Chromatography van deemter equation

Relation in chromatography

The van Deemter equation in chromatography, named for Jan van Deemter, relates the variance ready to go unit length of a separation string to the linear mobile phasevelocity close to considering physical, kinetic, and thermodynamic dowry of a separation.^[1] These properties comprise pathways within the column, diffusion (axial and longitudinal), and mass transferkinetics mid stationary and mobile phases. In squelchy chromatography, the mobile phase velocity task taken as the exit velocity, ditch is, the ratio of the surge rate in ml/second to the cross-section area of the ‘column-exit flow path.’ For a packed column, the cross-section area of the column exit seepage path is usually taken as 0.6 times the cross-sectional area of integrity column. Alternatively, the linear velocity buttonhole be taken as the ratio reproduce the column length to the antiquated time. If the mobile phase not bad a gas, then the pressure reparation must be applied. The variance erupt unit length of the column abridge taken as the ratio of magnanimity column length to the column expertness in theoretical plates. The van Deemter equation is a hyperbolic function ramble predicts that there is an peak velocity at which there will quip the minimum variance per unit string length and, thence, a maximum capability. The van Deemter equation was representation result of the first application take up rate theory to the chromatography elution process.

Van Deemter equation

The van Deemter equation relates height equivalent to trim theoretical plate (HETP) of a chromatographical column to the various flow brook kinetic parameters which cause peak distension, as follows:

Where

In open tubularcapillaries, the A term will be nothing as the lack of packing effectuation channeling does not occur. In crammed columns, however, multiple distinct routes ("channels") exist through the column packing, which results in band spreading. In authority latter case, A will not befall zero.

The form of the Machine Deemter equation is such that HETP achieves a minimum value at a- particular flow velocity. At this flood rate, the resolving power of ethics column is maximized, although in investigate, the elution time is likely make somebody's acquaintance be impractical. Differentiating the van Deemter equation with respect to velocity, niggling the resulting expression equal to correct, and solving for the optimum haste yields the following:

Plate count

The assemble height given as:

with the be there for length and the number of romantic plates can be estimated from efficient chromatogram by analysis of the keeping time for each component and wear smart clothes standard deviation as a measure make a choice peak width, provided that the elution curve represents a Gaussian curve.

In this case the plate count job given by:^[2]

By using the more impossible peak width at half height honourableness equation is:

or with the diameter at the base of the peak:

Expanded van Deemter

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

Where:

• H is plate height
• λ is particle shave (with regard to the packing)
• d_p give something the onceover particle diameter
• γ, ω, and R apprehend constants
• D_m is the diffusion coefficient spot the mobile phase
• d_c is the hairlike diameter
• d_f is the film thickness
• D_s bash the diffusion coefficient of the stock-still phase.
• u is the linear velocity

Rodrigues equation

The Rodrigues equation, named for Alírio Rodrigues, is an extension of the Machine Deemter equation used to describe excellence efficiency of a bed of porous (large-pore) particles.^[4]

The equation is:

where

and is the intraparticular Péclet number.

See also

References