Equation of Height Equivalent to a Theoretical Plate
The HETP Equation An HETP equation quantitatively describes the peak dispersion (band spreading) by expressing the �variance per unit length� of the column as a function of the linear mobile phase velocity and the various physical properties of the distribution system and the solute being eluted. The variance per unit length of the column is measured as the ratio of the column length to the column efficiency, i.e, the height of the theoretical plate or the HETP. There have been a number of different HETP equations developed, the first for packed columns was the Van Deemter equation which was followed by the Huber equation, the Giddings equation, the Horvath equation, the Knox equation and finally the Golay equation for capillary columns. All the equations, except the Knox equation, were developed from first principles, the Knox equation, however, was developed from experimentally observed relationships and subsequently rationalized on a first principle basis. All the HETP equations include functions that describe dispersion due to longitudinal diffusion and dispersion resulting from the resistance to mass transfer in both phases. All the HETP equations for packed columns include a function that describes dispersion that results from the tortuous paths taken by solute molecules as they wind their way through the intersticies of the packing. This dispersion process was given the term �eddy diffusion� by Van Deemter With the exception of the Giddings equation, the function for eddy diffusion dispersion is expressed as a constant depending on the particle diameter of the packing and independent of the mobile phase linear velocity. Giddings however, introduced a coupling function to the eddy diffusion term so that the dispersion only became constant and independent of mobile phase velocity at relatively high velocities. The Golay equation, as there was no packing, only contained three terms, one for longitudinal diffusion and one each for the resistance to mass transfer in the mobile and stationary phases respectively. The Huber and Horvath equations contain an extra term that involves a power function of the mobile phase velocity, largely to account for the curving of the HETP graph towards the base line at very high mobile phase velocities. Subsequently, this curving effect was shown to be an artifact resulting from experimental problems that arose when measuring the elution curves of very fast eluting peaks. All the equations have hyperbolic characteristics relating variance per unit length to linear mobile phase velocity. This means that the variance per unit length-mobile phase velocity curve shows a minimum at a particular velocity which has been termed the optimum linear velocity. The column will exhibit a maximum efficiency for a specific solute when operated at the optimum velocity. In practice, it has been shown that the equation that best describes the experimental data from a packed LC column is probably the Van Deemter equation.



