The Van Deemter equation relates the height equivalent to a theoretical plate (H) to the mobile phase velocity (u) in chromatography, describing band broadening and column efficiency. The equation shows there is an optimum flow rate that minimizes band broadening and maximizes column efficiency. The Van Deemter equation is given below-
H = A + (B/u) + C.u
where:
H = Height Equivalent to a Theoretical Plate (HETP)
A = Eddy diffusion (multiple flow paths) Parameter
B = Longitudinal Diffusion Parameter (related to molecular diffusion)
C = Resistance to mass transfer (between phases) Parameter
u = Linear velocity of the mobile phase
Factors Responsible for Band Broadening
The three terms in the Van Deemter equation represent the primary factors that contribute to peak broadening:
1. Eddy Diffusion/Multiple Path Effect (A term)
- In a packed column, molecules can travel by different routes of varying lengths because of the random arrangement of the particles (packing material).
- Result: Some analyte molecules exit faster, some slower > peak broadens.
- Minimized by: Using small, uniform, well-packed stationary phase particles.
Note: The A term is zero in open tubular (capillary) columns because there is no solid packing material to create multiple paths.
2. Longitudinal Diffusion (B/u term)
- Solute molecules naturally diffuse (spread) from areas of high to low concentration along the column length.
- More significant at low flow rates because molecules remain in the column longer.
- Minimized by: Increasing flow rate and lowering analyte diffusion (especially important in gas chromatography).
3. Mass Transfer Resistance (C·u term)
- Caused by the time taken for molecules to transfer between the stationary and mobile phases.
- If the mobile phase moves too quickly, molecules can’t equilibrate between phases, leading to band spreading.
- Minimized by: Using thin stationary phases, small particle sizes, and operating at the optimum flow rate.
Note: The C term is the most significant factor in Liquid Chromatography (LC) because of the low diffusion rate in liquids.
Significance of the Van Deemter Curve
- When HETP (H) is plotted against mobile phase velocity (u), it forms a characteristic curve with a minimum. This minimum point indicates the optimum flow velocity at which the column achieves its maximum efficiency (i.e., the lowest plate height and the narrowest peaks).
- Operating at velocities lower than the optimum results in increased band broadening due to dominant longitudinal diffusion (the B/u term).
- Operating at velocities higher than the optimum results in increased band broadening due to dominant mass transfer resistance (the C·u term).