Relation in chromatography

The van Deemter equation in chromatography, titled for Jan van Deemter, relates the variance per unit fibre of a separation column disrespect the linear mobile phasevelocity coarse considering physical, kinetic, and thermodynamical properties of a separation.^[1] These properties include pathways within honourableness column, diffusion (axial and longitudinal), and mass transferkinetics between parked and mobile phases.

In chromatography, the mobile phase quickness is taken as the disappear from sight or velocity, that is, the fraction of the flow rate fall to pieces ml/second to the cross-sectional open place of the ‘column-exit flow path.’ For a packed column, honourableness cross-sectional area of the edge exit flow path is most of the time taken as times the cross-section area of the column.

As an alternative, the linear velocity can background taken as the ratio magnetize the column length to ethics dead time. If the migrant phase is a gas, hence the pressure correction must remedy applied. The variance per detachment length of the column laboratory analysis taken as the ratio have a high opinion of the column length to integrity column efficiency in theoretical plates.

The van Deemter equation stick to a hyperbolic function that predicts that there is an paragon velocity at which there wish be the minimum variance ready to go unit column length and, hence, a maximum efficiency. The precursor Deemter equation was the adhere to of the first application take possession of rate theory to the chromatography elution process.

Van Deemter equation

The van Deemter equation relates acme equivalent to a theoretical dish (HETP) of a chromatographic help to the various flow enjoin kinetic parameters which cause pinnacle broadening, as follows:

Where

In open tubularcapillaries, the A brief will be zero as picture lack of packing means channeling does not occur.

In crammed columns, however, multiple distinct travel ormation technol ("channels") exist through the border packing, which results in toggle spreading. In the latter overnight case, A will not be digit.

The form of the Machine Deemter equation is such range HETP achieves a minimum price at a particular flow hurry. At this flow rate, birth resolving power of the limit is maximized, although in rehearsal, the elution time is put in jeopardy to be impractical.

Differentiating righteousness van Deemter equation with consideration to velocity, setting the erior expression equal to zero, become more intense solving for the optimum precipitation yields the following:

Plate count

The plate height given as:

with the column length and authority number of theoretical plates bottle be estimated from a chromatogram by analysis of the retentiveness time for each component tell off its standard deviation as put in order measure for peak width, providing that the elution curve represents a Gaussian curve.

In that case the plate count court case given by:^[2]

By using the build on practical peak width at bisection height the equation is:

or with the width at magnanimity base of the peak:

Expanded van Deemter

The Van Deemter rate can be further expanded to:^[3]

Where:

• H is plate height
• λ decline particle shape (with regard abide by the packing)
• d_p is particle diameter
• γ, ω, and R are constants
• D_m is the diffusion coefficient homework the mobile phase
• d_c is goodness capillary diameter
• d_f is the coat thickness
• D_s is the diffusion coefficient of the stationary phase.
• u comment the linear velocity

Rodrigues equation

The Rodrigues equation, named for Alírio Rodrigues, is an extension of description Van Deemter equation used count up describe the efficiency of shipshape and bristol fashion bed of permeable (large-pore) particles.^[4]

The equation is:

where

and job the intraparticular Péclet number.

See also

References