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Keywords = polymer electrolyte membrane

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15 pages, 6027 KiB  
Article
Study on Blended Terpolymer Electrolyte Membrane for Enhanced Safety and Performance in Lithium-Ion Batteries
by Wansu Bae, Sabuj Chandra Sutradhar, Subeen Song, Kijong Joo, Doyul Lee, Donghoon Kang, Hyewon Na, Jiye Lee, Whangi Kim and Hohyoun Jang
Batteries 2025, 11(3), 103; https://doi.org/10.3390/batteries11030103 - 11 Mar 2025
Viewed by 21
Abstract
The persistent emphasis on safety issues in lithium-ion batteries (LIBs) with organic liquid electrolytes revolves around thermal runaway and dendrite formation. The high thermal stability and non-leakage properties of polymer electrolytes (PEs) make them attractive as next-generation electrolytes for LIBs. This study presents [...] Read more.
The persistent emphasis on safety issues in lithium-ion batteries (LIBs) with organic liquid electrolytes revolves around thermal runaway and dendrite formation. The high thermal stability and non-leakage properties of polymer electrolytes (PEs) make them attractive as next-generation electrolytes for LIBs. This study presents a blended terpolymer electrolyte (BTPE) membrane, integrating the high ionic conductivity of dual ion conducting polymer electrolytes (DICPEs) with the elevated lithium transference number (t+) of single-ion conducting polymer electrolytes (SICPEs). The BTPE was synthesized by blending PAA–PVA with lithiated acrylic acid (LiAA), lithiated 2–acrylamido–2–methylpropane sulfonic acid (LiAMPS), and a 2–hydroxyethyl methacrylate (HEMA)–based terpolymer, using lithium bis(fluorosulfonyl)imide (LiFSI) as the lithium salt. The synthesized BTPE showed excellent physical and electrochemical stability; it also exhibited an enhanced lithium transference number (t+ = 0.47) and high ionic conductivity (5.21 × 10−4 S cm−1 at 30 °C), attributed to the interaction between the FSI anion and the NH group of AMPS. This research presents an innovative strategy for the design of next-generation LIB electrolytes by integrating polymer electrolytes. Full article
(This article belongs to the Special Issue Rechargeable Batteries)
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<p><sup>1</sup>H NMR spectrum of (<b>a</b>) HEMA, (<b>b</b>) LiAA, (<b>c</b>) LiAMPS and (<b>d</b>) poly (LiAA–HEMA–LiAMPS).</p>
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<p>FT-IR spectrum of (<b>a</b>) HEMA, (<b>b</b>) LiAA, (<b>c</b>) LiAMPS and (<b>d</b>) poly (LiAA-HEMA-LiAMPS).</p>
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<p>AFM image of BTPE–37 (<b>a</b>–<b>c</b>) and PAA–PVA (<b>d</b>–<b>f</b>): (<b>a</b>) 2D image of BTPE–37 (50 × 50 μm<sup>2</sup>), (<b>b</b>) 2D Image of BTPE-37 in the range indicated by the red box in (<b>a</b>) (20 × 20 μm<sup>2</sup>), (<b>c</b>) 3D image of BTPE–37 (50 × 50 μm<sup>2</sup>), (<b>d</b>) 2D image of PAA–PVA film (50 × 50 μm<sup>2</sup>), (<b>e</b>) 2D Image of PAA-PVA in the range indicated by the red box in (<b>d</b>) (20 × 20 μm<sup>2</sup>) and (<b>f</b>) 3D image of PAA–PVA film (50 × 50 μm<sup>2</sup>).</p>
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<p>DSC curves (<b>a</b>) and TGA curves (<b>b</b>) of BTPEs, pure terpolymer, and PAA–PVA.</p>
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<p>Temperature-dependent ionic conductivity of BTPEs from 30 to 80 °C.</p>
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<p>Linear sweep voltammetry (LSV) profiles of BTPE–37.</p>
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<p>CV profiles of BTPE-37.</p>
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<p>Li transference number (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>t</mi> </mrow> <mrow> <mo>+</mo> </mrow> </msub> </mrow> </semantics></math>) of BTPE–37.</p>
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<p>Rate capability of LFP/BTPE–37/Li metal battery.</p>
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<p>Electrochemical performance of LFP/BTPE–37/Li battery: (<b>a</b>) typical charge–discharge voltage profiles of BTPE–37-based battery, (<b>b</b>) variants of specific capacity and the coulombic efficiency plot.</p>
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<p>Synthesis of the terpolymer poly (LiAA-HEMA-LiAMPS).</p>
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12 pages, 3077 KiB  
Article
Electrochemical Hydrogen Pump/Compressor in Single- and Double-Stage Regime
by Galin Borisov, Nevelin Borisov and Evelina Slavcheva
Hydrogen 2025, 6(1), 14; https://doi.org/10.3390/hydrogen6010014 - 6 Mar 2025
Viewed by 185
Abstract
This study presents the integration and evaluation of commercially available gas diffusion electrodes (GDEs), specifically designed for high-temperature polymer electrolyte membrane fuel cells (HT-PEMFCs) within membrane electrode assemblies (MEA) for electrochemical hydrogen pump/compressor applications (EHP/C). Using Nafion 117 as a solid polymer electrolyte, [...] Read more.
This study presents the integration and evaluation of commercially available gas diffusion electrodes (GDEs), specifically designed for high-temperature polymer electrolyte membrane fuel cells (HT-PEMFCs) within membrane electrode assemblies (MEA) for electrochemical hydrogen pump/compressor applications (EHP/C). Using Nafion 117 as a solid polymer electrolyte, the MEAs were analyzed for cell efficiency, hydrogen evolution, and hydrogen oxidation reactions (HER and HOR) under differential pressure up to 16 bar and a temperature ranging from 20 °C to 60 °C. Key properties of the GDEs, such as electrode thickness and conductivity, were investigated. The catalytic layer was characterized via XRD and EDX analyses to assess its surface and bulk composition. Additionally, the effects of increasing MEA’s geometric size (from 1 cm2 to 5 cm2) and hydrogen crossover phenomena on the efficiency were examined in a single-cell setup. Electrochemical performance tests conducted in a single electrochemical hydrogen pump/compressor cell under hydrogen flow rates from 36.6 Ml·min⁻1·cm⁻2 to 51.3 mL·min⁻1 cm⁻2 at atmospheric pressure provided insights into the optimal operational parameters. For a double-stage application, the MEAs demonstrated enhanced current densities, achieving up to 0.6 A·cm⁻2 at room temperature with further increases to 1 A·cm⁻2 at elevated temperatures. These results corroborated the single-cell data, highlighting potential improvements in system efficiency and a reduction in adverse effects. The work underscores the potential of HT-PEMFC-based GDEs for the integration of MEAs applicable to advanced hydrogen compression technologies. Full article
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<p>Operation principle of electrochemical hydrogen pump/compressor.</p>
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<p>Principal of operation of electrochemical hydrogen pump/compressor under stack operation (<b>a</b>) with serial electrical connection (bipolarity) and (<b>b</b>) with parallel electrical connection.</p>
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<p>XRD spectra of commercial GDEs applicable for HT-PEMFC with 40%wt. and catalytic loading of 0.38 mg<sub>pt</sub>·cm<sup>2</sup> at the diffraction angle of 2θ in ranges of (<b>a</b>) 10° to 90° and (<b>b</b>) 40° to 90°.</p>
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<p>Voltampere characteristics U/j (<b>a</b>) and polarization curves E/j (<b>b</b>) of MEA with commercial gas diffusion electrode (0.38 mg<sub>Pt</sub>·cm<sup>−2</sup>) recorded at room temperature (25 C) with a potential scan rate of 1 mV·s<sup>−1</sup>.</p>
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<p>U/j curves of membrane electrode assembly in EHP/C regime with 51.3 mL·min<sup>−1</sup> hydrogen inflow at varying temperature; potential scan rate, 1 mV·s<sup>−1</sup>.</p>
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<p>Influence of differential pressure on the cell voltage at a constant current density of 0.6 A·cm<sup>−2</sup>, temperature of 60 °C, and hydrogen inflow rate of 51.3 mL·min<sup>−1</sup>.</p>
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<p>Influence of differential pressure (P<sub>diff</sub>) on hydrogen crossover (Jx-over,/mole cm<sup>−2</sup>·s<sup>−1</sup>) at different temperatures.</p>
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<p>Comparative data for MEAs with different working areas: (<b>a</b>) U/Pdiff curves recorded at a current density of 0.6 A·cm<sup>−2</sup>, temperature of 60 °C, and hydrogen inflow rate 51.3 mL·min; (<b>b</b>) calculated difference in the cell voltage measured at 1 and 10 bar differential pressure.</p>
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<p>U/P<sub>diff</sub> curve of the membrane electrode assembly in a double-stage compression regime with a current density of 0.6 A·cm<sup>−2</sup>, temperature of 60 °C, and a hydrogen inflow rate in the first single cell of 51.3 mL·min.</p>
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12 pages, 2430 KiB  
Article
High Electrochemical Performance of Sodium-Ion Gel Polymer Electrolytes Achieved Through a Sandwich Design Strategy Combining Soft Polymers with a Rigid MOF
by Hanjiao Huang, Zongyou Li, Yanjun Gao, Tianqi Wang, Zihan Chen, Songjie Gan, Caizhen Yang, Qiyao Yu and Jian-Guo Zhang
Energies 2025, 18(5), 1160; https://doi.org/10.3390/en18051160 - 27 Feb 2025
Viewed by 255
Abstract
Sodium-ion batteries (SIBs) are considered the next-generation candidates for partially substituting for commercial lithium-ion batteries in future energy storage systems because of the abundant sodium/potassium reserves and these batteries’ cost-effectiveness and high safety. Gel polymer electrolytes (GPEs) have become a popular research focus [...] Read more.
