Poisson-Cahn Theory

Segregation of dopant cations to the surface of mixed-ionic electronic conductors and to grain boundaries in solid electrolytes strongly influences the electrocatalytic activity and ionic conductivity of these materials. Existing continuum theories to describe the regions of charge accumulation near surfaces and interfaces (space charge zones) are based on dilute approximations. These dilute-case ‘Poisson-Boltzmann’ models cannot reproduce modern experimental measurements of space charge regions in solids, which show much thicker regions of charge separation than Poisson-Boltzmann theories predict. We have developed a variational framework (the Poisson-Cahn formalism) that treats dilute and concentrated cases with a unified theory, taking ion interactions and gradient energies into account.

The theory has been used to replicate experimentally-measured defect concentration profiles at surfaces and grain boundaries in concentrated systems, such as acceptor-doped ceria and mixed conducting perovskites. Most recently, Poisson-Cahn models have been shown to replicate the co-accumulation of differently-charged defects near grain boundaries in neodymium-doped ceria as measured by atom probe tomography.

 

Papers

• A Space-Charge Treatment of the Increased Concentration of Reactive Species at the Surface of a Ceria Solid Solution
  
• Kinetic modeling of near-interface defect segregation during thermal annealing of oxygen-conducting solid electrolytes
  
• A generalised space-charge theory for extended defects in oxygen-ion conducting electrolytes: from dilute to concentrated solid solutions 
  
• A variational approach to surface cation segregation in mixed conducting perovskites