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: Take 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 
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  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.
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”:
I(a) = 914; I(b) = 929.
than TZnecessary according to formula  = 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, TZnecessary 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) -
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  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.