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Polymers 2021, 13, 1258 11 of 13 Bias Voltage (V) −3 −2 −1 Net Charge of Dry Membrane (C) 8.71 × 10−18 6.07 × 10−18 3.99 × 10−18 Net Charge of Wet Membrane (C) 1.87 × 10−18 1.28 × 10−18 0.81 × 10−18 % Difference 78.5 78.9 79.8 The net electrical charge of the protons at each bias voltage and membrane condi- tion was estimated using (13). This approximation is conducted in several steps. First, because the phase lag value obtained for each membrane includes a contribution from the polarization-induced charge, the phase lag when there are no protons on the membrane surface is subtracted from this value. Then, the tip radius is calculated for each membrane using the blind tip reconstruction method [26]. Finally, the net charge of the protons is calculated using the second term of (13). The calculation results for the net charge are summarized in Table 2. In the dry membrane, the net charge is 8.71 × 10−18 C, 6.07 × 10−18 C, and 3.99 × 10−18 C at −3 V, −2 V, and −1 V, respectively. Hence, the net charge increases as the bias voltage is increased. The value at −1 V is much smaller than the net charge at other voltages, owing to the relatively small amount of proton generation at −1 V. This is consistent with the variation in local current with a swept bias voltage. However, the latter result does not provide absolute numerical information about the ionic domain. In the wet membrane, the net charge is 1.87 × 10−18 C, 1.28 × 10−18 C, and 8.06 × 10−18 C at −3 V, −2 V, and −1 V, respectively. This trend is similar to that observed for dry membranes. However, the amount of electrical charge is much smaller than that with dry membranes, possibly because of the partial movement of protons into the ionic channels. This result indicates that wet membranes have a larger ionic domain than dry membranes. Here, the repulsive force is only due to the protons that do not move into the ionic channel network. The difference between the net charge of dry and wet membranes is similar at each bias voltage and is ~79–80%. This result implies that 80% of the liberated protons move into the wet membrane; only 20% of the protons interact with the tip, and this ratio is independent of the bias voltage. From these results, it can be surmised that the area of the ionic channels on the surface of a wet membrane increases by ~80% compared with that on a dry membrane. Previous experimental results have shown that there is an approximately 80% difference between proton conductivity under ambient conditions and fully humid conditions [27,28]. Hence, our calculations are consistent with the literature. Table 2. Net charge of each membrane. In this study, we derived an NAM for analyzing proton exchange membranes. Based on Shen’s study [19], we used an interpretation method for EFM signals. We assumed that the capacitive force is a summation of two dominant electrostatic interactions: electrostatic force of induced charge-charged tip and free charge-charged tip. We derived the force gradient, which was recorded as the phase lag value on the EFM image, based on these two interactions. Thus, the NAM considers two terms: the polarization dominant term and the free charge dominant term. The backbone is ruled by the polarization dominant term, and the free charge dominant term is related to the ionic domain structure of proton exchange membranes. Thus, the structural change of the ionic domain can be characterized by adapting the NAM to measure the phase lag value of EFM. To examine the NAM, we determined the local charge density of a proton exchange membrane, which is directly related to the ionic domain, by using an approximation model. The wet and dry Nafion was scanned by increasing the applied bias voltage in intervals and applying protons from hydrolysis. The characterization by the NAM charge density of protons on the surface shows a clear difference between the dry and wet membranes. The results are in good agreement with those of previous studies [21]. Thus, we conclude that the NAM can be applied for studying proton exchange membranes. The enhancement of proton conductivity is the prime purpose for developing the proton exchange membranes. ProtonPDF Image | Ionic Domains on a Proton Exchange Membrane Electrostatics
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