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18 pages, 3039 KiB  
Article
Nanoscale “Chessboard” Pattern Lamellae in a Supramolecular Perylene-Diimide Polydiacetylene System
by Ian J. Martin, Francis Kiranka Masese, Kuo-Chih Shih, Mu-Ping Nieh and Rajeswari M. Kasi
Molecules 2025, 30(6), 1207; https://doi.org/10.3390/molecules30061207 - 7 Mar 2025
Viewed by 224
Abstract
The rational design of ordered chromogenic supramolecular polymeric systems is critical for the advancement of next-generation stimuli-responsive, optical, and semiconducting materials. Previously, we reported the design of a stimuli-responsive, lamellar self-assembled platform composed of an imidazole-appended perylene diimide of varying methylene spacer length [...] Read more.
The rational design of ordered chromogenic supramolecular polymeric systems is critical for the advancement of next-generation stimuli-responsive, optical, and semiconducting materials. Previously, we reported the design of a stimuli-responsive, lamellar self-assembled platform composed of an imidazole-appended perylene diimide of varying methylene spacer length (n = 3, 4, and 6) and a commercially available diacid-functionalized diacetylene monomer, 10, 12 docosadiynedioic acid, in a 1:1 molar ratio. Herein, we expound on the importance of the composition of the imidazole-appended perylene diimide of varying methylene spacer length (n = 3, 4, and 6) and 10, 12 docosadiynedioic acid in the ratio of 2:1 to the supramolecular self-assembly, final morphology, and properties. Topochemical polymerization of the drop-cast films by UV radiation yielded blue-phase polydiacetylene formation, and subsequent thermal treatment of the films produced a thermoresponsive blue-to-red phase transformation. Differential scanning calorimetry (DSC) studies revealed a dual dependence of the methylene spacer length and stimuli treatment (UV and/or heat) on the thermal transitions of the films. Furthermore, small-angle X-ray scattering (SAXS) and wide-angle X-ray scattering (WAXS) showed well-defined hierarchical semiconducting nanostructures with interconnected “chessboard”-patterned lamellar stacking. Upon doping with an ionic liquid, the 2:1 platform showed higher ionic conductivity than the previous 1:1 one. The results presented here illustrate the importance of the composition and architecture to the ionic domain connectivity and ionic conductivity, which will have far-reaching implications for the rational design of semiconducting polymers for energy applications including fuel cells, batteries, ion-exchange membranes, and mixed ionic conductors. Full article
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Graphical abstract
Full article ">Figure 1
<p>Schematic illustration of the supramolecular formation of <b>DCDDA</b> and <b>PDI-mono</b><span class="html-italic">(<b>n-</b></span><b>imz</b>) to form <b>2:1 PDI-mono</b>(<b><span class="html-italic">n</span>-imz</b>)<b>/DCDDA</b> and their subsequent polymerization to the blue phase by 254 nm UV radiation.</p>
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<p>(<b>Left</b>) <sup>1</sup>H NMR spectrum overlay of (a) <b>DCDDA</b>, (b) <b>PDI-mono</b>(<b>6-imz</b>), (c) 2:1 <b>PDI-mono</b>(<b>6-imz</b>)<b>/DCDDA</b>, (d) 2:1.5 <b>PDI-mono</b>(<b>6-imz</b>)<b>/DCDDA</b>, (e) 2:2 <b>PDI-mono</b>(<b>6-imz</b>)<b>/DCDDA</b>, and (f) 2:4 <b>PDI-mono</b>(<b>6-imz</b>)<b>/DCDDA</b> in THF-d<sub>8</sub> at 25 °C. The imidazole proton that is denoted by an asterisk (*) shifts from 7.48 ppm to 7.56 ppm, and the tertiary proton chemical shift at 5.18 ppm does not shift upon hydrogen bonding. (<b>Right</b>) Chemical shift change of PDI aromatic imidazole proton (labeled with * in the <sup>1</sup>H NMR spectrum overlay) upon the addition of increasing amounts of <b>DCDDA</b>. Points represent experimental data. The inset shows the <sup>1</sup>H NMR spectrum overlay of the aromatic imidazole proton peak from 7.64 ppm to 7.40 ppm of <b>PDI-mono</b>(<b>6-imz</b>)<b>:DCDDA</b> with increasing amounts of <b>DCDDA</b>.</p>
Full article ">Figure 3
<p>FTIR–ATR spectrum overlay of <b>PDI-mono</b>(<b>6-imz</b>) (black line), <b>DCDDA</b> (red line), 2:1 <b>PDI-mono</b>(<b>6-imz</b>)<b>/DCDDA</b> (blue line), 2:1.5 <b>PDI-mono</b>(<b>6-imz</b>)<b>/DCDDA</b> (pink line), 2:2 <b>PDI-mono</b>(<b>6-imz</b>)<b>/DCDDA</b> (green line), and 2:4 <b>PDI-mono</b>(<b>6-imz</b>)<b>/DCDDA</b> (purple line) powder at 25 °C. The downward arrow at ~1710 cm<sup>−1</sup> shows the decrease in free COOH absorbance after imidazole–acid complexation. The solid–to–dashed blue line shift from 1690 cm<sup>−1</sup> to 1693 cm<sup>−1</sup> represents the disruption of dimerized COOH moieties after imidazole–acid complexation.</p>
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<p>UV–Vis spectra of <b>2:1 PDI-mono</b>(<b>3-imz</b>)<b>/DCDDA</b> drop-cast films indicating (<b>a</b>) blue-phase PDA formation after UV irradiation, (<b>b</b>) no PDA formation after thermal treatment at 150 °C for 1 h, (<b>c</b>) blue-to-red-phase PDA transformation upon after thermal treatment at 150 °C for 1 h, and (<b>d</b>) stimuli-specific chromatic transition diagram of <b>2:1 PDI-mono</b>(<b>3-imz</b>)<b>/DCDDA</b> supramolecular system. The insets in (<b>a</b>,<b>d</b>) show photographs of <b>2:1 PDI-mono</b>(<b>3-imz</b>)<b>/DCDDA</b> drop-cast films before/after UV and after UV/after UV and heating, respectively.</p>
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<p>The % crystallinity of samples of <b>2:1 PDI-mono</b>(<b><span class="html-italic">n</span>-imz</b>)<b>/DCDDA</b> drop-cast films calculated from WAXS (% crystallinity,<sub>sample</sub>) as a function of the methylene spacer length, <span class="html-italic">n</span> (where <span class="html-italic">n</span> = 3, 4, or 6), where black squares, blue circles, and red triangles represent the stimuli treatment provided to the drop-cast films (UV mx Heat mx).</p>
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<p>The 1−D SAXS pattern of 2:1 <b>PDI-mono</b>(<b>4-imz</b>)<b>/DCDDA</b> after UV exposure (“UV” = 254 nm exposure for 10 min at room temperature, and “Heat” = 150 °C for 1 h). SAXS peak assignments (q<sub>n</sub>*) can be found in <a href="#molecules-30-01207-t001" class="html-table">Table 1</a>. Peak positions were determined using the fitting function in Origin.</p>
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<p>Schematic illustration of (<b>a</b>) self-assembled 2:1 <b>PDI-mono</b>(<b>4-imz</b>)<b>/PDCDDA</b> into “chessboard” pattern sheets after UV exposure (“UV” = 254 nm exposure for 10 min at room temperature, and “Heat” = 150 °C for 1 h.). (<b>b</b>) Single lamellar sheet, and (<b>c</b>) head-with-head and head-with-tail configurations of the polymer.</p>
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22 pages, 8618 KiB  
Article
Suitability of Electrodialysis with Monovalent Selective Anion-Exchange Membranes for Fractionation of Aqueous Mixture Containing Reactive Dye and Mineral Salt
by Katarzyna Majewska-Nowak, Arif Eftekhar Ahmed, Martyna Grzegorzek and Karolina Baraniec
Membranes 2025, 15(3), 85; https://doi.org/10.3390/membranes15030085 - 7 Mar 2025
Viewed by 177
Abstract
To fulfil the goals of the circular economy, the treatment of textile wastewater should be focused on the recovery of valuable components. Monovalent anion-selective electrodialysis (MASED) was applied for the separation of reactive dyes from mineral salts. Standard cation-exchange membranes (CM membranes) and [...] Read more.
