Qualitative Errors in Gas Chromatography caused by:

1  Partial or total peak overlapping because of non sufficient separation power
2  Wrong selectivity
3  Errors in the determination of retention index values.

What to do in case of 1) , peak overlapping ?

To 1: Use the best possible measure for the separation power the GC system in use offers. The best possible separation power measure is the “TRENNZAHL (TZ) ” - see below -  and check if the physical conditions are optimal: that is GAS FLOW measured as dead time tm and TEMPERATURE or temperature PROGRAM of the separation system in use.
NOTE: The raw retention time tms = ts + tm which is the sum of the residence time in the stationary phase plus the residence time in the mobile phase resulting in the total retention times.

To 2: Use the best possible measure for the selectivity the separation system in use offers under the physical conditions taken. This is the retention index I difference of two specifically selected test substances.

There is a simple correlation between the separation power measured as TZ and the difference between the retention indices of the two substances (a) and (b) to be separated in order to avoid the reason for qualitative errors: OVERLAPPING of peak (a) with peak (b). There is always a most critical pair of substances to be separated, therefore these two test substances will do it. They may overlap by 100%.

For the measurement of the separation power (TZ), the dead time (tm) as value for the gas flow speed, the retention index Ia and Ib of the two substances, which should not overlap and if the temperature taken is OK, we need test substances: a system series of consecutive homologues and the substances (a) and (b). The simplest system test substance series is a mix of n-alkanes, for instance n-hexane, n-heptane, n-octance, n-nonane, n-decane (or much larger members of the paraffine homologues like
C₁₂, C₁₃, ....C₂₅, C₂₆... easily available as diesel oil and much higher n-alkanes available as paraffin from candles). In case the chromatographer works entirely in the field of polar compounds the system series of homologue saturated esters of saturated fatty acids are applicable.

For a good understanding of the following use the figures and the numerical example given for the correlation of TZ, retention index, polarity, selectivity...

Trennzahl TZ = number of baseline separated peaks between one pair of system homologues. This separation power value is valid in isothermal as well as in temperature programmed GC and even in HPLC. This makes TZ fundamentally better applicable than the theoretical plate height HETP or the plate
number n = 5.545 * (tms/b05)². “n” is valid only for the data pair tms and the correlated b05 value and only uner strict isocratic conditions. The factor 5.545 is valid only for a strict Gaussian peak shape which in practice nearly never exists. Thus basically correct and in all ranges applicable is

TZ = (tms H(n) - tms H(n-1))/(b(n) + b(n-1)) - 1                                                   [1]

tms H(n) = total retention time of the homologue (n) in seconds.
tms H(n-1) = total retention time of the homologue (n-1) in seconds.
b(n) = peak width of homologue peak (n) measured in half height in seconds.
b(n-1) = peak width of homologue peak (n-1) measured in half height in seconds. The “minus 1” in the TZ formula above follows from the fact, that the half areas of two homologues already stay in the chromatogram range given by TZ.
TZ represents the number of baseline separated peaks. It is valid in isocratic (isothermal, isobaric, non programmed) GC as well as in HPLC. Baseline separated peaks still overlap by about 1%.
The TZ value is valid ONLY in the chromatogram range given by tms of homologues n-1 and n.
Therefore TZ should be measured near the end of the chromatogram time scale.
Basically TZ will be at least as large as the length of a separation system in m in case of standard GC but could easily be as large as five times the capillary length in meter for capillary GC.
The maximum TZ ever found experimentally reached a value of about 80. This means: 80 peaks are baseline separated between one homologue pair. About ten homologues can be separated in a programmed GC run, that is about 800 peaks may be baseline separated in a single capillary gas chromatogram. Double dimensional or GC x GC separation systems offer more, see the next GC symposium 2006 with already the third GC x GC symposium- click on www.richrom.com

TZ data are only correct in case the column / capillary is NOT overloaded by the test homologues like hydrocarbons, esters, alcohols. All types of errors in making and giving the test solutions result in too small - falsified - TZ values. The b05 values must correlate with non overloaded homologue peaks. tms is written “t” and b05 is written “b” in the figure below:

