Ionic Domains on a Proton Exchange Membrane Electrostatics

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polymers Article Analysis of Ionic Domains on a Proton Exchange Membrane Using a Numerical Approximation Model Based on Electrostatic Force Microscopy Byungrak Son 1 , JaeHyoung Park 2 and Osung Kwon 3,* 􏰁􏰂􏰃 􏰅􏰆􏰇 􏰈􏰉􏰊􏰋􏰌􏰂􏰍 Citation: Son,B.;Park,J.;Kwon,O. Analysis of Ionic Domains on a Proton Exchange Membrane Using a Numerical Approximation Model Based on Electrostatic Force Microscopy. Polymers 2021, 13, 1258. polym13081258 Academic Editor: Il Kim Received: 19 March 2021 Accepted: 12 April 2021 Published: 13 April 2021 1 2 3 * Correspondence:; Tel.: +82-53-580-5657 Abstract: Understanding the ionic channel network of proton exchange membranes that dictate fuel cell performance is crucial when developing proton exchange membrane fuel cells. However, it is difficult to characterize this network because of the complicated nanostructure and structure changes that depend on water uptake. Electrostatic force microscopy (EFM) can map surface charge distribution with nano-spatial resolution by measuring the electrostatic force between a vibrating conductive tip and a charged surface under an applied voltage. Herein, the ionic channel network of a proton exchange membrane is analyzed using EFM. A mathematical approximation model of the ionic channel network is derived from the principle of EFM. This model focusses on free charge movement on the membrane based on the force gradient variation between the tip and the membrane surface. To verify the numerical approximation model, the phase lag of dry and wet Nafion is measured with stepwise changes to the bias voltage. Based on the model, the variations in the ionic channel network of Nafion with different amounts of water uptake are analyzed numerically. The mean surface charge density of both membranes, which is related to the ionic channel network, is calculated using the model. The difference between the mean surface charge of the dry and wet membranes is consistent with the variation in their proton conductivity. Keywords: electrostatic force microscopy; proton exchange membrane; numerical approximation model; local dielectric constant; ionic domain; surface charge density; PEMFC 1. Introduction Proton exchange membrane fuel cells are a core technology of green energy devices for several reasons. They do not emit carbon dioxide; they can operate continuously under different environmental conditions without change in performance, and they have a relatively high energy conversion efficiency. However, many limitations must be overcome before they can be adopted, such as high cost, low reliability, and a lack of hydrogen gas infrastructure. Solving the low reliability issue is imperative; however, this is difficult because a proton exchange membrane’s reliability is related to its morphological structure. Proton exchange membranes typically act as proton conductors because of their hetero- geneous structures, which is the combination of a hydrophobic backbone with hydrophilic sulfonic acid groups. Sulfonic acid groups create ionic clusters that have an inverted micel- lar structure and can form a network under hydration. Typically, protons move through the ionic network through vehicle-type and Grotthuss-type mechanisms. In the vehicle-type mechanism, the protons pass into the medium with a solvent. Thus, proton conductivity is related to the solvent diffusion rate. In the Grotthuss-type mechanism, the protons move into the medium by creating and breaking hydrogen bonds without any solvent. In general, these mechanisms are not independent. In the proton exchange membrane, the vehicle-type mechanism is predominant, and the Grotthuss-type mechanism is observed Division of Energy Technology, DGIST, Daegu 42988, Korea; Corporate Research Center, HygenPower Co., Ltd., Daegu 42988, Korea; Tabula Rasa College, Keimyung University, Daegu 42601, Korea Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// 4.0/). Polymers 2021, 13, 1258.

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