Sodium-ion batteries (SIBs) are considered the next-generation candidates for partially substituting for commercial lithium-ion batteries in future energy storage systems because of the abundant sodium/potassium reserves and these batteries’ cost-effectiveness and high safety. Gel polymer electrolytes (GPEs) have become a popular research focus due to their advantages in terms of safety and performance in research on quasi-solid-state sodium-ion batteries (QSSIBs). Building on previous studies that incorporated MOF fillers into polymer-based gel electrolytes, we propose a 3D sandwich structure in which MOF materials are first pressed into thin films and then coated and protected by polymer materials. Using this approach, we achieved an ion conductivity of 1.75 × 10−4 S cm−1 at room temperature and an ion transference number of 0.69. Solid-state sodium-ion batteries using this gel film electrolyte exhibited long cycling stability at a 2 C current density, retaining 75.2% of their specific capacity after 500 cycles. Full article
(This article belongs to the Section D2: Electrochem: Batteries, Fuel Cells, Capacitors)
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<p>(<b>a</b>) The synthesis diagram of PUP. (<b>b</b>,<b>c</b>) SEM images of the UIO-66 membrane and PUP membrane. (<b>d</b>) XRD pattern of UIO-66. (<b>e</b>) The FT-IR spectrum of UIO-66. (<b>f</b>) DSC-TG curves of the PUP.</p>
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<p>(<b>a</b>,<b>b</b>) LSV and CV curves of PUP. (<b>c</b>) The I-t curve of PUP symmetric battery (illustrated with the AC impedance spectrum before and after polarization). (<b>d</b>) Temperature-dependent ionic conductivity of PUP.</p>
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<p>(<b>a</b>) Potential profiles of Na-symmetric cells assembled with PUP and pure PVDF-HFP at a current density of 0.1 mA cm<sup>−2</sup>. (<b>b</b>–<b>d</b>) Detail-enlarged diagram at 0–10 h, 145–155 h, and 290–300 h.</p>
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<p>(<b>a</b>) Long-term cycling performance of NVP|PUP|Na QSSIB. (<b>b</b>–<b>d</b>) The charge–discharge curves of NVP|PUP|Na QSSIB with different cycles at a current density of 2 C. (<b>e</b>–<b>g</b>) AC impedance spectrum of NVP|PUP|Na QSSIB with different cycles.</p>
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<p>The rate performance of NVP|PUP|Na QSSIB.</p>
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28 pages, 4151 KiB  
Article
Development of Deep Learning Simulation and Density Functional Theory Framework for Electrocatalyst Layers for PEM Electrolyzers
by Jaydev Zaveri, Shankar Raman Dhanushkodi, Michael W. Fowler, Brant A. Peppley, Dawid Taler, Tomasz Sobota and Jan Taler
Energies 2025, 18(5), 1022; https://doi.org/10.3390/en18051022 - 20 Feb 2025
Viewed by 266
Abstract
The electrocatalyst layers (ECLs) in polymer electrolyte membrane (PEM) electrolyzers are fundamentally comprised of IrOx catalysts, support material, and an ionomer. Their stability is critically dependent on structure and composition, necessitating a thorough understanding of ionization potential and work function. We employ Density [...] Read more.
The electrocatalyst layers (ECLs) in polymer electrolyte membrane (PEM) electrolyzers are fundamentally comprised of IrOx catalysts, support material, and an ionomer. Their stability is critically dependent on structure and composition, necessitating a thorough understanding of ionization potential and work function. We employ Density Functional Theory (DFT) to determine the ionization states of ECLs and to optimize their electronic properties. Furthermore, advanced deep learning simulations (DLSs) significantly enhance the kinetic and transport behaviors of these layers. This work integrates DFT and DLS to elucidate the characteristics of ECLs within PEM electrolyzer cells. We strategically utilize DFT to refine catalyst molecules and assess their electronic properties, while DLS is employed to predict the potential energy of support molecules in the catalyst layers. We establish a clear relationship between the energy and geometry of IrOx molecules. The DFT-DLS framework robustly calculates potential energy and reaction coordinates, effectively bridging theoretical computations with the dynamic behavior of molecules in catalyst layers. We validate our model by comparing it with the experimental polarization curve of the IrOx-based anode catalyst layer in a functioning electrolyzer. The observed Tafel slope and exchange current density unequivocally confirm that the oxygen evolution reaction (OER) occurs through a well-defined electrochemical pathway, with oxygen generation proceeding according to the charge transfer mechanism predicted by the DFT-DLS framework. Full article
(This article belongs to the Special Issue Nanomaterials and Their Applications in Energy Storage and Conversion)
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<p>Schematics of the PEM electrolyzer.</p>
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<p>DFT calculation methodology.</p>
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<p>DLS methodology and architecture.</p>
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<p>(<b>a</b>) The packed structure of iridium oxide is shown. (<b>b</b>) Unoptimized iridium oxide structure used for PES calculations.</p>
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<p>The HOMO-LUMO molecular orbitals obtained from the literature [<a href="#B75-energies-18-01022" class="html-bibr">75</a>,<a href="#B76-energies-18-01022" class="html-bibr">76</a>,<a href="#B77-energies-18-01022" class="html-bibr">77</a>] (<b>a</b>,<b>b</b>) and those obtained from this study.</p>
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<p>PES plot.</p>
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<p>Anode, cathode, and cell polarization curve at 40 <b>°</b>C, 60 <b>°</b>C, and 80 <b>°</b>C.</p>
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<p>Feature importance plot.</p>
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<p>t-SNE plot for our dataset.</p>
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<p>The graph of epoch vs. loss and parity plot for the 12-block model.</p>
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15 pages, 3554 KiB  
Article
Development of Hydrogen Fuel Cell–Battery Hybrid Multicopter System Thermal Management and Power Management System Based on AMESim
by JiHyun Choi, Hyun-Jong Park and Jaeyoung Han
Energies 2025, 18(2), 447; https://doi.org/10.3390/en18020447 - 20 Jan 2025
Viewed by 715
Abstract
Urban Air Mobility (UAM) is gaining attention as a solution to urban population growth and air pollution. Hydrogen fuel cells are applied to overcome the limitations of battery-based UAM, utilizing a PEMFC (Polymer Electrolyte Membrane Fuel Cell) with batteries in a hybrid system [...] Read more.
Urban Air Mobility (UAM) is gaining attention as a solution to urban population growth and air pollution. Hydrogen fuel cells are applied to overcome the limitations of battery-based UAM, utilizing a PEMFC (Polymer Electrolyte Membrane Fuel Cell) with batteries in a hybrid system to enhance responsiveness. Power management improves efficiency through effective power distribution under varying loads, while thermal management maintains optimal stack temperatures to prevent degradation. This study developed a hydrogen fuel cell–battery hybrid multicopter system using AMESim, consisting of a 138 kW fuel cell stack, 60 kW battery, DC–DC converters, and thrust motors. A rule-based power management system was implemented to define power distribution strategies based on SOC and load demand. The system’s operating range was designed to allocate power according to battery SOC and load variations. For an initial SOC of 45%, the power management system distributed power for flight, and the results showed that the state machine control system reduced hydrogen consumption by 5.85% and parasitic energy by 1.63% compared to the rule-based system. Full article
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<p>Fuel cell–battery hybrid multicopter system.</p>
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<p>Polarization curve characteristic of fuel cell stack.</p>
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<p>Fuel cell thermal management system structure.</p>
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<p>Hydrogen fuel cell–battery multicopter altitude cycle.</p>
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<p>Flowchart of hydrogen fuel cell–battery hybrid multicopter power management system.</p>
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<p>Power response with power management systems: (<b>a</b>) Rule-Based SOC 45%, (<b>b</b>) State Machine SOC 45%.</p>
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<p>Comparison of hydrogen consumption in fuel cell system with initial SOC.</p>
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<p>Change in SOC based on initial SOC.</p>
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<p>Results of the temperature reaction of the fuel cell stack with power management system SOC: (<b>a</b>) Rule-Based SOC 45%, (<b>b</b>) State Machine SOC 45%.</p>
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<p>Parasitic energy consumption with initial SOC.</p>
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15 pages, 6113 KiB  
Article
Influence of Synthesis Conditions on the Capacitance Performance of Hydrothermally Prepared MnO2 for Carbon Xerogel-Based Solid-State Supercapacitors
by Vania Ilcheva, Victor Boev, Mariela Dimitrova, Borislava Mladenova, Daniela Karashanova, Elefteria Lefterova, Natalia Rey-Raap, Ana Arenillas and Antonia Stoyanova
Gels 2025, 11(1), 68; https://doi.org/10.3390/gels11010068 - 15 Jan 2025
Viewed by 604
Abstract
In this study, the potential to modify the phase structure and morphology of manganese dioxide synthesized via the hydrothermal route was explored. A series of samples were prepared at different synthesis temperatures (100, 120, 140, and 160 °C) using KMnO4 and MnSO [...] Read more.