To fulfil the goals of the circular economy, the treatment of textile wastewater should be focused on the recovery of valuable components. Monovalent anion-selective electrodialysis (MASED) was applied for the separation of reactive dyes from mineral salts. Standard cation-exchange membranes (CM membranes) and monovalent selective anion-exchange membranes (MVA membranes) were used in the electrodialysis (ED) stack. The separation efficiency was evaluated for model solutions of various reactive dyes (varying in molecular weight and chemical reactivity) containing NaCl. In the course of MASED, the mineral salt was successfully removed from the dye solutions with an efficacy of 97.4–99.4%, irrespectively of the composition of the treated solution. The transport of dye molecules through the ion-exchange membranes (IEMs) from diluate to concentrate compartments was irrelevant. Nonetheless, a significant adsorption of dye particles on the membranes was observed. Around 11–40% of the initial dye mass was deposited in the ED stack. Dye adsorption intensity was significantly affected by dye reactivity. This study showed the potential of the MASED process for the separation of the reactive dye from the mineral salt on condition that antifouling membrane properties are improved. The obtained streams (the concentrate rich in mineral salt and the diluate containing the reactive dye) can be reused in the dye-house textile operations; however, some loss of dye mass should be included. Full article
(This article belongs to the Special Issue Research on Electrodialytic Processes)
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Figure 1
<p>Desalination of NaCl solutions by monovalent anion-selective electrodialysis (MASED): (<b>a</b>) diluate electrical conductivity versus operation time and (<b>b</b>) desalination efficiency versus operation time.</p>
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<p>Desalination of dye–salt mixtures by MASED for various reactive dyes (20 mg/L): (<b>a</b>) diluate electrical conductivity versus operation time and (<b>b</b>) desalination efficiency versus operation time; current: 0.15 A (2.35 mA/cm<sup>2</sup>).</p>
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<p>Desalination of dye–salt mixtures by MASED for various reactive dyes (50 mg/L): (<b>a</b>) diluate electrical conductivity versus operation time and (<b>b</b>) desalination efficiency versus operation time; current: 0.15 A (2.35 mA/cm<sup>2</sup>).</p>
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<p>Desalination of dye–salt mixtures by MASED for various reactive dyes (100 mg/L): (<b>a</b>) diluate electrical conductivity versus operation time and (<b>b</b>) desalination efficiency versus operation time; current: 0.15 A (2.35 mA/cm<sup>2</sup>).</p>
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<p>Desalination of dye–salt mixtures by MASED for various reactive dyes (20 mg/L): (<b>a</b>) diluate electrical conductivity versus operation time and (<b>b</b>) desalination efficiency versus operation time; current: 0.3 A (4.70 mA/cm<sup>2</sup>).</p>
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<p>Desalination of dye–salt mixtures by MASED for various reactive dyes (20 mg/L): (<b>a</b>) diluate electrical conductivity versus operation time and (<b>b</b>) desalination efficiency versus operation time; current: 0.45 A (7.05 mA/cm<sup>2</sup>).</p>
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<p>Desalination of dye–salt mixtures by MASED for various reactive dyes (20 mg/L): (<b>a</b>) dye concentration in diluate versus operation time and (<b>b</b>) dye concentration in concentrate versus operation time; current: 0.15 A (2.35 mA/cm<sup>2</sup>).</p>
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<p>Desalination of dye–salt mixtures by MASED for various reactive dyes (50 mg/L): (<b>a</b>) dye concentration in diluate versus operation time and (<b>b</b>) dye concentration in concentrate versus operation time; current: 0.15 A (2.35 mA/cm<sup>2</sup>).</p>
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<p>Desalination of dye–salt mixtures by MASED for various reactive dyes (100 mg/L): (<b>a</b>) dye concentration in diluate versus operation time and (<b>b</b>) dye concentration in concentrate versus operation time; current: 0.15 A (2.35 mA/cm<sup>2</sup>).</p>
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<p>Dye retention in diluate compartments for various reactive dyes at variable dye concentration (20, 50, and 100 mg/L); current: 0.15 A (2.35 mA/cm<sup>2</sup>).</p>
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<p>Mass of dye deposited on/in PC-MVA membranes for various reactive dyes at variable dye concentration (20, 50, and 100 mg/L); current: 0.15 A (2.35 mA/cm<sup>2</sup>).</p>
Full article ">Figure 12
<p>Desalination of dye–salt mixtures by MASED for various reactive dyes (20 mg/L): (<b>a</b>) dye concentration in diluate versus operation time and (<b>b</b>) dye concentration in concentrate versus operation time; current: 0.3 A (4.7 mA/cm<sup>2</sup>).</p>
Full article ">Figure 13
<p>Desalination of dye–salt mixtures by MASED for various reactive dyes (20 mg/L): (<b>a</b>) dye concentration in diluate versus operation time and (<b>b</b>) dye concentration in concentrate versus operation time; current: 0.45 A (7.05 mA/cm<sup>2</sup>).</p>
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<p>Dye retention in diluate compartments for various reactive dyes at variable NaCl concentration (2, 4, and 6 g NaCl/L); current: 0.15, 0.3, and 0.45 A, respectively.</p>
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<p>Mass of dye deposited on/in the PC-MVA membranes for various reactive dyes at variable NaCl concentration (2, 4, and 6 g NaCl/L); current: 0.15, 0.3, and 0.45 A, respectively.</p>
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<p>Specific electrical energy consumption during desalination of dye–salt mixtures by MASED for various reactive dyes at variable dye concentration (20, 50, and 100 mg/L); current: 0.15 A (2.35 mA/cm<sup>2</sup>).</p>
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<p>Specific electrical energy consumption during desalination of dye–salt mixtures by MASED for various reactive dyes at variable NaCl concentration (2, 4, and 6 g/L); current: 0.15; 0.3 and 0.45 A, respectively.</p>
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18 pages, 1993 KiB  
Article
In Search of Optimal Cell Components for Polyoxometalate-Based Redox Flow Batteries: Effect of the Membrane on Cell Performance
by Ángela Barros, Jacobus C. Duburg, Lorenz Gubler, Estibaliz Aranzabe, Beñat Artetxe, Juan Manuel Gutiérrez-Zorrilla and Unai Eletxigerra
Energies 2025, 18(5), 1235; https://doi.org/10.3390/en18051235 - 3 Mar 2025
Viewed by 251
Abstract
Redox Flow Batteries (RFBs) are promising large-scale Energy Storage Systems, which support the integration of renewable energies into the current electric grid. Emerging chemistries for electrolytes, such as Polyoxometalates (POMs), are being studied. POMs have attracted great interest because of their reversible multi-electron [...] Read more.
Redox Flow Batteries (RFBs) are promising large-scale Energy Storage Systems, which support the integration of renewable energies into the current electric grid. Emerging chemistries for electrolytes, such as Polyoxometalates (POMs), are being studied. POMs have attracted great interest because of their reversible multi-electron transfers and the possibility of tuning their electrochemical properties. Recently, the cobalt-containing Keggin-type species [CoW12O40]6− (CoW12) has been successfully implemented in a symmetric RFB, and its further implementation calls for new materials for the membrane to enhance its cell performance. In this work, different types of ion exchange membranes (Nafion™-NR212, FAPQ-330 and Amphion™) were tested. The electrolyte uptake, swelling, conductivity and permeability of the membranes in the CoW12 electrolyte, as well as a detailed cell performance study, are reported herein. Better performance results ascribed to the robustness, efficiency and energy density of the system were found for Nafion™-NR212, with 88.5% energy efficiency, 98.9% capacity retention and 3.1 Wh L−1 over 100 cycles at 20 mA cm−2. FAPQ-330 and Amphion membranes showed large capacity fade (up to 0.2%/cycle). Crossover and the low conductivity of these membranes in the mild pH conditions of the electrolyte were revealed to be responsible for the reduced cell performance. Full article
(This article belongs to the Special Issue The Materials for Energy Storage and Conversion)
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Figure 1
<p>(<b>a</b>) Electrolyte uptake and (<b>b</b>) volume swelling of the different membranes immersed in <b>CoW<sub>12</sub></b> electrolyte and the SE.</p>
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<p>(<b>a</b>) Nyquist plot for the impedance data of the membranes immersed in <b>CoW<sub>12</sub></b> electrolyte. Example of the results obtained for one membrane. (<b>b</b>) Nyquist plot for the impedance data of mPBI immersed in <b>CoW<sub>12</sub></b> electrolyte. From the fitted GEIS spectra, the extracted value is Rs = 2.4 Ω, which results in a 0.4 mS cm<sup>−1</sup> conductivity of the membrane (17.5 µm thickness) after being immersed in the <b>CoW<sub>12</sub></b> electrolyte.</p>
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<p>Diffusion test of all the membranes with the concentration of <b>CoW<sub>12</sub></b> electroactive species measured in the receiving <b>ZnSiW<sub>11</sub></b> tank by UV-Vis spectroscopy over 10 days.</p>
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<p>Polarization curves at 50% SoC for <b>CoW<sub>12</sub></b>-RFB assembled with N212, FAPQ330 and Amphion membranes.</p>
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<p>(<b>a</b>) CE, (<b>b</b>) VE, (<b>c</b>) EE and (<b>d</b>) normalized capacity at different current density for the <b>CoW<sub>12</sub></b>-RFB cell performance with different membranes. Results are given as the average of five stable cycles for each current density, while cycling consecutively.</p>
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<p>(<b>a</b>) CE, (<b>b</b>) VE, (<b>c</b>) EE and (<b>d</b>) normalized capacity and energy density for the <b>CoW<sub>12</sub></b>-RFB long-term cyclability test with different membranes at 20 mA cm<sup>−2</sup>.</p>
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12 pages, 2895 KiB  
Article
Ag3PO4 Particles Decorated into Fly-Ash-Incorporated Electrospun Polyurethane Nanofibers: Simultaneously Enhanced Photocatalytic and Antibacterial Activities
by Bishweshwar Pant, Allison A. Kim, Enkhtsatsaral Munkhtur and Mira Park
Photochem 2025, 5(1), 6; https://doi.org/10.3390/photochem5010006 - 1 Mar 2025
Viewed by 270
Abstract
Visible-light-responsive silver-phosphate-sensitized fly-ash particles loaded on polyurethane nanofiber (Ag3PO4–FA/PU NFs) membrane photocatalysts were prepared by electrospinning followed by an ion-exchange method and characterized with state-of-art techniques. With the assistance of Ag3PO4–FA/PU NFs, 98 % of [...] Read more.
