Mecanismos de FracionamentoEfeito Isotpico Termodinmico ou de equilbrioBaseia-se na diferena da energia livre entre dois istopos. Os istopos mais pesados tendem a se acumular nos compostos com energias de ligao mais fortes.Efeito Isotpico CinticoEm funo da diferena de massa, os istopos tendem a reagir a diferentes taxas. Desta forma, molculas com istopos mais leves tende a ter velocidade maior e a serem quebradas mais facilmente.Efeito Isotpico Spin NuclearComo os istopos diferem quanto ao spin nuclear, pode haver fracinamento. Embora esse efeito isotpico seja pequeno, pose ser mensuarvem em algumas situaes.

Fracionamento de EquilbrioAX + B*X A*X + BXConstante de equilbrio (K)K = (A*X)(BX)/(AX)(B*X)K = (A*X/AX)/(B*X/BX)K = *RA/*RB

G = -RTlnKDesta forma, o equilbrio isotpico funo da energia livre de uma determinada reao e da temperatura. As condies pressso pouco afetam as reaes isotpicas pois a variao do volume molar insignificante a presses abaixo de 20 kbars.

Zero point energy

Fator de Fracionamento Isotpico ()AX + B*X A*X + BX

Por definio,*A/B = *RA/*RBor*A/B = (1000 + *A)/(1000 + *B)

Ento, relaciona-se constante de equilbrio K

Fracionamento de equilbriomAXn + nB*Xm = mA*Xn + nBXm

K = (A*Xn)m(BXm)n/(AXn)m(B*Xm)nK = (A*Xn/AXn)m/(B*Xm/BXm)nK = *RAm/*RBn

Se m = n, entoK = (*RA/*RB)n

= K1/n

Fracionamento de Equilbrio13CO2g + H12CO3-aq 12CO2g + H13CO3-aq

K = [(12CO2g)(H13CO3-aq)]/[(13CO2g)(H12CO3-aq)]K = (H13CO3-aq/ H12CO3-aq)/(13CO2g/ 12CO2g)K = 13Raq/13Rg

13aq/g = 13Raq/13Rg13aq/g(0C) = 1.009213aq/g(30C) = 1.0068

Fracionamento de EquilbrioH218Og + H216Ol H216Og + H218Ol

18l/g = 18Rl/18Rg18l/g(0C) = 1.011718l/g(20C) = 1.0098__________

2l/g = 2Rl/2Rg2l/g(0C) = 1.1112l/g(20C) = 1.084

Dependncia de com a Temperatura

Separao Isotpica, Enriquencimento, DiscriminaoA/B = (1000 + A)/(1000 + B)

1000(A/B - 1) = (A - B)/(1 + B/1000)

DisciplinaTermoSmboloFrmulaGeoqumiaSeparaoEnriquecimentoA/BA/BA B1000(A/B - 1)BiologiaDiscriminaoEnriquecimentoA/BA/B1000(A/B - 1)1000ln(A/B)

HAROLD UREYPrmio Nobel de Qumica -1934

Descobriu o deutrio

Funo partioConstante de equilbrioReao de troca isotpicaO Clculo terico do fracionamento isotpico baseado na mecnica quntica estatstica (Urey, 1947; Bigeleisen e Mayer, 1947)Parmetro de simetriaMassaMomentum de inciaEnergia de rotao, translao e vibraao

No caso dos gases

Princpios de geotermometriaUso de fracionamento isotpico entre minerais como geotermmetro:1. par mineral formou-se ao mesmo tempo em equilbrio isotpico;2. no ocorreu alterao posterior;3. fracionamento isotpico em funo da temperatura conhecido.

Equaes de fracionamento isotpicoNolta:Para duas fase m e n:T in Kelvin

Valley 1998Anlises Isotpicas

Valley 1998Principais Processos de Difuso Isotpica

Cole e Chakraborty 2001

Equao de Dodson para temperatura de fechamentoE = energia de ativao; R = constante dos gases; A = parmetro de anisotropia geomtrica; Do = coeficiente de difuso; a = meia espessura ou raio; dT/dt = taxa de resfriamento.

Valley 1998

Giletti ModelGiletti 1986

Eiler 1993

Farquhar et al. 19993

Temperatura de formao de sulfetos em depsitos minerais

Fracionamento CinticoFenmenos de transporteReaes qumicasEfeitos biolgicos

Fracionamento Cintico: transportePara gases ideais, as molculas e tomos possuem a mesma energia cintica (ELeve= EPesado).

