Pore-Size-Dependent Calcium Carbonate Precipitation Controlled by

May 9, 2014 - Induced mineral precipitation is potentially important for the remediation of contaminants, such as during mineral trapping during carbo...
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Pore-Size-Dependent Calcium Carbonate Precipitation Controlled by Surface Chemistry Andrew G. Stack,*,† Alejandro Fernandez-Martinez,‡,§ Lawrence F. Allard,∥ José L. Bañuelos,† Gernot Rother,† Lawrence M. Anovitz,† David R. Cole,⊥ and Glenn A. Waychunas# †

Chemical Sciences Division, Oak Ridge National Laboratory, P. O. Box 2008, MS-6110, Oak Ridge, Tennessee 37831, United States Université Grenoble Alpes, ISTerre, F-38041 Grenoble, France § CNRS, ISTerre, F-38041 Grenoble, France ∥ Materials Science & Technology Division, Oak Ridge National Laboratory, P. O. Box 2008, MS-6064, Oak Ridge, Tennessee 37831 United States ⊥ School of Earth Sciences, Ohio State University, 275 Mendenhall Laboratory, 125 South Oval Mall, Columbus, Ohio, 43210, United States # Earth Sciences Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, MS74R316C, Berkeley, California 94720, United States ‡

S Supporting Information *

ABSTRACT: Induced mineral precipitation is potentially important for the remediation of contaminants, such as during mineral trapping during carbon or toxic metal sequestration. The prediction of precipitation reactions is complicated by the porous nature of rocks and soils and their interaction with the precipitate, introducing transport and confinement effects. Here X-ray scattering measurements, modeling, and electron microscopies were used to measure the kinetics of calcium carbonate precipitation in a porous amorphous silica (CPG) that contained two discrete distributions of pore sizes: nanopores and macropores. To examine the role of the favorability of interaction between the substrate and precipitate, some of the CPG was functionalized with a self-assembled monolayer (SAM) similar to those known to enhance nucleation densities on planar substrates. Precipitation was found to occur exclusively in macropores in the native CPG, while simultaneous precipitation in nanopores and macropores was observed in the functionalized CPG. The rate of precipitation in the nanopores estimated from the model of the X-ray scattering matched that measured on calcite single crystals. These results suggest that the pore-size distribution in which a precipitation reaction preferentially occurs depends on the favorability of interaction between substrate and precipitate, something not considered in most studies of precipitation in porous media.

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of fluids since there is a superlinear dependence of permeability on mean pore diameter.6 The efficacy of cap-rocks that seal carbon storage reservoirs could potentially be enhanced by a preference for precipitation in large pores since the precipitated material would reduce communication along faults and fractures that might comprise the dominant leakage pathway. Previous work has shown inhibition of precipitation in nanopores in silica aerogel (pore diameters of 100−500 nm) exposed to aqueous solutions supersaturated with respect to sparingly soluble salts.1,7 Consistent with the results from the gels, a preference for precipitation in large pores and inhibition of precipitation in nanopores has also been documented in natural cements in rocks.8−10 This phenomenon has been

INTRODUCTION Complicating our ability to predict environmental and geochemical reactions in soils and the subsurface is that these materials are porous in nature. Porous media are commonly known to affect the transport of dissolved species, inhibit mixing of fluids, and greatly diminish the ratio of fluid volume to mineral surface area relative to bulk solution. What is less well-known is how porous media affect the nature of the reactions themselves and if they contain any intrinsic pore-size dependence.1 Any pore-size-dependent reactivity could strongly affect the overall reactivity of a rock or soil because nanopores can dominate internal surface area.2 This becomes important, for example, when precipitation is induced in mineral trapping for carbon sequestration3 or to sequester toxic metals:4,5 the effective storage capacity of the porous medium will be determined by how much of the total pore space is filled with precipitate. A preference for precipitation in larger pores in particular could have disproportionate effects on the transport © 2014 American Chemical Society

Received: Revised: Accepted: Published: 6177

December 13, 2013 May 9, 2014 May 9, 2014 May 9, 2014 dx.doi.org/10.1021/es405574a | Environ. Sci. Technol. 2014, 48, 6177−6183

