### 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 |
---|---|

Pages (from-to) | 2992-2997 |

Number of pages | 6 |

Journal | Journal of Physical Chemistry B |

Volume | 122 |

Issue number | 11 |

DOIs | |

Publication status | Published - 22 Mar 2018 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Physical Chemistry B*,

*122*(11), 2992-2997. https://doi.org/10.1021/acs.jpcb.8b01975

**Crossover of the Power-Law Exponent for Carbon Nanotube Conductivity as a Function of Salinity.** / Uematsu, Yuki; Netz, Roland R.; Bocquet, Lydéric; Bonthuis, Douwe Jan.

Research output: Contribution to journal › Article › Research › peer-review

*Journal of Physical Chemistry B*, vol. 122, no. 11, pp. 2992-2997. https://doi.org/10.1021/acs.jpcb.8b01975

}

TY - JOUR

T1 - Crossover of the Power-Law Exponent for Carbon Nanotube Conductivity as a Function of Salinity

AU - Uematsu, Yuki

AU - Netz, Roland R.

AU - Bocquet, Lydéric

AU - Bonthuis, Douwe Jan

PY - 2018/3/22

Y1 - 2018/3/22

N2 - 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 pKa values. We apply our theory to recent experimental results on carbon nanotubes using the pKa 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 pKa.

AB - 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 pKa values. We apply our theory to recent experimental results on carbon nanotubes using the pKa 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 pKa.

UR - http://www.scopus.com/inward/record.url?scp=85044269322&partnerID=8YFLogxK

U2 - 10.1021/acs.jpcb.8b01975

DO - 10.1021/acs.jpcb.8b01975

M3 - Article

VL - 122

SP - 2992

EP - 2997

JO - The journal of physical chemistry (Washington, DC) / B

JF - The journal of physical chemistry (Washington, DC) / B

SN - 1520-6106

IS - 11

ER -