Supplementary material
Microbial ecology meets electrochemistry: electricity driven and driving communities
Korneel Rabaey1,2*, Jorge Rodríguez1, Linda Blackall1, Jurg Keller1, Damien Batstone1, Willy Verstraete2, Kenneth H Nealson4
Submitted to: The ISME Journal
1The Advanced Wastewater Management Centre, University of Queensland, Gehrman Building, Brisbane, Queensland 4072, Australia
2 Laboratory of Microbial Ecology and Technology (LabMET), University of Ghent, Coupure Links 653, 9000 Ghent, Belgium
3 Department of Earth Sciences, University of Southern California, Los Angeles, CA90089USA
*Corresponding author: Dr. Korneel Rabaey, The Advanced Wastewater Management Centre, Gehrman Building (60), The University of Queensland, Brisbane, Queensland 4072, Australia, Tel. +61 7 3365 7519, Fax. +61 7 3365 4726,
S1. Nernst Planck interactions and the relationship to diffusivity
It can be assumed that in biofilms and diffusion limited systems, redox shuttles will demonstrate differences in diffusivity through the biofilm based on their redox status. Negatively charged shuttles will be attracted by the more positively charged electrode, while a positively charged shuttle will be repulsed or at least less intensively attracted by the electrode. The influence of these electrostatic interactions on overall diffusivity can be evaluated using well established fundamentaltheory.
The Nernst Planck equation provides an adapted diffusivity of compounds, i.e. shuttles, moving to and from differently charged objects(MacGillivray 1968):
With J the flux of the shuttleaway from the electrode (molSH/m2·s), nthe electric charge of the shuttle, Dthe diffusivity constant (m2/s), Fthe Faraday’s number (C/mole), SSH the concentration of the shuttle at positionx (molSH/m3), E the electrostatic potential (V), Rthe universal gas constant (C·V/mole·K), T the temperature (K), x distance to the electrode (m).
Here the first term applies to the diffusive driving force and the second tothe electrostatic driving force. Since the shuttle is the key electrochemically active compound in the potential field it can be assumed that E = ESH.
The equation is discretized within the main biofilm model, for a static biofilm model with the differential terms calculated as follows:
ESH, and SSHare calculated from the difference between the values at layer i and layer
i-1. Boundary conditions at the anode and biofilm surface are applied as normal. Taking a shuttle similar to phenazine-1-carboxamide as an example, assuming the reduced form of the shuttle as charged -1 and the oxidised as 0, with some estimations for parameters:
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 chargeof reduced shuttle
nox / 0 / Electric charge of oxidized shuttle
E01 / -0.115 V / Standard potential of shuttle at pH 7
*the diffusion was calculated according to La-Scalea and co-workers(La-Scalea et al. 2005), using a McGowan Volume of 162.86 cm³/mol(Abraham & McGowan 1987) and of the molecular volume-diffusion correlation of Othmer and Thakar (Othmer & Thakar 1953).
With these parameters provided, a simulation using a microbial fuel cell model (under development) was conducted. The simulation consisted of a one hour experiment starting with equal concentrations of reduced and oxidised electron shuttle through the biofilm. Once the bioelectrochemical activity starts, the concentrations of reduced and oxidised electron shuttles change with time and between biofilm layers (layers 1 to 10), where reduction of the shuttle by the microorganisms occurstogether with its transport. In particular, the transport of shuttle between the last layer (layer 10) and the liquid bulk causes a loss of shuttle to the liquid bulk. In this case no generation of shuttle by the microorganisms was considered to illustrate the different rates of shuttle loss whenboth Nernst-Planck interactions and diffusion are considered versus the conventional case, whereonly diffusionis considered.
Figure S1 toFigure S4show the results obtained by considering only diffusive driving forces compare the relative retention of the redox shuttle in a 10-layer biofilm over time. The quantitative analysis of the shuttle over time indicates that the difference in retention based on Nernst-Planck interactions is very relevant in terms of the current production and the shuttle distribution along the biofilm.
Figure S1. Modelled current generation by a microbial fuel cell over time, depending on whether Nernst-Planck interactions were considered when calculating the diffusion of redox shuttles. The current generation could be sustained for much longer time periods due to the electrostatic attraction of the shuttle.
Figure S2. Modelled evolution of the potential versus standard hydrogen electrode (V) in a biofilm layer adjacent to the anodic electrode. The Nernst-Planck interactions cause a notable increase in stability as redox shuttles are retained better. The initial potential drop follows high bacterial activity and the subsequent generation of negatively charged shuttles, which are electrostatically attracted to the anode.
Figure S3. Modelled evolution of the redox shuttle concentration over time in the biofilm layer adjacent to an anode. Due to the increased attraction of redox shuttles when Nernst-Planck interactions are included in the diffusion calculations, the concentration remains notably higher over time, after an initial rise due to high bacterial activity
Figure S4. Modelled evolution of the redox shuttle concentration over time in the top layer of a biofilm. In the case Nernst-Planck interactions are incorporated in the diffusion calculations, due to the high initial bacterial activity, the redox shuttles migrate to lower levels of the biofilm. This causes a limited shuttle concentration in the top of the biofilm, which strongly decreases the efflux of redox shuttles towards the bulk liquid.
Conclusion
The electric charge of the oxidized/reduced shuttles, causes profound differences in diffusion rates and dynamic behaviour of bioelectrochemical systems. For this reason, it is essential to include Nernst-Planck-calculated electrostatic interactions in the MFC model.Presented here is only a limited approach that does not include the production of redox shuttles by bacteria themselves. Experimental validation will have to confirm these modelled results, which do corroborate the findings by several studies, in which the presence of shuttle producing organisms was found, also in continuous systems (Aelterman et al. 2006; Bond & Lovley 2005; Rabaey et al. 2005; Rabaey et al. 2004)
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