Hysteresis Loop
In case of isotherms for nonporous material, the desorption curve traces the adsorption curve. However, for the mesoporous and macroporous materials, desorption curve do not retrace the adsorption curve resulting in a wide loop. This is known as hysteresis loop and corresponds to the capillary condensation of adsorbate in the multilayer region, pore filling and emptying mechanism. The nature of the hysteresis loop is associated with different pore shapes and is shown in Fig 2.
Fig. 2. Different hysteresis loop as represented by IUPAC
Type A hysteresis is attributed to cylindrical or tubular type pores of adsorbent with a narrow distribution of uniform pores. It is characterized by steep and narrow parallel adsorption and desorption curves. Type B has a long flat plateau adsorption with a steep desorption curve. This is a complex structure of pores with interconnected networks or ink bottle shaped pores. Type C re presents aggregates of adsorbent that contain parallel plates, slit- shape pores or wide capillaries (> 500 A0). Type D is associated with slit- shape pores that are mainly in the micropore region.
Langmuir treatment of adsorption
Langmuir isotherm is derived based on the following assumptions:
- 1. Surface is energetically uniform, that is all the surface sites have the same activity for adsorption.
2. Adsorbed molecules do not interact with the other adsorbed molecules on the surface.
3. Heat of adsorption is therefore constant throughout the fractional surface coverage of 0 to 1.
4. Adsorption of all molecules occurs by the same mechanism and results in the same adsorbed structure.
5. Extent of adsorption is less than one complete monolayer coverage.
When a gas is in contact with a solid surface, the gas molecules continuously strike the surface and a fraction of these adhere. However, the more energetic molecules also continuously leave the surface. Eventually, the equilibrium is established so that the rate of adsorption equals the rate at which the molecules leave the surface.
Now, the rate of adsorption is equal to the rate of collision of molecules with the surface multiplied by a factor ‘s' representing the fraction of the colliding molecules that adhere to the surface. At a given temperature, the rate of collision will be proportional to the partial pressure ‘p' of the gas (its concentration) and the fraction ‘s' will be constant. Hence, the rate of adsorption per unit of bare surface will be ra = rc s = k΄ p s = k p, where k is the constant involving ‘s' and proportionality constant ‘k΄'.