x – length of the column u – measure of the peak width D - Diffusion coefficient of analyte in the gas phase D1 – Diffusion coefficient in the stationary phase
Deterministic relationship with retention time / gradient Further benefits associated with higher throughput and sustainability can also be achieved by a reduction in the film thickness, column diameter (both of which reduce the dispersion of the peak due to diffusion) or a decrease in the column length.
Deterministic relationship with
retention time / gradient Further benefi ts associated with higher throughput and sustainability can also be achieved by a reduction in the fi lm thickness, column diameter (both of which reduce the dispersion of the peak due to diffusion) or a decrease in the column length.
The following equations (Equation 2) can be used to determine the system parameters required to optimise performance using a smaller i.d., shorter, reduced film thickness column with the subsequent sections demonstrating the effects of varying some of the parameters listed in Equation 2.
The following equations can be used to determine the system parameters required to optimise performance using a smaller i.d., shorter, reduced fi lm thickness column with the subsequent sections demonstrating the effects of varying some of the parameters listed in Equation 2.
Equation 2 t 2
g
Figure 3: The mussel attractor found by Johnson et al. which is indicative of a chaotic system, reproduced with kind permission from [4].
Figure 3. The mussel attractor found by Johnson et al. which is indicative of a chaotic system, reproduced with kind permission from [12].
Benefits of introducing hydrogen
into the laboratory In terms of the benefi ts associated with the introduction of hydrogen, there is a massive price differential, of approximately a factor of 20 (prices quoted in June 2023). This will depend on the purity of the gases being used but highlights a signifi cant economic driver to look at alternative carrier gases. As well as the economic benefi ts associated with using hydrogen compared to helium, the higher diffusivity means that the optimal linear velocity is higher than that obtained when using helium. The higher diffusivity also means that there is a greater range over which the operating conditions do not have a signifi cant effect on the chromatographic performance, allowing for even faster analysis times.
ν1, ν2 T1, T2 β1, β2
l1 , l2
Where; tg1, tg2 - temperature gradient for original and new conditions ν1, ν2 - linear velocity of gas for original and new conditions T1, T2 - Hold time for isothermal part of separation for original and new conditions β1, β2 - Phase ratio for original and new conditions l1, l2
Where; tg1
, tg2
- temperature gradient for original and new conditions - linear velocity of gas for original and new conditions
- length of column for original and new conditions - length of column for original and new conditions
- hold time for isothermal part of separation for original and new conditions - phase ratio for original and new conditions
The use of narrow i.d. and thin film columns, coupled with very fast temperature gradients, is often referred to as Fast GC [17]. Significant improvements in the assay performance can be achieved without the need to make changes to the system set-up using a Fast GC column (20 m × 0.15 mm × 0.15 µm) compared to conventional column dimensions (30 m × 0.25 mm × 0.25 µm). The improved peak efficiencies obtained using a Fast GC column, without compromise in peak resolution, can be obtained provided:
The use of narrow i.d. and thin fi lm columns, coupled with very fast temperature gradients, is often referred to as Fast GC [17]. Signifi cant improvements in the assay performance can be achieved without the need to make changes to the system set-up using Fast GC column dimensions ((20 m × 0.15 mm × 0.15 µm for example) compared to conventional column dimensions (30 m × 0.25 mm × 0.25 µm). The improved peak effi ciencies obtained using a Fast GC column, without compromise in peak resolution, can be obtained provided:
This can be explained by the Golay equation, Equation 1 [15], which is a modifi ed form of the van Deemter equation [16]. In GC performed with open tubular columns, the absence of a packed bed means that the eddy dispersion term is omitted, which is associated with the stochastic pathways a mobile phase molecule can have going through a packed bed. Figure 4 shows a diagram of the chromatographic performance of hydrogen, nitrogen and helium (the three most common carrier gases) under isothermal conditions. For hydrogen it can be seen that the fl ow rate/linear velocity can be almost doubled without a loss in the chromatographic performance. However, this is not quite the case when running with temperature gradients where the temperature ramp rate for the oven also has to be changed. It should also be noted that the injection volume should also be changed to account for the higher linear velocity of the mobile phase, reducing it by approximately 50% when the fl ow rate is doubled.
well ventilated room small leaks would not present a problem, however the major safety issue is the source of the hydrogen. The two most common sources of hydrogen that are used by modern chromatographers are gas cylinders, which will contain up to 50 L of gas pressurised to 200 bar, or a hydrogen generator which typically stores around 60 mL of gas pressurised to less than 10 bar. It is very evident that for the safety aware chromatographer that the hydrogen generator provides a substantially safer environment and one that could be readily employed within a laboratory, whereas a gas cylinder would require extra safety precautions, and would require the storage of the hydrogen cylinder outside of the laboratory facility.
