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Polymers 2021, 13, 1258 12 of 13 References conductivity is governed by the morphological structure of the ionic channel network. Thus, the characterization of the ionic channel network is mandatory for developing the novel proton exchange membranes. The NAM for local charge density derived using electrostatic force microscopy has become an important tool for characterizing a novel proton exchange membrane. 5. Conclusions In this study, we proposed a NAM that focusses on free charge movement into the ionic channel network of a proton exchange membrane, based on the capacitance force between a conductive AFM tip and the proton exchange membrane surface. The model is expressed as a summation of induced charge distribution, which is connected with the backbone of the proton exchange membrane and free charge distribution which is related to the ionic channel network. This model can be used for ionic channel network variation under various conditions, such as hydration, as well as for composites with filler materials, by calculating induced and free charge distribution change. The NAM was verified by analysis of the experimental results, which were phase lags measured under different bias voltages for dry and wet proton exchange membranes. The enhancement of proton conductivity is the prime purpose of developing proton exchange membranes. Proton conductivity is governed by the morphological structure of ionic channel networks. Thus, the characterization of ionic channel networks is essential for developing novel proton exchange membranes. The NAM is shown to be an important tool for characterizing novel proton exchange membranes. Author Contributions: Conceptualization, B.S. and O.K.; validation, B.S., J.P., and O.K.; investigation, B.S., J.P., and O.K.; writing—original draft preparation, O.K.; writing—review and editing, B.S.; supervision, O.K.; project administration, O.K. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the DGIST R&D Program of the Ministry of Science and ICT [21-ET-08] and Research Institute R&DB Program through the Ministry of Science and ICT [2020-DG-RD-0031]. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Data are contained within the article. Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results. 1. Zuo, Z.C.; Fu, Y.Z.; Manthiram, A. Novel Blend Membranes Based on Acid-Base Interactions for Fuel Cells. Polymers 2012, 4, 1627–1644. [CrossRef] 2. Ketpang, K.; Lee, K.; Shanmugam, S. Facile Synthesis of Porous Metal Oxide Nanotubes and Modified Nafion Composite Membranes for Polymer Electrolyte Fuel Cells Operated under Low Relative Humidity. ACS Appl. Mater. Inter. 2014, 6, 16734–16744. [CrossRef] [PubMed] 3. Zhu, J.; Tang, H.L.; Pan, M. Fabrication and characterization of self-assembled Nafion-SiO2-ePTFE composite membrane of PEM fuel cell. J. Membrane Sci. 2008, 312, 41–47. [CrossRef] 4. Ke, C.C.; Li, X.J.; Shen, Q.A.; Qu, S.G.; Shao, Z.G.; Yi, B.L. Investigation on sulfuric acid sulfonation of in-situ sol-gel derived Nafion/SiO2 composite membrane. Int. J. Hydrogen. Energy 2011, 36, 3606–3613. [CrossRef] 5. Hsu, W.Y.; Gierke, T.D. Ion-Transport and Clustering in Nafion Perfluorinated Membranes. J. Membrane Sci. 1983, 13, 307–326. [CrossRef] 6. Schmidt-Rohr, K.; Chen, Q. Parallel cylindrical water nanochannels in Nafion fuel-cell membranes. Nat. Mater. 2008, 7, 75–83. [CrossRef] 7. Gupit, C.I.; Li, X.; Maekawa, R.; Hasegawa, N.; Iwase, H.; Takata, S.; Shibayama, M. Nanostructures and Viscosities of Nafion Dispersions in Water/Ethanol from Dilute to Concentrated Regimes. Macromolecules 2020, 53, 1464–1473. [CrossRef]PDF Image | Ionic Domains on a Proton Exchange Membrane Electrostatics
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