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Stochastic Simulation of Isotopic Exchange Mechanisms for Fe(II)-Catalyzed Recrystallization of Goethite Piotr Zarzycki, and Kevin M. Rosso Environ. Sci. Technol., Just Accepted Manuscript • Publication Date (Web): 12 Jun 2017 Downloaded from http://pubs.acs.org on June 12, 2017
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Stochastic Simulation of Isotopic Exchange
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Mechanisms for Fe(II)-Catalyzed Recrystallization
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of Goethite
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Piotr Zarzycki, 1,2,* Kevin M. Rosso3,*
5 6 7
1
Energy Geoscience Division, Lawrence Berkeley National Laboratory, Berkeley, CA, U.S.A. 2
Institute of Physical Chemistry, Polish Academy of Sciences, Warsaw, Poland 3
Pacific Northwest National Laboratory, Richland, Washington, U.S.A.
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KEYWORDS isotopic exchange, iron oxide, aggregation, reductive dissolution, redox, electron
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transfer, goethite, iron
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ABSTRACT. Understanding Fe(II)-catalyzed transformations of Fe(III)-(oxyhydr)oxides is
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critical for correctly interpreting stable isotopic distributions and for predicting the fate of metal
12
ions in the environment. Recent Fe isotopic tracer experiments have shown that goethite
13
undergoes rapid recrystallization without phase change when exposed to aqueous Fe(II). The
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proposed explanation is oxidation of sorbed Fe(II) and reductive Fe(II) release coupled 1:1 by
15
electron conduction through crystallites. Given the availability of two tracer exchange data sets
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that explore pH and particle size effects (e.g., Handler et al. Environ. Sci. Technol. 2014, 48,
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11302–11311; Joshi and Gorski Environ. Sci. Technol. 2016, 50, 7315–7324), we developed a
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stochastic simulation that exactly mimics these experiments, while imposing the 1:1 constraint.
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We find that all data can be represented by this model, and unifying mechanistic information
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emerges. At pH 7.5 a rapid initial exchange is followed by slower exchange, consistent with
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mixed surface- and diffusion-limited kinetics arising from prominent particle aggregation. At pH
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5.0 where aggregation and net Fe(II) sorption are minimal, that exchange is quantitatively
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proportional to available particle surface area and the density of sorbed Fe(II) is more readily
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evident. Our analysis reveals a fundamental atom exchange rate of ~10-5 Fe nm-2 s-1,
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commensurate with some of the reported reductive dissolution rates of goethite, suggesting
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Fe(II) release is the rate-limiting step in the conduction mechanism during recrystallization.
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INTRODUCTION
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Iron (III) oxides and oxyhydroxides are some of the most reactive and abundant minerals in
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soils and sediments, comprising a dominant sorbent and catalytic substrate for contaminant metal
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uptake and transformations. Their chemical behavior is tied closely to their mineralogy, which
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in turn depends on redox potential, pH, water activity, temperature, and particle size.1 Redox
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transformations from one phase to another are particularly facile, and understanding mechanisms
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of these transformations is key for reconstructing diagenetic history or predicting the mobility of
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an environmental contaminant. For example, natural reductive processes such as the anaerobic
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respiration of dissimilatory metal reducing bacteria produce and juxtapose aqueous Fe(II) with
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their parent Fe(III) phase. This condition triggers transformation from less stable forms (e.g.,
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ferrihydrite) to more stable forms (e.g., lepidocrocite, goethite, hematite, magnetite), a process
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that directly impacts metal binding and selectivity.2-6
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Despite the importance of these processes, mechanisms of Fe(II)-catalyzed phase
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transformations remain poorly understood. The difficulty arises in part because pathways for iron
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atom exchange between Fe(II) in solution and oxide Fe(III) are obscured by the prospect of
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Fe(II)/Fe(III) electron exchange at the interface. Until recently, the interaction of Fe(II) with
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stable Fe(III)-oxides, such as during sorption/desorption, has largely been deemed inert because
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of apparent reversibility and lack of phase change.1 However, recent 57Fe isotope tracer studies,
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such as those reported by Handler et al.7-9 for goethite and Frierdich et al.10-12 for hematite and
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goethite, demonstrate that these stable Fe(III) minerals undergo recrystallization when exposed
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to Fe(II).13 They show 56Fe-57Fe isotopic equilibration between the solid and solution phases up
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to 100% on the time scale of days, with no secondary mineral formation or significant change in
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particle size or shape.7-14 Although constituting an important advance because of its implications
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for metal uptake (e.g., by incorporation into the structure),10-14 these macroscopic tracer studies
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alone do not reveal the interfacial processes controlling the isotope exchange dynamics.
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Mechanistic insights are needed.
