Alfisol, LLC, Item 003:

LMMpro, version 1.06 The Langmuir Optimization Program plus The Michaelis-Menten Optimization Program.

What does LMMpro do? History of Linear Regression Methods Linear Regressions Deriving Linear Regression Methods

NLLS Regressions v-NLLS Optimization n-NLLS Optimization Axes Conversion Factor (ACF) Types of Errors

Correlation Coefficient (r2) Correlation Coefficient (η2) Correlation Coefficient (η*2) Do's & Don't's References Cited

The Langmuir Equation --- an overview.

The Langmuir Equation assumes that the adsorption reaction involves a single reaction with a constant energy of adsorption. Using mass action laws for its derivation, these are the only assumptions made. Because of its simplicity, it is often the first theory tested on any adsorption data set.

Properly optimizing the parameters involved (namely Γ_max and K) will greatly impact the conclusions made about the data collected. It may also impact the decisions made by the researcher as to which objective the current project should pursue next.

The equation can be derived as follows:

• Assume that only one reaction is involved, expressed as:
  

  S + A = SA

  where S is the solid surface with nothing on it, A is the compound in the liquid or gaseous phase, and SA is the solid surface with compound A on it.
• Let c = (A) = equilibrium concentration of compound A in the liquid or gaseous phase, and define the equilibrium constant, K, as products over reactants:
  

  K = {SA} {S} c

• Define the total number of reactive sites, Γ_max:
  

  Γmax = {SA} + {S}

• Combine the equations above in adsorption terms; that is, using {SA} terms:
  

  Γmax = {SA} + {SA} K c

• Finally, solve for {SA}, and let Γ = {SA}. The result is the Langmuir equation:
  

  Γ = Γmax K c 1 + K c

If K is known, if Γ_max is known, and if the reaction is as described above, then the amount adsorbed (Γ) can be predicted for any concentration (c) of compound A. The two parameters (Γ_max and K) are obtained by regression analysis of known c and Γ values.