# Glucose-Oxygen Biofuel Cell with Biotic and Abiotic Catalysts: Experimental Research and Mathematical Modeling

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}) and water (H

_{2}O) being the products of a multi-stage reaction.

## 2. Materials and Methods

#### 2.1. Cultivation of Microorganisms

_{3}—0–0.5; K

_{2}HPO

_{4}—0.5; MgSO

_{4}•7H

_{2}O—0.5; FeSO

_{4}•7H

_{2}O—10–4; CaCl

_{2}—0.02; Fedorov micronutrient concentrate. The nutrient medium was sterilized in an autoclave for 30 min at 0.5 atm (technical atmosphere of overpressure).

#### 2.2. Method for Preparing Electrodes

^{2}or 5 × 5 cm

^{2}was formed. Macroporous and microporous layers are the parts of commercial GDL (39BC). The active layer is formed by applying CM + BM mixture on the microporous layer. The structure of the bioanode is shown in Figure 2.

^{2}. Since bioanodes were prepared without adding a binder, a non-conducting fabric was pressed into the bioanode AL, which ensured a good mechanical strength of the electrode and free penetration of electrolyte into the active layer (Figure 2).

_{4}) was used as a precursor; the reduction was performed with sodium borohydride in the presence of a stabilizer—Citrate. The carrier was added to the cooled reaction mixture at constant stirring. A solution of sodium citrate and borohydride and HAuCl

_{4}solution were added to a suspension of the support (XC 72 or CNT) in water. After establishing of the solution constant color, stirring was continued until the solution became transparent. With XC72 carbon black usage, the deposition takes 24–32 h. In the case of nanotubes, the deposition time is up to 7 days. The obtained catalyst was thoroughly washed with deionized water to remove remains of sodium borohydride. Then, it was dried in a vacuum oven at 80 °C. The synthesized catalyst was placed in sealed glass containers and stored in a laboratory cabinet.

^{2}. According to the data of preliminary experiments, it corresponds to the minimum amount of catalyst required to obtain a reproducible anodic potential.

^{2}). Laccase was adsorbed from its solution in a phosphate-acetate buffer on the formed active layer. For the immobilization by spontaneous adsorption, GDL with prepared AL was held on the surface of a solution containing laccase for 24 h in a fridge. Then, the electrode was rinsed with a solution to remove the loosely bound enzyme from the surface and exposed to air for 20–30 min. After that, the electrode was placed in the BFC for testing. As it was shown earlier [39], a monolayer filling of the surface with laccase forms on the surface under these conditions as a result of spontaneous adsorption. It accelerates oxygen reduction by direct bioelectrocatalysis without mediators (electron transfer occurs between the carbon support, enzyme active center, and oxygen molecule).

#### 2.3. Experimental Campaign

_{2}) circuit.

^{3}. The dimensions of the electrodes were 5 × 5 cm

^{2}with an active surface area of 4 × 4 cm

^{2}. In tests, FC oxygen (tech.) entered into the cathode space of the cells at a flow rate of ~5 mL/min. After the open circuit voltage (Voc) was stable (stabilization time ~1 h), the anode potential was measured with respect to silver chloride reference electrode immersed in a container at the outlet of the anode space of the cell. The potentials collected with reference to Ag/AgCl were converted to reversible hydrogen electrode (RHE). MFCs were tested using measuring cyclic potentiodynamic polarization technique; cyclic potentiodynamic curves were measured at a scan rate of 0.1–0.3 mV/s from Voc to U = 0.

_{2}HPO

_{4}, 0.2 M glucose, and acetic acid was used as an electrolyte. According to [49], the glucose level can vary within a wide range depending on the experimental conditions (pH of a solution, etc.), and the catalytic system at the anode. The glucose concentration of 0.2 M and 0.5 M was chosen following the previously conducted studies into dependence of the characteristics of the oxidation process of glucose on its concentration in the electrolyte solution under model conditions.

^{2}. Active layers were applied to the surface of gas diffusion electrodes (GDE). Oxygen was fed into the cell through a serpentine in the end plate. The electrolyte was pumped through the anode space of the cell using a micropump, while the electrolyte was absorbed by the separator, which ensured ionic conductivity.

#### 2.4. Mathematical Modeling

_{1}), the bulk electrolyte solution (L

_{1}< × ≤L

_{2}), and the active layer of the cathode catalyst (L

_{2}< × ≤L

_{3}).