Visible-light-responsive silver-phosphate-sensitized fly-ash particles loaded on polyurethane nanofiber (Ag3PO4–FA/PU NFs) membrane photocatalysts were prepared by electrospinning followed by an ion-exchange method and characterized with state-of-art techniques. With the assistance of Ag3PO4–FA/PU NFs, 98 % of methylene blue (MB) was degraded within 60 min. The combination of FA and Ag3PO4 particles provided simultaneous adsorption and degradation of MB in an aqueous solution, resulting in the fast removal of the dye. Also, the Ag3PO4–FA/PU NFs exhibited excellent antibacterial performance toward Escherichia coli and Staphylococcus aureus bacteria. Thus, the prepared photocatalyst may provide a potential outcome for environmental remediation, especially wastewater treatment applications. Full article
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<p>XRD spectra of various formulations of electrospun nanofiber membranes.</p>
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<p>FESEM images of Pristine PU NFs (<b>A</b>), AgNO<sub>3</sub>–FA/PU NFs (<b>B</b>), and Ag<sub>3</sub>PO<sub>4</sub>–FA/PU NFs (<b>C</b>) membranes. Inset C is the TEM image of Ag<sub>3</sub>PO<sub>4</sub>–FA/PU NFs. (<b>A’</b>), (<b>B’</b>), and (<b>C’</b>) are their respective diameter distribution curves.</p>
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<p>Elemental mapping of Ag<sub>3</sub>PO<sub>4</sub>–FA/PU NFs showing the various content on them.</p>
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<p>FTIR spectra of various samples.</p>
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<p>Time-dependent absorbance intensity of MB aqueous solution in the presence of Ag<sub>3</sub>PO<sub>4</sub>–FA/PU NFs (<b>A</b>), photocatalytic removal of MB by various samples before and after visible light irradiation (<b>B</b>), proposed photocatalytic mechanism (<b>C</b>), and cyclic stability tests (<b>D</b>).</p>
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<p>Antibacterial performance of various samples against <span class="html-italic">E. coli</span> (<b>A</b>) and <span class="html-italic">S. aureus</span> (<b>B</b>).</p>
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16 pages, 6476 KiB  
Article
Investigation of the Anion Migration Mechanism in Microbial Desalination Cells: Interaction and Actual Operational Impact
by Jinyue Liang, Yong Gao, Wei Wu, Siqi Tong and Yi Wang
Water 2025, 17(4), 587; https://doi.org/10.3390/w17040587 - 18 Feb 2025
Viewed by 256
Abstract
Microbial desalination cells (MDCs) are an efficient method for the desalination of saline wastewater driven by the metabolism of bacteria via an organic oxidation mechanism. Systematic studies have been conducted to elucidate anion-dominated interactions to avoid unforeseen risks in microbial desalination cells during [...] Read more.
Microbial desalination cells (MDCs) are an efficient method for the desalination of saline wastewater driven by the metabolism of bacteria via an organic oxidation mechanism. Systematic studies have been conducted to elucidate anion-dominated interactions to avoid unforeseen risks in microbial desalination cells during the long-term treatment of complex wastewater containing various anions. Despite different anion migration interactions having less effect on MDC operation compared with cations, they are influenced by their own properties (hydrated ion radius, diffusion coefficient and equivalent conductance) and the ambient solution. This also led to the removal efficiency of different anions in MDC in the following sequence: NO3 > Cl > SO42−. The high Gibbs hydration energy of SO42− and the hydrophobicity of the anion exchange membrane affect the transmembrane migration of SO42−. However, the high steric hindrance formed on the membrane also inhibits reverse diffusion at the end of the cycle. In addition, the anodic biotopography and community caused by the migration of different anions change, such that the number of denitrifying bacteria increases and the relative abundance of electrogenic bacteria further improves. With decreasing anodic pH, electrogenic microorganisms form a shell to protect against anodic biogenesis. In this study, MDC was used to treat actual industrial tailwater, and the salt removal efficiency stabilized at 63.2–74.1%. Full article
(This article belongs to the Special Issue Low-Carbon Wastewater Treatment and Resource Recovery)
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Figure 1
<p>(<b>a</b>) Desalination efficiency of each anion in its individual MDC during 5 cycles; (<b>b</b>) recovery ratio of each anion in each cycle and after the membrane was washed in its individual MDC during 5 cycles; (<b>c</b>) pH changes in the anode chamber of three anionic MDCs in a cycle; (<b>d</b>) anion concentration changes in three anionic MDCs in the desalination chamber and the anode chamber within 110 h; (<b>e</b>) MDC current density changes over 5 cycles of operation of 3 anionic MDCs. (CC: cathode chamber; DC: desalination chamber).</p>
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<p>(<b>a</b>) Desalination efficiency of each ion in 5 cycles of composited anion MDC; (<b>b</b>) recovery ratio of each ion in 5 cycles and after membrane washing of composited anion MDC; (<b>c</b>) MDC current density and desalination efficiency of composited anion MDC changes over 5 cycles of operation.</p>
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<p>Nyquist plots used to determine the ohmic resistance: (<b>a</b>) anode + AEM at the beginning of each anionic MDC, (<b>b</b>) anode + AEM at the end of each anionic MDC, (<b>c</b>) whole system at the beginning of each anionic MDC, and (<b>d</b>) whole system at the end of each anionic MDC. (<b>e</b>) Cyclic voltammetry curves of anionic MDCs.</p>
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<p>Changes in the graphite felt anode surface in the composited cation MDC during a cycle: (<b>a</b>) unused graphite felt; (<b>b</b>) after 10 h of operation; (<b>c</b>) at the end of the cycle.</p>
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<p>(<b>a</b>) OTU Venn diagram; (<b>b</b>) bacterial structures in the initial sludge and anode of composited cation and anion MDCs at the class level; (<b>c</b>) bacterial structures in the initial sludge and anode of composited cation and anion MDCs at the genus level. The relative abundance was calculated as the percentage of the same taxon to the corresponding total sequence.</p>
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<p>Conceptual sketch of the different ion migration and ion-dominated interaction mechanisms. (The arrow length represents the velocity of ion migration.)</p>
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<p>(<b>a</b>) Removal efficiency of TDS, TOC and TN in actual chemical tailwater by MDC treatment for 90 cycles; (<b>b</b>) removal efficiency of anions in actual chemical wastewater.</p>
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16 pages, 4383 KiB  
Article
The Effect of pH on Aniline Removal from Water Using Hydrophobic and Ion-Exchange Membranes
by Karla Filian, Jonathan I. Mendez-Ruiz, Daniel Garces, Kateryna Reveychuk, Lingshan Ma, Jesus R. Melendez, Claudia Díaz-Mendoza, Emile Cornelissen, Priscila E. Valverde-Armas and Leo Gutierrez
Water 2025, 17(4), 547; https://doi.org/10.3390/w17040547 - 14 Feb 2025
Viewed by 424
Abstract
The presence of aniline, a toxic aromatic amine, has been recorded in different industrial wastewaters. This study aims to investigate the transport of charged and neutral aniline species in aqueous solutions through hydrophobic and ion-exchange membranes (IEMs). Hydrophobic polyoctylmethylsiloxane (POMS) and polydimethylsiloxane (PDMS) [...] Read more.
The presence of aniline, a toxic aromatic amine, has been recorded in different industrial wastewaters. This study aims to investigate the transport of charged and neutral aniline species in aqueous solutions through hydrophobic and ion-exchange membranes (IEMs). Hydrophobic polyoctylmethylsiloxane (POMS) and polydimethylsiloxane (PDMS) membranes and cationic (CEMs) and anionic (AEMs) exchange membranes were tested using diffusion cells and electrodialysis (ED). Diffusion experiments showed that neutral aniline removal reached 90% with POMS and 100% with PDMS due to the concentration gradient between feed (pH = 10) and receiving (pH = 3) solutions. For IEMs, neutral aniline exhibited a faster transport than charged species, with neutral-to-charged transport ratios of 6.6:1 for AEMs and 3.2:1 for CEMs, type I. During ED experiments, an external electric potential increased the charged aniline transport, achieving higher initial fluxes (124.7 mmol·m2·h1 at pH 4) compared to neutral aniline (43.6 and 53.2 mmol·m2·h1 for AEMs and CEMs, type I). ED also demonstrated that charged aniline can be removed up to 97% using IEMs. These findings demonstrate the effectiveness of hydrophobic and IEMs in removing aniline, providing insights into its transport mechanism, contributing to the optimization of membrane technologies in treating industrial wastewater effluents, and environmental sustainability. Full article
(This article belongs to the Special Issue Fate, Transport, Removal and Modeling of Pollutants in Water)
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Figure 1
<p>Concentration profile of the aniline in the feed (pH 10) and receiving solution (pH 3) using the POMS and PDMS membranes as a function of time.</p>
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<p>The concentration profiles of aniline using (<b>a</b>) AEM and (<b>b</b>) CEM type I and at a feed pH 7 and receiving solution pH 7, as a function of time.</p>
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<p>The concentration profiles of aniline using AEM type I and II at (<b>a</b>) feed pH 3 and receiving solution pH 10, (<b>b</b>) feed pH 10 and receiving solution pH 3, and using CEM I and II at (<b>c</b>) feed pH 3 and receiving solution pH 10, and (<b>d</b>) feed pH 10 and receiving solution pH 3.</p>
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<p>The transport of charged and neutral aniline through AEM type I, CEM type I, AEM type II, and CEM type II after 200 h.</p>
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<p>The desorption of aniline from CEM type I and type II.</p>
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<p>(<b>a</b>) Aniline concentration profiles in the diluate and concentrate channels during ED experiments. (<b>b</b>) Mass balances of aniline concentration in the diluate, doncentrate, and ERS channels.</p>
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<p>The current/voltage curve for (<b>a</b>) pH4 and (<b>b</b>) pH 10 conditions in the concentrate compartment.</p>
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<p>Schematic of the two-compartment diffusion cells.</p>
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<p>Representative duplicate experiments of the following: (<b>a</b>) a concentration profile of aniline in the feed (pH 10) and receiving solution (pH 3) using the POMS membrane as a function of time, and (<b>b</b>) concentration profiles of aniline using CEM type I and at a feed pH 7 and receiving solution pH 7, as a function of time.</p>
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24 pages, 2060 KiB  
Review
Challenges and Opportunities of Choosing a Membrane for Electrochemical CO2 Reduction
by Helene Rehberger, Mohammad Rezaei and Abdalaziz Aljabour
Membranes 2025, 15(2), 55; https://doi.org/10.3390/membranes15020055 - 8 Feb 2025
Viewed by 627
Abstract
The urgent need to reduce greenhouse gas emissions, particularly carbon dioxide (CO2), has led to intensive research into novel techniques for synthesizing valuable chemicals that address climate change. One technique that is becoming increasingly important is the electrochemical reduction of CO [...] Read more.
