Introduction

This article is a synopsis of the recently discovered mass-independent isotope effects in atmospheric trace gases. What was once believed to be an exception measured in meteoritic material appears to be a surprisingly common effect in the atmosphere which enhances the usefulness of isotope analysis in atmospheric chemistry studies.

Variations in stable isotope ratios in the environment have generally been well understood and put to good use. However, the atmosphere appears to be the scene for a host of isotope effects that we do not yet understand. The prime example is ozone, whose anomalous enrichment has repeatedly defied correct interpretation. Gas phase reactions in the atmosphere appear to lead rather frequently to anomalous or "mass independent fractionation" (MIF). These anomalies offer the opportunity to advance the science of atmospheric chemistry and to relate its findings to fundamental atomic and molecular processes.

Isotope fractionation

The generally small environmental variations in the isotope ratios of the light elementsi.e., mainly H, C, N, O, and Shave been measured extensively and have at times provided unrivaled data; for example, information about past climate derived from ¹⁸O/¹⁶O ratio measurements on ice cores and on carbonates from sediment cores. Atmospheric studies also benefit from stable isotope variations. An illustration is the ongoing decline of the ¹³C/¹²C ratio of atmospheric carbon dioxide, largely in consequence of the increasing fraction of fossil fuel-derived carbon dioxide. This isotope effect is thus directly related to the isotopic composition of an important source of the gas. Fossil fuels have about 2% less ¹³C than atmospheric carbon dioxide. This in itself is obviously not a source effect (ambient CO₂ is the carbon source for plants), but rather an isotope fractionation effect of photosynthesis. Plants favor ¹²CO₂ slightly over ¹³CO₂, so the assimilated carbon is depleted in ¹³C relative to the atmosphere. In isotope applications of interest to atmospheric chemistry, source signatures and fractionation effects in chemical reactions are both relevant.

Many processes in nature can cause isotope fractionation: diffusion, gravitation, thermal diffusion, phase transitions, escape from atmospheres, photolysis, or chemical reactions, among others. Kaye [1987] offers a good review of isotope effects in planetary atmospheres. As a rule of thumb, isotope fractionation is larger for the lighter elements and thus, the greatest isotope variations occur for hydrogen. HH reacts 65% faster with OH than HD [Ehhalt et al., 1989]. This very large effect can be understood qualitatively on the basis of the relative large mass difference between the hydrogen and deuterium atoms.

Generally, two classes of isotope fractionation are distinguished. The isotopic depletion of water vapor in contact with liquid water is a good example of a classic equilibrium isotope effect, which is purely mass dependent. For hydrogen this strict mass dependence is difficult to verify experimentally as it has only two stable isotopes. However, for oxygen with three stable isotopes, ¹⁶O(99.756%), ¹⁷O (0.038%) and ¹⁸O (0.205%), the proportionality of fractionation with mass difference can be verified accurately. In the evaporation of water vapor, a kinetic isotope effect based on differences in diffusion velocities sets in, which beyond reasonable doubt also is strictly mass dependent.

As atmospheric chemists we clearly are most interested in fractionation involved in chemical reactions. Here we distinguish between equilibrium and kinetic effects. For instance, the equilibrium hydrogen isotopic exchange HD + H₂O ´H₂ + HDO can be calculated on the basis of statistical mechanics using data about the vibrational spectra [Urey, 1947]. However, in the atmosphere we usually deal with kinetic isotope fractionation. Here calculations are based on transition state theory [Bigeleisen and Wolfsberg, 1958], where a transition complex is considered. Various degrees of refinement have been developed to calculate fractionation factors that are in agreement with measured data. A successful ab initio calculation of the isotope effects in the CH₄ + Cl reaction has recently been published [Roberto-Neto et al., 1998], giving results that agree with careful observations [Saueressig et al., 1995, 1996], which show large fractionation factors of 7% for carbon and 60% for hydrogen.

For decades after the experimental and theoretical frontier research by Urey, Bigeleisen, Craig, Nier, Keeling, Clayton, Epstein, Baertschi, Wolfsberg and others, it was believed that we understood all observed isotope effects. At this stage you may not be surprised to read that most naturally occurring isotope effects are mass dependent. But how do we know whether an isotope effect is mass dependent, and how is this defined?

Acceptance of the near universal applicability of mass dependence in isotope fractionation appears to have been guided by the success of theoretical models of fractionation processes. The mass dependence of isotope fractionation in chemical reactions according to transition state calculations and equilibrium calculations is mainly the result of differences in the normal vibrational frequencies for the individual isotopic species [Kaye, 1987]. Because the vibrational frequencies of a chemical bond depend on the masses of the atoms that form the bond, the heavy isotopes are usually more tightly bound, which leads to fractionation in chemical reactions. For multi-isotope systems like oxygen, and for small isotopic variations, it has been shown that such mass dependent fractionation processes produce shifts in the ¹⁷O/¹⁶O ratio which are half the size of the accompanying ¹⁸O/¹⁶O variations [Matuhisa et al., 1978; Hulston and Thode, 1965].