In this study, the potential to modify the phase structure and morphology of manganese dioxide synthesized via the hydrothermal route was explored. A series of samples were prepared at different synthesis temperatures (100, 120, 140, and 160 °C) using KMnO4 and MnSO4·H2O as precursors. The phase composition and morphology of the materials were analyzed using various physicochemical methods. The results showed that, at the lowest synthesis temperature (100 °C), an intercalation compound with composition K1.39Mn3O6 and a very small amount of α-MnO2 was formed. At higher temperatures (120–160 °C), the amount of α-MnO2 increased, indicating the formation of two clearly distinguished crystal structures. The sample obtained at 160 °C exhibited the highest specific surface area (approximately 157 m2/g). These two-phase (α-MnO2/K1.39Mn3O6) materials, synthesized at the lowest and highest temperatures, respectively, and containing an appropriate amount of carbon xerogel, were tested as active mass for positive electrodes in a solid-state supercapacitor, using a Na+-form Aquivion® membrane as the polymer electrolyte. The electrochemical evaluation showed that the composite with the higher specific surface area, containing 75% manganese dioxide, demonstrated improved characteristics, including 96% capacitance retention after 5000 charge/discharge cycles and high energy efficiency (approximately 99%). These properties highlight its potential for application in solid-state supercapacitors. Full article
(This article belongs to the Special Issue Gels for Flexible Electronics and Energy Devices (2nd Edition))
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Graphical abstract
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<p>XRD patterns of samples hydrothermally synthesized under the present experimental conditions (VV0 at 100 °C, VV1 at 120 °C, VV2 at 140 °C, and VV3 at 160 °C) for 2 h.</p>
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<p>SEM images of hydrothermally synthesized samples at varying temperatures for 2 h. The arrows in (<b>a</b>) indicate a few isolated nanorods, manifesting the initial formation of α-MnO<sub>2</sub> at 100 °C.</p>
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<p>Element (Mn, K, and O) mapping images of K<sub>1.39</sub>Mn<sub>3</sub>O<sub>6</sub>· and α-MnO<sub>2</sub> mixture in the VV3 sample.</p>
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<p>BF TEM micrographs at magnifications 10,000× (<b>a</b>,<b>e</b>) and 40,000× (<b>b</b>,<b>f</b>) and SAED pattern (<b>c</b>,<b>g</b>) for the VV0 and the VV3 samples, respectively, in each case. HRTEM for the VV0 sample (<b>d</b>) and HRTEM with FFT (<b>h</b>) and for the VV3 sample of the marked in red area as inset.</p>
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<p>N<sub>2</sub> adsorption–desorption isotherms of the samples, synthesized at 100 and 160 °C.</p>
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<p>Cyclic voltammograms of solid-state asymmetric supercapacitors at scan rates of 1 to 40 mV/s, within a voltage window of 0.0 to 1.6 V and different composite electrodes: (<b>a</b>) VV0-75%; (<b>b</b>) VV0-40%; (<b>c</b>) VV3-75%; and (<b>d</b>) VV3-40%.</p>
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<p>Discharge capacitance as a function of current load for symmetric and VV3 SCs (<b>a</b>) and cycling stability of discharge capacitance for 75% VV3 supercapacitors, with inset showing its voltage profiles (<b>b</b>).</p>
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18 pages, 5222 KiB  
Article
Electrochemical Performance of Guanidinium Salt-Added PVP/PEO Solid Polymer Electrolyte with Superior Power Density
by Anbazhagan Murugan, Vadivel Siva, Abdul Samad Shameem, Paranthaman Vijayakumar, Arangarajan Viji, Jintae Lee and Govindasamy Palanisamy
Polymers 2025, 17(2), 206; https://doi.org/10.3390/polym17020206 - 15 Jan 2025
Viewed by 637
Abstract
Solid polymer electrolytes (SPEs) for symmetrical supercapacitors are proposed herein with activated carbon as electrodes and optimized solid polymer electrolyte membranes, which serve as the separators and electrolytes. We propose the design of a low-cost solid polymer electrolyte consisting of guanidinium nitrate (GuN) [...] Read more.
Solid polymer electrolytes (SPEs) for symmetrical supercapacitors are proposed herein with activated carbon as electrodes and optimized solid polymer electrolyte membranes, which serve as the separators and electrolytes. We propose the design of a low-cost solid polymer electrolyte consisting of guanidinium nitrate (GuN) and poly(ethylene oxide) (PEO) with poly(vinylpyrrolidone) (PVP). Using the solution casting approach, blended polymer electrolytes with varying GuN weight percentage ratios of PVP and PEO are prepared. On the blended polymer electrolytes, structural, morphological, vibrational, and ionic conductivity are investigated. The solid polymer electrolytes’ morphology and level of roughness are examined using an FESEM. The interlinking bond formation between the blended polymers and the GuN salt is verified by FTIR measurements, indicating that the ligands are chemically complex. We found that, up to 20 wt.% GuN, the conductivity value increased (1.84 × 10−6 S/cm) with an increase in mobile charge carriers. Notably, the optimized PVP/PEO/20 wt.% solid polymer electrolyte was fabricated into a solid-state symmetrical supercapacitor device, which delivered a potential window of 0 to 2 V, a superior energy density of 3.88 Wh kg−1, and a power density of 1132 W kg−1. Full article
(This article belongs to the Special Issue Electrical Properties of Polymer Composites)
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<p>XRD patterns of solid polymer electrolytes.</p>
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<p>FTIR spectra of PVP/PEO/x wt.% GuN solid polymer electrolytes.</p>
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<p>SEM images of PVP/PEO/X wt.% GuN solid polymer electrolyte: (<b>a</b>) 5 wt.%, (<b>b</b>) 10 wt.%, (<b>c</b>) 15 wt.%, (<b>d</b>) 20 wt.%, and (<b>e</b>) 25 wt.%.</p>
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<p>Complex impedance plot of various compositions of PEO/PVP/GuN SPEs.</p>
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<p>Conductance spectra for different compositions of PEO/PVP/GuN SPEs.</p>
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<p>Dielectric constant (solid) and dielectric loss (open) versus frequency for different compositions of PEO/PVP/GuN SPEs.</p>
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<p>Variation in real modulus with frequencies of different compositions of PEO/PVP/X wt.% GuN SPEs.</p>
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<p>Variation in imaginary modulus with frequencies of different compositions of PEO/PVP/GuN SPEs.</p>
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<p>M″<sub>max</sub>, f<sub>max</sub>, stretching exponent parameter, and relaxation time versus GuN concentration.</p>
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<p>(<b>a</b>) Schematic view of symmetric supercapacitor device, (<b>b</b>,<b>c</b>) CV profile, (<b>d</b>,<b>e</b>) GCD curves, and (<b>f</b>) specific capacitance and current density.</p>
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<p>(<b>a</b>) Capacitance retention, (<b>b</b>) Ragone plot, and (<b>c</b>) EIS of fabricated symmetric supercapacitor device.</p>
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21 pages, 5078 KiB  
Article
Preparation of Zwitterionic Sulfobetaines and Study of Their Thermal Properties and Nanostructured Self-Assembling Features
by Yenglik Amrenova, Arshyn Zhengis, Arailym Yergesheva, Munziya Abutalip and Nurxat Nuraje
Nanomaterials 2025, 15(1), 58; https://doi.org/10.3390/nano15010058 - 2 Jan 2025
Viewed by 849
Abstract
Zwitterionic polymers have garnered significant attention for their distinctive properties, such as biocompatibility, antifouling capabilities, and resistance to protein adsorption, making them promising candidates for a wide range of applications, including drug delivery, oil production inhibitors, and water purification membranes. This study reports [...] Read more.