E = mv2

v(12CO2)/v(13CO2) = (m(13CO2)/m(12CO2)) = (45/44) = 1.0113

Fracionamento Cintico: reao qumicaMolculas com istopos mais leves possue vantagem cintica devido a dois fatores principais:Molculas com istopos leves movem-se mais rpido que molculas mais pesadas e, consequentemente, colidem com mais frequncia;Durante as colises, as molculas mais leves so mais facilmente dissociadas que as molculas mais pesadas.

Fracionamento Cintico: Efeito biolgicoReduo sulfato-sulfeto por bactria (Desulfovibrio desulfurcans): transformao SO42- =>S2- a baixa temperatura.

Bactria reage preferencialmente o istopo mais leve de forma que:Sulfetos formados so mais negativosSulfatos residuais so mais positivos

Sulfeto de zinco precipitado por reduo bacterianaChuch et al., 2007

Fracionamento Cintico: Efeito biolgicoFotossntese: nesse processo os CO2 atmosfrico incorporado no tecido vegetal.d13Catmosfera = -8 por mild13Ctecido vegetal = -15 a -35 por mil

Tipos de sistemasFechadosAbertos:Quando um dos reservatrios infinito.Destilao (Rayleigh)

FRACIONAMENTO RAYLEIGH

TIPOS DE FRACIONAMENTO CINTICO

Fracionamento Independente da MassMIF

Ono et al. 2003

Mojzsis et al. 2003

Figure 3. Schematic representation of the oxygen isotope zonation developed in a mineral by exchange with low 18O fluids through different mechan- isms: (A) volume diffusion inward from the grain boundary; (B) dis- solution and reprecipitation; (C) ex- change along a set of microfractures; and (D) exchange along multiple sets of microfractures. Distinguishing among these processes requires micro- analysis (Elsenheimer and Valley 1992). *Figure 23. (a) Arrhenius plot of oxygen isotope volume diffusion coefficients for an assortment of silicates, oxides and carbonates. Numbers along side each line refer to data summarized in Table 2 (see Appendix). Data from phases reacted under wet conditions (typically 100 MPa) are depicted with solid lines, whereas dry systems are represented by dashed lines. Note that the rates for the dry systems are generally slower and have higher activation energies (steeper slopes)*Figure 4. One-dimension diffusion profiles across the boundary of two touching minerals at constant temperature and variable times. Calculations assume an initial step in 18O of 10 and a final equilibrium fractionation of (A-B) = 0 . (A) Pinned boundary condition where Mineral A is modally dominant and has fast oxygen diffusion such that its 18O does not vary during exchange. (B) a diffusion couple where the abundance and diffusion properties are the same in both minerals, and (A-B) = 0 .*Figure 8. Schematic representation of O of quartz, feldspar and hornblende in an idealized granite undergoing diffusive exchange while cooling as described by the model of Giletti (1986). At high temperatures, above TC(Hb), all three minerals are open to exchange and maintain equilibrium (Period I). At lower tem- peratures (Period II) hornblende is closed to oxygen diffusion and only quartz and feldspar continue to equilibrate. In this period, (Fs- Hb) decreases although no feldspar-horn- blende exchange occurs. Finally, below Tc(Qt), no further exchange can take place (Period III) and final fractionations are preserved (from Eiler et al. 1992). *Figure 10. Contour plots of apparent temperatures and fractionations ( in italics) as a function of modal percentages in an idealized three-mineral rock com- posed of quartz, feldspar, and hornblende, predicted by the Fast Grain Boundary diffusion model to be recorded by: (a) quartz and hornblende, (b) feldspar and horn- blende, and (c) quartz and feldspar. These figures show the relation of discordance and the mode of each mineral in a rock (from Eiler et al. 1993).*Figure 11. Isotope Exchange Trajectories (IET) for magnetite from six rocks from the Sybille Fe-Ti-oxide quarry, Laramie anorthosite complex. The average temperature of intersection, 107725C, is higher than TC for any mineral in these rocks, and it is interpreted as the solidus temperature of the magma (from Farquhar et al. 1993). *Zinc sulfide spherule precipitated on the surface of what may have been a bacterium.Church et al. Geochemical Transactions 2007 8:10 doi:10.1186/1467-4866-8-10Download authors' original image*Figure7.4Thed17O, d18Orelationinchondrulesandrefractoryinclusionsofvariousmeteorites(CAI, calciumaluminuminclusions). For theseobjects thecorrelationis of slope1whereas theusual terrestrial fractionation(TF) correlationobservedis of slope 1 2, inline withthe mass difference between17Oand16Oand18Oand16O. This discovery madeby Robert Claytonetal. (1973) is interpretedbyThiemens(1999)asmass-independentfractionation, unlikeClaytonwhointerpretedit asanucleosyntheticeffect, andlaterasaphotochemical effect(Clayton, 2002). *