### Abstract

The dielectric constant and conductivity of a dilute ensemble of immobile, spherical particles with fixed surface (zeta) potential Φ_{o}, immersed in an electrolytic solution, is obtained in the thin double layer approximation δ≪α, δ being the thickness of the double layer, and α the radius of the particles. Equations of motion for coions and counter-ions are solved by the method of matched asymptotics. The equations of motions, linearized in the applied electric field E_{o} and with coefficients that are functions of the unperturbed potential (zeroth order in E_{o}), are solved to second order in (δ/α). The term giving enhancement in the real part of the effective dielectric constant of the ensemble ε′_{e}, is second order in δ/α; but the series converges if (δ/α)t^{2}/(1-t^{2})≪1, where t = tanh(eΦ_{o}/k_{B}T), e being the ionic charge, k _{B} the Boltzmann constant, and T the absolute temperature. The static value of ε′_{e} to this order, is ε′ _{e}∼36fε′t^{2}/(1-t^{2})^{2}, where f is the volume fraction of particles, ε′ the real part of the dielectric constant of the solution. When Φ_{o}→∞, therefore, t→1, ε′_{e} diverges as ε′ _{e}∼9/4fε′ exp[eΦ_{o}/k_{B}T). The present treatment is free from the approximations of previous analytical results. When applicable, the theory agrees well with experiments over three decades in frequency, with one adjustable parameter Φ_{o}. Comparison with other theories are made.

Original language | English (US) |
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Pages (from-to) | 4683-4693 |

Number of pages | 11 |

Journal | The Journal of Chemical Physics |

Volume | 77 |

Issue number | 9 |

DOIs | |

State | Published - Jan 1 1982 |

### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

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## Cite this

*The Journal of Chemical Physics*,

*77*(9), 4683-4693. https://doi.org/10.1063/1.444369