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SUPPLEMENTARY MATERIAL
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MICROBIAL ECOLOGY MEETS ELECTROCHEMISTRY: ELECTRICITY
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DRIVEN AND DRIVING COMMUNITIES
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Korneel Rabaey1,2*, Jorge Rodríguez1, Linda Blackall1, Jurg Keller1, Damien Batstone1, Willy
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Verstraete2, Kenneth H Nealson4
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Submitted to: The ISME Journal
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Building, Brisbane, Queensland 4072, Australia
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Links 653, 9000 Ghent, Belgium
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USA
The Advanced Wastewater Management Centre, University of Queensland, Gehrman
Laboratory of Microbial Ecology and Technology (LabMET), University of Ghent, Coupure
Department of Earth Sciences, University of Southern California, Los Angeles, CA 90089
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*Corresponding author: Dr. Korneel Rabaey, The Advanced Wastewater Management Centre,
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Gehrman Building (60), The University of Queensland, Brisbane, Queensland 4072,
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Australia, Tel. +61 7 3365 7519, Fax. +61 7 3365 4726, k.rabaey@uq.edu.au
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S1. Nernst Planck interactions and the relationship to diffusivity
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It can be assumed that in biofilms and diffusion limited systems, redox shuttles will
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demonstrate differences in diffusivity through the biofilm based on their redox status.
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Negatively charged shuttles will be attracted by the more positively charged electrode, while a
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positively charged shuttle will be repulsed or at least less intensively attracted by the
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electrode. The influence of these electrostatic interactions on overall diffusivity can be
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evaluated using well established fundamental theory.
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The Nernst Planck equation provides an adapted diffusivity of compounds, i.e. shuttles,
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moving to and from differently charged objects (MacGillivray 1968):
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nF
E 
 S
J  D   SH 
 S SH  
R T
x 
 x
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With J the flux of the shuttle away from the electrode (molSH/m2·s), n the electric charge of
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the shuttle, D the diffusivity constant (m2/s), F the Faraday’s number (C/mole), SSH the
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concentration of the shuttle at position x (molSH/m3), E the electrostatic potential (V), R the
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universal gas constant (C·V/mole·K), T the temperature (K), x distance to the electrode (m).
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Here the first term applies to the diffusive driving force and the second to the electrostatic
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driving force. Since the shuttle is the key electrochemically active compound in the potential
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field it can be assumed that E = ESH.
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The equation is discretized within the main biofilm model, for a static biofilm model with the
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differential terms calculated as follows:
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nF
E 
 S
J  D   SH 
 S SH  SH 
R T
x 
 x
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ESH, and SSH are calculated from the difference between the values at layer i and layer
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i-1. Boundary conditions at the anode and biofilm surface are applied as normal. Taking a
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shuttle similar to phenazine-1-carboxamide as an example, assuming the reduced form of the
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shuttle as charged -1 and the oxidised as 0, with some estimations for parameters:
Parameter
Value
Explanation
D
6.61·10-6 cm2 s-1
Diffusion constant of phenazine-1-carboxamide*
T
300 K
Temperature
pH
7.00
pH
SSH
5·10-5 mol L-1
Total shuttle concentration
nred
-1
Electric charge of reduced shuttle
nox
0
Electric charge of oxidized shuttle
E01
-0.115 V
Standard potential of shuttle at pH 7
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*the diffusion was calculated according to La-Scalea and co-workers (La-Scalea et al. 2005),
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using a McGowan Volume of 162.86 cm³/mol (Abraham & McGowan 1987) and of the
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molecular volume-diffusion correlation of Othmer and Thakar (Othmer & Thakar 1953).
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With these parameters provided, a simulation using a microbial fuel cell model (under
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development) was conducted. The simulation consisted of a one hour experiment starting with
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equal concentrations of reduced and oxidised electron shuttle through the biofilm. Once the
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bioelectrochemical activity starts, the concentrations of reduced and oxidised electron shuttles
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change with time and between biofilm layers (layers 1 to 10), where reduction of the shuttle
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by the microorganisms occurs together with its transport. In particular, the transport of shuttle
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between the last layer (layer 10) and the liquid bulk causes a loss of shuttle to the liquid bulk.
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In this case no generation of shuttle by the microorganisms was considered to illustrate the
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different rates of shuttle loss when both Nernst-Planck interactions and diffusion are
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considered versus the conventional case, where only diffusion is considered.
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Figure S1 to Figure S4 show the results obtained by considering only diffusive driving forces
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compare the relative retention of the redox shuttle in a 10-layer biofilm over time. The
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quantitative analysis of the shuttle over time indicates that the difference in retention based on
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Nernst-Planck interactions is very relevant in terms of the current production and the shuttle
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distribution along the biofilm.