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rationalized as a “pore-size controlled solubility” (PCS) effect, that calls for a higher solubility for precipitates in small pores due to an increased radius of curvature of the precipitate nuclei induced by the pore walls.9−11 The concept of a threshold supersaturation has also been used, wherein the supersaturation needed to induce precipitation is in excess of that required in bulk solution.8 In contrast, recent statistical physics simulations suggest that the presence of nanopores should reduce the thermodynamic barrier for nucleation, because of a lower surface-energy-to-volume ratio for a nuclei precipitating in a nanopore versus a flat substrate.12 This prediction has not been validated experimentally, but explicitly includes the interaction between the precipitate and the pore wall, whereas PCS theory does not. Here we show that the degree of favorability of interaction between substrate and precipitate is a controlling factor on the size distribution of pores in which precipitation reactions occur, with more favorable interactions allowing precipitation to occur in smaller pores. These results partially resolve these potentially conflicting views. Calcium carbonate was chosen as the precipitate of interest because of its importance as a potential mineral trap during long-term carbon sequestration,13 its proposed use as a host phase for strontium contamination,4,5 and its ubiquity as a biomineral.14 Controlled pore glass (CPG), a mesoporous amorphous silica, was used as a substrate because it is chemically similar to sandstones, yet contains discrete distributions of pores which are more easily interpreted and analyzed than the continuous distributions of pores observed in rocks.2,15 CPG consists of conchoidally fractured amorphous silica grains several tens of micrometers in diameter, each grain of which is nanoporous (Figure 1). Thus, a packed sample of

deionized (DI) water (18.2 mΩ-cm) and exposed to 0.2 M hydrochloric acid for 2 h, and again washed with water and dried in nitrogen gas. Lastly, the sample was exposed to 20 wt % anhydrous toluene solution of 3-(triethoxysilyl)propylsuccinic anhydride for 24 h, then washed with acetone and dried by nitrogen gas. Successful adherence of the SAM was confirmed by transmission Fourier transform infrared spectroscopy (FTIR), but coverage density was not measured explicitly. In small angle X-ray scattering (SAXS), regular inhomogeneities in the electron density of a sample, such as those created by a distribution of nanopores, causes X-rays to scatter at a small angle relative to the original beam.18 Rather than report the scattering as a function of angle, it is normally reported as the modulus of the scattering vector, or the momentum transfer (Q), to make it independent of the wavelength of the incident beam. By monitoring the scattering intensity as a function of Q over time, one can detect density changes in a sample, such as due to filling the pores with a material of different scattering length (electron) density. Here, measurements were performed at the Advanced Light Source at Lawrence Berkeley National Laboratory (beamline 7.3.3, SAXSWAXS). CPG samples were inserted into a ∼1 cm length of Kapton capillary (ID = 0.0813 cm), backed by glass wool and placed inside of another Kapton capillary (ID = 0.1461 cm), through which solutions were allowed to flow. This setup maintained a constant cross-sectional density of CPG and solution in the X-ray beam over the course of a single experiment, allowing SAXS patterns taken at different times to be quantitatively compared. Solutions flowed continuously through the capillary over the course of the experiment using peristaltic pumps at the inlet and outlet with a flow rate of ∼100 mL/h. Deionized (DI) water was initially pumped through the capillary to ensure the samples were wetted, followed by introduction of the supersaturated solution. Samples were exposed continuously to the X-ray beam over the course of an experiment, with SAXS patterns taken at 1 min intervals. The diffraction pattern of silver behenate was used as an internal standard to calibrate sample−detector distances at maximum momentum transfer (Q). Background subtraction was performed using an empty capillary. Data masking, calibration, and reduction was performed using the NIKA (Argonne National Laboratory)19 data reduction macros for the Igor Pro (Wavemetrics, Inc.; Lake Oswego, OR, USA) software package. Solutions used here were prepared using a constant supersaturation of calcium carbonate. This solution was prepared by mixing 996 mL of DI water with 1 mL each of 0.5 M Na2CO3 and 0.5 M NaHCO3 and 2 mL of 1.0 M CaCl2. Solution composition was calculated using the PHREEQC code (U.S. Geological Survey) with the Minteq v4 database.20 The saturation index (SI) with respect to calcite of this solution at 25 °C is 0.79 with [Ca2+]/[CO32−] = 107 (SI = log(aCaaCO3/ Ksp); Ksp = 10−8.48). Stock solutions were not treated as equilibrated with atmosphere (these were made a few days prior to an experiment and kept closed). For a given experiment, one liter of solution was prepared immediately prior to the start of the experiment. The solutions were apparently metastable, that is, no visible precipitation in the solution reservoir was observed over the course of the experiment. Scanning transmission electron microscopy (STEM) and energy dispersive spectrometry were performed on a JEOL

