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0 -0.1 Polymers 2021, 13, 1258 Polymers 2021, 13, x -0.2 10 of 13 -0.3 0.3 -0.4 -1.5 -1 -0.5 0 0.5 Bios Voltage 1 1.5 0.2 0.1 Figure 7. Variation in current with bias voltage applied to the Pt tip. 0 The phase lag generated at negative bias voltages includes a contribution from the interaction between the released protons and the ionic domains on the membrane surface. cover its surface. Thus, positive phase lag values are measured, because a repulsive force is induced between the positively charged tip and the proton-covered surface. The -0.1 As the membrane is negatively charged, owing to polarization, it attracts protons that -0.2 magnitude of the repulsive force is related to the density of the activated ionic channel network. When water uptake in the membrane increases, an ionic channel network is -0.3 developed, as the number of interconnections between the ionic channels grows. Protons are accelerated into the ionic channel by the external electric field, as shown in Figure 8. -0.4 The number of ionic domains increases as the number of protons on the membrane surface -1.5 -1 -0.5 0 0.5 1 1.5 10 of 14 Current (nA) Current (n Bias Voltage (V) −3 −2 −1 Dry Membrane (Degree) Wet Membrane (Degree) No. Protons (Degree) between Wet Membrane and No. Protons decreases. Thus, the repulsive force between the tip and the membrane and the area of the ionic domain have a reciprocal relationship. Bios Voltage Fiigurre7..VaarriiaattiioonininccurrreennttwitihthbbiaiassvvooltlataggeeaappplileieddtotoththeePPtttitpip. . The phase lag generated at negative bias voltages includes a contribution from the interaction between the released protons and the ionic domains on the membrane surface. As the membrane is negatively charged, owing to polarization, it attracts protons that cover its surface. Thus, positive phase lag values are measured, because a repulsive force is induced between the positively charged tip and the proton-covered surface. The magnitude of the repulsive force is related to the density of the activated ionic channel network. When water uptake in the membrane increases, an ionic channel network is developed, as the number of interconnections between the ionic channels grows. Protons are accelerated into the ionic channel by the external electric field, as shown in Figure 8. The number of ionic domains increases as the number of protons on the membrane surface decreases. Thus, the repulsive force between the tip and the membrane and the area of the ionic domain have a reciprocal relationship. Figure 8. Proton movement into the ionic channel with (a) negative and (b) positive sample bias voltages. Figure 8. Proton movement into the ionic channel with (a) negative and (b) positive sample bias voltages. Table 1 lists the mean phase lag values for dry and wet membranes, and the values Table 1 lists the mean phase lag values for dry and wet membranes, and the values when there are no protons on the membrane surface. The latter values were calculated when there are no protons on the membrane surface. The latter values were calculated using only negative bias voltages. With both dry and wet membranes, the phase lag using only negative bias voltages. With both dry and wet membranes, the phase lag increased with the bias voltage, which can be explained as the increase in proton generation increased with the bias voltage, which can be explained as the increase in proton due to hydrolysis. At all negative bias voltages, dry membranes have a larger phase lag value than wet membranes, which is consistent with our assumptions. Hence, the area of the ionic domain on the membrane can be approximated using a phase lag difference. Table 1. Mean phase lag value of each membrane. Phase Lag Difference Phase Lag Difference between Dry Membrane and No. Protons −1.134 Figure 8. Proton movement into the ionic channel with (a) negative and (b) positive sample bias voltages. 4.02 3.31 4.45 3.10 2.24 Table 1 lists the mean phase lag values for dry and wet membranes, and the values 5.15 2.54 −0.504 3.60 3.04 1.78 −0.126 2.36 1.90 when there are no protons on the membrane surface. The latter values were calculated using only negative bias voltages. With both dry and wet membranes, the phase lag increased with the bias voltage, which can be explained as the increase in protonPDF Image | Ionic Domains on a Proton Exchange Membrane Electrostatics
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