2. Langmuir Adsorption Isotherm

3. “Adsorption”!
“Isotherm”?

4. In this case, molecules do not adsorb or “stick” to the surface
Consider gas molecules striking a surface
In this case, molecules do not adsorb or “stick” to the surface
Surface

5. In this case, molecules do adsorb to the surface
Now, consider the following scenario…
In this case, molecules do adsorb to the surface
Surface

6. That is, adsorption at a fixed temperature
What about…
Isotherm
- it means…Constant Temperature
That is, adsorption at a fixed temperature

7. molecules in the gas phase molecules adsorbed at the surface
The objective of Langmuir Equation…
…To describe the equilibrium between the molecules in the gas phase and the molecules bound to the surface
molecules in the gas phase
molecules adsorbed at the surface

8. The Experiment… We will: Introduce molecules in this chamber
2. Wait for an equilibrium to reach
3. Plot number of molecules adsorbed versus the equilibrium pressure

9. The Experiment… No Gas Molecule Nadsorbed Amount Adsorbed Pressure, P1 2 3 4 5 6 7 8 9 10 11 12 13 14

10. Now, Let’s introduce 4 Molecules
The Experiment…
Pressure, P
Amount
Adsorbed
Nadsorbed 1 2 3 4 5 6 7 8 9 10 11 12 13 14

11. Now, Let’s introduce 4 Molecules
The Experiment…
Pressure, P
Amount
Adsorbed
Nadsorbed 1 2 3 4 5 6 7 8 9 10 11 12 13 14
1 in gas phase
3 adsorbed

12. Now, Let’s introduce 8 Molecules
The Experiment…
Pressure, P
Amount
Adsorbed
Nadsorbed 1 2 3 4 5 6 7 8 9 10 11 12 13 14
2 in gas phase
6 adsorbed

13. Now, Let’s introduce 12 Molecules
The Experiment…
Pressure, P
Amount
Adsorbed
Nadsorbed 1 2 3 4 5 6 7 8 9 10 11 12 13 14
4 in gas phase
8 adsorbed

14. Now, Let’s introduce 15 Molecules
The Experiment…
Pressure, P
Amount
Adsorbed
Nadsorbed 1 2 3 4 5 6 7 8 9 10 11 12 13 14
7 in gas phase
9 adsorbed

15. Now, Let’s introduce 21 Molecules
The Experiment…
Pressure, P
Amount
Adsorbed
Nadsorbed 1 2 3 4 5 6 7 8 9 10 11 12 13 14
11 in gas phase
10 adsorbed

16. Finally, Let’s introduce 24 Molecules
The Experiment…
Pressure, P
Amount
Adsorbed
Nadsorbed 1 2 3 4 5 6 7 8 9 10 11 12 13 14
14 in gas phase
10 adsorbed

17. We can plot this data as a fraction of molecules adsorbed
Fraction Adsorbed 
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Number Adsorbed
Fraction Adsorbed
Maximum Available sites 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Pressure, P

18. So, how to describe this behavior?
In 1916, Langmuir proposed a simple model…
Basic Assumptions…
Adsorption sites are homogeneous and equivalent
2. The adsorbed molecules are immobile and they do not interact
3. Only a monolayer coverage is possible
Irving Langmuir

19. So, how to describe this behavior?
In 1916, Langmuir proposed a simple model…
Based on these assumptions, Langmuir derived the following equation…
Equilibrium constant
Fraction Adsorbed
Equilibrium Pressure
Irving Langmuir

20. This is the Langmuir Equation describing (fitting) the Data
Fraction Adsorbed 
Recall, the data we collected
Based on these assumptions, Langmuir derived the following equation…
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Equilibrium constant
This is the Langmuir Equation describing (fitting) the Data
Fraction Adsorbed
Equilibrium Pressure 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Pressure, P

21. This is the Langmuir Equation describing (fitting) the Data
Fraction Adsorbed 
Recall, the data we collected
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Notice…
This is the Langmuir Equation describing (fitting) the Data
And at low concentration, adsorption is linearly proportional to P 1 2 3 4 5 6 7 8 9 10 11 12 13 14
i.e. reaches a monolayer
Pressure, P

22. The Langmuir Equation Now, that’s an equation for another video!
Stronger binding affinity
What about the Equilibrium Constant, K…
Larger the value of K, stronger the binding
Equilibrium constant can be used to calculate Gibb’s free energy of adsorption using the following equation…
Now, that’s an equation for another video!

23. Langmuir Equation - Application
Kinetics of Catalytic Reactions A B C
Product
Surface Reaction
Adsorption
Pollution Remediation
adsorption of contaminants to colloids
Material Science
e.g. adsorption on DSSCs

24. Tidbits about Langmuir
Historical
Tidbits about Langmuir
Was nearly blind for the first eleven years of his life
Graduated from Columbia’s School of Mines, NYC in 1903
Post graduate work at Univ. of Gottingen in Germany in Physical Chemistry under Walther Nernst
Irving Langmuir
3rd Law of Thermodynamics
Nernst Equation

25. Tidbits about Langmuir
Historical
Tidbits about Langmuir
Was nearly blind for the first eleven years of his life
Graduated from Columbia’s School of Mines, NYC in 1903
Post graduate work at Univ. of Gottingen in Germany in Physical Chemistry under Walther Nernst
Irving Langmuir
Worked at the General Electric Labs
3rd Law of Thermodynamics
Nernst Equation

26. Tidbits about Langmuir
Historical
Tidbits about Langmuir
Was nearly blind for the first eleven years of his life
Graduated from Columbia’s School of Mines, NYC in 1903
Post graduate work at Univ. of Gottingen in Germany in Physical Chemistry under Walther Nernst
Irving Langmuir
Worked at the General Electric Labs
1932 – First Industrial Chemist to receive Nobel Prize in Chemistry
“for his discoveries and investigations in surface chemistry “
This is the same year Schrodinger won the prize in Physics

27. Resources The End http://www.britannica.com/biography/Irving-Langmuir
Music: “Mouton Swing” by Robert R. Putnam –
Resources