Simulation of Multistep Enzyme-Catalyzed Methanol Oxidationin Biofuel Cells

Piyush Kar,a,* Hao Wen,a,** Hanzi Li,a Shelley D. Minteer,b,*

and Scott Calabrese Bartona,*,z

aDepartment of Chemical Engineering and Materials Science, Michigan State University, East Lansing,Michigan 48823, USAbDepartment of Chemistry, Saint Louis University, St. Louis, Missouri 63103, USA

We report a simulation of multi-step enzyme catalysis and cofactor-mediated electron transfer in a bio-anode of a methanol biofuelcell. Three nicotinamide adenine dinucleotide (NADþ) dependent dehydrogenase enzymes, namely alcohol dehydrogenase(ADH), aldehyde dehydrogenase (AlDH), and formate dehydrogenase (FDH) combine to achieve complete oxidation of methanolto carbon dioxide. Oxidation of methanol by the enzyme cascade produces the reduced co-factor, NADH, which is oxidized toregenerate NADþ at an electrode comprised of a poly(methylene green) catalyst electrodeposited on carbon paper. Kineticparameters for the enzymatic oxidation reactions were experimentally determined between pH 6.5 and 9 and were employed inthe simulation to evaluate the effect of pH. Model results compare closely to previously reported experimental data over a broadpH range. Model-based analysis indicates that cell performance is controlled by NADþ transport and NADH oxidation kineticsfor electrode specific areas lower than 3 m2 cm�3 and shifted to enzyme kinetic control at higher specific area. An optimalelectrode design is predicted to achieve current density exceeding 10 mA cm�2.VC 2011 The Electrochemical Society. [DOI: 10.1149/1.3561690] All rights reserved.

Manuscript submitted September 27, 2010; revised manuscript received February 7, 2011. Published March 28, 2011. This wasPaper 405 presented at the Vancouver, BC, Canada, Meeting of the Society, April 25–30, 2010.

Biofuel cells have evolved in myriad directions since their dis-covery in 1911.1 In the first biofuel cells, microorganisms catalyzedthe conversion of chemical energy of sugars to electrical energy.The limited current or power density generated by microbial biofuelcells led to the invention of enzymatic biofuel cells by Kimble andco-workers.2 Enzymatic biofuel cells use enzymes to catalyze oxida-tion and reduction reactions at the anode and cathode, respectively.A variety of fuels, including alcohols, fatty acids, carbohydrates andsugars can be used in enzymatic biofuel cells.3 Owing to enzymeselectivity, low operating temperature, activity at moderate pH andmanufacturability using biotechnology approaches, the applicabilityof enzymatic biofuel cells has widened and includes distributed,portable and implantable energy sources.4–14

Current areas of intensive research are the improvement of sta-bility of enzyme electrodes and maximization of current and powerdensities in enzymatic biofuel cells. Single enzymes electrodestypically achieve only partial oxidation of fuels.15,16 For example,glucose oxidase catalyzes the oxidation of glucose to gluconolac-tone, releasing only two of the available 24 electrons per glucosemolecule. In contrast, multiple enzyme cascades are capable ofcompletely oxidizing fuels,17 and facilitating improved energy den-sities.18 Such cascades represent a balance between the high powerdensity of enzymatic electrodes and high efficiency of microbialsystems.

For example, methanol may be fully oxidized to CO2 via the fol-lowing mechanism19

CH3OHþ NADþ �!ADHCH2Oþ NADHþ Hþ

CH2Oþ NADþ þ H2O �!A1DHCH2O2 þ NADHþ Hþ

CH2O2 þ NADþ �!FDHCO2 þ NADHþ Hþ

[1]

where each reaction is catalyzed by a NADH-dependent dehydrogen-ase enzyme: alcohol dehydrogenase (ADH), aldehyde dehydrogenase(AlDH), and formate dehydrogenase (FDH). As demonstrated byPalmore et al.,17 the cofactor, nicotinamide adenine dinucleotide(NADþ), is reduced in the enzyme-catalyzed reactions and trans-ported to the electrode, where it can be regenerated according to

