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Efficiency = Extensive Plates = Great Resolution
At the most basic level, column efficiency dictates the number of peaks that can be resolved per unit time. Efficiency is related to plates, expressed as N, which is determined as follows:
where:
tr = adjusted retention time of peak (isothermal)
W1/2 = width of peak at ½ height
The higher the column efficiency, the lower the rate of zone dispersion or zone broadening, and the lower the value for W1/2, resulting in a greater value for N. Based on the resolution (Rs) equation, if the retention and selectivity terms are held constant, an increase in the efficiency term results in an increase in resolution.
Higher N values positively influence resolution, assuming the effects are not offset by changes in retention and/or selectivity.
Dividing N by column length, in meters, results in plates/meter, and allows a direct comparison between columns with different I.D.s regardless of length. Table 1 summarizes the plates/meter as well as the total number of plates (N) for several columns.
| Table 1. Relationship of Column I.D. to Efficiency(1) |
| Column Dimensions |
Plates / meter |
Plates (N) |
| 30 m x 0.53 mm I.D., 0.50 µm |
2.260 |
67,800 |
| 30 m x 0.25 mm I.D., 0.25µm |
4,561 |
136,830 |
| 15 m x 0.10 mm I.D., 0.10 µm |
10,838 |
162,420 |
| (1) Data obtained off column test reports for the isothermal analysis of n-tridecane. |
To demonstrate the relationship between column efficiency and resolution, columns of different inner diameters were compared under similar run conditions for the resolution of several components in a US EPA Method 8270 semivolatile standard mix. Selectivity was held constant by using columns containing the same stationary phase (SLB-5ms) and similar beta values. Retention was held constant by using the same oven temperature program and carrier gas linear velocity. Due to its shorter length, retention was lower on the 0.10 mm I.D. column than the 0.25 mm and 0.53 mm I.D. columns. However, this difference was not enough to offset the positive effect on Rs resulting from the higher N for this column I.D.
Chromatograms from each column of the same elution range showing the resolution of two critical peak sets are presented in Figures 1-3. The difference in resolution exhibited by the columns can be directly related to column efficiency, due to differences in the plates/meter, because retention and selectivity were held constant.
Figure 1. SLB-5ms, 30 m x 0.53 mm I.D., 0.50 µm
Figure 2. SLB-5ms, 30 m x 0.25 mm I.D., 0.25 µm
Figure 3. SLB-5ms, 15 m x 0.10 mm I.D., 0.10 µm
| Conditions for Figures 1, 2, and 3 |
| column: |
(refer to figure title) |
| oven: |
40 °C (2 min.), 22 °C/min. to 240 °C, 10 °C/min. to 330 °C (1 min.) |
| inj.: |
250 °C |
| det.: |
FID, 330 °C |
| carrier gas: |
helium, 30 cm/sec @ 200 °C, set using methane |
| injection: |
0.5 µL (0.53 and 0.25 mm I.D. columns) and 0.10 µL (0.10 mm I.D. column), splitless (0.75 min.) |
| liner: |
4 mm I.D., single taper (0.53 and 0.25 mm I.D. columns) and 2 mm I.D., straight (0.10 mm I.D. column) |
| sample: |
50 ng on-column of a 72 component semivolatile standard and 8 surrogate compounds, plus 6 internal standards (at 40 ng on-column), in methylene chloride |
| Peak IDs for Figures 1, 2, and 3 |
| 1. |
Di-n-octyl phthalate |
| 2. |
Benzo(b)fluoranthene |
| 3. |
Benzo(k)fluoranthene |
| 4. |
Benzo(a)pyrene |
| 5. |
Perylene-d12 |
| 6. |
Indeno(1,2,3-cd)pyrene |
| 7. |
Dibenzo(a,h)anthracene |
| 8. |
Benzo(g,h,i)perylene |
Efficiency = Extensive Plates = Short Analysis Times
Achieving shorter analysis times can be accomplished by further exploiting the resolution equation. As shown earlier, efficiency and retention are both part of the resolution equation. Increased efficiency allows for retention to be decreased while achieving the same resolution. Decreasing retention can be accomplished in several ways: shortening column length, increasing linear velocity, and/or increasing oven temperature ramp rate.
An example of this is illustrated for the analysis of semivolatile compounds. Figure 4 shows that the mass resolution of 86 compounds required 20 minutes with a 30 m x 0.25 mm I.D., 0.25 µm SLB-5ms column. Figure 5 shows that these same compounds were mass-resolved in just 8.5 minutes with a 20 m x 0.18 mm I.D., 0.18 µm SLB-5ms column.
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