Lesson 2 · 25 min

Chromatography principles: retention, selectivity and Rf

Repeat an extraction hundreds of times and you have chromatography. Molecules shuttle between the mobile and stationary phases, and the retention factor k sets their pace; separate leaf pigments on a thin-layer plate and read their Rf values.

In this lesson

Explain the roles of the stationary and mobile phases and how repeated partition plus flow separates a mixture
Compute the retention factor $k$ and selectivity $\alpha$ from retention times, and $R_\mathrm{f}$ from thin-layer spots
Predict how eluent strength changes $R_\mathrm{f}$ in adsorption chromatography and choose a suitable eluent
Name the main kinds of chromatography and what each separates by

In 1906 the Russian botanist Mikhail Tswett poured a petroleum-ether extract of leaves onto a glass tube packed with chalk powder and kept washing it with solvent: the green extract spread down the tube into separate yellow, green and orange bands. He called the method chromatography — “colour writing”. More than a century later, doping control, pesticide residues in food and the purity of vaccines all begin with a chromatographic separation. Colour is no longer needed, but the principle has not changed at all.

Predict first

Two solutes are partitioned tube by tube along a row of tubes: solute 1 has retention factor k = 1 (half its time in the mobile phase) and solute 2 has k = 3. After the mobile phase has been moved on 20 times, where are the centres of the two bands?

Pick an answer and lock it in before you look. A wrong guess teaches more than no guess.

Both at tube 20 Solute 1 at tube 10, solute 2 at tube 5 Solute 1 at tube 20, solute 2 at tube 10 Solute 1 at tube 10, solute 2 at tube 15

Two phases, one competition

A column holds two phases: a stationary phase that does not move (silica, C18 chains bonded to silica, a polymer film on the wall of a capillary) and a mobile phase that flows past it (a gas or a liquid). Solute molecules keep entering and leaving both phases, obeying the partition equilibrium of the last lesson at every moment. They advance only while in the mobile phase, so the longer they linger in the stationary phase the slower they travel.

The ratio of those lingering times is the retention factor $k$ : the amount of solute in the stationary phase divided by the amount in the mobile phase. A compound that is not retained at all (methane in GC, say) comes out with the mobile phase at the dead time $t_\mathrm{M}$ ; a solute’s retention time $t_\mathrm{R}$ is longer, and the extra $t_\mathrm{R} - t_\mathrm{M}$ is exactly the time it spent hiding in the stationary phase. Whether two compounds separate depends on the ratio of their k values — the selectivity $\alpha$ .

k = \frac{n_\mathrm{s}}{n_\mathrm{m}} = K\,\frac{V_\mathrm{s}}{V_\mathrm{m}} = \frac{t_\mathrm{R} - t_\mathrm{M}}{t_\mathrm{M}}\qquad t_\mathrm{R} = t_\mathrm{M}(1 + k)\qquad \alpha = \frac{k_2}{k_1}

The retention factor combines the partition coefficient K with the phase ratio V_s/V_m; a selectivity α > 1 is the precondition for any separation.

$n_\mathrm{s}, n_\mathrm{m}$: amounts of solute in the stationary and mobile phases
$K$: partition coefficient c_s/c_m
$t_\mathrm{M}$: dead time: elution time of an unretained compound
$t_\mathrm{R}$: retention time
$\alpha$: selectivity (relative retention), later over earlier

Thin-layer chromatography (TLC) spreads the stationary phase as a thin layer on glass or aluminium. The sample is spotted on an origin line, the eluent climbs the plate by capillary action, and the spots move with it. The distance a spot travels divided by the distance of the solvent front is its retardation factor $R_\mathrm{f}$ . Ideally the solute moves only $1/(1 + k)$ of the time, so $R_\mathrm{f} = 1/(1 + k)$ and $k = (1 - R_\mathrm{f})/R_\mathrm{f}$ .

Silica is covered with polar Si–OH groups that hold polar molecules. The more polar solvent (acetone here) the eluent contains, the better it displaces adsorbed molecules and the higher $R_\mathrm{f}$ climbs. A good eluent puts the spots of interest between $R_\mathrm{f}$ 0.2 and 0.8: lower and they crowd the origin, higher and they crowd the front.

