Van Deemter equation
The van Deemter equation in
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:
Where
- HETP= a measure of the resolving power of the column [m]
- A = Eddy-diffusionparameter, 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
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:
Plate count
The plate height given as:
with the column length and the number of theoretical plates can be estimated from a
In this case the plate count is given by:[2]
By using the more practical
or with the width at the base of the peak:
Expanded van Deemter
The Van Deemter equation can be further expanded to:[3]
Where:
- H is plate height
- λ is particle shape (with regard to the packing)
- dp is particle diameter
- γ, ω, and R are constants
- Dm is the diffusion coefficientof the mobile phase
- dc is the capillary diameter
- df is the film thickness
- Ds is the diffusion coefficient of the stationary phase.
- u is the linear velocity
Rodrigues equation
The Rodrigues equation, named for Alírio Rodrigues, is an extension of the Van Deemter equation used to describe the efficiency of a bed of permeable (large-pore) particles.[4]
The equation is:
where
and is the intraparticular Péclet number.
See also
References
- .
- ^ Kazakevich, Yuri. "Band broadening theory (Van Deemter equation)". Seton Hall University. Retrieved 5 February 2014.
- PMID 9392367.