Study on adsorption isotherm for understanding adsorption mechanism

Adsorption isotherm is a mathematical equation that explains the transmission of adsorbate from solution to the adsorbent at equilibrium condition. Langmuir, Freundlich, and Temkin isotherms were used to evaluate the experimental results.

1. ADSORPTION ISOTHERMS Presented by: Pramadha S P230148CH

2. BET ISOTHERM

3. STATEMENT Brunauer–Emmett–Teller ( BET ) theory aims to explain the physical adsorption of gas molecules on a solid surface and serves as the basis for an important analysis technique for the measurement of the specific surface area of material s. In 1930, it became clear that the physisorption of gas on a solid adsorbent is not restricted to a monolayer formation, but if the pressure becomes sufficiently high, a multilayer of adsorbed species can be formed. For describing the multilayer adsorption, Brunauer, Emmett, and Teller developed a theory (so-called BET theory) in which the Langmuir theory is extended to the multilayer adsorption. The BET theory is based on Langmuir assumptions, for the monolayer adsorption.

4. ASSUMPTIONS Adsorption occurs at fixed sites with no migration to adjacent sites. There are n o molecular interactions. The heat of adsorption during monolayer formation is constant. Heat effect associated with the formation of subsequent layers is equal to the heat of condensation.

5. LIMITATIONS Tends to overestimate the adsorption at high pressures and underestimate it at low pressures. BET isotherm may fail at low pressures or low surface areas due to the accuracy of the measured pressure or volume change of the gas. If there is little adsorption, the measured value is small, and it may be comparable to the error of measurement. BET isotherm may also fail at higher gas partial pressures due to several reasons, such as the assumptions made not holding up as the thickness of the adsorbed layer increases.

6. APPLICATIONS Adsorbent surface area determination. In cement and concrete industry to measure the specific surface area to differentiate between cements. In catalysis - surface area of catalyst - important factor in catalytic activity. Surface area analysis of nanoparticles. To determine the specific surface area of porous materials including amorphous and crystalline materials.

7. The BET isotherm can be mathematically expressed as: The BET isotherm

8. Dubinin - Radushkevich (DR) Model

9. The Dubinin- Radushkevich (D-R) equation, which was originally proposed as an empirical adaptation of the Polanyi adsorption potential theory, has been the fundamental equation to quantitatively describe the adsorption of gases and vapours by microporous sorbents. Dubinin Radushkevich (D-R) model is a more general model in which assumption is not based on homogenous surface or constant adsorption potential , it gives insight into the biomass porosity as well as the adsorption energy . The value of adsorption energy further provides information as to whether adsorption process is physical or chemical in nature. D-R model is expressed mathematically by: ln q e =ln q o - 𝞫𝞮 2

10. where q e is the amount of RhB ions adsorbed per unit weight of adsorbent (mg/g), q o is the maximum adsorption capacity, β is the activity coefficient useful in obtaining the mean sorption energy E (kJ/mol) and Ɛ is the Polanyi potential. Ɛ and E are expressed by the following Eqs.; where R is the gas constant (J/mol K) and T is the temperature (K). q o and β (mol2/kJ2) can respectively be calculate from the intercept and the slope of the plot of lnq e vs Ɛ 2 . 𝟄 = RTln [1+ (1/Ce)] E = √1/2 β

11. The Adsorption energy (E) obtained from Dubinin–Radushkevich (D-R) isotherm was 6.11 kJ/mol suggesting that the uptake of RhB onto RH was by physisorption. D-R model is least applicable for microporous adsorbents with a wide micropore distribution. The D-R isotherm does not reduce to Henry's law at low pressures , which is a necessity for a thermodynamically consistent isotherm. RESULTS & LIMITATIONS

12. Langmuir Model

13. The Langmuir isotherm which assumes a monolayer adsorption, surface with homogeneous binding sites, equivalent sorption energies, and no interactions between adsorbed species is expressed by the mathematical relation where C e is the equilibrium concentration of RhB dye (mg/L), q e is the quantity of RhB dye adsorbed onto the adsorbent at equilibrium (mg/g), q max is the maximum monolayer adsorption capacity of adsorbent (mg/g) and KL is the Langmuir adsorption constant (L/mg). The plot of C e /q e against C e gives a straight line with a slope and intercept of 1/q max and 1/q max KL respectively. KL is an important tool in the calculation of the dimensionless equilibrium parameters (RL) that explains the favorability of adsorption process;

14. RL is calculated using Because isotherm data from protein adsorption studies often appear to be fit well by the Langmuir isotherm model, estimates of protein binding affinity have often been made from its use despite that fact that none of the conditions required for a Langmuir adsorption process may be satisfied for this type of application. It fails to account for the surface roughness of the adsorbent . Rough inhomogeneous surfaces cause some parameters to vary from site to site.

