Electrical Responses of Modified Mineral Surfaces as Observed With Spectral Induced Polarization and Atomic Force Microscopy

Atomic force microscopy (AFM) and spectral induced polarization (SIP) are widely used to investigate the electrical properties of mineral surfaces at vastly different scales of measurement. We compare AFM and SIP measurements made on two different materials (glass beads and silica gel) subjected to etching, deposition of iron oxide particles, and inclusion of calcite grains. We found that the treatments produced qualitatively consistent behaviors in the AFM and SIP data. Direct AFM measurements of surface charge density for silica and calcite surfaces were quantitatively compared to values estimated from the SIP results using a grain polarization model. No statistically significant difference (at a 95% confidence level) was found between the surface charge density of silica estimated by AFM (2.3 ± 6.6 mC/m2 for glass beads and 1.6 ± 0.1 mC/m2 for silica gel) versus SIP (5.4 ± 4.4 mC/m2 for glass beads and 1.6 ± 0.5 mC/m2 for silica gel). The surface charge density for calcite determined by AFM (43.5 ± 12.9 mC/m2) was approximately 19 times higher than that found for silica. While the charge density of calcite surfaces determined by SIP was also generally higher than that found for silica, different treatments produced significantly different values between 4.7 and 258 mC/m2 (with a maximum 95% CI of ±8.7 mC/m2). Several possible explanations exist for the range of the observed SIP measurements, including aging of the calcite surfaces. Overall, this study suggests the potential for the complementary use of AFM and SIP measurements to constrain future investigations of polarization mechanisms in porous media.


Introduction
Spectral induced polarization (SIP) is an increasingly important method for investigation of environmental processes in the subsurface.A variety of laboratory studies have investigated the dependence of SIP signals on biogeochemical processes, such as ionic adsorption and desorption (Hao et al., 2015;Vaudelet et al., 2011), mineral precipitation and dissolution (Placencia-Gómez et al., 2013;Wu et al., 2010;Zhang et al., 2012), and microbial growth in porous media (Davis et al., 2006;Mellage et al., 2018;Ntarlagiannis et al., 2005;Williams et al., 2009).These studies have shown that physical and biogeochemical processes can alter the pore structure and interfacial properties of the porous media, which in turn affect SIP signals.For instance, Koch et al. (2011) showed that compaction of a sample, which impacts pore size distribution but not grain size distribution, influences the frequency response of SIP signals.Hao et al. (2015) used radioactive 22 Na to show a direct correlation between SIP response and the mass of sodium ions sorbed to silica gel surfaces as the number of available sorption sites increased with pH.The study directly illustrated the importance of mineral surface charge density as a control on the complex conductivity of porous media, which is suggested by many mechanistic models for complex conductivity (Leroy et al., 2008).Among these studies, there has been a growing set of literature focused on understanding the effects of abiotic calcite precipitation in porous media on SIP measurements.For example, Wu et al. (2010) observed strong SIP responses in measurements between 100 and 1,000 Hz during the precipitation of calcite grains in columns of glass beads.Leroy et al. (2017) were later able to fit these responses using a grain polarization model.Recent experiments by Placencia-Gomez et al. (2023) observed SIP responses occurring at both low frequencies (0.001-0.1 Hz) and high frequencies (100-10,000 Hz) during calcite precipitation experiments using columns of soil from the Hanford site (WA, USA).These authors observed the high frequency response to be almost three times larger than the low frequency response.Bücker et al. (2019) provide an excellent historical perspective on models used to represent the SIP response of porous media and develop a new model to illustrate how the polarization of ions around calcite grains and in pore throats constricted by calcite precipitates contribute to SIP responses between 0.1 and 1000 Hz.While these and other studies typically presume that calcite precipitation is distributed throughout a porous medium, other behaviors may also occur.For example, Izumoto et al. (2022) recently showed that high frequency (100-10,000 Hz) SIP responses similar in magnitude to those observed by Placencia-Gomez et al. (2023) could be generated by the formation of a solid wall of calcite precipitated along a reaction front between solutions of CaCl 2 and Na 2 CO 3 in microfluidics experiments.Despite these and many other studies, there remains a lack of experimental evidence providing direct links between the electrical properties of mineralfluid interfaces, such as the surface of calcite precipitates, and the overall electrical response of a composite porous medium captured by SIP measurements.
Atomic force microscopy (AFM) allows for direct imaging of nanoscale heterogeneities at material interfaces and has been widely used to characterize both surface topography and surface charge density (Obeid et al., 2019;Taboada-Serrano et al., 2005).AFM operates by measuring the interaction forces between a charged cantilever tip and the material surface as the tip is scanned across the interface (Li et al., 2020).Deflection of the AFM tip toward or away from the mineral surface is a function of the magnitude of the surface charge relative to the fixed charge on the tip and the distance to the surface (Heinz & Hoh, 1999).Local surface charge density has been successfully determined by fitting force curves collected as the AFM tip is lowered toward a surface using Derjaguin-Landau-Verwey-Overbeck (DLVO) theory (Ducker et al., 1991;Heinz & Hoh, 1999;Pashley, 1981).For example, the linearized Poisson-Boltzmann equation can be used to directly obtain the local charge density on a surface as experienced by the AFM (Q AFM ): where Ψ is the force applied to the AFM tip to maintain it at a fixed distance D from the sample surface, Q tip is the charge density on the tip, R tip is the radius of the tip, ε f is the dielectric permittivity of the fluid, and κ 1 is the Debye length for the wetted surface.
The purpose of this study is to investigate how direct measurements of material surface properties determined via AFM relate to SIP signals measured in porous media.To this end, we vary the physical, chemical, and electrical properties of glass beads and silica gel by etching, deposition of iron oxide particles, and the addition of calcite.Furthermore, we adapt the complex conductivity model developed by Leroy et al. (2017) for calcite precipitation in granular media to estimate the surface charge density of silica and calcite surfaces in the samples based on the measured SIP data.The resulting surface charge density estimates are then quantitatively compared to direct measurements made by AFM to evaluate whether consistent estimates of surface charge density are obtained using these vastly different measurement approaches for investigating the surficial properties of a porous medium.

