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I used an ion chromatography system (Dionex IC-2000) to determine the inorganic ions and acid from the samples collected in the atmosphere.

For measuring $\ce{SO4^2-, NO3, Cl-}$, and low molecular acid together, I used a gradient elution method to divide them and quantify their amount.

However, I found that an artifactual band always overlapped with malonic acid shown like this:

enter image description here

This figure was captured in the situation of the single standard of malonic acid.

I want to divide the overlapped peaks efficiently, and have not found any solutions?

Any useful suggestions or tips would be highly appreciated.

My gradient dissolution method

0.000   Autozero
        Concentration =     1.50 [mM]
        Curve =     5
        Load
        Wait    CycleTimeState
        Inject  
        ECD_1.AcqOn
        ECD_Total.AcqOn
        Channel_Pressure.AcqOn
        Concentration =     1.50 [mM]
        Curve =     5

7.000   Concentration =     1.50 [mM]
        Curve =     5

8.000   Concentration =     3.00 [mM]
        Curve =     5

59.000  Concentration =     3.00 [mM]
        Curve =     5

59.500  Concentration =     1.50 [mM]
        Curve =     5

60.000  ECD_1.AcqOff
        ECD_Total.AcqOff
        Channel_Pressure.AcqOff
        Concentration =     1.50 [mM]
        Curve =     5
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  • $\begingroup$ Never did ion chromatography. But it immediately occurs to me that malonic acid is a dicarboxylic acid. Could it be two different species of malonic acid? What is the pH of the eluent? $\endgroup$
    – MaxW
    Jul 6, 2018 at 15:27
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    $\begingroup$ See this paper Determination of Anions and Carboxylic Acids in Urban Fine Particles $\endgroup$
    – MaxW
    Jul 6, 2018 at 15:37
  • $\begingroup$ @MaxW. Thanks for your reply. But one peak occurred even in the situation of clean water. So, I assumed it was $CO_3^{2-}$. The eluent we used is $KOH$ $\endgroup$
    – Han Zhengzu
    Jul 7, 2018 at 0:55
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    $\begingroup$ I'm not quite sure what you want but if you want to analyse them as two peaks just to obtain their areas then there are standard methods with which to do this. The simplest is to assume peak shapes, say gaussian/Voight etc and add them in proportion via least squares until you fit your data. $\endgroup$
    – porphyrin
    Jul 7, 2018 at 7:21
  • $\begingroup$ @porphyrin. Thanks for your reply. One of the peaks was an impurity introduced to the system, and the other one was malonic acid for detection. $\endgroup$
    – Han Zhengzu
    Jul 9, 2018 at 0:53

1 Answer 1

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A mixture of roughly-symmetric peaks can be achieved by a sum of exponential functions.

$$f(x; \vec a, \vec m, \vec s) \triangleq a_{1}\exp\left(-\frac{1}{2}\left(\frac{x-m_{1}}{s_{1}}\right)^{2}\right)\ +\ a_{2}\exp\left(-\frac{1}{2}\left(\frac{x-m_{2}}{s_{2}}\right)^{2}\right)$$

enter image description here

There are a variety of ways that you might fit $f(x; \vec a, \vec m, \vec s)$ including gradient-based methods or Monte Carlo methods.

Edit: You can of course add other terms. From the appearance of the plot above, one may wish to include a constant baseline parameter $\beta_0$.

$$f(x; \vec a, \vec m, \vec s, \beta_0) \triangleq a_{1}\exp\left(-\frac{1}{2}\left(\frac{x-m_{1}}{s_{1}}\right)^{2}\right)\ +\ a_{2}\exp\left(-\frac{1}{2}\left(\frac{x-m_{2}}{s_{2}}\right)^{2}\right) + \beta_0$$

Edit: If you want to create skewed peaks I would looks at a couple of options.

Having different standard deviations to the left and right of the mean is one way of getting asymmetric peaks, which you can model as mixtures.

A second option is to look at transforming (hopefully simplifying) existing skewed distributions into non-distribution peaks which can be put into linear combinations. An extreme example is the skewed generalized $t$ distribution.

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    $\begingroup$ In this answer, I miss the keyword deconvolution which often is used to introduce the technique of multipeak fit in general and in programs (e.g., fityk). $\endgroup$
    – Buttonwood
    Aug 16 at 8:10
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    $\begingroup$ @Buttonwood I agree, one could use deconvolution. Although the OP did not mention the requisite conditions, sometimes signals can also be separated tensor decomposition. And there are further techniques for separating signals. In every case we must suppose something about in what sense the signals can be separated. $\endgroup$
    – Galen
    Aug 16 at 13:30

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