We now introduce the common delta notation for representing the "small" natural isotope variations, e.g., d¹⁸O = [¹⁸R_sample/¹⁸R _standard ­1] x 1000 in which ¹⁸R denotes the ¹⁸O/¹⁶O atomic ratios. The reference standard for oxygen is ocean water in the form of V-SMOW (Vienna-Standard Mean Ocean Water). Atmospheric oxygen has d¹⁸O_V-SMOW = 23.5 (parts per thousand). Using this notation, mass dependence for oxygen takes the form d¹⁷O 0.5 * d¹⁸O. This can be regarded as the conventional definition of a mass dependent fractionation for oxygen isotopes.

For mass independent isotope effects (MIF) this relationship is violated. A recent review of MIF is given by Thiemens [1999]. A means of expressing the ¹⁷O excess (or deficiency) relative to the mass dependent fractionation equation defined above is D¹⁷O = d¹⁷O ­ r d¹⁸O, in which r is the expected ratio for the compound considered.

In summary, mass dependence of fractionation exists on several levels and has many well understood causes. Again, this is most easily confirmed for oxygen. By measuring the ¹⁷O/¹⁶O ratio and the ¹⁸O/¹⁶O ratio of any compound, it can be verified whether pure mass dependence applies.

Ozone

The notion of mass dependence had become thoroughly engrained in the environmental isotope community when Clayton et al. [1973] observed deviations from this simple relationship for oxygen in certain meteoritic material. Understandably, they concluded that the anomalous composition could not be due to a chemical fractionation process, and instead ascribed it to nucleosynthetic processes. However, no anomalous effects were detected for sulfur [Hulston and Thode, 1965], which is also suited for detecting deviations as it has 4 stable isotopes.

Mauersberger [1981] measured the ozone isotopic composition in the stratosphere using a balloon-borne mass spectrometer. The discovery of enhancements up to 40% in mass 50i.e., the ¹⁸O-substituted ozone isotopomer was extensively debated but not explained. The violation of mass dependence for oxygen in such a simple laboratory experiment as the production of ozone by an electrical discharge changed conventional thinking about isotope effects [Thiemens and Heidenreich, 1983]. The surprising fact is that ¹⁸O and ¹⁷O are enriched in the ozone product approximately equally, rather than in a 2 : 1 ratio. This led to the concept of mass independent (or non-mass dependent) fractionation in chemical reactions. Since then numerous investigations firmly established that both stratospheric and tropospheric ozone exhibit MIF [Schueler et al., 1990; Johnston and Thiemens, 1997; Krankowsky et al., 1995].

It has taken years to unravel the secrets of the anomalous isotope fractionation of ozone, perhaps the most extensively studied reactive atmospheric trace gas. In regard to molecular symmetry, ¹⁷O and ¹⁸O in an ozone molecule are identical (they are simply different from the abundant ¹⁶O isotope); consequently, several theories of symmetry selection in the ozone formation process were proposed. Figure 1 shows the now famous picture of the strange isotopic mix of ozone produced from enriched oxygen mixtures, with illusive preferences for asymmetric configurations. However, theories based on symmetry have been challenged by the latest experimental data.

Figure 1. The distribution of ozone isotopomers measured by using enriched mixtures. The asymmetric molecules are formed preferentially. Numbers next to bars indicate molecular composition, e.g., "667" = 16O16O17O.

By carefully measuring the individual rate constants of selected ozone production channels, Anderson et al. [1997] and Mauersberger et al. [1999] have produced the necessary evidence to pin down the origin of ozone enrichment. Table 1 lists some of their interesting experimental results, which show that certain reaction channels have enormous rate coefficient advantages. For instance, ¹⁶O reacts with ¹⁸O¹⁸O a staggering 50% faster than does ¹⁸O.

Paradoxically, the results shown in Table 1 suggest mass dependence after all. The fastest reaction occurs for the heaviest isotopomer with the lightest atom, the slowest rate constants for the heaviest atom reacting with the lightest molecule. It seems clear now that the anomalous fractionation in ozone formation is not caused by a "mass independent" symmetry selection processes, but rather by some unknown parameter in the three body collision process that depends strongly on the masses of the atoms and molecules involved. New theories for explaining the odd behavior of ozone are cheerfully in development.

Table 1: Measured relative rate coefficients of six individual ozone formation channels, compared to the homonuclear rate constants for formation of 16O16O16O, 17O17O17O and 18O18O18O, which are approximately equal [Mauersberger et al., 1999].

