The synthesis method was adapted from Burleson and Penn. 43 Using a peristaltic pump at a rate of 4.58 mL/min, 1.0 L of 0.4799 M NaHCO₃ (Fisher, ACS grade) was added dropwise to a continuously stirred 1.0 L solution of 0.4000 M Fe(NO₃)₃·9H₂O (Fisher, ACS grade). During the transfer, the solution changed from bright orange to dark brownish red with no visible precipitate. The suspension was separated into 250 mL Nalgene bottles and microwaved one at a time until boiling occurred, shaking every 40 s (most boiled after 120 s). Immediately after heating, each suspension was plunged into an ice bath until it reached ~20°C. In order to remove the counter ions present from the synthesis, the cooled suspensions were placed into dialysis bags (MWCO = 2000), which were placed in Milli-Q^® H₂O. The water was changed three times per day for three days. The resulting suspensions were placed in a number of weigh boats, covered, and placed in a fume hood to dry. The justification for drying the particles is that previous results have shown that the six-line ferrihydrite nanoparticles prepared using this method are not stable in aqueous suspension because they grow by oriented aggregation accompanied by phase transformation to goethite in a relatively short period of time, even at room temperature (i.e., within a few weeks). 43 Using a mortar and pestle, the dry, dark reddish brown particles were ground into a fine powder and stored in a glass vial.

The synthesis method was adapted from Schwertmann and Cornell. 44 With stirring, 20 g of solid Fe(NO₃)₃·9H₂O was added to 2.0 L of Milli-Q H₂O at 75°C. The solution temperature was maintained at 75°C for 12 min. After heating, the solution was plunged into an ice bath until it reached ~20°C (~30 min). The cooled suspension was dialyzed, dried, and ground as described earlier.

The synthesis of the nanorods began by using the 4 nm-6LF synthesis procedure (Sec. II A). After dialysis, the pH of the ferrihydrite suspension was quickly adjusted to 12 using 5 M NaOH (Fisher, ACS grade). A deep maroon suspension formed. The suspension was heated at 90°C for 24 h, after which a deep orange precipitate had settled to the bottom quarter of the bottle. The supernatant was discarded, and the remaining suspension was placed into dialysis bags, which were placed in Milli-Q H₂O. The water was changed three times per day for three days. The resulting suspension was dried and ground as described above.

The synthesis method was adapted from Schwertmann and Cornell. 44 With stirring, 40 g of Fe(NO₃)₃·9H₂0 was added to 900 mL of Milli-Q H₂O. While stirring, the pH was adjusted to 12 using 5 M NaOH. A deep maroon suspension formed. The suspension was heated in an oven at 90°C for one week, after which a yellow-orange precipitate had settled to the bottom quarter of the bottle. The supernatant was discarded, and the remaining suspension was placed into dialysis bags, which were placed in Milli-Q H₂O. The water was changed three times per day for three days. The resulting suspension was dialyzed, dried, and ground as described earlier.

All preparations and reactions were performed in a catalytically maintained anaerobic environment (~3% H₂ in N₂, vinyl anaerobic chamber, Coy Laboratory Products Inc., O₂ < 100 ppm, as measured by an oxygen/hydrogen gas analyzer). Suspensions were stirred using Teflon™-coated stir bars, and all reaction bottles were covered with aluminum foil to prevent exposure to light.

Known masses (75, 50, 25, or 12.5 mg) of particles were placed in clean, 30 mL Nalgene bottles containing 5.0 mL of 40 mM, pH 3.75 acetate buffer [prepared using glacial acetic acid (Mallinckrodt, ACS grade) and NaOH] that had been purged with N₂ gas for at least 20 min. The suspensions were capped, removed from the anaerobic chamber, and sonicated for 10 min. After returning the bottles to the anaerobic chamber and stirring overnight, the appropriate volume of acetate buffer (to bring the final reaction volume to 25.0 mL) and 10 mM hydroquinone (QH₂, Sigma, 99%) stock solution were added. The samples were stirred continuously throughout the experiment. At desired time intervals, 1.0 mL aliquots were removed and filtered using a 0.2 μm Pall nylon filter membrane. The concentration of p-benzoquinone (Q) at time t, [Q]_t, was immediately quantified (<1 min) via high performance liquid chromatography (HPLC). Stop time was recorded as the time of filtering. The solid concentration was assumed to be constant since no settling or clumping of the particles was observed during sampling.

Blank samples containing only QH₂ in acetate buffer were used to account for the spontaneous oxidation of QH₂ to Q.

