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Online Supplemental Material
Integrated IR absorption intensities and calibration.
From Beer-Lambert’s law, the absorption cross-section of a compound J at a specific wavenumber is given by , where is the napierian absorbance, is the transmittance, nJ is the number density of J and l is the path length over which the absorption takes place. The integrated absorption intensity, Sint, is given by:
The integrated cross-sections of the absorption bands of the compounds under study were determined by plotting the integrated absorbance intensities against the product of the number density and pathlength. Conservative estimates of systematic errors are: pressure measurements (0.5%), path length (1%), temperature (1%), and definition of the baseline in the integration procedure (1%). Tables Supplemental Tables 4 1 and 5 2 summarizes the calibration results while Figure 5Supplemental Figure 1 (see Supplemental Digital Content 1, see Figure 1 legend at end of supplement) displays the linear relationship between number density times pathlength and the measured integrated absorbance.
The integrated absorption cross-section (often referred to as the integrated band intensity, or IBI) of the 2000-450 cm-1 region of isoflurane has previously been reported by Sihra et al.(1) who gave a value of 27.44×1017 cm2 molecules-1 cm-1. The two results for IBI2000-450 are within the estimated systematic errors in the two studies. Brown et al.(2) have reported a value of (15.9 ± 0.8) ×1017 cm2 molecules-1 cm-1 for the 1200-800 cm-1 region of isoflurane. For the same region the present result is IBI1200-800 = (16.2 ± 0.2) ×1017 cm2 molecules-1 cm-1.
For sevoflurane Brown et al.(2) reported a value of IBI1200-800 = (10.4 ± 0.6) ×1017 cm2 molecules-1 cm-1 for sevoflurane. The present result is somewhat larger, (11.6 ± 0.3) ×1017 cm2 molecules-1 cm-1. However, it should be noted that that one of the integration limits used in the study of Brown et al.(2) fall in a cluster of bands and we therefore consider the two results consistent. For desflurane, Imasu et al. (3) reported a value of IBI2000-500 = (29.9 ± 0.7) ×1017 cm2 molecules-1 cm-1 in perfect agreement with the present result.
IR absorption cross-sections and radiative forcing.
The infrared absorption cross-sections were derived from the absorbance spectra assuming that the gases were ideal. The absorption cross-sections (base e) of isoflurane and sevoflurane in the 1600 – 400 cm-1 region are shown in Supplemental Figures 6 2 (see Supplemental Digital Content 2, see Figure 2 legend at end of supplement) and 73 (see Supplemental Digital Content 3, see Figure 3 legend at end of supplement). We routinely use the absorption cross-section of HCFC-22, which has been critically evaluated by Ballard et al. ,(4) as a benchmark (5-12). Our measurements of HCFC-22 (CHClF2) are constantly within 5% of the absorption intensities reported by Ballard and co-workers. As can be seen in Supplemental Table 36, the statistical variance in the integrated absorption cross-section of the compounds is at most 2%. Adding to this the above-mentioned systematic errors allows us to suggest that our spectroscopic results are accurate to within 5%.
Pinnock et al.(13) have provided a simple method for estimating the instantaneous cloudy-sky radiative forcing (IF) directly from a molecule’s absorption cross-sections. The instantaneous cloudy-sky radiative forcings are summarised in Supplemental Table 36 in which the previously reported results for desflurane (14) have been included for comparison.
It is interesting that sevoflurane, which has the largest integrated absorption cross section of the three anaesthetics, has the smallest instantaneous radiative forcing. This is due to the fact that several of the strongest absorption bands in sevoflurane fall in wavenumber regions where the CO2, O3 and water vapour dominates the radiative transfer properties of the atmosphere. Supplemental Figures 6-82 ( see Figure 2 legend at end of supplement), 3 ( see Figure 3 legend at end of supplement), and -4(see Supplemental Digital Content 4, see Figure 4 legend at end of supplement) illustrate this point.
Atmospheric Lifetimes and Global Warming Potentials.
