CHROMATOGRAPHIC RESOLUTION — Impact of k, α and N
Rs = (tR2 − tR1) / ((W1+W2)/2) = (√N/4) · (α−1)/α · k/(1+k)
| Parameter | Value |
|---|---|
| Retention factor k | |
| Selectivity α | |
| Plate number N | |
| t0 (min) |
Calculated:
Resolution Rs = 0
tR1 = 0 min
tR2 = 0 min
VAN DEEMTER EQUATION — Kinetic Performance & Plate Height
H = A + B/u + C·u (reduced: h = a + b/ν + c·ν) | ΔP = Φ·η·L·u/dp² (Darcy's law)
| Parameter | Value |
|---|---|
| Column length L (mm) | |
| Column i.d. dc (mm) | |
| Particle size dp (μm) | |
| Flow rate F (mL/min) | |
| Porosity ε |
t0 = 0 min
u (linear vel.) = 0 mm/s
N (plates) = 0
ΔP (pressure) = 0 bar
REVERSED-PHASE RETENTION — Impact of analyte lipophilicity (log P)
log kw = 0.83·log P + 0.21 | log k = log kw − S·Φ (S = 4 for low MW compounds)
| Compound | log P |
|---|---|
| Compound 1 | |
| Compound 2 | |
| Compound 3 | |
| % Methanol (Φ·100) |
log P < 0 : hydrophilic (poorly retained)
log P > 0 : lipophilic (well retained)
IONIZATION & pH — Impact of mobile phase pH and analyte pKa
Acid: log D = log P − log(1 + 10pH−pKa) | Base: log D = log P − log(1 + 10pKa−pH)
| Parameter | Compound A | Compound B |
|---|---|---|
| log P | ||
| pKa | ||
| Type |
| Mobile phase | Value |
|---|---|
| pH | |
| % Methanol |
TEMPERATURE EFFECTS — Kinetic & Thermodynamic Performance
Dm ∝ T/η (Wilke–Chang) | log k vs 1/T (van't Hoff): k roughly halved every 30–40 °C
| Parameter | Value |
|---|---|
| Column L (mm) | |
| Column i.d. (mm) | |
| dp (μm) | |
| Flow (mL/min) | |
| % MeOH | |
| Temperature (°C) |
ISOCRATIC MODE — Retention & Selectivity vs Mobile Phase Composition
Linear Solvent Strength (LSS) theory: log k = log kw − S·Φ (S = 0.5·√MW)
| Cmpd | log P | S | Color |
|---|---|---|---|
| 1 | |||
| 2 | |||
| 3 | |||
| 4 | |||
| 5 |
| Condition | Value |
|---|---|
| % Methanol | |
| N (plates) |
GRADIENT MODE — Separation of Diverse Compounds
W = 4·t0(1+ke)/√N | Peak capacity nc = (√N/4)·(b/(b+1))·ln(1 + b·((1+b)/b)·eS·ΔΦ − 1)
| Cmpd | log P | S |
|---|---|---|
| 1 | ||
| 2 | ||
| 3 | ||
| 4 | ||
| 5 |
| Gradient | Value |
|---|---|
| % MeOH initial | |
| % MeOH final | |
| Gradient time (min) | |
| Flow (mL/min) |
Peak capacity nc = 0
Rs,min = 0
Rs,min = 0
INJECTED VOLUME — Impact on Sensitivity & Band Broadening
σ²tot = σ²col + σ²inj | σ²inj = Kinj·Vinj²/12 (K=2) | Nobs/Ncol = 1 / (1 + σ²inj/σ²col)
| Parameter | Value |
|---|---|
| Column L (mm) | |
| Column i.d. (mm) | |
| dp (μm) | |
| Flow (mL/min) | |
| % MeOH | |
| log P (3 cmpd) | |
| Vinj (μL) | |
| Concentration |
Vcol = 0 μL
Vinj/Vcol = 0 %
Vinj/Vcol = 0 %
TUBING GEOMETRY — Extra-Column Band Broadening
σ²tube = π·dtube4·Ltube·F/(768·Dm) | ΔPtube = 128·η·Ltube·F/(π·dtube4) (Hagen-Poiseuille)
| Parameter | Value |
|---|---|
| Column L (mm) | |
| Column i.d. (mm) | |
| dp (μm) | |
| Flow (mL/min) | |
| % MeOH | |
| log P (3 cmpd) | |
| Tube length (cm) | |
| Tube i.d. (μm) |
Vtube/Vcol = 0 %
ΔPtube = 0 bar
ΔPtube = 0 bar
MOLECULAR WEIGHT — Impact on Thermodynamic & Kinetic Performance
Dm ∝ 1/MW0.6 (Wilke-Change) | S = 0.5·√MW | Optimal flow rate ∝ Dm/dp
| Parameter | Value |
|---|---|
| Column L (mm) | |
| Column i.d. (mm) | |
| dp (μm) | |
| Flow (mL/min) | |
| % ACN | |
| MW cmpd 1 | |
| MW cmpd 2 | |
| MW cmpd 3 |