Method transfer & column scaling
Geometric scaling between columns (e.g. HPLC → UHPLC), including the gradient table and dwell-volume compensation, with checks against the USP <621> allowances.
Gradient table
Enter the original program. Times are scaled to keep the same gradient volume per column volume. Leave a single row for an isocratic method.
| Original time (min) | %B | Remove |
|---|
| New time (min) | %B | Flow (mL/min) |
|---|
Equations used
- Flow: F2 = F1 · (dc2²/dc1²) · (dp1/dp2). The dp term is optional.
- Injection volume: V2 = V1 · (L2 dc2²)/(L1 dc1²)
- Gradient times: t2 = t1 · (F1/F2) · (L2 dc2²)/(L1 dc1²). F2 includes any extra flow adjustment, so the gradient slope per column volume stays the same.
- Pressure ratio (same mobile phase and temperature): P2/P1 = (F2/F1)(L2/L1)(dc1/dc2)²(dp1/dp2)²
- Dwell: the original dwell volume is scaled to the new column volume and compared with the new system's dwell volume. A shortfall is made up with an initial isocratic hold. An excess can be offset by delaying injection, if the system supports it.
USP <621> (harmonized; official 1 Dec 2022) adjustment summary, based on USP's notice of the harmonized chapter:
- L/dp: −25% to +50% of the original, for isocratic and gradient methods. When switching between fully and superficially porous particles, the efficiency criterion is used instead: N (isocratic) or (tR/w½)² (gradient) within −25% to +50%.
- Flow: scaled with dc² and dp. A further ±50% is permitted.
- Column temperature: ±10 °C (isocratic), ±5 °C (gradient). Mobile-phase pH: ±0.2 units. Minor components: ±30% relative or ±10% absolute.
- Injection volume: may be adjusted, provided system suitability is met.
Always confirm against the current official chapter and the monograph, and verify system suitability after any change.
Gradient design
Linear-solvent-strength estimates for reversed-phase gradients: the gradient retention factor k*, the gradient time for a target k*, peak capacity, and an isocratic-or-gradient check from a scouting run.
Isocratic or gradient? (scouting run)
Run a wide scouting gradient (e.g. 5–95 %B), then enter the first and last peak retention times.
Equations & rules of thumb
- k* = tG·F / (1.15·Vm·Δφ·S), with Δφ the change in organic fraction (e.g. 5→95% gives 0.90) and Vm = ε·π(dc/2)²·L.
- k* between about 2 and 10 is the usual working range; a value near 5 is a common target. To keep the separation unchanged when you change column, flow or gradient range, keep k* constant.
- S ≈ 4 is typical for small molecules (MW below ~500). It is much larger for peptides and proteins, so their retention is far more sensitive to %B.
- Peak capacity nc = 1 + tG/w, with w the average 4σ (baseline) peak width.
- Scouting rule of thumb (Snyder & Dolan): ΔtR/tG < 0.25 suggests isocratic elution is feasible; > 0.40 suggests gradient elution; in between, either may work.
System suitability
Retention factor, selectivity, plate count, resolution, symmetry, replicate precision and signal-to-noise. Use consistent time units.
Replicate injections
Resolution what-if (Purnell equation)
Equations used
- k = (tR − t0)/t0; α = k2/k1
- N = 5.54 (tR/w½)² or N = 16 (tR/wb)²; reduced plate height h = (L/N)/dp. A well-packed column gives h ≈ 2–3.
- Rs = 1.18 (tR2 − tR1)/(w½1 + w½2) or Rs = 2 (tR2 − tR1)/(wb1 + wb2)
- Symmetry factor As = W0.05/(2f). Ph. Eur. 2.2.46 applies a default of 0.8–1.8 unless the monograph states otherwise. USP monographs set their own limits (often NMT 2.0).
- S/N = 2H/h, with h the peak-to-peak noise range measured in a blank over at least 5× the peak width at half height (USP <621>). The LOD and LOQ estimates assume a linear response through zero: c × 3/(S/N) and c × 10/(S/N).
- %RSD = 100 · s/x̄, with the sample standard deviation s (n − 1).
- Purnell: Rs = (√N/4) · ((α−1)/α) · (k/(1+k)); required N = 16 Rs² (α/(α−1))² ((1+k)/k)²
Buffer preparation
Amounts of the acid and conjugate-base forms to weigh for a target pH, total buffer concentration and volume. Calculated from the full charge balance with activity corrections, not just Henderson–Hasselbalch.
pH of an acid additive in water
Method, pKa values and reagent data
- Every pair here differs by one proton, so the charge balance gives nbase = C·α − [H⁺] + [OH⁻] and nacid = C − nbase, with α the fraction in the base form. The [H⁺] term matters below about pH 3. There, plain Henderson–Hasselbalch overstates the base form (e.g. KH₂PO₄ at pH 2.5).
- Activity: the pH-meter reading is treated as −log aH⁺. The effective pKa′ = pKa + A·(2za − 1)·(√I/(1+√I) − 0.3I), with A = 0.509 (25 °C) and za the charge of the acid form, iterated on ionic strength I. The Davies equation is reasonable up to I ≈ 0.1–0.5 M.
- Organic solvent shifts both the pKa and the measured pH; these values apply to the aqueous buffer.
Back-pressure & viscosity
Estimates mobile-phase viscosity for water–acetonitrile or water–methanol and the column pressure drop from Darcy's law. Enter a measured pressure to calibrate the estimate to your column.
Equations & limits
- ΔP = φ · η · L · u0/dp², with u0 = F/(ε·π dc²/4), the chromatographic linear velocity (L/t0). φ is commonly quoted as roughly 500–1000 for packed columns. It varies with packing quality and particle type, so for the best estimate, enter a measured pressure and the tool back-calculates φ for your column.
- Viscosity: Chen & Horváth (1993) correlation, ln η = φ(a₁ + b₁/T) + (1−φ)(a₂ + b₂/T) + φ(1−φ)(a₃ + b₃/T), with φ the organic volume fraction and T in kelvin. It reproduces the pure-solvent viscosities and the methanol–water maximum (≈1.6 cP near 40–50% at 25 °C). Mid-range values are approximate (±10–15%). It ignores buffer salts and additives.
- System pressure (tubing, mixer, detector) is not included.
Column volume, t0 & solvent use
Equations used
- Vm ≈ ε · π (dc/2)² · L; t0 = Vm/F
- Linear velocity u = L/t0
- Dwell time tD = VD/F, the delay before the gradient reaches the column head.
- Re-equilibration time = (n · Vm + VD)/F
- Porosities are typical values. Measure t0 with an unretained marker (e.g. uracil in reversed phase) for an exact figure.