The main atmospheric removal process for the compounds under investigation is the reaction with OH radicals. For isoflurane there are several reports of the rate coefficient for this reaction. In 1990 Brown et al. (2) reported a value of kOH+Isoflurane = (2.1 ± 0.7) × 10-14 cm3 molecule–1 s–1 in a study employing the discharge-flow resonance-fluorescence technique. In 1999 appeared three kinetic studies of the OH reaction with isoflurane. Tokuhashi et al.(15) studied the temperature dependency of the reaction rate constant using the flash photolysis, laser photolysis, and discharge-flow methods combined with the laser induced fluorescence technique to monitor the OH radical concentration and reported kOH+Isoflurane(T) = (1.12 ± 0.18) × 10-12 × exp(-1280 ± 50 K/T) cm3 molecule–1 s–1. Langbein et al.(16) reported kOH+Isoflurane = (2.3 ± 0.19) × 10-14 cm3 molecule–1 s–1 from the pseudo first-order decay of OH using the laser long-path absorption technique. Nolan et al.(17) reported kOH+Isoflurane = (2.3 ± 0.19) × 10-14 cm3 molecule–1 s–1 from relative rate experiments employing GC separation and flame ionisation detection. Finally, Beach et al.(18)determined the temperature dependency of the reaction rate constant using the discharge-flow resonance-fluorescence technique and reported kOH+Isoflurane(T) = (4.5 ± 1.3) × 10-13×exp(-940 ± 100 K/T) cm3 molecule–1 s–1. The available kinetic data are summarised in Supplemental Figure 5 (see Supplemental Digital Content 5, see Figure 5 legend at end of supplement)9. The data are generally in good agreement although it can be seen that the k(298 K) data of Beach et al. (18), Brown et al. (2) and Nolan et al. (17) apparently are 25-40% higher than the other data. A fit of the Arrhenius expression to the other data give kOH+Isoflurane(T) = (1.11 ± 0.12) × 10-12 × exp(-1275 K/T) cm3 molecule–1 s–1.
There are only two sets of kinetic data for the OH reaction with sevoflurane. Brown et al.(2) reported results for two temperatures from a study employing the discharge-flow resonance-fluorescence technique and gave kOH+Sevoflurane = 1.53 × 10-12 × exp(-900 ± 500 K/T) cm3 molecule–1 s–1. The other study is by Langbein et al.(16) who reported kOH+Sevoflurane = (2.7 ± 0.5) × 10-14 cm3 molecule–1 s–1 at 298 K from the pseudo first-order decay of OH using the laser long-path absorption technique. The scatter in the available data, Supplemental Figure 5 ( see Figure 5 legend at end of supplement)9, only allows a rough estimate of the reaction rate constant. Assuming Ea/R to be the same in sevoflurane as in isoflurane results in kOH+Sevoflurane(T) = 3.3 × 10-12 × exp(-1275 K/T) cm3 molecule–1 s–1 as a first approximation.
For comparison we include literature data for desflurane, CF3CHF-O-CHF2.(14) There are only two kinetic studies of the OH radical reaction with this compound, both carried out at room temperature. Langbein et al.(16) reported kOH+Desflurane = (4.4 ± 0.8) × 10-15 cm3 molecule–1 s–1 from the pseudo first-order decay of OH using the laser long-path absorption technique. Oyaro et al.(14) reported kOH+Desflurane = (6.5 ± 0.8) × 10-15 cm3 molecule–1 s–1 from relative rate measurements employing GS-MS detection. Taking the average of these and assuming Ea/R to be the same as in sevoflurane and isoflurane results in kOH+Desflurane(T) = 3.9 × 10-13 × exp(-1275 K/T) cm3 molecule–1 s–1 as a first approximation.
The atmospheric lifetime of a long-lived compound due to removal by reaction by OH radicals may be estimated once its rate coefficient for reaction with OH is known. Assuming that the compounds studied here (fluorinated ethers, FE) will have the same atmospheric distribution as CH3CCl3 their atmospheric lifetimes, , may be calculated relative to that of CH3CCl3 from:(19)
where years (20) is the atmospheric lifetime of CH3CCl3 with respect to reaction with OH, and the scaling temperature of 272 K is chosen to compensate for the tropospheric OH distribution.(21) Using kOH+CH3CCl3(272 K) = 6.14 10-15 cm3 molecule–1 s–1 from the latest JPL evaluation,(22) the following lifetimes in the gas-phase are found: ~3.6 years, ~1.2 years, ~ 10 years.
