Temperature dependence of isotopic fractionation in the CO2‐O2 isotope exchange reaction

Rationale Oxygen isotope exchange between O2 and CO2 in the presence of heated platinum (Pt) is an established technique for determining the δ 17O value of CO2. However, there is not yet a consensus on the associated fractionation factors at the steady state. Methods We determined experimentally the steady‐state α 17 and α 18 fractionation factors for Pt‐catalyzed CO2‐O2 oxygen isotope exchange at temperatures ranging from 500 to 1200°C. For comparison, the theoretical α 18 equilibrium exchange values reported by Richet et al. (1997) have been updated using the direct sum method for CO2 and the corresponding α 17 values were determined. Finally, we examined whether the steady‐state fractionation factors depend on the isotopic composition of the reactants, by using CO2 and O2 differing in δ18O value from −66 ‰ to +4 ‰. Results The experimentally determined steady‐state fractionation factors α 17 and α 18 are lower than those obtained from the updated theoretical calculations (of CO2‐O2 isotope exchange under equilibrium conditions) by 0.0024 ± 0.0001 and 0.0048 ± 0.0002, respectively. The offset is not due to scale incompatibilities between isotope measurements of O2 and CO2 nor to the neglect of non‐Born‐Oppenheimer effects in the calculations. There is a crossover temperature at which enrichment in the minor isotopes switches from CO2 to O2. The direct sum evaluation yields a θ value of ~0.54, i.e. higher than the canonical range maximum for a mass‐dependent fractionation process. Conclusions Updated theoretical values of α 18 for equilibrium isotope exchange are lower than those derived from previous work by Richet et al. (1997). The direct sum evaluation for CO2 yields θ values higher than the canonical range maximum for mass‐dependent fractionation processes. This demonstrates the need to include anharmonic effects in the calculation and definition of mass‐dependent fractionation processes for poly‐atomic molecules. The discrepancy between the theory and the experimental α 17 and α 18 values may be due to thermal diffusion associated with the temperature gradient in the reactor.


| INTRODUCTION
Measurements of Δ 017 O (defined in Equation 1) of oxygen-containing molecules can provide insight into, for example, the carbon cycle and its link to the hydrological cycle [1][2][3][4][5][6][7][8][9][10] and are also used to reconstruct paleoclimate. [10][11][12][13][14] The Δ 017 O of CO 2 is a promising tracer to study the CO 2 exchange flux between the biosphere/hydrosphere and the atmosphere. 3,5,6,15 However, due to the mass interference of 13 C 16 O 16 O and 12 C 17 O 16 O, it is difficult to measure δ 17 O of CO 2 with existing isotope ratio mass spectrometers, because the required mass resolving power of about 55,000 (Δm/m) is a challenge for even the highest resolution instruments. 16 High precision and accuracy are needed for measurements of both δ 18 O and δ 17 O in order to capture the small, but non-zero deviations to use Δ 017 O as a tracer. Since the measurement of δ 17 O directly from CO 2 with isotope ratio mass spectrometry (IRMS) is impossible due to the interference of δ 13 C, except from the fragment ions formed in the ion source, 16 The CO 2 -O 2 exchange method was first developed by Mahata et al 18 and has been established in several laboratories, including our own. 11,12,16,19 Recently, the method has been extended to measure the Δ 017 O of water. 20 The CO 2 The index I is a placeholder for either 17  One explanation for these differences may be variations in the effective isotope exchange temperature, as the fractionation factor is expected to be temperature dependent. Furthermore, the mechanism of the CO 2 -O 2 isotope exchange in the presence of a platinum catalyst is unknown. 16,18,19,26,28,29 In this study we determined α 17 (CO 2 /O 2 ) and α 18 (CO 2 /O 2 ) for the CO 2 -O 2 exchange method over a temperature range from 500 C to 1200 C. We investigated whether there is a dependency on the initial oxygen isotopic composition of CO 2  A is either CO 2 or O 2 ). [30][31][32][33] Since in the measurements of the equilibrium constants multi-substituted species have been neglected, we define quantities α and β slightly differently:  39 and an agreement to better than five significant digits is obtained across the temperature range. However, our current results are slightly different from a previously published parametrization 40 the less than 0.2 ‰ difference being mainly due to the identification and removal of an error in the calculation of a correction term.
Unfortunately, application of Dunham's approach to larger molecules is not straightforward, because the isotope scaling of anharmonic vibrational constants is neither theoretically well constrained nor experimentally known, and the constant zero-point energy offset G 0 is not known either. 30 We have therefore calculated the total internal partition functions of the 16 Table S1, supporting information). We have discovered a subtle difference in the molecular constants used in this study and that of Richet et al. (1997) 30 but such slight differences cannot account for the observed discrepancy.
We have compared partition function ratios Q( 13 CO 2 )/Q( 12 CO 2 ) of 16 16 is shown in Figure S1 (supporting information). The main difference between the current setup and the one used in the previous study 16 is an electropolished stainless steel extension.

| Samples
Three commercial O 2 gases with different isotope compositions were used for the measurements (   and δ 18 O f (CO 2 ) for reaction temperatures ranging from 500 to 1200 C. In Figure 3B the fractionation factors α 17 (CO 2 /O 2 ) and α 18 (CO 2 /O 2 ) derived from these steady state enrichments are shown.

| CO 2 -O 2 isotope steady state
As can be seen, α 17 and α 18 decrease with increasing reaction temperature. The exchange reactions were carried out using gases   .