Figure 1. Scanning electron microscope micrographs of CPG-75. Each grain of CPG is nanoporous (8.1 nm diameter) and the intergranular spaces form macropores.

these materials contains two distributions of pores: the intergranular spaces, which we will refer to as macropores, and the nanopores. To tune the favorability of interaction between substrate and precipitate, some CPG was functionalized with a self-assembled monolayer (SAM) containing an anhydride with a polar functional group. SAMs have been shown to enhance nucleation densities during precipitation by 1 to 2 orders of magnitude on planar substrates in biomineralization studies.16,17

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EXPERIMENTAL AND MODELING METHODS CPG was obtained from Millipore (Lincoln Park, NJ, USA). Two samples were used as received: CPG-75 and CPG-350, with nominal mean nanopore diameters of 8.1 and 31.8 nm, respectively (reported by manufacturer). The CPG-75 sample functionalized with the anhydride-terminated SAM was modified at the Molecular Foundry, a U.S. Department of Energy funded Nanoscience Research Facility. The procedure for this was as follows: CPG was washed with distilled, 6178

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Figure 2. SAXS intensity as a function of Q showing the precipitation of calcium carbonate in CPG-75. The 8.1 nm nanopore distribution results in a peak at ∼0.3 nm−1. (a) Native CPG. Significant increases in scattering over time occur at low Q but no changes are observed in the nanopores, indicating that precipitation occurs in macropores but not nanopores. (b) SAM-functionalized CPG (SAM structure shown in inset). The precipitation proceeds through three distinct phases denoted by color: 0−10 min, no changes in nanopores small changes in macropores (green/ black), 12−20 min large changes in scattering from nanopores (blue/light blue) and 22−34 min no further changes in nanopores, continued changes in macropores (red).

or genetic algorithm). Here, a variety of different form and structure factors were tested to find an optimum description of the data. It was found that the “core-shell” form factor22 coupled to the interprecipitate structure factor23 and assuming Gaussian distributions of pores gave an accurate description of the data with a minimum of fit parameters. In the core−shell model, each pore (i.e., the core) is treated as spherical and is partially or completely occluded by a homogeneous coating of precipitated material (i.e., the shell) (schematic in Supporting Information, Figure S2c). Two sets of form and structure factor combinations were used, one set each for the macropores and nanopores. It is possible that other fit functions could provide an equally good fit to the data. While nonspherical pores such as cylinders are possible to model, this requires an increased number of fit parameters and in practice, we did not observe a noticeably better fit using cylinders so have refrained from attempting to model complex pore geometries. The fitting routine was as follows: initial guesses for fit parameters of the core were made on the first data set (collected prior to the precipitation reaction). Shell thicknesses were fixed at zero and fitting done solely on the CPG pore distributions prior to injection of the supersaturated solutions. The X-ray scattering lengths for the CPG and water were fixed at 19.23 × 1010 cm−2 and 9.42 × 1010 cm−2,21 respectively. Once the model is calibrated on the unreacted CPG, the best fit parameters describing the CPG were then fixed for subsequent fitting of the precipitation reaction. The model was next fit to the last data set collected by allowing the nanopore and macropore shell thicknesses and their X-ray scattering length densities to vary. The X-ray scattering length of the shell material was then fixed, and the remainder of the time series fit