The urgent need to reduce greenhouse gas emissions, particularly carbon dioxide (CO2), has led to intensive research into novel techniques for synthesizing valuable chemicals that address climate change. One technique that is becoming increasingly important is the electrochemical reduction of CO2 to produce carbon monoxide (CO), an important feedstock for various industrial processes. This comprehensive review examines the latest developments in CO2 electroreduction, focusing on mechanisms, catalysts, reaction pathways, and optimization strategies to enhance CO production efficiency. A particular emphasis is placed on the role of ion exchange membranes, including cation exchange membranes (CEMs), anion exchange membranes (AEMs), and bipolar membranes (BPMs). The review explores their advantages, disadvantages, and the current challenges associated with their implementation in CO2 electroreduction systems. Through careful analysis of the current literature, this report aims to provide a comprehensive understanding of state-of-the-art methods and their potential impact on sustainable CO production, with a special focus on membrane technologies. Full article
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<p>CO<sub>2</sub> Emissions in Austria from 1990 to 2022 [<a href="#B1-membranes-15-00055" class="html-bibr">1</a>].</p>
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<p>Principle of CO<sub>2</sub> electrolyzer. Reprinted with permission from Ref. [<a href="#B7-membranes-15-00055" class="html-bibr">7</a>]. Copyright The Author(s) 2018. Published by ECS.</p>
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<p>The proposed mechanism on electrochemical CO<sub>2</sub> reduction. Reprinted with permission from Ref. [<a href="#B12-membranes-15-00055" class="html-bibr">12</a>]. Copyright 2022 Lin, J., Yan, S., Zhang, C., Hu, Q., &amp; Cheng, Z.</p>
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<p>Types of electrocatalysts. Reprinted with permission from Ref. [<a href="#B13-membranes-15-00055" class="html-bibr">13</a>]. Copyright© 2020 The Author(s).</p>
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<p>Summary of CO2RR results reported in the literature [<a href="#B18-membranes-15-00055" class="html-bibr">18</a>,<a href="#B22-membranes-15-00055" class="html-bibr">22</a>,<a href="#B23-membranes-15-00055" class="html-bibr">23</a>,<a href="#B24-membranes-15-00055" class="html-bibr">24</a>,<a href="#B25-membranes-15-00055" class="html-bibr">25</a>,<a href="#B26-membranes-15-00055" class="html-bibr">26</a>,<a href="#B27-membranes-15-00055" class="html-bibr">27</a>,<a href="#B28-membranes-15-00055" class="html-bibr">28</a>,<a href="#B29-membranes-15-00055" class="html-bibr">29</a>,<a href="#B30-membranes-15-00055" class="html-bibr">30</a>,<a href="#B31-membranes-15-00055" class="html-bibr">31</a>,<a href="#B32-membranes-15-00055" class="html-bibr">32</a>,<a href="#B33-membranes-15-00055" class="html-bibr">33</a>].</p>
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19 pages, 2112 KiB  
Review
Electrochemical Direct Lithium Extraction: A Review of Electrodialysis and Capacitive Deionization Technologies
by Jeongbeen Park, Juwon Lee, In-Tae Shim, Eunju Kim, Sook-Hyun Nam, Jae-Wuk Koo and Tae-Mun Hwang
Resources 2025, 14(2), 27; https://doi.org/10.3390/resources14020027 - 3 Feb 2025
Viewed by 958
Abstract
The rapid expansion of lithium-ion battery (LIB) markets for electric vehicles and renewable energy storage has exponentially increased lithium demand, driving research into sustainable extraction methods. Traditional lithium recovery from brine using evaporation ponds is resource intensive, consuming vast amounts of water and [...] Read more.
The rapid expansion of lithium-ion battery (LIB) markets for electric vehicles and renewable energy storage has exponentially increased lithium demand, driving research into sustainable extraction methods. Traditional lithium recovery from brine using evaporation ponds is resource intensive, consuming vast amounts of water and causing severe environmental issues. In response, Direct Lithium Extraction (DLE) technologies have emerged as more efficient, eco-friendly alternatives. This review explores two promising electrochemical DLE methods: Electrodialysis (ED) and Capacitive Deionization (CDI). ED employs ion-exchange membranes (IEMs), such as cation exchange membranes, to selectively transport lithium ions from sources like brine and seawater and achieves high recovery rates. IEMs utilize chemical and structural properties to enhance the selectivity of Li+ over competing ions like Mg2+ and Na+. However, ED faces challenges such as high energy consumption, membrane fouling, and reduced efficiency in ion-rich solutions. CDI uses electrostatic forces to adsorb lithium ions onto electrodes, offering low energy consumption and adaptability to varying lithium concentrations. Advanced variants, such as Membrane Capacitive Deionization (MCDI) and Flow Capacitive Deionization (FCDI), enhance ion selectivity and enable continuous operation. MCDI incorporates IEMs to reduce co-ion interference effects, while FCDI utilizes liquid electrodes to enhance scalability and operational flexibility. Advancements in electrode materials remain crucial to enhance selectivity and efficiency. Validating these methods at the pilot scale is crucial for assessing performance, scalability, and economic feasibility under real-world conditions. Future research should focus on reducing operational costs, developing more durable and selective electrodes, and creating integrated systems to enhance overall efficiency. By addressing these challenges, DLE technologies can provide sustainable solutions for lithium resource management, minimize environmental impact, and support a low-carbon future. Full article
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<p>Graphical representation of world lithium reserves created by the authors based on data from [<a href="#B8-resources-14-00027" class="html-bibr">8</a>].</p>
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<p>The number of publications related to Li based on Google Scholar searched in 2024 with the keywords ‘Lithium’ (black) and ‘Direct lithium extraction’ (red).</p>
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<p>Conventional process to concentrate lithium brine and manufacturing lithium.</p>
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<p>Classification of DLE process.</p>
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<p>Scheme of ED system.</p>
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<p>Schematic diagram of adsorption (<b>left</b>) and desorption (<b>right</b>) processes of CDI.</p>
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20 pages, 3878 KiB  
Article
Energy Scheduling of Hydrogen Hybrid UAV Based on Model Predictive Control and Deep Deterministic Policy Gradient Algorithm
by Haitao Li, Chenyu Wang, Shufu Yuan, Hui Zhu, Bo Li, Yuexin Liu and Li Sun
Algorithms 2025, 18(2), 80; https://doi.org/10.3390/a18020080 - 2 Feb 2025
Viewed by 593
Abstract
Energy scheduling for hybrid unmanned aerial vehicles (UAVs) is of critical importance to their safe and stable operation. However, traditional approaches, predominantly rule-based, often lack the dynamic adaptability and stability necessary to address the complexities of changing operational environments. To overcome these limitations, [...] Read more.
Energy scheduling for hybrid unmanned aerial vehicles (UAVs) is of critical importance to their safe and stable operation. However, traditional approaches, predominantly rule-based, often lack the dynamic adaptability and stability necessary to address the complexities of changing operational environments. To overcome these limitations, this paper proposes a novel energy scheduling framework that integrates the Model Predictive Control (MPC) with a Deep Reinforcement Learning algorithm, specifically the Deep Deterministic Policy Gradient (DDPG). The proposed method is designed to optimize energy management in hydrogen-powered UAVs across diverse flight missions. The energy system comprises a proton exchange membrane fuel cell (PEMFC), a lithium-ion battery, and a hydrogen storage tank, enabling robust optimization through the synergistic application of MPC and DDPG. The simulation results demonstrate that the MPC effectively minimizes electric power consumption under various flight conditions, while the DDPG achieves convergence and facilitates efficient scheduling. By leveraging advanced mechanisms, including continuous action space representation, efficient policy learning, experience replay, and target networks, the proposed approach significantly enhances optimization performance and system stability in complex, continuous decision-making scenarios. Full article
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<p>An UAV flight profile diagram.</p>
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<p>Hydrogen hybrid UAV energy system structure diagram.</p>
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<p>The MPC and DDPG flowchart.</p>
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<p>The MPC flowchart.</p>
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<p>The DDPG flowchart.</p>
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<p>Schematic diagram of the DDPG policy network and value network structure.</p>
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<p>Mean and range of random operating conditions.</p>
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<p>Comparison between MPC predicted power and reference value.</p>
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<p>DDPG training cumulative reward.</p>
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<p>Hydrogen fuel cell and SOC scheduling during 0–19 min.</p>
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<p>Hydrogen fuel cell and SOC scheduling during 19–36 min.</p>
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<p>Hydrogen fuel cell and SOC scheduling during 346–360 min.</p>
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14 pages, 2658 KiB  
Article
Integrated Purification Systems for the Removal of Disinfectants from Wastewater
by Aleksandra Klimonda and Izabela Kowalska
Membranes 2025, 15(2), 43; https://doi.org/10.3390/membranes15020043 - 2 Feb 2025
Viewed by 510
Abstract
The efficiency of integrated treatment systems for wastewater generated during the washing of disinfectant production lines was investigated. The high organic load (COD 2000 mg/L, TOC 850 mg/L) and 300 mg/L of toxic benzalkonium chloride (BAC) make wastewater an environmental hazard that requires [...] Read more.
