Environ. Sci. Technol. 2008, 42, 6593–6597
Kinetic Experiments for Evaluating the Nernst-Monod Model for Anode-Respiring Bacteria (ARB) in a Biofilm Anode ´ SAR I. TORRES,* CE ANDREW KATO MARCUS, PRATHAP PARAMESWARAN, AND BRUCE E. RITTMANN Center for Environmental Biotechnology, Biodesign Institute at Arizona State University, Tempe, Arizona 85287
Received April 8, 2008. Revised manuscript received June 8, 2008. Accepted June 14, 2008.
Anode-respiring bacteria (ARB) are able to transfer electrons from reduced substrates to a solid electrode. Previously, we developed a biofilm model based on the Nernst-Monod equation to describe the anode potential losses of ARB that transfer electrons through a solid conductive matrix. In this work, we develop an experimental setup to demonstrate how well the Nernst-Monod equation is able to represent anode potential losses in an ARB biofilm. We performed lowscan cyclic voltammetry (LSCV) throughout the growth phase of an ARB biofilm on a graphite electrode growing on acetate in continuous mode. The jV response of 9 LSCVs corresponded well to the Nernst-Monod equation, and the halfsaturation potential (EKA) was -0.425 ( 0.002 V vs Ag/AgCl at 30 °C (-0.155 ( 0.002 V vs SHE). Anode-potential losses from the potential of acetate reached ∼0.225 V at current density saturation, and this loss was determined by our microbial community’s EKA value. The LSCVs at high current densities showed no significant deviation from the Nernst-Monod ideal shape, indicating that the conductivity of the biofilm matrix (κbio) was high enough (g0.5 mS/cm) that potential loss did not affect the performance of the biofilm anode. Our results confirm the applicability of the Nernst-Monod equation for a conductive biofilm anode and give insights of the processes that dominate anode potential losses in microbial fuel cells.
Introduction Anode-respiring bacteria (ARB) have two abilities that are of great interest to humans: oxidizing organic compounds from water and producing an electrical current out of the electrons from those organic compounds. Their capability to generate electrical current from various organic compounds and waste streams was demonstrated in many studies (e.g., reviewed in refs 1–3. However, information about the anode-potential losses that occur at the biofilm created by ARB is limited, even though describing these losses is essential for understanding the rate of current generation. Only a handful of publications describe current density as a function of anode potential and correlate this relationship to a bioelectrochemical process (4–8). Most of these publications were performed by researchers studying bacteria that produce * Corresponding author e-mail:
[email protected]; phone: 1-480-7270432; fax: 1-480-727-0889. 10.1021/es800970w CCC: $40.75
Published on Web 07/24/2008
2008 American Chemical Society
electron-shuttles, whose redox potentials can be studied by cyclic voltammetry (CV) (9–11). The kinetic response of electron shuttles to anode potential (jV response) is defined by mass-transport processes and the Butler-Volmer equation (12), and it has been modeled previously for the anode of a microbial fuel cell (13). A recent discovery is the possibility that some ARB species, such as Shewanella (14) and Geobacter (15), can transfer electrons through solid conductive matrices that they produce. Producing a conductive matrix also seems to extend to other microorganisms and metabolic interactions (14). The solid conductive matrix creates an electrical connection between the anode and ARB, who take advantage of this to respire electrons to the anode. Since the solid conductive matrix is directly connected to the anode and acts as a conductor, we can consider it an extension of the anode itself. Thus, we call the biofilm containing a solid conductive matrix a “biofilm anode” (16, 17). Since ARB using a biofilm anode are directly connected to the anode, their jV response is directly coupled to bacterial kinetics. Bacterial kinetics are often modeled by the Monod relationship (18), which captures simply the complexity of reversible and irreversible reactions that compose bacterial metabolism. The Monod equation is shown here for the case of electron acceptor limitation in a biofilm: rut ) qmaxXfLf
SA K A + SA
(1)
