Multi Component Analysis (MCA):
Have you already understood the
General Beer-Lambert Law[1]
in it's full extend?
If not, then please study it first, otherwise you will have only very little success by applying MCA to your work !
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MCA Practice I:
Do you know Exactly!, what "Real MCA" has to do with the "General Beer-Lambert Law"?
If NOT — Then you will NOT HAVE ANY Benefit WITHOUT
studying the required, little Theory[2] before !!
The Recipe: How to do a Real MCA Method/Calibration!
| The Second "Golden" Rule of Doing MCA:[3] |
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USE NEVER Mixtures for ANY Calibration of a MCA Method,
WITHOUT BEING READY to PAY LATER the HIGH PRICE for making such an IMPORTANT
MISTAKE !!
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| A.) |
Measure all Standards, and check their Linearity[4]! |
| B.) |
Do an "IDEAL MCA": — and check for
- Correctness of results,
- Rel. Standard deviation of results,
- Relative Fit Error (RFE)! |
| C.) |
Decision: "IDEAL MCA" OK? |
| D.) |
Do a "REAL MCA": — and check for
- Correctness of results,
- Rel. Standard deviation of results,
- Relative Fit Error (RFE)! |
| E.) |
Decision: "REAL MCA" OK? |
| F.) |
Do "MCA of Real Samples": — and check for
- Correctness of results,
- Rel. Standard deviation of results,
- Relative Fit Error (RFE)! |
| G.) |
Decision: Is the "Elaborated Model adequate" ? |
| H.) |
Document: "The whole Calibration" ! |
Discussion of the Recipe:
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| 1.) |
If you try to use Mixtures for your Calibration of any MCA Method you have to accept, that you have lost a Lot of possible AND required Information for any reliable Analytics.
For one Example, - but only one - , the Statement of Prof. Dr. S. Ebel[5],
that with Mixtures you are able to detect "Interactions"[6] between the Species in Solution,
can NEVER be true, because in case of Mixtures you have ALREADY build the Interactions into
all and every standard, and so you will NEVER be abel, NOT in ANY way!!, to divide this Interactions
out of your results ANYMORE!
BE TOLD: Sooner or later you will have to pay a high Price for taking the Risk NOT TO KNOW some/all important Influences of your installed Calibration into Routine Work!!
But there is an easy way to satisfy the requirements formulated by the "Falk"-Diagram of Prof. Dr. S. Ebel[5]
in a little different, but even a somewhat more secure Procedure!
In case you find any Interactions, it will be in Step D.) and E.) of the Recipe, there are enough other Methods to correct/complete the Model! We will talk about it later! |
| 2.) |
During the Screening for the best Solvent, pH (Buffer!), and other Parameters, it is allowed without any risk, - you will realise it later - , to skip the Check for Linearity!
But DON'T forget to complete your Report for your MCA Calibration with the Linearities in the Solvent-Mixture you have found!
Delay the Linearities in this kind to the last Step of the Recipe speeds the Calibration procedure by several Factors, and makes this kind of Analytics very attractive over quite a Lot of other Methods. |
| 3.) |
What is an "IDEAL MCA" AND what is its Benefit? (Why is it required?)
Don't be surprised, it's for checking the Collinearity!
YES, Yes, yes, - it's still true, that we do NOT to have to take care for the Collinearity as the "Real World Theory" is telling us!
But we are able to use this circumstance to make a more reliable, a more secure Calibration for all times!
It's a Benefit you should NEVER miss, and so NEVER skip this Step of the Recipe!!!
For the "IDEAL MCA" you generate a mathematical "Real World Sample" in a very easy way:
Count all measured Standard spectra together and add a NOISE-Spectrum to the sum.
The NOISE-Spectrum you can easy create from one or two "Baseline" and a Gain-Factor, corresponding to your knowledge of the Noise feature of your Spectrometer.
From this generic "Real World Sample" you know all and anything, but specially the results, the standard deviation, and the RFE, in case you analyse it now with only the Standard spectra, and without the NOISE-Spectrum.
What you are now able to detect in contrast is the - maybe a little misleading called - "Physical Collinearity".