Now let us revisit the conventional, well-behaved mass dependence. As noted above, small fractionations in ¹⁷O are half as large as the accompanying variations in ¹⁸O. Is this strictly 0.500? No, the exact ratio between d¹⁷O and concomitant d¹⁸O variations depends on the nature of the fractionation process and on the molecular masses involved [Matsuhisa, 1978]. For diffusion, which is easy to handle mathematically with the diffusion speed being inversely proportional to the square root of the masses, the ratios range from 0.523 for atomic oxygen to 0.500 for very heavy molecules.

Carbon dioxide

After ozone, it was found that carbon dioxide in the stratosphere exhibits MIF [Thiemens et al., 1995, Gamo et al., 1989]. A chemical mechanism was proposed by Yung et al. [1991], who showed that the observed ¹⁷O excess in CO₂ could be explained by transfer of the enrichment present in ozone to CO₂ via the excited oxygen radical O(¹D):

OOP + hn Æ OO + P(¹D)

P(¹D) + CO₂ Æ COOP* and

COOP* Æ COP + O

where P denotes the rare isotopes ¹⁸O or ¹⁷O and the asterisk an excited intermediate complex.

Refinements were later proposed by Barth and Zahn [1997] and Yung et al. [1997]. However, it is still not clear whether additional mass dependent or even mass independent fractionations occur in the CO₃* formation or breakup, although the mechanism has in principle been firmly established in the laboratory [Wen and Thiemens, 1993].

This all made CO₂, which had been of little interest to atmospheric chemists due to its lack of reactivity in the lower regions, suddenly a molecule of some importance: MIF in CO₂ is a marker of its exposure to O(¹D). The predominantly stratospheric signal is diluted when CO₂ is transferred into the troposphere and finally washed out over a period of several years by isotopic exchange with the large reservoir of soil, leaf, and ocean water. Thus, the ¹⁷O excess in CO₂ determined on stratospheric air samples correlates well with another stratospheric tracer, ¹⁴CO, as displayed in Figure 2. Figure 3 shows the mass dependent fractionation line, and the typical ¹⁷O and ¹⁸O values for important gases and V-SMOW.

Figure 2. The correlation in the lowermost stratosphere between the two independent variables 14CO and D17O in CO2. Note that the vertical scale is only 0.6. Despite that, the correlation is excellent.

Figure 3. A three-isotope plot showing the mass dependent line and the most important deviations for CO2, CO, and tropospheric O3. Stratospheric ozone (not shown here) is further enriched.

This is good news for atmospheric research, although the experimental determination is elaborate. One has to collect air samples and extract the CO₂. A further problem arises with the mass spectrometric measurement. When CO₂ is analyzed in an isotope ratio mass spectrometer, masses 44, 45 and 46 are collected. This gives two isotope ratios only, whereas there are three unknown ratios: i.e., ¹³C/¹²C, ¹⁷O/¹⁶O and ¹⁸O/¹⁶O. A way around this is to convert the CO₂ to O₂ by using aggressive reagents like BrF₅. This process is time consuming and can be hazardous. New experimental methods are being developed [Brenninkmeijer and Röckmann, 1998]. Spectroscopic methods may also be promising.

Nitrous oxide

Remarkably, MIF is not restricted to CO₂ and ozone alone. Cliff and Thiemens [1997] have shown that atmospheric N₂O has a small excess of ¹⁷O. In view of the uncertainties in the budget of N₂O, this is a welcome fact of nature, yet the race for finding an explanation is still on. Photolysis, or reaction with O(¹D), does not seem to cause MIF [Yung and Miller, 1997; Johnston et al., 1995]. Isotope exchange could be a possibility. Recently an atmospheric source of N₂O has been proposed [Zipf and Prasad, 1998], which may hold some promise of being the mysterious source of excess ¹⁷O in N₂O.

Carbon monoxide

The atmospheric MIF hit list features another prominent member, carbon monoxide (CO), which is a major player in atmospheric chemistry, as over 50% of all OH radicals are engaged in its removal from the atmosphere. Excess ¹⁷O was first detected in several CO samples collected in New Zealand [Hodder, 1994], and the occurrence of MIF in CO was confirmed by many subsequent independent analyses [Röckmann et al., 1998a, b; Huff and Thiemens, 1998].

For CO, the hunt for the source of MIF has been fortunate, so we will devote some discussion to it. It was shown that the ozonolysis of unsaturated hydrocarbons like isoprene, b-pinene and ethene does produce CO, the oxygen of which is derived from ozone with its excess ¹⁷O [Röckmann et al., 1998a]. However, the ozonolysis source could not adequately explain the atmospheric values. Subsequent research showed that the important reaction CO + OH introduces MIF in the remaining CO. More precisely, CO that has not reacted gains a small excess of ¹⁷O [Röckmann et al., 1998b].