NADH �!catalystNADþ þ Hþ þ 2e� [2]

The cofactor NADH can therefore be considered to be a mediator,because it transports electrons between the enzymes and electrode.20

The formal redox potential of NADþ/NADH is �0.56 V/SCE;21

however the oxidation of NADH on carbon electrodes has poorkinetics and requires large overpotentials.22 The first methanol bio-fuel cell employed a diaphorase/benzyl viologen couple as NADHoxidation catalyst.17 Recently, azine dyes such as methylene green,toluidine blue, and neutral red have been electropolymerized on car-bon surfaces to form stable and adherent coatings with enhancedcatalytic activity toward NADH oxidation.23–25

Electropolymerized poly(methylene green) was used by Addo etal. for a methanol biofuel cell anode.26 ADH, AlDH, and FDH wereimmobilized in hydrophobically modified Nafion and incorporatedinto carbon paper coated with an electropolymerized poly(methy-lene green) film.27 Marked improvement in methanol oxidation cur-rent densities were reported for the three-enzyme cascade as com-pared to single and two-enzyme systems. A similar improvement inperformance is reported for ethanol oxidation in an enzymatic bio-fuel cell using multiple immobilized NADþ dependent enzymes.28

The above-described multistep methanol anode serves as an ex-perimental basis for a simulation of multi-enzyme oxidation, toenhance quantitative understanding of the parameters affecting bio-fuel cell performance. Kjeang et al.29 have reported a modeling studyof fluid dynamics and multiple enzymes in a enzymatic biofuel cellwith microfluidic channels. Hettige et al.30 built upon this model byintroducing the electrochemical kinetics of cofactor regeneration asdescribed by Eq. 2, and considered the effects of convection and seg-regation of enzymes to optimize pH and kinetics of individual reac-tion steps. Here, we focus on a single phase in which all enzymes areimmobilized, which is more analogous to experimental systems.26,31

The effects of pH, fuel, co-factor and enzyme concentrations, cellpotential and electrode surface area are addressed. Kinetic parame-ters of ADH, AlDH and FDH experimentally determined at pHbetween 6.5 and 9 are incorporated in the model. Findings of themodel are directly applicable to biofuel cells and biosensors operat-ing on similar methodology. The modeling approach can be extendedto other types of multi-step enzymatic electrodes, including thosemimicking metabolic and electrolytic processes.18,28,31

Model Development

The enzymatic biofuel cell for multi-step catalytic oxidation ofmethanol is described schematically in Fig. 1. The anode is assumed

* Electrochemical Society Active Member.** Electrochemical Society Student Member.

z E-mail: scb@msu.edu

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to have uniform cross-section and a thickness, w, and consists of acatalyst-coated solid porous conductor, e.g. poly(methylene green)coated carbon paper, whose void volume is completely filled withan immobilization phase (e.g. Nafion) that contains all threeenzymes and that is permeable to all aqueous species. Electrons gen-erated by enzyme catalyzed oxidation (Eq. 1) are transported viaaqueous NADH to the catalyzed carbon surface, where NADH iselectro-catalytically re-oxidized (Eq. 2), transferring the electrons tothe solid phase. Protons formed in the anodic process diffuse to thecathode through the aqueous electrode phase and bulk solution, andelectrons are directed to the cathode through an external circuit. Aplatinum-catalyzed oxygen cathode with relatively fast kinetics isassumed for this study.

Each enzyme step involves NADþ as the enzyme cofactor. Thecomplete oxidation of a single molecule of methanol involves thetransfer of six electrons to three molecules of NADþ. All reactionsare assumed to be irreversible, which is a reasonable assumption forhighly polarized electrodes, but less appropriate near the open cir-cuit potential.

