TÍTULO VI: LA HABITUALIDAD
6.2. La casi empresa y la habitualidad:
An adsorption isotherm is used to represent the equilibrium states of an adsorption system for a given adsorbent and adsorbate depending upon the adsorption of gas or solute components at a fixed temperature of adsorption. The reason for using the adsorption isotherm instead of adsorption isobar is because it is the most convenient and practical method to determine adsorption at a constant temperature. Therefore, it is the most extensively used method for representing the equilibrium states of an adsorption system. The adsorption isotherm gives valuable information regarding the adsorbate and adsorbent interaction and the adsorption process. It helps to determine the SA, PV and pore size distribution of the adsorbents [18].
The adsorption data can be represented by many isotherm model equations from Freundlich, Langmuir, Brunauer Emmett Teller (BET), Sips, Toth, Dubinin-Radushkevich¸ Dubinin- Astakhov, Myers-Ou, VSM and others [47-49]. Among these, the most commonly used adsorption isotherms are Freundlich, Langmuir and BET. Both Langmuir and Freundlich isotherm equations can be applied equally to physisorption as well as to chemisorption and both gas and liquid phases. However, in practical terms, they are mainly used on liquid phases of the adsorption isotherm [18]. The BET is the most important equation for the analysis of physisorption of gas onto porous materials. This will be discussed more in section 1.3.3.1.
1.3.1.1 Adsorption isotherm of gas
The quantity of gas adsorbed may be measured in any convenient units such as moles, grams and cubic centimetres, at standard temperature and pressure. Facilitating the comparison of the adsorption data, the amount adsorbed was plotted against the equilibrium relative pressure (P/P0), where P0 is the saturation pressure of the adsorptive at the temperature of the
measurement and P is the pressure of the pure adsorptive vapour. The volume adsorbed can also be plotted against P, when the temperature is above the critical temperature of the adsorptive [26, 50, 51]. Adsorption data, for gas-solid systems, has been classified by the
IUPAC, into six types, as shown in Figure 1-8 [26] and each type of isotherm can be related to a pore model structure of a solid, as discussed in section 1.2.2.2.
Figure 1-8 The IUPAC classification of physisorption isotherms [26]
Figure 1-9 Types of hysteresis loops [26]
The hysteresis loop can be classified into four types as shown in Figure 1-9. Hysteresis of types H1 and H2 can occur from ink-bottle-shaped pores (see Figure 1-4 in section 1.2.2.2) or from a difference in adsorption-desorption behaviour in near cylindrical through pores. Type
H3 and H4 hysteresis can occur from slit-shaped pores, which are plate or edge particles, like
cubes. The difference between these two types of hysteresis loops is that Type H1 and H4 is uniform in size and shape, while Type H2 and H3 is non-uniform. There is no hysteresis form in the cases of blind cylindrical, cone and wedge shaped pores [25, 26].
The Kelvin equation is very often used to explain the capillary condensation that produces hysteresis loops, which has been useful for developing the adsorption isotherm theory, such as the Barrett-Joyner-Halenda method (see section 1.3.3.3). The equation is based on the assumption that there is a flat surface and it is derived from the Young-Laplace equation, Equation 1-1, which relates the differential pressure across a vapour/liquid meniscus within a pore to a function of its curvature radii. As the pressure increases and the adsorbate layers are built up on the pore walls, r1 and r2 become equal. Capillary condensation occurs at this point.
At the pressure called the critical pressure, the pore becomes completely filled with condensate. Therefore, the equation can be written as Equation 1-2 [52].
2 11
1
r
r
P
Equation 1-1 k r P 2
Equation 1-2 where;γ is surface tension of liquid adsorbate
ΔP is different pressure of liquid and vapour across meniscus r1 and r2 are radii curvatures
rk is mean radius of meniscus curvature, which is known as Kelvin radius.
Assuming a constant temperature is used, which is lower than the critical value, the vapour side of the meniscus behaves like an ideal gas; the Kelvin equation is used to determine the radius of the hemispherical meniscus and can be written as shown in Equation 1-3.
k L
RTr
V
P
P
2
cos
ln
0
Equation 1-3where;
rk is the Kelvin radius
γ is the surface tension of the liquid condensate R is the ideal gas constant
T is the absolute temperature (K) θ is the contact angle (for N2 = 0)
VL is the molar volume (liquid molar volume of N2 = 0.00156).
For the determination of the pore size, pore radius can be calculated by assuming that it is directly related to the Kelvin radius by the addition of the thickness (t) layer that is already adsorbed on the pore walls when the capillary condensation occurs. The pore radius can be calculated as shown in Equation 1-4.
P P
RT t V t r r L k p 0 ln 2
Equation 1-41.3.1.2 Adsorption isotherm of liquid and solid systems
Unlike the gas/solid system, the liquid/solid system may involve both the physical and chemical interaction of adsorbate-adsorbent. Several types of bonds can occur, which include chemisorption, hydrogen bonding, hydrophobic bonding and van der Waals forces. The interaction of the adsorbate-adsorbent molecules can involve more than one type of interaction depending on the chemical structure of both the adsorbent and adsorbate. In order to investigate the adsorption mechanisms, the most common approach is to study the isotherm [53]. The isotherm of a liquid/solid system can be plotted by using the amount of solute adsorbed per unit weight of adsorbent against equilibrium concentration of solute remaining in the system. The amount of constituent-adsorbed solute can be calculated using the Equation 1-5 [54].
M V C V C M X 0 e Equation 1-5 where;C0 is constituent concentration before carbon treatment (mg/l)
Ce is constituent concentration after carbon treatment (mg/l)
V is volume of sample (litre) M is weight of carbon (gram)
X/M is constituent adsorbed per unit weight of carbon (mg/g).
The significant aspects of the adsorption isotherm include the adsorption rate, isotherm shape, the importance of the plateau found in the isotherms, the extent of solvent adsorption (whether it is monomolecular or there are several layers of adsorption), the adsorbate molecules orientation, the temperature effect and the nature of the interaction between adsorbate and adsorbent [53]. From these vital aspects, the isotherms were classified by Giles et al. [55] into four main classes of isotherm shapes based on the initial part of the isotherm, as shown in Figure 1-10. The subgroups relate to the shape of parts of the curves’ distance from the origins, which are nearest or the farthest group, from 1 to max, respectively; the key aspects of the plateaux and the changes of the slope are described as followed [53, 55, 56];
Figure 1-10 Classification of liquid/solid isotherm shapes [55]
Type S isotherms indicate the vertical orientation of adsorbed molecules at the surface. Type L isotherms or “Langmuir”: The L2 curve usually occurs in most types of adsorption from
the isotherm shows very steep curves at the initial stage in which the solute has a high affinity and the solute is completely adsorbed from the dilute solutions, or the measurable solute cannot be detected in the remaining solution. An example of this isotherm type is the large organic unit of adsorbed species or sometimes the single ions, which are exchanged with others of much lower affinity to the surface. Type C isotherm or “Constant partition”: This curve is given by solutes that penetrate into the solid more readily than associated with the solvent. When the adsorption reaches the maximum capacity, the curve suddenly changes to become a horizontal plateau.
Note that the 2c subgroup indicates micropore in the adsorbent. In the C-class, the 2C curve may be horizontal or a less steep (ci) or a steeper (cii) slope than the main portion, according to the nature of the system [55].