Chromatography Column: Van Deemter Plate Theory

Column Chromatography

Flow velocity (u) 0.50 mm/s

Column length (L) 15 cm

Particle size (dₚ) 5.0 μm

Analyte B polarity (K₂) 16.5

Retention time — A / B

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Plate count N (min of A,B)

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Resolution Rₛ

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How it works

Each analyte distributes between the flowing mobile phase and the stationary phase coating the packing according to its partition coefficient K. A larger K means the molecule spends more time adsorbed and less time being carried forward, so it lags behind. That lag is expressed as the capacity factor k' = K/β (β is the phase ratio), which sets the retention time.

k' = K / β
t_R = t_M · (1 + k')   ,  t_M = L / u

A sharp injection band does not stay sharp — random eddy paths, longitudinal diffusion and finite mass-transfer speed between phases smear it out as it travels. The Van Deemter equation combines all three into an effective plate height H, and the number of theoretical plates N = L/H measures how many equilibration steps the column delivers:

H(u) = A + B/u + C·u
A = eddy diffusion (∝ particle size)
B = longitudinal diffusion (∝ Dm)
C = mass-transfer resistance (∝ dp², k'/(1+k')²)

H is U-shaped in u: too slow and longitudinal diffusion (B/u) dominates; too fast and mass transfer (C·u) can't keep up. There is one flow velocity that minimizes H and maximizes N — that optimum is what the "Flow velocity" slider lets you hunt for.

σ_t = t_R / √N   ,   w = 4σ_t
Rₛ = (t_R,B − t_R,A) / (σ_A + σ_B)

Resolution Rₛ needs both a time gap between the peaks (set by how different K₁ and K₂ are — the "Analyte B polarity" slider) and narrow peaks (set by N, via flow velocity, column length and particle size). Rₛ ≥ 1.5 is generally considered baseline separation.

Analyte A (K₁=15, fixed) Analyte B (K₂ = slider)

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