van Deemter equation
Band broadening theory (Van Deemter equation)
It is well recognized now that column band broadening originates from three main sources:
1. multiple path of an analyte through the column packing;
2. molecular diffusion;
3. effect of mass transfer between phases.
In 1956 J.J. Van Deemter introduced the equation which combined all three sources and represented them as the dependence of the theoretical plate height (HETP) on the mobile phase linear velocity. Originally, it was introduced for gas chromatography, but it happened that the same physical processes occurs in HPLC, and this equation is perfectly fit for liquid chromatography.
Multiple path
The velocity of mobile phase in the column may vary significantly across the column diameter, depending on the particle shape, porosity, and the whole bed structure. This is schematically shown below.
Variation of the zone flows
Band broadening is caused by differing flow velocities through the column, which may be written in form (8) where Hp is the HETP arising from the variation in the zone flow velocity, dp is the particle diameter (average), and is the constant which is almost close to 1.
This shows that Hp may be reduced (efficiency increased) by reducing the particle diameter (which will lead to the increasing of the column back pressure). Coefficient lambda depends on the particle size distribution. The narrower the distribution, the smaller (which actually lead to decreasing of the column backpessure also).
Analyte diffusion
It is well-known that molecules disperse or mix due to the diffusion. The longitudinal diffusion (along the column long axis) leads to the band broadening of the chromatographic zone. This process may be described by equation: (9) where Dm is the analyte diffusion coefficient in the mobile phase,
is the factor which is related to the diffusion restriction by column packing, v is the flow velocity.
It is obvious from the above equation that
It is well recognized now that column band broadening originates from three main sources:
1. multiple path of an analyte through the column packing;
2. molecular diffusion;
3. effect of mass transfer between phases.
In 1956 J.J. Van Deemter introduced the equation which combined all three sources and represented them as the dependence of the theoretical plate height (HETP) on the mobile phase linear velocity. Originally, it was introduced for gas chromatography, but it happened that the same physical processes occurs in HPLC, and this equation is perfectly fit for liquid chromatography.
Multiple path
The velocity of mobile phase in the column may vary significantly across the column diameter, depending on the particle shape, porosity, and the whole bed structure. This is schematically shown below.
Variation of the zone flows
Band broadening is caused by differing flow velocities through the column, which may be written in form (8) where Hp is the HETP arising from the variation in the zone flow velocity, dp is the particle diameter (average), and is the constant which is almost close to 1.
This shows that Hp may be reduced (efficiency increased) by reducing the particle diameter (which will lead to the increasing of the column back pressure). Coefficient lambda depends on the particle size distribution. The narrower the distribution, the smaller (which actually lead to decreasing of the column backpessure also).
Analyte diffusion
It is well-known that molecules disperse or mix due to the diffusion. The longitudinal diffusion (along the column long axis) leads to the band broadening of the chromatographic zone. This process may be described by equation: (9) where Dm is the analyte diffusion coefficient in the mobile phase,
is the factor which is related to the diffusion restriction by column packing, v is the flow velocity.
It is obvious from the above equation that