# Dispersion in Chromatography Columns - The Van Deemter Equation > Page 57

Now, l = nH_{min}, thus, substituting for l, and
rearranging,

_{}.
(40)

Substituting
for u_{opt}and H_{min},

_{} (41)

_{} (42)

or, (43)

It is seen
from equation (43) that, if an LC column is operated at its optimum linear
velocity, the maximum efficiency obtainable for well retained peaks will be
directly proportional to the inlet pressure available (P) and the square
of the particle diameter of the packing. Thus, the larger the particle
diameter, the greater efficiency attainable at a given pressure. This is
because, as the particle diameter is increased the column permeability is also
increased allowing a longer column to be used. The permeability increases as
the square of the particle diameter but the variance per unit length only
increases linearly with the particle diameter. Thus, doubling the particle
diameter will allow a column four times the length to be used but the number of
plates *per unit length* will be halved. Consequently, the column
efficiency will be increased by a factor of two. It is also seen that the
higher efficiencies will be obtained with mobile phases of low viscosity and
for solutes of low diffusivity. Solvent viscosity and solute diffusivity tend
to be inversely proportional to each other and so the sensitivity of the
maximum obtainable efficiency to either solvent viscosity or solute diffusivity
will generally not be large. The approximate length of a column that will
provide the maximum column efficiency when operated at optimum velocity is
given by, l = nH_{min}_{.}