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The Electrochemical Isotope Effect – Redox driven stable isotope fractionation

Redox reactions (involving an electron transfer) drive many chemical transformations in the environment and are vital in biological cycles for energy production. Many elements are redox sensitive, with multiple oxidation states stable on our planetary surface. Of these, the transition metal elements are of interest, as some of the largest stable isotope fractionations seen in these metal systems are associated with redox transformations. Therefore, stable isotopes may be used for a wide range of applications, from studying the transport and deposition of metals in the environment for the purposes of monitoring and remediation of contaminants, to reconstructing the chemistry on the surface of our planet in the past. In order to do this an understanding of what drives stable isotope partitioning during a redox reaction is needed.

In the Mineral Physics Lab at UCLA we use a combination of experimental electrochemical techniques combined with theoretical ab initio computational approaches to study stable isotope fractionation during controlled electrochemical reactions (electrodeposition). To date we have studied fractionation of iron, zinc, lithium and molybdenum with plans to extend the studies further to investigate copper, chromium, mercury and uranium isotope fractionation during redox processes. Figure 1 shows a schematic of the electrochemical cell used for iron studies, and a microscopic view of processes operating at the electrode surface, which may contribute to an observed isotope effect.

Figure 1:.(LEFT) Schematic of water jacketed electrochemical cell with three electrode arrangement connected to an autolab potentiostat for controlled electrodeposition at cathode. (RIGHT) Microscopic schematic of the surface of the electrode with the potential processes that may contribute to the overall isotopic signature in the plated metal (gray spheres) labeled next to the arrows. In a series of papers investigating iron and zinc stable isotope fractionation during

electrodeposition Kavner et al. [Geochim. Cosmochim. Acta, 2005, 2008] derived an equation which combined equilibrium stable isotope theory (Urey, Bigeleisen and Mayer) with a statistical mechanic description of charge transfer processes at an electrode (Rudy Marcus):

(Equation 1)

where v, ΔG, kB, T, m, αeq, QP/QR, z, e and λ denote collision frequency, activation free energy, Boltzmann’s constant, temperature, mass in motion, equilibrium fractionation factor, partition function ratio of abundant isotopologues of product (P) and reactant (R), number of electrons, charge of electron and Marcus reorganization energy, respectively (Black et al., 2009, in review). Equation 1 makes a number of testable predictions about how stable isotopes will be partitioned during a charge transfer reaction:

1) Fractionation will be a linearly dependent upon applied voltage (overpotential = η = V-V0) or in other words the driving force or extend of disequilibrium.

2) The magnitude and slope of the fractionation will scale with the equilibrium fractionation factor between product and reactant divided by the Marcus reorganization energy.

3) Fractionation will decrease with increasing temperature, primary controlled by the change in magnitude of the equilibrium fractionation factor, which scales proportionally with 1/Temperature^2.

These predictions were tested by running a series of experiments to investigate the effect

of overpotential, time and temperature on the composition of metal deposited. Analysis of metal products was made by high resolution multiple collected inductively coupled plasma mass spectrometry (MC-ICP-MS) on Thermo-Finnigan Neptune instruments housed at UCLA (Fe) and Caltech (Zn). The results are plotted in Figure 2. Strikingly there is a difference between the earlier studies of Kavner et al. (2005, 2008) (hollow markers, Fig. 2) and the temperature dependent study (solid markers, Fig. 2, Black et al., 2009a, in prep.). The main difference between the studies is the temperature control (not fixed in earlier work) and the use of a salt bridge and magnetic stir bar in the later investigations.

Figure 2. Difference in the (LEFT) 56Fe/54Fe and (RIGHT) 66Zn/64Zn composition of metal deposits and an aqueous stock solution of 1M FeCl2 and 1M ZnSO4 in 1M H2SO4, respectively (Solid markers: Black et al., 2009a, in prep.; Hollow markers: Fe, Kavner et al., 2005; Zn, Kavner et al., 2008). Solid lines represent calculated equilibrium fractionation factors betweent he metal products and hexaaqua aquaoues complexes (Schauble et al., 2001; Black et al., 2009b in prep.)

Examination of Figure 2 points towards a number of systematic trends and further hypotheses to test:

1) All metal deposits are lighter isotopically than the aqueous salt baths, with fractionations observed up to two times that predicted by equilibrium stable isotope theory.

2) In the recent experiments (solid markers, Fig. 2) the fractionation decreases with increasing overpotential. This is the opposite effect from what was seen in previous FeCl2 experiments (hollow markers), where solutions were also acidified with 1M HCl.

3) The fractionation of zinc is around 1.5 per mil larger in recent experiments (solid markers), the only difference being the temperature control and stirring of solutions.

4) In both the recent iron and zinc data (solid markers, Fig. 2) fractionation increases with increases temperature. This is the opposite of what is predicted by Equation 1 and equilibrium stable isotope theory.