R_\mathrm{f} = \frac{d_\text{spot}}{d_\text{front}} = \frac{1}{1 + k}

Retardation factor in TLC. Distances are measured from the origin to the centre of the spot.

$d_\text{spot}$: distance moved by the spot centre
$d_\text{front}$: distance moved by the solvent front

Silica plate · hexane–acetone eluent · Rf from an adsorption model

Thin-layer chromatography of leaf pigments

Acetone in the eluent (volume) · 70 : 30

Development time 0.0 / 12 min

1 Leaf extract
2 Std: chlorophyll a
3 Std: β-carotene

Rf against eluent composition (computed)

β-Carotene
Chlorophyll a
Chlorophyll b
Lutein

Spots in the extract lane

Develop the plate, then measure.

Press “Develop” and watch the front climb, ever more slowly (z² ∝ t). Measure the four Rf values at 30 % acetone, then run plates at 10 % and 60 %: which composition keeps every neighbouring pair above Rs = 1? Use the standards in lanes 2 and 3 to identify the spots.

Worked example

k and α from chromatographic data

On a silica plate the solvent front moved 6.0 cm, the chlorophyll a spot 3.1 cm and the chlorophyll b spot 2.6 cm. Find $R_\mathrm{f}$ and $k$ for each and the selectivity $\alpha$ .

By stationary phase and mechanism, chromatography falls into a few families:

adsorption: adsorption on silica or alumina surfaces (TLC, Tswett’s column);
partition: the solute dissolves in a liquid film or bonded phase — the polysiloxane film of a GC column, the C18 phase of reversed-phase LC;
ion exchange: a charged stationary phase holds oppositely charged ions; used for amino acids and inorganic ions;
size exclusion: a porous gel sorts molecules by size, large ones first; used for polymer molar-mass distributions;
affinity: antibodies or ligands on the stationary phase bind one target specifically, purifying a protein in one step.

With a gas as mobile phase it is gas chromatography (GC); with a liquid, liquid chromatography (LC) — the subject of the next two lessons.

Concept check

On a silica plate the eluent is changed from 9 : 1 to 6 : 4 hexane–acetone. What happens to the leaf-pigment spots?

All Rf values fall; the spots stay nearer the origin All Rf values rise; the spots move toward the front Rf values do not change; development is just faster The order reverses: polar pigments move to the top

Try the calculation

A peak elutes at 7.50 min and an unretained marker at 1.50 min. What is the retention factor k of the compound?

Key takeaways

A solute moves only in the mobile phase; the retention factor $k = (t_\mathrm{R} - t_\mathrm{M})/t_\mathrm{M}$ measures how long it lingers in the stationary phase.
Selectivity $\alpha = k_2/k_1 > 1$ is required for separation and depends on the chemistry of the two phases.
In TLC $R_\mathrm{f} = 1/(1 + k)$ ; a more polar eluent raises $R_\mathrm{f}$ on silica, ideally to 0.2–0.8.
Band centres advance at 1/(1 + k) of the flow while widths grow only as √n, so bands separate as they travel.

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Data and references

D. C. Harris, Quantitative Chemical Analysis, 9th ed. (2016), Ch. 23 (introduction to analytical separations).
M. Tswett, “Adsorptionsanalyse und chromatographische Methode. Anwendung auf die Chemie des Chlorophylls”, Ber. Dtsch. Bot. Ges. 24, 384–393 (1906).
L. C. Craig, D. Craig, “Laboratory extraction and countercurrent distribution”, in Technique of Organic Chemistry, vol. III (Interscience, 1950).
E. Soczewiński, “Solvent composition effects in thin-layer chromatography systems of the type silica gel–electron donor solvent”, Anal. Chem. 41, 179–182 (1969).
H. T. Quach, R. L. Steeper, G. W. Griffin, “An improved method for the extraction and thin-layer chromatography of chlorophyll a and b from spinach”, J. Chem. Educ. 81, 385 (2004).