Of course, it's only an Estimation of the Sensitivity of "Physical Collinearity", but it has a quite high Significance!
Now, in presence of any (more or less) Collinearity the results of the "IDAL MCA" will very soon significantly differ from the mathematical "exact" Solution,
indicating also how strong the influence will result to all other samples, too. (Do you know why, too?!!)
In this early State of Method development you have now plenty of possibilities to overcome also this "Physical Collinearity", once and for all! |
| 4.) |
But what the hell is now a "REAL MCA" without any "Real Sample"?:
It's just the next important Step of the Recipe to secure, that you never will run into false Results caused by any Interaction of any Species in Solution.
From this description, do you know already how you have to do it?
Precisely, — generate several Sample by pipetting different ratios of all Standards, as exactly as possible, together.
Now it's the second time, the RFE presents its very much higher significance than the individually concentrations itself, AND all other statistical Parameters!
As you may find some minor pipetting errors, for the RFE in contrast it's NEVER allowed do leave the close "neighbourhood" of 1.000!
As soon as you detect such Interactions[6] - of any kind - you know at the same moment, that you have to correct your postulated model a second time.
Later we will also talk about the different possibilities you still have in such a case! |
| 5.) |
Now it's Time for the FINAL TEST: Do "MCA of Real Samples" (Use your "Test Set"!)
With this final Test you ENSURE, that your "Elaborated Model" will fit the Real World of your later Routine Work!!
Now you may be absolutely surprised, that NOT the "Correctness of the results", BUT also NOT the "Rel. Standard deviation of results" will
play the important role of the "FINAL JUDGMENT" for the given "Fitness" of your "Elaborated Model"
Once again, only the RFE with its absolutely incredible Significance IS the onely graduated Master to do this important "JUDGMENT" at all!
Don't worry about the Fact that you have first to elaborate a few Calibrations and to do some Routine Work to discover the Importance of this absolutely incredible Parameter
called "Relative Fit Error" (RFE) at its full extent !!!
Maybe you have realised, that this Statement 5.) contains some Extrapolation ("of your later Routine Work!!")? —
It's for sure one of the most rarely Places in Science, where Extrapolation is NOT ONLY ALLOWED!
As a Quintessence: With the "Relative Fit Error" (RFE),
NEVER BEFORE in whole Science there was a similar INDEPENDENT Parameter/Guard existent, who guaranteed the Quality of your Daily Work to
such an Extent! — It's like feeling yourself all times in the "Arms of Abraham and Moses"
Now it's also absolutely clear to you that in Relation all other statistical Parameters such as:
RSS, SEE, PRESS, MCC, MSEP, RMSEC, RMSEP, SED, RMSECV, EIV, and others, are only "Strongmans" of weak kind! |
| 6.) |
The only thing now left to you is The Documentation of your "Whole Calibration"!
But DON'T forget now to complete your Report with the required Linearities[4]
of your Standards in use!
That's it! — You have all done, what's required!
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| 7.) |
I think it's more or less obvious - if not already discussed - what you have to do if you fail during Step: C.), E.), or G.)! |
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ARGUS IS THE TOOL which allows you to carry out this previous Steps in an easy and quick way,
and to GUARD your Daily Quality!
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Now I'm sure, it's quite easy for you to formulate the requirements for doing MCA:
— Thus, The following conditions have to be respected imperatively :
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Each Component/Standard must obey the
General Beer-Lambert Law[1]. |
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No unknown physical or chemical reaction must occur between two or more Compounds/Standards in the mixture or between Compound and Solvent. |
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All measurements (Standards AND Samples AND Routine-Samples) have to be carried out in the same Cuvette! |
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Compounds/Standards and Samples must be dissolved in the same Solvent or Solvent-Mixture!
It is generally necessary to use buffered solutions, since a great number of Substances show pH dependent absorbance spectra! |
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The absorbance contribution of each Component to the Mixture Spectrum should be significantly higher, than three times the Noise of the Spectrometer! |
With these Requirements in mind it is easy to follow the Recipe to develop a MCA Calibration AND to test the created model!!
So the next Chapter will cover:
"The Manually Elaboration of a MCA Calibration" and is entitled:
MCA Practice II
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 References:
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