NOTE: The beauty of TZ as separation power value for a column/capillary are the following characteristics:
a) TZ is a practical number. It means “number of baseline separated substances” within the chromatography range given by the homologues eluted ain the time window between t1 and t2.
b) TZ allows to optimize all physical conditions of chromatography just for this chromatogram range which is enclosed by the just mentioned two homologues.
c) TZ and the substance quality value “retention index” are strictly correlated. If one knows the retention indices of two substances a and b which must become baseline separated for the best possible quantity results then TZ is measured with the two homologues enclosing the positions for substances a and b. The found TZ value must be equal or larger [100/(Ib-Ib) + 1] as given in formula [2] below. If the TZ measured in this chromatogram range is (a bit) smaller, then the mobile phase flow and / or the separation temperature is changed until this TZ value reaches a maximum.
The homologue at t1 above may be n-heptane, then the homologue at t2 is n-octane. The used homologues must differ by one CH2 group. In this chromatogram range a total of TZ substances can be baseline separated. TZ values depend on the position of the homologues at t2 and t1 thus the separation power value given by TZ is not a constant number along the whole chromatogram range, but it can be maximized as mentioned above but also by improving the sampling conditions. For the TZ over the whole retention time scale see the “ABT” concept discussed in HPLC.

The Retention index is the best possible “address” of any substance eluted in GC. This is based on the series of n-alkane HOMOLOGUE retention times. The standard series of test substances starts with methane (C₁, index 100) and ends with the normal hydrocarbon C₁₀₀, index 10,000, but more practically with C₄₀, index 4000. The retention indices of the n-hydrocarbons is independent of the stationary phase, the type, length, diameter, temperature, mode of pressure or temperature programming, or phase flow speed. The retention index of any n-alkane is ALWAYS 100 times its carbon number. Thus the retention index of n-heptane is fundamentally always and under any conditions seven hundred.

This is NOT true for any non n-hydrocarbon substances like alcohols, esters, acids or one of the millions of other substances available for GC separation.
Their retention indices depend on the temperature of the separation system and on further details of the working mode. Under isothermal conditions the retention index Ia is calculated by logarithmic interpolation between the index of the normal hydrocarbon eluting prior substance (a) - which is I(n-1) - and the normal hydrocarbon I(n) which elutes after substance (a). In temperature programmed GC the calculation of the retention indices needs the use of polynomial interpolation, as there is no any linearity between retention time and index. For “Index calculation in GC” see the correlated GC SOFTWARE.

The correlation of retention index differences for a baseline separation and of the Trennzahl is simple: The substance (a) has the retention index I(a). The substance (b) has the retention index I(b). These two substances will just be baseline separated if the column / capillary has the necessary Trennzahl TZ for this substance pair (a) and (b). This value is called “TZ necessary”:

                   TZ _necessary >= 1 + 100 / (I(b) - I(a))                          [2]

Data example:
I(a) = 914; I(b) = 929.
than TZ_necessary according to formula [2] = 100/(929-914) + 1 = 7.7

As in classical “packed column GC” the TZ value is often double the column length in meter, the data example above tells which technique to use. Classical packed columns will fail, TZ_necessary is too large for a packed column. It is a good idea for error free analysis to know retention index data of the substances to be separated and the available TZ value of the column/capillary in question. It is a good concept to master chromatography ahead of sampling: it saves time and material. The needed small formulas are easy enough to use them even in daily routine work.

The retention index concept as basis for the optimization of qualitative GC (and HPLC) is of utmost power but widely underestimated or - even not anymore known. It boomed in the sixties - seventies of the last century, however NOTHING has changed in this respect in this century. But there is no any better concept visible.
The simple example above tells, that the retention index concept helps also to optimize quantitative analyses - but especially it optimizes the stationary phase selection. Because the retention index difference of two non hydrocarbon substances depends entirely on the stationary phase selectivity. Thus otimization means FIRST to take the best available stationary phase and THEN to use the best mode of operation. This is the mobile phase flow speed and the best available mode for programming the temperature (and or the pressure) in GC and the mobile phase composition in HPLC.

Optimization costs time, but there are possibilities for auto-optimization. The “necessary TZ” value can be entered prior an optimization series of runs. The used optimization software finds this way the shortest possible analysis time for the necessary baseline separation of the most critical substance pair in a given sample.

