Chromatography Fundamentals

The core principles behind every separation: how columns work, what drives selectivity, and how to think about resolution.

What is chromatography?

Chromatography separates molecules by partitioning them between a stationary phase (the column matrix) and a mobile phase (the buffer flowing through it). Molecules that interact more strongly with the stationary phase travel more slowly — different affinities produce different elution times.

The van Deemter equation

Column efficiency is described by the height equivalent to a theoretical plate (HETP):

H = A + B/u + C·u

Where u is linear flow rate, A accounts for eddy diffusion,B for longitudinal diffusion, and C for mass transfer resistance. Velocity conventions and coefficients must agree: superficial velocity is Q/Acol, whereas interstitial velocity is Q/(εiAcol), with Acol the column cross-sectional area and εi the interparticle void fraction. The simulator below uses interstitial velocity. This is a simplified efficiency model; its useful operating range and the observed optimum depend on the column, mobile phase, analyte, and instrument. Evaluate performance against the selected column’s instructions and a defined test method.

Resolution

For two resolved features, report retention coordinates and base widths consistently:

Rs = 2(tR₂ − tR₁) / (wb₁ + wb₂)
  • tR — retention time; calculate both peaks in the same time coordinate (or consistently transform both to volume).
  • wb — base width in that same coordinate, measured under a stated convention.
  • Rs — a description of the observed pair of peaks, not proof of identity or a pure collected fraction.

The familiar Rs ≈ 1.5 “baseline separation” rule is an idealized heuristic for suitably shaped, similarly responding peaks—not a universal pooling or purity guarantee. The plate/selectivity/retention relationship shown in many textbooks is an isocratic model with stated assumptions; do not apply it as a general gradient-elution equation. In practice, compare methods using measured resolution and the decision’s relevant orthogonal assay.

Plate count

A practical way to measure column health. For a symmetric peak eluting at retention volume VRwith peak width at half-maximum w½:

N = 5.545 × (VR / w½)²

Record the test solute, flow, detector, peak-width convention, and whether the result is reported as plates or plates per metre. Vendor specifications are method- and column-specific; a change in measured efficiency warrants investigation but does not by itself identify fouling or a void.

Resolution and plate number measured on two Gaussian peaksTwo peaks at retention volumes 9 and 12.5 mL measured from injection. Dashed tangents at the inflection points define base widths of 2.4 and 3 mL; horizontal lines at half height mark widths of 1.41 and 1.77 mL. Resolution 1.30.0246810121416Retention volume (mL)Detector response (normalized)injectionwh1VR1wb1 = 4σwh2VR2wb2 = 4σ
Figure 1. Width conventions on two Gaussian peaks (widths exaggerated). Tangents through the inflection points (μ ± σ, at 0.607 of peak height) meet the baseline at μ ± 2σ, so wb = 4σ; they cross above the apex at 1.21 of peak height. The half-height width is wh = 2√(2 ln 2)·σ ≈ 2.355σ. Here Rs = 2(VR2 − VR1)/(wb1 + wb2) = 1.30, and N = 5.545(VR/wh)² = 16(VR/wb)² gives 225 and 278 plates. For real, asymmetric peaks the two width conventions give different N; state which was used.

Plate height, plate number and resolution (idealized model)

Plate height follows the reduced van Deemter form h = a + b/ν + c·ν with h = H/dp and ν = u·dp/Dm (u is interstitial velocity). The optimum is νopt = √(b/c), hmin = a + 2√(bc). The bed then gives N = L/H, and the lower plot shows two equal-amount Gaussian peaks eluting isocratically at VR/V0 = 1 + k with the same N, and Rs computed from their base widths (4σ).

Plate height versus interstitial velocityVan Deemter curve with its A, B/u and C·u contributions on a logarithmic velocity axis. The optimum is at 1.2 mm/s with H_min 6.5 µm; the operating point is 1 mm/s, H 6.55 µm.05101520250.0010.010.1110Interstitial velocity u (mm/s, log scale)Plate height H (µm)u_optResulting two-peak chromatogramTwo Gaussian peaks at V/V0 = 3.00 and 3.20 with N = 22901; base-width resolution 2.44.2.9533.053.13.153.23.253.3Elution volume V / V₀ (void volumes)Detector response (normalized)k₁k₂
Solute
H
6.55 µm
N = L/H
22,900
Reduced velocity ν
5
u / u_opt
0.833
H_min
6.5 µm
Rs (base width)
2.44

c between 0.02 and 0.05 is the range quoted for well-packed columns; larger values illustrate slower mass transfer. For large proteins in porous media, ν is high at usual flows and the C term dominates.

Idealized: one plate height for both species, Gaussian peaks, isocratic retention, no extra-column broadening; a and b fixed at 0.7 and 1.8, Dm values are orders of magnitude only. It does not describe gradient elution or predict a real column. Reduced van Deemter form, optimum, typical coefficients and N = L/H from Pirok & Schoenmakers, Analytical Separation Science course, lesson 03 (ass-ets.org, read 2026-09-25); base-width Rs as on this page.

Peak asymmetry and tailing

Real peaks are not perfect Gaussians. An asymmetry calculation, such as As = b/a at a stated percentage of peak height, is only comparable when the convention and test conditions are recorded. Tailing or fronting can arise from several causes—including sample load, solvent mismatch, extra-column effects, kinetics, or column/sample interactions—and needs troubleshooting evidence rather than a fixed acceptance boundary or a single-cause diagnosis.

Gradient elution vs. isocratic

In isocratic elution, mobile phase composition is constant — common in SEC. In gradient elution (IEX, HIC, RPC), a changing mobile phase progressively elutes bound molecules: increasing salt in IEX, decreasing salt in HIC, increasing organic modifier in RPC.

Gradient slope can change selectivity, retention, peak compression, run time, and dilution. Compare candidate gradients experimentally under a defined objective; shallower or steeper is not universally better.

Sources and scope

IUPAC Gold Book: peak resolution (authoritative definition, accessed 2026-09-25) supports the displayed base-width equation. Cytiva™ Superdex™ 200 Increase instructions for use (official, accessed 2026-09-25) illustrates that a specific column’s efficiency test is reported as plates per metre under stated conditions. Neither source supports a universal resolution threshold, gradient equation, plate-count specification, or peak-asymmetry acceptance band. The simulator’s reduced van Deemter form, optimum, typical coefficients and N = L/H follow Pirok and Schoenmakers, Analytical Separation Science, lesson 03 (course notes, accessed 2026-09-25); its numbers are illustrative.

Try it on a trace

Open a two-column chromatogram in the workbench, or load the synthetic example. No account needed.

Open the workbench

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