| Comparison with theoretical calculations
In Figure 5B  with temperature ( Figure 6). This trend diminishes at temperatures above 800 C.  temperature range between 0 C and 1200 C. We suspect that the drop in θ (CO 2 /O 2 ) at temperatures >1250 C in Figure 7 is an artefact, likely to be due to not including some high-energy states in the calculations. 43 Mahata and co-authors 28  These effects are strongly temperature dependent and vanish at high temperatures. Such behavior is not compatible with our observation of a temperature-independent offset and we consequently exclude the notation non-Born-Oppenheimer effects could explain the observed discrepancy.
Mahata and co-authors 18 also reported α 18 (CO 2 /O 2 ) < 1, ranging from 0.998128 to 0.99463, even at 680 C. A possible explanation for the discrepancy between the calculation and the experimental results is isotopic separation due to thermal diffusion. [59][60][61][62][63][64] In this study, one end of the reactor is positioned inside an oven at a specific temperature (500 C to 1200 C), whereas the other end is at room temperature (see  Table 1), using a similar experimental setup except that in the previous study the volume of the cold zone of the reactor was smaller and without a stainless-steel extension (see Figure 1 and Figure S1, supporting information). As shown in Figure 6, the offset between theory and experiment depends on the temperature gradient between the hot and cold zones of the reactor.
The cross-over temperature and the discrepancy between the theoretically calculated equilibrium and experimentally determined steady-state α values might depend on the geometry of the reactor, the pressure in of the reactor, the volume of the reactor, and the proportion of the cold and hot part of the reactor.
Oxygen three-isotope phenomena due to thermal diffusion have been investigated previously using pure gases 63,64 and the experiments indicate that fractionation effects are well established in static reactors exposed to spatial temperature gradients. Due to mass balance, fractionation effects in these studies disappeared when the temperature gradient was removed after the experiment and the system was allowed to equilibrate. This is different to our situation, where cooling the reactor to room temperature implies that the O 2 -CO 2 exchange shuts down. and O 2 changes, see Figure 7). These observations are a consequence of a singular behavior of θ close to the crossover, a well described anomaly in isotope equilibria. 32 lead to values of θ = ln( 17 α)/ln( 18 α) which are outside the "canonical" range, i.e. θ > 0.5305 (see Figure 7). The upper bound of this conventional range arises from the high temperature limit (HTL) of the harmonic oscillator approximation (e.g. Young et al, 50 Cao and Liu, 31 Dauphas and Schauble, 53 Matsuhisa et al, 51 Kaiser et al 76 ).  Figure S2 (supporting information). The three-isotope exponent for atom-molecule exchange (κ) is calculated as shown in Equation 6) following Cao and Liu. 31 where κ XO or θ OÀXO ð Þ is the three-isotope exponent for atommolecule exchange, which should also be restricted to the parameter range < θ HTL . This is indeed the case for O 2 , but κ CO2 clearly exceeds the expected range. According to our calculations, it reaches a HTL of around 0.533. We suppose that some structure in the results above 800 C is likely to be due to the smallness of the isotopic signatures, as well as to the precision and potential incompleteness of excited states in the line lists. While our κ O2 value further agrees with the calculation of Cao and Liu, 31 to the fourth decimal place (or even better), our κ CO2 value is higher by 0.0027 to 0.0035 over the full T range and it falls well above the canonical range, even at room temperature, where κ CO2 (25 C) = 0.5317 (see Figure S2, supporting information).
Cao and Liu 31 have shown that the three-isotope exponent (θ aÀb ) for isotope exchange between two molecules a and b can also be calculated as a linear combination of the three-isotope exponents κ a and κ b of the atom-molecule exchange equilibria for molecules a and b (see Equation 6), respectively: Interestingly, the coefficient c in Equation 7 does not depend on 17 O, it only depends on 18  We can use this relationship and the well-studied H 2 O-CO 2 system for an independent estimate of κ CO2 . The three-isotope relationship between liquid water and gaseous CO 2 (θ CO2ÀH2O l ð Þ ) was experimentally determined to be 0.5229 at 25 C (α 18 CO2ÀH2O l ð Þ = 1.041036). 77 Using κ H2O = 0.5300 calculated for water vapor by Cao and Liu 31 (a similar κ H2O value was derived by the same authors from literature data on the gas vapor equilibrium) and 18 β CO2 = 1.1194 (this study), κ CO2 can be calculated using Equation (7), yielding 0.5324 at 25 C. This also is clearly larger than the canonical HTL. The result is only slightly different (+0.0001) when 18   implies that analysis of three-isotope effects in CO 2 needs to go beyond the simple rigid-rotor harmonic oscillator analysis. This might also apply to other non-diatomic molecules and clumped isotope effects. 79 The above analysis of the CO 2 -H 2 O system seems to support this hypothesis concerning the oxygen isotopic fractionation of the H 2 O molecule.
Nevertheless, all our experimentally determined values are lower than those obtained from the updated theoretical calculations of equilibrium fractionation, and the offset is strictly mass-dependent.
The discrepancy between the theoretical and experimental fractionation factors might be caused by thermal diffusion effects.
While this requires further investigation, it provides an explanation for the inconsistent values reported in the literature.
We have shown that the CO 2 -O 2 isotopic exchange under equilibrium conditions is characterized by unusual oxygen threeisotope behavior. Calculated θ (CO 2 -O 2 ) values based on the direct sum method for CO 2 , which includes anharmonic corrections, are larger than the canonical range limit for mass-dependent fractionation processes (0.5305), which possibly needs to be extended to 0. 54