where rut ) rate of substrate utilization per surface area (e- meq/cm2-d); qmax ) maximum specific rate of substrate utilization (e- meq/mg VSS-d); Xf ) concentration of active biomass in the biofilm (mg VSS/cm3); Lf ) biofilm thickness (cm); KA ) half-saturation electron-acceptor concentration (e- meq/cm3); and SA ) electron-acceptor concentration (e- meq/cm3). The Monod equation cannot be used in its original form to describe the jV response of an ARB biofilm anode, as we do not have an electron-acceptor concentration; instead, we have the anode potential. Marcus et al. (17) proposed the Nernst-Monod model for describing the bacterial kinetics under the influence of the anode potential E (V):
(
j ) jmax
1 F 1 + exp - (E - EKA) RT
[
]
)
(2)
where j ) current density (A m-2); jmax ) maximum current density (A m-2); R ) ideal gas constant (8.3145 J mol-1 K-1); F ) Faraday constant (96,485 Coulomb per mol-e-); T ) temperature (303.15 K); and EKA ) potential at which j ) 1/2 jmax. WerefertothetermintheparenthesisastheNernst-Monod term, because the Nernst equation is modifying the Monod equation for describing the anode potential availability as a terminal electron acceptor for ARB. In eq 2, jmax is proportional to the terms qmaxXfLf shown in eq 1 (19): jmax ) γsqmaxXfLf(1 - fs0)
(3)
where γs is a conversion factor from mass of substrate to coulombs (e- eq/[MW × F]) and fs0 is the fraction of electrons used for cell synthesis (we assume a negligible current generation due to biomass decay). Our main objective is to experimentally evaluate the Nernst-Monod equation as a model for anode-potential VOL. 42, NO. 17, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 1. Plot of the Nernst-Monod term for EKA ) 0 V and T ) 30 °C. losses in an ARB biofilm anode. Characterizing these losses is an important factor in the development of microbial fuel cells (MFCs) and microbial electrolysis cells (MECs). We also present a methodology to estimate the important parameters (e.g., EKA) for the Nernst-Monod model from experimental results.
Model Description Figure 1 shows the shape of the Nernst-Monod equation. The main difference between the Nernst-Monod and the Monod term (S/(Ks + S)) lies on their reference points. While the Monod term has two points that define its shape (q ) 0 at S ) 0 and q ) 1/2 qmax at S ) Ks), the Nernst-Monod has only one reference point, EKA (j ) 1/2 jmax at E ) EKA). The exponential in the Nernst-Monod term, inherited from the Nernst equation, has caused a loss of point [0,0] as a reference point. Thus, the response of the biofilm anode to potential always has the same shape, for which EKA is its inflection point at j ) 1/2 jmax. Another difference is the way in which the terms approach saturation, or j ) jmax. The Nernst-Monod term saturates at approximately 0.1 V greater than EKA (for T ) 25 °C), whereas the Monod term requires more than 10 times the Ks value to reach saturation. Since the Nernst-Monod term is derived from the Monod equation, the main assumption for its use is that microbial kinetics control the rate of current generation. The NernstMonod equation describes the rate of electrical generation of each individual bacterium. A deviation from the ideal jV response described by the Nernst-Monod model can occur from the potential losses throughout the biofilm. Although these potential losses have not been characterized in any study, Marcus et al. (17) assumed that the biofilm anode acts as a linear conductor and described the inefficiencies in the biofilm anode using Ohm’s law and biofilm conductivity κbio (mS/cm). Low biofilm conductivity causes a large potential gradient within the biofilm anode, resulting in an increase in potential loss and slowed kinetics. We performed experiments to determine whether or not the Nernst-Monod equation is a good descriptor of the jV response of an ARB biofilm anode. We achieved this goal by performing low-scan cyclic voltammetry (LSCV) on an ARB biofilm that has a high presence of Geobacter sulfurreducens throughout its growth phase and saturation. We also compare these values with amperometric (j-V) experiments performed in an ARB biofilm anode that was grown under substrate limitation. Finally, we estimate κbio based on the deviation of the jV response from Nernst-Monod curve at high current densities.