These two observations suggest that a third process is operating and affecting the overall

isotopic composition of metal samples plated: mass-transport limitations in the boundary layer adjacent the electrode (Fig. 1). The role of mass transport can be evaluated by comparing the measured currents (proportional to flux of metal at the electrode surface) with a calculated diffusion limited current (Cottrell current, see Bard and Faulkner, Electrochemical Methods, 2001). Figure 3 plots fractionation in the samples as a function of this current ratio.

Figure 3. Fractionation as a function of measured current to Cottrell diffusion-limited current ratio. Legend: Same as Fig. 2. Earlier zinc data (Kavner et al. (2008) plotted assuming a 100% deposition efficiency.

At low current ratios fractionation is larger and under electrochemical control / electron-

transfer kinetics are rate-limiting. At higher current ratios fractionation systematically decreases and is under mass-transport control / diffusion is rate limiting. The counterintuitive temperature effect (increasing fractionation with increasing temperature) seems to be explained by mass-transport properties, as lower current ratios are observed at the higher temperatures, and thus the larger fractionation is produced. The opposing trends seen in earlier vs. more recent iron experiments (LEFT, Fig. 3) are now delineated from one another. Kavner et al. (2005) fit

equation 1 to the trends seen in the hollow data points, with reasonable values for reorganization energy (on the order of 100 kJ mol-1) being obtained.

Further studies are being developed to investigate fractionation in the absence of mass-transport limitation with the use of a rotating disc electrode (RDE, pictured right) (Black et al, 2009a, in review). The RDE allows for controlled hydrodynamics in solution and resupply of dissolved metal to the electrode surface. In the case of an RDE the diffusion limiting current (Levich-current, see Bard and Faulkner, 2001) can be calculated as a function of the rotation rate (ω) of the electrode (ilevich ∝ SQRT(ω)). The results of preliminary experiments where metal has been plated from solutions of iron(II) chloride and iron(II) sulphate are shown in Figure 4.

Figure 4. Preliminary RDE iron results (Black et al., 2009a). (LEFT) Iron isotope fracitonation as a function of the electrodes rotations rate; (RIGHT) Iron isotope fractionation as a function of the mass-transport limited current ratio (see Eq. 2 in text). Legend: Squares (Fe plated from FeCl2 stock solutions); diamonds (Fe plated from FeSO4 stock solutions); Shade of markers, applied overpotential: -0.5 (yellow), -0.75 (orange), -1.0 (red), -1.5 (purple) to -2.0 (blue).

A number of systematic and predictable trends fall out of the RDE data shown in figure 4:

1) Fractionation increases as a function of rotation rate (LEFT), as expected as mass-transport limitations are not as pronounced with increasing rotation rate.

2) At a low enough overpotential (-0.5 V) fractionation appears to be at a steady state from

2.5 to 10 krpm. This is predictable as mass-transport limitations are not as pronounced at lower overpotentials, where the competing electrodeposition kinetics are slower.

3) Thus conditions can be found at high enough rotation rates and low enough

overpotentials where mass-transport limitations are entirely eliminated. A series of experiments are currently underway to investigate the effects of temperature and overpotential in this non-mass-transport limited regime.

References: Bard, A. J. and Faulkner, L. R., 2001. Electrochemical Methods: fundamentals and applications. John Wiley & Sons, Inc., USA. Black, J. R., Young, E., and Kavner, A., 2009a (in review). Electrochemically controlled iron isotope fractionation. Black, J. R., Kavner, A., and Schauble, E. A., 2009b. (manuscript in prep.). Density functional theory calculation of equilibrium stable isotope partition functions for aqueous zinc complexes. Bigeleisen, J. and Mayer, M. G., 1947. Calculation of equilibrium constants for isotopic exchange reactions. J. Chem. Phys. 15, 261-7. Kavner, A., Bonet, F., Shahar, A., Simon, J., and Young, E., 2005. The isotopic effects of electron transfer: An explanation for Fe isotope fractionation in nature. Geochim. Cosmochim. Acta 69, 2971-2979. Kavner, A., John, S. G., Sass, S., and Boyle, E. A., 2008. Redox-driven stable isotope fractionation in transition metals: Application to Zn electroplating. Geochim. Cosmochim. Acta 72, 1731-1741. Kavner, A., Shahar, A., Black, J. R., and Young, E., 2009. Iron Isotopes at an Electrode: Diffusion-Limited Fractionation. Chem. Geol. (in press). Marcus, R. A., 1965. Theory of electron-transfer reactions. VI. Unified treatment for homogeneous and electrode reactions. J. Chem. Phys. 43, 679-701. Schauble, E. A., Rossman, G. R., and Taylor, H. P., 2001. Theoretical estimates of equilibrium Fe-isotope fractionations from vibrational spectroscopy. Geochim. Cosmochim. Acta 65, 2487-2497. Urey, H. C., 1947. Thermodynamic properties of isotopic substances. J. Chem. Soc., 562-81.