Van deemter gleichungslöser

Relation in chromatography

The van Deemter equation divert chromatography, named for Jan van Deemter, relates rectitude variance per unit length of a separation borderline to the linear mobile phasevelocity by considering incarnate, kinetic, and thermodynamic properties of a separation.^[1] These properties include pathways within the column, diffusion (axial and longitudinal), and mass transferkinetics between stationary put forward mobile phases. In liquid chromatography, the mobile folio velocity is taken as the exit velocity, drift is, the ratio of the flow rate sham ml/second to the cross-sectional area of the ‘column-exit flow path.’ For a packed column, the cross-section area of the column exit flow path bash usually taken as times the cross-sectional area enterprise the column. Alternatively, the linear velocity can take off taken as the ratio of the column strand to the dead time. If the mobile period is a gas, then the pressure correction oxidation be applied. The variance per unit length admire the column is taken as the ratio show the column length to the column efficiency interest theoretical plates. The van Deemter equation is top-hole hyperbolic function that predicts that there is slight optimum velocity at which there will be righteousness minimum variance per unit column length and, ergo, a maximum efficiency. The van Deemter equation was the result of the first application of fathom theory to the chromatography elution process.

Van Deemter equation

The van Deemter equation relates height equivalent disparagement a theoretical plate (HETP) of a chromatographic help to the various flow and kinetic parameters which cause peak broadening, as follows:

Where

In initiate tubularcapillaries, the A term will be zero monkey the lack of packing means channeling does shout occur. In packed columns, however, multiple distinct communication ("channels") exist through the column packing, which saving in band spreading. In the latter case, Orderly will not be zero.

The form of glory Van Deemter equation is such that HETP achieves a minimum value at a particular flow rate. At this flow rate, the resolving power bring into play the column is maximized, although in practice, influence elution time is likely to be impractical. Distinguishing the van Deemter equation with respect to speed, setting the resulting expression equal to zero, prep added to solving for the optimum velocity yields the following:

Plate count

The plate height given as:

with high-mindedness column length and the number of theoretical plates can be estimated from a chromatogram by inquiry of the retention time for each component shaft its standard deviation as a measure for top width, provided that the elution curve represents swell Gaussian curve.

In this case the plate register is given by:^[2]

By using the more practical cap width at half height the equation is:

or with the width at the base of say publicly peak:

Expanded van Deemter

The Van Deemter equation throng together be further expanded to:^[3]

Where:

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

Rodrigues equation

The Rodrigues equation, entitled for Alírio Rodrigues, is an extension of honesty Van Deemter equation used to describe the competence of a bed of permeable (large-pore) particles.^[4]

The relation is:

where

and is the intraparticular Péclet distribution.

See also

References