Electrical current generation
0.0135
0.013
Current generation (A)
0.0125
0.012
0.0115
0.011
0.0105
0.01
Only diffusion
0.0095
Diffusion + Nernst-Planck
0.009
0
500
1000
1500
2000
2500
3000
3500
Time (s)
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Figure S1. Modelled current generation by a microbial fuel cell over time, depending on
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whether Nernst-Planck interactions were considered when calculating the diffusion of redox
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shuttles. The current generation could be sustained for much longer time periods due to the
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electrostatic attraction of the shuttle.
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S4
Electrical Potential at the Biofilm Layer #1
-0.1
Only diffusion
-0.11
Diffusion + Nernst-Planck
Electrical potential (V)
-0.12
-0.13
-0.14
-0.15
-0.16
-0.17
-0.18
0
500
1000
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1500
2000
Time (s)
2500
3000
3500
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Figure S2. Modelled evolution of the potential versus standard hydrogen electrode (V) in a
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biofilm layer adjacent to the anodic electrode. The Nernst-Planck interactions cause a notable
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increase in stability as redox shuttles are retained better. The initial potential drop follows
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high bacterial activity and the subsequent generation of negatively charged shuttles, which are
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electrostatically attracted to the anode.
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Concentration of Shuttle at the Biofilm Layer #1
2.0E-04
Total electron shuttles concentration (molSH/L)
Only diffusion
1.8E-04
Diffusion + Nernst-Planck
1.6E-04
1.4E-04
1.2E-04
1.0E-04
8.0E-05
6.0E-05
4.0E-05
2.0E-05
0.0E+00
0
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500
1000
1500
2000
2500
3000
3500
4000
Time (s)
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Figure S3. Modelled evolution of the redox shuttle concentration over time in the biofilm
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layer adjacent to an anode. Due to the increased attraction of redox shuttles when Nernst-
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Planck interactions are included in the diffusion calculations, the concentration remains
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notably higher over time, after an initial rise due to high bacterial activity
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Concentration of Shuttle at the Biofilm Layer #10
5.0E-05
Only diffusion
Diffusion + Nernst-Planck
Total electron shuttles concentration
(molSH/L)
4.5E-05
4.0E-05
3.5E-05
3.0E-05
2.5E-05
2.0E-05
1.5E-05
1.0E-05
5.0E-06
0.0E+00
0
500
1000
1500
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2000
Time (s)
2500
3000
3500
4000
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Figure S4. Modelled evolution of the redox shuttle concentration over time in the top layer of
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a biofilm. In the case Nernst-Planck interactions are incorporated in the diffusion calculations,
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due to the high initial bacterial activity, the redox shuttles migrate to lower levels of the
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biofilm. This causes a limited shuttle concentration in the top of the biofilm, which strongly
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decreases the efflux of redox shuttles towards the bulk liquid.
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Conclusion
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The electric charge of the oxidized/reduced shuttles, causes profound differences in diffusion
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rates and dynamic behaviour of bioelectrochemical systems. For this reason, it is essential to
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include Nernst-Planck-calculated electrostatic interactions in the MFC model. Presented here
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is only a limited approach that does not include the production of redox shuttles by bacteria
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themselves. Experimental validation will have to confirm these modelled results, which do
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corroborate the findings by several studies, in which the presence of shuttle producing
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organisms was found, also in continuous systems (Aelterman et al. 2006; Bond & Lovley
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2005; Rabaey et al. 2005; Rabaey et al. 2004)
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References
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1. Abraham MH, McGowan JC (1987) The Use of Characteristic Volumes to Measure Cavity
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Terms in Reversed Phase Liquid-Chromatography. Chromatographia 23: 243-246.
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2. Aelterman P, Rabaey K, The Pham H, Boon N, Verstraete W (2006) Continuous electricity
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generation at high voltages and currents using stacked microbial fuel cells. Environ.
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Sci. Technol. 40: 3388 -3394.
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3. Bond DR, Lovley DR (2005) Evidence for Involvement of an Electron Shuttle in
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Electricity Generation by Geothrix fermentans. Appl. Environ. Microbiol. 71: 2186-
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2189.
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4. La-Scalea MA, Souza Menezes CM, Ferreira EI (2005) Molecular volume calculation
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using AM1 semi-empirical method toward diffusion coefficients and electrophoretic
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mobility estimates in aqueous solution. Journal of molecular structure. Theochem
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730: 111-120.
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5. MacGillivray AD (1968) Nernst-Planck equations and the electroneutrality and Donnan
equilibrium assumptions. Journal of Chemical Physics 48: 2903-2907.
6. Othmer DF, Thakar MS (1953) Correlating Diffusion Coefficients in Liquids. Industrial
and Engineering Chemistry 45: 589-593.
7. Rabaey K, Boon N, Höfte M, Verstraete W (2005) Microbial phenazine production
enhances electron transfer in biofuel cells. Environ. Sci. Technol. 39: 3401 -3408.
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8. Rabaey K, Boon N, Siciliano SD, Verhaege M, Verstraete W (2004) Biofuel cells select for
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microbial consortia that self-mediate electron transfer. Appl. Environ. Microbiol. 70:
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5373-5382.
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