Langmuir Adsorption Isotherm

“Adsorption”! “Isotherm”?

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

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

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

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

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

The Experiment… No Gas Molecule Nadsorbed Amount Adsorbed Pressure, P 1 2 3 4 5 6 7 8 9 10 11 12 13 14

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

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

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

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

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

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

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

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

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 1881 -1957

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 1881 -1957

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

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

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!

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

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 1881 -1957 3rd Law of Thermodynamics Nernst Equation

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 1881 -1957 Worked at the General Electric Labs 3rd Law of Thermodynamics Nernst Equation

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 1881 -1957 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

Resources The End http://www.britannica.com/biography/Irving-Langmuir http://www.nobelprize.org/nobel_prizes/chemistry/laureates/1932/langmuir-bio.html http://www.aip.org/history/newsletter/spring2007/photos.htm http://www.nndb.com/people/776/000079539/ Music: “Mouton Swing” by Robert R. Putnam – https://archive.org/details/MoutonSwing Resources