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The concept put forward to qualitatively explain isotopic equilibration without phase change is
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the conduction mechanism,15,16 where any given crystallite oxidative adsorption of Fe(II) by
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surface Fe(III) is coupled by bulk15,17 or surface18 conduction of electrons to remote Fe(III) that
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is reductively released as Fe(II). This nominally 1-to-1 coupled redox growth/dissolution process
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could thereby facilitate progressive exchange between goethite and solution iron isotopes
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without altering solid mass or physical characteristics necessarily. Implicit elementary steps
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including Fe(II) adsorption and interfacial electron transfer to oxide Fe(III), as well as electron
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transport through the lattice to distinct Fe(III) sites, have all been indirectly validated through
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Mössbauer measurements19,20 and molecular modeling.18,21-24
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A recent
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Fe tracer and microscopy study by Joshi and Gorski27 of Fe(II) interaction with
goethite qualitatively corroborated the applicability of the conduction mechanism for exchange,
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but also showed that additional processes such as particle coarsening could also be operative. In
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particular, through detailed microscopy work that validated molecular modeling predictions18
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that oxidative Fe(II) adsorption occurs preferentially on nanorod edge faces while reductive
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release occurs preferentially on nanorod tips, consistent with the conduction mechanism of
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exchange.
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In the present study we quantitatively test how well the simulation based on the conduction
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mechanism fits measured equilibration data across its breadth of conditions, from two
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comprehensive studies on Fe(II)/goethite.
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have direct implications for understanding metal uptake during Fe(II)-catalyzed Fe(III)-oxide
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recrystallization. For example, resolving the extent to which the conduction mechanism plays a
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role in the redox behavior of Fe(III)-oxides could improve mobility prediction for toxic metals
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that strongly associate with these minerals.
8,27
The new insights derived from our simulations
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COMPUTATIONAL METHODS
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In order to provide a mechanistic insight into Fe-exchange between aqueous and solid phase,
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we developed a stochastic simulation that computes the shape requirement for the isotopic
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equilibration curves evolving simultaneously based on the 1:1 conceptual model for exchange.
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We consider two pools of exchangeable iron and we neglect the interface for the computational
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simplicity. The latter approximation is justified because all experimental and theoretical reports so far are
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consistent with the moving dissolving-precipitating interfaces,7-19,24-27 which continually exposes a fresh
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layer of oxide to be exchanged in aqueous solution. If on the other hand, only the surface atoms are
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exchangeable, isotopic exchange is minimal in stark contrast to the experimental data at pH 7.5.7,8,27
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For simplicity, the simulation reduces the steps of the conduction mechanism into a single 1:1
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exchange event: one iron isotope from solution (i.e., Fe(II)) is randomly swapped with an iron
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isotope from the solid (i.e., Fe(III)), preserving the mass of iron in the solid and that in solution.
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While this simplification is consistent with the conduction mechanism (oxidative Fe(II)
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adsorption coupled to reductive Fe(III) release) it is not necessarily exclusive to it (e.g., in the
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real system acidic Fe(III) release and subsequent encounter/electron exchange with Fe(II) in
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solution could yield the same 1:1 isotopic exchange signature, though such pathways are unlikely
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to be significant given the low aqueous solubility of Fe(III)).
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Note also that the observed equilibration rate is not the rate of iron atom exchange nor
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interfacial electron transfer, per se, because the experiments are blind to the concomitant like
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isotopic exchanges (e.g.,
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encompasses all possible exchanges, including the ones to which the experiments are blind, and
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treats them on an equal basis. The total isotopic compositions of the solid and solution phase Fe
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are evolved stochastically through unitless numeric time steps, yielding the shapes of the coupled
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isotope exchange curves. The time step, as a sole fitting parameter, is then scaled to fit the
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measured equilibration data. Thus, the fitted time step has the prospect of carrying information
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on rates of processes underlying observed tracer exchange rates.
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Simulation input and assumptions
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Fe-56Fe,
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Fe-57Fe, etc.) that also undoubtedly occur. Our simulation
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The stochastic modeling algorithm begins with experimental mass ratios as inputs and consists
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of the following iterative sequence of steps: (i) random selection of one iron atom in the aqueous
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phase and another in the solid phase; (ii) assignment of their isotopic identity (57Fe or 56Fe) with
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probabilities proportional to current isotopic compositions of these phases; (iii) carry out an
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exchange step (i.e., atoms are swapped) and (iv) update the isotopic composition of the two
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phases (as well as any other macroscopic descriptors such as fractionation factors). In addition to
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this basic algorithm, adaptation has been implemented to explore the effect of evolving
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aggregation state on isotopic equilibration behavior, as described later.
