Langmuir equation Totally Explained

Everything about The Langmuir Equation totally explained

The Langmuir equation or Langmuir isotherm or Langmuir adsorption equation relates the coverage or adsorption of molecules on a solid surface to gas pressure or concentration of a medium above the solid surface at a fixed temperature. The equation was developed by Irving Langmuir in 1916. The equation is stated as:
ť

heta  =frac

A plot of (c/Γ) versus (c) yields a slope = 1/Γ_max and an intercept = 1/(KΓ_max). This regression is often erroneously called the Hanes-Woolf regression. The Hanes-Woolf regression was proposed in 1932 and 1957 for optimizing the Michaelis-Menten equation, which is similar in form to the Langmuir equation. Nevertheless, Langmuir proposed this linear regression technique in 1918, and it should be referred to as the Langmuir linear regression when applied to adsorption isotherms. The Langmuir regression has very little sensitivity to data error. It has some bias toward fitting the data in the middle and high concentration range.
   There are two kinds of nonlinear least squares (NLLS) regression techniques that can be used to optimize the Langmuir equation. They differ only on how the goodness-of-fit is defined. In the v-NLLS regression method, the best goodness-of-fit is defined as the curve with the smallest vertical error between the optimized curve and the data. In the n-NLLS regression method, the best goodness-of-fit is defined as the curve with the smallest normal error between the optimized curve and the data. Using the vertical error is the most common form of NLLS regression criteria. Definitions based on the normal error are less common. The normal error is the error of the datum point to the nearest point on the optimized curve. It is called the normal error because the trajectory is normal (that is, perpendicular) to the curve.
   It is a common misconception to think that NLLS regression methods are free of bias. However, it's important to note that the v-NLLS regression method is biased toward the data in the low concentration range. This is because the Langmuir equation has a sharp rise at low concentration values, which results in a large vertical error if the regression doesn't optimize this region of the graph well. Conversely, the n-NLLS regression method doesn't have any significant bias toward any region of the adsorption isotherm.
   Whereas linear regressions are relatively easy to pursue with simple programs, such as excel or hand-held calculators, the nonlinear regressions are much more difficult to solve. The NLLS regressions are best pursued with any of various computer programs.

Further Information

Get more info on 'Langmuir Equation'.

External Link Exchanges

Do you know how hard it is to get a link from a large encyclopaedia? Well we're different and will prove it. To get a link from us just add the following HTML to your site on a relevant page:

<a href="http://langmuir_equation.totallyexplained.com">Langmuir equation Totally Explained</a>

Then simply click through this link from your web page. Our crawlers will verify your link, extract the title of your web page and instantly add a link back to it. If you like you can remove the words Totally Explained and embed the link in article text.
As long as your link remains in place, we'll keep our link to you right here. Please play fair - our crawlers are watching. Your site must be closely related to this one's topic. Any kind of spamming, dubious practises or removing the link will result in your link from us being dropped and, potentially, your whole site being banned.