The efficiency of integrated treatment systems for wastewater generated during the washing of disinfectant production lines was investigated. The high organic load (COD 2000 mg/L, TOC 850 mg/L) and 300 mg/L of toxic benzalkonium chloride (BAC) make wastewater an environmental hazard that requires advanced treatment. Initial tests on model BAC solutions (in concentrations corresponding to those found in wastewater), using nanofiltration and ultrafiltration membranes, resulted in up to 70% retention of BAC. To enhance purification, ion exchange and adsorption were introduced as post-membrane treatment steps. In the second part of the investigation, membrane modules characterized by the best separation properties were integrated together with macroporous cation-exchange resin and activated carbon into the purification system to treat wastewater. The research carried out showed that the purification of multicomponent wastewater is a complex task. Significantly lower BAC removal (30%) was achieved in membrane processes compared to the model solutions treatment. In integrated systems, the BAC concentration was reduced to 100 mg/L, TOC to 200 mg/L, and COD to 120 mg/L. Full article
(This article belongs to the Section Membrane Applications for Water Treatment)
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<p>Experimental studies plan.</p>
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<p>Benzalkonium chloride micelle size distribution (<b>A</b>) and the dependence of light scattering on surfactant concentration (<b>B</b>) (CMC determined as the intersection point of the approximating lines).</p>
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<p>Laboratory set-up: 1—membrane module, 2—feeding tank (10 L), 3—manometer, 4—thermometer, 5—pump, 7—control panel, 8—cooler.</p>
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<p>Removal of BAC (model surfactant solutions, filtration time 120 min, TMP = 0.3 MPa, T = 22 °C).</p>
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<p>Changes in BAC concentration as a function of contact time with PAC and C150H resin.</p>
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<p>Conceptual diagrams of the integrated treatment systems.</p>
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<p>Effectiveness of pollutants removal in integrated purification systems.</p>
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<p>Permeate volumetric flux of ESP04 and AFC30 modules (process time 120 min, TMP = 0.3 MPa).</p>
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<p>TOC and BAC concentrations in the treated wastewater with the use of ESP04 and AFC30 modules vs. concentration factor (CF, calculated as the ratio of the initial volume of treated wastewater to the final volume of concentrated wastewater; process performed to two-fold concentration of feed solution, TMP = 0.3 MPa).</p>
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<p>BAC and TOC concentrations during post-treatment with the use of PAC and C150H resin.</p>
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18 pages, 24223 KiB  
Article
Impact of Cross-Linking-Monomer Characteristics on Pore-Filling-Membrane Performance and Durability in Anion-Exchange Water Electrolysis
by Jong-Hyeok Park, Yeri Park, Tae-Seok Jeon, Yuna Seo and Jin-Soo Park
Appl. Sci. 2025, 15(3), 1495; https://doi.org/10.3390/app15031495 - 1 Feb 2025
Viewed by 653
Abstract
This study investigates the development of pore-filling anion-exchange membranes (PFAEMs) for water-electrolysis applications. Ionomers using two different cross-linking monomers, namely hydrophilic C10 and hydrophobic C11, along with a common electrolyte monomer, E3, were compared in terms of through-plane ion conductivity, hydrogen permeability, mechanical [...] Read more.
This study investigates the development of pore-filling anion-exchange membranes (PFAEMs) for water-electrolysis applications. Ionomers using two different cross-linking monomers, namely hydrophilic C10 and hydrophobic C11, along with a common electrolyte monomer, E3, were compared in terms of through-plane ion conductivity, hydrogen permeability, mechanical and chemical stability, I-V polarization, and water-electrolysis durability. The results revealed that the E3-C10 PFAEM exhibited 40% higher OH conductivity (98.7 ± 7.0 mS cm−1) than the E3-C11 PFAEM with a similar ion-exchange capacity. This improvement was attributed to improved separation of hydrophobic and hydrophilic domains, creating well-connected ion channels by the hydrophilic C10. Alkaline stability tests demonstrated that the E3-C10 retained higher ion conductivity compared to E3-C11, due to the absence of ether linkages and increased resistance to nucleophilic attack. During water-electrolysis operations, the E3-C10 PFAEMs showed 10% better durability and 87% lower hydrogen permeability, confirming their suitability for anion-exchange-membrane water electrolysis (AEMWE). Despite the higher ion conductivity of the E3-C10 PFAEM, performance was limited by interfacial resistance. It is suggested that ionomer-coated electrodes could further enhance AEMWE performance by leveraging the higher ion conductivity of the E3-C10. Overall, this study provides valuable guidance on strategies for utilizing pore-filling membranes in water electrolysis. Full article
(This article belongs to the Section Energy Science and Technology)
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<p>Cross-sectional and surface FE-SEM image: (<b>a</b>) 95 μm thick, porous PP substrate utilized in this study; (<b>b</b>,<b>c</b>) pore size analysis.</p>
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<p>Schematic illustration for the preparation of PFAEMs.</p>
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<p>Schematic illustration of single cell components for AEMWE.</p>
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<p>FE-SEM images of the porous PP substrate and PFAEMs: (<b>a</b>) cross-sectional view and (<b>b</b>) surface view of the PP substrate; (<b>c</b>) cross-sectional view of the E3-C10 PFAEM; (<b>d</b>) surface view of the E3-C10 PFAEM; (<b>e</b>) cross-sectional view of the E3-C11 PFAEM; (<b>f</b>) surface view of the E3-C11 PFAEM.</p>
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<p>FT-IR spectra of the PP substrate and fabricated PFAEMs.</p>
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<p>Through-plane ion conductivity of E3-C10 and E3-C11 PFAEMs in 1.0 M KOH at 60 °C.</p>
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<p>Hydrogen permeability of E3-C10 and E3-C11 PFAEMs.</p>
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<p>Tensile strength–strain curves of the porous PP substrate and the fabricated PFAEMs: (<b>a</b>) wet E3-C10 and E3-C11 PFAEMs; (<b>b</b>) dry E3-C10 and E3-C11 PFAEMs.</p>
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<p>Chemical stability of PFAEMs: (<b>a</b>) variation in ion conductivity of E3-C10 and E3-C11 PFAEMs stored at 4 M KOH and 60 °C as a function of storage time; (<b>b</b>) the decrement of OH<sup>−</sup> conductivity change between BOT and EOT.</p>
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<p>Performance of PFAEM-based AEMWE: (<b>a</b>) I-V polarization curves; (<b>b</b>) Tafel plots; (<b>c</b>) ohmic overpotentials and <span class="html-italic">R<sub>Total</sub></span> (= <span class="html-italic">R<sub>HFR</sub> </span>+ <span class="html-italic">R<sub>CTR</sub></span>); (<b>d</b>) <span class="html-italic">R<sub>HFR</sub></span> and <span class="html-italic">R<sub>CTR</sub></span> from 1.0 M KOH-fed AEMWE.</p>
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<p>Performance of PFAEM-based AEMWE: (<b>a</b>) I-V polarization curves; (<b>b</b>) Tafel plots; (<b>c</b>) ohmic overpotentials and <span class="html-italic">R<sub>Total</sub></span> (= <span class="html-italic">R<sub>HFR</sub> </span>+ <span class="html-italic">R<sub>CTR</sub></span>); (<b>d</b>) <span class="html-italic">R<sub>HFR</sub></span> and <span class="html-italic">R<sub>CTR</sub></span> from 1.0 M KOH-fed AEMWE.</p>
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<p>In situ and ex situ durability of PFAEM-based AEMWE: (<b>a</b>) long-term durability of the asymmetric 1.0 M KOH-fed operation at 60 °C, 500 mA cm<sup>−2</sup> of current density for 100 h; (<b>b</b>) BOT and EOT variations in IEC using AEMs of different samples; (<b>c</b>) relationship between the loss in ion conductivity of PFAEM and degradation slope in single cell durability evaluation.</p>
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<p>Performance of E3-C10 PFAEM-based AEMWE using ionomer layer-coated electrode from 1.0 M KOH-fed AEMWE at 60 °C: (<b>a</b>) I–V polarization curves; (<b>b</b>) Nyquist plots at 1.7 V.</p>
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38 pages, 1875 KiB  
Article
Reduced-Order Model for Cell Volume Homeostasis: Application to Aqueous Humor Production
by Riccardo Sacco, Greta Chiaravalli, Giovanna Guidoboni, Anita Layton, Gal Antman, Keren Wood Shalem, Alice Verticchio, Brent Siesky and Alon Harris
Math. Comput. Appl. 2025, 30(1), 13; https://doi.org/10.3390/mca30010013 - 24 Jan 2025
Viewed by 572
Abstract
The ability of a cell to keep its volume constant irrespective of intra- and extracellular conditions is essential for cellular homeostasis and survival. The purpose of this study is to elaborate a theoretical model of cell volume homeostasis and to apply it to [...] Read more.