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The algorithm assumes a constant, mass-independent exchange rate that swaps Fe isotopes
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between the two Fe compartments (solid, solution) initially populated at the δ57/56Fe levels used
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in the reported experiments. Note, that the solid and aqueous phases should also differentiate in
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terms of mass-dependent Fe-fractionation after reaching mixing equilibrium; however, it will
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result in small fractionation that becomes evident over a longer period than reported in the
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experiments.7,8,27
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In practice, at every simulation step we select two Fe atoms in both iron compartments with
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their isotopic identity assigned probabilistically based on the current δ57/56Fe ratio in each
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compartment. The isotopic compositions are updated every successful isotope swap with
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exchange dynamics expressed in solid recrystallization cycles (1 cycle is defined to have
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occurred when the number of successful swaps equals the number of oxide Fe atoms in the
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system).
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The isotopic compositions are expressed in the δ notation (reported in ‰): [ఱళ ୣ/ఱల ୣ]
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ߜ ହ/ହ Fe = 10ଷ ቀ [ఱళ ୣ/ఱల ୣ] − 1ቁ
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where [ହ Fe/ହ Fe] is isotopic ratio of a given iron compartment (i.e., aqueous Fe(II) or solid
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Fe(III)), [ହ Fe/ହ Fe]௦௧ௗ is the reference isotopic ratio (i.e., average for terrestrial igneous rocks,
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[ହ Fe/ହ Fe]௦௧ௗ =0.023).
ೞ
(1)
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Here, we discuss primarily just the effect of pH on Fe(II) sorption and exchange-active
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surface site density as the most plausible explanation of the incomplete exchange at pH 5 and
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complete exchange at pH 7 without change in the mass of the goethite (discussed below). The
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incomplete exchange at pH 5 could also be explained by an excluded exchange volume due to
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aggregation or mass transfer (e.g., via precipitation), but these processes are not observed
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experimentally8 and they are unlikely to be significant at pH 5.31 The observed incomplete Fe-
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exchange is most likely due to limited interaction of aqueous Fe(II) with the net positively
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charged goethite surface,8,27 as implemented in our simulation approach.
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RESULTS AND DISCUSSION
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Stochastic simulation of isotopic exchange
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In Figure 1a we illustrate the generic Fe isotopic exchange system, as modeled in our
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simulation. Each exchange event has been postulated to proceed via a sequence of elementary
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steps at the solid/solution interface, yielding 1:1 atom exchange. 7-18 For the sake of simplicity,
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our model considers only the net outcome of pairwise Fe atom swapping between the solid and
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solution phases, maintaining a constant ratio of Fe in the solid phase to Fe in the solution phase.
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As shown in Figure 1b, a large number of such swaps ultimately yields isotopic the same
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isotopic composition in both phases that depends on the mole ratio of iron in the solution relative
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to the solid and their respective initial isotopic compositions (δ57/56Fe).
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The time step in the simulations is unitless, and is scaled to establish the actual time step that
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shows best possible correspondence with the real-time equilibration data. To portray this scaling
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in terms of an additional physically useful quantity, we express time in terms of recrystallization
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cycles: one cycle corresponds to a total number of swap events that equals the number of Fe
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atoms in the solid phase (Fig. 1b). At the end of one cycle every Fe atom in the solid, in effect,
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will have resided in the solution phase at least once. The scaling of the time constant can be
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considered a simple stretching operation along the cycles/time axis that does not modify the
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functional form of the simulated equilibration curves. The solid and solution equilibration curves
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are fit simultaneously with this single adjustable parameter.
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Fitting pH 7.5 data reported by Handler et al.8
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In Handler et al.,8 despite a relatively high initial
57
Fe(II) isotopic enrichment in the solution
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phase (840‰), the low total amount of Fe in the solution phase relative to that in the solid phase
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(Fe(II):Fe(III) = aqueous:solid = 1:21.3) means that the overall change in δ57/56 for the solid
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phase is small. Modeling the evolution of δ57/56 in the solid phase alone is rather insensitive to
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simulation details. Thus we focus attention on the evolution of the solution phase δ57/56 for the
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highest resolving power in the experiments; the corresponding δ57/56 evolution for the solid phase
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is always well fit within measurement error limits.
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We first examine the pH 7.5 equilibration data for both the goethite microrods and nanorods,
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both of which are based on 1 mM Fe(II) and a constant 2 g/L solids loading.8 At this pH, within
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approximately 10 minutes almost a half (49% nanorods, 44% microrods) of the aqueous Fe(II) is
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sorbed to the goethite solids, the remaining aqueous Fe(II) concentration remained relatively
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constant for the rest of experiment; the first isotopic exchange measurement was collected at 10
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minutes.8 In Figure 2 we show best fits of simulated 1:1 exchange curves to the experimental
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results for goethite microrods (reported BET surface area = 40 m2/g) (Fig. 2a) and nanorods (110
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m2/g) (Fig. 2b). At this pH, for both microrods and nanorods, an equal tracer enrichment in solid
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and solution phase iron is observed within 30 days, with no significant change in the physical
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characteristics of the goethite detected at the end of the reaction.8
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For pH 7.5, using a single time constant the 1:1 model is unable to provide a comprehensive fit
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to the whole time-domain of the experimentally reported δ57/56 values. The deviation is resolved
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most prominently in δ57/56 for the aqueous phase in the intermediate time domain of 1-6 days for
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the microrods (Fig. 2a) and 1-5 days for the nanorods (Fig. 2b). Prior to this domain, initial rapid
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iron isotope exchange within the first day is observed for both the microrods and nanorods (87 %
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equilibrated by day 1), and this early stage for both particle sizes are well fit with an equal
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exchange rate of 6.5 days/cycle. This initial rapid exchange is followed in both cases by the
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requirement of a slower exchange rate, that was furthermore found to be particle-size dependent.