Samples were quantified using an Agilent Technologies 1100 Series HPLC equipped with a Zorbax^® C₁₈ Stable Bond column. The flow rate was 0.75 mL/min, and the mobile phase consisted of 65 vol % 40 mM, pH 3.75 acetate buffer, and 35 vol % acetonitrile (Pharmco, HPLC grade). The detecting wavelength was 235 nm. The injection volume was 10 μL. Using this method, the retention time of QH₂ was 2.4 min, and the retention time of Q was 3.4 min. An eight-point calibration curve from 0 to 1 × 10^-2 M QH₂ and an eight-point calibration curve from 0 M to 1 × 10^-3 M Q (Acros, 99 + %) were used.

Aqueous [Fe(II)] was determined using an adaptation of the Ferrozine assay45 for a subset of experiments in order to confirm that the reaction proceeded via reductive dissolution and to verify the stoichiometry of the reaction for each particle type. Immediately after HPLC analysis, 0.80 mL of the filtered sample was combined with 0.25 mL of 5 g/L Ferrozine (Acros, 99.9%) and 3.25 mL 40 mM, pH 3.75 acetate buffer. Absorbance at 562 nm was measured using a Spectronic 20D+ visible spectrophotometer. A standard Ferrozine/acetate buffer solution was used as a blank. An eight-point calibration curve from 0 M to 1 × 10^-4 M FeCl₂·4H₂O (Fisher, ACS grade) was used. Blanks containing particles in buffer (no reductant) were also tested. For at least one sample of each particle type, the amount of Fe(II) adsorption onto the nanoparticles was determined by difference between the total Fe(II) equivalents in solution and the benzoquinone equivalents produced.

Particles were characterized by three different methods: x-ray diffraction (XRD), transmission electron microscopy (TEM), and Brunauer-Emmett-Teller surface area analysis (BET). 46

XRD was performed using a PANalytical X'Pert Pro theta-theta diffractometer equipped with a Co anode and an X'Celerator detector. Data collection ranges and collection times were 10° to 90° 2θ and 120 min, respectively, for ferrihydrite samples and 15° to 90° 2θ and 30 min for goethite samples. The diffraction patterns were compared to PDF (powder diffraction file) No. 29-0712 (six-line ferrihydrite) and PDF No. 29-0713 (goethite).

TEM samples were prepared by diluting and sonicating the dried samples and then placing one drop onto a 3 mm holey carbon coated Cu grid (SPI Supplies). Samples were characterized using a Tecnai T12 TEM equipped with a Gatan CCD camera. The specific surface area for each sample of nanoparticles was measured by two methods. First, specific surface area by TEM (SA_TEM) was estimated by using particle size and size distribution data from a minimum of 500 particles. Ferrihydrite nanoparticles were modeled as spheres, and the specific surface area was calculated for each particle measured using the density (3.96 g/cm³) from Cornell and Schwertmann. 3 Then, an average specific surface area was calculated. Goethite nanoparticles were modeled as rhomboidal prisms bounded by {011}, and a schematic of the cross section of the assumed morphology is shown in Fig. 1. The TEM-measured width (w_TEM) was converted to the width of the Oil-type faces (w_{011}) to account for the preferred orientation of particles on the grid, and a specific surface area was calculated for each particle measured using the density of goethite (4.26 g/cm³) from Cornell and Schwertmann,3w_{011}, L_TEM, and θ (the angle between the 011-type faces). The assumed morphology is consistent with atomic force microscopy images (unpublished data) and with the TEM images, which show unequal projected facet lengths at the goethite crystallite tips (see Sec. III A). An average specific surface area was then calculated. Second, specific surface area (SA_BET) was estimated using eleven-point adsorption data from the linear portion of N₂ adsorption isotherms47 in the relative pressure range 0.05–0.2 using BET theory. Prior to BET analysis, samples were degassed for 12 h at room temperature (24–34°C).

Figure 2 shows XRD patterns for each particle type. The patterns clearly show that both the microrods [Fig. 2(a)] and the nanorods [Fig. 2(b)] are goethite with no peaks consistent with six-line ferrihydrite or hematite observed. The pattern [Fig. 2(c)] for 6 nm-6LF particles clearly shows that this material is six-line ferrihydrite, and no peaks consistent with goethite or hematite were observed. In contrast, the pattern for the 4 nm-6LF particles shows that the material is predominantly six-line ferrihydrite with a small amount of goethite. In order to estimate the goethite to ferrihydrite ratio, an XRD pattern from a mixture of known goethite and ferrihydrite masses was collected, and by comparing to Fig. 2(d), the goethite content of 4 nm-6LF was estimated to be approximately 10 wt %. In addition, by quantifying the full width at half maximum of the goethite {011} peak and using the Scherrer equation,48 an average goethite size of 3.5 nm was calculated.

