Introduction to clumped isotopes Ivan Prokhorov Empa / Air Pollution and Environmental Technologies / Emissions and Isotopes 1 Today I will present ... ... fundamental principles of clumped isotopes (example of CO2) ... current and emerging analytics ... selected applications of CO2 and CH4 2 Example of CO2 molecule O C O ISOTOPOLOGUE - a molecular entity that differs only in isotopic composition 99.76% 16 12 98.9% 18 isotopic combinations (4 symmetric) 12 isotopologues 0.2% 18 13 1.1% no heavy isotopes - principal isotopologue 1 heavy isotope - singly-substituted 0.04% 17 14 < 1 ppt 2 and more heavy isotopes - clumped or multiply-substituted 3 Random distribution of isotopes Assumption: isotopes are randomly (stochastically) distributed among isotopologues. [isotopologue] = П [isotopes] x statistical factor Example: 13C16O2 = 13C x (16O)2 12C16O18O = 12C x 16O x 18O x 2 R13C = 13C/12C δ13C = R13C/R13Cref - 1 R*(13C16O18O) = R13C x 1 x R18O Isotopologue ratio assuming random distribution of isotopes 1Formulae 16 13 16 R 13 =R O R C R O O CO ⇥ ⇥ Abundance of CO2 isotopologues 18 12 16 R 18 =2 R O R C R O OCO ⇥ ⇥ ⇥ 18 13 16 R⇤18 13 =2 R O R C R O O CO ⇥ ⇥ ⇥ R 18O13CO =(1+∆)R⇤18O13CO K 44 ppm OCO + 17O13CO 1 O13CO + 17OCO ! K OCO + 17OC17O 2 2 17OCO ! K OCO + 18O13CO 3 O13CO + 18OCO ! K OCO + 17OC18O 4 17OCO + 18OCO ! K 2OCO+ 17O13C17O 5 O13CO + 2 17OCO ! 44 45 46 45 47 46 48 47 46K49 48 47 OCO + 18OC18O 6 2 18OCO Mass / mu ! ∆ - deviation from random distribution of isotopesK among isotopologues 2OCO+ 17O13C18O 7 O13CO + 17OCO + 18OCO ! 5 K 2OCO+ 18O13C18O 8 O13CO + 2 18OCO ! K 16O12C16O+16O13C17O 1 16O13C16O+16O12C17O ! K 16O12C16O+17O12C17O 2 2 16O12C17O ! K 16O12C16O+16O13C18O 3 16O13C16O+16O12C18O ! K 16O12C16O+17O12C18O 4 16O12C17O+16O12C18O ! K 2 16O12C16O+17O13C17O 5 16O13C16O+216O12C17O ! K 16O12C16O+18O12C18O 6 2 16O12C18O ! K 2 16O12C16O+17O13C18O 7 16O13C16O+16O12C17O+16O12C18O ! K 2 16O12C16O+18O13C18O 8 16O13C16O+216O12C18O ! 1 How big is ∆ ? Note: 1‰ = 1/1000 Published data: Affek2005, Came2014, Halevy2011, Kluge2015, Mekler2011, Yeung2009 6 www.nature.com/scientificreports/ www.nature.com/scientificreports www.nature.com/scientificreports identifed with the isotopologue specifc enrichment or fractionation values (CO2 denoting any particular iso- topologue in the following equation) [CO] [C12 16O] ∆ = 2 2 − + ∆ (CO)2 ⁎ / 12 16 ⁎ 1ln(1(CO2)), [CO]2 [CO]2 (3) commonly used for the quantifcation of isotopomers21 or multiply substituted isotopologues22,23: www.nature.com/scientificreports/ ⎛ 13 16 18 12 16 ⎞ www.nature.com/scientificreports⎛ 13 16 18 ⎞ ⎛ 12 16 18 ⎞ ⎛ K ⎞ [COO] [CO] ⎟ [COO] ⎟ [COO] ⎟ −ln⎜ 1 ⎟ = ln⎜ 2 ⎟ = ln⎜ ⎟ − ln⎜ ⎟. ⎜ ⁎ ⎟ ⎜ 13 16 12 16 18 ⎟ ⎜ 13 16 ⎟ ⎜ 12 16 ⎟ ⎝⎜K1 ⎠ ⎝⎜ [CO]2 [COO] ⎠ ⎝⎜ [CO]2 ⎠ ⎝⎜ [CO]2 ⎠ (4) identifed withT thee right isotopologue hand side expression specifc enrichment is applicable or to fractionation the optical measurement, values (CO which2 denoting provides any theparticular two particular iso- isotopo- topologue loguein the ratios following as independent equation) observables. As evident from Eq. (4), the temperature information contained in the equi- librium constant does only depend on two12 16 concentration ratios, that may be regrouped diferently. ln (K1) is completely [CO] [CO] 17 OPEN independent of∆ the(C bulkO) =isotope 2composition./ 2 Consequently,− 1l n(1( the+ ∆ OCO isotopic)), composition does not at all afect the Optical2 clumped⁎ 12 16 ⁎ isotope2 determination of the equilibrium[CO]2 constant.