2200FS STEM/TEM instrument at the Advanced Microscopy Laboratory (AML) at Oak Ridge National Laboratory. Functionalized CPG samples for these measurements were prepared in the same way as described in the SAXS experiments above, and a supersaturated solution (same composition) flowed through the CPG for 3.5 h. The CPG was removed from the capillary, centrifuged at 14k rpm for 6 min and the supernatant was decanted. Samples were then suspended in ethanol and evaporatively deposited onto a beryllium TEM grid (used in a “low-background” specimen holder, to minimize the contribution of Cu to the spectrum from a standard Cu specimen grid, and from the standard specimen holder). By imaging the same location for approximately an hour and comparing the initial and final images, the CPG and calcium carbonate precipitate were both found to degrade in the STEM beam (Supporting Information, Figure S1). Imaging time in any one area of the sample was therefore minimized to minimize changes in the sample. Scanning electron microscopy to characterize CPG morphologies was performed using an Hitachi S-4800 SEM, also at the AML. Modeling of the SAXS patterns was performed using the IRENA software package21 and Igor Pro. In fitting SAXS data, one generates a model scattering function by providing an initial guess about the mean size and distribution width of scattering objects (i.e., the form factor), in this case pores, their scattering length densities, and how the scattering from nearby objects interferes (i.e., the structure factor). The scattering intensity as a function of Q is calculated and compared to the measured intensity. Parameter values are then adjusted iteratively to produce the closest fit possible between experiment and model (e.g., using a χ2 goodness-of-fit statistic 6179

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scattering. For the functionalized CPG, the decrease in scattering in the nanopores is likely due to a large number of nuclei that form and coat and/or fill the interior of the nanopores and reduces the contrast to X-rays and the volume of the nanopores. The initial increase of scattering in the macropore region of the curve is likely due to some nuclei forming in the macropores similar to the case of the native, but the subsequent reduction in scattering after the nanopores are filled may be due to coating of the exterior of the CPG grains with calcium carbonate. Ultimately a conclusive interpretation of the scattering in the macropores is elusive since much of the reactions are happening outside the accessible Q-range of the instrument. To confirm the identity of the precipitated material, highangle annular dark-field (HAADF) and bright-field (BF) scanning transmission electron microscopy (STEM) images and energy-dispersive X-ray spectroscopy (EDS) hypermaps were obtained on functionalized CPG reacted to the same supersaturated solution as the SAXS data. The results are shown in Figure 3. The unreacted material contains very little

using the nanopore and macropore shell thicknesses as the only remaining adjustable parameters. This was done in order to provide the most robust fit possible. By using this method, we assume that the precipitation of the CaCO3 is homogeneous and can be represented by an average shell thickness. It is unclear what the effect would be on the fit quality if this were not true, for example, if there was a heterogeneous coverage of precipitate, but it is most likely that it would cause the fitted shell thickness to be representative of a statistical average over the entire sample.

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RESULTS AND DISCUSSION SAXS intensity as a function of momentum transfer (Q) and time for the native and functionalized CPG are shown in Figure 2. On these plots, objects further apart (and generally larger) are located at smaller Q and objects closer together (generally smaller) are at larger Q, with an instrument range of ca. 3−160 nm distance (Q is related to distance between scatterers, d, and the traditional powder diffraction 2θ via |Q| = 2π/d = 4π sin(θ)/λ). CPG-75 contains a distinctive peak at a Q-value diagnostic of the mean distance between nanopores, ∼27.0 nm. The characteristic distances between macropores, if any, were outside the accessible Q-range of the instrument and thus the scattering intensity does not plateau or peak at low Q. For the native CPG (Figure 2a), no change in the amount of scattering from the nanopore peak was observed over the course of 1.75 h under constant flow of a supersaturated solution. A statistically significant increase in scattering intensity is observed at low Q, indicating that precipitation occurred in macropores. Control experiments where DI water was allowed to flow through the CPG showed no changes in scattering intensity over time (data not shown). Data from CPG-350 (31.8 nm pores) also showed changes in scattering intensity dominantly in macropores (Supporting Information, Figure S3). In contrast, the anhydride-SAM functionalized CPG shows a complex evolution of scattering intensity over time. In the first ∼10 min, no changes in scattering from nanopores were observed, but slight increases in scattering within macropores were detected (Figure 2b). From ca. 10−20 min, there was a sharp reduction in scattering intensity from the nanopores (relative to the native CPG), and continued increases in scattering intensity from macropores. In the final ∼12 min, no further changes in scattering from nanopores were observed, but decreases in scattering were observed in the macropores. It is clear from these results that precipitation in nanopores can be driven by the functionalized CPG. The different trends in scattering over time in nano- and macropores in both the native and functionalized CPG indicate different processes that are occurring within the CPG samples over the course of the experiments. In general, X-ray scattering intensity will increase when there is an increased number of primary particles (scattering objects), consisting of interfaces between phases with high contrast to X-rays, such as silica−water or calcium carbonate−water (see below for quantitative values of the X-ray scattering densities that determine the contrast). Scattering intensity will be reduced if the contrast between scattering objects is reduced, such as when a silica−calcium carbonate interface forms in place of a s−water. In native CPG, the increase in scattering observed in the macropore Q range is therefore likely due to a small number of nuclei that form within the macropores, each nuclei of which grows rapidly. The nuclei increase the amount of high contrast surface area and hence increases the contrast for

