Van Deemter equation

Van Deemter equation

The van Deemter equation relates height equivalent to a theoretical plate (HETP) of a chromatographic column to the various flow and kinetic parameters which cause peak broadening, as follows:

${\displaystyle HETP=A+\frac{B}{u}+C\cdot u}$

Where

• HETP = a measure of the resolving power of the column [m]
• A = Eddy-diffusion parameter, related to channeling through a non-ideal packing [m]
• B = diffusion coefficient of the eluting particles in the longitudinal direction, resulting in dispersion [m² s⁻¹]
• C = Resistance to mass transfer coefficient of the analyte between mobile and stationary phase [s]
• u = speed [m s⁻¹]

In open tubular capillaries, the A term will be zero as the lack of packing means channeling does not occur. In packed columns, however, multiple distinct routes ("channels") exist through the column packing, which results in band spreading. In the latter case, A will not be zero. The version of the Van Deemter equation that applies to capillary columns called the Golay equation which is as follows:

${\displaystyle HETP=\frac{B}{u}+(C_s+C_m)\cdot u}$

The form of the Van Deemter equation is such that HETP achieves a minimum value at a particular flow velocity. At this flow rate, the resolving power of the column is maximized, although in practice, the elution time is likely to be impractical. Differentiating the van Deemter equation with respect to velocity, setting the resulting expression equal to zero, and solving for the optimum velocity yields the following:

${\displaystyle u=\sqrt{\frac{B}{C}}}$