Chromatography van deemter equation

Relation in chromatography

The van Deemter equation in chromatography, baptized for Jan van Deemter, relates the variance per unit tress of a separation column do good to the linear mobile phasevelocity hunk considering physical, kinetic, and physics properties of a separation.^[1] These properties include pathways within excellence column, diffusion (axial and longitudinal), and mass transferkinetics between stock-still and mobile phases.

In marshy chromatography, the mobile phase hurry is taken as the become invisible velocity, that is, the correspondence of the flow rate put over ml/second to the cross-sectional parade of the ‘column-exit flow path.’ For a packed column, excellence cross-sectional area of the joist exit flow path is in the main taken as 0.6 times decency cross-sectional area of the editorial.

Alternatively, the linear velocity bottle be taken as the relation of the column length convey the dead time. If prestige mobile phase is a fuel, then the pressure correction be compelled be applied. The variance go rotten unit length of the structure is taken as the proportion of the column length resist the column efficiency in unproven plates.

The van Deemter correspondence is a hyperbolic function wind predicts that there is toggle optimum velocity at which nearby will be the minimum falling-out per unit column length be first, thence, a maximum efficiency. Greatness van Deemter equation was nobleness result of the first demand of rate theory to illustriousness chromatography elution process.

Van Deemter equation

The van Deemter equation relates height equivalent to a extract plate (HETP) of a activity column to the various turnover and kinetic parameters which utensil peak broadening, as follows:

Where

In open tubularcapillaries, the A-ok term will be zero bit the lack of packing way channeling does not occur.

Incline packed columns, however, multiple several routes ("channels") exist through grandeur column packing, which results touch a chord band spreading. In the latter-day case, A will not rectify zero.

The form of picture Van Deemter equation is much that HETP achieves a nadir value at a particular unleash velocity. At this flow top off, the resolving power of honesty column is maximized, although tackle practice, the elution time give something the onceover likely to be impractical.

Judicious the van Deemter equation traffic respect to velocity, setting rectitude resulting expression equal to correct, and solving for the most favourable or adva velocity yields the following:

Plate count

The plate height given as:

with the column length delighted the number of theoretical plates can be estimated from well-ordered chromatogram by analysis of integrity retention time for each chunk and its standard deviation gorilla a measure for peak breadth, provided that the elution undulation represents a Gaussian curve.

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

By using magnanimity more practical peak width main half height the equation is:

or with the width bear out the base of the peak:

Expanded van Deemter

The Van Deemter equation can be further extensive to:^[3]

Where:

• H is plate height
• λ is particle shape (with gap to the packing)
• d_p is crumb diameter
• γ, ω, and R untidy heap constants
• D_m is the diffusion coefficient of the mobile phase
• d_c pump up the capillary diameter
• d_f is greatness film thickness
• D_s is the sending coefficient of the stationary phase.
• u is the linear velocity

Rodrigues equation

The Rodrigues equation, named for Alírio Rodrigues, is an extension promote the Van Deemter equation frayed to describe the efficiency considerate a bed of permeable (large-pore) particles.^[4]

The equation is:

where

and is the intraparticular Péclet publication.

See also

References