Computer Modeling of Proton Exchange Membrane Fuel … · field and charge distribution in the...
1
In determining the charge distribution, we first modeled the kinetics of the Stern layer with the Butler-Volmer equation for electrochemical reactions, Next, the diffuse layer is represented by equations for the relation between field and charge density, Poisson’s equation, and the movement of ions across the membrane including the concentration gradient and electric potential, Nernst-Planck equation, The field in the electrolyte for the Stern layer is derived from the BV equation , Since an electric field must be continuous, the field from the Stern layer must match the field in the diffuse layer. The Poisson and NP equation can be solved simultaneously for a function of the potential, Here the fractional surface charge density change is, ABSTRACT The modeling of proton-conducting membranes with computer simulation has two parts. We begin by developing an understanding of the equilibrium structure of Nafion. We then study how protons are transported through the Nafion membrane. The goal of this research is to model the electric field and charge distribution in the proton exchange membrane. Our model consists of a distribution of charge for particular current strengths in the Stern and diffuse layers. Computer Modeling of Proton Exchange Membrane Fuel Cells Kaytlin Brinker Professor Philip Taylor (Case Western Reserve University, Physics) EXISTING THEORY Recent research has modeled the effects of diffuse charge on the electron-transfer rate [1]. Bazant et al. theorize that there is a nonzero total membrane charge that gives the thermodynamic constant for the membrane of the fuel cell. When the diffuse layer is not thin, diffuse charge has a considerable effect on the rate of electron transfer [1]. When an electric charge transfers from the electrode to the electrolyte, the kinetics of the electrochemical reaction are given by the Butler-Volmer (BV) equation. Along with the Frumkin correction, this equation describes the charge transfer across the Stern layer for a membrane. Fig 1. A model of the electrostatic potential profile in the fuel cell membrane is given by Bazant et al. In Fig. 1a, excess protons exist in the anodic polarization layer and a deficit on the cathodic side. Fig. 1b I is the same case; II has an excess of protons on both sides; while III displays a deficit of protons on both sides. The dashed lines show the electrical voltage increase through the external circuit [1]. BACKGROUND Fuel cells are an important alternative option for providing electrical power to devices where energy is limited. These devices often run on batteries and require energy from a chemical reaction within the battery. What if, instead, the energy were to come from an electrochemical reaction of hydrogen and oxygen? Since the byproducts of this reaction are simply water and air, fuel cells are an environmentally sound energy source. One major area for fuel cell applications is in automobiles, where they provide clean energy and are more fuel efficient than the current combustion engine. Fuel cells offer a much needed shift in energy production. A fuel cell is a combination of two electrodes and an electrolyte. One electrolyte for the proton-exchange membrane (PEM) is Nafion from DuPont. This is a thin polymer that conducts protons from the anode but blocks electrons, which are forced to enter an external circuit. The electrons and protons recombine at the cathode creating a current, and in turn, electrical power. For a higher voltage, more fuel cells are connected together creating a stack. RESULTS CONCLUSIONS We have succeeded in calculating the charge distribution and field distribution in an ionomer membrane. Our results show it is important to include the charge imbalance in the membrane when calculating fuel cell properties. ACKNOWLEDGMENTS This research was supported by the Physics REU program at Case Western Reserve University, a Research Experience for Undergraduates (REU) funded by the NSF grant DMR-0850037 REFERENCES Biesheuvel, P.M., Franco, A.A., Bazant, M.Z. (2009). “Diffuse Charge Effects in Fuel Cell Membranes” Journal of The Electrochemical Society. 156, B225-B233. Allahyarov, E. and P. Taylor (2009). “Simulation Study of the Correlation between Structure and Conductivity in Stretched Nafion” Journal of Physical Chemistry 113, 610-617. Yuan, X. and H. Wang. “PEM Fuel Cell Electrocatalysts and Catalyst Layers”. New York: Springer, 2008. MODEL The potential gradient in the Stern layer depends on the charge density in the membrane. The charge density in the diffuse layer depends on the potential gradient in the diffuse layer. Because the electric field must be continuous we can self-consistently determine these quantities. By graphing the potential gradient from both the diffuse and Stern layers, we can obtain a value for the position, r s , where they cross. From this we know the entire charge distribution in the membrane. Stern and Diffuse Layers Stern Layer Diffuse Layer
Transcript of Computer Modeling of Proton Exchange Membrane Fuel … · field and charge distribution in the...