The ability of a cell to keep its volume constant irrespective of intra- and extracellular conditions is essential for cellular homeostasis and survival. The purpose of this study is to elaborate a theoretical model of cell volume homeostasis and to apply it to a simulation of human aqueous humor (AH) production. The model assumes a cell with a spherical shape and only radial deformation satisfying the property that the cell volume in rest conditions equals that of the cell couplets constituting the ciliary epithelium of the human eye. The cytoplasm is described as a homogeneous mixture containing fluid, ions, and neutral solutes whose evolution is determined by net production mechanisms occurring in the intracellular volume and by water and solute exchange across the membrane. Averaging the balance equations over the cell volume leads to a coupled system of nonlinear ordinary differential equations (ODEs) which are solved using the θ-method and the Matlab function ode15s. Simulation tests are conducted to characterize the set of parameters corresponding to baseline conditions in AH production. The model is subsequently used to investigate the relative importance of (a) impermeant charged proteins; (b) sodium–potassium (Na+/K+) pumps; (c) carbonic anhydrase (CA) in the AH production process; and (d) intraocular pressure. Results suggest that (a) and (b) play a role; (c) lacks significant weight, at least for low carbon dioxide values; and (d) plays a role for the elevated values of intraocular pressure. Model results describe a higher impact from charged proteins and Na+/K+ ATPase than CA on AH production and cellular volume. The computational virtual laboratory provides a method to further test in vivo experiments and machine learning-based data analysis toward the prevention and cure of ocular diseases such as glaucoma. Full article
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Graphical abstract
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<p>A schematic representation of the processes involved in AH dynamics. (1): AH production; (2): AH flow; (3): AH outflow. Reprinted from R. Ramakrishnan et al., <span class="html-italic">Diagnosis &amp; Management of Glaucoma</span>, Chapter 9 Aqueous Humor Dynamics, 10.5005/jp/books/11801_9, (2013) [<a href="#B21-mca-30-00013" class="html-bibr">21</a>]; used in accordance with the Creative Commons Attribution (CC BY) license.</p>
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<p><b>Left</b> panel: a light micrograph of the ciliary body epithelium. It consists of two epithelial cell layers: a non-pigmented inner layer and an outer pigmented layer. Under the epithelium, there is a highly vascularized stroma. Reprinted from [<a href="#B23-mca-30-00013" class="html-bibr">23</a>]; used in accordance with the Creative Commons Attribution (CC BY) license. <b>Right</b> panel: a compartmental representation of the CE cell couplet.</p>
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<p>The “equivalent cell”. Solid line: initial cell configuration. Dashed line: deformed cell configuration. The cyan arrows indicate water flow. The cell is increasing its volume (cell swelling).</p>
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<p>A schematic representation of the structure of the cell membrane. AQP: aquaporin (cyan). The ion channel is drawn in green. Water molecules (red and dark blue), charged solutes (magenta), and neutral solutes (brown) are illustrated. The lipid constituent is drawn in yellow. The AQP is selective to water molecules whereas the ion channel permits the co-transport of ions and water.</p>
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<p>A three-dimensional schematic representation of an aquaporin. The cylindrical domain <math display="inline"><semantics> <msub> <mi>ω</mi> <mi>p</mi> </msub> </semantics></math> is the pore channel, <math display="inline"><semantics> <msub> <mi>t</mi> <mi>m</mi> </msub> </semantics></math> is the membrane thickness, and <math display="inline"><semantics> <msub> <mi>r</mi> <mi>p</mi> </msub> </semantics></math> is the aquaporin radius.</p>
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<p>Transmembrane electric potential.</p>
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<p><b>Left</b> panel: a plot of <math display="inline"><semantics> <mrow> <mi>f</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </semantics></math>. <b>Right</b> panel: a plot of <math display="inline"><semantics> <mrow> <mi mathvariant="script">V</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>/</mo> <msub> <mi mathvariant="script">V</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mrow> </semantics></math> in the time interval <math display="inline"><semantics> <mrow> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>10</mn> <mo>]</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. The values of the input data are as follows: <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mrow> <mi>c</mi> <mi>e</mi> <mi>l</mi> <mi>l</mi> </mrow> </msub> <mo>=</mo> <mn>10</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>6</mn> </mrow> </msup> <mspace width="3.33333pt"/> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msup> <mo>Φ</mo> <mrow> <mi>A</mi> <mi>Q</mi> <mi>P</mi> </mrow> </msup> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>; <math display="inline"><semantics> <mrow> <mover> <mi>v</mi> <mo>¯</mo> </mover> <mo>=</mo> <mo>−</mo> <mn>30</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>6</mn> </mrow> </msup> <mspace width="3.33333pt"/> <mi mathvariant="normal">m</mi> <mspace width="0.166667em"/> <msup> <mi mathvariant="normal">s</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>; <math display="inline"><semantics> <mrow> <msub> <mi>κ</mi> <mi>a</mi> </msub> <mo>=</mo> <mn>1</mn> <mspace width="3.33333pt"/> <msup> <mi mathvariant="normal">s</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>; and <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>d</mi> </msub> <mo>=</mo> <mn>3</mn> <mspace width="3.33333pt"/> <msup> <mi mathvariant="normal">s</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>.</p>
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<p><b>Left</b> panel: a plot of <math display="inline"><semantics> <mrow> <mi mathvariant="script">V</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>/</mo> <msub> <mi mathvariant="script">V</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mrow> </semantics></math> in the time interval <math display="inline"><semantics> <mrow> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>10</mn> <mo>]</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. The value of fluid velocity (expressed in <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>) is indicated for each computed normalized cell volume. <b>Right</b> panel: a plot of <math display="inline"><semantics> <mrow> <mi mathvariant="script">V</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>/</mo> <msub> <mi mathvariant="script">V</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mrow> </semantics></math> in the time interval <math display="inline"><semantics> <mrow> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>1</mn> <mo>]</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>.</p>
Full article ">Figure 9
<p><b>Left</b> panel: a plot of the water volume net production rate <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="script">R</mi> <mi>w</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> in the time interval <math display="inline"><semantics> <mrow> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>10</mn> <mo>]</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. <b>Right</b> panel: a plot of <math display="inline"><semantics> <mrow> <mi mathvariant="script">V</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>/</mo> <msub> <mi mathvariant="script">V</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mrow> </semantics></math> in the time interval <math display="inline"><semantics> <mrow> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>1</mn> <mo>]</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">s</mi> </mrow> </semantics></math> in the case where <math display="inline"><semantics> <mrow> <mi mathvariant="script">R</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> for every <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>1</mn> <mo>]</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. Fluid velocity varies in the range <math display="inline"><semantics> <mrow> <mrow> <mo>[</mo> <mo>−</mo> <mn>30</mn> <mspace width="0.166667em"/> <mo>+</mo> <mn>30</mn> <mo>]</mo> </mrow> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>6</mn> </mrow> </msup> <mspace width="3.33333pt"/> <mi mathvariant="normal">m</mi> <mspace width="0.166667em"/> <msup> <mi mathvariant="normal">s</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>. The arrow indicates velocity increase from negative to positive values.</p>
Full article ">Figure 10
<p><b>Left</b> panel: blue curve, <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mrow> <msup> <mrow> <mi mathvariant="normal">H</mi> </mrow> <mo>+</mo> </msup> <mo>,</mo> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>; red curve, pH<math display="inline"><semantics> <mrow> <mmultiscripts> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <none/> <none/> <mprescripts/> <mrow> <mo>,</mo> <mi>i</mi> <mi>n</mi> </mrow> <none/> </mmultiscripts> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>50</mn> <mo>·</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>12</mn> </mrow> </msup> <mo>]</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. <b>Right</b> panel: blue curve, <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mrow> <mi>c</mi> <mi>e</mi> <mi>l</mi> <mi>l</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>; red curve, <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi mathvariant="script">V</mi> <mo>%</mo> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>50</mn> <mo>·</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>12</mn> </mrow> </msup> <mo>]</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. Middle panel (bottom): total AH volumetric flow rate <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mi>AH</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>50</mn> <mo>·</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>12</mn> </mrow> </msup> <mo>]</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>.</p>
Full article ">Figure 11
<p><b>Top left</b> panel: blue curve, <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mrow> <msub> <mi>CO</mi> <mn>2</mn> </msub> <mo>,</mo> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>; red curve, <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">H</mi> <mn>2</mn> </msub> <msub> <mi>CO</mi> <mrow> <mn>3</mn> <mo>,</mo> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>5</mn> <mo>]</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. <b>Top right</b> panel: blue curve, <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi mathvariant="normal">H</mi> </mrow> <mrow> <mi>i</mi> <mi>n</mi> </mrow> <mo>+</mo> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>; red curve, <math display="inline"><semantics> <mrow> <msub> <mi>pH</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>5</mn> <mo>]</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. <b>Bottom left</b> panel: blue curve, average cell normal surface velocity, <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mrow> <mi>c</mi> <mi>e</mi> <mi>l</mi> <mi>l</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>; red curve, percentage volume variation, <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi mathvariant="script">V</mi> <mo>%</mo> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>5</mn> <mo>]</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. <b>Bottom right</b> panel: total AH volumetric flow rate <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mi>AH</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>5</mn> <mo>]</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>.</p>
