LMMpro Lesson 1: Introduction to LMMpro.
Objective: Learn how to navigate around the program & graphs.
Focus Group: Langmuir Equation.
Contributed by: C.P. Schulthess (6 January 2008), University of Connecticut, USA.
Requirements: Demo Mode version of LMMpro
Difficulty level: Very easy.
Copyright © 2008 by Alfisol.
The Langmuir equation predicts the amount of adsorption of an element or molecule (Γ) as a function of the
amount of that element or molecule in the liquid (or gaseous) phase (c). The Langmuir equation has two
parameters: the maximum amount of adsorption (Γ_{max}) and the reaction equilibrium constant (K).
The trick, of course, is to know the correct values of these two parameters for a given adsorption
reaction. We determine these values by use of various regression methods and by collecting a set of
data known as an adsorption isotherm.
Most regression methods are difficult to do by hand. Fortunately, various software programs
will perform these regressions for us. We will use the LMMpro program distributed by www.alfisol.com
to calculate the correct values for us. The focus of this set of exercises is to teach you how to
use the LMMpro software and how to navigate around the graphs.
Steps 1 and 2 below focus on getting you started.
It is assumed that someone prior to your use of this
LMMpro software might have manipulated the settings such that you can't seem
to find anything right away.
Steps 3 to 6 focus on very basic features about the display.
Steps 7 to 9 below focus on selecting which data are used and how they are displayed. They also introduce
you to manipulation of the optimization options by showing you how to fix one or both of the
Langmuir parameters with a specific value.
Steps 10 and 11 discuss what may happen if you do unusual things with the
parameters or data options. Step 12 explains the difference between Demo Mode and Full Access Mode.
Step 13 encourages you to snoop around and click on various buttons. Practice makes perfect.

Click on the LMMpro icon to start the program.
The first window you will see is the main menu window.
Make sure that the words "The Langmuir Optimization Program" appears in the top portion of this window.
If they do not, then ask your instructor for help with the following step if necessary:
go to "Options", "Start Up", and make sure that a check mark appears next to
"Start Langmuir Optimization Program". Click "Save", close the software and restart the software.
You have just preset LMMpro to run the Langmuir optimization program.
When it restarts, the words "The Langmuir Optimization Program"
should be visible on the main menu window.

On the main menu
window, click on "Run Demo". A new window will open with the words "Choose a Demo" across the top
on the title bar. You might notice two options at the top,
namely "Langmuir O.P." and "MichaelisMenten O.P.". The letters "O.P." are for
optimization program. LMMpro will show you these two options if it
is preset to run either of these optimization programs. We will not discuss the MichaelisMenten
Equation, but its form is very similar to the Langmuir Equation. The LMMpro software can
optimize the parameters to this equation also and, therefore, it is quite possible that someone
prior to your use of this software has manipulated the program to hide one O.P. and only
show the other.
Review step 1 above and explore by
yourself to see how you can manipultate this preset condition. You should notice that if only
one (1) optimization program is preset (say Langmuir O.P., but not MichaelisMenten O.P.) then
you will have only one title line on the main menu window, and the Run Demo command will not
ask you which O.P. version you wish to perform. It will already know which one if only one option
is allowed in the options menu.

You will practice with a data set that happens to be perfect. No surprises here.
Select "Demo 1" in the "Choose a Demo" window, and click "Run". A new window opens in the
background. Click on it anywhere to bring it into the foreground.
(For now, ignore the fact that the main menu window is still active and will respond to new commands.
We do now wish to go there today.) The name of the new window that you just opened is
"Langmuir Regression Analysis" window as shown across the top on the title bar. The title
bar will also have the name of the data set that is being displayed in the window.

Notice 10 boxes inside the Langmuir Regression Analysis window. You are able to close each
box by clicking on the "X" on the upper right corner of each box.
You can enlarge each box by clicking on its name.
This step is required if you wish to print a particular drawing. To print the Regression Results
table you simply click on the printer icon shown on the upper right corner of the table.
You are asked not to print anything at this time since it is not really necessary for this exercise
and there is no need to waste paper.

Press the <down> arrow on your keyboard. Each time you press this key,
you will notice that the results table highlights a new row. You will also notice
that the corresponding lines or curves are highlighted on the graphs. For example, if you highlight the
"LineweaverBurk" regression, the top left graph also shows this line highlighted. You will also
see the corresponding curves highlighted in the graph labeled "Semilog Ads. Isotherm" and the graph
labeled "Adsorption Isotherm", but this is not very significant now because all the lines in those
two graphs look the same (... well, they at least look the same for this part of this exercise, that is).
Try the <up> arrow on the keyboard also. Using the mouse to click on the regression name on
the Regression Results table has the same effect as the keyboard arrows.