A short summary in between: Not only TZ depends strongly on the mobile phase flow speed.
The retention indices of some selected test substances are a very good measure of the polarity / selectivity of stationary phases, as already mentioned. This allows to pre calculate which phase is the best for a critical substance pair separation. Knowing the retention index values for the most critical substance pair allows to pre calculate the necessary Trennzahl. From this value the chromatographer knows which type and length of column / capillary he needs for a successful separation. With other words: Retention index and Trennzahl allow to master chromatography. The theoretical plate number concept - main aspects of the classical theory - is useless in any programmed chromatography. The most weak fact of the classical theory is its single substance basis. As chromatography is a separation technique, all concepts based on a single substance data are nearly useless in practice. In this site therefore quite some classical theoretical concepts which are based on single substance values are not supported.

Back to the retention index introduced into gas chromatography by E. Kovats and repeated:

The complete series of the normal alkanes is the substance fundament and ranges from methane CH₄ , index = 1 x 100 = 100 practically to C₅₀H₁₀₂, index = 50 x 100 = 5000. In extreme cases higher normal hydrocarbons than C₅₀H₁₀₂ are applicable as GC ends only near C₁₀₀H₂₀₂.
Thus n-heptane (C₇H₁₆)  has by definition the retention index 700 and n-hexane (C₆H₁₄)  has by definition the index 600. Homologues with carbon numbers differing by one therefore have retention index differences of 100 units. The retention index of these n-alkane test substances is independent of all variables in GC as they have a fixed index value by definition. All GC laboratories have an easy access to n-alkanes which are the main compounds in diesel oil. This is basis of the global usefulness of the retention index concept. Retention index data can - in limits - be pre calculated if the structure formula of a substance is given.

It is important to know, that the retention index of nearly all non - n-alkanes depend on nearly all variables a chromatographic system can have, thus identification errors - systematic qualitative errors - can be found with the help of accurate retention index measurements, see under “Qual. Error HPLC” mainly because the index concept is applicable in HPLC as well.
The fact, that the length of a separation systems correlates nearly linear with the Trennzahl and the analysis time correlates nearly linear with the separation system length, we have no big chance to reach with a single column / capillary system a very high Trennzahl. This is even more critical in PLC. There the total Trennzahl of a one direction separation is limited to 50 (versus 800 in GC and about 100 in HPLC). Thus we need for multi component analysis a better concept than offered by single dimensional chromatography. The way out is two dimensional PLC (TZ total around 400), two up to multi dimensional HPLC, chromatography system combination like GC x GC, GC x HPLC, GC x PLC, HPLC x PLC, HPLC X HPLC. Meanwhile the GC x GC concept reached a high level of practical applicability. The third international symposium on GC x GC is scheduled for May 2006 in Riva del Garda (It) -
   see www.richrom.com
lComprehensive GC is a next name for GC x GC and was the main topic of the international series on capillary chromatography symposia already in 2003 in Las Vegas, USA.

What to do in case of 2) , wrong polarity ?

When is the polarity wrong ?
It is wrong, if the critical pair of two substances “a” and “b” which we MUST quantitize and therefore first separate from each other, have the same retention index. They have the same retention time and the same peak width in half height and therefore the corresponding “Trennnzahl necessary” is unlimited large - see the formula [1] above, which would mean an unlimited long separation system. Even GC x GC or any other mode of comprehensive chromatography cannot solve the problem physically. We MUST find a stationary phase with a selectivity making the retention indices Ia differing from Ib, the more the better.
There are some technical limits to change mechanically columns / capillaries often until an acceptable selectivity is found.
There are better ways: IfC found very early the physical change of selectivity / polarity in GC and HPLC without replacing columns/capillaries.
The concept is very simple and therefore was for a long time not accepted by classical theoreticians:
Chromatography is TIME based. We connected two chemically differing stationary phases P with N in series and changed the residence time of the substances in the two series connected phases. P means “polar”, N means “non polar”. The residence time in GC changes either with the temperature and / or with the mobile phase flow speed. Both effects can be used simultaneously: warmer and faster makes the residence time of a substance shorter. A cooler phase P and a warmer phase N makes the total system polar. A higher mobile phase flow speed in N and a lower in P also makes the total system polar. If now the critical substance pair differs in polarity, the residence time changes will allow for a separation. The polarity / selectivity change of flow speed and / or temperature in P and N series connected columns/capillaries can be managed fully electronically, that is completely software driven.
As in practice there are more multi compound mixtures to be analyzed than analytical duties based on a critical pair of two substances, the auto optimization is controlled by the total number of separated substances. The larger this number, the less is remaining overlapping. Finally we may have reached a selectivity optimum but still peaks may overlap. In this case we need the column switching concept introduced by David DEANS, the “Deans switching” technique, see figure 1 below).