Zwitterionic polymers have garnered significant attention for their distinctive properties, such as biocompatibility, antifouling capabilities, and resistance to protein adsorption, making them promising candidates for a wide range of applications, including drug delivery, oil production inhibitors, and water purification membranes. This study reports the synthesis and characterization of zwitterionic monomers and polymers through the modification of linear, vinyl, and aromatic heterocyclic functional groups via reaction with 1,3-propanesultone. Four zwitterionic polymers with varying molecular structures—ranging from linear to five and six membered ring systems—were synthesized: poly(sulfobetaine methacrylamide) (pSBMAm), poly(sulfobetaine-1-vinylimidazole) (pSB1VI), poly(sulfobetaine-2-vinylpyridine) (pSB2VP), and poly(sulfobetaine-4-vinylpyridine) (pSB4VP). Their molecular weights, thermal behavior, and self-assembly properties were analyzed using gel permeation chromatography (GPC), thermogravimetric analysis (TGA), differential scanning calorimetry (DSC), transmission electron microscopy (TEM), and zeta potential measurements. The glass transition temperatures (Tg) ranged from 276.52 °C for pSBMAm to 313.69 °C for pSB4VP, while decomposition temperatures exhibited a similar trend, with pSBMAm degrading at 301.03 °C and pSB4VP at 387.14 °C. The polymers’ self-assembly behavior was strongly dependent on pH and their surface charge, particularly under varying pH conditions: spherical micelles were observed at neutral pH, while fractal aggregates formed at basic pH. These results demonstrate that precise modifications of the chemical structure, specifically in the linear, imidazole, and pyridine moieties, enable fine control over the thermal properties and self-assembly behavior of polyzwitterions. Such insights are essential for tailoring polymer properties for targeted applications in filtration membranes, drug delivery systems, and solid polymer electrolytes, where thermal stability and self-assembly play crucial roles. Full article
(This article belongs to the Section Nanocomposite Materials)
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<p>Schematic illustration of zwitterionic polymers investigated in this study.</p>
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<p><sup>1</sup>H NMR Spectra of Polyzwitterionic Polymers. (<b>a</b>) pSBMAm, (<b>b</b>) pSB1VI, (<b>c</b>) pSB2VP, and (<b>d</b>) pSB4VP.</p>
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<p>FTIR Analysis of Synthesized Polymers. (<b>a</b>) pSBMAm, (<b>b</b>) pSB1VI, (<b>c</b>) pSB2VP, and (<b>d</b>) pSB4VP.</p>
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<p>Wide-angle X-ray patterns for the different polymer systems.</p>
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<p>TGA and DSC of Polyzwitterionic Polymers. (<b>a</b>) TGA; (<b>b</b>) DSC.</p>
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<p>TEM images of polymers pSBMAm and pSB2VP. (<b>a</b>,<b>d</b>) pH = 4, (<b>b</b>,<b>e</b>) pH = 8, and (<b>c</b>,<b>f</b>) pH = 12.</p>
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<p>Zeta Potential Measurements of PZIs at Various pH Levels.</p>
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<p>GPC analysis results for pSBMAm and pSB2VP.</p>
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<p>Reaction Schemes for the Synthesis of Monomers via Nucleophilic Ring Opening of 1,3-PS by Various Tertiary Amines: (<b>a</b>) DMAPMAPS, (<b>b</b>) SB1VI, (<b>c</b>) SB2VP, and (<b>d</b>) SB4VP.</p>
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<p>Polymerization Schemes for the Synthesis of Polymers: (<b>a</b>) pSBMAm (<b>b</b>) pSB1VI; (<b>c</b>) pSB2VP; (<b>d</b>) pSB4VP.</p>
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12 pages, 7218 KiB  
Article
Fabrication and Characterization of Pt-Pr6O11 Nano Cathode Electrode for Polymer Electrolyte Membrane Fuel Cells via Co-Sputtering Method
by Ki Won Hong, Ye Rim Kwon, Dong Kun Song, Do Yeong Jung, Byung Kyu Kang, Soon Ki Kwon, Sangbong Ryu and Gu Young Cho
Sustainability 2025, 17(1), 198; https://doi.org/10.3390/su17010198 - 30 Dec 2024
Viewed by 964
Abstract
In this study, the performance and durability of polymer electrolyte membrane fuel cells (PEMFCs) were improved using a Pt-Pr6O11 composite electrode fabricated through a co-sputtering technique. Platinum (Pt), widely used as the catalyst material in PEMFCs, often faces stability issues [...] Read more.
In this study, the performance and durability of polymer electrolyte membrane fuel cells (PEMFCs) were improved using a Pt-Pr6O11 composite electrode fabricated through a co-sputtering technique. Platinum (Pt), widely used as the catalyst material in PEMFCs, often faces stability issues under various electrical load conditions. These issues require greater efforts to enhance PEMFC durability. Various approaches, including replacement of catalyst supports with electrically stable materials (such as metal oxides) or adoption of core-shell and alloy structures to stabilize Pt, have been attempted. In this research, a thin film electrode combining Pr6O11 and Pt was fabricated. Pr6O11, a lanthanide oxide, enhances the oxygen reduction reaction (ORR) through strong interactions with Pt, and its multi-valence state contributes to improved durability. Scanning electron microscopy (SEM) and X-ray photoelectron spectroscopy (XPS) were employed to analyze the composition, morphology, and chemical characteristics of the electrodes. I-V curves and electrochemical impedance spectroscopies (EIS) were measured to evaluate electrochemical properties of fuel cells. A cyclic voltammetry (CV) test was conducted to calculate the electrochemical surface area of the cell. As a result, the incorporation of Pr6O11 improved the pristine cell performance by 7.6% and increased performance after degradation testing by 121% compared to Pt-only cases. This demonstrates the effectiveness of the Pt-Pr6O11 composite in enhancing both the initial performance and the durability of PEMFCs. Full article
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<p>Schematics of experiments. (<b>a</b>) Sputter process chamber, (<b>b</b>) cell assembly, (<b>c</b>) sputtered Pt-Pr6O11 thin films on GDL.</p>
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<p>SEM and SEM-EDS results. (<b>a</b>) Pt thin films on Si wafer, (<b>b</b>) Pt thin films on MPL, (<b>c</b>) Pt mapping of Pt-Pt-Pr<sub>6</sub>O<sub>11</sub> thin films deposited on MPL, (<b>d</b>) Pt-Pt-Pr<sub>6</sub>O<sub>11</sub> thin films on Si wafer, (<b>e</b>) Pt-Pt-Pr<sub>6</sub>O<sub>11</sub> thin films on MPL, (<b>f</b>) Pr mapping of Pt-Pr<sub>6</sub>O<sub>11</sub> films on MPL, (<b>g</b>) bare MPL cross-section, (<b>h</b>) Pt sputtered MPL cross-section, (<b>i</b>) Pt-Pr<sub>6</sub>O<sub>11</sub> sputtered MPL cross-section.</p>
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<p>XPS results of sputtered Pt-Pr6O11 thin films on Si wafer. (<b>a</b>) Peak analysis results, (<b>b</b>) detailed Pt 4f peak.</p>
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<p>Performance of PEMFCs. (<b>a</b>) Polarization curves of PEMFCs before AST, (<b>b</b>) Nyquist plots of fuel cells at 0.5 V before AST, (<b>c</b>) polarization curves of PEMFCs after AST, (<b>d</b>) Nyquist plots of fuel cells at 0.5 V after AST, (<b>e</b>) Tafel plots of fuel cells before AST, (<b>f</b>) Tafel plots of fuel cells after AST.</p>
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<p>Electrochemical characteristics of the fuel cell test using CV. (<b>a</b>) Cyclic voltammetry curve of PEMFC using Pt cathode, (<b>b</b>) cyclic voltammetry curve of PEMFC using Pt-Pr<sub>6</sub>O<sub>11</sub> cathode.</p>
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<p>Summary of experiments. (<b>a</b>) Performance of fuel cells, (<b>b</b>) ohmic resistances of fuel cells, (<b>c</b>) Faradaic resistances of fuel cells.</p>
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22 pages, 5851 KiB  
Article
Ion Activity Coefficient of Sodium Halides in Anion-Exchange Polymers: Empirical Model Based on Manning’s Counterion Condensation Theory
by Guiming Liu and Dandan Gao
Separations 2024, 11(12), 360; https://doi.org/10.3390/separations11120360 - 23 Dec 2024
Viewed by 667
Abstract
The theory of electrolyte solution provides a precise description of the thermodynamic state and non-ideality of electrolyte solutions, allowing for the accurate prediction of the crystallization separation process of Salt Lake brine. Analogously, we attempt to describe the non-ideality of ions in ion-exchange [...] Read more.