Background and Models for SIP Responses in Porous Media
Understanding of the behavior of electrolytes near a charged surface, such as the mineral interface of a porous medium, has evolved over the past one and half centuries as double layer theory.It is now generally understood that there is an excess concentration of counterions in the fluid near a charged surface relative to the bulk fluid (Striolo, 2011).The region immediately adjacent to the surface is called the Stern layer (or Helmholtz layer).
Counterions in this region are tightly bound to the surface, restricting them to tangential movements along the surface (Stern, 1924).Beyond the Stern layer, the surface potential decays resulting in a region of electrostatically attracted, loosely bound counterions known as the diffuse layer (or Gouy-Chapman layer).The concentration of counterions in the diffuse layer decreases with distance from the surface to approach that of the bulk fluid and ions in this region can move away from the surface to freely exchange with those in the bulk fluid (Grahame, 1947).
Triple layer models better represent the geochemical conditions of a mineral surface as they allow for different functional groups to be exposed at the terminal edge of the mineral crystal lattice (Davis et al., 1978) and account for differences in counterions bound to the mineral surface as inner or outer sphere complexes, respectively (Leroy et al., 2008).Overall, the concentration of ions present, their distance from the surface, and their distribution between tightly and weakly bound regions (i.e., Stern vs. diffuse layers) depends on the surface charge and ionic composition of the pore fluid.
In general, the material parameter of most interest in SIP is the frequency-dependent complex electrical conductivity (σ* = σ' + iσ").The real component of the complex conductivity (σ') is related to the ability of a porous medium to conduct charge, whereas the imaginary portion (σ") is related to the ability of the medium to store charge (Knight et al., 2010).In both cases, charged mineral surfaces play an important role as the migration of counterions in both the Stern and diffuse layer can contribute to these processes (Chapman, 1913;Gouy, 1909;Stern, 1924).For suspensions of colloidal particles, it is well known that the distribution of counterions in the diffuse layer can be shifted around an individual grain by an applied electric field to cause charge polarization (Dukhin et al., 1974;Schwarz, 1962;Vaudelet et al., 2011).In porous media, however, it is often thought that ions can migrate between grains as the diffuse layer effectively spans grain contacts, in which case the diffuse layer contributes primarily to charge conduction (σ') in parallel with electrolytic conduction in the bulk fluid of the pore space (Lesmes & Morgan, 2001).
The diffuse layer may also contribute to the imaginary conductivity by membrane polarization (Bücker et al., 2019).This mechanism of polarization takes place when cations and anions in the diffuse layer carry an unequal fraction of current due to constrictions in the pore space, such as at pore throats (Revil, 1999;Vaudelet et al., 2011).When pore throats or other constricted regions of the pore space are small compared to the thickness of the double layer the movement of ions may be restricted.As a result, an excess or depletion of ions may occur on either side of the constricted pore space or throat under an applied external electric field, thus producing a local charge imbalance, or polarization, that counters the applied field.The rate at which this polarization response occurs is reflected by the relaxation time constant τ.The relaxation time is controlled by the rate of mutual ion diffusion as ions return to a neutral state across a characteristic length for the medium, such as the square of the pore throat length (Román, 1973;Titov et al., 2002).
Unlike the free exchange of ions with electrolyte that occurs in the more distal diffuse layer, all counterions in the Stern layer are thought to be bound tightly enough to limit charge migration to tangential movement along the mineral surface under an applied electric field, which prevents these ions from transferring between individual grains.This restriction on ionic movement produces a polarization of charge across a mineral grain that is correlated to ion density (i.e., mineral surface charge), ion mobility, and size of the mineral particles (Schwarz, 1962).The effective grain diameter, d, can be related to a single Debye relaxation time for the porous medium, τ, as shown in Equation 2 (Leroy et al., 2017;Schwarz, 1962): where f b is the Debye relaxation frequency, D b is the diffusion coefficient of counter ions in the Stern layer, k is Boltzmann's constant (∼1.381 × 10 23 J/K), T is the absolute temperature, β b is the surface ionic mobility of counter ions in the Stern layer, and |q| is the magnitude of the counter-ion charge, that is, counter-ion charge number multiplied by the elementary charge (∼1.602 × 10 19 C).It is likely, however, that loosely bound ions in the diffuse layer also interact with more tightly bound ions in the Stern layer to impact the net polarization response of a porous medium.To account for this effect, Leroy et al. (2017) adopted the modification to τ proposed by Lyklema et al. (1983) where Equation 2 is multiplied by a factor 1/M, which is dependent on factors such as the type and concentration of electrolytes present in the bulk solution.
Mechanistic models that relate complex conductivity to grain polarizations controlled by geochemical conditions at functional groups on mineral surfaces have been developed using the triple layer model for porous materials that include clays (Leroy & Revil, 2004), glass beads (Leroy et al., 2008), sands (Skold et al., 2011), and calcite grains (Leroy et al., 2017).In the last of these examples, Leroy et al. (2017) modeled transient patterns of complex conductivity that were observed by Wu et al. (2010) during a flow experiment investigating how SIP signals change during the precipitation of calcite crystals within a column of glass beads.Leroy et al. assumed that the glass beads were insulators and did not contribute directly to the electrical response of the medium.The authors then used differential effective medium theory to determine the complex conductivity of the column (σ*) by combining the complex conductivities of the calcite particles (σ * s ) and water (σ * w ): where F = σ w /σ' = ϕ m is the formation factor (Archie, 1942), ϕ is porosity, and m is the empirical cementation exponent.We note that F represents an empirical estimate of the formation factor that does not separate out the effects of surface charge, as is done in some studies (e.g., Wang & Revil, 2020).Following Lesmes and Morgan (2001), the complex conductivity of the calcite particles (σ * s ) used in the mixing formula (Equation 3) was represented as a linear combination of values averaged over the grain size distribution of the porous medium.The complex conductivity of an individual calcite grain of diameter d is represented in the model as: where Σ b s is the specific surface conductivity of the Stern layer, Σ DC s is the DC specific surface conductivity which has only a real component and in practice was equated to the specific surface conductivity contributed by the diffuse layer, ε s is the surface dielectric permittivity of the calcite particles which captures Maxwell-Wagner interfacial polarization effects at high frequencies (>1 kHz), and ω is angular frequency of the applied electric field.Leroy et al. (2017) related the surface conductivity of the Stern layer to the surface charge density of adsorbed ions (Q b ) and ion mobility in this region (β b ): In addition, the value of τ in Equation 4 was modified from the form given in Equation 2 by a factor of 1/M, which reflects the effect of interactions between the diffuse and Stern layers impacting the timing of the polarization response (Lyklema et al., 1983); notably the diffuse layer does not impact the magnitude of the polarization response in the model, which is primarily dependent on Σ b s and grain diameter (Equation 6).
Leroy et al. ( 2017) estimated surface charge density using a geochemical surface complexation model for calcite, thereby allowing the authors to make predictive estimates of complex conductivity of a porous medium during calcite precipitation.These authors found that the model was able to accurately predict the transient σ′′ s spectra observed by Wu et al. (2010) during their calcite precipitation experiment, illustrating that the observed SIP response was consistent with grain polarization of the calcite crystals.Key parameters were assumed from the literature in these past modeling efforts, such as surface site density of functional groups on the mineral surface needed to estimate Q b and the mobility of ions in the Stern layer.