Materials and Methods We used two dual-chamber microbial electrolysis cells (MECs) to carry out the experiments: one for feeding a highacetate concentration and the other for feeding a low-acetate concentration. The use of an MEC for the experiments 6594
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reduced the error caused by oxygen diffusion to the anode compartment, a factor when an MFC is used. The cells held 300 mL in each chamber and contained a 0.4-cm OD graphite rod (6.83 and 7 cm2) and a 0.8-cm OD graphite rod as cathode (15 cm2; graphitestore.com). We placed an Ag/AgCl reference electrode 0.6 cm away from the anode in the anode chamber (BASI Electrochemistry, MF-2052) to control the anode potential using a potentiostat. Due to our medium composition and temperature, the Ag/AgCl electrode was ∼0.27 V vs SHE. We agitated the contents of each chamber with a magnetic stir bar at 200 rpm and maintained the temperature at 30 or 32 °C. We also wrapped MEC in aluminum foil to shield it from light. The medium contained the following components in reverse-osmosis water: 100 mM phosphate buffer as Na2HPO4/ KH2PO4 (pH ) 7.5), 7.1 mM NH4Cl, and a mineral solution with the following final concentrations (in 1 L): 5 mg of EDTA, 11.6 mg of MgCl2, 5.9 mg of MnCl2 · 4H2O, 0.8 mg of CoCl2 · 6H2O, 1.14 mg of CaCl2 · 2H2O, 0.5 mg of ZnCl2, 0.1 mg of CuSO4 · 5H2O, 0.1 mg of AlK(SO4)2, 0.1 mg of H3BO3, 0.2 mg of Na2MoO4 · 2H2O, 0.01 mg of Na2SeO3, 0.1 mg of Na2WO4 · 2H2O, and 0.2 mg of NiCl2 · 6H2O. The medium also contained NaCH3COO as substrate at 1 mM for the low concentration experiment and 25 mM for the high concentration experiment. For the high-concentration experiment, we also added 3 mM of 2-bromoethanesulfonate (BES) to suppress acetoclastic methanogenesis (20). We prepared the medium, autoclaved it, and sparged it with N2 for 30 min. Then, we added an anaerobic solution containing Fe(II)Cl2 · 2H2O (20 µM final concentration) and Na2S · 9H2O (15 µM final concentration) through a sterile syringe filter. The medium was constantly sparged with N2 at a low flow rate throughout the experiment. We controlled the anode potentials with a multipotentiostat (Princeton Applied Research, mModel VSP, TN) at -0.40 V vs Ag/AgCl for the high-acetate concentration experiments and at -0.385 V vs Ag/AgCl for the lowacetate experiments, except for short-term amperometric (j-V) experiments and low-scan cyclic voltammetry (LSCV) experiments. We collected data in intervals of 2 min using EC Laboratory software and carried out short-term j-V experiments by waiting at least 30 min at each condition and averaging the last 10 min of data, collecting data in intervals of 30 s. J-V experiments were performed in triplicate, and error bars in the results indicate the standard deviation of the results. We performed LSCV experiments at 1 mV/s between -0.6 and -0.1 V vs Ag/AgCl and normalized the reported current to the geometrical anode surface area. LSCV experiments were repeated in duplicates, but only the second LSCV curve is presented for simplicity. A total of ∼700 data points were collected in each curve (one curve includes a forward and backward scan). We seeded the anode chamber with an acclimated ARB community from previous acetate experiments. The ARB inoculum showed a high presence of Geobacter sulfurreducens, as explained in Lee et al. (21). The original inoculum was from return activated sludge from Mesa Northwest Water Reclamation Plant (Mesa, AZ). We grew a biofilm capable of generating current from acetate in batch mode for 4 days. Then, we fed the medium to the reactor continuously at 0.47 mL/min (10.6 h hydraulic retention time). We analyzed effluent samples for acetate concentrations using high-performance liquid chromatography (HPLC; Shimadzu LC-20AT, Japan) with an Aminex HPX-87H column (Biorad Laboratories, Milan, Italy) at 30 °C and with diode array detector. The eluent was 2.5 mM H2SO4 at 0.6 mL/min.