The theory of electrolyte solution provides a precise description of the thermodynamic state and non-ideality of electrolyte solutions, allowing for the accurate prediction of the crystallization separation process of Salt Lake brine. Analogously, we attempt to describe the non-ideality of ions in ion-exchange polymers based on Manning’s Counterion Condensation Theory, which was originally used to describe the thermodynamics of polyelectrolyte solutions, has amply proven the potential to extend to ion-exchange polymers. In this article, equilibrium solvent and solute concentrations in aminated cross-linked polystyrene AEM were determined experimentally as a function of external NaCl concentration, and ion activity coefficients in the membranes were obtained via a thermodynamic treatment. With the recombination and empirical parameters added to Manning’s model, the ion activity coefficient of NaCl and NaBr in the aminated cross-linked polystyrene AEM can be accurately described in concentration ranges of 0.01 mol·kg1~3 mol·kg1. Compared with the original model, the Coefficient of Determination between the improved model and the experimental data was increased from 0.65 to 0.95. The Residual Sum of Squares is reduced by about one order of magnitude, significantly improving the Manning model’s adaptability when applied to AEM. Full article
(This article belongs to the Special Issue Green and Efficient Separation and Extraction of Salt Lake Resources)
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Figure 1
<p>The process for preparing aminated cross-linked polystyrene (ACLP) involves bulk polymerization followed by amination [<a href="#B43-separations-11-00360" class="html-bibr">43</a>].</p>
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<p>The “equilibrium–desorption–exchange” step was employed to measure concentrations within the AEM [<a href="#B10-separations-11-00360" class="html-bibr">10</a>], as illustrated by the different colors in this figure. After the AEM reached swelling equilibrium in the solution, the internal co-ions (Na<sup>+</sup>) and some counter-ions (Cl<sup>−</sup>, Br<sup>−</sup>) contributed by mobile electrolytes could be determined through multiple desorptions of secondary water. Subsequently, the electrostatically bound counter-ions on the fixed groups were exchanged with a 0.1 mol·L<sup>−</sup><sup>1</sup> Na<sub>2</sub>SO<sub>4</sub> solution.</p>
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<p>The influence of external solution molality and cross-linking on the water uptake of ACLP AEMs (excluding the internal PP fiber) is significant. Water uptake decreases with increasing external solution molality and cross-linking. The water uptake values are reported as the mass of water per unit mass of the ion-exchange polymer in the membrane.</p>
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<p>The molal concentrations of co-ions, <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi mathvariant="italic">m</mi> </mrow> <mrow> <msup> <mrow> <mi>Na</mi> </mrow> <mrow> <mo>+</mo> </mrow> </msup> </mrow> <mrow> <mi mathvariant="normal">m</mi> </mrow> </msubsup> </mrow> </semantics></math>, and counter-ions, <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi mathvariant="italic">m</mi> </mrow> <mrow> <msup> <mrow> <mi mathvariant="normal">X</mi> </mrow> <mrow> <mo>−</mo> </mrow> </msup> </mrow> <mrow> <mi mathvariant="normal">m</mi> </mrow> </msubsup> <mtext> </mtext> </mrow> </semantics></math> (X = Cl, Br), in the anion-exchange polymer are presented as a function of external electrolyte concentration for NaCl (<b>a</b>,<b>b</b>) and NaBr (<b>c</b>,<b>d</b>).</p>
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<p>The influence of external electrolyte concentration <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi mathvariant="italic">m</mi> </mrow> <mrow> <mi>NaX</mi> </mrow> <mrow> <mi mathvariant="normal">s</mi> </mrow> </msubsup> </mrow> </semantics></math> on the activity coefficients of the membrane in NaCl (<b>a</b>) and NaBr (<b>b</b>) is presented and obtained experimentally via Equation (10). Additionally, the respective ionic activity coefficients of the co-ions <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mo mathvariant="italic">γ</mo> </mrow> <mrow> <msup> <mrow> <mi>Na</mi> </mrow> <mrow> <mo>+</mo> </mrow> </msup> </mrow> <mrow> <mi mathvariant="normal">m</mi> </mrow> </msubsup> </mrow> </semantics></math> (<b>c</b>) and counter-ions <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mo mathvariant="italic">γ</mo> </mrow> <mrow> <msup> <mrow> <mi mathvariant="normal">X</mi> </mrow> <mrow> <mo>-</mo> </mrow> </msup> </mrow> <mrow> <mi mathvariant="normal">m</mi> </mrow> </msubsup> </mrow> </semantics></math> (<b>d</b>) in the membrane were determined experimentally using Equation (7).</p>
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<p>(<b>a</b>) illustrates the scenarios described by Manning’s theory, specifically for the cases where <span class="html-italic">b</span> &gt; <span class="html-italic">λ</span><sub>b</sub> and <span class="html-italic">b</span> &lt; <span class="html-italic">λ</span><sub>b</sub>. In the case where <span class="html-italic">b</span> &lt; <span class="html-italic">λ</span><sub>b</sub>, the overlap of the Bjerrum length creates a localized energy minimum region where counterions are likely to reside, leading to “counterion condensation” [<a href="#B28-separations-11-00360" class="html-bibr">28</a>]. (<b>b</b>) mathematically presents the left and right limits predicted by the Manning model under this assumption, as expressed by Equation (13).</p>
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<p>(<b>a</b>) In the assumptions of Manning’s theory, the polymer in a dilute polyelectrolyte solution is modeled as a chain of linear charges, with the solvent and counter-ions shielded from the effects of other nearby charge chains [<a href="#B28-separations-11-00360" class="html-bibr">28</a>]. (<b>b</b>) The swollen ion-exchange membrane cannot be regarded as a dilute solution, and obviously cannot be approximated as a linear chain charge. The Rayleig–Flory model of an irregular free link chain is closer to the real situation [<a href="#B47-separations-11-00360" class="html-bibr">47</a>], The resulting line charge density deviation is corrected by <span class="html-italic">α</span>. (<b>c</b>) The distance between the chain charges of the swelling ion-exchange membrane is much smaller than that of the dilute polyelectrolyte solution, which makes it difficult for the solvent and counter-ions to shield the nearby chain. This shielding may gradually fail at low concentrations, which is reflected by the electric field superposition of multi-segment chains, and leads to the further decrease in the ion activity coefficient that the deviation is corrected by <span class="html-italic">β</span>.</p>
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<p>Ion activity coefficients in ion-exchange membranes as a function of external NaCl concentration obtained experimentally (ACLP-2% (●), ACLP-3% (◆), and ACLP-4% (■)) and predicted by Manning’s limiting laws (ACLP-2% (red dashed line), ACLP-3% (green dashed line), and ACLP-4% (black dash-dotted line)). As shown in (<b>a</b>), (<b>b</b>), (<b>c</b>), respectively, represent the introduction of correction parameter <span class="html-italic">α</span>; and the prediction results after introducing correction parameters <span class="html-italic">α</span> and <span class="html-italic">β</span>.</p>
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<p>Ion activity coefficients in ion-exchange membranes as a function of external NaBr concentration obtained experimentally (ACLP-2% (●), ACLP-3% (◆), and ACLP-4% (■)) and predicted by Manning’s limiting laws (ACLP-2% (yellow dashed line), ACLP-3% (teal dashed line), and ACLP-4% (indigo dash-dotted line)). As shown in (<b>a</b>), (<b>b</b>), (<b>c</b>), respectively, represent the introduction of correction parameter <span class="html-italic">α</span>; And the prediction results after introducing correction parameters <span class="html-italic">α</span> and <span class="html-italic">β</span>.</p>
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<p>The empirical expression of <span class="html-italic">β</span> as a function of <math display="inline"><semantics> <mrow> <mrow> <mi>ln</mi> <mo>(</mo> </mrow> <msubsup> <mrow> <msubsup> <mrow> <mi mathvariant="italic">m</mi> </mrow> <mrow> <mi mathvariant="normal">A</mi> </mrow> <mrow> <mi mathvariant="normal">m</mi> </mrow> </msubsup> <mo>/</mo> <mi mathvariant="italic">m</mi> </mrow> <mrow> <mi mathvariant="normal">s</mi> </mrow> <mrow> <mi mathvariant="normal">m</mi> </mrow> </msubsup> <mo>)</mo> </mrow> </semantics></math> is obtained by fitting the experimental data of ACLP-2%, ACLP-3%, and ACLP-4% equilibrium with NaCl solution. According to the hypothesis of the modified model, the mobile salt concentration affects the shielding of the surrounding chain charge. When the value of <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi mathvariant="italic">m</mi> </mrow> <mrow> <mi mathvariant="normal">s</mi> </mrow> <mrow> <mi mathvariant="normal">m</mi> </mrow> </msubsup> </mrow> </semantics></math> decreases, the value of <math display="inline"><semantics> <mrow> <msubsup> <mrow> <msubsup> <mrow> <mi mathvariant="italic">m</mi> </mrow> <mrow> <mi mathvariant="normal">A</mi> </mrow> <mrow> <mi mathvariant="normal">m</mi> </mrow> </msubsup> <mo>/</mo> <mi mathvariant="italic">m</mi> </mrow> <mrow> <mi mathvariant="normal">s</mi> </mrow> <mrow> <mi mathvariant="normal">m</mi> </mrow> </msubsup> </mrow> </semantics></math> increases. In this case, the shielding gradually weakens and shows the chain electric field superposition scenario shown in <a href="#separations-11-00360-f007" class="html-fig">Figure 7</a>c, which further reduces the ion activity coefficient, the resulting reduction factor is captured by the correction factor <span class="html-italic">β</span>; However, in high concentration solutions, the value of <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi mathvariant="italic">m</mi> </mrow> <mrow> <mi mathvariant="normal">s</mi> </mrow> <mrow> <mi mathvariant="normal">m</mi> </mrow> </msubsup> </mrow> </semantics></math> will be very large, providing enough shielding for nearby chain charges and making the value of <math display="inline"><semantics> <mrow> <msubsup> <mrow> <msubsup> <mrow> <mi mathvariant="italic">m</mi> </mrow> <mrow> <mi mathvariant="normal">A</mi> </mrow> <mrow> <mi mathvariant="normal">m</mi> </mrow> </msubsup> <mo>/</mo> <mi mathvariant="italic">m</mi> </mrow> <mrow> <mi mathvariant="normal">s</mi> </mrow> <mrow> <mi mathvariant="normal">m</mi> </mrow> </msubsup> </mrow> </semantics></math> very low, in which case <span class="html-italic">β</span> = 1 and returning to the situation of <a href="#separations-11-00360-f007" class="html-fig">Figure 7</a>b.</p>
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<p>Ion activity coefficients for NaCl in anion- and cation-exchange resins [AR103 (<b>a</b>) and CR61 (<b>b</b>)]; Circular points denote values obtained experimentally, dashed lines denote values obtained by Manning’s original model (The yellow and blue regions represent the acceptable prediction range of the original model); and the solid line represents the predicted value of the improved model as Equation (26) after introducing the empirical parameters, the expression of parameter β can obtained by nonlinear curve fitting of experimental data, using similar form of Equation (25).</p>
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15 pages, 5333 KiB  
Article
Ultrasonic Effect on the Growth of Crystals from Aqueous Electrolyte Solutions on Polymer Substrates: The Role of Isotopic Composition of Liquid
by Nikolai F. Bunkin, Polina N. Bolotskova, Sergey V. Gudkov, Valery V. Voronov, Vladimir I. Pustovoy, Valery N. Sorokovikov, Oleg T. Kamenev and Yulia V. Novakovskaya
Polymers 2024, 16(24), 3580; https://doi.org/10.3390/polym16243580 - 21 Dec 2024
Viewed by 593
Abstract
The peculiarities of the crystal formation from supersaturated aqueous solutions of CuSO4 on polymer substrates were studied using X-ray diffractometry. During the crystal formation, the test solutions were irradiated with one or two counter-propagating ultrasonic beams. Test solutions were prepared using natural [...] Read more.