Enzymes are considered as immobilized species having fixedconcentrations, whereas methanol, NADþ, and the intermediatereaction products (i.e. formaldehyde, formic acid and NADH) aremobile. Pore sizes of Tetra Butyl Ammonium Bromide (TBAB)modified Nafion are of the order of 1–10 lm (Refs. 32 and 33) andhence much larger than those in un-modified Nafion.34 Therefore,faster species transport occurs in TBAB modified Nafion, which jus-tifies omitting transport limitations on the scale of electrode pores.With this assumption, the system can be treated as one-dimensionalwith a steady state material balance20 for each mobile species(methanol, formaldehyde, formic acid, NADþ, NADH) given by

Di

d2Ci

dx2� v

dCi

dx¼X

sijRj [3]

In Eq. 3, x is the position within the one-dimensional electrode do-main, i denotes species and j denotes reactions in Eqs. 1 and 2, Ci

and Di are the concentration and diffusivity of species i, and v is theflow velocity. Rj is the rate of the jth reaction (mol per volume pertime) and sij is the stoichiometric coefficient of the species i in reac-tion j.

NAD-dependent dehydrogenase enzyme kinetics generally fol-low the ordered sequential bi-bi model,35 wherein the enzyme binds

NADþ followed by the substrate to form a ternary complex. Ratesof enzyme–catalyzed reactions (Eq. 1) are expressed using an or-dered bi-bi form

REnz ¼kcat;EnzCEnzCNCi

KiN;EnzKC;Enz þ KN;EnzCi þ KC;EnzCN þ CNCi

[4]

In Eq. 4, KiN,Enz is a dissociation constant for the cofactor (NADþ)and enzyme complex. KN,Enz and KC,Enz are Michaelis constants forNADþ and substrate, respectively. Substrates are methanol, formal-dehyde and formic acid for the ADH, AlDH and FDH enzymes,respectively. kcat,Enz is the turnover number. Ci, CN, and CEnz repre-sent the substrate, co-factor and enzyme concentrations, respec-tively. Subscript “Enz” refers to enzymes in this paper, and may bereplaced with subscripts “ADH”, “AlDH” or “FDH” to refer to aspecific enzyme reaction.

The electrode reaction rate, RNADH (dimensions mol per volumeper time), depends on NADH concentration, potential, and electrodesurface area. These dependencies are considered using Eq. 5, whichis adapted from experimental measurements of NADH oxidation atelectrodes modified by electro-polymerized poly(methylene green)(Ref. 23)

RNADH ¼akCNh

KS þ CNh

expðV � UÞ=b

1þ expðV � UÞ=b

� �[5]

The first term in Eq. 5 represents dependence on NADH concentra-tion, CNh, reflecting Langmuir adsorption, with an adsorption coeffi-cient KS. The parameter a is the specific area per unit volume of thecarbon electrode, and k is the rate constant for NADH oxidation,related to the maximum steady state current density for NADH oxida-tion, i0, on the surface of poly(methylene green) by k¼ i0/2F, whereF is Faraday’s constant. The second term (in braces) is a Nernstianexpression accounting for potential dependence, where V is the elec-trode potential, U the half-wave potential, and b the Tafel slope. Theparameters U and b were obtained from experimental data for pH val-ues between 6 and 9, as described in the experimental section.

The material balance equations (Eq. 3) may be converted to theirrespective non-dimensional forms by normalizing all species con-centrations by the bulk concentration of methanol, CM0, normalizingposition within the electrode by the electrode thickness, w, and nor-malizing all diffusivities by the methanol diffusivity (DM).

Figure 1. (Color online) Schematic of thebiofuel cell operating on multi-stepenzyme kinetics and mediated electrontransfer.