Figure 3. STEM images and EDS hypermaps of elemental distributions for the SAM-functionalized CPG-75. Green boxes show areas selected for EDS. Only background counts of calcium are detected in the unreacted sample, but abundant calcium and a change in the STEM image contrast is detected in the reacted sample.

calcium, whereas the reacted material contains significant amounts, as well as changes in contrast in the STEM images. In some cases, much larger calcium-containing nuclei were observed (Supporting Information, Figure S1). One possible source of these larger nuclei could be an incomplete coating of the SAM on the CPG. The EDS results and changes in contrast in the STEM images show that the changes in scattering intensity are likely due to precipitation of calcium carbonate rather than dissolution and reprecipitation of the CPG itself. What was not observed were lattice-fringes indicating a crystalline material. Thus, what precipitated was most likely a form of amorphous calcium carbonate, but the precise composition is not clear. Our results on the native CPG are consistent with previous experimental work that shows that precipitation of other sparingly soluble salts in porous silica occurs preferentially in 6180

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large pores.1,7 As described above, the observed inhibited precipitation in smaller pores has been usually attributed to the PCS effect9,10 in which an energetic term must be overcome.24 Specifically, according to the Young−Laplace equation, the pressure difference, Δpsl, across a solid−liquid (sl) interface is proportional to the curvature of the interface, κsl, with the interfacial tension being the proportionality constant: Δpsl = γslκsl = RT ln(a /a0)/Vm

rate used here (100 mL/h), these realities together suggest that fluid transport to the nanopores is not likely limiting the precipitation (see Bracco et al.5 for detailed analysis of transport control for growing calcite). However, the possibility that unequal concentrations of Ca2+ and CO32− are present in the nanopores cannot be totally excluded. The nanopores could be acting as chemically selective membranes, limiting carbonate transport into the nanopores due to the negative charge of their SiO2 walls at the solution pH used here (pH ≅ 8.4). In this scenario, the terminal moiety of the SAM-functionalized CPG may promote transport of both calcium and carbonate into the pores. SAMs have been shown to enhance both the kinetics and overall coverage of nucleation on planar substrates where transport is not an issue,16 so an enhancement due to transport is not required to explain these results. This result points to the predominant effect of the surface chemistry over any confinement effects in controlling nucleation in nanoporous systems. The scattering data in Figure 2b can be modeled quantitatively. The mean fitted nanopore radius of the functionalized CPG-75 was 6.9 nm using a core−shell model with a Gaussian distribution half-width, half-maximum of 1.7 nm and an interprecipitate interference function. The nanopore radius is larger than the manufacturer’s specification (4.1 nm), which could be an artifact of assuming spherical pores in the model when the actual pores are elongate, due to some irregularity in the pore structure (Figure 1), or just different model-dependent results. The fitted mean distance between pores is 17.1 nm, consistent with the nanopore peak position in Figure 2. The fitted macropore radius was ∼5 μm with a halfwidth, half-maximum of ∼30 nm. While this is a reasonable estimate for the size for pores of a closest-packed structure of the CPG grains (Figure 1), this is well outside the accessible distance (or Q) range of the instrument so the fits may have large uncertainty. The best-fit X-ray scattering length density for the shell material is 19.68 × 1010 cm−2 for the nanopores and 21.79 × 1010 cm−2 for the macropores. These do not precisely match calcite (23.74 × 1010 cm−2), nor bulk amorphous calcium carbonate (13.74 × 1010 cm−2), but are close to calcium carbonate monohydrate (20.52 × 1010 cm−2).21 We speculate that this match is an artifact due to the assumption within the model that the shell material occludes all pores simultaneously. It is likely that inhomogeneity of precipitation leaves some pores containing mixed solution and precipitate within the area treated as “shell” material in the model, but we cannot distinguish between water contained within the structure of the precipitated material and water located between precipitate grains. The quality of the two representative fits and their deconvolution are shown in the Supporting Information, Figure S2. The calculated shell thickness inside the nanopores as a function of time are shown in Figure 4a. This analysis confirms that the reaction proceeds through three distinct stages, with an initial lag for the first ca. 10−15 min, followed by a nucleation/ precipitation event in the nanopores indicated by rapidly increasing shell thickness, and at last a cessation of precipitation. The initial lag may be due to a delay in the amount of time needed for the supersaturated solution to make it to the sample cell after it was introduced, but may also be affected by an induction time for formation of the calcium carbonate nuclei. After cessation of the reaction, the fitted shell thickness (5.3 nm) does not occupy the entirety of the original fitted nanopore radius (6.9 nm). We speculate that this is

