Isotope Fractionation. Lecture 15 Physical Principles of Isotopic Fractionation. 1(a) Effusion vs. diffusion
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1 Isotope Frctiontion ecture 5 Physicl Principles o Isotopic Frctiontion. Non-equiliriu (unidirectionl) eects. iusion/eusion. Evportion/condenstion c. Kinetic (ond reing/ing) d. Metolic (cointion o ll the ove). Equiliriu eects. Bond strength. Avilility o sttes (sttisticl echnics) () Eusion vs. diusion In n idel gs t therl equiliriu, ll olecules hve the se trnsltionl inetic energy. Igine two isotopes ( nd ) v v v v The lighter isotope trvels ster on verge Eusion en ree pth, > l not diusion te collisions/c v C 45 l e. g.,.0 6 C 44 (chrcteristic diension o continer) Typiclly low pressure (vcuu syste) ehvior 6
2 l < l iusion dc d x For diusion o gs through gs : where iusion coeicient: B T v Fic s irst lw BT v, reduced ss iusion o Isotopic Species in Gses For two isotopic species o gs = C 6, = = C 6, = iusing in ir = 8.9 C C = Typiclly higher pressure ehvior Consider N in iusion o Isotopic Species in Condensed Medi Expected or C in H on the sis o reduced ss C C. 00 C served: C ierence indictes tht H -C interctions (e. g., H-onding) re very signiicnt Cheicl Equiliri: Phse Chnge H (l) + H (g) H (l) + H (g) G G (H( l) ) G (H ( g) ) - [ G (H ( l) ) G (H( g) )] (-54.64) -[( ) (-55.79)] cl/ol G 45 ln K K T Alterntively, H (l) H (g) G = 05 cl/ol p H (l) H (g) G = 098 cl/ol p H H. 0789
3 Alph is esure o enrichent/depletion in rection is positive nuer generlly very close to (e.g., or.0) e.g. ddition o soe cron y cheicl rection C C C C X S.005 A A B C C C C X X A B C C C C S B S A B AB AB B A A Isotope tio Anoly etter thn crrying lot o decils rctionl devition ro soe stndrd delt or dierence or devition usully in per il (prts per 000) cn e negtive or positive 8 X X S 6 SMW e.g., He 4 X Alwys reltive to He He 000 He reerence stndrd 4 He Air Generl ules ighter isotopes ove ster lighter isotopes or weer onds eect strongly depends on inding energy covlent onds generlly weer, ore strongly ected isotope eects generlly stronger or igger reltive ss dierences directly proportionl or se eleent e.g. 6, 7, 8 : 8 = x 7 isotope eects stronger t lower tepertures s T >>, or low T, ~ /T or high T, ~ /T Prtitioning etween phses E.g., oxygen isotope prtitioning etween vpor nd droplets in cloud.005 < <.05 (liquid hevier)
4 Prtitioning etween phses pour-droplet prtitioning in cloud Hydrogen & oxygen isotopes tend to correlte in nture Hydrogen eect ~ 0x xygen xygen Isotope Frctiontion ( 8 / 6 ) Sller scle => Hydrogen Isotope Frctiontion ( H/ H) BIGGE <= SCAE Why the ltitude trend? C04/C /00 titude Trend in Precipittion titude trend: due to tep. eect? depends on teperture teperture decreses polewrd 8 = T = Isotope rctiontion: the yleigh Eqution escries how the rtio chnges with progressive reovl o teril, e.g. y evportion ro wter droplet: = rction let 0 4
5 The yleigh Eqution For vpor where droplets re oring = For evportion For the cwrds rection, then the eect is / e.g. or evportion o droplet the reining liquid is given y the vpour is given y Multiple Steps Multiple rctiontions ultiply e.g., or two sequentil rections => => = - = - = - - = - in generl then, Totl... n i i Since Multiple Steps i 000 i A convenient pproxition is Totl i i or sll s only (ind o inoil expnsion pproxition) 5
6 The hydrologic cycle Successive distilltions increses eect polewrd Precipittion gets lighter towrd poles Hydrogen & oxygen isotopes tend to correlte in nture Hydrogen eect ~ 0x xygen polewrd lightening Equtor Pole isolted sins go o trend with severe evportion C04/C /00 Frctiontion ctors re relted to, ut not necessrily equl to, equiliriu constnts For n l X A + h X n B n h X A + l X n B XA/XB K h n l X X nb l n h X A X hxa lxa n n lxnb hxnb = oleculr syetry nuer. or heteronucler ditoic olecule, or hoonucler ditoic or ethne. K / n Energy evels or Siple Hronic scilltor Criss, 999 owest level, n = 0, hs energy = hν/. This is the Zero-Point Energy, ZPE. is the orce constnt is the reduced ss, nd in turn the ZPE, is thus ss-dependent. See Schule, 004 6
7 Energy evels in Isotopiclly Sustituted Molecules In n exchnge rection, the question is which olecule hs the greter ZPE Zeee & Wol-Gldrow, 00 The ZPE o the ond with the light isotope is greter thn tht o the ond with the hevy isotope. G G ( H ) cl/ol ( C ) -9. cl/ol ZPE l irtionl requencies ro spectroscopic dt C 6 + H 8 C H 6 l h? Greter ZPE or C pulls equiliriu to right, vors ccuultion o 8 in C. Fctors voring lrge ZPE And thus leding to concentrtion o the hevy isotope Kinetic Isotope Eects ow tepertures Sti onds Short Strong (ultiple onds) Atos with siilr electronegtivities The hevy isotope goes preerentilly to the cheicl copound in which the eleent is ound ost strongly. Bigeleisen, J. (965) Cheistry o Isotopes, Science 47, l E h E Zeee & Wol-Gldrow, 00 Bonding in trnsition stte is weer thn in rectnts. Activtion energy or light isotopic species is thereore sller. Ae E T ight isotopic species rect ore rpidly. 7
8 Kinetic Isotope Eect Terinology Priry nd Secondry Cron Kinetic Isotope Eects Norl = ight isotopic species rects ore rpidly Inverse = Hevy isotopic species rects ore rpidly Priry = Isotopic sustitution t position to which cheicl ond is de or roen inluences the rection rte Secondry = Isotopic sustitution t reote position inluences the rection rte C- H C C- C- H + Pyruvte ecroxylse C-.007 C-.05 H C H C C eniro, M. J. & Epstein, S. (977) Mechnis o cron isotopic rctiontion ssocited with lipid synthesis. Science 97, 6-6. Coexistence o Equiliriu nd Kinetic Frctiontions C + H H + + HC - H + + HC - C + H.0.0 Equiliriu rctiontion HC/C Net eect o opposing KIEs. But note: prior to equilirtion, HC - cn e depleted in C due to KIE. 8
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