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Multiplication on both sides of Eq. 3 by w2/DM CM0 yields the non-dimensional material balance

di

d2C0idx02� Pe

dC0idx0¼X

sijrj [6]

In Eq. 6, C0i¼Ci/CM0 are non-dimensional concentrations, di¼Di/DM dimensionless diffusivities and Pe¼ v w/DM is the Peclet num-ber, a ratio of the rate of convection to the rate of diffusion. For themodel described in this paper, the velocity, v, is zero and thereforePe is zero for all species.

Non-dimensional reaction rate expressions, rj, for the enzyme-catalyzed reactions can be expressed as rEnz and are given by

rEnz ¼DaEnzC0NC0i

½riN;EnzrC;Enz þ rN;EnzC0i þ rC;EnzC0N þ C0NC0i�[7]

In Eq. 7, C0i and C0N represent the normalized substrate and co-factorconcentrations, respectively, and DaEnz are the Damkohler numbersfor the enzymatic reactions, defined as

DaEnz ¼kcat;EnzCEnzw2

DMCM0

[8]

The Damkohler number represents the ratio of reaction rate to diffu-sion rate, and is comparable to the Thiele modulus. Damkohlernumbers for the enzymatic reactions (Eq. 1) are also referred to asDaEnz in this paper. The parameter riN,Enz¼KiN,Enz/CM0 is the

non-dimensional dissociation constant for NADþ and enzyme com-plex. rN,Enz¼KN,Enz/CM0 and rC,Enz¼KC,Enz/CM0 are non-dimen-sional Michaelis Menten constants. Similarly, the non-dimensionalform of the electrode reaction rate, rNADH , given by

rNADH ¼DaNADHC0Nh

ðrS þ C0NhÞ[9]

where rS¼KS/CM0. In this case, the Damkohler number, DaNADH,is given by

DaNADH ¼akw2

DMCM0

exp½ðV � UÞ=b�1þ exp½ðV � UÞ=b�

� �[10]

At the electrode-electrolyte interface (left side in Fig. 1), the dimen-sionless methanol and NADþ concentrations were assumed to befixed at their bulk values (CM0 and CN0, respectively) and the con-centrations or all other species were assumed to be zero. At theelectrode-current collector interface (right side in Fig. 1), the con-centration gradients for all species were assumed to be zero. Thusthe boundary conditions are given by

x0 ¼ 0 : C0M ¼ 1; C0N ¼CN0

CM0

; C0Nh ¼ C0A ¼ C0F ¼ 0 [11]

x0 ¼ 1 :dC0idx0¼ 0 [12]

Table I. Parameters and nominal values.