Full article ">Figure 12
<p><b>Top left</b> panel: a zoom of the membrane potential <math display="inline"><semantics> <mrow> <msub> <mi>ψ</mi> <mi>m</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> (units: <math display="inline"><semantics> <mrow> <mspace width="3.33333pt"/> <mi>mV</mi> </mrow> </semantics></math>) in the time interval <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>10</mn> <mo>]</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. <b>Top right</b> panel: a zoom of <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mrow> <msup> <mrow> <mi>Na</mi> </mrow> <mo>+</mo> </msup> <mo>,</mo> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> (blue curve), <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mrow> <msup> <mrow> <mi mathvariant="normal">K</mi> </mrow> <mo>+</mo> </msup> <mo>,</mo> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> (red curve), and <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mrow> <msup> <mrow> <mi>Cl</mi> </mrow> <mo>−</mo> </msup> <mo>,</mo> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> (green curve) (units: <math display="inline"><semantics> <mrow> <mspace width="3.33333pt"/> <mi>mM</mi> </mrow> </semantics></math>) in the time interval <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>120</mn> <mo>]</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. <b>Middle left</b> panel: a zoom of the chlorine molar flux density <math display="inline"><semantics> <mrow> <msubsup> <mi>j</mi> <mrow> <msup> <mrow> <mi>Cl</mi> </mrow> <mo>−</mo> </msup> </mrow> <mrow> <mi>e</mi> <mi>c</mi> <mi>w</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> (units: <math display="inline"><semantics> <mrow> <mspace width="3.33333pt"/> <mi>mM</mi> <mspace width="0.166667em"/> <mi mathvariant="normal">m</mi> <mspace width="0.166667em"/> <msup> <mi mathvariant="normal">s</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>) in the time interval <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>10</mn> <mo>]</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. <b>Middle right</b> panel: a zoom of <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mrow> <mi>c</mi> <mi>e</mi> <mi>l</mi> <mi>l</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> (blue curve) and <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi mathvariant="script">V</mi> <mo>%</mo> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> (red curve) in the time interval <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>120</mn> <mo>]</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. <b>Bottom center</b> panel: a zoom of the total AH volumetric flow rate in the time interval <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>300</mn> <mo>]</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>.</p>
Full article ">Figure 13
<p><b>Left</b> panel: total AH volumetric flow rate <math display="inline"><semantics> <msub> <mi>Q</mi> <mi>AH</mi> </msub> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>600</mn> <mo>]</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">s</mi> </mrow> </semantics></math> as a function of <math display="inline"><semantics> <msub> <mi>σ</mi> <mi>X</mi> </msub> </semantics></math>. The black dashed line indicates the physiological value of <math display="inline"><semantics> <msub> <mi>Q</mi> <mi>AH</mi> </msub> </semantics></math>, equal to <math display="inline"><semantics> <mrow> <mn>2.75</mn> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">L</mi> <mspace width="0.166667em"/> <msup> <mi>min</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>, when IOP = 15 mmHg. <b>Right</b> panel: the total osmo-oncotic pressure difference <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mo>Π</mo> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>600</mn> <mo>]</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">s</mi> </mrow> </semantics></math> as a function of <math display="inline"><semantics> <msub> <mi>σ</mi> <mi>X</mi> </msub> </semantics></math>.</p>
Full article ">Figure 14
<p>Total AH volumetric flow rate <math display="inline"><semantics> <msub> <mi>Q</mi> <mi>AH</mi> </msub> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>5400</mn> <mo>]</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">s</mi> </mrow> </semantics></math> as a function of <math display="inline"><semantics> <msub> <mi>M</mi> <mrow> <mi>A</mi> <mi>T</mi> <mi>P</mi> </mrow> </msub> </semantics></math>. The black dashed line indicates the physiological value of <math display="inline"><semantics> <msub> <mi>Q</mi> <mi>AH</mi> </msub> </semantics></math>, equal to <math display="inline"><semantics> <mrow> <mn>2.75</mn> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">L</mi> <mspace width="0.166667em"/> <msup> <mi>min</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>, when IOP = 15 mmHg.</p>
Full article ">Figure 15
<p>Plot of <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>Q</mi> <mo>%</mo> </msub> <mrow> <mo>(</mo> <mi>IOP</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> for IOP in interval [15, 150] mmHg, with <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>5400</mn> <mo>]</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>.</p>
Full article ">Figure A1
<p>Red solid line: a plot of <math display="inline"><semantics> <mrow> <mo>〈</mo> <msub> <mi>c</mi> <mi>α</mi> </msub> <mo>〉</mo> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mo>[</mo> <mn>0</mn> <mo>:</mo> <mn>20</mn> <mo>]</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>X</mi> <mi>α</mi> </msub> <mrow> <mo>(</mo> <mi>τ</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>τ</mi> <mo>−</mo> <mn>10</mn> </mrow> </semantics></math>, with <math display="inline"><semantics> <mi>τ</mi> </semantics></math> being a dimensionless time. The endpoint values of <math display="inline"><semantics> <msub> <mi>c</mi> <mi>α</mi> </msub> </semantics></math> are <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mrow> <mi>α</mi> <mo>,</mo> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>τ</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>1</mn> <mspace width="0.166667em"/> <mspace width="3.33333pt"/> <mi>mM</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mrow> <mi>α</mi> <mo>,</mo> <mi>e</mi> <mi>x</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>5</mn> <mspace width="0.166667em"/> <mspace width="3.33333pt"/> <mi>mM</mi> </mrow> </semantics></math> for every <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>:</mo> <mn>20</mn> <mo>]</mo> </mrow> </semantics></math>. Black dashed line: the arithmetic average of <math display="inline"><semantics> <msub> <mi>c</mi> <mi>α</mi> </msub> </semantics></math>.</p>
Full article ">Figure A2
<p>Schematic representation of intracellular reactions and transmembrane transport mechanisms. MIT: mitochondrium. ATP: adenosinetriphosphate. CA: carbonic anhydrase. Exchangers perform multiple ion transport across membrane.</p>
Full article ">
14 pages, 1251 KiB  
Article
Enhancing Virus Filter Performance Through Pretreatment by Membrane Adsorbers
by Solomon Isu, Shu-Ting Chen, Raheleh Daneshpour, Hironobu Shirataki, Daniel Strauss, Andrew L. Zydney, Xianghong Qian and Sumith Ranil Wickramasinghe
Membranes 2025, 15(1), 34; https://doi.org/10.3390/membranes15010034 - 17 Jan 2025
Viewed by 1485
Abstract
Virus filtration is used to ensure the high level of virus clearance required in the manufacture of biopharmaceutical products such as monoclonal antibodies. Flux decline during virus filtration can occur due to the formation of reversible aggregates consisting of self-assembled monomeric monoclonal antibody [...] Read more.
Virus filtration is used to ensure the high level of virus clearance required in the manufacture of biopharmaceutical products such as monoclonal antibodies. Flux decline during virus filtration can occur due to the formation of reversible aggregates consisting of self-assembled monomeric monoclonal antibody molecules, particularly at high antibody concentrations. While size exclusion chromatography is generally unable to detect these reversible aggregates, dynamic light scattering may be used to determine their presence. Flux decline during virus filtration may be minimized by pretreating the feed using a membrane adsorber in order to disrupt the reversible aggregates that are present. The formation of reversible aggregates is highly dependent on the monoclonal antibody and the feed conditions. For the pH values investigated here, pretreatment of the feed using a hydrophobic interaction membrane adsorber was the most effective in minimizing flux decline during virus filtration. Ion exchange membranes may also be effective if the monoclonal antibody and membrane are oppositely charged. Consequently, the effectiveness of ion exchange membrane adsorbers is much more dependent on solution pH when compared to hydrophobic interaction membrane adsorbers. Size based prefiltration was found to be ineffective at disrupting these reversible aggregates. These results can help guide the development of more effective virus filtration processes for monoclonal antibody production. Full article
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Figure 1

Figure 1
<p>Variation of virus filter flux versus throughput for feed streams at different pH after pretreatment with a 0.2 μm bottle top filter. When flux values dropped to below 40 L m<sup>−2</sup> h<sup>−1</sup>, a buffer flush was initiated and the flux increased.</p>
Full article ">Figure 2
<p>Variation of permeate flux through the BioEx virus filter versus throughput for feed streams pretreated using the various prefilters and membrane adsorbers listed in <a href="#membranes-15-00034-t001" class="html-table">Table 1</a>. The feed pH was 5.0.</p>
Full article ">Figure 3
<p>Variation of permeate flux through the BioEx virus filter versus throughput for feed streams pretreated using the various membrane adsorbers listed in <a href="#membranes-15-00034-t001" class="html-table">Table 1</a>. The feed pH was 7.5.</p>
Full article ">Figure 4
<p>Variation of permeate flux through the BioEx virus filter versus throughput for feed streams pretreated using the various membrane adsorbers listed in <a href="#membranes-15-00034-t001" class="html-table">Table 1</a>. The feed pH was 8.6.</p>
Full article ">Figure 5
<p>Variation of permeate flux through the BioEx virus filter versus hydrodynamic diameter using the various pretreatments listed in <a href="#membranes-15-00034-t002" class="html-table">Table 2</a>. Results are given for virus filter flux at 150 L m<sup>−2</sup> throughput.</p>
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15 pages, 2287 KiB  
Article
Transport Numbers and Electroosmosis in Cation-Exchange Membranes with Aqueous Electrolyte Solutions of HCl, LiCl, NaCl, KCl, MgCl2, CaCl2 and NH4Cl
by Simon B. B. Solberg, Zelalem B. Deress, Marte H. Hvamstad and Odne S. Burheim
Entropy 2025, 27(1), 75; https://doi.org/10.3390/e27010075 - 15 Jan 2025
Viewed by 734
Abstract
Electroosmosis reduces the available energy from ion transport arising due to concentration gradients across ion-exchange membranes. This work builds on previous efforts to describe the electroosmosis, the permselectivity and the apparent transport number of a membrane, and we show new measurements of concentration [...] Read more.
