Figure 4 shows a diagram of the additivity of the three terms in the van Deemter equation. Note that the B term is dominant
at low flow velocities, while the C term is dominant at high flow velocities. The minimum of the van Deemter curve represents
the ideal flow velocity where maximum column efficiency is obtained. It is a compromise between the B and C terms. Figure
4 is an idealized representation of the curves shown in Figure 1. The A and C van Deemter terms are influenced by the particle
size. Smaller particles tend to reduce the value of H, which means that the column is more efficient — that is, it provides more theoretical plates per unit length. Small particles
tend to allow solutes to transfer into and out of the particle more quickly because their diffusion path lengths are shorter.
Thus, the solute is eluted as a narrow peak because it spends less time in the stationary and stagnant mobile phase where
band broadening occurs.
One advantage of using smaller particles is that the column can be shortened and the plate count remains the same or nearly
so. A shorter column means a faster separation can be achieved because separation time is proportional to column length. A
shorter column run at the same linear velocity as a longer column also uses less solvent.
Another fallout of the decrease in particle size is that the van Deemter curves tend to flatten out at higher linear velocities
and the minimum shifts toward the right. Figure 5 shows a series of van Deemter curves for 5, 3.5 and 1.8 μm bonded spherical
silica columns. One can easily see that the column packed with 1.8 μm particles gives a flatter curve at high linear velocity
than the 5 μm column. Thus, one can run faster flow-rates (linear velocities) and peaks maintain their efficiency yet the
separation time decreases proportional to the increase in flow-rate.
Are There Any Downsides to Reducing the Particle Size?
There are a number of experimental parameters one should be aware of when reducing the particle size. One is the column pressure.
Equation 2 shows the dependence of column head pressure on a number of experimental parameters including the particle size.
Note that the pressure is inversely proportional to the square of the particle size.
P = pressure drop;
- φ = 500, flow resistance parameter;
- η = viscosity (mPa/s);
- μ = linear velocity (mm/s);
L = column length (mm);
= particle size (μm).
So when the particle size is halved, the pressure goes up by a factor of four. However, often for fast and ultrafast separations,
the column length is also reduced so the pressure increase is not nearly as high as one would expect because pressure is proportional
to column length. Of course, if longer lengths of columns, say 100 or 150 mm, are required to achieve higher plate counts,
then higher pressure pumps might be required. Currently, there are commercial HPLC systems with upper pressure limits as high
as 2 × 104 psig. It should be noted that the total pressure that the HPLC system experiences is the sum of the column backpressure
and the instrument backpressure. The latter results when small internal diameter capillaries are used in the flow paths to
reduce extra column effects and the gradient delay volume. As the flow-rate increases, the back pressure due to these capillaries