Modeling of ion conductivity in Nafion membranes

  • Yang Zhen 
  • Peng Xiaofeng 
  • Wang Buxuan 
  • Duan Yuanyuan 
  • Lee Duujong 
Research Article


A theoretical investigation was conducted to describe the ion transport behavior in a Nafion Membrane of proton exchange membrane fuel cells (PEMFC). By analyzing the surface energy configuration of the ionic clusters in a Nafion membrane, an equivalent field intensity, E e , was introduced to facilitate the analysis of surface resistance against ion conduction in the central region of clusters. An expression was derived for ionic conductivity incorporating the influence of surface resistance. A face-centered cubic (FCC) lattice model for a spatial cluster distribution was used to modify the effect of water content on ionic conductivity in the polymeric matrix, i.e., the regions between clusters. Compared with the available empirical correlations, the new expression showed much better agreement with the available experimental results, which indicates the rationality to consider the structural influence on ion conduction in water-swollen Nafion membranes.


cluster the equivalent field ionic conductivity surface energy 



factional volume of water (−)


factional volume of ion-exchange site, defined by ΔV′/(1 + ΔV) (−)


diameter of a water molecule (m)


elemental electricity (C)


Boltzmann’s constant (J/K)


equivalent cubic length of a cluster (nm)


the equivalent weight of Nafion (g/mol)


density of dipoles on cluster surface (nm−2)


Avogadro’s constant (mol−1)


cluster radius (nm)


absolute temperature (K)


volume of a single ion exchange site (cm3)


fractional volume change of membrane due to water absorption (−)


defined by (N A ·V i ) /(M e /ρ d ) (−)



defined by [3] (m2·mol/kg)


specific surface energy (J/m2)


surface energy relate to dipole-change (J/m2)


effective conductivity of membrane (S/cm)


conductivity of water (S/cm)


conductivity of dry membrane (S/cm)


density of dry membrane (g/cm3)


density of water (g/cm3)


effective density (defined by (ρ d + ΔV·ρ w )/(1 + ΔV))(g/cm3)


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Copyright information

© Higher Education Press and Springer-Verlag 2007

Authors and Affiliations

  • Yang Zhen 
    • 1
  • Peng Xiaofeng 
    • 1
  • Wang Buxuan 
    • 1
  • Duan Yuanyuan 
    • 1
  • Lee Duujong 
    • 2
  1. 1.Department of Thermal EngineeringTsinghua UniversityBeijingChina
  2. 2.Department of Chemical EngineeringTaiwan UniversityTaipeiChina

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