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In this intermediate time domain, the equilibration rates of the microrods and nanorods remain
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similar, albeit with an intriguing slower time constant for the smaller nanorods (12.5 days/cycle)
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compared to that for the microrods (8 days/cycle), which we address below. Because the fits
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become increasingly insensitive to the time constant in the late stages of equilibration,
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determining whether the decrease in exchange rate is temporary or persists to experiment
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completion is not possible. In any event the decrease in exchange rate and the emergence of
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particle-size dependence in the intermediate domain is clear from the data, and does not preclude
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near complete equilibration of both microrods and nanorods within 30 days. Assuming a two-
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stage process, the 1:1 model comprehensively describes this system.
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Fitting pH 7.5 data reported by Joshi et al.27
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The recent data set by Joshi and Gorski26 on a nearly identical system (nanorods, pH 7.5,
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with key differences discussed below) allows a further test of the 1:1 model. This system also
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entails 2 g/L solids loading, contacted with 0.8 mM Fe(II) which shows substantial rapid Fe(II)
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sorption (60% within the first day), and isotopic equilibration within 30 days. Following the
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same fitting procedure except applied to this data set (see Supporting Information) also yields
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two clear time-domains: A fast initial equilibration stage is followed by a substantially slower
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one that leads to equality of Fe-fractionation in solid and aqueous phases. The intermediate time
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domain is most evident between 1-15 days. This is striking overall similarity to the data in
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Handler et al.8 However, the time constants obtained from fitting the Joshi and Gorski27 data are
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significantly larger than those obtained by fitting the Handler et al.8 data (see Supporting
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Information). For example, comparing the initial rapid equilibration domain that is evident to 1
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day duration, the nanorods in the Joshi and Gorski27 system equilibrate (76% equilibrated) about
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3 times more slowly (19.5 days/cycle) than the nanorods in the Handler system (6.5 days/cycle).
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These time constants can be directly compared because they intrinsically account for the
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differences in the exact initial Fe isotopic compositions of the solutions and solids and their
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evolution over time, between the two studies. They do not yet, however, account for the slightly
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lower Fe(II) concentration used in Joshi and Gorski,27 which entails a 28:1 solid:solution Fe ratio
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in contrast to a 21.3:1 ratio in Handler et al.8 If we additionally account for this difference (see
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Supporting Information) the time constant distinction in the initial equilibration stage between
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the studies is reduced from a factor of 3 to a factor of 2.5. Note that, the exchange rates depend
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on the initial composition. Thus, they are normalized with respect to the surface Fe-sites density
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and initial Fe(II) concentration. The intrinsic differences in the oxide particles (e.g.,
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defects/impurities density) may also contribute to the exchange rate discrepancies.
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Aggregation affects exchange
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Conceptually, it is logical to attempt to explain the equilibration rates similarities (nanorods to
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microrods in Handler et al8) and differences (Handler et al8 nanorods and Joshi and Gorski27
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nanorods) in terms of available reactive surface area (based on the reported Fe-site density8, and
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Fe sorption31-32). As deduced in Handler et al,8 rates of exchange should be controlled by the
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probability of Fe(II) interaction with the goethite surface. However, particle aggregation is a
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documented but poorly quantified major system observable in all pH 7.5 experiments discussed
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so far between the two studies.8,27
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interactions between particles, to the extent that attractive van der Waals interactions start to
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dominate
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Aggregation is observed for pH near the point of zero charge.29-33 At pH 7.5 goethite is well
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within its expected point of zero charge range, typically pH = 6.7-9.5.33 While this net neutral
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surface charge facilitates Fe(II) interaction with the goethite surface31,32 (hence the strong
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observed Fe(II) sorption throughout all experiments), prior to this interaction goethite particles
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will have condensed into aggregates with poorly predictable partially occluded surface area.
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Compiling the observations about aggregation reported in both Handler et al8 and Joshi and
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Gorski,27 at pH 7.5 nanorods and microrods formed aggregates of similar sizes (Handler et al8),
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and nanorod “bundles” comprised ~50% of nanorod suspensions, a value that remained
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unchanged upon exposure to Fe(II) and throughout the 30 days of isotopic equilibration Joshi
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and Gorski.27 Fe(II) interaction with goethite aggregates, as opposed to individual particles, is an
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important enduring characteristic in all pH 7.5 experiments during the observed Fe isotope
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exchange timescales.