• The ratio of column length to i.d. remains the same
• The ratio of column length to i.d. remains the same • The column stationary phase should not alter • The column phase ratio (β) is consistent between the two columns.
Further improvements in productivity can be obtained by combining higher optimal linear velocity, with an increase in the temperature ramp rate.
Equation 2
n = n
t 1 g
1 2
b b
1 2
l l
2 1
T2
n = n
T1
2 1
b b
2 1
l l
1 2
5
Benefits of introducing hydrogen into the laboratory In terms of the benefits associated with the introduction of hydrogen, there is a massive price differential, of approximately a factor of 20 (prices quoted in June 2023). This will depend on the purity of the gases being used but highlights a significant economic driver to look at alternative carrier gases. As well as the economic benefits associated with using hydrogen compared to helium, the higher diffusivity means that the optimal linear velocity is higher than that obtained when using helium. The higher diffusivity also means that there is a greater range over which the operating conditions do not have a significant effect on the chromatographic performance, allowing for even faster analysis times.
This can be explained by the Golay equation, equation 1 [15], which is a modified form of the van Deemter equation [16]. In GC performed with open tubular columns, the absence of a packed bed means that the diffusion term is omitted, which is associated with the stochastic pathways a mobile phase molecule can have going through a packed bed. Figure 4 shows a diagram of the chromatographic performance of hydrogen, nitrogen and helium (the three most common carrier gases) under isothermal conditions. It can be seen that the flow rate/linear velocity can be almost doubled without a loss in the chromatographic performance. However, this is not quite the case when running with temperature gradients where the temperature ramp rate for the oven also has to be changed. It should also be noted that the injection volume should also be changed to account for the higher linear velocity of the mobile phase, reducing it by approximately 50% when the flow rate is doubled.
Insert Figure 4 here please
Figure 4. Golay plots showing the chromatographic performance for hydrogen, nitrogen and helium carrier gases.
Figure 4: Golay plots showing the chromatographic performance for hydrogen, nitrogen and helium carrier gases.
Equation 1 The Golay equation [15]
– linear velocity of the carrier gas k – retention factor r0
Where; v0
– column radius
x – length of the column u – measure of the peak width D - Diffusion coeffi cient of analyte in the gas phase D1
– Diffusion coeffi cient in the stationary phase
Another advantage of using a narrow bore column is that optimal linear velocity of carrier gas also increases, which allows shorter analysis time. There are, however, some practical considerations with the use of narrow bore columns, including lower sample loading capacity which means that higher split ratios or reduced sample injection may be required to prevent column overload.
= $2 !
Equation 1 The Golay equation [15]
+ (1+6 +11")!! 24(1+)" + #!! " " 6(1+)""$ 1$
h Linear velocity 180 μm 250 μm 100 μm 320 μm
Figure 5. Effect of reducing the column diameter on the chromatographic performance when using GC.
Figure 5: Effect of reducing the column diameter on the chromatographic performance when using GC.
Figure 5 illustrates that by reducing the column diameter; effi ciency increases and as a consequence so does the resolution. The effi ciency is always greater in the narrower bore column, thus shorter columns can be used to reduce analysis time, whilst offsetting the reduced effi ciency arising from shorter column length. Table 1 shows normalised effi ciency for column length and diameter.
Table 1. Comparisons of the effi ciency relative to column length and diameter compared to a 30 m x 0.25 mm column.
Figure 4: Golay plots showing the chromatographic performance for hydrogen, nitrogen and helium carrier gases.
Column I.D (mm) Column length (m) 60
30
0.15 0.18 0.25 0.32 0.53
3.3 2.8 2.0 1.6 0.9
1.7 1.4 1.0 0.8 0.5
20
1.1 0.9 0.7 0.5 0.3
15
0.8 0.7 0.5 0.4 0.2
10
0.6 0.5 0.3 0.3 0.2
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