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

Yuki Uematsu, Roland R. Netz, Lydéric Bocquet, Douwe Jan Bonthuis

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 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.

Original languageEnglish
Pages (from-to)2992-2997
Number of pages6
JournalJournal of Physical Chemistry B
Volume122
Issue number11
DOIs
Publication statusPublished - Mar 22 2018

All Science Journal Classification (ASJC) codes

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

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