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

Now, l = nHmin, thus, substituting for l, and rearranging,

                        .                            (40)

Substituting for uoptand Hmin,

                                                  (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 = nHmin.