## Abstract

On the basis of the Poisson-Boltzmann equation in cylindrical coordinates, we calculate the conductivity of a single charged nanotube filled with electrolyte. The conductivity as a function of the salt concentration follows a power-law, the exponent of which has been controversially discussed in the literature. We use the co-ion-exclusion approximation and obtain the crossover between different asymptotic power-law behaviors analytically. Numerically solving the full Poisson-Boltzmann equation, we also calculate the complete diagram of exponents as a function of the salt concentration and the pH for tubes with different radii and pK_{a} values. We apply our theory to recent experimental results on carbon nanotubes using the pK_{a} as a fit parameter. In good agreement with the experimental data, the theory shows power-law behavior with the exponents 1/3 at high pH and 1/2 at low pH, with a crossover depending on salt concentration, tube radius and pK_{a}.

Original language | English |
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Pages (from-to) | 2992-2997 |

Number of pages | 6 |

Journal | Journal of Physical Chemistry B |

Volume | 122 |

Issue number | 11 |

DOIs | |

Publication status | Published - Mar 22 2018 |

## All Science Journal Classification (ASJC) codes

- Physical and Theoretical Chemistry
- Surfaces, Coatings and Films
- Materials Chemistry