Global warming potentials for the FEs relative to CFC-11 (CCl3F), HGWP(t), can then be calculated from the following expression:(23)
where M is the molecular mass and t is the time horizon over which the instantaneous forcing is integrated. Global warming potentials for a 20-year, 100-year and 500-year time horizon for the FEs are summarized in Supplemental Table 47. The data on CFC-11 were taken from the IPCC 2007 report. (24) For compounds with atmospheric lifetimes in excess of 1 year, the Global warming potentials relative to CO2, GWP(t), were estimated from that of CFC-11 referenced to CO2:(25)
GWPFE(t) = HGWPFE(t) × GWPCFC-11(t)
Pinnock et al.(13) has reported that their model for estimating the instantaneous radiative forcing generally overestimates the real forcing when calculating the instantaneous radiative forcing directly from the absorption cross-sections. It is therefore likely that the present results provide upper estimates for the global warming potentials of the three FEs studied here. For comparison the values listed in the latest IPPC report for the GWP of isoflurane are included in Supplemental Table 47. The present estimates of the GWP for isoflurane compares quite well with the results of the more elaborate calculations behind the IPPC recommendation (24) suggesting that the more simplified estimation method gives reliable values. The slightly lower values in GWP for desflurane in the present work than in the previous study by Oyaro et al. (14) is due to a lowering of the estimated atmospheric lifetime from 10.288 to 10.08 years.
Supplemental Table 1. Integrated absorption intensity and absorption cross-section (base e) of the 2000-450 cm-1 region of isoflurane.
Table 4. Integrated absorption intensity and absorption cross-section (base e) of the 2000-450 cm-1 region of isoflurane.
Pressure Number densityIntegrated absorption Integrated absorption Pathlength intensity (base e) cross-section (base e)
/mbar/1017molecules cm-2/cm-1/1017 cm2 molecules-1cm-1
1.08 ± 0.012.62 ± 0.0474.08 ± 1.1728.24 ± 0.4
1.52 ± 0.023.69 ± 0.05104.66 ± 0.3628.35 ± 0.4
1.89 ± 0.024.59 ± 0.06129.58 ± 0.6128.23 ± 0.4
2.55 ± 0.036.19 ± 0.09174.93 ± 0.6728.25 ± 0.4
2.66 ± 0.036.46 ± 0.09186.53 ± 2.5328.88 ± 0.4
2.67 ± 0.036.48 ± 0.09184.61 ± 0.4628.47 ± 0.4
3.01 ± 0.037.31 ± 0.10206.38 ± 1.2628.23 ± 0.4
4.67 ± 0.0511.3 ± 0.2325.12 ± 2.7728.67 ± 0.4
9.93 ± 0.1024.1 ± 0.3694.74 ± 1.9428.81 ± 0.4
28.5 ± 0.3 (average)
Supplemental Table 1. Integrated absorption intensity and absorption cross-section (base e) of the 2000-450 cm-1 region of isoflurane.
Supplemental Table 2. Integrated absorption intensity and absorption cross-section (base e) of the 2000-475 cm-1 region of sevoflurane.
Table 5. Integrated absorption intensity and absorption cross-section (base e) of the 2000-475 cm-1 region of sevoflurane.
Pressure Number densityIntegrated absorption Integrated absorption Pathlength intensity (base e) cross-section (base e)
/mbar/1017molecules cm-2/cm-1/1017 cm2 molecules-1cm
1.05 ± 0.012.55 ± 0.0478.29 ± 0.8230.70 ± 0.4
1.41 ± 0.023.42 ± 0.05106.73 ± 0.6331.17 ± 0.4
1.49 ± 0.023.62 ± 0.06112.93 ± 0.4131.21 ± 0.4
1.90 ± 0.034.61 ± 0.09139.15 ± 0.5630.16 ± 0.4
2.50 ± 0.036.07 ± 0.09187.18 ± 0.2430.83 ± 0.4
2.69 ± 0.036.53 ± 0.09202.04 ± 0.3030.93 ± 0.4
3.34 ± 0.038.11 ± 0.10241.50 ± 0.9829.77 ± 0.4
4.16 ± 0.0510.1 ± 0.2299.03 ± 0.4929.60 ± 0.4
4.62 ± 0.1011.2 ± 0.3343.06 ± 0.4930.58 ± 0.4
30.6 ± 0.6 (average)
Supplemental Table 2. Integrated absorption intensity and absorption cross-section (base e) of the 2000-475 cm-1 region of sevoflurane.
Supplemental Table 3. Instantaneous radiative forcing (IF) of isoflurane, sevoflurane and desflurane. a Data from Oyaro et al.((26))
Table 6. Instantaneous radiative forcing (IF) of isoflurane, sevoflurane and desflurane.
