In this article, controlling the particle size distribution (PSD) variable has been examined as a possible route to further
improvement in performance of particle-based columns.
Silica particles prepared in tubular column formats dominate high performance liquid chromatography (HPLC), and the technique
would not be as important without them. Over the years, silica particles have been optimized in shape, purity, and size. They
have steadily become smaller to improve efficiency, which allows for more speed, sensitivity, and resolution at the cost of
higher pressure. Knox (1) and others published early papers showing accurate insight into particle and pressure requirements
for improving HPLC speed and performance.
When discussing column performance, it is always helpful to start with the van Deemter relationship, which describes three
additive processes that influence bandspreading within the column.
H stands for height equivalent to one theoretical plate (HETP) and is calculated from a measurement of column efficiency, N, and the relationship, H = L/N, where L is column bed length. The μ term is the linear velocity of the mobile phase. A plot of H versus μ is commonly called a van Deemter curve and represents how efficiency behaves as a function of μ (proportional to
flow rate). The lower the H value, the greater efficiency a column displays. In equation 1, the A term represents contributions from flow and diffusion processes within the mobile phase flowing around the particles (names
include eddy diffusion, eddy dispersion, flow inequality, and multipath term), the B term is total axial (longitudinal) diffusion within mobile and stationary phases, and the C term represents speed of mass transfer between mobile phase and stationary phase that lies mainly within particle pores.
If a narrower particle distribution can create more uniform beds, it should show up as a smaller A term, which is not very sensitive to flow velocity compared to the other two terms. The A term dominates in the middle of the velocity curve and controls the lowest value of plate height at which efficiency of a
column is highest, while the B term dominates at low velocity and the C term dominates at high velocity. A complete discussion of factors affecting band dispersion is beyond the scope of this article
and for an in-depth discussion of van Deemter relationships, refer to Neue (2) and other excellent HPLC books.
Figure 1: A van Deemter plot for small porous particles. Columns: 50 mm × 4.6 mm Zorbax Eclipse XDB-C18 (1.8-μm column was
30 mm in length); eluent: 85:15 acetonitrile–water; flow rates: 0.05–5.0 mL/min; temperature: 20 °C; sample: 1.0 μL octanophenone
in eluent. (Courtesy of Ron Majors and Agilent Technologies.)
Typical van Deemter curves are shown in Figure 1 for several sizes of porous C18 silica to demonstrate the two-fold advantage
of selecting smaller particles (3). Not only can smaller H (larger N) be achieved by using smaller particles, this better column performance can be sustained even at higher velocities (smaller
slope for the C term). Note that Figure 1 uses interstitial linear velocity rather than classical linear velocity, which is more easily obtained
from the relationship, μ = L/t0, where L is column bed length and t0 is the time for an unretained peak. Neue (2) and other texts provide definitions of different linear velocity terms and other
HPLC column fundamentals. Plots of H (or h, called the reduced plate height, H/dp where dp is the average particle diameter in the same units as H) against classical linear velocity are usually adequate and will be used in this article. Reduced plate height allows performance
to be compared when columns use different particle sizes. Until modern core-type particles were introduced in 2006, the lowest
hmin values observed for silica particles were 2–3.
Figure 2: Fast gradient assay with a 5-μm core-type column. Column: 20 mm × 2.1 mm, 5-μm dp Ascentis Express C18; mobile-phase A: water with 0.1% trifluoroacetic acid; mobile-phase B: acetonitrile with 0.1% trifluoroacetic
acid; mobile phase: 11:89 A–B; flow rate: 2 mL/min; pressure: 172 bar; temperature: 40 °C; detection: UV absorbance at 254
nm; injection volume: 0.5 μL; flow cell: 1-μL micro. Peaks: 1 = atenolol, 2 = pindolol, 3 = propranolol, 4 = indoprofen, 5
= naproxen, 6 = coumatetralyl. (Courtesy of Advanced Materials Technology.)
Although Figure 1 creates the impression that nearly unlimited separation speed might be possible with sub-2-μm particle columns,
column resistance and instrument pressure rating quickly become limiting factors. Measurement of H-μ (or h-μ) curves with simple, ideal solutes is very useful in column research; however, real samples contain solutes that may vary
greatly in curve shape. When high speed methods are being developed, kinetic performance with H-μ plots should be compared for both ideal and target solutes during column screening. For example, the best performing column
with toluene or naphthalene may not yield equally good performance for drug metabolites. Plots of column efficiency, N, and resolution, R, against linear velocity can also be very valuable during the development of a high-speed method. Column stability toward
high flow and pressure conditions should also be confirmed. Figure 2 illustrates how well modern HPLC columns can operate
at very high linear velocity (circa 20 mm/s) under gradient conditions (4). Gradients are often used in high-throughput assays
to clean the column between sample injections. The 20 mm × 2.1 mm C18 column prepared with 5-μm core-type silica particles
required a starting system pressure of 172 bar (78 bar from the column and 94 from the ultrahigh-pressure liquid chromatography
New insight about van Deemter relationships was provided by Knox (5,6), who suggested that the A term is much more important than previously thought and should receive more attention as a path to improved HPLC column performance.
According to Knox, a lower A term will come from better column preparation techniques and more uniform bed structures. In this article, the particle size
distribution (PSD) variable has been examined as a possible route to higher performance for particle-based columns.