increasing concentration or pressure.
This equation does not change to a linear isotherm in the small residual concentration range and no maximum loading at high concentrations exists. The linear form of Freundlich isotherm is also shown in Table 3.2.
THEORETICAL BACKGROUND
Table 3.2: Isotherm models and their linear forms.
Isotherm Linear form Plot
Langmuir-1
e L
e L
e K C
C q K
q = +
max1
max max
1 1 1 1
q C q K
qe = L e +
e e vs C q
. 1 1
Langmuir-2
L e
e e
K C q
q q C
max max
1
1 +
= e
e e vsC q C .
Langmuir-3 K q K qmax
C q
L e L e
e =− + e
e e vsq C
q .
Freundlich qe =KF
( )
Ce n1F eF F
e C
K n
q 1 ln
ln
ln = + lnqevs.lnCe