15. Assumptions made in LAI The solid surface should be homogenous. It should have a fixed number of adsorption sites. Each site must adsorb only one molecule (mono-layered adsorption). The adsorption of molecules is confined to a monomolecular layer. The adsorbed gas behaves ideally in the vapor phase. There is no interaction between the adsorbed molecules. The rate of adsorption and desorption becomes equal at their dynamic equilibrium. Uses of LAI Langmuir adsorption isotherm gives a quantitative explanation of adsorption. Unlike Freundlich adsorption isotherm, it explains the mechanism of chemisorption. It gives a more satisfactory quantification of adsorption as compared to Freundlich’s adsorption isotherm when explaining the adsorption of gases on solid surfaces.

16. Limitations of LAI Langmuir adsorption isotherm is only applicable at low pressure and fails at high pressures. P/x = 1/k’ + P/k’’ At low pressure, P/k’’ may be ignored and the isotherm becomes x = k’ P. At high pressures, 1/k’ may be ignored and the isotherm becomes x = k’’. This theory does not explain all the experimentally observed adsorption isotherms. It assumes that the surface of a solid is capable of adsorbing a single layer molecule thickness, but in actual practice, it is a much thicker layer. The adsorption saturation value is generally independent of temperature, but the experiment shows that the saturation value decreases with an increase in temperature.

17. The given graph is the verification of Langmuir isotherm for adsorption of nitrogen molecules on mica at the temperature of 90K. A plot between C e /q e versus C e will generate a straight line with a slope of 1/q o (adsorption capacity) and an intercept equals to 1/K L q o (equilibrium constant). Intercept = 1/K L q o Slope = 1/q o

18. Freundlich Model

19. I n 1909, Herbert Freundlich gave an empirical relationship to explain the variation of the amount of gas adsorbed per unit mass of the adsorbent (solid) with pressure at a constant temperature. w/m = kP 1/n Where, w = mass of gas adsorbed; m = mass of adsorbent; P = pressure; k = constant; n = number of moles. According to the above equation, a curved isotherm is obtained when plotting the mass of the gas adsorbed per unit mass of adsorbent (w/m) against the equilibrium pressure.

20. The graph between log w/m against the log P at higher pressure shows a slight curvature , which makes this isotherm, invalid for higher pressures . The above graph shows that the Freundlich isotherm is not applicable at higher pressure. By taking the log on both sides of the Freundlich equation, we get; log w / m = log k + 1 / n log P

21. Uses of FAI Freundlich adsorption isotherm is used to determine the extent of the adsorption of gases on solids at low pressures. It is also used for the adsorption of solute in a solution. Limitations of FAI Freundlich equation is purely empirical. It does not have any theoretical basis. The constants in the equations ‘k’ and ‘n’ vary at different temperatures. It is valid only for a specific range of pressure.

22. Reference. Hutson, N.D., Yang, R.T. Theoretical basis for the Dubinin-Radushkevitch (D-R) adsorption isotherm equation. Adsorption 3 , 189–195 (1997). https://doi.org/10.1007/BF01650130 . A.A. Inyinbor, F.A. Adekola, G.A. Olatunji, Kinetics, isotherms and thermodynamic modeling of liquid phase adsorption of Rhodamine B dye onto Raphia hookerie fruit epicarp, Water Resources and Industry, Volume 15, 2016, Pages 14-27, ISSN 2212-3717. https://doi.org/10.1016/j.wri.2016.06.001 . Latour RA. The Langmuir isotherm: a commonly applied but misleading approach for the analysis of protein adsorption behavior. J Biomed Mater Res A. 2015 Mar;103(3):949-58. https://doi: 10.1002/jbm.a.35235. Epub 2014 Jun 3. PMID: 24853075. Surface and Colloid Chemistry: (Principles and Applications) by K.S Birdi (Berkeley, University of California & Unilever, Copenhagen, Denmark) Essential of Physical Chemistry: 2nd edition By B.S Bahl (Gurdaspur, India) and Arun Bahl (RSC, UK) and G.D. Tuli (Delhi University, India) Principle of Physical Chemistry by Haq Nawaz Bhatti (University of Agriculture, Faisalabad, Pakistan) Adsorption isotherms (toppr.com)