Kovats retention index

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

${\displaystyle I_{i}=100\left[n+{\frac {log(t_{i}-t_{0})-log(t_{n}-t_{0})}{log(t_{n+1}-t_{0})-log(t_{n}-t_{0})}}\right],}$ 

where the variables used are:

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

The Kovats index also applies to packed columns with an equivalent equation:

${\displaystyle I_{i}=100\left[n+{\frac {log(V_{i}^{0})-log(V_{n}^{0})}{log(V_{n+1}^{0})-log(V_{n}^{0})}}\right]}$ 

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 ${\displaystyle k_{i}}$ :

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

where the variables used are:

• ${\displaystyle R}$  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 β:

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

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]

IUPAC defines the temperature programmed chromatography Kovats index equation:

${\displaystyle I_{i}=100\left[n+{\frac {t_{i}-t_{n}}{t_{n+1}-t_{n}}}\right]}$ 

• ${\displaystyle t_{n}}$  & ${\displaystyle t_{n+1}}$  retention times of trailing and heading n-alkanes, respectively.

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

ASTM method D6730 defines the temperature programmed chromatography Kovats index equation:

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

Measured Kovats retention index values can be found in ASTM method D 6730 databases. An extensive Kovats index database is compiled by NIST [1].

The equations produce significant different Kovats indices.

Faster GC methods have shorter times but Kovats indexes of the compounds may be conserved if proper method translation is applied. Temperatures of the temperature program stay the same, but ramps and times change when using a smaller column or faster carrier gas. If column dimensions Length×diameter×film are divided by 2 and gas velocity is doubled by using H2 in place of Helium, the hold times must be divided by 4 and the ramps must be multiplied by 4 to keep the same index and the same retention temperature for the same compound analyzed. Method translation rules are incorporated in some chromatography data systems.