In determining the charge distribution, we first modeled the kinetics of the Stern layer with the Butler-Volmer equation for electrochemical reactions,
Next, the diffuse layer is represented by equations for the relation between field and charge density, Poisson’s equation,
and the movement of ions across the membrane including the concentration gradient and electric potential, Nernst-Planck equation,
The field in the electrolyte for the Stern layer is derived from the BV equation ,
Since an electric field must be continuous, the field from the Stern layer must match the field in the diffuse layer. The Poisson and NP equation can be solved simultaneously for a function of the potential,
Here the fractional surface charge density change is,
ABSTRACT The modeling of proton-conducting membranes with computer simulation has two parts. We begin by developing an understanding of the equilibrium structure of Nafion. We then study how protons are transported through the Nafion membrane. The goal of this research is to model the electric field and charge distribution in the proton exchange membrane. Our model consists of a distribution of charge for particular current strengths in the Stern and diffuse layers.
Computer Modeling of Proton Exchange Membrane Fuel Cells Kaytlin Brinker
Professor Philip Taylor (Case Western Reserve University, Physics)
EXISTING THEORY Recent research has modeled the effects of diffuse charge on the electron-transfer rate [1]. Bazant et al. theorize that there is a nonzero total membrane charge that gives the thermodynamic constant for the membrane of the fuel cell. When the diffuse layer is not thin, diffuse charge has a considerable effect on the rate of electron transfer [1]. When an electric charge transfers from the electrode to the electrolyte, the kinetics of the electrochemical reaction are given by the Butler-Volmer (BV) equation. Along with the Frumkin correction, this equation describes the charge transfer across the Stern layer for a membrane.
Fig 1. A model of the electrostatic potential profile in the fuel cell membrane is given by Bazant et al. In Fig. 1a, excess protons exist in the anodic polarization layer and a deficit on the cathodic side. Fig. 1b I is the same case; II has an excess of protons on both sides; while III displays a deficit of protons on both sides. The dashed lines show the electrical voltage increase through the external circuit [1].
BACKGROUND Fuel cells are an important alternative option for providing electrical power to devices where energy is limited. These devices often run on batteries and require energy from a chemical reaction within the battery. What if, instead, the energy were to come from an electrochemical reaction of hydrogen and oxygen? Since the byproducts of this reaction are simply water and air, fuel cells are an environmentally sound energy source. One major area for fuel cell applications is in automobiles, where they provide clean energy and are more fuel efficient than the current combustion engine. Fuel cells offer a much needed shift in energy production.
A fuel cell is a combination of two electrodes and an electrolyte. One electrolyte for the proton-exchange membrane (PEM) is Nafion from DuPont. This is a thin polymer that conducts protons from the anode but blocks electrons, which are forced to enter an external circuit. The electrons and protons recombine at the cathode creating a current, and in turn, electrical power. For a higher voltage, more fuel cells are connected together creating a stack.
RESULTS
CONCLUSIONS We have succeeded in calculating the charge distribution and field distribution in an ionomer membrane. Our results show it is important to include the charge imbalance in the membrane when calculating fuel cell properties.
ACKNOWLEDGMENTS This research was supported by the Physics REU program at Case Western Reserve University, a Research Experience for Undergraduates (REU) funded by the NSF grant DMR-0850037
REFERENCES Biesheuvel, P.M., Franco, A.A., Bazant, M.Z. (2009). “Diffuse Charge Effects in Fuel Cell Membranes” Journal of The Electrochemical Society. 156, B225-B233. Allahyarov, E. and P. Taylor (2009). “Simulation Study of the Correlation between Structure and Conductivity in Stretched Nafion” Journal of Physical Chemistry 113, 610-617. Yuan, X. and H. Wang. “PEM Fuel Cell Electrocatalysts and Catalyst Layers”. New York: Springer, 2008.
MODEL
The potential gradient in the Stern layer depends on the charge density in the membrane. The charge density in the diffuse layer depends on the potential gradient in the diffuse layer. Because the electric field must be continuous we can self-consistently determine these quantities. By graphing the potential gradient from both the diffuse and Stern layers, we can obtain a value for the position, rs, where they cross. From this we know the entire charge distribution in the membrane.
Stern and Diffuse Layers
Stern Layer Diffuse Layer
