Nanopores have been explored for various biochemical and nanoparticle analyses, primarily via characterizing the ionic current through the pores. At present, however, size determination for solid-state nanopores is experimentally tedious and theoretically unaccountable. Here, we establish a physical model by introducing an effective transport length, L_eff, that measures, for a symmetric nanopore, twice the distance from the center of the nanopore where the electric field is the highest to the point along the nanopore axis where the electric field falls to e^–1 of this maximum. By , a simple expression S₀ = f (G, σ, h, β) is derived to algebraically correlate minimum nanopore cross-section area S₀ to nanopore conductance G, electrolyte conductivity σ, and membrane thickness h with β to denote pore shape that is determined by the pore fabrication technique. The model agrees excellently with experimental results for nanopores in graphene, single-layer MoS₂, and ultrathin SiN_x films. The generality of the model is verified by applying it to micrometer-size pores.

中文翻译：

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通过电导测量快速准确确定纳米孔尺寸的物理模型

已经通过主要表征通过孔的离子电流来探索用于各种生化和纳米颗粒分析的纳米孔。然而，目前，固态纳米孔的尺寸确定在实验上是繁琐的，并且在理论上是不负责任的。在这里，我们通过引入有效传输长度L _eff建立一个物理模型，该长度对于对称的纳米孔而言，是从电场最高的纳米孔中心到沿着纳米孔轴的点的距离的两倍。电场降至此最大值的e ^–1。通过，一个简单表达式S ₀ = f（G，σ，h，β）导出到相关成分的代数最小纳米孔的横截面面积š ₀到纳米孔电导G ^，电解质电导率σ，和膜厚度ħ与β到由所述孔的制造技术来确定分别表示孔形状。该模型与石墨烯，单层MoS ₂和超薄SiN _x膜中纳米孔的实验结果非常吻合。通过将其应用于微米大小的孔，可以验证模型的一般性。