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Ionic Domains on a Proton Exchange Membrane Electrostatics

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Ionic Domains on a Proton Exchange Membrane Electrostatics ( ionic-domains-proton-exchange-membrane-electrostatics )

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Polymers 2021, 13, 1258 3 of 13 using a widely accepted methodical model [18] to explain local charge movement at the SiO2/LDPE boundary. In this model, the phase value reflects the net force between the tip and the sample surface and the net force caused by local charge. They used low-density polyethylene (LDPE) as an insulating matrix material to minimize electrical interaction between the tip and the sample surface. Thus, the phase value refers to the amount of local charge, and its movement can be clearly seen. Shen et al. [19] studied the degree reduction of a monolayer graphene oxide (GO) sheet by utilizing electrostatic force spectroscopy; they considered the difference in the dielectric constant of graphene and mica. They assumed that a tip and sample surface can create a parallel capacitor with a dielectric material and derived a capacitive force that includes the dielectric constant between the tip and sample surface. Previous studies that attempted to understand the local charge distribution and dielectric constant by analyzing EFM signals have obtained remarkable results. EFM signal interpretation is based on characterizing the capacitive force between a tip and sample surface. This capacitive force is due to the electrical interaction between the conductive tip and surface charge of the sample. For calculating the net force, individual electrical interactions that contribute to the net force have to be specified, and this requires a deep understanding of the system. Each suggested analysis based on the capacitive force agreed well with specific systems. In several studies, EFM signals are used to provide additional morphology informa- tion. Thus, the phase value distribution on the surface is used for observing conducting/non- conducting areas of composite membranes [20,21]. A few groups have studied the ionic structure of proton exchange membranes using EFM [22,23]. One such remarkable study is that of Barnes and Buratto [22]. They measured several individual ionic channels of Nafion by using EFM under different bias voltages and analyzed the obtained results using a well-known simple parallel capacitor model. They found particular channel shapes such as connected cylindrical channels, dead-end cylinder channels, and bottleneck channels by characterizing the differences in the EFM signal. In this study, we derived a numerical approximation model (NAM) for interpreting EFM signals from proton exchange membrane measurements. The subject of our study is similar to the work of Shen et al., whose method focused on understanding locally charged areas, encompassed by non-conducting areas. Further, their approach for analyzing EFM signals was systematic and logical. However, the proton exchange membrane structure is more complicated. The sulfonic acid groups in the membrane, which create ionic clusters, are scattered over the entire surface. Owing to hydration, the ionic clusters are connected with each other, and they create ionic channels. In ionic channels, free charges from ionized sulfonic acid groups or that are externally supplied exist and move. The polarized external electric field caused by applying bias voltage between the tip and surface of the proton exchange membrane causes free charges to coexist near ionic channels. Thus, the capacitive force between the tip and proton exchange membrane simultaneously includes both electrical interactions. To analyze the EFM signal from a proton exchange membrane, the NAM was derived by considering two assumptions. First, the conductive tip and proton exchange membrane surface creates a nanoscopic capacitor, and the geometry of this capacitor can be simplified as a parallel plate. Second, a polarized surface and free charge independently interact with the conductive tip. The electrical interaction of free charge is also considered. NAM considers the sum of two independent electrical interactions: electrostatic force between a conductive tip and polarization surface, and that between a tip and free charges. By considering these two terms, the ionic domain structure can be analyzed. Using this numerical model, we characterize the ionic channel network of proton exchange membranes with different amounts of water uptake. We also extract quantitative information relating the ionic channel network to the proton exchange membrane. Furthermore, we attempt to provide a general model for interpreting changes in the morphology of a proton exchange membrane.

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