Figure 4. The increase in D17O of the remaining CO after reaction with OH. With lower pressures, or He as carrier gas, the enrichment is smaller.

Figure 4 shows the ¹⁷O excess in the remaining CO fraction after reaction with OH in He and N₂ as carrier gas for different periods of time. The more CO has reacted, the higher is the mass independent component in the remaining CO. Furthermore, the excess ¹⁷O increases with increasing total pressure. Referring to the reaction mechanism for CO + OH (see below), this suggests an important role of the intermediate HOCO in the fractionation process, although it is difficult to relate the occurrence of MIF to a specific reaction step. Another peculiarity of the reaction is that C¹⁸O reacts about 1% faster with OH than C¹⁶O, an inverse isotope effect, which is almost independent of pressure. To produce the observed excess ¹⁷O enrichment (Figure 4) at all pressures, the rate coefficients of C¹⁶O and C¹⁷O for reaction with OH must be equal at atmospheric pressure.

The annual cycle of CO (Figure 5) at mid- and high latitudes is strongly driven by the seasonality in OH. This is the cause for the observed anti-correlation between CO mixing ratios and D¹⁷O. In summer, with maximum OH, CO decreases rapidly, in phase with the increase in D¹⁷O. In winter, the CO inventory is replenished with CO with D¹⁷O values close to zero. Consequently, D¹⁷O declines. A comparison with d¹⁸O also shows a strong similarity. The reason for the negative correlation in this case is that the reaction with OH preferentially removes ¹⁸O due to the negative kinetic isotope effect [Stevens et al., 1980].

Figure 5. The large annual cycle in CO and its oxygen isotopes measured for surface air in Spitsbergen.

Very large isotope effects have been reported to occur in photochemical reactions by selective ionization, and for certain ion-molecule reactions [Gellene, 1992]. These effects, of course, are of importance for molecular studies. Besides this, the large reaction rate enhancement effects in ozone and the extremely large effects measured by Gellene imply that very small sources of atmospheric trace gases may measurably affect the overall isotopic composition. This may allow the identification of certain sources.

To finish our discussion, we draw attention to some attractive features of MIF. One as pect (and this applies to CO₂ in exchange reaction with O(¹D), and to CO in reaction with OH) is that the original CO₂ and CO, respectively, do not have any excess ¹⁷Othat is, D¹⁷O = 0. This means we are dealing with an isotope effect for which the source signature is precisely defined. An example may make this clearer. When we study ¹⁸O variations in CO, the various sources have different d¹⁸O values. This makes it to some extent more complicated to interpret the decline in d¹⁸O in terms of reaction with OH. For D¹⁷O, we do not have the same problem if we make the reasonable assumption that the fraction of CO derived from ozonolysis generally is small.

Another attractive aspect of MIF is that the signal is more difficult to corrupt. A second example will clarify this. If an air sample is collected and part of the CO is lost, this often causes isotope fractionation, rendering the ¹³C and ¹⁸O isotope ratio useless. However, D¹⁷O will not change in this process. Another robust feature of D¹⁷O is that, if the signal is corrupted by dilution or exchange, the end member in the process has nearly always a D¹⁷O value of zero. This facilitates any necessary corrections for dilution and exchange.

Conclusions and outlook

The list of MIF is not yet complete. Firm evidence exists that H₂O₂ also possesses MIF [Lee et al., 1998]. We postulate that NO₂ too (and generally NO_x and NO_y) have MIF, in the first instance simply because it is formed predominantly in the atmosphere by NO + O₃. Even OH may have MIF, yet due to exchange (Dubey et al., 1997) with the ubiquitous water vapor, this signature is erased rapidly in the lower troposphere. Stratospheric water vapor, however, may well have a significant signal.

To what degree MIF will be a useful tool in atmospheric chemistry remains to be seen. Two practical points are of consideration here: One, that isotope mass spectrometry allows smaller samples to be analyzed using GC-IRMS; secondly, that D¹⁷O can be measured with increasing precision. Random errors as small as 0.03 appear to be attainable.

Another consideration is that MIF effects need to be understood at the theoretical level, where they may help to describe atomic and molecular reactions even more accurately. Finally, we note that expressions like MIF and non-mass dependent fractionation are not proper definitions of the anomalous fractionation, but then the word "anomalous" may be no longer applicable. However, for practical purposes, and in the absence of a theoretical framework for the process(es) causing MIF, we suggest the use of MIF for those cases when conventional mass dependence is violated. Those who dislike the expression "mass independent" can use MIF as an acronym for "Missing Information about Fractionation". For us, however, the main question will be: What can MIF teach us about atmospheric chemistry? The answer is that more work is required!

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