[C BulkO]2 isotopic compositions are only introduced when isotopologue(3) concen- ∆ ⁎⁎12 16 18 13 16 ⁎ trations are replaced by values as21 defined in Eq. (3). Using K1 ==1[22,23 COO] [CO]2 / commonly used12 16 for the⁎ 13 quanti16 18fcation⁎ of isotopomers or multiply substituted isotopologues : thermometry([ CO2 ][ COO] ) and keeping only the of leading termscarbon in the Taylor series expansiondioxide on both sides, one obtains ⎛ ⎞ ⎛ 13 16 18 12 16 ⎞ ⎛ 13 16 18 ⎞ ⎛ 12 16 18 ⎞ ⎜ K1 ⎟ ⎜[COOK ] [CO]2 ⎟ ⎜[COO] ⎟ ⎜[COO] ⎟ −ln⎜ ⎟ = ln⎜ 1 −∆1( 13CO16⎟ =18O)ln⎜−∆(C13 16O)⎟ −−∆ln⎜(C12 16OO18 ), ⎟. Ivan⎜ P⁎r⎟okhor⎜ov 13 1,2,316 ⁎ 12 16K18luge⎟1,2 & Christof⎜ 13 16 Jans2⎟sen ⎜ 1,312 16 ⎟ ⎝K1 ⎠ ⎝ [CKO]1,2 Tobias[C OO] ⎠ ⎝ [CO]2 ⎠ ⎝ [CO]2 ⎠ (4) (5) Te rightSwhereimultaneous hand the side expression sign analysis indicates is applicable of the carbon approximative to dioxidethe optical isotopologuescharacter measurement, of the which relation.involved provides T inis the equation, the isotope two particular which exchange may isotopo also between- be derived the Received: 4 September 2018 22 logue ratiosdoublydirectly as independent substitutedfrom Eq. observables. (24) 13 ofC Wang16O 18AsO et evident moleculeal. , is from very and Eq. similar 12(4C),16 the toO thetemperature has commonly become information usedan exciting defnition contained new of ∆tool in47 inthe for clumped equi geochemical,- isotope librium constant does only depend on two14,24 concentration ratios, that may2 be regrouped diferently. ln (K ) is completely Accepted: 22 February 2019 atmosphericmass spectrometry and paleoclimaticof CO2 , research with applications ranging from stratospheric1 chemistry to independent of the bulk isotope composition. Consequently, the 17O isotopic composition does not at all afect the Published: xx xx xxxx carbonate-based geothermometry studies.47 Full exploitation46 of45 this isotope proxy and thermometer is determination of the equilibrium constant. Bulk∆47 isotopic= ∆−(C compositionsO)2 ∆−(C areO) only2 introduced∆(CO)2 when, isotopologue concen- (6) limited due to time consuming and costly analysis using mass⁎⁎ spectrometric12 16 18 instrumentation.13 16 ⁎ Here, we trations are replaced by ∆ values as defined in Eq. (3). Using K1 ==1[COO] [CO]2 / 12 16 ⁎where13 16 isotopologues18 ⁎ are replaced by m/z signals, because they cannot be measured individually. Comparison of ([ CO][presentCO anO] all) opticaland keeping clumped only the C Oleading2 isotopologue terms in the thermometer Taylor series expansion with capability on both sides, for onerapid obtains analysis and 2 ⁎ simplifedEqs (5) and sample (6) leads preparation. to the identif Thecation current of ∆−47 developmentKK11/1 with also the provides relative deviationthe option of forthe analysisequilibrium of con- 24 stant K1 from Kits1 statistical value.13 16 It 18has been