The peculiarities of the crystal formation from supersaturated aqueous solutions of CuSO4 on polymer substrates were studied using X-ray diffractometry. During the crystal formation, the test solutions were irradiated with one or two counter-propagating ultrasonic beams. Test solutions were prepared using natural deionized water with a deuterium content of 157 ± 1 ppm. The other liquid used was deuterium-depleted water with a deuterium content of 3 ppm. It was shown that irradiation with one/two ultrasonic beams resulted in drastic changes in the structure of the crystal deposit formed on the polymer substrate in the case when natural deionized water was chosen for preparing the supersaturated solution of CuSO4. Full article
(This article belongs to the Special Issue Challenges and Trends in Polymer Composites—2nd Edition)
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<p>Oscillogram of electrical pulses supplied to a piezoelectric transducer.</p>
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<p>Diffraction patterns of CuSO<sub>4</sub> crystals deposited on a polymer substrate from DDW-solution (CuSO<sub>4</sub> × 5H<sub>2</sub>O, black curve) and NW-solution (CuSO<sub>4</sub> × 3H<sub>2</sub>O, red curve) in the absence of ultrasonic treatment. A set of crystallographic indices (h,k,l) for some of the highest peaks is given; the indices highlighted in red refer to the trihydrate, whereas the indices highlighted in black refer to the pentahydrate.</p>
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<p>Diffraction patterns of CuSO<sub>4</sub> crystal hydrates grown on a polymer substrate from NW- solution under irradiation with a single ultrasonic beam at a pulse voltage on the piezoelectric element of <span class="html-italic">U</span><sub>0</sub> = 60 V (black curve), under irradiation with two counter-propagating ultrasonic beams at a pulse voltage on the piezoelectric elements of <span class="html-italic">U</span><sub>0</sub> = 60 V (red curve), and in the absence of irradiation (blue curve). Black ovals mark reflexes related to the structure of CuSO<sub>4</sub> × 5H<sub>2</sub>O pentahydrate included in the trihydrate matrix as a result of ultrasonic treatment.</p>
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<p>X-ray diffraction patterns of CuSO<sub>4</sub> crystal hydrates deposited on the Nafion substrate from NW-solution under irradiation with a single ultrasonic beam at a pulsed voltage on the piezoelectric element of <span class="html-italic">U</span><sub>0</sub> = 60 V (black curve) and <span class="html-italic">U</span><sub>0</sub> = 6 V (red curve), as well as deposited on the Nafion substrate from the DDW-solution at a pulsed voltage of <span class="html-italic">U</span><sub>0</sub> = 60 V (blue curve). Panel (<b>a</b>) shows the reflexes in a range of 15–35°. Panel (<b>b</b>) shows the reflexes in a range of 30.5–34°.</p>
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<p>CuSO<sub>4</sub> crystal hydrate formed on the Nafion substrate from NW-solution under the irradiation with one ultrasonic beam at a pulse voltage of <span class="html-italic">U</span><sub>0</sub> = 6 V. Panels (<b>a</b>,<b>b</b>): the formation of the deposit continues, since the solution has not completely evaporated. Panel (<b>c</b>): the end of the formation of the deposit; water is absent in the cuvette. It is seen that the deposit is formed predominantly near the piezoelectric transducer.</p>
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<p>The dependences of pH vs. deuterium content of water; the parameter of these dependences is the soaking time τ. Explanations are in the text.</p>
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<p>Locally stable configurations of a model fragment of the Nafion polymer matrix with folded (<b>left</b>), unfolded (<b>right</b>), and partially unfolded and hydrated side polymer chains in the presence of 35 water molecules (<b>bottom</b>).</p>
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21 pages, 7965 KiB  
Article
Investigation of the Impact of an Electric Field on Polymer Electrolyte Membranes for Fuel Cell Applications
by Hamdy F. M. Mohamed, Esam E. Abdel-Hady, Mohamed H. M. Hassanien and Wael M. Mohammed
Physics 2024, 6(4), 1345-1365; https://doi.org/10.3390/physics6040083 - 17 Dec 2024
Viewed by 791
Abstract
A systematic study was carried out on Nafion® 112 membranes to evaluate the effects of different electric field strengths on the structural and electrical properties of the membranes. The membranes were subjected to different electric field strengths (0, 40, 80, and 140 [...] Read more.
A systematic study was carried out on Nafion® 112 membranes to evaluate the effects of different electric field strengths on the structural and electrical properties of the membranes. The membranes were subjected to different electric field strengths (0, 40, 80, and 140 MV/m) at a temperature of 90 °C. Proton conductivity was measured using an LCR meter, revealing that conductivity values varied with the electric field strengths, with the optimal conductivity observed at 40 MV/m. Positron annihilation lifetime (PAL) spectroscopy provided insights into the free volume structure of the membranes, showing an exponential increase in the hole volume size as the electric field strength increased. It was also found that the positronium intensity of the Nafion® 112 membranes was influenced by their degree of crystallinity, which decreased with higher electric field strengths. This indicates complex interactions between structural changes and the effects of the electric field. Dielectric studies of the membranes were characterized over a frequency range of 50 Hz to 5 MHz, demonstrating adherence to Jonscher’s law. The Jonscher’s power law’s s-parameter values increased with the electric field strength, suggesting a transition from a hopping conduction mechanism to more organized ionic transport. Overall, the study emphasizes the relationship between the free volume, crystallinity, and macroscopic characteristics, such as ionic conductivity. The study highlights the potential to adjust membrane performance by varying the electric field. Full article
(This article belongs to the Section Applied Physics)
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<p>The chemical structure of the Nafion<sup>®</sup> 112 membrane.</p>
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<p>The o-Ps lifetime <span class="html-italic">τ</span><sub>3</sub>, o-Ps intensity <span class="html-italic">I</span><sub>3</sub>, and free volume size <span class="html-italic">V</span><sub>o-Ps</sub> derived from Equations (2) and (3) as a function of the electric field strengths applied to Nafion<sup>®</sup> 112 membranes at 90 °C. The ‘’as received’’ denotes the factory-supplied sample.</p>
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<p>Wide-angle X-ray diffraction (WAXD) patterns for the as-received Nafion 112 membranes and those with different electric field strengths at 90 °C. The red line represents the fit of the experimental data.</p>
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<p>The free volume size distribution deduced using the LT9.0 program for the as-received Nafion<sup>®</sup> 112 membrane and those affected with different electric field strengths at 90 °C.</p>
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<p>Variations of (<b>a</b>) τ<sub>m</sub> (<b>b</b>) τ<sub>b</sub> (<b>c</b>) <span class="html-italic">K<sub>d</sub></span><sub>1</sub> (<b>d</b>) <span class="html-italic">K<sub>d</sub></span><sub>2</sub> (<b>e</b>) <span class="html-italic">V<sub>+</sub></span> and (<b>f</b>) <span class="html-italic">V</span><sub>Ps</sub> with the electric field strengths. See text for details.</p>
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<p>Variations in the (<b>a</b>) dielectric constant ε′ and (<b>b</b>) dielectric loss ε″ with frequency for the as-received Nafion<sup>®</sup> 112 and Nafion<sup>®</sup> 112 exposed to different strengths of the applied electric field at 90 °C.</p>
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<p>(<b>a</b>) The influence of the frequency on the ac conductivity, and (<b>b</b>) the variation in the Jonscher’s power law’s <span class="html-italic">s</span>-parameter with the applied electric field for the as-received Nafion<sup>®</sup> 112 and Nafion<sup>®</sup> 112 exposed to different strengths of the applied electric field at 90 °C.</p>
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<p>The frequency dependence of the (<b>a</b>) real impedance Z′ and (<b>b</b>) imaginary impedance Z″ of the as-received Nafion<sup>®</sup> 112 and Nafion<sup>®</sup> 112 exposed to different strengths of the applied electric field at 90 °C.</p>
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<p>(<b>a</b>) Cole–Cole plot and (<b>b</b>) the dc conductivity <span class="html-italic">σ</span><sub>dc</sub> of the as-received Nafion<sup>®</sup> 112 and Nafion<sup>®</sup> 112 exposed to different strengths of the applied electric field at 90 °C.</p>
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<p>The correlations between the free volume size <span class="html-italic">V</span><sub>o-Ps</sub> and both the (<b>a</b>) barrier height <span class="html-italic">W</span><sub>h</sub> and (<b>b</b>) dc conductivity σ<sub>dc</sub> of Nafion<sup>®</sup> 112 exposed to different strengths of the applied electric field at 90 °C. See text for details.</p>
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20 pages, 2009 KiB  
Review
Graphene-Based Nanostructured Cathodes for Polymer Electrolyte Membrane Fuel Cells with Increased Resource
by Adriana Marinoiu, Mihaela Iordache, Elena Simona Borta and Anisoara Oubraham
C 2024, 10(4), 105; https://doi.org/10.3390/c10040105 - 14 Dec 2024
Viewed by 849
Abstract
Pt on carbon black (Pt/C) has been widely used as a catalyst for both ORR and hydrogen oxidation reaction (HOR), but its stability is compromised due to carbon corrosion and catalyst poisoning, leading to low Pt utilization. To address this issue, this study [...] Read more.
