Van Deemter equation

Equation describing the efficiency of separation in chromatography

The Van Deemter equation is a fundamental equation in the field of chromatography that describes the relationship between the linear velocity of the mobile phase and the efficiency of the separation process. It is used to optimize the performance of chromatographic columns by minimizing the height equivalent to a theoretical plate (HETP).

Equation

The Van Deemter equation is expressed as:

<math>H = A + \frac{B}{u} + C \cdot u</math>

where:

• H is the height equivalent to a theoretical plate (HETP),
• A is the eddy diffusion term,
• B is the longitudinal diffusion term,
• C is the mass transfer term,
• u is the linear velocity of the mobile phase.

Terms of the Equation

Eddy Diffusion (A)

The eddy diffusion term accounts for the multiple pathways that solute molecules can take through the packed column. Variations in path length lead to band broadening, which is independent of the flow rate.

Longitudinal Diffusion (B)

Longitudinal diffusion refers to the natural diffusion of solute molecules along the length of the column. This effect is more pronounced at lower flow rates, as molecules have more time to diffuse.

Mass Transfer (C)

The mass transfer term describes the resistance to mass transfer between the mobile and stationary phases. This resistance increases with higher flow rates, as solute molecules have less time to equilibrate between phases.

Optimization

The Van Deemter equation is used to find the optimal flow rate that minimizes the HETP, thereby maximizing the efficiency of the separation. The optimal flow rate is a balance between the different terms in the equation.

Applications

The Van Deemter equation is widely used in the design and operation of chromatographic systems, including gas chromatography and liquid chromatography. It helps in selecting the appropriate column and operating conditions to achieve the best separation performance.

Images

Graphical representation of the Van Deemter equation.

Effect of flow rate on retention time and efficiency.

Related pages

• Chromatography
• Gas chromatography
• Liquid chromatography

References

• van Deemter, J. J., Zuiderweg, F. J., & Klinkenberg, A. (1956). Longitudinal diffusion and resistance to mass transfer as causes of nonideality in chromatography. Chemical Engineering Science, 5(6), 271-289.
• Giddings, J. C. (1965). Dynamics of Chromatography: Principles and Theory. Marcel Dekker, Inc.

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