Materials and Methods
The study was conducted using glass beads (manufacturer: Sartorius) and silica gel (manufacturer: Sigma-Aldrich 236802, Grade 636) with grain diameters ranging from 0.25 to 0.3 mm and 0.25-0.5 mm, respectively.These materials have significantly different pore structures but are similar in terms of material composition.Glass beads approximate idealized spherical grains and are known to produce a minimal SIP response from prior work (e.g., Wu et al., 2010).In contrast, the silica gel grains have a high internal porosity (pore size = 6 nm per manufacturer specifications) that yields a higher specific surface area and SIP response than the glass beads, despite having a similar range of grain diameters (Hao et al., 2015).It was therefore expected that filling intergranular pore spaces between grains by precipitation would impact SIP responses of both materials in a similar way, but effects related to changes associated with the electrochemical properties of the silica surfaces would impact SIP measurements of the silica gel to a much greater extent than for the glass beads.
The glass beads were modified to achieve four kinds of treatments: untreated, etched, iron-oxide coated, and calcite coated.To etch the surface of the glass beads, grains were immersed in hydrofluoric acid and stirred for 2 hr before rinsing.The iron-oxide coated beads were prepared using the method provided by Szecsody et al. (1994).Acid-washed glass beads were mixed with a ferric oxyhydroxide slurry and allowed to equilibrate for approximately 24hr at pH 7.5.The mixture was then aged for approximately 3 days before washing with deionized water and letting the iron-oxide coated grains dry naturally.The calcite-coated glass beads were prepared by packing untreated beads in a column through which 0.05 M CaCl 2(aq) and 0.05 M Na 2 CO 3(aq) solutions were mixed via injection from ports located at the bottom and middle of the column respectively, thereby allowing for the precipitation of CaCO 3(s) on the beads and in the pore spaces of the column upon mixing of the fluids.This treatment is parallel to past experiments (e.g., Wu et al., 2010) and allows calcite crystals to form on silica surfaces, fill the pore space, and contribute to blockage of pore throats.
Five different conditions were investigated for the silica gel, which we refer to as: untreated, iron-oxide coated, calcite-evap, calcite-aged, and calcite-fresh.The iron-oxide coated silica gel was prepared following the same procedure described above for the glass beads.Two different procedures were used to introduce calcite to the silica gel.In the first procedure, calcite-evap, clean silica gel was placed in a saturated calcium carbonate solution that was slowly allowed to evaporate, concentrating the CaCO 3(aq) solution until a precipitate was clearly visible on the silica gel grains (i.e., 0.05 M solutions of CaCl 2(aq) and Na 2 CO 3(aq) were mixed to produce a 4L mixture, which was then mixed with the silica gel and reduced to 3.2 L).The goal of this procedure was to coat the surfaces of the silica gel with calcite while minimizing the presence of calcite grains in intergranular pore spaces.In contrast, the calcite-aged and calcite-fresh treatments attempted to fill the intergranular pore spaces between silica gel grains by mixing 5g of dry calcite powder with the silica gel prior to packing the mixture in experimental columns.Since the age and exposure of the material to the atmosphere could affect its surface properties (Flis & Kanoza, 2006;Sykora et al., 2010), commercial calcite powder that had been sitting on a shelf for several years was used to produce a sample of "aged" calcite (i.e., calcite-aged) and a calcite slurry precipitated in the lab was mixed with the silica gel to produce a sample containing "fresh" calcite (i.e., calcite-fresh).This treatment was expected to minimize membrane polarization effects compared to the glass bead sample where in situ precipitation could cause blockages of pore throats.
Representative samples of each treatment for both the glass beads and silica gel were imaged using a scanning electron microscope (SEM, Hitachi S3400) to provide a visual characterization of the effect of each procedure on the grain surface.The specific surface area of each material was determined using nitrogen physisorption (ASAP 2020 analyzer, Micromeritics Instrument Corp., USA) and the Brunauer-Emmett-Teller (BET) model.Characterization of the surfaces was conducted using an atomic force microscope (AFM, MFP-3D Asylum, Veeco Dimension 3100).Both the untreated glass beads and silica gel surfaces were investigated to determine whether these materials had consistent surface charge densities.Given that we expect the local nanoscale electrochemical response of the treatments on a silica surface would be similar for both materials, only the glass bead treatments were investigated with the AFM.For the AFM measurements, beads were glued to a sample holder that was then saturated with a 0.001 M NaCl solution.The AFM was then used to measure surface height and tip deflection within 20 μm × 20 μm scanning regions on the surface of each glass bead sample.As the AFM tip was scanned over the surface of a glass bead, it was maintained at a fixed distance from the mineral surface (D = 0.3 nm).The force required to maintain the tip at this distance was used to determine the density of fixed surface charge (Q AFM ) in the scan window (Equation 1).A carboxyl terminated tip was used for the procedure with a charge density of Q tip = 0.01 C/m 2 and radius of R tip = 25 nm.The permittivity of the NaCl fluid was ε f = 6.923 × 10 10 C 2 /Nm 2 and the Debye length was approximately ∼10 nm in 0.001 M NaCl (Gun'ko et al., 2014;Lyklema, 1991).
The SIP experiments were conducted by packing the treated grains in a cylindrical sample holder as shown in Figure 1 (length: 4.5 cm, inner diameter: 2.54 cm) and saturating the sample with NaCl solution (0.001 M/L for glass beads and 0.01 M/L for silica gel grains).To account for experimental and sample packing variability, SIP measurements were performed on multiple repacked columns per treatment (two replicates for glass beads and three replicates for silica gel), with the exception that only a single column of glass beads was used for the flowthrough calcite precipitation experiment.SIP measurements were collected as phase and magnitude of complex conductivity at distinct frequencies using a dynamic signal analyzer (PCI-4461, National Instruments, Austin, TX) operating over the frequency range of 0.01-1000 Hz.Channel 1 of the signal analyzer was designated to record the applied current waveform by measuring the voltage response across a precision reference resistor in series with the column.Channel 2 of the signal analyzer recorded the voltage response of the sample.Both current injection and potential measurements were made using non-polarizing electrodes (12-gauge silver wires coated with silver chloride) placed in the column caps allowing electrolytic contact with the porous medium.