Press the <right> arrow on your keyboard.
You will notice that the data points on each graph are highlighted. The original (x,y) values of each
point highlighted are shown on the lower left corner of the Langmuir Regression Analysis window.
It is important to notice that the highlighted point in each graph has the same original (x,y)
values. They only appear in different places because the plots shown do not have the same
xaxis and yaxis labels. That is, the data in each graph have been modified. The original,
unmodified data are plotted in the lower left corner graph, labeled "Adsorption Isotherm".
Try the <left> arrow on the keyboard also. Finally, depending on the options settings, when you
scroll over the data points with the mouse, you can also see the modified and unmodified (x,y) values
in the tooltip.

Click on the "Data" option on the top left corner of the Langmuir Regression Analysis window.
A new window will open called "Langmuir Data", followed by the name of the data set on the
title bar. This is one of the most used windows in the LMMpro software. If you are running
your program in "Demo Mode", then the "Edit Data" button will be deactivated. You must have a
registered software program for this button to be activated. It is through this button that
you modify the "units", "comments" and "ACF" values. For this present exercise, you do not need
to worry about these items.
 In this window, if you uncheck the "usage" box, then that particular
data entry will be ignored in the regression analysis. Uncheck a few of these, and press
the "Run Regression" button. Notice that a new Langmuir Regression Analysis window will open in
the background. You will need to bring it to the foreground by clicking on it (you will probably
find it at the bottom of your monitor on the task bar). Now study the graphs.
Depending on the options settings, you should
notice that some of the data are drawn differently than the others. Under the
default options, the "not used" data are drawn as red triangles, while the "used" data are drawn as
brown boxes. Use the keyboard arrows to see how these data are displayed. Notice also that the
number of data points used in the regression (N) has now changed. If 3 data points are not used,
then you will see "N= 13 of 16" on the lower left corner of the window.
 Return to the Langmuir Data window, and check several boxes under the "Marked" column. Click on
"Run Regressions" again and study the graphs. This has no effect on the regressions, but it does
draw certain points differently. This option is only useful if you wish to illustrate a point, or
several points, on the graph in a special way for some reason. The need to do this will be rare,
but one reason can be to show that two points exist overlayed on top of each other. You may want to
play around later with how the marked points are illustrated (go to the Options menu for this).

Return to the Langmuir Data window, check to see that all the data are used,
and enter a specific K value. You would do this if you
want the regression results to find the best Γ_{max} value for a specific K value.
Presumably you have reason to believe that your K value is better or was predetermined by other
methods. Check the "Fix K" box and enter a new value. Note that if a value is entered but the box
is not checked, then the entered value is ignored (that is, it is not fixed). Change the K value to
0.03 and click on "Run Regression". Remember to bring the new Langmuir Regression Analysis to the
foreground. You will notice the Regression Results table has the word "fixed" on the top of the
K column, with the values you entered below. You will also notice that this had a major effect on
the results displayed. The plotted curves now seem to be all over the place. Notice that the r^{2}
value of the LineweaverBurk regression is excellent (0.987 is shown on the Regression Results table).
This makes sense because on the upper left graph we see that a very nice fit of the data is still
maintained. However, the corresponding curve on the original data (lower left graph) illustrates a
terrible fit. The goodnessoffit with the original unmodified data is expressed by the
η^{2} and η_{*}^{2} correlation coefficients tabluated on the
Regression Results table. We will not explore this topic any more today.
We leave this for another lesson.

Return to the Langmuir Data window, check to see that all the data are used,
and enter a specific Γ_{max} value. You would do this if you
want the regression results to find the best K value for a specific Γ_{max} value.
Presumably you have reason to believe that your Γ_{max} value is better or
was predetermined by other methods.
Check the "Fix Γ_{max}" box and enter a new value. Note that if a value is entered
but the box
is not checked, then the entered value is ignored (that is, it is not fixed).
Change the Γ_{max} value to
900 and click on "Run Regression". Remember to bring the new Langmuir Regression Analysis to the
foreground. You will notice the Regression Results table has the word "fixed" on the top of the
Γ_{max} column, with the values you entered below.
You will also notice that this had some effect on
the results displayed. The effect for this particular data set is not that great, but the
goodnessoffit is not as good as it was before when the LMMpro software optimizing both the K
and the Γ_{max} values.

Note that if you fix both the K and the Γ_{max} values in the Langmuir Data window,
then you are not optimizing anything at all. You are merely using LMMpro to calculate the various
correlation coefficient values that correspond to these speficied, fixed values.

Do note that if you fix the parameters, some selected values can cause the software to
display very strange results. It may even warn you that certain limits have been reached or that
certain mathematical computations are not allowed. The program will not crash (or, at least, it should
not crash), but the implicated regression involved might not be displayed. We will not discuss
these problems or how to handle them in today's exercise. Just be aware of them at this time.

One final comment. You can save your data shown in the Langmuir Data window, but you cannot retrieve
it if you are using LMMpro in "Demo Mode". You can view and print the saved data
if you use any one of various text editors. Also, you cannot edit or invent your own data if you are
using LMMpro in "Demo Mode".

Play around with the program on your own. There are several features that are easy to figure out.
Review the tutorial that comes with the software. For today, review only the pages that
appear under "Tutorial: Overview of Software".