The average specific surface areas (SA_BET and SA_TEM) for each particle type, along with w_TEM and L_TEM, are shown in Table I, and representative TEM images are shown in Fig. 3. In the cases of 6 nm-6LF, nanorods, and microrods, the SA_BET and SA_TEM values are similar, although the former are consistently and slightly lower than the latter. This probably reflects a small amount of aggregation due to drying. However, SA_BET for 4 nm-6LF is inexplicably high. Thus, surface-area-normalized rate constants calculated using SA_TEM were deemed most appropriate for comparisons between the ferrihydrite nanoparticles.

The anticipated half reactions and overall reaction of ferrihydrite [Eq. (1)] or goethite [Eq. (2)] with hydroquinone (QH₂) can be written as

2Fe₅HO₈·4H₂O(s) + l0e^- + 30H⁺(aq) → 10Fe²⁺(aq) + 24H₂O(1),

5QH₂(aq) → 5Q(aq) + 10e^- + 10H⁺(aq),

2Fe₅HO₈·4H₂O(s) + 5QH₂(aq) + 20H⁺(aq) → 5Q(aq) + 10Fe²⁺(aq) + 24H₂O(l),     (1)

10α- FeOOH(s) + l0e^- + 30H⁺(aq) → 10Fe²⁺(aq) + 20H₂O(1),

5QH₂(aq) → 5Q(aq) + 10e^- + 10H⁺(aq),

10α- FeOOH(s) + 5QH₂(aq) + 20H⁺(aq) → 5Q(aq) + 10Fe²⁺(aq) + 20H₂O(1).     (2)

The concentrations (in equivalents/L) of Q versus time for experiments using 2.0 g/L of 4 nm-6LF particles with 1.0, 0.50, 0.20, and 0.10 mM initial QH₂ are shown in Fig.4(a). Figure 4(b) shows an example of [Fe(II)] versus [Q] (in equivalents/L) for 2.0 g/L of 4 nm-6LF particles with 1.0 mM QH₂ confirms the expected reaction stoichiometry. Conversion of concentration to equivalents was based on the number of electrons transferred from QH₂ to Fe(III) and reflects the 2:1 Fe(II):Q reaction stoichiometry [Eqs. (1) and (2)]. NMR confirms QH₂ and Q as the only organic products of the reactions (results not shown). QH₂ blanks showed rates of oxidation to Q two orders of magnitude slower than the slowest observed rate of reaction with oxide (results not shown). Dissolved Fe(II) was not observed in any particle blanks (results not shown). Previous work shows that Fe(II) adsorbs onto Fe(III) oxide surfaces,49 and based on that work, less than 10% of the total Fe(II) was expected to adsorb onto the nanoparticles. In all cases, results were consistent with that expectation.

For Semiquantitative comparisons between different phases, initial rates were computed by fitting the linear portion [solid lines shown in Fig.4(a)] of the graph to a least squares regression following the method of initial rates. 50 Rate constants and reaction orders with respect to both QH₂and the reactive surface sites can be found using Eq. (3) (adapted from the method used by Stack et al.40)

d[Q]/dt = r = k[QH₂]^m[S]ⁿ,     (3)

where r is the rate of formation of Q, k is the rate constant, [QH₂] is the initial concentration of QH₂ used, m is the reaction order with respect to QH₂, [S] is the initial concentration of reactive surface sites, which is assumed to be proportional to the total oxide concentration at time zero, and n is the reaction order with respect to the reactive surface sites. An example of the log-log graph used to determine m for 4 nm-6LF is shown in Fig. 4(c), and an example of the log-log graph used to determine n for 4 nm-6LF is shown in Fig. 4(d). Reaction orders and rate constants for all particle types are presented in Table II, and all errors listed represent standard errors. Comparing the surface-area-normalized rate constants demonstrates that the ferrihydrite rate constants are up to two orders of magnitude larger than those for goethite. This is unsurprising since previous results have demonstrated that ferrihydrite is substantially more reactive than more crystalline iron oxides (i.e., goethite, hematite, etc.), and this was attributed to differences in crystallinity. 7928293031 Thus,100-fold greater reactivity observed for ferrihydrite versus goethite is most likely due to a combination of greater crystallinity and larger size of the goethite particles in comparison to the ferrihydrite particles.

The method of initial rates, which uses only the initial, linear portion of the data, provides for excellent, semiquantitative comparison between the goethite and ferrihydrite samples. However, it is not adequate for a quantitative comparison between the 4 nm-6LF and 6 nm-6LF ferrihydrite samples and the nanorod and microrod goethite samples. In order to refine the quantitative comparisons, the data were fit using one-dimensional (1D) diffusion kinetics for ferrihydrite and two-dimensional (2D) diffusion kinetics for goethite. These diffusion models are based on the idea that the kinetics are governed by the movement of the particles through the solution.