FIGURE 2. Growth curve of the high-acetate MEC. Each gray circle represents a time when we performed an LSCV experiment. At day 13, we changed the reactor temperature from 30 to 32 °C.
Results and Discussion High-Acetate Concentration Experiments. Figure 2 shows the growth phase of the high-acetate MEC. The effluent concentrations were always above 22 mM throughout the experiment; this ensured that the reactor had a concentration well above the Ks for acetate, as previously reported (19). Since the reactor had excess substrate, we operated under anode-potential limitation (-0.400 V vs Ag/AgCl) to decrease the ARB growth rate and be able to perform experiments during the growth phase. Current generation started within 4 days of operation. Once current was generated, we started performing LSCV experiments at different time points. We performed a total of 15 LSCV experiments, 9 of which are presented in this work for simplicity; the times of the 9 experiments are shown by numbered symbols in Figure 2. At day 13, we changed the temperature from 30 to 32 °C in order to perform an additional LSCV at a higher current density. The increase in temperature resulted in a 19% increase in the potential-limited current and jmax (reported below in Figure 3a). Figure 3a shows the results of the 9 LSCV experiments. We corrected the results from the LSCV experiments for the ohmic losses occurring between the anode and the reference electrode in our experimental setup (12, 22). Using our medium conductivity (κsln ) 14.4 mS/cm) and the distance between the anode and reference electrode (L ) 0.6 cm), we calculated the drift in potential caused by ohmic loss: ∆E ) -
jL κsln
(4)
where ∆E is the drift between the potential measured at the reference electrode and the actual anode potential. This drift in potential is a function of j and reached a maximum of 0.042 V for the highest current density obtained in LSCV 9. LSCV curves with low current density (curves 1-4) were not affected significantly by ohmic losses. When compared to its growth curve under potential limitation (-0.400 V, Figure 2), the LSCV scans in Figure 3 have higher current densities for high anode potential. All curvesshowasimilarshape,characteristicoftheNernst-Monod equation (Figure 1b). The jmax values obtained for steadystate conditions were 10.22 ( 0.02 A/m2 at 32 °C and 8.55 ( 0.01 A/m2 at 30 °C. The jmax obtained at 32 °C is consistent with our previously reported value of proton-transport limitation using a 100-mM phosphate buffer (8). Thus, the highest jmax is probably determined by proton-transport limitation. The saturation of all the LSCV curves occurred between -0.35 and -0.25 V vs Ag/AgCl. To determine EKA from the LSCV experiments, we measured the midpoint potential (E at 0.5 jmax) for each experiment. The midpoint potentials for the LSCV experiments 1-8 were similar at -0.425 ( 0.002
V vs Ag/AgCl (- 0.155 ( 0.002 V vs SHE), which is the EKA value for this ARB community. This EKA value is similar to the midpoint potential found by Srikanth et al. (23) while comparing immobilized cultures with naturally grown biofilms of Geobacter sulfurreducens using CV. Their results show a response that resembles the Nernst-Monod curve, with a midpoint potential of -0.15 vs SHE. This EKA is also similar to the one we previously reported (8). When we increased the temperature to 32 °C, the midpoint potential decreased to -0.432 V, a possible indication that EKA depends on temperature. Thus, we used this value as the EKA at 32 °C