Parameter* Value References

Bulk concentration of methanol, CM0 0.5 M 26

Bulk concentration of NADþ, CN0 1.5 mM 26

Diffusivity of methanol, DM 4.0� 10�6 cm2 s�1 42

Anode Potential, V 0.8 V/RHE 26

pH 7.5 26

Temperature 25�C 26

Diffusivities of NADþ(DN) and NADH (DNh) b 3.3� 10�8 cm2 s�1 36 and 37

Diffusivity of formaldehyde, DAa 4.0� 10�6 cm2 s�1

Diffusivity of formic acid, DF 3.9� 10�6 cm2 s�1 43

Electrode thickness, w 190 mm 26

Specific area (carbon paper), a 0.2 m2 cm�3 44

Half-wave potential for NADH oxidation, U 0.778 V/RHE Fig. 3

Tafel slope, b 53 mV/decade Fig. 3

Surface adsorption constant for NADH, KS 3.76 6 0.5 mM Measured

Rate constant for NADH oxidation, k 0.27 mmol cm�2 s�1 Fig. 3

Partition coefficient for methanol 1 38

Partition coefficient for NADþ 1 Assumed

Turnover number, kcat, ADH 0.17 6 0.01 s�1 Fig. 2

Michaelis constant for mediator, KN, ADH 0.19 6 0.04 mM Fig. 2

Michaelis constant for substrate, KC, ADH 0.29 6 0.04 M Fig. 2

Dissociation constant KiN,ADH 0.60 6 0.30 mM Measured

Turnover number, kcat, AlDH 1.22 6 0.05 s�1 Fig. 2

Michaelis constant for mediator, KN, AlDH 0.28 6 0.06 mM Fig. 2

Michaelis constant for substrate, KC, AlDH 0.10 6 0.02 mM Fig. 2

Dissociation constant KiN,AlDH 0.20 6 0.08 mM Measured

Turnover number, kcat, FDH 6.15 6 0.32 s�1 Fig. 2

Michaelis constant for mediator, KN, FDH 0.09 6 0.02 mM Fig. 2

Michaelis constant for substrate, KC, FDH 19 6 3 mM Fig. 2

Michaelis constant for mediator, KiN, FDH 0.80 6 0.3 mM Measured

DaNADH 0.04 Using Eq. 10 and Ref. 26

DaADH 0.38 Using Eq. 8 and Ref. 26

DaAlDH 2.22 Using Eq. 8 and Ref. 26

DaFDH 26.29 Using Eq. 8 and Ref. 26aAssumed to be identical to diffusivity of methanol.bThe diffusivity of NADþ and NADH were assumed to be equal.cFor pH-dependent parameters, the nominal value at pH 7.5 is given, with pH dependence shown in Figs. 2 and 3.

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The non-dimensional rate of NADH oxidation, rNADH, was inte-grated over the dimensionless electrode length, x0, to obtain the cur-rent per unit electrode area, I (A cm�2), using the expression

I ¼ 2FDMCM0

w

� �ð1

0

rNADHdx0 [13]

Relevant dimensional parameters and assumed nominal values aretabulated in Table I. These parameters are intended to match the ex-perimental study of Addo et al.26 In that work, ADH, AlDH andFDH were immobilized in tetra butyl ammonium bromide (TBAB)modified Nafion. The TBAB modification process, reported byThomas et al.,33 enlarges the micellar pores within Nafion, whicheffects faster diffusion of aqueous species. NADH diffusivity inNafion (�10�9 cm2 s�1) (Ref. 36) is much lower than that in phos-phate buffer solution (�3.3� 10�6 cm2 s�1).37 The NADH diffusiv-ity assumed for this study (�3.3� 10�8 cm2 s�1) is larger than thatin Nafion and still 100-fold lower than that in buffer. The partitioncoefficient of methanol into Nafion is estimated as one, which isconsistent with the literature reported value.38 Partitioning of NADþ

in Nafion is not reported in literature and a value of one is assumed.The non-dimensional material balance equations (Eq. 6) and

accompanying boundary conditions (Eqs. 11 and 12) were solvedusing the commercially available finite element software package,COMSOL, in combination with the mathematical utility software,MATLAB.

Experimental

The enzymes ADH from Saccharomyces cerevisiae (EC 1.1.1.1),and FDH from Candida boidinii (EC 1.2.1.2) were purchased fromSigma Aldrich. AlDH from Pseudomonas putida (EC 1.2.1.46) waspurchased from Fisher Scientific. Enzymes were suspended into abuffer solution in small vials and frozen at �70�C before use.The co-factor NADþ, methanol, formaldehyde, and formic acidwere from Sigma Aldrich and used as received. Kinetic parameterswere measured in between pH 6.5 and 9.0, using a UV-Vis spec-trometer (Cary 50, Varian). A solution of NADþ and methanolmixture was made with phosphate buffer at the desired pH, withenzymes added to the solution immediately before measurement.The initial rate of NADH formation, as observed by optical densityat 339 nm with an extinction coefficient of 6220 M�1cm�1 wasobtained under each condition. Measured rate versus substrate con-centration were fitted to the ordered bi-bi kinetic equation (Eq. 4) toevaluate the kinetic parameter values. Dissociation constant KiN,Enz

was determined for pH 7.0 for the three enzymes and is assumed tobe constant over the range of pH. Values of 0.60, 0.15 and 0.80 mMfor the ADH, AlDH and FDH catalyzed reactions, respectively.Experimentally determined turnover numbers, kcat and Michaelisconstants, KN,Enz and KC,Enz for the cofactor and substrate respec-tively, are illustrated in Fig. 2. Interpolation was applied to obtainenzyme kinetic parameters at desired pH values.