_{exo}is the exogenous respiration rate of microorganisms, mol/(m

^{3}s); ρ

_{b}is the active biomass density (amount of biomass per AL volume), kg(BM)/m

^{3}(AL); µ

_{b}is a specific growth rate of active biomass, 1/s; X

_{b}is a volume fraction of active biomass (dimensionless); Y

_{b}is the active biomass growth yield, expressed as a dry biomass to consumed oxygen (chemical oxygen demand (COD)) mass ratio, kg

_{dry biomass}/kg

_{COD}; γ

_{cod}is COD equivalence of glucose, expressed as oxygen consumed to glucose ratio, kg

_{COD}/mol

_{glucose}; [G] is a glucose concentration in the anode AL, mol/m

^{3}; K

_{G}is the half velocity constant, (Monod) for glucose, mol/m

^{3}; α is the anodic charge transfer coefficient; n is the number of electrons participating in the electrochemical reaction; F is the Faraday constant, C/mol; η is overpotential, V; R is the universal gas constant, J/(mol·K); T is temperature, K.

_{endo}is the rate of microorganisms endogenous respiration, mol/(m

^{3}s); b

_{endo}is microorganism decay constant, 1/s.

_{c}is the rate of oxygen electroreduction at the cathode, mol/(m

^{3}s); k

_{c}is oxygen electroreduction rate constant, 1/s; [O

_{2}] is the oxygen concentration in the cathode active layer, mol/m

^{3}.

^{j}

_{γ}is the diffusion coefficient of the component within the porous active layer, m

^{2}/s

^{γ}; related to general diffusion coefficient by D

_{γ}= D

^{γ}S

^{(1-γ)}; S is a channel cross-sectional area available for the electrolyte flow, m; D

_{j}is the diffusion coefficient of the particle, m

^{2}/c; z

_{j}is the particle charge; x is the electrode thickness coordinate, m; t is time, s.

_{l}is the potential of the liquid (ion-conducting) phase, V.

_{a}= Φ

_{s}− Φ

_{l}

_{s}is the potential of the solid (electron-conducting) phase, V.

_{j}is a conductivity of electron (s) and ion (l) conducting phases, A/(Vm); i is the local current density, A/m

^{3}.

^{3}, and ${\beta}_{\gamma}^{{o}_{2}}$ is the modified oxygen mass transfer (from the inlet flow to the cathode active layer) coefficient, m/s

^{γ}.

_{a}is the applied potential, V.

## 3. Results and Discussion

#### 3.1. Experimental Results

_{2}HPO

_{4}, pH = 8 (unless otherwise indicated). P

_{max}(at U, mV) is the maximum power density and voltage at which it is reached, i

_{max}is the maximum achievable current density (at U ~ 0). E

_{anode}and E

_{cathode}are stationary potentials of the anode and cathode, respectively. Table 1 shows the average values obtained for each pair of catalytic systems; tests are conducted in triplicate.

^{2}) and GDL with deposited CNTs (at the rate of 0.4 mg/cm

^{2}) mixed with biomaterials with different ratios of fungal and bacterial cultures were applied. Here, bio(black)—the prevalence of P. glabrum, up to 75% of fungal cultures, bio(white)—up to 75% of the nitrogen-fixing community, the rest is fungal cultures. Figure 7b shows current–voltage curves and dependencies of the power density on the current density of FCs with phosphate electrolyte (pH 4.7 and 8) containing 0.5 M glucose. The anodes based on the initial GDL with deposited expanded graphite (0.4 mg/cm

^{2}) mixed with BM (bio (white)) were applied.

- BFC with the structure CoFe/C (cathode)—20Au/CNT (anode) has the highest characteristics among the tested FCs. The results are achieved with the acetate-phosphate buffer solution at pH 8 and can be further improved by increasing the glucose concentration from 0.2 to 0.5 M. The maximum power density of the system was 137 μW/cm
^{2}, which corresponds to the level of the best indicators for fuel cells without a membrane described in the literature [60,61]. - The overvoltage of the electrodes makes comparable contributions to the total voltage drop of the BFC at the application of the laccase-based cathode and Au/C anode in an electrolyte with pH 4.7. At pH 8, the BFC characteristics are limited by the overvoltage increase of the cathodic process. However, with the usage of Au/C anode, the growth of the cathodic overpotential at going from pH 4.7 to pH 8 is compensated by the anode overpotential decrease. This causes an increase in the maximum power density of BFC laccase-Au/CNTs from 2.3 μW/cm
^{2}(pH 4.7) to 42.5 μW/cm^{2}(pH 8). - The most effective approach to the formation of an anode based on biological material is the preliminary immobilization of the microorganisms on carbon material (CNT or TEG), followed by applying of CM+ BM mixture on GDL. The maximum power density of the BFC bioanode—CoFe cathode reached 2 µW/cm
^{2}with using BM + CNT anode. The best results obtained at testing FCs with a biocathode and bioanode correspond to 2.75 μW/cm^{2}in the BFC laccase cathode—BM+TRG in an electrolyte with pH 8 at a glucose concentration of 0.5 M. These characteristics are higher than those obtained in the development of BFC with bioelectrodes [62]. The ratio of bacterial (nitrogen-fixing associate) and fungal cultures in the microbiological community was 75:25.

#### 3.2. Results of Mathematical Modeling

^{2}. To solve the mathematical model equations, the kinetic parameters were determined. The reactions rates constants were derived using the scanning method.

## 4. Conclusions

^{2}vs. the maximum value of power density obtained in the cited work 5.16 μW/cm

^{2}), represents an advantage of the proposed BFC over the commercial cell.

^{2}to 3–5 mW/cm

^{2}. Despite the moderate characteristics, such FCs attract the attention of researchers due to their mild operating conditions and environmental friendliness. In many cases, their advantages are explained by the absence of a membrane. Further research will be aimed at finding new anode catalysts based on microbiological communities and enzymes, as well as methods for microorganisms immobilization.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Microorganisms immobilized in TEG, (

**a**) fungal cultures with bacteria in thermally expanded graphite; (

**b**) predominance of fungal cultures in thermally expanded graphite.

**Figure 3.**Scheme of the experimental setup: 1—BFC; 2—Reservoir with electrolyte solution; 3—Circulation pump; 4—Reservoir with water (control of O

_{2}flow through the system); 5—Oxygen cylinder; 6—Reducer with pressure gauges; 7—Fine adjustment valve; 8—Electric engine.

**Figure 5.**Comparison of characteristics for BFC 20Au/XC-72 (anode)—laccase (cathode), measured in the Electrochem™ cell (cell 1) and in the developed BFC (cell 2), 0.2 M glucose, pH 4.7, (

**a**) current–voltage curves, (

**b**) partial curves.

**Figure 6.**Discharge and specific power characteristics for two systems: (

**a**) laccase (cathode)—Au/CNT (anode) BFC; (

**b**) laccase (cathode)—BM + TEG (anode) BFC.

**Figure 7.**Current–voltage potentiodynamic curves and dependences of power density on current density, (

**a**) BFC bioanode—CoFe cathode, (

**b**) BFC bioanode—biocathode (laccase).

**Figure 8.**Current–voltage potentiodynamic curves and dependences of power density on current density for MFC CoFe/CNT + BM.

**Figure 12.**Calculated power density values vs. current density for MFC CoFe/ CNT + BM at different fuel concentrations.

Cathode-Anode Active Material | C_{G}, M | OCV, mV | P_{max}, (at U, mV), μW/cm^{2} | i_{max}, μA/cm^{2} | E_{anode} (RHE), mV | E_{cathode} (RHE), mV |
---|---|---|---|---|---|---|

CNT_{N}-Au/XC-72 * | 0.2 | 373 | 14.3 (168) | 236 | 561 | 934 |

0.2 | 371 | 14.5 (160) | 233 | 555 | 926 | |

0.2 | 366 | 14.2 (150) | 230 | 563 | 929 | |

CoFe/C-Au/CNT * | 0.2 | 520 | 29.7 (241) | 350 | 494 | 1014 |

0.2 | 526 | 30.2 (245) | 354 | 495 | 1021 | |

0.2 | 514 | 29.5 (238) | 347 | 496 | 1010 | |

0.5 | 700 | 86 (308) | 623 | 312 | 1012 | |

0.5 | 704 | 90 (311) | 626 | 312 | 1016 | |

0.5 | 697 | 83 (305) | 619 | 310 | 1007 | |

Laccase—Au/CNT ** | 0.2 pH4.7 | 342 | 2.1 (415) | 17 | 754.3 | 1096.3 |

0.2 pH4.7 | 339 | 1.6 (413) | 15 | 720.9 | 1059.4 | |

0.2 pH4.7 | 345 | 2.6 (417) | 20 | 677.5 | 1022.5 | |

0.5 pH4.7 | 401 | 2.3 (209) | 24 | 709.3 | 1110.3 | |

0.5 pH4.7 | 390 | 2.0 (220) | 22 | 690.2 | 1080.3 | |

0.5 pH4.7 | 412 | 2.6 (202) | 26 | 721.0 | 1133.0 | |

0.2 pH8 | 372 | 1.5 (337) | 25 | 554 | 926 | |

0.2 pH8 | 350 | 1.2 (350) | 23 | 520 | 870 | |

0.2 pH8 | 394 | 1.8 (324) | 27 | 588 | 982 | |

0.5 pH8 | 628 | 42.5 (192) | 488 | 281 | 909 | |

0.5 pH8 | 590 | 38.3 (210) | 500 | 250 | 870 | |

0.5 pH8 | 666 | 46.7(174) | 476 | 312 | 978 | |

Laccase—BM+TEG ** | 0.5 pH4.7 | 526 | 2.20 (381) | 12 | 575.3 | 1101.3 |

0.5 pH4.7 | 480 | 1.90 (401) | 14 | 550.3 | 1070.4 | |

0.5 pH4.7 | 445 | 2.50 (280) | 21 | 670 | 1123 | |

CoFe/C-BM+CNT ** | 0.2 pH8 | 291 | 1.99 (208) | 24 | 726 | 1017 |

0.2 pH8 | 293 | 2.03 (212) | 27 | 727 | 1020 | |

0.2 pH8 | 291 | 1.96 (205) | 22 | 723 | 1014 |

Parameter | Symbol, Dimension | Value | References |
---|---|---|---|

Cell operating temperature | T, K | 298 | given |

pH | 8 | given | |

Initial glucose concentration | [G]^{0}, mol/m^{3} | 200 | given |

Open circuit voltage | Voc, V | 0.291 | given |

Anode applied potential | E_{a},_{anode} V | 0.726 | given |

Cathode applied potential | E_{a},_{cathode} V | 0.1017 | given |

Monod constant | K_{G}, mol/m^{3} | 19 | [38] |

Active biomass density | ρ_{b}, kg_{BM}/m^{3}_{AL} | 116 | calculated from experiment |

Active biomass specific growth rate | μ_{b}, 1/s^{γ} | 2.78 × 10^{−5} | fitted |

Biomass decay rate constant | b_{b}, 1/s^{γ} | 1 × 10^{−6} | fitted |

Active biomass volume fraction | X_{b} | 0.6 | assumed |

Active biomass growth yield, ratio of dry biomass to consumed oxygen | Y_{b}, kg_{drybiomass} / kg_{COD} | 0.01 | measured by Koch’s micromethod |

COD for glucose | γ_{COD}, kg_{COD}/mol_{glucose} | 192 × 10^{−3} | calculated from stoichiometry |

Charge transfer coefficient | α | 0.5 | assumed |

Faraday constant | F, C/mol | 96,485 | |

Universal gas constant | R, J/(mol·K) | 8.314 | |

Oxygen electroreduction reaction rate constant | k_{c}, 1/s^{γ} | 1.43 × 10^{−13} | fitted |

Oxygen mass transfer coefficient | β, m/s | 0.1 | fitted |

Ion-conducting phase conductivity | κ_{l}, A/(V·m) | 0.55 | [21] |

Electron-conducting phase conductivity | κ_{s}, A/(V·m) | 0.46 | [21] |

Microbial phase conductivity | κ_{b}, A/(V·m) | 5 × 10^{−2} | [38] |

Volume fraction of the liquid phase on the electrode | ε | 0.8 | [21] |

Anode CM porosity | γ_{a} | 0.9 | assumed |

Cathode CM porosity | γ_{c} | 0.75 | assumed |

Glucose diffusion coefficient in electrolyte | D_{G}, m^{2}/s | 5 × 10^{−12} | Initial [21] |

Protons diffusion coefficient in electrolyte | D_{H+}, m^{2}/s | 1 × 10^{−9} | [21] |

Oxygen diffusion coefficient in electrolyte | D_{O2}, m^{2}/s | 2 × 10^{−9} | [25] |

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## Share and Cite

**MDPI and ACS Style**

Vasilenko, V.; Arkadeva, I.; Bogdanovskaya, V.; Sudarev, G.; Kalenov, S.; Vocciante, M.; Koltsova, E. Glucose-Oxygen Biofuel Cell with Biotic and Abiotic Catalysts: Experimental Research and Mathematical Modeling. *Energies* **2020**, *13*, 5630.
https://doi.org/10.3390/en13215630

**AMA Style**

Vasilenko V, Arkadeva I, Bogdanovskaya V, Sudarev G, Kalenov S, Vocciante M, Koltsova E. Glucose-Oxygen Biofuel Cell with Biotic and Abiotic Catalysts: Experimental Research and Mathematical Modeling. *Energies*. 2020; 13(21):5630.
https://doi.org/10.3390/en13215630

**Chicago/Turabian Style**

Vasilenko, Violetta, Irina Arkadeva, Vera Bogdanovskaya, George Sudarev, Sergei Kalenov, Marco Vocciante, and Eleonora Koltsova. 2020. "Glucose-Oxygen Biofuel Cell with Biotic and Abiotic Catalysts: Experimental Research and Mathematical Modeling" *Energies* 13, no. 21: 5630.
https://doi.org/10.3390/en13215630