(see
It originates from a decrease of repulsive electrostatic
Derjaguin-Landau-Verwey-Overbeek
theory
of
suspension
stability28).
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The obscuring effect of aggregation on actual reactive surface makes full reconciliation
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of the pH 7.5 isotopic equilibration rates difficult. On the one hand, the fact that equilibration
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goes to completion suggests that occluded surface area is only partially occluded and remains
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accessible to Fe(II). On the other hand, the extent to which it is accessible between the systems
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can only be qualitatively assessed. It is quite likely that the found two-stages of equilibration
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arise directly from the effect of aggregation; the initial rapid stage derives largely from surface-
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controlled interaction between Fe(II) and well exposed goethite particles along the periphery of
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aggregates, whereas the trailing slower stage derives more from diffusion-limited interaction in
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interior domains. Other explanations must invoke some unexpectedly unique properties of the
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nanorod crystallites themselves, relative to the microrods, such as a lower defect density or the
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prospect of electrostatic coupling of interfacial processes across the ~ 10 nm rod widths that slow
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the rate of exchange.17,22,24 The same notion of smaller particles yielding a higher proportion of
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partially occluded interior domains can also explain the slowest equilibration rates found, for
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Joshi and Gorski27 nanorods. In that study nanorods were both geometrically smaller (254%
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lower geometric surface area per particle on average by TEM) and exposed less BET surface
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area (by 18%) than Handler et al8 nanorods. Aggregates of these smallest particle sizes yet
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considered would be expected to possess the highest proportion of partially occluded interior
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domains, and conceptually this is consistent with the slowest rates found overall in Joshi and
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Gorski’s study.27 However, this does not necessarily explain the 2.5x slower initial stage for
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their nanorods, if it indeed primarily reflects exchange via the most accessible surface area. The
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extent to which aggregation could partly encumber even this initial rapid stage of equilibration is
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indeterminate.
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Fitting pH 5.0 data reported by Handler et al.8In contrast to the experiments at pH 7.5, the pH
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5 experiments of Handler et al8 are much more useful for mechanistic interpretation because the
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aggregation is not observed in the reported experimental studies.8 At pH 5, isotopic exchange is
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observed to be incomplete, converging to a substantially lower amount of exchange over 30
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days.8 At pH 5 the oxide surface is positively charged due to H+ binding to surface hydroxyl
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groups (e.g.,29-31 ≡FeOH-1/2 + H+ ↔ ≡FeOH2+1/2). Inverse to the situation discussed above for pH
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7.5, this not only reduces the tendency to aggregate but also limits Fe(II) sorption to the surface.
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In the pH 5 experiments, no net Fe(II) sorption was detected8. However, other relevant Fe(II)
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sorption experimental studies and their surface complexation modelling31,32 suggest net Fe(II)
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sorption on goethite in the vicinity of 7% of the aqueous Fe(II) at this pH, for similar Fe(II)
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loading and particle sizes. At pH 5 the experiments are thus on the cusp of the Fe(II) sorption
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edge, and it is reasonable to assume that net Fe(II) interaction with the goethite surface is
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minimal but not zero.
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Despite these small amounts of net Fe(II) sorption, the aqueous and goethite phases still
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exchange Fe and some isotopic exchange occurs (i.e., δ57/56Fe(II) drops from 840‰ to 334‰ for
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the nanorods, and to 588‰ for the microrods – see ref.,8 Supporting Information and Fig. 1).
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Here the observed particle-size dependence is free of the counterintuitive behavior found for pH
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7.5. At pH 5 higher surface area nanorods exchange faster and to a greater extent than the lower
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surface area microrods, on an equal mass basis. In the absence of the complicating effects of
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aggregation, the rate and extent differences should therefore be more clearly relatable to
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available particle surface area, which is about 2.8 times higher for the nanorods than the
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microrods. If the mechanism of exchange is indeed controlled by interfacial processes, one can
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anticipate that this ratio might manifest in either the relative rate of approach to equal isotopic
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fractionation in solid and aqueous phase, the extent of equilibration, or both. In order to fit
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simulated 1:1 exchange to the pH 5 experimental data8 the model must account for both the
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observed rate of equilibration and the extent of exchange (Fig. 3). To do so without changing
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goethite mass requires that only a fraction of the total goethite mass is exchange-active. The
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equilibration rates for the nanorods and microrods are well fit each with a single time constant in
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our model, with recrystallization cycle times of 205 days for the nanorods, and 615 days for the
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microrods. Although the available data are more sparse than those available for pH 7.5, the time
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constants are well constrained by the intermediate time point. The rate of nanorod equilibration
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is thus about 3 times faster than that for the microrods, consistent with the surface area ratio
292
between them.
