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Counterion volume effects in mixed electrical double layers.

P M Biesheuvel1, M van Soestbergen

  • 1The Netherlands Institute for Metals Research, Mekelweg 2, 2628 CD Delft, The Netherlands. m.biesheuvel@nimr.nl

Journal of Colloid and Interface Science
|September 18, 2007
PubMed
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At high surface charge, smaller ions outcompete larger ones, deviating from Poisson-Boltzmann theory. A modified model including ion size and volume interactions accurately predicts this counterion segregation.

Area of Science:

  • Physical Chemistry
  • Colloid Science
  • Electrochemistry

Background:

  • Poisson-Boltzmann theory (PBT) predicts ion behavior in electrical double layers.
  • Large deviations from PBT occur with mixed-size and mixed-valency counterions at high surface charge.
  • Smaller counterions preferentially accumulate at the interface, displacing larger ones.

Purpose of the Study:

  • To develop and validate a modified Poisson-Boltzmann theory (PBT) that accounts for ion size and volume interactions.
  • To investigate counterion segregation at charged interfaces.
  • To accurately model ion concentration profiles, energies, pressures, and capacities.

Main Methods:

  • Modified PBT incorporating an extended Carnahan-Starling equation of state for hard-sphere interactions.

Related Experiment Videos

  • Theoretical calculations of ion concentration profiles, free energies, surface pressures, and differential capacities.
  • Comparison of model predictions with experimental data, adjusting divalent ion hydrated size.

    • Main Results:

    • Significant deviations from PBT at high surface charge due to volume interactions.
    • Counterion segregation observed, with smaller ions outcompeting larger ones.
    • Dominance of volume and electrostatic field effects over entropic contributions to energy and pressure at high surface charge.

    Conclusions:

    • The modified PBT accurately describes counterion segregation and electrical double-layer behavior.
    • Ion size and volume effects are critical for understanding ion distribution at high surface charge.
    • The model provides a better framework than traditional PBT for systems with mixed counterions.