Surface Morphology
SEM images indicate that the glass beads and silica gel were successfully modified under the different treatments (Figures 2-4).Prior to the treatments, the glass beads were roughly spherical and clean with specific surface area around 0.06 m 2 /g (Figure 2a and Table 1).The silica gel grains were angular with a much larger specific surface area of 512 m 2 /g (Figure 2b and Table 1).Figure 3a illustrates how the etching process qualitatively increased the roughness of the grains by creating large pits in the surface of the glass beads.The iron oxide coatings also increased surface roughness, but in this case by producing small particles covering both the glass bead and silica gel grains (Figures 3b and 3c).In addition to changing the roughness of the surface, these iron oxide particles may change the surface chemistry, the geometry of pore spaces and throats, as well as the electrical properties of the glass surface since the presence of iron oxides could increase the electrical conductivity (Murawski, 1982).Table 1 indicates that a small (∼7%) decrease in the surface area of silica gel was caused by the iron oxide coatings (surface area values for glass bead treatments were not measured).It is possible that this change in surface area was caused by blockage of a portion of the silica gel's internal porosity by a relatively diffuse iron oxide coating.
SEM images of glass beads affected by calcite precipitation in the flow-through experiment, that is, the calcite coated treatment, show distinct rhombohedral crystals formed on the bead surfaces and within intergranular pore spaces connecting individual beads (Figure 4a).In contrast, grains of silica gel for the calcite-evap treatment appear to be encased in carbonate sheets (Figure 4b).The calcite-aged and calcite-fresh treatments resulted in particle aggregates that were packed onto the silica gel surfaces, though the aged calcite sample visually appears to form more tightly packed aggregates (Figure 4c) than the sample with fresh calcite grains added to it (Figure 4d).
All three calcite treatments resulted in a decrease in surface area relative to untreated silica gel (Table 1), likely indicating that access to the intragranular porosity of the silica gel was restricted.The largest decrease in surface area (46%) occurred for the calcite-evap sample, where silica gel grains are coated by the precipitate (Figure 4b), compared to the other two treatments where calcite powders were mixed with the silica gel when it was packed in the column (calcite-aged: 25%, calcite-fresh: 32%).It is notable that these observed decreases in surface area were much greater (4-7x) for the calcite treatments compared to that observed for the iron oxide coated silica gel (Figure 3c).Though calcite grains were introduced as particles in the intergranular pore space, it is possible that  some degree of dissolution and reprecipitation of the calcite occurred for the calcite-aged and calcite-fresh treatments, with the precipitate forming in areas that restricted access to the internal porosity of the silica gel.

AFM Measurements of Material Surfaces
Average surface roughness and charge density measured within the AFM scan window for each glass bead treatment are reported in Table 2. Also reported are measurements of the surface charge density for the untreated silica gel, though surface roughness is not available for this sample.The AFM surface roughness data indicate that the iron oxide-coated beads had a significantly higher degree of surface heterogeneity than the untreated glass beads, whereas no significant difference in roughness was observed for either the etched glass beads or the beads precipitated with calcite.The small change in surface roughness observed in the latter two cases likely resulted from the comparable size of the scan window (20 μm × 20 μm) relative to the size and geometry of the surface pits produced by etching (Figure 3a) and crystals produced by the calcite precipitation, which provided large flat surfaces (Figure 4a).We believe that the AFM scan was completed on the surface of a large precipitated calcite grain, such that the properties reported for the calcite-coated glass bead are reflective of the surface properties of calcite rather than silica.
There is no statistical difference in the charge density of the silica surfaces measured for the untreated glass beads and silica gel.Further AFM measurements on treated samples are therefore only available for the glass beads since the nanoscale environment impacting the AFM tip is expected to be the same for both silica surfaces.Neither the etching nor iron oxide coatings were found to significantly impact the electrical properties of the treated surfaces as measured by AFM.In contrast, the calcite surface (calcite-coated glass bead) has a significantly greater (∼19x) surface charge density compared to the silica surfaces.

