deficits in abiotic methane
The Δ12CH2D2 values
here exhibit pronounced disequilibrium, in sharp contrast with those of
Δ13CH3D. The
Δ12CH2D2 values are
exclusively of negative sign, ranging from −3.0 ± 2.5‰ (1σ) at 210 °C to
−32.0 ± 1.6‰ at 183 °C. These values are substantially lower than the
expected equilibrium values of 9.2‰ and 4.3‰ at 130 and 250 °C,
respectively. We argue that the
Δ12CH2D2 deficits are
apparent disequilibrium signatures resulting from combinatorial effects.
In general, combinatorial effects arise when a molecule contains
indistinguishable atoms of the same element, and that these atoms come
from pools with distinct isotope ratios, as has been predicted and shown
for methane previously both from theory and in the laboratory (Röckmann
et al., 2016; Taenzer et al., 2020; Yeung, 2016). Among the two mass-18
isotopologues of methane, only
Δ12CH2D2 can be
affected by combinatorial effects, because it is the isotopologue with
two indistinguishable deuterium substitutions for hydrogen.
The root of the combinatorial effect comes from the notation convention
used with clumped isotopes. As an example, consider a sample of methane
gas with δD = –100 ‰ relative to SMOW and δ13C = -10
‰ relative to PDB, corresponding to a measured bulk D/H ratio of
1.40184⋅10-4 and a13C/12C ratio of 0.01112483. In this
example we will use a measured12CH2D2/12CH4ratio of 1.11600×10-7. To calculate the value for
Δ12CH2D2, we compute
the stochastic ratio from the measured bulk carbon and hydrogen isotope
ratios. Isotope-specific mole fractions for singly-substituted
isotopologues are closely approximated as: