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An intrinsic time-dependent one-dimensional (1D) model and a macro two-dimensional (2D) model for the anode of the direct methanol fuel cell (DMFC) are presented. The two models are based on the dual-site mechanism, which includes the coverage of intermediate species of methanol, OH, and CO (

Compared with hydrogen fuel cells, direct methanol fuel cells (DMFCs) have significant advantages such as higher efficiency, easier design and operation, simple storage, and refilling of liquid fuel. However, DMFCs show serious disadvantages such as lower current density, larger polarisation, and lower limiting currents resulting from more complex kinetics of methanol oxidation in the anode of DMFCs than that for hydrogen fuel cells [

A reason for the disadvantages of DMFCs was the adsorption coverage of intermediates, which accompany the kinetics of methanol oxidation, and play a crucial function in the behavior of DMFCs [

Meyers and Newman [

In general, describing electrode performance by Tafel or dual-site kinetics, the dynamic equations were always nonlinear because of the exponential functions of potential. Since Newman [

The present model aims to combine the dual-site methanol oxidation mechanism with material and charge balances in order to simulate time-dependent current-voltage response and predict the anode behavior under different operating temperatures and concentrations, and to especially focus on the distributions of methanol concentration, overpotential, and current density inside of the catalyst layer.

Figure

Kinetics parameters for modeling [

Kinetics parameters | 303 K | 333 K | 363 K |
---|---|---|---|

^{−1}) | |||

^{−2} s^{−1}) | |||

^{−2} s^{−1}) | |||

^{−2} s^{−1}) | |||

^{−2} s^{−1}) | |||

^{−2} s^{−1}) | |||

1.0 | |||

0.79 | |||

^{−1}) | 0.5 | ||

^{−1}) | 0.5 |

The schematic view of the modeling domain.

The assumptions adopted in the present model were as follows.

Methanol concentration was defined as constant at the interface of catalyst layer (

Carbon dioxide bubbles were formed beyond the catalyst layer. It was possible for nucleation of carbon dioxide to take place in diffusion layer or limited to a partial region of the catalyst layer by choosing appropriate operating condition [

The porous catalyst layer was assumed to be isothermal, isotropic, and homogeneous.

Steady state for mass and charge transport was assumed in the porous catalyst layer for the 2D model.

According to dual-site kinetics which was widely accepted for methanol absorption and electrochemical oxidation on the surface of Pt-Ru catalyst, the methanol oxidation mechanism can be described as the following four elemental steps below:

It was assumed that steps (_{ads} to CO_{2} occurs on Ru, and Pt serves as an active surface of adsorption and dehydrogenation of methanol [

The rates of changes of surface coverage of different intermediates with respect to time were as follows:

Numerous papers indicate that OH_{ads} was preferentially formed on the surface of Ru, not on the surface of Pt [

Intrinsic kinetic current density can be obtained by combining Faraday’s Law:

Mass transport of methanol in porous catalyst layer can be described by Fick’s first law

According to a mass balance [

Charge transport of methanol in the porous catalyst layer can be described by Ohm’s law:

The boundary conditions for the second-order differential equation above were

Equations (

The dimensionless modulus,

According to Ohm’s law, the local current density described by concentration and charge flux was

Thus, the dimensionless current density was defined as

Effectiveness factor was introduced to evaluate the impact of physical parameters such as thickness and specific surface area of the catalyst layer, effective diffusion coefficient, and effective conductivity of the anode, and was defined as

Substituting (

Hence, the expressions of

1D and 2D models were established and solved in the PDE module of COMSOL Multiphysics software in order to analysis firstly the change of surface coverage of different intermediates (

Equations (

It was worthwhile to note that the macro kinetic model was established by coupling (

The parameters used in the present model were listed in Table

Physical parameters for modeling.

Electrode parameters | References |
---|---|

Catalyst layer thickness | |

[ | |

[ | |

[ | |

[ | |

[ | |

[ | |

Special area of anode ^{−1}) | |

[ | |

118317 | [ |

[ | |

Porosity of anode | |

0.3 | [ |

Diffusion coefficients ^{2} s^{−1}) | |

[ | |

Effective diffusion coefficients ^{2} s^{−1}) | |

[ | |

Effective conductivity ^{−1}) | |

3.4 | [ |

The simulated polarisation curves of the DMFC anode at different operating temperature and methanol concentration are shown in Figure

Comparison of calculated and experimental anode polarisation data at various temperature and methanol concentration, ^{−1} m^{−1}, ^{2} s^{−1}; experiment data: (■) ^{−1}; dash line: ^{−1}.

Figure

The influence of different operating temperature, methanol concentration, and overpotential on the transient surface coverage of methanol is shown in Figure

Transient of the coverage of methanol with different operating (a) temperature, (b) methanol concentration, and (c) overpotential.

Figure

Transient of current density with different operating (a) temperature, (b) methanol concentration, and (c) overpotential.

As stated in (

Figures

Distribution of dimensionless methanol concentration at ^{−1} m^{−1}, ^{2} s^{−1}; (a) ^{−1}; (b) ^{−1}; (c) ^{−1}; (d) ^{−1}; arrow: the gradient of dimensionless methanol concentration.

Distribution of dimensionless methanol concentration at ^{−1}, ^{−1} m^{−1}, ^{2} s^{−1}; (a)

The arrows in Figure

The contours in Figures

Distribution of dimensionless overpotential at ^{−1} m^{−1}, ^{2} s^{−1}; (a) ^{−1}; (b) ^{−1}; (c) ^{−1}; (d) ^{−1}.

Distribution of dimensionless overpotential at ^{−1}, ^{−1} m^{−1}, ^{2} s^{−1}; (a)

Similar to the distribution of methanol concentration, the dimensionless overpotential was very low at the edge whilst it was very high close to the middle of the modeling domain. The distributions of dimensionless overpotential in Figures ^{−1}) was approximately ten orders of magnitude higher than the efficient diffusion coefficient (^{2} s^{−1}) of the catalyst layer. This led to the significant difference of the restriction between the diffusions of methanol and charge.

The lines in Figures

The distribution of dimensionless overpotential at A-A′ with different thickness and specific area of catalyst layer; ^{−1} m^{−1}, ^{2} s^{−1}, solid line: ^{−1}, dash line: ^{−1}, dot line: ^{−1}, dash dot line: ^{−1}.

The distribution of dimensionless overpotential at A-A′ with different operation temperature and methanol concentration; ^{−1}, ^{−1} m^{−1}, ^{2} s^{−1}, solid line:

The distribution of dimensionless overpotential at particular ^{−1}, ^{−1} m^{−1}, ^{2} s^{−1}, lines A-A′ to F-F′ are from up to down.

Figures

Distribution of dimensionless current density at ^{−1} m^{−1}, ^{2} s^{−1}; (a) ^{−1}; (b) ^{−1}; (c) ^{−1}; (d) ^{−1}; (e) ^{−1}, the dimensionless current densities on the points of A are (a) 0.0674, (b) 0.0312, (c) 0.0214, (d) 0.1080, and (e) 0.0275.

Distribution of dimensionless current density at ^{−1}, ^{−1} m^{−1}, ^{2} s^{−1}; (a)

Apparently, an increase in operating temperature, methanol concentration, and overpotential increases the dimensionless current density. However, higher dimensionless current density is observed in the catalyst layer with smaller thickness and specific area. It is because of the higher utilization rate of the interface of the catalyst layer. Moreover, the apparent current density (

Figure

The effects of temperature and methanol concentration were not significant with a ten-micrometer thick layer because the distributions of methanol concentration and overpotential were not as great with such a thin catalyst layer. As a result, the polarisation curves simulated by macro kinetics were very close to those for intrinsic kinetics.

Briefly, the reason for the nonlinearity of the distribution of dimensionless current density was the speed of the electrochemical reaction which was accelerated by larger thickness and specific area and higher temperatures, methanol concentrations and overpotentials.

Figures

The distribution of dimensionless current at A-A′ with different thickness and specific area of catalyst layer; ^{−1} m^{−1}, ^{2} s^{−1}, solid line: ^{−1}, dash line: ^{−1}, dot line: ^{−1}, dash dot line: ^{−1}, dash dot dot line: ^{−1}.

The distribution of dimensionless current at A-A′ with different operation temperature and methanol concentration ^{−1}, ^{−1} m^{−1}, ^{2} s^{−1}, solid line:

The distribution of dimensionless current at particular ^{−1}, ^{−1} m^{−1}, ^{2} s^{−1}, lines A-A′ to F-F′ are from down to up.

Figure

Efficiency factor for different thickness and specific area of the catalyst layer; ^{−1} m^{−1}, ^{2} s^{−1}, (^{−1}, dash line: ^{−1}, dot line: ^{−1}, dash dot line: ^{−1}, dash dot dot line: ^{−1}.

Figure

Efficiency factor for different temperature and methanol concentration; ^{−1}, ^{−1} m^{−1}, ^{2} s^{−1}, (

The 1D model of the DMFC, based on the intrinsic kinetics, demonstrated that the change in coverage of OH (

The 2D model indicated that the performance of the porous Pt-Ru anode depended on the kinetics parameters of the dual-site mechanism of methanol oxidation as well as physical parameters such as thickness, specific area of the catalyst layer. The distributions of methanol concentration, overpotential and current density became more nonlinear with increased operating temperature, methanol concentration, and overpotential, as well as increased thickness and specific area of the catalyst layer. The nonlinearity of all the distributions, including methanol concentration, overpotential, and current density, were higher near the edges of the modeling surface and lower in the middle. At the two corners of the modeling surface, the highest current density appeared due to the maximum difference of the derivative of methanol concentration and overpotential. The distribution of methanol concentration was more obvious than that of overpotential and current density, because the coefficient of mass transport was approximate ten orders of magnitude smaller than the coefficient of charge transport.

The effectiveness factor of the catalyst layer was higher with lower operating temperature, methanol concentration, overpotential, thickness, and specific area. The efficiency factor also went through a minimum value with increasing dimensionless overpotential, at higher temperatures and methanol concentrations. This was probably a result of the change of the rate determining step from element step (

Site density (mol m^{−2})

Aspect ratio of the rectangular electrode =

Electrochemical transfer coefficient

^{−1})

Porosity

Coverage ratio

Effective conductivity (Ω^{−1} m^{−1})

Charge transfer modulus

Effectiveness factor

Potential of open-circuit (V)

Potential of electrolyte (V)

Potential of matrix (V)

Dimensionless relative overpotential

Adsorbed

Effective

Species j

Local state

Methanol

Total or apparent state.

At the boundary of the diffusion layer

The authors of this paper gratefully acknowledge the financial support from EPSRC Supergen Fuel Cell Consortium award. Mr. L. Xing would like to say thanks to Wenxiao Huang, who is the master student in Bristol University, for her great help for the figures processing in this paper.