argued13 16 that the last12 two1816 18terms on the right hand side are zero , but additional multiply-substituted−∆1( CO isotopologues,O) −∆(CO) such−∆ as(C C OOO2. Since), the instrument unambiguously ⁎ 2 ∆ 22 this premise isK not completely consistent12 16with the13 de16fnition18 of13 16 in Eq. 12(3) 16and18 thermodynamic calculations measuresLaser all isotopologues1 Fiber ofDetector the C O 45+ C O O 46 C O + C O O exchange, its(5 equilibrium) 4439 nm 2 2 that respectively yield −4 and −11 ppm for ∆( CO2) and ∆( CO2) for CO2 equilibrated at 300 K. Te reason for where the constantthe sign con indicatesficting and theresults the corresponding approximative is that in the onecharacter temperature case approximate of the arerelation. measured but Tpreciselyis equation, directly. measurable which Being mayand essentially inalso the be other derived independent case exact but of Laser 4329 nm 22 directly fromtheonly Eq. isotope approximatively (24) of composition Wang et accessible al. , ofis verythe atomic calibrationsimilar isotope to the gas, ratios commonly an are uncalibrated used used in de thefnition calculations working of ∆ 47reference inof clumpedthe statistical is sufcientisotope abundances. and usage 14,24 mass spectrometryofNonetheless, international of CO the2 so calibration de, fned ∆ 47standards is overwhelmingly is obsolete. infuenced Other byisotopologues the frst of the andthree molecules terms, which can in be turn accessed is to a 9 cm Detector usinglarge extent the methodology, (97%, see Table opening 1) dominated up new by the avenues 13C16O 18inO isotope isotopologue. research. Here we demonstrate the high- 10 m 47 46 45 Unlike the direct ∆measurement47 = ∆−(C O)of2 ln (K∆−1)(C accordingO)2 to∆ (CEq. (O)42), ,mass spectrometer determinations(6) of ∆47 not precisionReference performanceGas of the instrument with frst gas temperature measurements of carbon dioxide only require measurementhandling of heavyVacuum isotopologue abundances. Te ‘absolute’ or bulk isotope composition must samplesSample from unitgeothermal sources. where isotopologuesalso be known are replaced in order byto m/zdetermine signals, the because statistical they abundance cannot be measuredof the m/z individually. = 47 signal. ComparisonTis implies determiningof 13 12 18 16 17 16 ⁎ 13 18 17 Eqs (5) andatomic (6) leads C/ to C,the identiO/ Of cationor O/ ofO ∆− ratios47 KK (traditionally11/1 with quanti the relativefed in deviationterms of δ ofC, the δ equilibriumO and δ O convalues),- neces- 24 stant K1 fromsitating its statistical that international value. It has standard been argued substances that the are last used two and terms that on assumptions the right hand on side the are17O zero isotope, but content are 22 this premiseMassmade. isFigure not spectrometry In completelythis 2. wayScheme systematic of consistent of multiply the home biases withsubstituted built of the dual-laser up de tof 40isotopologuesnition system.ppm of are Lasers∆ introduced in Eq.or are clumped ( connected3) 24and. Equally thermodynamic isotopes to the important, optical has become cell calculationsmass via optical an spectrometers extremely fibres and powerful optical can