Pt on carbon black (Pt/C) has been widely used as a catalyst for both ORR and hydrogen oxidation reaction (HOR), but its stability is compromised due to carbon corrosion and catalyst poisoning, leading to low Pt utilization. To address this issue, this study suggests replacing carbon black with graphene in the catalyst layer. The importance of this work lies in the detailed examination of novel electrocatalysts with high electrocatalytic activity for large-scale power generation. In this paper, we discuss the use of regulatory techniques like structure tuning and composition optimization to construct nanocatalysts impregnated with noble and non-noble metals on graphene supports. Finally, it highlights the limitations and advantages of these nanocatalysts along with some future perspectives. Our objective is that this summary will help in the research and rational design of graphene-based nanostructures for efficient ORR electrocatalysis. The results of this study showed that the performances of graphene-based catalysts show high electrochemical active surface areas for Pt-Fe/GNPs and Pt-Ni/GNPs catalysts (132 and 136 m2 g−1, respectively) at 100 operating cycles. Also, high current densities and power densities were observed for Pt3-Ni/G and Pt-Co/G catalysts used at the cathode. The values for current density were 1.590 and 1.779 A cm−2, respectively, while the corresponding values for power density were 0.57 and 0.785 W cm−2. Full article
(This article belongs to the Topic Application of Graphene-Based Materials, 2nd Edition)
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<p>ORR catalyst diagram.</p>
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<p>A schematic representation of a typical membrane electrode assembly (MEA).</p>
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<p>Performance of graphene-based electrocatalysts in PEMFCs. (<b>a</b>) Electrochemical durability (ESCA); (<b>b</b>) the MEA cathode catalyst’s current density; (<b>c</b>) the MEA cathode catalyst has a high power density.</p>
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<p>Performance of graphene-based electrocatalysts in PEMFCs. (<b>a</b>) Electrochemical durability (ESCA); (<b>b</b>) the MEA cathode catalyst’s current density; (<b>c</b>) the MEA cathode catalyst has a high power density.</p>
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12 pages, 9226 KiB  
Article
High-Performance Fluorine-Lean Thin Aromatic Hydrocarbon Membranes Based on Polyvinylidene Fluoride for Hydrogen Fuel Cells
by Tamas Nemeth, Zongyi Han and Lorenz Gubler
Membranes 2024, 14(12), 263; https://doi.org/10.3390/membranes14120263 - 7 Dec 2024
Cited by 1 | Viewed by 831
Abstract
The impeding ban on per- and polyfluoroalkyl substances (PFAS) prompted researchers to focus on hydrocarbon-based materials as constituents of next-generation proton exchange membranes (PEMs) for polymer electrolyte fuel cells (PEFCs). Here, we report on the fuel cell performance and durability of fluorine-lean PEMs [...] Read more.
The impeding ban on per- and polyfluoroalkyl substances (PFAS) prompted researchers to focus on hydrocarbon-based materials as constituents of next-generation proton exchange membranes (PEMs) for polymer electrolyte fuel cells (PEFCs). Here, we report on the fuel cell performance and durability of fluorine-lean PEMs prepared by the post-sulfonation of co-grafted α-methylstyrene (AMS) and 2-methylene glutaronitrile (MGN) monomers into preirradiated 12 µm polyvinylidene fluoride (PVDF) base film. The membranes were subjected to two distinctly different accelerated stress test (AST) protocols performed at open-circuit voltage (OCV): the US Department of Energy-similar chemical AST (90 °C, 30% relative humidity (RH), H2/air, 1 bara), developed originally for perfluoroalkylsulfonic acid (PFSA) membranes, and the high relative humidity AST (80 °C, 100% RH, H2/O2, 2.5 bara), designed for aromatic hydrocarbon membranes. We found that doping the grafted membranes with a metalated porphyrin antioxidant can simultaneously reduce membrane aging and improve fuel cell performance. Full article
(This article belongs to the Special Issue Recent Advances in Fluorine-Free Membranes)
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<p>Chemical structure of (<b>a</b>) the PVDF base film, (<b>b</b>) the AMS, (<b>c</b>) MGN monomers, and of (<b>d</b>) Cu(II)-NH<sub>2</sub>-tetraphenylporphyrin (TPP), the radical repair agent used in this study.</p>
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<p>Reaction kinetics for co-grafting the monomers α-methylstyrene and 2-methylene glutaronitrile into 12 µm PVDF base film with irradiation doses of 25 (blue triangles), 50 (green triangles), and 100 kGy (red circles), at 65 °C.</p>
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<p><b>Left</b>: transmission FT-IR spectra of pristine PVDF films (black), grafted films (red), and sulfonated membranes (blue). <b>Right</b>: expanded spectra of characteristic peaks for S-O and SO<sub>2</sub> stretching vibration.</p>
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<p>FTIR as a tool to quantify the graft level. <b>Left</b>: the peak area at around 3000 cm<sup>−1</sup> is normalized to the peak area at around 614 cm<sup>−1</sup>. <b>Right</b>: the obtained linear correlation between the normalized peak area at around 3000 cm<sup>−1</sup> and the graft level.</p>
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<p>SEM image (<b>a</b>) and EDX mapping (<b>b</b>) of a cross-section of an ETFE-<span class="html-italic">g</span>-poly(AMSSA-<span class="html-italic">co</span>-MGN) membrane with a graft level of 37%.</p>
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<p><b>Left</b> <span class="html-italic">y</span>-axis: polarization curves of the tested membranes, 43% GL (blue squares), 52% GL (black circles), 63% GL (red triangles), and of the reference N211 (green diamonds). <b>Right</b> <span class="html-italic">y</span>-axis: high-frequency resistance (HFR) of the tested membranes. Data were recorded at 80 °C with 2.5 bar<sub>a</sub> back pressure, fully humidified gases at the inlet, a minimum flow of 200 mL<sub>n</sub> min<sup>−1</sup>, and a stoichiometry of 1.5 for both H<sub>2</sub> and O<sub>2</sub>. Commercial Pt-coated gas diffusion electrodes featuring a PFSA-based binder (Johnson Matthey ELE 0244, 0.4 mg Pt cm<sup>−2</sup>) were used.</p>
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<p>AST at high relative humidity: decay of cell potential (<b>left</b> <span class="html-italic">y</span>-axis) and changes in high-frequency resistance (<b>right</b> <span class="html-italic">y</span>-axis) of the tested membranes with 43% GL (blue squares), 52% GL (black circles), 63% GL (red triangles). Data were recorded at OCV, 80 °C with 2.5 bar<sub>a</sub> back pressure and fully humidified H<sub>2</sub> and O<sub>2</sub> at the inlet.</p>
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<p>Effect of antioxidant doping on performance. Polarization curves of the tested membranes, 52% GL (black circles) <span class="html-italic">w</span>/<span class="html-italic">o</span> antioxidant and w/ antioxidant (golden triangles), and of the reference N211 (green diamonds). Data were recorded at 80 °C with 2.5 bar<sub>a</sub> back pressure, fully humidified gases at the inlet, a minimum flow of 200 mL<sub>n</sub> min<sup>−1</sup>, and a stoichiometry of 1.5 for both H<sub>2</sub> and O<sub>2</sub>.</p>
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<p>AST at high relative humidity: decay of cell potential (<b>left</b> <span class="html-italic">y</span>-axis) and changes in high-frequency resistance (<b>right</b> <span class="html-italic">y</span>-axis) of the tested membranes with 52% GL <span class="html-italic">w</span>/<span class="html-italic">o</span> doped antioxidant (black circles) and w/ doped antioxidant (golden triangles). Data were recorded at OCV, 80 °C with 2.5 bar<sub>a</sub> back pressure and fully humidified H<sub>2</sub> and O<sub>2</sub> at the inlet.</p>
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<p>AST under DOE-like conditions. <b>Left</b> <span class="html-italic">y</span>-axis: decay of cell potential of the tested membranes with 50% GL <span class="html-italic">w</span>/<span class="html-italic">o</span> doped antioxidant (black circles), w/ doped antioxidant (golden triangles), and N211 reference. <b>Right</b> <span class="html-italic">y</span>-axis: changes in hydrogen crossover current density. Data were recorded at OCV, 90 °C at ambient pressure, 30% RH at the inlet for H<sub>2</sub> and air.</p>
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<p>Preparation of the PVDF-g-poly(AMS-co-MGN) films.</p>
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23 pages, 11122 KiB  
Article
Numerical Investigation of Water Transport and Effective Electrical Conductivity in Perforation of Gas Diffusion Layer Using Lattice Boltzmann Method
by Jae Yong Cho, Hee Min Lee, Muhammad Nasir Bashir and Joon Sang Lee
Fractal Fract. 2024, 8(12), 719; https://doi.org/10.3390/fractalfract8120719 - 5 Dec 2024
Viewed by 823
Abstract
In polymer electrolyte membrane fuel cells, the gas diffusion layer (GDL) is composed of porous media and serves a critical role as a mass transport layer, facilitating reactant gas diffusion, removal of water generated in the catalyst layer, and electron transport. Artificial spacings [...] Read more.
