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 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 - Mar 22 2018 |
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All Science Journal Classification (ASJC) codes
- Physical and Theoretical Chemistry
- Surfaces, Coatings and Films
- Materials Chemistry
Cite this
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.
In: Journal of Physical Chemistry B, Vol. 122, No. 11, 22.03.2018, p. 2992-2997.Research output: Contribution to journal › Article
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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.
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U2 - 10.1021/acs.jpcb.8b01975
DO - 10.1021/acs.jpcb.8b01975
M3 - Article
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 -