CompoundMInt. absorption cross sectionIF
/g mol-1/10-17 cm2 molecule-1 cm-1/W m-2
Isoflurane184.528.5 ± 0.30.453
Sevoflurane200.030.6 ± 0.60.365
Desflurane a168.030.3 ± 0.70.447
Supplemental Table 3. Instantaneous radiative forcing (IF) of isoflurane, sevoflurane and desflurane.
a Data from Oyaro et al.((26))
Supplemental Table 4. Estimated Global Warming Potentials HGWP(t) and GWP(t) for 20-year, 100-year and 500-year Time Horizons relative to CFC-11 and CO2, respectively.
a From IPPC 2007, (24). b From Brown et al. (2). c From Oyaro et al., (14) d From Imasu et al. (3)
Table 7. Estimated Global Warming Potentials HGWP(t) and GWP(t) for 20-year, 100-year and 500-year Time Horizons relative to CFC-11 and CO2, respectively.
CompoundLifetimeHGWP20HGWP100HGWP500GWP20GWP100GWP500
/year
CFC-11 a45111630046001600
Sevoflurane1.190.0700.0270.02334910632
Isoflurane3.570.2800.1070.0931401429130
2.6 b1100 a340 a110 a
Desflurane10.080.7430.3280.28437141314398
10.288 c0.753 c0.335 c3766 c1341 c
5.8d3100a960a300a
Supplemental Table 4. Estimated Global Warming Potentials HGWP(t) and GWP(t) for 20-year, 100-year and 500-year Time Horizons relative to CFC-11 and CO2, respectively.
a From IPPC 2007, (24). b From Brown et al. (2). c From Oyaro et al., (14) d From Imasu et al. (3)
Figure Legend
Supplemental Figure 1. Integrated absorption intensities (base e) of the 2000-450 cm-1 region in isoflurane and the 2000-475 cm-1 region in sevoflurane. The sevoflurane data have been shifted by 100 for the sake of clarity.
Figure 5. Integrated absorption intensities (base e) of the 2000-450 cm-1 region in isoflurane and the 2000-475 cm-1 region in sevoflurane. The sevoflurane data have been shifted by 100 for the sake of clarity.
Figure 6Supplemental Figure 2. Absorption cross section of isoflurane and radiative forcing per unit cross section for a 0 to 1 ppbv increase in mixing ratio.
Figure 7Supplemental Figure 3. Absorption cross section of sevoflurane and radiative forcing per unit cross section for a 0 to 1 ppbv increase in mixing ratio.
Figure 8Supplemental Figure 4. Absorption cross section of desflurane and radiative forcing per unit cross section for a 0 to 1 ppbv increase in mixing ratio. Infrared data from Ref. (26).
Figure 9Supplemental Figure 5. Arrhenius plots of rate constants for the reactions of OH radicals with isoflurane and sevoflurane. (×)Tokuhashi et al.(15); (●) Brown et al.(2); (o) Langbein et al.(16); (▲) Nolan et al.(17); (♦)Beach et al.(18) The dotted line corresponds to kOH+isoflurane(T) = 1.11 × 10-12 × exp(-1275 K/T) cm3 molecule–1 s–1, the full line corresponds to kOH+sevoflurane(T) = 3.3 × 10-12 × exp(-1275 K/T) cm3 molecule–1s–1. The data and curve for sevoflurane have been shifted by ln(10) for the sake of clarity.
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Figure Legends
Supplemental Figure 1. Integrated absorption intensities (base e) of the 2000-450 cm-1 region in isoflurane and the 2000-475 cm-1 region in sevoflurane. The sevoflurane data have been shifted by 100 for the sake of clarity.
Supplemental Figure 2. Absorption cross section of isoflurane and radiative forcing per unit cross section for a 0 to 1 ppbv increase in mixing ratio.
Supplemental Figure 3. Absorption cross section of sevoflurane and radiative forcing per unit cross section for a 0 to 1 ppbv increase in mixing ratio.
Supplemental Figure 4. Absorption cross section of desflurane and radiative forcing per unit cross section for a 0 to 1 ppbv increase in mixing ratio. Infrared data from Ref. (26).
Supplemental Figure 5. Arrhenius plots of rate constants for the reactions of OH radicals with isoflurane and sevoflurane. (×)Tokuhashi et al.(15); (●) Brown et al.(2); (o) Langbein et al.(16); (▲) Nolan et al.(17); (♦)Beach et al.(18) The dotted line corresponds to kOH+isoflurane(T) = 1.11 × 10-12 × exp(-1275 K/T) cm3 molecule–1 s–1, the full line corresponds to kOH+sevoflurane(T) = 3.3 × 10-12 × exp(-1275 K/T) cm3 molecule–1s–1. The data and curve for sevoflurane have been shifted by ln(10) for the sake of clarity.
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