从纳米管到纳米孔：通过1：1电解质的Dukhin数缩放均匀带电纳米孔的选择性
From nanotubes to nanoholes: scaling of selectivity in uniformly charged nanopores through the Dukhin number for 1:1 electrolytes
摘要：
纳米器件行为的缩放意味着器件功能（选择性）是缩放参数的唯一平滑和单调函数，该缩放参数是系统参数的适当组合。对于这里研究的均匀带电的圆柱形纳米孔，这些参数是电解质浓度$c$、电压$U$、纳米孔的半径和长度$R$和$H$以及纳米孔表面上的表面电荷密度$σ$。由于选择性对这些参数的非线性依赖性，缩放只能在某些限制下应用。我们表明，Dukhin数，$\mathrm{Du}=|σ|/eRc\sim |σ|λ_{\mathrm{D}}^{2}/eR$（$λ_{\mathrm{D}}$是德拜长度），是一个适当的尺度参数在纳米管极限（$H\rightarrow\infty$）。减小纳米孔的长度，即，接近纳米孔极限（$H\rightarrow 0$），已经获得了包含孔长度的替代缩放参数，并且被称为修改的Dukhin数：$\mathrm{mDu}\sim \mathrm{Du}\, H/λ_{\mathrm{D}}\sim |σ|λ_{\mathrm{D}}H/eR$。我们发现非线性的原因是在径向上聚集在孔壁处的双电层与两侧靠近膜的孔入口处的双电层相关。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-普朗克理论提供浓度，通量和选择性的配置文件，显示是否表面或体积传导占主导地位的纳米孔的给定区域中的给定的变量的组合。我们提出，标度曲线的拐点可以用来表征表面传导和体积传导之间的过渡点。
英文摘要：
Scaling of the behavior of a nanodevice means that the device function (selectivity) is a unique smooth and monotonic function of a scaling parameter that is an appropriate combination of the system's parameters. For the uniformly charged cylindrical nanopore studied here these parameters are the electrolyte concentration, $c$, voltage, $U$, the radius and the length of the nanopore, $R$ and $H$, and the surface charge density on the nanopore's surface, $σ$. Due to the non-linear dependence of selectivites on these parameters, scaling can only be applied in certain limits. We show that the Dukhin number, $\mathrm{Du}=|σ|/eRc\sim |σ|λ_{\mathrm{D}}^{2}/eR$ ($λ_{\mathrm{D}}$ is the Debye length), is an appropriate scaling parameter in the nanotube limit ($H\rightarrow\infty$). Decreasing the length of the nanopore, namely, approaching the nanohole limit ($H\rightarrow 0$), an alternative scaling parameter has been obtained that contains the pore length and is called the modified Dukhin number: $\mathrm{mDu}\sim \mathrm{Du}\, H/λ_{\mathrm{D}}\sim |σ|λ_{\mathrm{D}}H/eR$. We found that the reason of non-linearity is that the double layers accumulating at the pore wall in the radial dimension correlate with the double layers accumulating at the entrances of the pore near the membrane on the two sides. Our modeling study using the Local Equilibrium Monte Carlo method and the Poisson-Nernst-Planck theory provides concentration, flux, and selectivity profiles, that show whether the surface or the volume conduction dominates in a given region of the nanopore for a given combination of the variables. We propose 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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