# How do small particle size columns increase sample throughput?

## Learning Links

The Van Deemter equation is an empirical formula describing the relationship between plate height (H, the length needed for one theoretical plate) which is a measure of column efficiency, and linear velocity (µ) (Figure 1). Smaller plate height values corresponds to greater peak efficiencies, as more plates, or analyte partitioning, can occur over a fixed length of column.

The Van Deemter equation is governed by three cumulative terms: (A) eddy diffusion, (B) longitudinal diffusion, and (C) mass transfer. A loss in peak efficiency can be observed as a wider analyte band, and therefore, these three terms can also be viewed as factors that contribute to band broadening. **Figure 1 **illustrates the effect of these terms, both individually and cumulatively. Eddy diffusion, the A term, is caused by a turbulence in the solute flow path and is mainly unaffected by flow rate. Longitudinal diffusion, the B, or difference, term, is the movement of an analyte molecule outward from the center to the edges of its band. Higher column velocities will limit this outward distribution, keeping the band tighter. Mass transfer, the C term, is the movement of analyte, or transfer of its mass, between the mobile and stationary phases. Through this type of diffusion, increased flows have been observed to widen analyte bands, or lower peak efficiencies.

Decreasing particle size has been observed to limit the effect of flow rate on peak efficiency—smaller particles have shorter diffusion path lengths, allowing a solute to travel in and out of the particle faster. Therefore the analyte spends less time inside the particle where peak diffusion can occur. **Figure 2** illustrates the Van Deemter plots for various particle sizes. We notice that as the particle size decreases, the curve becomes flatter, or less affected by higher column flow rates. Smaller particle sizes yield better overall efficiencies, or less peak dispersion, across a much wider range of usable flow rates.

If we look at an empirically determined Van Deemter plot of efficiency versus flow rate, when using a 1.9µm particle size Pinnacle DB column (**Figure 3**), the benefit is apparent—column efficiency does not diminish when flow rate increases, as denoted by the relatively flat slope of the curve. Peak efficiency was comparable even when the flow was increased to 1mL/min. This illustrates the most considerable affect that small particles have on chromatographic separations—a much wider range of usable flow rates translates into significantly faster analysis times. This benefit, coupled with a shorter column length needed for similar resolution, allows much higher sample throughput, without the compromising the chromatographic quality of the analytical method.

**Figure 3:** An empirically determined Van Deemter plot shows that column efficiency does not diminish as flow rate increases on a 1.9 µm particle size Pinnacle DB column—significantly reducing analysis time and increasing sample throughput.

Column: |
Pinnacle DB C18, 1.9 µm 50 mm X 2.1 mm |

Mobile Phase: |
55:45 water:acetonitrile |

Flow rate: |
Varied |

Wavelength: |
254 nm |

Temperature: |
Ambient |

Injection: |
2 µL Reversed Phase Test Mix |