Questions about how practical proposed gas chromatography (GC) method changes are often come up during optimization for speed
and resolution, or while converting to a different carrier gas. Related objective measurements such as the optimum practical
carrier gas velocity were defined more than 40 years ago. This installment reviews such metrics in light of their relevance
to today's GC challenges.
One of the classical trade-offs in gas chromatography (GC) separations lies between speed of analysis and peak resolution.
Chromatographers can increase the speed of analysis in a number of ways, including the use of shorter and narrower columns,
higher temperatures and temperature program ramp rates, and faster flow rates, but higher speeds do not guarantee equal or
better peak resolution. The relationships between flow or velocity and resolution have received attention recently in the
context of a drive toward faster separations, and the on-going substitution of hydrogen carrier gas for helium in many laboratories
also fuels the discussion. This installment of "GC Connections" discusses the effects of increased carrier-gas flow or velocity
in an example separation that includes two pairs of solutes.
Optimum Practical Velocity
One of the more neglected separation metrics is the optimum practical carrier-gas velocity (OPGV). This idea is not new: The
pioneers of gas chromatography formulated the OPGV as one way to measure the trade-offs between speed of analysis and resolution.
As the carrier-gas flow increases above an optimum value, peaks become broader and their resolution starts to decline but
they are eluted sooner in proportion to the higher flow. Scott and Hazeldean (1) proposed that an optimum compromise between
the two could be found by increasing the flow until the corresponding increase in a plot of plate height versus average carrier-gas
velocity becomes essentially linear. An optimum velocity would be reached at the point where additional losses of resolution
because of further increases in velocity could not be compensated for by a corresponding increase in column length.
Without experimental measurements from multiple columns, the OPGV has been considered as the velocity at which a tangent line
from the origin meets a plot of measured values of the plate height, H
meas, versus the average linear carrier-gas velocity, ū. This is the velocity at which the quantity H/ū hits a minimum (2). A plot of experimental H
meas versus ū departs from the linear at higher velocities because of secondary gas-compression effects at higher pressures and extracolumn
broadening from the detector if the peaks become narrow enough. The basic Golay equation, however, neglects such effects.
A plot of the theoretical plate height, H
theor, versus ū will never become completely linear:
where H is the height of one theoretical plate, ū is the average carrier-gas linear velocity, B describes the broadening of a peak because of gas diffusion along the direction of carrier-gas flow, and C describes broadening because of the effects of solute molecules entering and leaving the stationary phase. As the linear
velocity (flow) increases, a decreasingly small fraction of the total theoretical plate height is due to the B term, and the C term dominates.
These effects are shown in Figure 1 for the basic Golay equation using a 25 m × 0.53 mm column. In this, and the subsequent
column treatments, the influence of the stationary phase on solute broadening is minimal; the stationary-phase film thickness
used was 0.4 μm, which influenced this plot by less than 2%. Plot (a) is the total theoretical plate height; plot (b) is the
B term contribution; and plot (c) is the C term contribution. Plot (c) also represents a tangent that meets the total plate height (a). That this junction occurs at
infinite linear velocity shows the fundamental difficulty with using the basic Golay equation this way for OPGV calculations.
Figure 1: Plot of the basic Golay equation for n-hexane: (a) total plate height, (b) B term contribution to the plate height,
(c) C term contribution to the plate height, (d) OPGV where the B term contribution accounts for 10% of the total plate height,
and (e) optimum carrier-gas velocity. Theoretical column parameters: 25 m × 0.53 mm, 0.4-μm nonpolar stationary-phase film
thickness, 130 °C, helium carrier gas.
The basic Golay equation yields an infinite linear velocity if a tangent-line construction is used to find the OPGV because
the theoretical relationship neglects the effects on plate height of operating at higher inlet pressures and of producing
potentially very narrow peaks. The theoretical plot does not curve away from a linear relationship at elevated velocities,
but experimental data do. Although it is a convenient way to explain idealized column band-broadening behavior without making
arduous measurements of H
meas versus ū data for multiple columns, widespread use of the basic Golay equation has resulted in the neglect of OPGV as a means of expressing
a practical upper limit for average linear velocity in specific separations.
A simple approach to determining a finite value for OPGV from the basic Golay equation is to choose an arbitrary point that
sets the OPGV at the velocity where gas–gas diffusion contributes a fixed percentage of the overall band broadening. Figure
1 illustrates an example at the point labeled (d), where gas–gas diffusion contributes 10% of the total band-broadening and
ū = 117 cm/s. The optimum velocity, ū
opt — the point at which H is at a minimum — is shown as well at point (e), where ū = 39.2 cm/s. But this idealized and arbitrary OPGV point is not connected to physical properties that accommodate the effects
of an increasing inlet pressure gradient on peak broadening; the velocity of 117 cm/s seems too high for a reasonable upper
limit. Extended band-broadening theories that do include such effects can produce a better theoretical picture of the effects
of increasing the velocity.