Kinetic parameters for poly(methylene green) catalyzed NADHelectro-oxidation were measured in phosphate buffer of pH 6.0, 7.4and 8.2 at room temperature. A glassy carbon working electrodewas coated with poly(methylene green) by electro-polymerization.39

The NADH concentration was 0.5 mM. An AgjAgCl reference anda platinum wire counter electrodes were employed. The electrolytewas purged with argon and the working electrode was rotated at aconstant speed of 900 rpm. Potential was stepped at distinct inter-vals in the range of �0.15 to 0.4 V/AgjAgCl, and steady statecurrent density at each potential was recorded. In a separate experi-ment, in order to obtain concentration dependent oxidation rates,NADH concentration was varied between 1 and 20 mM at a con-stant potential of 0.05 V/AgjAgCl and a pH of 7.5.

Polarization results are shown in Fig. 3, with the potential plottedrelative to the reversible hydrogen electrode (RHE, URHE¼UAgjAgClþ 0.22þ 0.059� pH). It can be seen that the three curves

overlap when plotted in this way, suggesting that NADH oxidationis a two-electron, two-proton reaction. A KS value of 3.7 mM wasobtained by fitting 2FRNADH/a to the concentration dependentsteady state current densities, where, RNADH is as defined in Eq. 5.i0, U and b were obtained by a sigmoid fits of the polarization curvesand are given in Table II. The parameters i0, U and b do not displaysignificant variation with pH. The measured values for the kineticparameters U, i0, KS and b are consistent with literature data.40

Results and Discussion

Concentration profiles.— Steady-state concentrations of reac-tants and cofactors govern biofuel cell current and power. Figure 4shows non-dimensional concentration profiles under the baseline

Figure 2. (Color online) Kinetic parameters for the three enzymes, (a) kcat,Enz,(b) KN,Enz, and (c) KC,Enz.

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conditions (Table I), intended to match experimental conditionsemployed by Addo et al.26 The overall reaction is limited by thesupply of NADþ, both by transport from bulk solution and regenera-tion via the electrode reaction (Eq. 5); the concentration of NADþ

drops to near zero far from the electrode-solution interface (x/w¼ 0). In contrast, the NADH concentration increases until itattains an approximately constant value corresponding to the inletNADþ concentration. The concentration profiles for the other spe-cies are more or less flat, with formaldehyde and formic acid attain-ing near-zero concentrations owing to the significantly higher ratesof enzymatic consumption of these species (rAlDH and rFDH) as com-pared to methanol consumption (rADH).

Electrochemical kinetic effects.— The baseline condition consid-ers a relatively low surface area per unit volume, a, of carbon paper(0.2 m2 cm�3) which can be increased 100-fold by addition of nano-materials on the surface of carbon support.41 Figure 5 provides anindication of the effect of increase in specific area on electrode per-formance. At baseline conditions, oxidation current density fallsbelow 0.5 mA cm�2 independent of pH, indicating control by theNADH oxidation reaction. Increasing the specific area by 2 ordersof magnitude transfers overall control of the rate to the ADH reac-tion (rADH). Thus the overall current density becomes pH dependentand increases over twenty fold at pH 8.

The effect of pH on electrode kinetics is shown in Fig. 5. At highelectrode surface areas (>10 m2 cm�3) anode current density varieswith respect to pH (Fig. 5b) due to enzyme control of the reactionrate. Thus observed variation arises from the pH dependence of thesecond order rate constant, kcat,ADH/KC,ADH, for the ADH reaction,which is rate controlling under these conditions. Figure 5a showsthe variation of kcat,ADH/KC,ADH with pH.