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Fe(II) sorption dictates exchange
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Furthermore, from the observed extents of isotopic exchange, the fraction of exchange-active
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sites over 30 days can be estimated at 7% for the nanorods, and 2% for the microrods (Fig. 3).
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These values are tightly constrained by the measured isotopic compositions at the final time
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point, and should be considered to be determined primarily from the data itself, as opposed to a
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fitting outcome. They are calculated from the difference in the aqueous and solid isotopic
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compositions (i.e., ∆= ∆δ= δ(57/56Fe(II)) - δ(57/56Fe(III))) after 30 days. In the case of nanorods,
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this difference (∆=309.5‰) corresponds to 7% Fe(III) being exchangeable (~35% of Fe is
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exposed at nanorod surfaces), whereas in case of microrods (∆=576.1‰) only about 2% of oxide
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Fe(III) is exchangeable (28% of Fe is exposed at the surface) (see Supporting Information). Here
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again the surface area ratio of 2.8 appears to manifest directly, this time in the relative amounts
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of exchange-active sites (7% / 2%), based on exchange extent.Given the clear role of interfacial
305
area in these experiments, and the proposed conduction mechanism, it is logical to hypothesize
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that the observed limited exchange-active mass is directly proportional to the sorbed Fe(II)
307
density at goethite surfaces. Further, if this density can be independently estimated, because our
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numerical simulation provides the real-time frequency of the process underlying tracer mixing
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and because the surface area is known (particularly at pH 5), we can estimate rates of
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microscopic processes per sorbed Fe(II) that nominally give rise to the observed atom exchange
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behavior.
The reader is here reminded that because our simulation encompasses all atom
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exchange events, including the exchanges to which the experiments are blind, the computed
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exchange frequency is that associated with the underlying process step sustaining the
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macroscopically observed tracer mixing rate.
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Exchange-active surface site density
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According to Handler et al.8, the nominal crystallographic density of surface-exposed Fe is
317
about 12.2 Fe/nm2. Surface complexation models31,32 used to fit pH-dependent Fe(II) sorption at
318
two types of goethite particles assume lower surface sites densities of 2 sites/nm2 or 3 sites/nm2,
319
respectively. In those studies, the experimental Fe(II) sorption data32 was obtained for particle
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sizes (i.e., specific surface area, SSA of 54 and 78 m2/g) very similar to those in Handler et al.,8
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(40 and 110 m2/g), and the resulting sorption isotherms provide a systematic basis predicting
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both pH- and particle-size dependent sorbed Fe(II) densities. We therefore emphasize this
323
approach, and use the nominal crystallographic density as the bounding upper limit.
324
instance, at pH 7.5 predicted sorbed Fe(II) densities are 1.54 Fe/nm2 (particles SSA= 78m2/g)31
325
and 1.91 Fe/nm2 (SSA=54m2/g)32. This equates to 12.7% and 15.6% of surface exposed Fe(III)
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atoms in contact with sorbed Fe(II), for nano- and microgoethite, respectively. At pH 5, sorbed
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Fe(II) densities are much smaller: 0.2 Fe/nm2 (SSA=78 m2/g)31 and 0.24 Fe/nm2 (54 m2/g)32, and
328
corresponding surface Fe(III) contact values are 1.64% and 2%, respectively. By using these
329
Fe(II) surface densities as the those of exchange-active surface sites, we can estimate the atom
330
exchange rate per sorbed Fe(II) species, for all explored experimental conditions.
331
Fundamental rate of exchange
For
332
Table 1 shows calculated Fe atom exchange rate constants per exchange-active site, i.e., a
333
sorbed Fe(II) site, computed from our simulation results for exchange experiments in Handler et
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al.8 Computed rates encompassed the breath of assumed sorbed Fe(II) densities discussed above,
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to establish sensitivity to such assumptions. For the pH 7.5 experiments, we approach the
336
complication of aggregation by assuming that because of its larger particle size the microrod data
337
is least prone to kinetics that are not surface controlled. The fitted results for the microrods show
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an exchange rate per Fe(II) site that ranges from order 10-5 s-1 for the upper limit of 12.2
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sites/nm2 to 10-4 s-1 for the likely more realistic SCM-fitting based estimate of 1.91 sites/nm2,
340
irrespective of the fast or slower domains. In an attempt to extract meaningful information from
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pH 7.5 nanorod data, if we assume the exchange rate constant for the fast domain of the
342
microrod data also applies to the nanorod data in the fast domain we can back calculate the
343
effective active surface area in the highly aggregated nanorod experiments (down to 49.61 m2/g
344
from 110 m2/g). Using this effective surface area in the slow domain of the nanorod experiments
345
yields an exchange rate per site on the order of 10-5 s-1. Turning now to the more straightforward
346
pH 5 data, despite their markedly slower observed tracer exchange kinetics and lower sorbed
347
Fe(II) densities, our numerical simulations predict that the underlying exchange rate constants
348
are also in the vicinity of 10-5 s-1, for both nanorods and microrods. Thus, although the observed
349
tracer mixing rates and extents are substantially different across the range of experiments in
350
Handler et al.,8 our simulations reveal that the rate of the underlying process necessary to
351
describe all observed mixing rates is rather constant, ranging between 10-4 s-1 to 10-5 s-1. Taking
352
the pH 5 data as the most reliable, the average calculated exchange per Fe(II) site is
353
2.3±1 × 10-5 s-1.
