Sampling: Possible Source of Systematic errors BEFORE Chromatography starts.

As chromatography acts everywhere, the sample taking step may already falsify the true sample composition. Adsorption on any surface, “preparatively acting” displacement chromatography, removal of now unstable compounds which had been stable inside their “mother compounds” and many other effects like a water saturated surface in the sample transfer tube or the raw sample container and all steps of the so-called sample preparation procedure may end up with something no longer even similar to the original substance composition at the raw sample source.

The place, the time, the physical conditions during the sample taking steps are of utmost importance so that the optimization of all sample taking details are reason to take quite a lot of analyses prior the finalization of the method optimization. Regulation DOES NOT help, as no regulator could know what the real substance situation is on that date and hour the analytical sample has to be taken from the source. In fact this situation is enough reason to refuse regulation as it would press the analyst to “make errors”
If now the sample giving, the starting process for the chromatography, the separation, the quantitation (integration), the data analysis and the decision making have their own error impact then we have an error chain to be cleared step by step.

These are reasons why so many warnings and hints are given here in order to help the chromatographer for accurate and precise (enough) analytical results.

The best strategy to check the possible error chain is the stepwise clearing from its end, not from the beginning.
This is possible with a clever TEST program with a well known quantitative test mixture of not too simple composition containing at least some of the main substances one has to quantitize in the real main sample of interest. The conditions “quantitative”, “not too simple”, “well known” are important. “Well known” is a not too simple test mixture. Its qualitative and quantitative composition must remain constant over a long(er) period of time. According to tests the author and his coworkers made for many years globally we have to refuse all test sample containers with soft plastics whatever shape they have. A narrow longer extremely well sitting hard PTFE stopper may be acceptable for some months. But in order to keep (expensive) quantitatively certified test mixtures or your own “not too simple” one for years as “well known”, the principle and materials shown in the following figure will help.



Cheap but of best economy for expensive materials:

GT = glass tube             
TS = test substance in a syringe
        (2...5 ml)
N2 = nitrogen in an airtight syringe
GT+N2+TS = filling of the glass tube
F = a fine flame, which melts easily the glass of the tube GT, closing two sides at once.
The resulting small tube containers are partially filled by substance and by N2.
The inner diameter of the mini tubes must fit with the outside diameter of the used analytical sampling syringe.

Analytical data have to be quantitatively AND qualitatively correct. This means the whole chain of quantity effects must be checked. Again the possible error chain is at best analyzed from the end to the beginning. Thus the quantitation / integration must be OK and the detection must be correct. There is no GC-, HPLC- or HPTLC detector known, which is linear within its whole working range. Thus the “linearity” (or more correct: the NON linearity) must be found out. There are quite some details which must be tested, therefore the following is given in “points”:

Linearity - Calibration Function -
Tests and Statistics of Quantitative Chromatography Data

Statements: )1

    1.   No detector is linear.
    2.   All detectors have a limited working range.
    3.   Each substance in each detector needs a substance specific calibration.
    4.   No calibration line is linear.
    5.   No calibration line is free from noise.
    6.   The single point calibration is absolutely useless in GC, HPLC, µ-PLC / HPTLC.
    7.   At least four, better five to seven calibration points are necessary for a
          qualified quantitative result in GC, HPLC, µ-PLC / HPTLC. The signal size over
          substance concentration or substance amount MUST be enclosed by a lower and
          a higher part of the calibration line.
    8.   Most of calibration substances have a limited purity, the real purity must be known.
    9.   Calibration substances or mixtures should be stored in the dark, under inert gas,
          in molten glass liners (not ampoules) and in portions small enough for
          four consecutive injections only to be done within a shortest period of time.
    10. Taking, giving and transmitting a sample into GC or HPLC is easily source of
          serious quantitative errors due to “natural chromatography” prior to the analytical
          chromatography and due to dead volumes and the time necessary for a
          complete solution of all substances into the mobile phase. If technically possible, a sample
          focussing inside the separation system is helpful. Correct sampling in
          TLC / HPTLC is even more prone to quantity errors, focussing after sampling is a MUST.

    )1 statements still correct in 2005 since the first book on quantitative GC was written by the author in the late fifties.

To 1: Linearity tests are so critical to be done correctly, that one should better use calibration statistics as this “repairs” non linearity towards correct quantitative results.

To 2: The working range starts at the detectability limit and ends when the statistics of the upper end of a calibration line goes significantly outside the accepted level of precision - this is seen in the graphics display of the calibration line statistics. However one should know at which signal height the “translation” from “gram per second” into volt or ampere deviates from applicability. A logarithmic signal display and an electronic signal overshoot warning may help but in this respect many even latest instruments would need an improvement. To show and use only digital signal data is one of the reasons for serious systematic quantity errors. A graphics display helps immediately to see if something went wrong.
Use “line chromatograms

To 3: Substance specific correction factors help only in a very limited range of absolute amounts in gram per second or per milliliter / microliter / nanoliter. Preferrable is the use of substance specific calibration functions.