(1)

where κsl = 2/r, in the case of a spherical pore of radius r, and γsl is the interfacial free energy. The right half of eq 1 is imposed as a condition for equilibrium in the case of a small precipitate nucleus or a nucleus in a pore (assuming that crystal and pore have the same shape).10 Vm is the molar volume of the precipitating phase (in m3/mol), a is the concentration of reactant, a0 is its concentration in equilibrium with a solid phase, R is the ideal gas constant, and T is the temperature. Solving for the radius, r, gives r=

2Vmγsl RT ln(a /a0)

(2)

This formalism allows one to evaluate if the effect of the curvature is enough to explain the observed inhibition of nucleation in the pores by calculating the size of the critical radii (rc) for nucleation in bulk solution (i.e., homogeneous nucleation) and in nanopores. Under the experimental conditions used, and assuming calcite as the nucleated phase (Vm = 3.69 × 10−5 m3/mol; γsl = 0.094 J/m2),25 rc = 1.5 nm. Using eq 2 we can also calculate the effective solubility of calcite in a pore of radius r. Results indicate that a 8.1 nm diameter pore should hold a threshold supersaturation (a/a0) that is 2.1 times higher than bulk solution, while a pore of 31.8 nm diameter holds a supersaturation 1.2 times higher than the bulk without precipitation. The critical radii of nuclei formed in the nanopores can also be calculated by applying eq 2 again with these modified solubilities to replace the bulk solubility. This yields values smaller than the pore sizes, 2.6 and 1.7 nm for the 4.1 and 15.9 nm radius pores, respectively. However, given the STEM evidence in Figure 3 and the SAXS fitting discussed later, the precipitated material may not be calcite and may be amorphous calcium carbonate (ACC) (nominally CaCO3· H2O)26 (Vm = 5.39 × 10−5 m3/mol)27 or monohydrocalcite (CaCO3·H2O) (Vm = 4.88 × 10−5 m3/mol).28 We do not know the interfacial energy for these phases (likely lower, which reduces the critical radius size), but assuming it is the same as calcite yields critical nuclei sizes of 3.7 and 2.5 for ACC and of 3.4 and 2.3 nm for monohydrocalcite for the 4.1 and 15.9 nm radius pore sizes, respectively. In none of these possibilities is the critical nucleus size larger than the size of the pores, which means that pore-size controlled solubility effects can be neglected in this system under the experimental conditions used here. This data raises the possibility that other factors besides the radius of curvature need to be considered to determine the rate of nucleation events in the nanopores, such as kinetic effects and the interaction energy between precipitate and substrate. Another possible explanation for the observed inhibition of precipitation in nanopores could be that transport of dissolved calcium and carbonate is limiting the rate of precipitation. Our SANS experiments showed that the nanopores are completely filled by an aqueous solution that is readily replaced (see Supporting Information, Figure S4). Coupled to the fast flow 6181