for our modeling efforts. Nernst-Monod Fitting. Using the average EKA obtained in Figure 3b and the jmax of each curve, we fit the LSCV results using only the ideal Nernst-Monod equation (eq 2). Figure 4a shows the fitting of LSCV curves 1-4, which fall into the low current density range (1 A/m2) also showed good fitting with the Nernst-Monod equation (Figure 4b). A small deviation occurred mainly in the upper part of curves 7-9. These deviations could be the effect of a low κbio in the biofilm, but the deviations are too small to draw any conclusions and are most probably due to experimental variability. Calculation of Biofilm Conductivity (Kbio). Figure 5 shows the expected effect of biofilm conductivity in the jV response of an ARB biofilm anode producing 10 A/m2, according to our conduction model. For the calculation, we used an EKA ) -0.425 V vs Ag/AgCl, fs0 ) 0.1, jmax ) 10 A/m2, and Lf ) 79 µm, which is the biofilm thickness obtained from our highacetate concentration reactor (see Supporting Information). Based on these values, we obtained qmaxXf ) 862 mg BOD/ cm3-d, according to eq 3. Under these conditions, κbio needs to be higher than 0.5 mS/cm in order to maintain the ideal Nernst-Monod curve. As κbio decreases, the current density produced by the biofilm deviates from the Nernst-Monod curve due to the build up of a potential gradient within the biofilm anode. Therefore, we should be able to estimate κbio based on the deviation of our experimental results from the ideal Nernst-Monod curve. However, all our LSCV curves were successfully fitted with the ideal Nernst-Monod. This supports that the biofilm anode was highly conductive so that potential losses across the biofilm were negligible. Since the biofilm was highly conductive, we were not able to calculate an exact value of κbio from our experiments, but we know it should be higher than 0.5 mS/cm2 in order to maintain the ideal Nernst-Monod shape. The lack of significant potential losses due to transport of electrons across a 79-µm biofilm clearly indicates that our ARB biofilm is using a solid conductive matrix. Potential losses would necessarily be expected from any ARB biofilm that relies on soluble electron shuttles, as a significant concentration gradient is needed to transport these shuttles to and from the anode surface by diffusion. This occurrence of high potential losses is exemplified in theoretical model results for electron shuttles (13), as well as experimental results (9). The fact that our ARB community was able to generate a high current density without significant potential loss over a distance of ∼ 79 µm for our high-acetate experiment suggests that ARB could transfer the electrons to distances at least an order of magnitude higher than this biofilm VOL. 42, NO. 17, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 3. (a) LSCV curves at different time points throughout the growth phase of the high-acetate MEC. The numbering of the curves matches the numbering in Figure 2, indicating the point at which the curve was generated. (b) Midpoint potentials of each LSCV run. The EKA selected was based on the midpoint potentials from LSCV curves 1-4. Notice that the vertical scale in panel (b) goes from -0.44 to -0.42 V.
FIGURE 4. Nernst-Monod fitting for LSCV curves 1-4 (a) and LSCV curves 5-9 (b) based on EKA (30 °C) ) -0.425 V vs Ag/AgCl, EKA (32 °C) ) -0.432 V vs Ag/AgCl, and the average jmax of each individual curve. The dotted lines indicate the fitting of the Nernst-Monod equation (eq 2).