In the case of the spherical ferrihydrite particles, 1D diffusion kinetics yield the best fits since the particles essentially act as spheres moving through the solution, and this is consistent with the approach used by Dold. 51 Using Eq. (4),52 in which r represents the 1D dissolution rate and α represents the fraction of solid dissolved at any given time, t, the data were fit by minimizing the unsigned mean error between the data and the model curve,

α² = rt.     (4)

An example is shown in Fig. 5 for 4 nm-6LF (closed circles) and 6 nm-6LF (open circles) using 0.1 mM QH₂ and 2.0 g/L particles with the model curves shown as solid and dashed lines. Since r changes with [QH₂] and [S], the 1D rate constants and reaction orders with respect to both QH₂ and reactive surface sites were determined using Eq. (3). After finding r for each experiment, m, n, and k were found using the above-described log-log graphing method. Reaction orders and rate constants for 4 nm-6LF and 6 nm-6LF are presented in Table III. Results clearly show that 1D, SA_TEM normalized rate constants for the 4 nm-6LF nanoparticles are up to 16 times larger than for the 6 nm-6LF nanoparticles. This is a large difference, with the smaller particles exhibiting a substantially higher reactivity than the larger particles.

Alternative explanations for the reactivity difference include the presence of trace goethite in 4 nm-6LF, the presence of carbonate in 4 nm-6LF, and a possible difference in crystallinity between the 4 nm-6LF and 6 nm-6LF samples. The presence of goethite in 4 nm-6LF most likely means that the reactivity difference observed is a minimum estimate because goethite particles are dramatically less reactive than ferrihydrite particles (Table II). Next, 4 nm-6LF particles were prepared using carbonate while 6 nm-6LF particles were prepared without addition of carbonate (see methods, Secs. IIA and IIB). Preliminary results using similarly sized particles that were prepared with and without carbonate suggest a small decrease in reactivity with the inclusion of carbonate (reductive dissolution is only 1.3 times faster for the carbonate-free particles). This suggests, again, that the reactivity difference observed is a minimum. Finally, it is possible that the reactivity difference is due to a crystallinity difference between the ferrihydrite samples. XRD patterns demonstrate that both ferrihydrites can be clearly classified as six-line ferrihydrite. However, the pattern for 6 nm-6LF exhibits narrower peaks than does the pattern for 4 nm-6LF, which could be attributed to both a larger particle size and a higher degree of crystallinity. TEM results demonstrate a difference in particle size, which suggests that the primary difference between these two ferrihydrites is one of size. It is likely that surface energy varies as a function of size,2 and such an effect could be a consequence of the relative number of atoms at kinks versus facets and the relative number of atoms contained at or near the surface in comparison to the bulk. We conclude that the size-dependent reactivity observed here is a direct consequence of a difference in surface energy between these materials and that the surface energy of 4 nm-6LF is greater than that of 6 nm-6LF. Finally, the difference in reaction orders is interesting. This result suggests that the mechanism by which the reductive dissolution occurs may change as a result of the synthetic procedure (i.e., the use of carbonate).

For the acicular goethite particles, 2D diffusion kinetics yield the best fits since the particles act as cylinders moving through the solution, and this is consistent with the approach used by Houben. 29 Using Eq. (5),52 in which r represents the 2D dissolution rate and α represents the fraction of solid dissolved at any given time, t, the data were fit by minimizing the unsigned mean error between the data and the model curve,

(1 - α)In(1 - α) + α = rt.     (5)

An example is shown in Fig. 6 for nanorods (closed circles) and microrods (open circles) using 0.1 mM QH₂ and 2.0 g/L with the model curves shown as solid and dashed lines. Since r changes with [QH₂] and [S], the 2D rate constants and reaction orders with respect to both QH₂ and reactive surface sites were determined using Eq. (3), as described earlier. Reaction orders and rate constants for nanorods and microrods are presented in Table IV. Results clearly show that both the SA_TEM and SA_BET normalized, 2D rate constants for the nanorods are nearly two times larger than for the microrods, which is a significant but not large effect. The nanorods in this study have dimensions near the quantum refinement regime 53 – that is, the smallest dimension (h, in Fig. 1) is approximately 4 nm, on average. However, recent work has shown that quantum size effects are shape dependent and that these effects are weakened in rod-shaped particles. 53 Thus, we conclude that the overall size of the nanorods is likely near the maximum size at which such quantum size effects could be observed. While it is difficult to predict what effect the quantum refinement would have on the relative rates of reduction, that the minimum dimension is near the maximum size at which such quantum size effects could be observed suggests that the reactivity difference observed is not due to quantum refinement. A final consideration is defects, which are known to cause higher reactivity. 5455 Variations in contrast in TEM images, taken at multiple tilt conditions, demonstrate that the microrods have a much higher concentration of defects than the nanorods. Thus, we conclude that the twofold difference is an underestimate of the reactivity difference that would be expected solely as a result of size effects.