Results for Glass Beads
The SIP responses for the glass bead treatments are shown in Figure 5 with summary values reported in Table 3.The results are shown as an averaged response for replicate measurements made in separately packed sample holders, except for the calcite coated glass beads for which the SIP response was monitored in the flow-through cell throughout the calcite precipitation experiment with the equilibrium response reported here.
For the calcite coated treatment σ' is observed to be almost 20x larger than for the untreated glass beads, primarily due to the fact that the fluid conductivity is also about 26x larger in this case because the solution was at saturation for calcite (Table 3).We therefore also report the formation factor (F = σ w /σ'), which normalizes for the effect of fluid conductivity.An increase in F relative to the untreated beads is observed for the calcite coated and etched glass beads, which represents a net decrease in the ability of these materials to conduct charge.No significant change in F was observed for the iron oxide coated beads.For the calcite coated glass beads, reduction of pore space due to mineral precipitation is the likely reason for the observed increase in F. Based on the values reported in Table 3, the definition F = ϕ m , and assuming that m = 1.3, which is in the range of typical values for the cementation exponent observed for glass bead packs, the observed change in formation factor suggests that the calcite precipitation produced a 7% decrease in porosity of the column.In contrast, etching of the beads is not expected to alter pore geometry.The observed decrease in real conductivity for the etched samples may therefore be due to a reduction in the average surface conductivity associated with the pitting produced by the etching (Figure 3), which could result in a higher effective surface roughness and tortuosity for current pathways at the grain scale.It is notable, however, that the surface roughness and charge density of the etched beads measured with the AFM was not significantly different from the untreated beads (Table 2).The discrepancy between the SIP and AFM results may be due to a difference in measurement scales: SIP measurements are an integrated measurement that averages over the entirety of the grains, whereas AFM provides a spatially localized measurement of surface properties.The lack of significant change in F for the iron oxide coated glass beads may be a result of the relatively small amount of iron oxide mineral diffusely precipitated on the beads relative to the calcite coated glass beads (Figure 3b vs. 4a).
The etched treatments did not have an obviously different response in σ" compared to the plain glass beads.The iron oxide coated samples have a small, but significantly higher σ" response compared to the untreated glass beads across a broad frequency range.In contrast, the imaginary conductivity of the calcite coated glass beads was much larger than the untreated beads demonstrating an increase in the capacity of the system to store charge.The significant increase in the surface charge density of the calcite-coated beads relative to plain beads observed with the AFM supports this interpretation (Table 2).Given the nature of the flow experiment, however, it is also possible that the formation of calcite within the pore spaces of the sample could contribute to enhanced membrane polarization-that is, pore throat blockages caused by the calcite grains could produce a polarization effect similar to that frequently observed for clays in natural samples (Leroy & Revil, 2009).
A distinct peak in the σ" spectrum of the calcite coated glass bead sample occurs around 0.9 Hz.Using Equation 2 to estimate a characteristic grain size for the system, this frequency is roughly equivalent to grains that are 5 μm in diameter, given T = 293K and Leroy et al.'s (2017) assumption that β b = 5.7 × 10 9 m 2 s 1 V 1 .Using the modified version of Equation 2 that includes the factor 1/M to account for interactions between the Stern and diffuse layer and the value M = 30.70calculated by Leroy et al. (2017) for Wu et al.'s (2010) calcite precipitation experiment yields an effective grain size of 28 μm.This grain size is consistent with the size of calcite grains imaged by SEM in Figure 4a.We note that a full inversion of the imaginary conductivity spectrum would be required to obtain an estimate of the grain size distribution (Revil et al., 2014), which we have not done here.

Results for Silica Gel
A decrease in the formation factor by almost half was observed for the silica gel relative to the glass beads.The difference indicates an overall increase in the ability of the silica gel to conduct charge through the bulk pore fluid and along the silica surfaces (Table 3), which was contributed by the high internal porosity and large surface area of the silica gel (Table 2).The untreated silica gel had an imaginary conductivity spectrum with a peak at approximately 0.16 Hz and a maximum σ" value of 3.2 μS/cm, which is over 300 times larger than that observed for the glass beads (i.e., 0.01 μS/cm) (Figures 5c, Table 3).The increased magnitude of the silica gel's polarization response relative to the glass beads is consistent with the larger intragranular surface area contributing to an overall greater polarization response.
Coating the silica gel with iron oxide particles yielded a 9% increase in formation factor, but a factor of seven decrease in peak imaginary conductivity (Figure 6, Table 3).These effects could be related to blockage of the internal micro-porosity of the silica gel by iron oxide grains.Given the apparent importance of the intragranular porosity for producing the σ" response of the plain silica gel, polarization effects are likely more sensitive to blockage of access to internal pore space than is charge conduction.The 7% reduction in surface area measured for the iron oxide coated silica gel samples (Table 1) also supports an interpretation of intragranular pore blockage.
The addition of calcite grains (i.e., calcite-aged and calcite-fresh) produces small increases (11%-17%) in the formation factor compared to the untreated silica gel.This change in the formation factor again suggests blockage of current transmission pathways within the porous medium.The calcite-evap sample exhibited a large variability in F, thus is not statistically different from the other samples despite having the greatest observed reduction in surface area (Table 1).
In contrast, an enhancement of polarization processes caused by the calcite addition is indicated by large increases in the imaginary conductivity observed for all three treatments (Figure 6, Table 3).Relative to the untreated silica gel, the peak imaginary conductivity reported in Table 3 increased by a factor of 12 for the calcite-fresh treatment, 8 for the calcite-aged treatment, and 9 for the calcite-evap treatment.Shifts in the frequency of the peak imaginary conductivity also occurred (Table 3).The effect of the calcite addition was also found to be reversible as the SIP response of the silica gel following removal of calcite by acidification was almost identical to that observed for untreated silica gel (Figure 6, Table 3).