In polymer electrolyte membrane fuel cells, the gas diffusion layer (GDL) is composed of porous media and serves a critical role as a mass transport layer, facilitating reactant gas diffusion, removal of water generated in the catalyst layer, and electron transport. Artificial spacings known as perforations can be introduced to improve water management within this mass transport system. However, the impact of these perforations on the effective electrical conductivity has not been adequately studied. This study employs numerical methods to investigate water management and effective electrical conductivity in the presence of perforations, aiming to provide indicators for optimal design. The pseudopotential lattice Boltzmann method is utilized, which is particularly advantageous for modeling two-phase flow and electron transport in complex geometries. Using this numerical approach, we analyze water penetration in GDL structures and effective electrical conductivity based on electric potential fields focusing on geometric parameters such as the perforation size. Our results demonstrate a relationship between water management efficiency and effective electrical conductivity, suggesting the existence of an optimal perforation diameter. Moreover, when there is a water-induced penetration pattern due to the perforated structure, both the effective electrical conductivity and water management are enhanced at a lower porosity of the GDL structure. Full article
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<p>A schematic of the cathode side of the operating PEMFC with the corresponding processes.</p>
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<p>Diagrams of LBM. (<b>a</b>) D3Q19 and (<b>b</b>) D3Q7 models [<a href="#B37-fractalfract-08-00719" class="html-bibr">37</a>]; (<b>c</b>) lattice nodes for a ghost fluid layer constructed on a solid wall [<a href="#B42-fractalfract-08-00719" class="html-bibr">42</a>]; and (<b>d</b>) a schematic of fluid on a solid wall with a contact angle scheme.</p>
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<p>Diagrams of LBM. (<b>a</b>) D3Q19 and (<b>b</b>) D3Q7 models [<a href="#B37-fractalfract-08-00719" class="html-bibr">37</a>]; (<b>c</b>) lattice nodes for a ghost fluid layer constructed on a solid wall [<a href="#B42-fractalfract-08-00719" class="html-bibr">42</a>]; and (<b>d</b>) a schematic of fluid on a solid wall with a contact angle scheme.</p>
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<p>Mesh independent test: (<b>a</b>) the simulation case according to the number of grids; and (<b>b</b>) the time evolution of total water saturation.</p>
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<p>Simulation domain by reconstructing the lattice structure for GDL. (<b>a</b>) Outline of the entire 3D domain; and (<b>b</b>) the <span class="html-italic">yz</span> plane view.</p>
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<p>The coexistence curves from the simulation and Maxwell construction on the Peng–Robinson equation of state [<a href="#B61-fractalfract-08-00719" class="html-bibr">61</a>].</p>
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<p>The results of effective electrical conductivity simulations for the GDL microstructures according to porosity [<a href="#B38-fractalfract-08-00719" class="html-bibr">38</a>,<a href="#B62-fractalfract-08-00719" class="html-bibr">62</a>].</p>
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<p>The time evolution of water transport in a GDL structure without perforation.</p>
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<p>Water transport in the GDL structure without perforation. (<b>a</b>) Water penetration on the <span class="html-italic">xy</span> plane at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0.0164</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>; (<b>b</b>) electric potential distribution on the <span class="html-italic">xy</span> plane at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0.0164</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>; (<b>c</b>) time evolution of the total water saturation; and (<b>d</b>) local water distribution in the entire GDL structure at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0.0164</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>.</p>
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<p>GDL structure with a perforation of diameter <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math> centered on the <span class="html-italic">xy</span> plane, and water transport for perforation diameters of 10–30 <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0.0164</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>.</p>
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<p>The water penetration pattern in structures with perforation diameters of 0–30 <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0.0164</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math> on the <span class="html-italic">yz</span> plane at the center of the <span class="html-italic">x</span>-axis.</p>
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<p>Water transport in GDL structures with perforation diameters of 0–30 <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>. (<b>a</b>) Time evolution of total water saturation; and (<b>b</b>) local water distribution in relative thickness along the <span class="html-italic">z</span>-axis at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0.0164</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>.</p>
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<p>The dimensionless ratio of effective electrical conductivity to bulk solid electrical conductivity in structures with perforation diameters of 0–30 <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> (porosity range: 0.7347–0.7661).</p>
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<p>GDL structure with multiple perforations of diameter <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math> on the <span class="html-italic">xy</span> plane, and water transport in structures with multiple perforations and diameters of 10–20 <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0.0164</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>.</p>
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<p>Water penetration pattern in structures with multiple perforations and diameters of 10–20 <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0.0164</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math> on the <span class="html-italic">yz</span> plane when <span class="html-italic">x =</span><math display="inline"><semantics> <mrow> <mn>18.75</mn> <mo> </mo> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>.</p>
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<p>Water transport in structures with multiple perforations and diameters of 0–30 <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>. (<b>a</b>) Time evolution of the total water saturation; and (<b>b</b>) local water distribution in relative thickness along the <span class="html-italic">z</span>-axis at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0.0164</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>.</p>
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<p>The dimensionless ratio of effective electrical conductivity to bulk solid electrical conductivity in structures with multiple perforations and diameters of 0–30 <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> (porosity range: 0.7347–0.7661).</p>
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<p>Reconstructed GDL structures with perforation diameter <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>20</mn> <mo> </mo> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> at the center of the <span class="html-italic">xy</span> plane and water transport for porosities in the range of 0.5948–0.8664 at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0.0164</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>.</p>
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<p>Water transport in GDL structures with porosities ranging from 0.5948 to 0.8664 on the <span class="html-italic">yz</span> plane at the center of the <span class="html-italic">x</span>-axis domain and <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0.0164</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. (<b>a</b>) Water penetration pattern; and (<b>b</b>) electric potential distribution.</p>
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<p>Water transport in GDL structures with porosities ranging from 0.5948 to 0.8664, a single-perforation case in <a href="#fractalfract-08-00719-f011" class="html-fig">Figure 11</a>, and a multi-perforation case in <a href="#fractalfract-08-00719-f015" class="html-fig">Figure 15</a>. All structures have a 20 <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>-diameter size of perforation. (<b>a</b>) Time evolution of total water saturation; and (<b>b</b>) local water distribution in relative thickness along the <span class="html-italic">z</span>-axis at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0.0164</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>.</p>
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<p>The dimensionless ratio of effective electrical conductivity to bulk solid electrical conductivity in perforation cases with a porosity range of 0.5948–0.8664. The GDL perforation diameter was 20 <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>.</p>
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