Two phases
Every kind of chromatography has a stationary phase that stays put (the cellulose of paper, the silica gel of a TLC plate, the packing in a column) and a mobile phase that flows past it (a solvent, or a gas in gas chromatography). Each compound in the mixture constantly moves between the two: while dissolved in the mobile phase it travels, while stuck to the stationary phase it waits. A compound that spends more of its time stuck moves more slowly, so compounds that differ in how strongly they stick come apart.
The ratio of time stuck to time moving is the retention factor k. A compound with k = 1 spends half its time moving and travels at half the speed of the solvent.
Polarity
Silica and cellulose are polar, covered in OH groups that hydrogen-bond. Polar compounds (sugars, amino acids, chlorophyll b) cling to them; nonpolar ones (carotene, fats) hardly do. The solvent competes for the same sites: a more polar solvent dislodges polar compounds and carries them further. So on a silica plate, hexane moves only nonpolar compounds, ethyl acetate moves moderately polar ones, and ethanol or water moves nearly everything that dissolves. Reversed-phase columns, coated with long hydrocarbon chains, turn this around: there, nonpolar compounds stick.
Rf values
On paper or a TLC plate the solvent creeps up from the bottom and the run is stopped before it reaches the top. Each spot has traveled a fixed fraction of the solvent's distance:
Rf = distance moved by the spot ÷ distance moved by the solvent front = 1 ÷ (1 + k)
Both distances are measured from the baseline where the sample was put. Rf lies between 0 and 1, and for a given plate, solvent and temperature each compound has about the same Rf every time, so an unknown spot can be matched against a standard run beside it.
A worked example
A spinach extract is run on a silica plate in hexane and acetone, 9 to 1. The front stops 6.0 cm above the baseline.
- An orange spot at 5.7 cm: Rf = 5.7 ÷ 6.0 = 0.95, β-carotene, the least polar pigment.
- A blue-green spot at 2.7 cm: Rf = 0.45, chlorophyll a; k = 1 ÷ 0.45 − 1 = 1.2.
- A yellow-green spot at 2.1 cm: Rf = 0.35, chlorophyll b, which has an extra C=O group and is more polar.
- A yellow spot at 1.5 cm: Rf = 0.25, the xanthophylls, with OH groups that grip the silica.
The order follows polarity, least polar at the top. Published values for these pigments vary from lab to lab with the plate, the solvent mixture and how dry the plate is, which is why standards are run alongside.
Columns and chromatograms
In column chromatography (and HPLC and gas chromatography) the mobile phase flows through a packed tube and the compounds come out at the end one after another, into a detector that draws a peak for each. The solvent itself takes the dead time t₀ to get through; a compound with retention factor k takes
tR = t₀ (1 + k)
Peaks spread as they travel, because molecules take different paths through the packing and diffuse. A column's efficiency is its number of theoretical plates N: the peak width (standard deviation) is σ = tR ÷ √N. A good HPLC column has 10,000 or more plates; a hand-packed gravity column, perhaps a few hundred.
Continuing the example on a column with t₀ = 2.7 min and N = 2,000: chlorophyll a (k = 1.22) comes out at 2.7 × 2.22 = 6.0 min with σ = 6.0 ÷ √2000 = 0.13 min; chlorophyll b (k = 1.86) at 7.7 min with σ = 0.17 min.
Resolution
Whether two neighbors are separated depends on both the gap between them and their widths:
Rs = 2 (tR2 − tR1) ÷ (w₁ + w₂), with the base width w = 4σ
For the two chlorophylls, Rs = 2 × 1.72 ÷ (0.54 + 0.69) = 2.8: cleanly separated. Rs = 1.5 gives separation down to the baseline; at 1 the peaks overlap by about 2%; below that they merge. The Purnell equation shows the three ways to improve it:
Rs = (√N ÷ 4) × ((α − 1) ÷ α) × (k ÷ (1 + k))
with α = k₂ ÷ k₁. A better column (larger N) helps only as the square root; changing the solvent to change α, how differently the two compounds stick, usually helps far more.
Using the simulation
In the Chromatography Simulator, things to try:
- Leaf pigments in hexane and acetone, then in pure hexane: in hexane only carotene moves; the chlorophylls stay near the baseline.
- Black ink in water: the dyes separate; in hexane they do not move at all, because they do not dissolve.
- Amino acids in butanol, acetic acid and water: nothing shows until you tick the ninhydrin stain, then leucine and phenylalanine nearly overlap.
- Make the spot 6 mm wide: every spot grows and neighbors merge.
- On the column, lower N from 2,000 to 200 and watch the peaks broaden and the resolution fall.
What the model assumes
- A single polarity scale. Each compound has one polarity number, chosen so its Rf matches a published value in one reference solvent, and each solvent has one on a 0 to 1 scale; k = e8(p − s). Real retention depends on hydrogen bonding, acidity, size and shape, not one number.
- Solubility as a switch. Ink dyes dissolve only in polar solvents, leaf pigments in anything but water, amino acids only in fairly polar solvents; otherwise Rf = 0.
- The same stationary phase for paper, TLC and the column.
- A front that rises as the square root of time (the Lucas–Washburn law), at a speed that depends on the solvent.
- Spots and peaks that are Gaussian, widening with distance by diffusion; small amounts, so no overloading.
- A 25 cm column, 4.6 mm across, 65% open space, so t₀ = 2.7 mL ÷ the flow rate.
Edge cases
- Rf near 0 or 1: compounds pile up at the baseline or the front and cannot be told apart. Aim for Rf values between about 0.2 and 0.8 by choosing the solvent.
- Solvent above the baseline: the spots wash into the solvent at the bottom instead of running.
- Colorless compounds need a stain (ninhydrin for amino acids, iodine vapor, UV light on a fluorescent plate) to be seen at all.
- Identical Rf does not prove two compounds are the same; run them in a second solvent, or side by side and mixed (co-spotting).
Where the model stops being right
- Tailing and overloading. Too much sample, or acidic and basic compounds on silica, make streaks and comet-shaped spots rather than neat circles.
- Mixed solvents separate themselves. The more polar part of a mixture is held back by the plate, so the solvent composition changes up the plate, and a dry, unsaturated tank lets the solvent evaporate from the plate as it climbs; both shift Rf values.
- Temperature and humidity change Rf, and silica that has picked up water from the air becomes less active.
- Gradient elution, where the solvent is made gradually stronger during a column run, is how most HPLC is done; this model keeps the solvent fixed.
- Other mechanisms. Ion-exchange, size-exclusion and affinity chromatography separate by charge, size and specific binding, not by polarity.
Related tools
The Gel Electrophoresis Simulator separates DNA by size, a different way of taking a mixture apart; the Spectrophotometer and Beer-Lambert Law Simulator shows how a detector measures how much of a compound comes off; and the 3D Molecule Viewer shows the polar groups that make molecules stick.