Comparison of Surface Charge Density Estimates
The complex conductivity values measured by SIP represent an average over multiple components of the porous medium and are not a direct representation of material surficial properties.To make a quantitative comparison between the SIP and AFM results requires estimation of the surface properties from the measured complex conductivity spectra, specifically we consider the surface charge density of the Stern layer (Q b ).Whereas the Bruggeman-Hanai-Sen mixing formula (Eq. 3) is typically used to estimate the complex conductivity of a composite media from pure materials (e.g., mineral grains and water), we follow the example of Lesmes and Morgan (2001) and use Equation 7to estimate the properties of an "embedded" component from the measured properties of the composite material: where σ * i is the complex conductivity of the material component of interest, that is, the embedded inclusion, σ * h is the complex conductivity of the host material in which the inclusion is embedded, and σ * m is the measured complex conductivity of the composite sample, that is, effective conductivity for the combined host and inclusion.For example, the column containing untreated glass beads can be considered as an inclusion of glass beads embedded within water as the host.In this case, σ * h = σ * w and σ * m is the measured complex conductivity spectrum shown in Figure 5 for the untreated beads.The resulting complex conductivity obtained for the embedded inclusion, σ * i , is therefore the grain-size averaged spectrum for the glass beads themselves.In contrast, the calcite coated glass beads can be considered as a mixture of calcite crystals as the inclusion within the water saturated glass beads as the host.In this case, σ * m is the measured complex conductivity spectra for calcite coated glass beads and σ * h is the measured spectra for untreated glass beads as the host, both of which are given in Figure 5.The complex conductivity spectra of calcite crystals, which was not measured directly, is then estimated from these two spectra as σ * i .We take an analogous approach to estimate the complex conductivity of calcite grains as an inclusion in the silica gel samples.For grain-like materials where the low-frequency polarization response is dominated by surface charge displacement, such as for calcite crystals, the imaginary conductivity of an individual grain is given by Equation 6, which reaches a maximum value when ω = τ, such that: Thus the Stern layer charge density for the inclusion can be obtained from the peak value in the imaginary conductivity spectrum obtained from Equation 7if the ion mobility in the Stern layer and grain size are known (note for clarity in this case that σ s " = σ i ").Leroy et al. (2017) pointed out that the mobility of sodium and calcium ions within the Stern layer are not known, but approximated it as 10% of their average mobility in dilute water at 25°C, that is, the value β b = 5.7 × 10 9 m 2 s 1 V 1 used earlier.
It is important to note that the charge density estimates obtained using Equation 8 assume that inclusions are granular such that the grain polarization model in Equation 4 holds.It is also assumed that the SIP response of the host is independent of and unchanged by the precipitates.In other words, the approach is equally valid for estimating the surface charge of precipitated calcite grains in a host of either glass beads or silica gel if the precipitated grains behave as particles and the SIP response of the host itself is unchanged by the presence of the calcite.Likewise, treating the untreated glass bead samples as an inclusion of glass beads in water is likely to provide reasonable surface charge estimates for silica.In contrast, it is unclear whether Equation 4 would hold for the more complex geometry of the silica gel, making estimates of charge density for silica from these samples less reliable.In all cases, the model does not directly account for membrane polarization effects emerging from precipitation of calcite in pore throats, though it is likely that such effects would be included within the effective complex conductivity value determined by this procedure as the spectral responses produced by grain and membrane polarization are often similar, making them difficult to distinguish (Bücker et al., 2019).Despite these potential limitations, we estimate the charge density of the Stern layer using the measured values of the formation factor given in Table 3, assuming the value of β b given earlier, and choosing representative values of m = 1.5, d = 275 μm for the glass beads, d = 6 nm for the silica gel (i.e., the intragranular pore size reported by the manufacturer), and d = 1 μm for the calcite grains.We note that 1 μm is likely low for the calcite particles based on the values of 28 μm calculated earlier.However, since Q b scales proportionally with d in Equation 8, one may consider the values reported for calcite as equivalent to Q b /d and scale them by alternative values of d as appropriate.Since a clear relaxation peak is not observed for the untreated glass beads, calculations with this sample are performed for σ s " at 0.9 Hz.
To estimate errors in Q b a Monte Carlo approach was used where 100,000 samples of the complex conductivity spectra were randomly drawn for each sample based on the measurement uncertainties illustrated in Figures 5 and  6.Each of these spectra were used within Equations 7 and 8 to obtain a distribution of Q b .We note that the high standard deviation in the real conductivity for the calcite-evap sample (i.e., 556.6 μS/cm) produced strongly skewed distributions of Q b .Given that the measured σ' spectra for each replicate sample had a low standard deviation across frequencies (<60 μS/cm), we instead chose to use the average of the standard deviation within each measured σ' spectrum for this treatment (i.e., 41.5 μS/cm) in the analysis.
Table 4 shows overall agreement between the AFM and SIP results.There is no statistically significant difference between Q b estimates of a silica surface obtained by either AFM or SIP measurements for the glass beads and silica gel samples.Though greater variability is apparent in the Q b estimates for the calcite surfaces, the surface charge densities are all significantly higher than those estimated for the silica surfaces with the exception of the calcite-aged silica gel sample.Independent AFM measurements of calcite surface charge are not available for the silica gel samples as it was initially assumed that this value would not change significantly across samples, thus the experimental design focused instead on manipulating the geometry of calcite in the pore space (i.e., coating grains vs. filling pores).Note.Sensitivity of the results to choice of the cementation exponent (m) is also shown.a Treatments using silica gel samples.b Standard deviation of σ' in error analysis taken as the average variation across each measured spectra.
One possible explanation for the difference in estimated surface charge between untreated samples versus those containing calcite are the notable differences in pH shown in Table 3, that is, pH = 6.3-7.1 for untreated samples versus pH = 8.8-10.7 for the calcite treatments.Past work by Hao et al. (2015) using the same silica gel as this study demonstrated that increasing pH causes deprotonation of silanol sites on the silica surface, thereby increasing the surface charge and number of counter ions in the Stern layer.These authors used sorption of radioactive 22 Na to demonstrate that a change in pH from 5 to 8 produced an increase in surface sites on the silica gel of 4.58 × 10 16 sites/m 2 , which translates to an increase in surface charge density of 7.3 mC/m 2 assuming that each site contributes a single elementary charge.While the surface site density for the calcite-aged sample is close to this value (4.7 ± 0.5 mC/m 2 ), it seems unlikely that this silanol deprotonation mechanism alone could account for the higher surface charge densities found for the calcite-fresh (19.7 ± 2.4 mC/m 2 ) and calcite-evap (26.3 ± 8.7 mC/m 2 ) samples-especially considering that the introduction of calcite also appeared to block intragranular microporosity of the silica gel, drastically reducing the surface area of the samples (Table 1).
Similarly, the glass bead flow-through experiment (calcite-coated) had the highest pH (10.7), but it is unlikely that deprotonation of surface sites on the beads, which have a relatively low surface area, could alone lead to the high estimated value surface charge with calcite present (258 mC/m 2 ).It is therefore much more likely that the observed increase in polarization in the treated samples comes from the contribution of surface charge from calcite itself.Regardless, it is important to recognize that our methodology for estimating surface charge density assumed that the contribution of a silica surface was the same between treated and untreated samples, which is likely not correct due to this pH effect.The estimated surface charge densities for the silica gel therefore probably represent some average between the effect of increased charge on the silica gel surface and the contributions from the calcite grains.
The reason for the high calcite surface charge density estimated for the glass beads relative to the silica gel samples remains unclear.One possibility is related to measurement errors associated with the low signal strength produced by glass beads.It was observed that if the measured spectrum for untreated glass beads was replaced with the theoretical spectrum for water as the host material, then the SIP calculations for calcite coated glass beads would produce an estimated surface charge density for calcite of only 14.8 mC/m 2 , which is more closely aligned to the other measurements.Alternatively, the estimated value of Q b for the glass beads could also be brought into alignment with other measurements by reducing the assumed size of the calcite grains by an order of magnitude to 0.1 μm, though from the representative grain sizes observed in the SEM images this does not seem like an appropriate adjustment (Figure 4a).
In contrast, Leroy et al. (2017) found that SIP measurements are moderately sensitive to the value of the cementation exponent (m), which they found to vary between 1.35 and 1.9 over the course of an in-situ calcite precipitation experiment.In their analysis, the authors justified their choice to vary m using SEM images of calcite grains extracted from different portions of the experimental column representative of different phases of precipitation and pore clogging.The influence of changing m on our results is shown in Table 4.It is clear that the results are sensitive to the choice of m, however, we have no basis to choose any particular value of m in our experiment given that the samples were prepared in very different ways and there is no value of m that consistently improves the agreement between AFM and SIP data across all of samples.Similarly, we do not have any means to consider the contribution of calcite precipitation to membrane polarization in the glass bead samples as the spectral response between grain and membrane polarization are expected to be similar (Bücker et al., 2019).
Given that only the glass bead samples were prepared by in-situ precipitation of calcite, the high values of the calcite surface charge density for this case could reflect the net effects of both enhanced grain and membrane polarization mechanisms.
A final possibility could be that true material differences in surface charge density of calcite are responsible for the higher value of Q b for the calcite-coated glass bead sample (258 mC/m 2 ) considering that the measurements were taken in situ as new calcite surfaces were forming during the column experiment.For comparison, Leroy et al. ( 2017) calculated a surface charge density of 560 mC/m 2 for calcite based purely on geochemical considerations (pH = 9.0), which can be considered a theoretical upper limit.Perhaps fresh calcite surfaces are particularly active for charge migration, whereas aging of the surface reduces either the available charge density and/or ion mobility on the mineral surface as these effects would be indistinguishable in our analysis using Equation 8.The effect of aging calcite surfaces is somewhat supported by a potential trend in Q b for the different calcite treatments.The highest value of Q b is observed for the calcite-coated glass beads, which represents an insitu measurement of the flow-through column as calcite was precipitated.The next highest surface charge density is for the calcite-evap samples where the calcite was precipitated in the silica gel by evaporative concentration (26.3 ± 8.7 mC/m 2 ); these silica gel samples had a short period of time between precipitation and measurement that was on the order of days.The silica gel samples prepared by packing calcite crystals precipitated a few weeks earlier (i.e., calcite-fresh) had a lower value of Q b (19.7 ± 2.4 mC/m 2 ), though the difference is not statistically significant at a 95% confidence level.Finally, the sample packed with aged calcite particles that had sat exposed to the atmosphere on a lab shelf for several years had the lowest Q b value (4.7 ± 0.5 mC/m 2 ).This decreasing trend in Q b with increasing age of the samples supports the idea that aging of the surface could be a relevant factor, though further experiments explicitly designed to address such a phenomenon are needed.