 Even process capillary gas chromatographs use micro DEANS switching concepts in order to separate critical substance pairs.
 

A few seconds later the carrier gas switches are set back to the condition at start. Thus remaining substances in column A continue the separation. Meanwhile the “critical” pair is separated in column B which will surely happen if both substances have truly a differing polarity. If NOT, no separation of substance a from b is possible and only an excessive Trennzahl will solve the problem. The technical TZ limit is near 80 as long as no excessively narrow super separation capillaries are applicable.
The DEANS switching concept is now improved by the use of “micro in line detectors” which work inside the separation capillary - let say a few millimeters prior the end of column / capillary A. This way the gas switching can be started well in time the “critical” pair arrives. Modern micro GC is developing very fast.

To repeat: there is nevertheless a more promising way to change the separation selectivity - the column / capillary polarity: these are instruments with two differing columns / capillaries connected in series. As chromatography is based on time, the selectivity can be changed by changing the residence time in one of two columns / capillaries. This is possible just by physical means:

1) by selective changes of the carrier gas flow speed - faster in A, slower in B
2) by selective change of the column / capillary temperature - warmer in A, colder in B.

To 1): The mobile gas phase flow speed is made larger in column A and smaller in column B by adding or releasing gas at the connection point thus changing the polarity from a mean effect A + B to a larger or smaller  A- or B-effect. Flow speed changes are easily done electronically with very high precision. Such a chromatography system allows for computer controlled auto optimization for the best possible separation of substance a from substance b.
To 2): The selective change of the temperature for column A versus column B does the same: A warmer stationary phase A reduces the A- polarity and a lower B- temperature enlarges the B- polarity and vice versa. If the polarity of substance a differs from substance b we will get them separated, again under auto- optimized conditions, as changing the flow speed and/or the temperature is easily controlled by software. It is the residence time in the stationary phase(s), which controls chromatography by selectivity changes of a column tandem. If however the polarity and molecular shape of the critical substance pairs are equal, we succeed only with larger TZ numbers.

There is a further and even more powerful mode of electronically controlled and switchable column / capillary selectivity. The peak cutting concept of DEANS is combined with the just mentioned electronic selectivity change of IfC, thus combining both concepts. As the correct quantitation of critical substance pairs is more often very important, this GC modification is the utmost we can do for reduced quantitative systematic errors in GC.

To 3: Errors in the determination of retention index values.

3.1: Retention index errors in isothermal gas chromatography
3.2: Retention index errors in temperature programmed gas chromatography.

To 3.1:
Retention indices are the best quality values in gas chromatography and no any other concept - even not the best adjusted retention time concept - is more useful in practice.
The following conditions however must exist:
a) The temperature must be kept at +- 0.05 degr centigrade or better. The mobile phase pressure must stay constant within a few millibars (possible, no problem technically with proper hardware quality), the fluctuations of the laboratory air pressure must be excluded from impact by the use of an elevated inlet-outlet carrier gas pressure (using constant gas flow resistors) and the peak amount does not overload the sorption capacity of the stationary phase. With other words: no oversampling.
b) The integration software and the signal producing hardware are so qualified, that the peak retention time is measured based on quartz clock precision and is polynomial interpolated by fifth degree around the top of each peak to a precision of +- 0.001 seconds (is possible without problems. Qualified chromatography instrument companies used this technique already in the last century).

Under those conditions the retention index values reach a precision of +- 0.01 unit. Such a precision allows very sharp and safe identifications in case n-alkanes exist in the sample for qualitative GC or are mixed to the sample. The added alkanes must be kept in such a low concentration, that there is no impact on the overall polarity / selectivity. How errors in this respect act is shown in line chromatograms LOG/LOG
Even a much weaker retention index precision than +- 0.01 unit is often good enough in practice.