Figure 6 shows polarization curves for the baseline (a¼ 0.2 m2

cm�3) and a high specific area (10 m2 cm�2) condition. The contri-bution of individual enzyme steps (ADHþAlDH andADHþAlDHþ FDH) on overall current density at baseline condi-tions, as shown in Fig. 6, cannot be distinguished from that of thesingle (ADH only) reaction step because of control by the electro-chemical NADH oxidation reaction. At a higher specific area(a¼ 10 m2 cm�3), when the ADH reaction controls current density,addition of AlDH and FDH doubles and then triples the current den-sity, because these reaction steps are fast and essentially go to com-pletion. This effect is comparable to that observed experimentallyby Addo et al.26

Biofuel cell performance.— Current and power densities for thebiofuel cell were experimentally determined at various potentialsand pH by Addo et al.26 Their experimental data may be comparedto model-generated current densities at baseline conditions at vari-ous fixed cathode potentials, as shown in Figs. 7a and 7b, whereFig. 7a shows the cell potential at various pH and Fig. 7b shows thecorresponding cell current densities. Calculated current densitiesagree reasonably well with experimental values at high cathodepotential. Differences between experimental and calculated results

Figure 3. (Color online) Oxidation of NADH at a poly(methylene green)electrode at various pH at NADH concentration of 0.5 mM.

Table II. Kinetic parameters for NADH oxidation on the surface

of poly(methylene green).

pHHalf-wave potential,

U(V/RHE)Tafel slope,

b(mV decade�1)Maximum current

density, i0a (lA cm�2)

6.0 0.755 6 0.010 54 6 7 26.73 6 1.46

7.4 0.778 6 0.002 46 6 2 26.66 6 0.34

8.2 0.781 6 0.011 59 6 9 24.72 6 1.12ai0 was estimated by normalizing maximum current densitiesobtained from Fig. 3 by CNh/(KSþCNh), where CNh¼ 0. 5 mM andKS¼ 3.70 mM.

Figure 4. (Color online) Plots of non-dimensional concentration profilesand the non-dimensional reaction rate for NADH oxidation, at baseline con-ditions (Table I).

Figure 5. (Color online) Effect of pH on electrode kinetics: (a) Alcohol de-hydrogenase specificity, kcat/KC. (b) Anodic current density at various spe-cific areas. All other conditions are at baseline (Table I).

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may be attributed to factors such as internal ohmic resistance andpH-dependence of oxygen reduction kinetics, which are not incorpo-rated in the model.

Optimum condition.— Damkohler numbers for NADH oxidationreaction, DaNADH, and enzymatic reactions, DaEnz (i.e. DaADH,

DaAlDH and DaFDH), depend on electrode width, kinetic parameters,and species concentrations. In addition, DaNADH depends on thespecific area of the electrode and the applied anode potential andDaEnz depends on enzyme concentrations. The Damkohler numbersfor each reaction provide an indication of the relative rate (com-pared to other reactions) and the degree to which mass transportlimits that particular reaction. As indicated in Table I for baselineconditions, DaNADH is less than one and smaller than DaEnz, sug-gesting negligible mass transfer limitation and indicating thatNADH oxidation is rate limiting at baseline conditions. A relatively

easy way to increase DaNADH is to increase the surface area per unitvolume, a, of the carbon support.