Conclusions
AFM and SIP are two drastically different measurement techniques that are both sensitive to the surface properties of porous media.The effects of different treatments to glass beads by etching, deposition of iron oxide grains, and inclusion of calcite were investigated by measuring surface topography and surface charge density by AFM.A large increase was observed in surface roughness for the iron oxide treatment, whereas a large increase in surface charge was observed for the calcite coated beads.The effect of these treatments on the SIP response of glass beads were generally consistent with the AFM results, with changes in the real complex conductivity largely related to blockage of intergranular pore space and only the calcite treatment producing a major increase in the observed imaginary complex conductivity spectra.SIP measurements performed on silica gel produced much higher imaginary conductivity responses than glass beads due to a high internal surface area resulting from its substantial intragranular porosity.Deposition of iron oxide grains on the surface of the silica gel reduced both the real and imaginary components of the complex conductivity.In contrast, significant increases in the imaginary conductivity of the silica gel were observed following the addition of calcite prepared by three different methods.Dissolution of the precipitated calcite by acidification also showed that the influence of calcite inclusions on the SIP measurements was completely reversible.Overall, these results highlight that calcite plays a substantial role on controlling the electrical properties of porous media, particularly the imaginary portion of the complex conductivity that is highly dependent on mineral surface properties.Calcite likely influences SIP responses through both direct polarization of calcite grains and by the geochemical manipulation of other surfaces (e.g., silica) through modification of pore fluid pH.
To allow for quantitative comparison of the AFM and SIP results, the SIP data were processed using differential effective medium theory and a grain polarization model developed by Leroy et al. (2017) to estimate the surface charge density in the Stern layer of silica and calcite using treated samples of glass beads and silica gel.Quantitative agreement between AFM and SIP estimates of surface charge density for silica was achieved in all cases.When silica gel grains were coated with calcite prior to packing a column, quantitative agreement between the SIP and AFM estimates of calcite surface charge density could be achieved.When calcite grains were mixed with silica gel prior to packing the column, SIP results underestimated calcite surface charge densities compared to the AFM though the values were qualitatively similar.In contrast, when calcite was added to a column of glass beads by in situ precipitation, SIP produced significantly higher estimates of the surface charge density of calcite than were obtained by AFM.Potential causes of this discrepancy were identified as: (a) measurement errors associated with the low SIP response produced by plain glass beads; (b) the geometric distribution of calcite grains in the porous medium (including sensitivity to the cementation exponent, m, and membrane polarization effects); and (c) true differences in the surface properties of calcite associated with aging of the mineral surface.
Overall, this study demonstrates that bulk electrical properties of a porous medium measured with SIP can be combined with grain polarization models to produce estimates of mineral surface charge density that are consistent with those obtained directly by AFM.The quantitative agreement between the surface charge density estimated by AFM and SIP indicate that these distinctly different measurement approaches are both fundamentally sensitive to the same underlying phenomena of charge migration in the Stern layer of mineral grains.In future studies, these complimentary measurements may be used to further constrain our understanding of polarization mechanisms in porous media.For example, future studies could use AFM to independently determine how aging of a surface or changes in the chemical environment adjacent to a mineral surface impact surface charge density.Such measurements could then be combined with SIP measurements to test and validate polarization models (e.g., Bücker et al., 2019;Leroy et al., 2017).By using AFM measurements to reduce uncertainties related to surficial properties, the interpretation of SIP measurements could focus on identifying the influence of macroscopic properties of a porous media (e.g., mineral heterogeneity, formation of precipitate walls, or pore blockage and membrane polarization).

