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

N1 - Funding Information:
The authors acknowledge funding from ANR, Projet de Recherche Collaborative − Internationale (PRCI) and the Deutsche Forschungsgemeinschaft (DFG) via grant NE 810/11. Y.U. was supported by Grant-in-Aid for JSPS Fellows 16J00042.
Publisher Copyright:
© 2018 American Chemical Society.

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.

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U2 - 10.1021/acs.jpcb.8b01975

DO - 10.1021/acs.jpcb.8b01975

M3 - Article

C2 - 29489370

AN - SCOPUS:85044269322

VL - 122

SP - 2992

EP - 2997

JO - Journal of Physical Chemistry B

JF - Journal of Physical Chemistry B

SN - 1520-6106

IS - 11

ER -