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Table 1. Exchange rates estimated by fitting the stochastic simulation to experimental data from Handler et al.8 For pH 7.5 we distinguish two kinetic regimes nominally arising from aggregation (see text); no such effects pertain at pH 5. Specific results discussed in the text are highlighted. Recrystallization cycle time (days)
Specific Surface Area (SSA) [m2/g]
Exchange-Active Site Density (NFe) [Fe/nm2]
Exchange rate per site [s-1]
pH 7.5 nanorods 6.5 (fast)
12.5 (slow)
110
a
49.61e 49.61h
12.2b 3c 1.54d 1.54d 1.54d
8.993E-6 3.657E-5 7.124E-5 1.580E-4f 8.214E-5g
pH 7.5 microrods a
6.5 (fast)
40
8 (slow)
40a
12.2b 3c 1.91d 12.2b 3c 1.91d
2.473E-5 1.006E-4 1.580E-4 2.009E-5 8.171E-5 1.283E-4
pH 5.0 nanorods 205
110
a
12.2b 3c 0.2d
2.851E-7 1.160E-6 1.739E-5
pH 5.0 microrods 615 359 360 361 362 363 364 365
40
a
12.2b 3c 0.24d
2.614E-7 1.063E-6 1.329E-5
a
surface area determined (BET method) as reported by Handler et al.8,bexchange site density (Fe/nm2) estimated from crystallographic data by Handler et al.8,cFe(II) sorption density used in surface complexation modeling of Fe(II) sorption on goethite, dactive surface site density determined from the SCM fitting31,32 of the Fe(II) sorption edge based on most relevant particle sizes and at specific respective pH values,,eeffective surface area for (aggregated) nanorod suspension in the fast domain determined by fassuming the microrod fast domain exchange rate constant at the same pH, gexchange rate approximately corrected for surface area occlusion hthe effective surface area estimated for the (aggregated) nanorod suspension in the fast domain.
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Identifying the rate-limiting step
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In the 1:1 conceptual model, because each atom exchange event is facilitated by a set of
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reactions nominally linked in series (Fe(II) sorption, interfacial ET to goethite Fe(III), solid-state
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electron transport, Fe(II) release), this estimated rate would thus correspond to the rate-limiting
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step in the series. Using molecular dynamics simulations, Zarzycki et al.18 showed that Fe(II)
372
can form strong inner-sphere surface complexes to low-index goethite rod prismatic faces (e.g.,
373
101 and 100, space group Pnma), and that formation of these complexes from more distal outer-
374
sphere complex locations is largely free of energy barriers. This suggest Fe(II) adsorption into
375
surface-associated configurations compatible with interfacial electron transfer is not kinetically
376
inhibited. These inner-sphere Fe(II) surface complexes were found to be capable of exchanging
377
electrons with underlying goethite Fe(III) at rates ranging from ~ 1-100 s-1, at least five orders of
378
magnitude faster than the exchange rate that appears to govern tracer mixing based on the
379
present study. Likewise, molecular dynamics simulations revealed relatively fast subsurface
380
electron hopping pathways on these goethite faces as well (up to 106 s-1).18 By elimination, this
381
implicates the reductive Fe(II) release step of the conduction mechanism as the most likely rate
382
limiting process, the one that gives rise to the discovered ~ 2 × 10-5 s-1 fundamental exchange
383
rate underlying atom exchange.
384
Exchange and reductive dissolution rates
385
The rate of iron oxides reductive dissolution strongly depends on the type of reductant,1 however
386
in the case of dissolution by ascorbic acid, the process is believed to be controlled by Fe-release.
387
Therefore, we used the reported rates of goethite dissolution by ascorbate as proxies for Fe-
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release/Fe-exchange rate. Handler et al.8 measured the reductive dissolution rate of their
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nanorods and microrods in 10 mM ascorbic acid at pH 3 and reported very similar surface-area
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normalized rate coefficients for both particles, ~ 3 × 10-4 g m-2 d-1, which corresponds to an Fe
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atom release rate of 3.7 × 10-5 nm-2 s-1. The reductive release rate of Fe(II) from goethite by
392
ascorbic acid is known to be relatively insensitive to pH changes in the acidic domain.34 Re-
393
expressing the fundamental exchange rate in similar terms for pH 5 data (microrods, slow
394
domain) yields 5.5 × 10-5 Fe nm-2 s-1.