FIGURE 5. Effect of biofilm conductivity (Kbio) on the jV response of an ARB biofilm anode. We used the following typical values for the calculation: EKA ) -0.425 V vs Ag/AgCl, Lf ) 79 µm (obtained from confocal microscopy images of our biofilm anode), jmax ) 10 A/m2, fs0 ) 0.1. A qmaxXf ) 862 mg BOD/cm3-d was calculated based on eq 3. thickness without losing a significant amount of energy. Although we as yet have no direct evidence of bacterial electron transfer over longer distances (e.g., mm or cm scale), our results support the idea of this capability, which has been already proposed by Ntarlagiannis et al. (24). Low-Acetate Concentration Experiments. We used an MEC fed with 1 mM acetate to form an ARB biofilm that was substrate limited. We operated the reactor for 14 days under substrate limitation at 30 °C (data not shown) and generated a j-V curve by changing the anode potential. These results are in Figure 6a, and the effluent concentration was 0.13 ( 0.02 mM. At day 14, we spiked the reactor with acetate up to 25 mM and performed a j-V curve, which is compared to one performed under low-acetate concentrations in Figure 6. The j-V curves were also corrected for ohmic losses between the anode and reference electrode, according to eq 4. The drift in anode potential reached a maximum of 0.015 V at saturation of the high-acetate concentration j-V curve. At low acetate concentrations, the jV response saturated over a narrow range of anode potential, showing a midpoint 6596
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FIGURE 6. Effect of substrate concentration on the j-V response. Comparison of the j-V response for an acetate-limited condition (0.13 mM; blue line) and after a 25-mM acetate spike (red line). The dotted line indicates the fitting of the Nernst-Monod equation (eq 2). potential of -0.463 V vs Ag/AgCl (Figure 6). This midpoint potential is not equal to EKA, because the saturation current is not jmax when the anode biofilm is substrate limited. When the MEC was spiked with acetate, the resulting j-V curve followed the Nernst-Monod relationship, with an EKA ) -0.430 V vs Ag/AgCl. This EKA is slightly lower than the average obtained by the LSCV experiments; this small deviation could be due to the longer time it took to perform the j-V experiment (approximately 6 h), which resulted in biomass growth as the experiment was performed. The effect of biomass growth is evidenced in Figure 6, because the highacetate j-V curve did not saturate completely; instead, it had a slight increase as the potential was increased. Therefore, we suggest the use of LSCV to determine the EKA, especially when the biofilm is not at steady state. Our results at low-acetate concentrations demonstrate that the midpoint potential of a j-V curve is not always equal to the EKA. Deviations due to substrate or potential gradients within the biofilm anode can affect the measurement of EKA. Thus, we recommend measuring EKA by performing a LSCV while the ARB biofilm anode is starting to grow and the
current density is still low. Under these conditions, the biofilm is still thin, minimizing substrate or potential gradients. Implications of the Nernst-Monod Equation Modeling. Our overall results show that the Nernst-Monod equation effectively represented the anode potential loss of an ARB biofilm anode. Only two parameters were needed to fit the results: jmax and EKA. The Nernst-Monod fitting confirms that microbial metabolism controlled the anode-potential loss of the biofilm anode. Anode-potential losses in our biofilm anode were determined by our microbial community’s EKA value and reached ∼0.225 V at saturation current. Our estimation of a high κbio (g0.5 mS/cm) indicates that potential losses were not limiting current density; as previously hypothesized (8), only proton transport seems to be the limiting factor. We must point out that, similar to the Monod KA, EKA depends on the microbial community and the metabolic pathway used by that community. Thus, our EKA value is applicable only to our biofilm community. Similarly, the high κbio obtained in our experiments probably is affected by the manner in which we ran experiments with a simple substrate (acetate) and low anode potentials. The latter would seem to be a strong selective force for ARB to have a highly conductive biofilm. Also, it is possible that the presence of non-ARB organisms in the biofilm could decrease κbio, whereas our community was largely composed of ARB. Thus, our work is focused on establishing a groundwork and methodology for ARB kinetic modeling rather than presenting generalizable parameters for it.
Acknowledgments
(7) (8) (9)
(10)
(11) (12) (13) (14)
(15)
The funding for this work was provided by OpenCEL and NZ Legacy.
Supporting Information Available Determination of the ARB biofilm thickness using confocal microscopy and a discussion on the evidence that our ARB utilize a biofilm anode as the main electron transfer pathway. This material is available free of charge via the Internet at http://pubs.acs.org.
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