Capacity Factor k

2.2.5.2 Capacity Factor k

The retention time t R depends on the flow rate of the mobile phase and the length of the col- umn. If the mobile phase moves slowly or the column is long, t 0 is large and so is t R . Thus t R is not suitable for the comparative characterisation of a substance, e. g. between two laboratories.

R to the dead time: t 0 t R t 0

phase and represents the molar ratio of a particular component in the stationary and mobile

0 V k 1 (12)

V g where V 1 = volume of the stationary phase

V g = volume of the mobile phase

2 Fundamentals

Fig. 2.110 The chromatogram and its parameters. W Peak width of a peak. W = 4 with = the standard deviatiion of the Gaussian peak.

t 0 Dead time of the column; the time which the mobile phase requires to pass through the column. The linear velocity u of the solvent is calculated from uˆ L

t 0 with L ˆ length of the column A substance which is not retarded, i. e. a substance which is not held by the stationary phase, appears at t 0 at the detector. t R

Retention time : the time between the injection of a substance and the recording of a peak maximum.

Net retention time. From the diagram it can be seen that t R =t 0 R .

t 0 is the same for all eluted substances and is therefore the residence time in the mobile phase. The R . The longer a substance stays in the stationary phase, the later it is eluted.

The capacity factor is therefore directly proportional to the volume of the stationary phase

(or for adsorbents, their specific surface area in m 2 /g).

a is a measure of the relative retention and is given by: k 0 2 K 2

aˆ k 0 ˆ K 1 …k 0 2 > k 0 1 †

1 In the case where a = 1, the two components 1 and 2 are not separated because they have

The relative retention a is thus a measure of the selectivity of a column and can be manipu- lated by choice of a suitable stationary phase. (In principle this is also true for the choice of the mobile phase, but in GC/MS helium or hydrogen are, in fact, always used.)

2.2.5.3 Chromatographic Resolution

A second model, the theory of plates, was developed by Martin and Synge in 1941. This is based on the functioning of a fractionating column, then as now a widely used separation technique. It is assumed that the equilibrium between two phases on each plate of the col- umn has been fully established. Using the plate theory, mathematical relationships can be

2.2 Gas Chromatography

derived from the chromatogram, which are a practical measure of the sharpness of the se- paration and the resolving power.

The chromatography column is divided up into theoretical plates, i. e. into column sec- tions in the flow direction, the separating capacity of each one corresponding to a theoretical plate. The length of each section of column is called the height equivalent to a theoretical plate (HETP). The HETP value is calculated from the length of the column L divided by the number of theoretical plates N:

HETP = L in mm (14) N

The number of theoretical plates is calculated from the shape of the eluted peak. In the se- parating funnel model it is shown that with an increasing number of partition steps the sub- stance partitions itself between a larger number of vessels. A separation system giving sharp separation concentrates the substance band into a few vessels or plates. The more plates there are in a separation system, the sharper the eluted peaks.

The number of theoretical plates N is calculated from the peak profile. The retention time t R at the peak maximum and the width at the base of the peak measured as the distance be- tween the cutting points of the tangents to the inflection points with the base line are deter- mined from the chromatogram (see Fig. 2.108).

t 2 g (15) W

where t R = retention time W = peak width

For asymmetric peaks the half width (the peak width at half height) is used: t g 2

(16) W n

where t R = retention time W n = peak width at half height

Consequence: A column is more effective, the more theoretical plates it has (Fig. 2.111). The width of a peak in the chromatogram determines the resolution of two components

at a given distance between the peak maxima (Fig. 2.112). The resolution R is used to assess the quality of the separation:

retention difference (17) peak width

2 Fundamentals

Fig. 2.111 Substance exchange and transport in a chromatography column are optimal when there are as many phase transfers as possible with the smallest possible expansion of the given zones (after Schomburg).

Fig. 2.112 Resolution. (A/C) Peaks with the same retention time (A/B) Peaks with the same peak width (B/C) Separation with the same resolution

The resolution R of two neighbouring peaks is defined as the quotient of the distance be- tween the two peak maxima, i. e. the difference between the two retention times t R and the arithmetic mean of the two peak widths:

where W h = peak width at half height Figure 2.113 shows what one can expect optically from a value for R calculated in this way.

At a resolution of 1,0 the peaks are not completely separated, but it can definitely be seen that there are two components. The tangents to the inflection points just touch each other and the peak areas only overlap by 2%.

For the precise determination of the peak width the tangents to the inflection points can

be drawn in manually (Fig. 2.114). For a critical pair, e. g. stearic acid (C 18–0 ) and oleic acid (C 18–1 ) the construction of the tangents is shown in Fig. 2.115.

2.2 Gas Chromatography

Fig. 2.113 Resolution of two neighbouring peaks (after Snyder and Kirkland).

Fig. 2.114 Manual determination of the peak width using tangents to the inflection points.

Fig. 2.115 Determination of the resolution and peak widths for a critical pair.

2 Fundamentals 2.2.5.4 Factors Affecting the Resolution

R –t 0 )/t 0 , the se-

2 1 and the number of theoretical plates N gives an important basic equation for all chromatographic elution processes. The resolution R is related to the selectivity a (relative retention), the number of theoreti-

1 k 0 p 

Rˆ 4 …a

1‡k …18†