Assuming realistic parameter values, DaNADH can be variedbetween zero and ten and DaEnz can be varied between zero andthirty. Thus the model can be used to evaluate the effect ofDaNADH values between zero and ten for DaEnz values of one andthree. For DaEnz¼ 1, enzyme kinetics controls overall current den-sity, which remains less than a representative mass-transport lim-ited value given by imt¼ 6FDMCM0/w. The opposite occurs forDaEnz¼ 3, in that current density is the mass-transport controlledand falls below than the enzyme kinetics limited values. Figure 8shows the predicted current densities normalized by imt for bothvalues of DaEnz. Theses normalized current density values arestrongly dependent on DaNADH. Optimum conditions occur whenDaNADH is at least three times DaEnz. The factor of three can beexplained by the fact that three molecules of NADH are oxidizedfor every molecule of methanol that is converted to CO2. A three-fold increase in current density is observed (Fig. 8) when DaEnz isincreased from one to three and corresponding DaNADH increasesfrom three to nine.

Kinetic cases.— From an engineering standpoint, the anodicprocess can be categorized into two kinetic cases, each specified

Figure 6. (Color online) Effect of enzyme addition on anodic current densitiesat two values of specific area, a. Other conditions are at baseline (Table I).

Figure 7. (Color online) Comparison of experimental and calculated biofuelcell performance. (a) cell potential and (b) current density at various pH.Other conditions are at baseline (Table I).

Figure 8. (Color online) Effect of Damkohler number on current densitynormalized by imt ¼ 6FDmM0/w. Concentration of NADþ¼ 15 mM, andother conditions are at baseline (Table I). Optimum values of DaNADH¼ 3and 9 are observed for DaEnz¼ 1 and 3, respectively.

Figure 9. (Color online) Electrode performance for two design cases. Con-centration of NADþ¼ 5 mM and other conditions are at baseline (Table I).

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by a set of Damholer numbers for the four reactions. Case 1:DaNADH � DaEnz � 3, and control is shared by all four reac-tions with some incipient mass transfer limitation. Case 2:DaNADH � 15, and DaEnz � 3; the optimal case in which thethree enzyme reactions share overall controll. The current den-sity versus pH curves representing these two cases are illus-trated in Fig. 9. Current densities for Case 2 are highest becausethis is an optimal condition (see Fig. 8) and the pH profile isdictated by enzyme kinetics. Current density for Case 1 is lowerthan that for Case 2 because of lower electrode area (and theresulting lower DaNADH). Concentration profiles for the twocases are shown in Fig. 10. A steeper concentration gradient isobserved for methanol in Case 2 as compared to Case 1 becauseof comparatively higher surface area combined with highenzyme loading. In Case 2, NADH is oxidized at a fast rate dueto large DaNADH (high surface area), causing close to completeregeneration of NADþ. In Case 1, residual unoxidized NADHremains on the electrode surface due to relatively slow electro-chemical regeneration.

Conclusions

A numerical simulation of a biofuel cell anode operating onmulti-step enzyme catalysis is presented and the impact on perform-ance of a number of design parameters is described. NADH oxida-tion kinetics control current density at low electrode specific areas,as in the case of carbon paper. With increase in specific area of theelectrode, control shifts to methanol oxidation by ADH. FDH andAlDH catalyzed reactions have faster kinetics and therefore do notaffect the cell current and power densities. At high specific areas,typically more than 3 m2 cm�3, peak anodic current densities arepredicted to exceed 10 mA cm�2 at pH 8 and sharply fall at pH val-ues higher than 8.5 and lower than 7.5. Model findings agree withexperimental data in terms of cell current density at various pH andcell potentials. Improved prediction near open circuit will requireconsideration of reversible electrode and enzyme kinetics that are

not included here. These results indicate the potential performancethat may be enabled by improved electrode design.

Acknowledgments

The authors gratefully acknowledge financial support from theAir Force Office of Scientific Research (Award FA9550-06-1-0264through the University of New Mexico).

Michigan State University assisted in meeting the publication costs ofthis article.

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Figure 10. (Color online) Concentration profiles for two design cases. Con-centration of NADþ¼ 5 mM and other conditions are at baseline (Table I).

Journal of The Electrochemical Society, 158 (5) B580-B586 (2011)B586

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