Figure 1 .
Figure 1.Schematic diagram of the SIP experimental setup showing column design with electrode configurations.

Figure 4 .
Figure 4. (a)-(d): SEM images of the carbonate treatments for glass beads and silica gel grains.(a) Calcite coated glass beads produced by chemical precipitation in a flow-through experiment.(b) Silica gel encased with precipitate following evaporation of the CaCO 3(aq) solution for the calcite-evap treatment.(c) Silica gel coated with aged commercial calcite powder for the calcite-aged treatment.(d) Silica gel coated with fresh calcite from chemical precipitation for the calcite-fresh treatment.

Figure 5 .
Figure 5. Measured complex conductivity spectra for glass beads that are untreated, etched with acid, coated with iron oxide, or subjected to the precipitation of calcite: (a) real component of the complex conductivity, (b) formation factor, and (c) imaginary component of complex conductivity.Shaded area shows the 95% confidence interval based on 3 replicate measurements.Fluid conductivity of the NaCl solution used for plain, etched, and iron oxide-coated beads: 260 μs/cm, calcite-coated beads: 6,780 μs/cm.

Figure 6 .
Figure 6.Complex conductivity spectra of silica gel for the (a) real component, (b) formation factor, and (c) imaginary component.Results from six different cases are shown: untreated silica gel, coated with iron oxide particles, three different additions of calcite (aged, fresh, and evaporated), and the response of the calcite-treated silica gel after acidification.Shaded area shows the 95% confidence interval based on 3 replicate measurements; formation factor error for calcite-evap case is outside of the plot window and not shown.

Table 1
Surface Area of Samples Estimated by the Nitrogen Adsorption (BET) Method a Reported means and standard deviations are calculated values for the AFM scan window.HAO ET AL.

Table 3
Comparison of the Complex Conductivity Responses and the Formation Factor Measured by SIP for Different Treatments Applied to Glass Beads and Silica Gel.(CI = 95% Confidence Interval) a Values averaged below 100 Hz given that no peak exists.b Only one sample investigated via precipitation during a flow-through experiment.c Peak value is selected as maximum observed below 100 Hz.

Table 4
Stern Layer Charge Density (Q b ) for Silica Surfaces (i.e., Glass Beads or Silica Gel) Versus Embedded Calcite Inclusions as Determined by AFM and