To 4: Again: use the substance specific calibration line.

To 5: Use the calibration line mathematics in full range and check by graphics.

To 6: The single point calibration line is source of serious quantity errors as is the “rule of three”. Although very many “regulations”  insist to use this mathematically illegal procedure it is too simple to show that errors easily reach full percentages in many quantitative chromatography jobs.
See figure 2 below.


S       = signal (volt, ampere)
W      = substance weight, concentration
CL     = calibration line
WCP  = weight, concentration, volume of substance
             injected for calibration
SCP   = correlated signal

This defines the calibration function as
SCP   = a * WCP. (a is constant)

This calibration line “goes through zero”, at S=0 is W=0
“zero” however cannot be measured.
SA     = found signal at analysis for the same substance as
             used for calibration.
WA    = found result of “quantitative” analysis.
This calibration line is strictly linear, but nothing has been done to check for.
For a linearity check AT LEAST three calibrations at differing signals are necessary.

Rule of Three - The Correctness Overkill :

All analyses based on the “rule of three” would need a non existing perfect calibration linearity. The relation of any size of an analysis signal to any size of an analytical quantity for the calibration substance is kept as a signal independent constant. There is no working range limit. Even highest signals are transformed this way into a correlated quantity when the detector may have left already long before its correct functionality.

This fundamental problem of overrunning the working range limit is solved using EXPORT software which automatically checks the reduced post integration raw data and alarms (for instance just by a change of the data color on screen or in printed reports) when the working range limit is left.

To 7: A minimum of three calibration points surrounding the total range of chromatography signals - BUT MEASURED AS PEAK HEIGHT -  is a must to check for linearity within the practical working range. As most of detector signal functions are of second or third order, five or six calibration points are the necessary minimum for correct calibration functions. The best mathematical model which handles this range of signal-to-quantity in analytical chromatography is the polynomial interpolation mathematics. The formula is simple:

                Signal = A + B*weight + C*weight2 + D*weight3                                  [1]

A, B, C, D are constant polynom factors which are found immediately using the proper software, which together with the graphics display of the found calibration function provides all ldata quality statistics but upon demand only. Trouble users may see is the fact, that they ask for weight data which are based on the signal values they got from their integrators. Polynomial interpolation software iterates weight-values from signal data. There is a ten page publication available in J. Planar Chromatogr. 18 (2005) 256-263 discussing all details of the polynomial interpolation mathematics in quantitative chromatography, so that here is no need to go into all details of the correlated statistics. Figure 3 below shows an application example, figure 4 clears the source for errors in calibration, not too seldom to find...

To 8: Most calibration substances have a limited purity. If it is known, all weight data for calibration substance “cs” must be corrected by the factor f = 0.01 * purity [weight %] using the purity value for substance “cs” given in weight-%.

To 9: Even very expensive or highly toxic test substances are often stored in “heavy weight mini” glasses closed by plastics. The latter guarantees a quite limited life time. Much more economical and especially safe for correct quantitative chromatography are “containers” which can be used for only four consecutive test runs and cost nearly nothing. Glass tube with 1.5 ... 2 mm outside, 0.5 mm inside diameter, closed by a micro flame on both ends does it. These micro ampoules contain only about 2...10 microliter solution good for 4 repeated calibration runs per selected concentration, see figure 1 above.

To 10:
As chromatography acts everywhere, it also acts on any type of surface in any tool. No surface is completely free from water and after the first use for sample taking and giving, this surface is saturated with substances of the sample. The sample substances remain causing displacement chromatography. Thus we have a sorption process with saturation of the water layer, adsorption on the solid part of the surface and following “preparative” displacement  chromatography. The surface is normally rough, thus the real surface size is easily ten times and more larger than calculated. Many surfaces are not only water wet but keep the substances used at production. On glass surfaces water can be removed only under flowing extremely dry gas at temperatures near the glass melting point or stay even in very high vacuum but in the second the glass surface is in contact with any wet gas, vapor or liquid, strong sorption starts quickly again. Thus the “substance memory” of any surface is a standard problem for trace analysis but also for high precision chromatography. Sample falsification by taking / giving the next sample is serious. What to do ?
10.1 Enrich traces prior sampling. This statement is correct although there is opposition against it.
10.2 Saturate surfaces, let the correct sample flow through prior final sampling.
10.3 Think of “dead volumes” where the sample flow is turbulent and remixes with mobile phase.
10.4 Keep mechanical inner diameters of containers as small as possible, avoid large diameter changes and have the total inner volume small enough, but think of the necessary saturation and equilibration when the sample is finally transferred into the analytical system. Every surface prior the separation column / capillary is of equal sample falsifying nature, keep it at a minimum.
10.5 Have the inner surface of any container or connection tube as smooth as possible.
10.6 Avoid temperature changes from cold at taking to warm at giving: the specifically substance saturated surface acts like a sponge which fills itself at low temperature and is pressed empty when getting warm.
10.7 Why not directly sampling into the separation system ? The successful way if traces count. This of course need separation systems which are easy portable and can be installed fast and tight.
10.8 If there is any way to “focus” the given sample into the smallest length along the separation direction, do it.
10.9 Syringes are sample containers falsifying the next sample. Any needle surface - often VERY rough and sorption active - is source for serious data falsification up to critical court cases especially when a critical (legal) limit of substance concentration counts. Water only is not the best cleaning liquid to get rid of polar substances like di ethylene glycol just as one example. The calibration syringe should not be used as analysis syringe in case concentrations of a critical substance differ between calibration and analysis.