Electroosmosis reduces the available energy from ion transport arising due to concentration gradients across ion-exchange membranes. This work builds on previous efforts to describe the electroosmosis, the permselectivity and the apparent transport number of a membrane, and we show new measurements of concentration cells with the Selemion CMVN cation-exchange membrane and single-salt solutions of HCl, LiCl, NaCl, MgCl2, CaCl2 and NH4Cl. Ionic transport numbers and electroosmotic water transport relative to the membrane are efficiently obtained from a relatively new permselectivity analysis method. We find that the membrane can be described as perfectly selective towards the migration of the cation, and that Cl does not contribute to the net electric current. For the investigated salts, we obtained water transference coefficients, tw, of 1.1 ± 0.8 for HCl, 9.2 ± 0.8 for LiCl, 4.9 ± 0.2 for NaCl, 3.7 ± 0.4 for KCl, 8.5 ± 0.5 for MgCl2, 6.2 ± 0.6 for CaCl2 and 3.8 ± 0.5 for NH4Cl. However, as the test compartment concentrations of LiCl, MgCl2 and CaCl2 increased past 3.5, 1.3 and 1.4 mol kg−1, respectively, the water transference coefficients appeared to decrease. The presented methods are generally useful for characterising concentration polarisation phenomena in electrochemistry, and may aid in the design of more efficient electrochemical cells. Full article
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Figure 1

Figure 1
<p>Sketch of the concentration cell used for the cation-exchange membrane (CEM) electric potential measurements, <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>ϕ</mi> </mrow> </semantics></math>. The composition is described by the molality, <math display="inline"><semantics> <msub> <mi>m</mi> <mrow> <mi mathvariant="normal">M</mi> <mi mathvariant="normal">C</mi> <msub> <mi mathvariant="normal">l</mi> <mrow> <mi mathvariant="normal">z</mi> <mo>+</mo> </mrow> </msub> </mrow> </msub> </semantics></math>, and the superscript “ref” denotes the reference compartment which always has a salt concentration of <math display="inline"><semantics> <mrow> <msubsup> <mi>m</mi> <mrow> <mrow> <mi mathvariant="normal">M</mi> <mi mathvariant="normal">C</mi> <msub> <mi mathvariant="normal">l</mi> <mrow> <mi>z</mi> <mo>+</mo> </mrow> </msub> </mrow> </mrow> <mi>ref</mi> </msubsup> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>. Arrows show the ionic species transport directions that contribute to the electron direction displayed and the measured net electric potential.</p>
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<p>(<b>a</b>) Non-linear regression (solid lines) of the measured electric potential, <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>ϕ</mi> </mrow> </semantics></math>, as a function of the chemical potential difference across the membrane, <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>μ</mi> <mrow> <mi mathvariant="normal">M</mi> <mi mathvariant="normal">C</mi> <msub> <mi mathvariant="normal">l</mi> <mrow> <mi>z</mi> <mo>+</mo> </mrow> </msub> </mrow> </msub> </mrow> </semantics></math>, of the salts HCl (left-facing triangles), LiCl (circles), NaCl (squares) and MgCl<sub>2</sub> (right-facing triangles). Red shaded areas show the 95% confidence interval of the regression curves. (<b>b</b>) The regression residuals, <math display="inline"><semantics> <msub> <mi>ϵ</mi> <mi>ϕ</mi> </msub> </semantics></math>, of the non-linear curves of NaCl and MgCl<sub>2</sub> illustrating the difference in variance of the repeated measurements compared to between different measurements.</p>
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<p>The apparent transport numbers, <math display="inline"><semantics> <msubsup> <mi>t</mi> <mrow> <mrow> <mi mathvariant="normal">M</mi> <mi mathvariant="normal">C</mi> <msub> <mi mathvariant="normal">l</mi> <mrow> <mi>z</mi> <mo>+</mo> </mrow> </msub> </mrow> </mrow> <mi>app</mi> </msubsup> </semantics></math>, as a function of the chemical potential difference across the membrane, <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>μ</mi> <mrow> <mi mathvariant="normal">M</mi> <mi mathvariant="normal">C</mi> <msub> <mi mathvariant="normal">l</mi> <mrow> <mi>z</mi> <mo>+</mo> </mrow> </msub> </mrow> </msub> </mrow> </semantics></math>, of the salts HCl (left-facing triangles), LiCl (circles), NaCl (squares) and MgCl<sub>2</sub> (right-facing triangles). Red shaded areas show the 95% confidence interval of the regression curves.</p>
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<p>Linear regression (solid lines) of the permselectivity, <math display="inline"><semantics> <mi>α</mi> </semantics></math>, as a function of the chemical potential ratio, <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>μ</mi> <mi>w</mi> </msub> <mo>/</mo> <mo>Δ</mo> <msub> <mi>μ</mi> <mrow> <mi mathvariant="normal">M</mi> <mi mathvariant="normal">C</mi> <msub> <mi mathvariant="normal">l</mi> <mrow> <mi>z</mi> <mo>+</mo> </mrow> </msub> </mrow> </msub> </mrow> </semantics></math> in the linear (low-salt-concentration) region. Red shaded areas show the 95% confidence interval of the linear regressions, and non-linear curves (dotted lines) show the deviation from linearity at high salt concentrations for some salts.</p>
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<p>The membrane water transference coefficients, <math display="inline"><semantics> <msub> <mi>t</mi> <mi>w</mi> </msub> </semantics></math>, from the linear region of the curves of <a href="#entropy-27-00075-f004" class="html-fig">Figure 4</a>, compared to the hydrated cation radius in bulk solutions, <math display="inline"><semantics> <msub> <mi>r</mi> <mi>h</mi> </msub> </semantics></math>, communicated by Nightingale [<a href="#B42-entropy-27-00075" class="html-bibr">42</a>]. The filled symbols show the values for Nafion 117 [<a href="#B29-entropy-27-00075" class="html-bibr">29</a>,<a href="#B39-entropy-27-00075" class="html-bibr">39</a>], and the dotted lines show general trends.</p>
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<p>The estimated average cation molal concentration across the membrane, <math display="inline"><semantics> <msub> <mover accent="true"> <mi>m</mi> <mo stretchy="false">¯</mo> </mover> <msub> <mi mathvariant="normal">M</mi> <mrow> <mi>z</mi> <mo>+</mo> </mrow> </msub> </msub> </semantics></math>, compared to the average external test solution concentration, <math display="inline"><semantics> <msubsup> <mover accent="true"> <mi>m</mi> <mo stretchy="false">¯</mo> </mover> <mrow> <msub> <mi mathvariant="normal">M</mi> <mrow> <mi>z</mi> <mo>+</mo> </mrow> </msub> </mrow> <mi>ext</mi> </msubsup> </semantics></math>. Curves are generated using the apparent transport numbers of <a href="#entropy-27-00075-f003" class="html-fig">Figure 3</a> together with the ionic transport number and water transference coefficient from the linear region of curves from <a href="#entropy-27-00075-f004" class="html-fig">Figure 4</a>. A solid red line shows the arithmetic mean of the external concentrations.</p>
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40 pages, 10424 KiB  
Article
Optimising the Design of a Hybrid Fuel Cell/Battery and Waste Heat Recovery System for Retrofitting Ship Power Generation
by Onur Yuksel, Eduardo Blanco-Davis, Andrew Spiteri, David Hitchmough, Viknash Shagar, Maria Carmela Di Piazza, Marcello Pucci, Nikolaos Tsoulakos, Milad Armin and Jin Wang
Energies 2025, 18(2), 288; https://doi.org/10.3390/en18020288 - 10 Jan 2025
Cited by 1 | Viewed by 908
Abstract
This research aims to assess the integration of different fuel cell (FC) options with battery and waste heat recovery systems through a mathematical modelling process to determine the most feasible retrofit solutions for a marine electricity generation plant. This paper distinguishes itself from [...] Read more.
This research aims to assess the integration of different fuel cell (FC) options with battery and waste heat recovery systems through a mathematical modelling process to determine the most feasible retrofit solutions for a marine electricity generation plant. This paper distinguishes itself from existing literature by incorporating future cost projection scenarios involving variables such as carbon tax, fuel, and equipment prices. It assesses the environmental impact by including upstream emissions integrated with the Energy Efficiency Existing Ship Index (EEXI) and the Carbon Intensity Indicator (CII) calculations. Real-time data have been collected from a Kamsarmax vessel to build a hybrid marine power distribution plant model for simulating six system designs. A Multi-Criteria Decision Making (MCDM) methodology ranks the scenarios depending on environmental benefits, economic performance, and system space requirements. The findings demonstrate that the hybrid configurations, including solid oxide (SOFC) and proton exchange (PEMFC) FCs, achieve a deduction in equivalent CO2 of the plant up to 91.79% and decrease the EEXI and the average CII by 10.24% and 6.53%, respectively. Although SOFC-included configurations show slightly better economic performance and require less fuel capacity, the overall performance of PEMFC designs are ranked higher in MCDM analysis due to the higher power density. Full article
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<p>The methodology flowchart.</p>
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<p>Sample data: Power output distribution of D/Gs.</p>
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<p>The conventional and investigated hybrid design for marine power distribution unit.</p>
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<p>The specific fuel consumption curve of the marine diesel engine.</p>
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<p>The algorithm scheme of the model and EMS (The red, blue, and purple dashed boxes delineate the modelling frameworks for the load sharing of FC, battery, and ICE respectively).</p>
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<p>Usage hour distribution of equipment.</p>
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<p>Fuel consumption distribution of scenarios.</p>
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<p>The operational and upstream (<b>a</b>) CO<sub>2-eq</sub>, (<b>b</b>) CO<sub>2</sub>, (<b>c</b>) N<sub>2</sub>O, and (<b>d</b>) CH<sub>4</sub> emissions of the scenarios.</p>
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<p>The operational and upstream (<b>a</b>) SOx, (<b>b</b>) NOx, (<b>c</b>) PM, and (<b>d</b>) VOC emissions of the scenarios.</p>
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<p>Attained EEXI values of combinations.</p>
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<p>The CII variation of base and zero-carbon cases was attained.</p>
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<p>LCOE of hybrid scenarios considering the economic projection cases and year.</p>
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<p>EPC of hybrid scenarios considering the economic projection cases and year.</p>
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