通过1：1电解质的修正Dukhin数缩放均匀带电纳米孔中的选择性
Scaling of selectivity in uniformly charged nanopores through a modified Dukhin number for 1:1 electrolytes
摘要：
我们表明，修改后的版本的Dukhin数是一个适当的缩放参数的离子选择性均匀带电的纳米孔。修正的Dukhin数是变量$σ$（表面电荷）、$R$（孔半径）和$c$（盐浓度）的明确函数，并定义为$\mathrm{mDu}=|σ|/e(R/λ)$，其中$λ$是具有$c$依赖性（$λ\sim c^{-1/2}$）的电解质的屏蔽长度。缩放意味着器件功能（选择性）是mDu的平滑和（在这种情况下）单调函数。引入定义为$\mathrm{Du}=|σ|/eRc$（$c^{-1}$依赖性）的原始Dukhin数以指示在孔中表面传导还是体积传导占主导地位。修改后的版本满足缩放和特征的选择性在中间政权，其中表面和体传导都存在和孔既不是完美的选择性，也不是完美的非选择性。我们的建模研究使用局部平衡蒙特卡罗方法和泊松-能斯特-普朗克理论提供的径向通量分布，从径向选择性分布可以计算。这些曲线显示了对于变量$σ$、$R$和$c$的给定组合，在纳米孔的哪个区域中表面或体积传导占主导地位。我们表明，标度曲线的拐点可以用来表征表面和体积传导之间的过渡点。
英文摘要：
We show that a modified version of the Dukhin number is an appropriate scaling parameter for the ionic selectivity of uniformly charged nanopores. The modified Dukhin number is an unambiguous function of the variables $σ$ (surface charge), $R$ (pore radius), and $c$ (salt concentration), and defined as $\mathrm{mDu}=|σ|/e(R/λ)$, where $λ$ is the screening length of the electrolyte carrying the $c$ dependence ($λ\sim c^{-1/2}$). Scaling means that the device function (selectivity) is a smooth and (in this case) monotonic function of mDu. The original Dukhin number defined as $\mathrm{Du}=|σ|/eRc$ ($c^{-1}$ dependence) was introduced to indicate whether the surface or the volume conduction is dominant in the pore. The modified version satisfies scaling and characterizes selectivity in the intermediate regime, where both surface and bulk conductions are present and the pore is neither perfectly selective, nor perfectly non-selective. Our modeling study using the Local Equilibrium Monte Carlo method and the Poisson-Nernst-Planck theory provides the radial flux profiles from which the radial selectivity profile can be computed. These profiles show in which region of the nanopore the surface or the volume conduction dominates for a given combination of the variables $σ$, $R$, and $c$. We show that the inflection point of the scaling curve may be used to characterize the transition point between the surface and volume conductions.
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