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indicating that both terms in the equation decreased as the bias voltage was reduced. For Polymers 2021, 13, 1258 the dry membrane, the phase lag values were 4.0°, 3.4°, and 2.5° at –3 V, –2 V, and –1 V, respectively. Wet membranes typically have higher proton conductivities than dry membranes, and a high ionic channel network density, because of their creation of a new ionic channel network. The difference between the phase lag values of wet and dry 9 of 13 membranes is thus related to the second term in (13). At 1 V, this value is close to zero. In contrast, at 2 V and 3 V, both membranes have similar negative phase values. Both membranes have similar phase values at 2 V and 3 V. Specifically, dry and wet membranes have the same lag values at 3 V.. Thiis rresulltt iimplliies tthat tthe ellectrical iinteraction is only between the charged tip and the polarized surface charge. Thus, the second term in (13) does not have any effect on the phase lag in this case.. Figure 6. Variation in phase lag with bias voltage for different membrane conditions. Figure 6. Variation in phase lag with bias voltage for different membrane conditions. 4. Analysis 4. Analysis Local charge density, which reflects the ionic channel network, can be approximated Local charge density, which reflects the ionic channel network, can be approximated based on the first and second terms of (13). For this, the phase lag value at each bias voltage based on the first and second terms of (13). For this, the phase lag value at each bias must be related to a microscopic electrostatic phenomenon. To understand the generation voltage must be related to a microscopic electrostatic phenomenon. To understand the of positive phase lag at a negative sample bias voltage, the operation of a tip when bias generation of positive phase lag at a negative sample bias voltage, the operation of a tip voltage is applied during scanning must be analyzed. There is typically a water layer when bias voltage is applied during scanning must be analyzed. There is typically a water between the tip and the sample surface. When a bias voltage is applied, hydrolysis occurs, layer between the tip and the sample surface. When a bias voltage is applied, hydrolysis hydrogen is produced, and protons are created because of the Pt-coated tip. Figure 7 occurs, hydrogen is produced, and protons are created because of the Pt-coated tip. Figure depicts the local variation in the current flowing through the Pt tip, and the half membrane 7 depicts the local variation in the current flowing through the Pt tip, and the half electrode assembly as bias voltage is swept. Current flows when the magnitude of the bias membrane electrode assembly as bias voltage is swept. Current flows when the voltage is larger than 1.5 V, indicating that protons are created when a voltage is applied to magnitude of the bias voltage is larger than 1.5 V, indicating that protons are created when the Pt tip. a voltage is applied to the Pt tip. 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.PDF Image | Ionic Domains on a Proton Exchange Membrane Electrostatics
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