Van Deemter Equation

The equation and its application in the chromatography technique help in measuring the column efficiency. The equation, and its subsequent deviation, helps in understanding the parameters that affect the separation of band broadening during the chromatographic process. It is the basic interpretive equation detailing factors that lead to the broadening of a compound as it travels along the column.

Van Deemter equation band broadening helps understand the overall dispersion or widening of a sample peak as it passes through a separation system. The equation signifies the relation between variance per unit length of a separation column to the linear mobile phase velocity in a chromatography setup. The topic explains what is the Van Deemter equation, the derivations, and how it connects to chromatography.

Understanding the concept of band broadening

• Band broadening is an important concept to understand the derivation of the Van Deemter equation. In the chromatographic system, as the compound moves through the chromatographic column, it leads to the broadening of the peaks
• Van Deemter equation band broadening is influenced by multiple factors. The column efficiency is governed majorly by four general contributions which are longitudinal diffusion, eddy diffusion, and mass transport broadening in the stationary and mobile phase
• The factors that affect plate efficiency are column length, particle size, linear velocity, packing quality, dead volume and retention factor
• The band broadening in the column is contributed by multiple factors. One is the dead volume representing all volume in the column from the injector to the detector, precisely the space where separation does not occur. It contributes to peak broadening without participating in separation
• The other source of broadening is within the column where the actual separation occurs. The Van Deemter equation band broadening indicates the relation between band broadening and chromatographic peak. In chromatography with less band broadening, it has more resolved peaks. N is proportional to the retention time and inversely proportional to the peak width at half height

Van Deemter equation and defining factors

The Van Deemter equation is a hyperbolic function which is crucial for chromatographic techniques. It predicts the optimum velocity at which there will be minimum variance per unit column length and hence maximum efficiency. Now that we know what is the Van Deemter equation, understanding the derivation helps in clarifying concepts.

The column efficiency is defined by the number of plates in a column and is represented by N. Higher the number of plates in a column, the more efficient the column is and hence better separation between two solutes. L is the length of the column.

H = L / N

Whereas H is the height equivalent to the plate, also represented by HETP (height equivalent to theoretical plate)

Here is the derivation of the Van Deemter equation where the equation relates to a height equivalent to a theoretical plate (HETP) of a chromatographic column to several flows and is associated with several kinetic parameters that cause peak broadening.

HETP = A + B/u (C_S + C_m). u

Where

A = Eddy diffusion parameter

B = diffusion coefficient of eluting particles in the longitudinal direction

C = Resistance to mass transfer coefficient of the analyte between the stationary and mobile phase

u = speed

Factors impacting the equation

• The plate number in the column shows the relation between the retention time and the width of the peak. It is integral for describing the column quality and separation power
• The plate number is inversely related to the particle size packed within the column. The plate number and separation power are high when the column is packed with smaller particles
• The flow along the column and column efficiency is described using the derivation of the Van Deemter equation
• The peak height and band broadening while the mobile phase flows along the stationary phase is governed by kinetic processes in the column including factors like molecular dispersion, slow mass transfer and diffusion

Factors that affect the column efficiency in chromatography

There are factors which impact the column efficiency in the chromatography and variation in the Deemter equation value. Some of the major contributing factors include column packing, the particle size of the adsorbent, column dimension, solvents and the flow rate. The column separation improves with a reduction in the size of the particle. The dimension of the column plays a significant role where the increasing column length results in achieving better separation. The solvent and its compatibility with the column play a significant role and hence impact the flow rate. Hence, the Van Deemter equation considers various physical, thermodynamic, and kinetic properties involved in the separation.

Conclusion

In summary, the topic explains what is the Van Deemter equation and its role in chromatography column efficiency and separation. Van Deemter equation helps in showing the relation between HETP (height equivalent to theoretical plate) of a chromatographic column to the flow efficiency in the column and parameters impact the band broadening. Chromatography includes the concept of band broadening which is the overall widening or dispersion of the same peak as it passes through the separation system in the column. The topic provides the derivation of the Van Deemter equation and the parameters that affect band broadening allowing control of the component separation.