Ion selectivity is the basis for designing smart nanopore/channel-based devices, e.g., ion separators and biosensors. Quantitative characterization of ion selectivities in nanopores often employs the Nernst or Goldman–Hodgkin–Katz (GHK) equation to interpret transmembrane potentials. However, the direction of the measured transmembrane potential drop is not specified in these equations, and selectivity values calculated using absolute values of transmembrane potentials do not directly reveal the ion for which the membrane is selective. Moreover, researchers arbitrarily choose whether to use the Nernst or GHK equation and overlook the significant differences between them, leading to ineffective quantitative comparisons between studies. This work addresses these challenges through (a) specifying the transmembrane potential (sign) and salt concentrations in terms of working and reference electrodes and the solutions in which they reside when using the Nernst and GHK equations, (b) reporting of both Nernst-selectivity and GHK-selectivity along with solution compositions and transmembrane potentials when comparing different nanopores/channels, and (c) performing simulations to define an ideal selectivity for nanochannels. Experimental and modeling studies provide significant insight into these fundamental equations and guidelines for the development of nanopore/channel-based devices.

中文翻译：

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解决纳米孔离子选择性表征的挑战

离子选择性是设计基于智能纳米孔/通道的设备（例如离子分离器和生物传感器）的基础。纳米孔中离子选择性的定量表征通常采用 Nernst 或 Goldman-Hodgkin-Katz (GHK) 方程来解释跨膜电位。然而，这些方程中没有指定测量的跨膜电位下降的方向，并且使用跨膜电位的绝对值计算的选择性值并不能直接揭示膜对其具有选择性的离子。此外，研究人员随意选择使用Nernst方程还是GHK方程，而忽略了它们之间的显着差异，导致研究之间的定量比较无效。这项工作通过 (a) 在使用能斯特和 GHK 方程时指定工作电极和参比电极及其所在溶液的跨膜电位（符号）和盐浓度，(b) 报告能斯特选择性，解决了这些挑战比较不同纳米孔/通道时的 GHK 选择性以及溶液成分和跨膜电位，以及 (c) 进行模拟以确定纳米通道的理想选择性。实验和建模研究为开发基于纳米孔/通道的器件提供了对这些基本方程和指南的重要见解。