NOTE: columns / capillaries having a (quite good) separation power of Trennzahl TZ at 33 can just only baseline separate two substances with a retention index difference of 3 units.
Now we need the formula for isothermal index calculations to see, where is the danger of serious systematic errors:
Isothermal GC retention index according to E.Kovats in a formula IfC prefers:

Retention Index of subst. X = (IB - IA) * [log (tsX/tsB) / log (tsA/tsB)] + IA           [3]

for isocratic separation only !
IB = Index of the n-alkane eluted before substance X
IA = Index of the n-alkane eluted after substance X
tsX = the net retention time of substance X in the stationary phase.
tsA, tsB = the net retention times of the two n-alkanes given above.

NOTE: If no any programming is used, the series of n-alkane homologues elute very precisely in logarithmic shape. Under programmed conditions - by flow or temperature programming - the homologue series elutes nearly in a linear shape but NOT precisely linear enough Homologue series of many other substance classes behave under isothermal conditions similar like the saturated normal hydrocarbons.

Example:
The n-alkane eluting before substance X = n-hexane, C₆H₁₄; IB by definition = 600
The n-alkane eluting after substance X = n-heptane, C₇H₁₆; IA by definition = 700
Only the non adjusted (raw) retention time values tms can be measured, but the index calculation needs adjusted (corrected) net-retention time values ts. As tms = tm + ts which is ts = tms - tm
it follows, that we must find a way either to measure or to calculate the dead time tm.
In the following example we use capillary GC data and work first with a wrong dead time of tm = 122.38 seconds and next with a correct dead time of tm = 119.55 seconds. The measured non adjusted retention time values of the two n-alkanes and the substance X are correct. tms-data are not influenced by wrong or correct dead time values, but the needed adjusted (net) retention time values ts are wrong if tm is wrong. In both tables the following data are used:

tmsB = 450.066 seconds; tmsX = 455.876 seconds; tmsA = 512.754 seconds

A dead time error of 3 seconds, which is a relative time error of only 0.7 %, results in an retention index error of 5 full units. Remember the possible qualification of index data: 0.1 to 0.01 units is possible.

tm wrong   tm correct

IX wrong   IX correct

Using the same raw retention time data as above but the correct dead time value and now with a
tms-error of only 0.1 seconds for the substance X, we find a retention index error of 0.2 units in the data range given above.

Conclusion:
for accurate qualitative GC analyses based on retention index values the acceptable time error cannot be small enough. Overlapping peaks which shift the retention time values drastically make correct qualitative analyses - which also means: correct identifications - impossible. In such cases two and multi dimensional GC with high resolution capillaries is a must - and available. Total peak overlapping disables correct qualitative as well as quantitative analysis. The same is true for over sampled peaks. Their retention time is falsified, most often shifted to too large ts-values.

The power of the retention index as quality scale is the fact, that data tables for automatic identification are stable in mass analyses for many months, whilst other time based identification values like the relative adjusted retention time values
tsX / ts_(reference) are easily unstable and the relative values of non adjusted relative retention values tmsX / tms_(reference) simply are useless. They even change with the outside weather conditions.

To 3.2:
Retention indices in temperature programmed gas chromatography are correct only, if one leaves the classical definition given by the inventors of the index. In a longer discussion Prof. Kovats accepted, that correct TGC indices need polynomial interpolation mathematics, as there is no real linear correlation of index over the carbon number of the reference series of homologues. All index values must be non linearly interpolated even between two consecutive n-alkane homologues enclosing the substance X.
Temperature programmed retention index calculations have the following formula:

Index substance X = a + b*tmsX+c*tmsX²+d*tmsX³+e*tmsX⁴+f*tmsX⁵                        [4]

a, b, c, d, e, f are constant polynom factors found for the n-alkane homologue series of seven members, which at best are mixed to the sample. This guarantees, that all physical conditions of programmed temperature with the additional effect of changed mobile phase flow during the analytical run are kept equal.
For the polynom analysis see “Calibration” and under “software”.

Conclusion: identification by GC should be done isothermally. Backflush and cut techniques allow to do this with such a big success, that the application of MS and MS/MS for identification purposes only are often not necessary. The precision retention index and the use of high resolving separation systems does it. The situation however is different if structure elucidation is the task. Then capillary GC, at best GCxGC online a detector pair FID parallel to ECD or ECD parallel to MS/MS is necessary.
ECD = erlectron capture detector, highly non linear with a very narrow working range; FID flame ionization detector, S-shaped non linear but with a wide working range. ECD and FID are quite sensitive detectors.