Application example:
Polynomial Interpolation
of five calibration samples given once.
The data are so poor, that only a first degree polynom is applicable.

To check for the source of errors, N=4 sampling repetition would help to find out, if the chromatography fails or the calibration sample concentration is wrong.

See figure 4 for the answer.

Polynomial Interpolation
Error check:

The main error source is the quality of the calibration samples taken: at least two serious “runaways” in the 23 samples are seen in the samples TWO and FOUR. Runaways MUST be removed.
The calibration function is clearly of third order independent of the sampling errors but the data are so bad because of sampling errors, that the calibration must be redone - see figure 5, where the 95% error area is nearly equal the function line itself.

Strict improvement of all factors for correct calibration using the “sf4” procedure (see “sf4”)

Although the calibration function is of third order, the overall data precision reaches +- 0.19% (+- 0.13 %)

A first degree polynom would result in an overall data precision of only
1.00 % as mean deviation of measured values versus calculated with a standard deviation
of +- 0.58 %

The quantities in figure 5 are given here:

The polynom degree to be taken is THREE because of the following values:
Using first order would offer polynom factors which cannot be better interpolated than
at +- 1.00 % (+-0.58).
The second order polynom offers a data quality of +- 0.55 % (+-0.42).
The third order has a data quality of +- 0.19 % (+-0.13) for all measured to all interpolated signal
values. All injections were repeated 4 times, five differing amounts (10, 20, 30, 40, 50) were used:

 Test sample peak “T” of interest injected:       Signal for “T” found:  Signal interpolated:
                                                    10 units                10255                   10253.532
                                                    10                         10298                   10253.532
                                                    10                         10257                   10253.532
                                                    10                         10261                   10253.532
                                                    20                         19535                   19591.621
                                                    20                         19533                   19591.621
                                                    20                         19539                   19591.621
                                                    20                         19532                   19591.621
                                                    30                         29105                   29041.943
                                                    30                         29109                   29041.943
                                                    30                         29195                   29041.943
                                                    30                         29100                   29041.943
                                                    40                         38148                   38198.371
                                                    40                         38144                   38198.371
                                                    40                         38135                   38198.371
                                                    40                         38139                   38198.371
                                                    50                         46697                   46654.782
                                                    50                         46682                   46654.782
                                                    50                         46602                   46654.782
                                                    50                         46695                   46654.782

    Here is the found calibration function, a third degree polynom:
    Signal = A + B*weight + C*weight2 + D*weight3  with the polynom factors
    A =  1433.80
    B =  842.5178
    C = 4.6224107
    D = -0.0676875

The ultimative TEST is the following:

after the final analysis is done and all is cleared qualitatively and quantitatively, the sample is “reproduced” practically by a quantitative mix of all the substances found.

We NEVER found a full error free comparison. But although chromatography cannot be replaced by anything else (as some MS, MS/MS or other spectroscopy-only experts believe having never injected a sample themselves and never had to master chromatography up to correct quantitative data) we must realize: top accuracy and precision both in chromatography are not in easy reach.

As correct quantitation is based on correct calibration and as the calibration mathematics and statistics is widely underestimated - a majority tries still today everything to get things ‘linear’ - this topic has been intensified in all Sites of this author.
Because of the fast change of system software (Windows, Linux, Mac) quite some programs for calculating calibration line data disappeared from the labs. The author found a very powerful new programming language = PureBasic . He wrote an only 90 KB small program for polynomial interpolation. This program needs only a very few MOUSE clicks, has a key based program caroussel,  offers Windows based calibration data file handling, print reporting and high resolution graphics on screen. By now there is only a German HELP file available but most of us do not need any help when having a user friendly most simple program on screen which tells everything and forgives error inputs. The English program is available as PI-rek-E11 and the German version as PI-rek-D11 .

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