395
dissolution rates of goethite8 are consistent with the rate of the underlying process revealed by
396
our stochastic simulations. This suggest that reductive Fe-release is in control of macroscopically
397
observed tracer exchange behavior.
398
Mechanistic insights
The correspondence is striking– these
reductive
399
Stochastic simulation analysis of two comprehensive experimental data sets for Fe isotopic
400
tracer mixing in the Fe(II)/goethite system reveal behavior consistent with the conduction
401
mechanism of atom exchange. Application of a 1:1 exchange constraint between solid and
402
solution phase Fe yields equilibration curves that can largely reproduce the macroscopically
403
observed shapes. Under pH 7.5 conditions aggregation appears to play a significant role in the
404
mixing kinetics, consistent with speculation in the original experimental studies.8,27 Two kinetic
405
regimes are present at pH 7.5, initial rapid Fe-exchange is followed by much slower, size-
406
dependent exchange that nonetheless enables complete equilibration of the isotopic compositions
407
within 30 days. At this pH, the mixing kinetics for smaller particle sizes is likely more strongly
408
overprinted by aggregation effects, suggesting care needs to be taken in their mechanistic
409
interpretation.
410
simulations reveal an underlying fundamental exchange rate consistent with the known release
411
rate of Fe(II) during reductive dissolution by ascorbic acid, one that is otherwise incompatible
412
with the remaining steps implicit in the conduction mechanism. The collective findings thus
At lower pH values where aggregation is not significant, our stochastic
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validate to some extent the applicability of the conduction mechanism of atom exchange in this
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system, with the reductive Fe(II) release step as rate-limiting.
415
Environmental implications
416
The findings support a conceptual model for trace, heavy and/or radioactive ion fate and
417
transport in the subsurface with kinetics potentially dominated by the kinetics of incorporation
418
into and release from Fe(III)-(oxyhydr)oxide minerals. This geochemical pathway would be
419
driven by changes in redox conditions in iron rich soils and sediments and depend upon oxide
420
phase, particle size, relative proportions of Fe(II) and Fe(III), and solution pH.
421 422
ASSOCIATED CONTENT
423
Supporting Information. The results of the extraction and accumulation procedures applied to
424
the experimental data reported by Handler et al.8 Details of computations and fitting the
425
simulation to data reported by Handler et al.8 and Joshi et al.26).
426 427
AUTHOR INFORMATION
428
Corresponding Author
429
*e-mail:
[email protected], tel. +48 730 628 237, fax. +48 22 343 0000;
430
[email protected] 431
Author Contributions
432
The manuscript was written through contributions of all authors. All authors have given approval
433
to the final version of the manuscript.
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ACKNOWLEDGMENT
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This work is based on research sponsored by the U.S. Department of Energy (DOE), Office of
436
Science, Office of Basic Energy Sciences (BES), Division of Chemical Sciences, Geosciences
437
and Biosciences, through its Geosciences program at Pacific Northwest National Laboratory
438
(PNNL). The authors acknowledge helpful discussions with Clark Johnson, Michelle Scherer,
439
and Andrew Frierdich during conceptualization of this study. A portion of this research was
440
performed using EMSL, a national scientific user facility sponsored by the DOE's Office of
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Biological and Environmental Research and located at PNNL. PNNL is a multiprogram national
442
laboratory operated for DOE by Battelle.
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Figure 1. Stochastic model of Fe isotopic exchange between solid (δ57/56Fe(III)) and aqueous
532
(δ57/56Fe(II)) pools of iron (a). The simulated isotopic exchange dynamics for systems with a
533
varying ratio of solid to liquid iron pools (Fe(II) : Fe(III)) and initial isotopic compositions equal
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to δ57/56Fe(II)=840‰ (aqueous) and δ57/56Fe(III)=-0.12 (iron oxide), respectively.
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Figure 2. Fitting of stochastic modeling simulations to the experimental data reported by Hander
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et al. for goethite microrods (a) and nanorods (b) at pH=7.5. Fast initial exchange is shown in
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black curves, the slower second stage of exchange is shown in red.
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Figure 3. Fitting of stochastic exchange simulations to experimental data reported by Hander et
544
al.8 for goethite nanorods (a) and microrods (b) at pH=5.0. That exchange is incomplete after 30
545
days is well constrained by the data, indicating substantially less than 100% exchangeable Fe
546
(%exc.). A recrystallization cycle time of 205 days with 7% exchangeable Fe fits the nanorod
547
data, whereas 615 days and 2% exchangeable Fe fits the microrod data. Nanorods (110 m2/g)8
548
should have about 3 times more Fe exchanged than microgoethite (40 nm2/g)8, which is
549
consistent with the kinetics and differences in δ57/56Fe(III)solid (7% nanorods and 2 %
550
microrods) found here. For comparison, system behavior expected for 100% exchange at the
551
same respective recrystallization cycle times is shown in red curves.
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