Question

Explain each term in the Van Deempter Equation. What major advantage is gained through open tubular GC in reference to this equation.

H= A+(b/u)+cu

Answer 1

The Van Deemter equation(Van Deempter Equation)
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.

Factors affecting column efficiency (plate number)

Column length
Particle size
Packing quality
Linear velocity (flow)
Instrument quality (dead volume)
Retention factor
Stationary phase particle size is one of the most important factors in the van Deemter equation. For a given column length, the plate number (Nth) is inversely related to the particle size of the column packing. The smaller the particles, the higher the plate number and the separation power.

The plate number is also dependent on the flow rate (F) of the mobile phase. There is a certain velocity, the so-called optimum flow, at which the plate number is highest (and H is lowest). A lower or a higher flow rate provides less plates (higher H). In routine HPLC, columns are always operated at velocities above the optimum. The reduced column efficiency is less significant than the shorter analysis time at the higher than optimal flow rates.

To describe the contribution of the above factors, several so-called plate height equations have been developed. A plate height equation expresses the correlation between plate height and mobile phase velocity. Best known is the 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+(b/u)+cu

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.