# Kovats retention index

In gas chromatography, Kovats retention index (shorter Kovats index, retention index; plural retention indices) is used to convert retention times into system-independent constants. The index is named after the Hungarian-born Swiss chemist Ervin Kováts, who outlined this concept during the 1950s while performing research into the composition of the essential oils.[1]

The retention index of a certain chemical compound is its retention time normalised to the retention times of adjacently eluting n-alkanes. While retention times vary with the individual chromatographic system (e.g. with regards to column length, film thickness, diameter, carrier gas velocity and pressure, and void time), the derived retention indices are quite independent of these parameters and allow comparing values measured by different analytical laboratories under varying conditions and analysis times from seconds to hours. Tables of retention indices are used to identify peaks by comparing measured retention indices with the tabulated values.[2] [3] [4]

## Expression

The Kovats index applies to organic compounds. The method interpolates peaks between bracketing n-alkanes. Kovats index of n-alkanes is carbon number times 100 like n-Butane index is 400. The Kovats index is dimensionless, contrary to retention time or retention volume. For isothermal gas chromatography, the Kovats index is given by the equation:

${\displaystyle I_{i}=100\left[n+(N-n){\frac {log(t_{i}-t_{0})-log(t_{n}-t_{0})}{log(t_{N}-t_{0})-log(t_{n}-t_{0})}}\right]}$

Symbols stand for:

• ${\displaystyle I_{i}}$ the Kováts retention index of peak i
• ${\displaystyle n}$ carbon number of n-alkane peak heading peak i
• ${\displaystyle N}$ carbon number of n-alkane peak trailing peak i
• ${\displaystyle t_{i}}$ retention time of compound i, minutes
• ${\displaystyle t_{0}}$ air peak, void time in average velocity ${\displaystyle u=L/t_{0}}$, minutes

## Kovats and Properties

Compounds elute in the carrier gas phase only. Compounds solved in the stationary phase stay put. The ratio of gas time ${\displaystyle t_{0}}$ and residence time ${\displaystyle t_{i}-t_{0}}$ in the stationary liquid polymer phase is called the capacity factor ${\displaystyle k_{i}}$:

${\displaystyle k_{i}={\frac {t_{i}-t_{0}}{t_{0}}}={\frac {RTS_{i}}{P^{i}}}}$ ß

Symbols represent physical properties:

• ${\displaystyle R}$ gas constant (8.314J/mole/k)
• ${\displaystyle T}$ temperature [k]
• ${\displaystyle S_{i}}$ solubility of compound i in polymer stationary phase [mole/m3]
• ${\displaystyle P^{i}}$ vapor pressure of pure liquid i [Pa]

Capillary tubes with uniform coatings have this phase ratio ß:

ß${\displaystyle ={\frac {V_{L}}{V_{G}}}={\frac {4d_{f}}{d_{c}}}}$

Capillary inner diameter ${\displaystyle d_{c}}$ is well defined but film thickness ${\displaystyle d_{f}}$ reduces by bleed and thermal breakdown that occur after column heating over time, depending on chemical bonding to the silica glass wall and polymer cross-linking of the stationary phase. Above capacity factor ${\displaystyle k_{i}}$ can be expressed explicit for retention time:

${\displaystyle t_{i}=t_{0}({\frac {RTS_{i}}{P^{i}}}{\frac {4d_{f}}{d_{c}}}+1)}$

Retention time ${\displaystyle t_{i}}$ is shorter by reduced ${\displaystyle d_{f}}$ over column life time. Column length ${\displaystyle L}$ is introduced with average gas velocity ${\displaystyle u=L/t_{0}}$:

${\displaystyle t_{i}={\frac {L}{u}}({\frac {RTS_{i}}{P^{i}}}{\frac {4d_{f}}{d_{c}}}+1)}$

${\displaystyle R}$ and temperature ${\displaystyle T}$ have a direct relation with ${\displaystyle t_{i}}$. However, warmer columns ${\displaystyle T}$↑ do not have longer ${\displaystyle t_{i}}$ but shorter, following temperature programming experience. Pure liquid vapor pressure ${\displaystyle P^{i}}$ rises exponentially with ${\displaystyle T}$ so that we do get shorter ${\displaystyle t_{i}}$ warming the column ${\displaystyle T}$↑. Solubility of compounds ${\displaystyle S_{i}}$ in the stationary phase may rise or fall with ${\displaystyle T}$, but not exponentially. ${\displaystyle S_{i}}$ is referred to as selectivity or polarity by gas chromatographers today. Isothermal Kovats index in terms of the physical properties becomes:

${\displaystyle I_{i}=100\left[n+{\frac {log(S_{i}/P^{i})-log(S_{n}/P^{n})}{log(S_{n+1}/P^{n+1})-log(S_{n}/P^{n})}}\right]}$

Isothermal Kovats index is independent of ${\displaystyle R}$, any GC dimension ${\displaystyle L}$ or ß or carrier gas velocity ${\displaystyle u}$, which compares favorable to retention time ${\displaystyle t_{i}}$. Isothermal Kovats index is based on solubility ${\displaystyle S_{i}}$ and vapor pressure ${\displaystyle P^{i}}$ of compound i and n-Alkanes (${\displaystyle i=n}$). ${\displaystyle T}$ dependence depends on the compound compared to the n-alkanes. Kovats index of n-alkanes ${\displaystyle I_{n}=100c}$ is independent of ${\displaystyle T}$. Isothermal Kovats indices of hydrocarbon were measured by Axel Lubeck and Donald Sutton [5].

## Temperature Programmed Kovats index

ASTM method D 6730 defines the temperature programmed chromatography Kovats index equation:

${\displaystyle I_{i}=100\left[n+{\frac {log(t_{i})-log(t_{n})}{log(t_{n+1})-log(t_{n})}}\right]}$
• ${\displaystyle t_{n}}$ & ${\displaystyle t_{n+1}}$ retention times of heading and trailing n-alkanes.

NOTE: TPGC index does depend on temperature program, gas velocity and the column used !

Method Translation Proper method translation aims at keeping the same retention temperatures in a smaller and faster column. Downsize the column of your certified method using method translation to ensure that the on-line fast analysis index corresponds to the certified lab method index. Method translation rules are incorporated in some chromatography data systems.

Measured Kovats retention index values can be found in ASTM method D 6730 databases. An extensive Kovats index database is compiled by NIST .

## References

1. Institute of Chemical Sciences and Engineering, KOVATS Ervin, Prof. Hon.
2. Kovats, E. (1958). "Gas-chromatographische Charakterisierung organischer Verbindungen. Teil 1: Retentionsindices aliphatischer Halogenide, Alkohole, Aldehyde und Ketone". Helv. Chim. Acta. 41 (7): 1915–32. doi:10.1002/hlca.19580410703.
3. IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006) "retention index, I in column chromatography". doi:10.1351/goldbook.R05360
4. Retention index guide
5. [J.o.Hi.Res.Chro.(1982,1983)Data Cards]