Crossover of the Power-Law Exponent for Carbon Nanotube Conductivity as a Function of Salinity
Crossover of the Power-Law Exponent for Carbon Nanotube Conductivity as a Function of Salinity
复制标题
碳纳米管电导率与盐度函数的幂律指数的交叉
DOI：
10.1021/acs.jpcb.8b01975
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发表时间：
2018
期刊：
影响因子：
3.3
通讯作者：
Bonthuis Douwe Jan
中科院分区：
文献类型：
--
作者：
Uematsu Yuki;Netz Roland R.;Bocquet Lyderic;Bonthuis Douwe Jan
根据柱坐标系中的泊松-玻尔兹曼方程，我们计算了填充电解质的单个带电纳米管的电导率。电导率作为盐浓度的函数遵循幂律，其指数在文献中一直存在争议。我们使用共离子排除近似并分析获得不同渐近幂律行为之间的交叉。通过数值求解完整的泊松-玻尔兹曼方程，我们还计算了具有不同半径和 pKa 值的管的盐浓度和 pH 值函数的完整指数图。我们将我们的理论应用到最近的碳纳米管实验结果中，使用 pKaas 拟合参数。与实验数据非常吻合，该理论显示了幂律行为，高 pH 下指数为 1/3，低 pH 下指数为 1/2，交叉取决于盐浓度、管半径和 pKa。
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 pKavalues. We apply our theory to recent experimental results on carbon nanotubes using the pKaas 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.