Question

Van Deemter equation is written as: H = A + B/u + Cu where u is mobile phase linear velocity. Sketch a typical van Deemter plot to show how H depends on u, and briefly explain each term in the equation and sketch how each depends on u.

Answer 1

The efficiency of a column is measured by theoretical plates, Nth, and can be normalized with the length of the column to give the height equivalent theoretical plate, called HETP or H. The Van Deemter equation describes the various factors influencing H, and is divided into eddy diffusion, longitudinal diffusion, and mass transfer terms. The relative importance of these factors varies with mobile phase velocity. Particle size and morphology contribute to H, along with a variety of other factors. Understanding the van Deemter equation allows the determination of the optimum mobile phase velocity.

van Deemter equation, which describes the various contributions to plate height (H). In this equation the parameters that influence the overall peak width are expressed in three terms:

H=A+Bu+C×u

H = HETP (plate height)
A = eddy diffusion term
B = longitudinal diffusion term
u = linear velocity
C = Resistance to mass transfer coefficient  

Peak height and peak broadening are governed by kinetic processes in the column such as molecular dispersion, diffusion and slow mass transfer. Identical molecules travel differently in the column due to probability processes. The three processes that contribute to peak broadening described in the van Deemter equation are:

A-term: eddy diffusion: The column packing consists of particles with flow channels in between. Due to the difference in packing and particle shape, the speed of the mobile phase in the various flow channels differs and analyte molecules travel along different flow paths through the channnels.
B-term: longitudinal diffusion: Molecules traverse the column under influence of the flowing mobile phase. Due to molecular diffusion, slight dispersions of the mean flow rate will be the result.
C-term: resistance against mass transfer. A chromatographic system is in dynamic equilibrium. As the mobile phase is moving continuously, the system has to restore this equilibrium continuously. Since it takes some time to restore equilibrium (resistance to mass transfer), the concentration profiles of sample components between mobile and stationary phase are always slightly shifted. This results in additional peak broadening.

van Deemter H-u curve

The van Deemter equation is graphically expressed in the H-u curve, which is a plot of the plate height as a function of the mobile phase velocity.

The H-u curve shows that:

The A-term is independent of u and does not contribute to the shape of the H-u curve..
The contribution of the B-term is negligible at normal operating conditions. This is due to the fact that the molecular diffusion coefficient in a liquid medium is very small.
The C- term increases linearily with mobile phase velocity and its contribution to the H-u curve is therefore considerable. A small C-term leads to a fairly flat ascending portion of the H-u curve at higher mobile phase velocities. This means that the separation can be carried out at higher mobile phase velocities without sacrificing separation quality.

The H-u curve is very useful to determine the optimum mobile phase velocity uopt at which the highest column efficiency wil be attained. Below this velocity the column efficiency will decrease rapidly, whereas above the optimum velocity there is only a slight decrease in efficiency.

General rules

The smaller the plate height H, the more efficient the column. However, at the optimum flow rate (with the lowest H), the analysis time will in most cases be unacceptably long.
Below the optimum flow rate the analysis time is too long and the quality of the separation suffers because of longitudinal diffusion (contribution of the B-term).
At extremely high flows, both the separation quality and the pressure drop across the column will become unacceptable.
The practical flow is often two or three times the optimum velocity. At these values, the minor loss of efficiency is still acceptable.
Small particles (< 5 µm) allow an increase in the flow to reduce the analysis time without significantly lowering resolution between the peaks of interest.