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in parameter estimates. For example, the rate estimate will be reduced if it is indeed a hydrated and/or amorphous calcium carbonate phase that formed due to increased molar volumes relative to calcite described above. If the precipitate is treated as ACC or monohydrocalcite, the rate estimate is 57% and 64% that of calcite, respectively (Figure 4b), but these still fall within the 95% confidence intervals for the calcite rate model. Second, we have treated the surface area available for precipitation as a constant. After the initial nucleation event, the available surface area for precipitation may go up as surface area of precipitated material is created but then may then go down as the nanopores become occluded by precipitated material. Regardless, since the kinetics of precipitation fall within the 95% confidence intervals to what has been measured previously on single crystals of calcite, the result is encouraging. If the precipitated material is a hydrated or amorphous phase, this suggests that the heterogeneous growth rate of this phase is similar to that of calcite growth from seed crystals under these solution conditions. These results may enhance our understanding of the longterm storage security of carbon dioxide in the subsurface. We hypothesize that rocks in which constituent mineral grains represent a facile epitaxial substrate for the precipitating phase, for example, calcite precipitation in a limestone, will demonstrate behavior similar to the functionalized CPG. This is a desirable behavior in a rock being used as a reservoir for carbon dioxide or during induced precipitation, where one would want to use all available porosity to trap as much contaminant in a solid form as possible. Alternately, rocks whose constituent mineral grains present a low affinity for the precipitated phase, for example, calcite precipitation in a sandstone, may demonstrate behavior similar to the native CPG. This may act as a “sealing” behavior of any fractures in the cap-rock, enhancing the storage security of the site. This work will have implications for the modeling of precipitation/ dissolution in pore networks30,31 since any pore-size dependencies would need to be accounted for in reactive transport models, but the optimum functional form for this is not yet clear.

Figure 4. SAXS model fit results and rate estimates. (a) Black circles show the fitted shell thickness of precipitate in nanopores as a function of time. The horizontal red line shows the original fitted nanopore radius (6.9 nm). Blue circles plotted against the right axis show an estimated growth rate assuming that calcite precipitated, with a peak growth rate at ∼21 min. (b) The peak growth rate assuming different phases precipitated compared to growth rates from single crystals measured by AFM.29 The solid curve is a best fit model and dashed lines are 95% confidence intervals.

because nanopores near the exterior of the CPG grains become filled with precipitated material and block transport of solution to nanopores on the interior of the CPG grains. Once the shell thickness is known, an estimate of the precipitation rate can be made that depends both on the molar volume of the precipitated material (Vm) and the surface area available for precipitation (A). We assume that the original nanopore surface area (A = 6.0 × 102 nm2) is the best estimate for available surface onto which precipitation can occur and, initially, that the precipitated material is calcite (again, Vm = 3.69 × 10−5 m3/mol). The derivative of the shell thickness as a function of time yields the rate (mol/m2/s): rate =

1 dVshell VmA d t

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ASSOCIATED CONTENT

S Supporting Information *

Details of the SAXS fits, SAXS fits on CPG-350, SANS data, and additional TEM images. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

(3)

*E-mail: [email protected].

where t is time (seconds) and Vshell is the volume of precipitated shell material (m3): 4π 3 Vshell = [rorig − (rorig − rshell)3 ] (4) 3

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Research sponsored by the Center for Nanoscale Control of Geologic CO2, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number (DE-AC0205CH11231). Portions of this research were performed at Oak Ridge National Laboratory’s High Flux Isotope Reactor, sponsored by the U.S. Department of Energy, Office of Basic Energy Sciences. The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences,

where rorig is the radius of the original nanopore, rshell is the shell thickness from the SAXS curve fits (Figure 4a). The calculated rates follow the expected pattern, with an initial rate close to zero that increases to a maximum followed by a rapid decline back to zero (Figure 4a). Remarkably, the peak rate falls precisely on the trend line for a model fit to calcite single crystal growth rates measured using the atomic force microscope (Figure 4b).29 However, this remarkable agreement may benefit from a fortuitous cancellation of errors 6182

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of the U.S. Department of Energy under Contract No. DEAC02-05CH11231. Work at the Molecular Foundry was supported by the Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. Special thanks to Frantisek Svec (Molecular Foundry, Berkeley) for his help with the CPG functionalization and Francois Renard for fruitful discussions. ISTerre is part of Labex OSUG@2020 (ANR10 LABX56).

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dx.doi.org/10.1021/es405574a | Environ. Sci. Technol. 2014, 48, 6177−6183