Open-tubular Liquid Chromatography

In gas chromatography (GC) open-tubular columns are the norm. In liquid chromatography (LC) they are not. Why is this the case? This is explored in this article.

The following equation shows how the unretained time (t₀) depends on various parameters, most of which are the same for GC and LC.

t_{\text{0}}=\frac{L}{u_{\text{0}}}=\frac{N \cdot H}{u_{\text{0}}}=\frac{N \cdot h}{\nu_{\text{0}}} \cdot \frac{d^2_{\text{c}}}{D_{\text{m}}}

Here, $L$ is the column length, $u_{\text{0}}$ the linear velocity, $N$ the plate number, $H$ the plate height, $h$ the reduced plate height, $\nu_{\text{0}}$ the reduced linear velocity, $D_{\text{m}}$ the diffusion coefficient, and $d^2_{\text{c}}$ the diameter of the column.

When working at the optimum in the van Deemter curve (with a standard reduced film thickness of 0.3) we have $h$ = 0.7 and $\nu_{0}$ = 5.6. To produce 100,000 theoretical plates for an analyte with a typical diffusion coefficient in the mobile phase of 5×10^-6 m²s^-1, a standard GC column with an internal diameter of 250 µm will have a hold-up time of about 150 s (two-and-a-half minutes). For an open-tubular LC column to yield the same umber of plates in about the same time, a (low-molecular-weight) analyte with a typical diffusion coefficient of 10^-9 m²s^-1 would need to have an internal diameter of about 3.5 µm. This is small, but not entirely impossible.

The main difficulty of using open-tubular columns for LC arises from the peak volume. The standard deviation in volume units can be described by the following equation.

A stationary-phase diffusion coefficient of 5×10^-11 m²s^-1, typical for a poly(dimethyl siloxane) film, and a retention factor of 3 result in a standard deviation of about 10 µL for the GC column, but about 25 pL for the open-tubular LC (OTLC) column. Such extremely small volumes make detection in OTLC virtually impossible. Even if detection can be achieved, the working range between the detection limit and the point where the chromatographic system is overloaded will be minimal (if not negative).

For SFC, assuming a diffusion coefficient of 10^-9 m²s^-1, the situation is only slightly more favourable, with a required column internal diameter of about 11 µm and a peak standard deviation of a bit less than 1 nL, with added problems associated with pressure control and variations in mobile-phase density (and thus $<i>D_{\text{m}}</i>$ ) during the run.