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Boulif N, Houben M, Borneman Z, Nijmeijer K. Using Layer-by-layer Assembled Clay Composite Junctions to Enhance the Water Dissociation in Bipolar Membranes. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2024; 40:24795-24807. [PMID: 39533785 PMCID: PMC11603776 DOI: 10.1021/acs.langmuir.4c02514] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2024] [Revised: 11/06/2024] [Accepted: 11/07/2024] [Indexed: 11/16/2024]
Abstract
Bipolar membranes (BPMs) with a layer-by-layer (LbL) assembled montmorillonite (K30 MMT) clay-polyelectrolyte (PE) composite junction coated onto a sulfonated poly(ether ether ketone (SPEEK)) electrospun support are prepared, characterized and their water dissociation performance is analyzed. In particular, the focus is on the effect of the presence of the K30 MMT clay as a catalyst for water dissociation, the bilayer number (three, six, and nine), and the PE strength (poly(ethylenimine) (PEI) as a weak PE and poly(diallyl dimethylammonium chloride) (PDADMAC) as a strong PE) on the BPM performance. The BPMs are prepared by electrospinning and hot pressing SPEEK and the Fumion FAA-3 polymer. Adding the composite multilayers in the BPM junction decreases the membrane area resistance in reverse bias from 560 to 21 Ohms cm2 for the best-performing modified BPM. The bilayer number has limited influence on the overall membrane resistance, while the PDADMAC BPMs outperform the PEI BPMs due to the higher and more stable PE and clay adsorptions. Electrochemical impedance spectroscopy shows that the depletion layer thickness decreases exponentially with the number of bilayers as the water dissociation reaction becomes less dependent on the junction electric field. Furthermore, the higher Donnan exclusion at the modified junctions improves the BPM permselectivity 3-fold compared to the BPM containing no catalyst. Altogether, these improvements lead to 6.7 times less energy being used in BPM electrodialysis for the production of acid and base when a BPM with composite LBL junction is used compared to a BPM without catalyst. Thus, adding MMT clay composite LbL catalyst to BPM junctions is a promising method to improve the efficiency and reduce the energy consumption of electrochemical processes that rely on BPMs.
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Affiliation(s)
- Nadia Boulif
- Membrane Materials and Processes, Department
of Chemical Engineering and Chemistry, Eindhoven
University of Technology, P.O. Box 513, Eindhoven 5600 MB, The Netherlands
| | - Menno Houben
- Membrane Materials and Processes, Department
of Chemical Engineering and Chemistry, Eindhoven
University of Technology, P.O. Box 513, Eindhoven 5600 MB, The Netherlands
| | - Zandrie Borneman
- Membrane Materials and Processes, Department
of Chemical Engineering and Chemistry, Eindhoven
University of Technology, P.O. Box 513, Eindhoven 5600 MB, The Netherlands
| | - Kitty Nijmeijer
- Membrane Materials and Processes, Department
of Chemical Engineering and Chemistry, Eindhoven
University of Technology, P.O. Box 513, Eindhoven 5600 MB, The Netherlands
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Liang CM, Wang CC, Hung YT, Cheng HW, Yang CF. Optimization of operating parameters for 2,5-furandicarboxylic acid recovery using electrodialysis with bipolar membrane and traditional electrodialysis systems. Heliyon 2024; 10:e34706. [PMID: 39149025 PMCID: PMC11325056 DOI: 10.1016/j.heliyon.2024.e34706] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2024] [Revised: 06/30/2024] [Accepted: 07/15/2024] [Indexed: 08/17/2024] Open
Abstract
Electrodialysis (ED) is an eco-friendly and feasible method to separate or recover ionic compounds by electric field attraction and configuration of ion exchange membranes. Strain Burkholderia sp. H-2 could biotransform 5-hydroxymethylfurfural (5-HMF) into a green platform compound, 2,5-furandicarboxylic acid (FDCA), using a bioreactor system. In this study, electrodialysis with the bipolar membrane (EDBM) and traditional ED systems were applied to recover and concentrate FDCA. Artificial and real FDCA effluents of the 5-HMF biotransformation bioreactor were used as the feedstock to establish the optimal conditions for FDCA recovery. The optimal FDCA concentration and pH of the artificial FDCA effluent were 2100 mg/L and 5, respectively. The suitable current density of the EDBM was 8.93 mA/cm2. For FDCA recovery and concentration using the ED, the feedstock volume and FDCA concentration in the concentration chamber were 1.5 L and 1000 mg/L, respectively. The FDCA recovery efficiency of the real FDCA effluent was 55.6 %. Suppose the pretreatment procedure of the real bioreactor effluent is further optimized. It is believed to benefit the enhancement of FDCA recovery efficiency and reduce energy consumption.
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Affiliation(s)
- Chih-Ming Liang
- Department of Environmental Engineering and Science, Feng Chia University, Taichung, 40724, Taiwan
| | - Chun-Chin Wang
- Department of Safety Health and Environmental Engineering, Hungkuang University, Taichung, 43302, Taiwan
| | - Yi-Ting Hung
- Department of Safety Health and Environmental Engineering, National Yunlin University of Science and Technology, Yunlin, 64002, Taiwan
| | - Hao-Wei Cheng
- Department of Safety Health and Environmental Engineering, National Yunlin University of Science and Technology, Yunlin, 64002, Taiwan
| | - Chu-Fang Yang
- Department of Safety Health and Environmental Engineering, National Yunlin University of Science and Technology, Yunlin, 64002, Taiwan
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Lopez M, Cornaglia LM, Gutierrez LB, Bosko ML. Electrodialysis as a potential technology for 4-nitrophenol abatement from wastewater. ENVIRONMENTAL SCIENCE AND POLLUTION RESEARCH INTERNATIONAL 2023; 30:102198-102211. [PMID: 37665445 DOI: 10.1007/s11356-023-29510-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2023] [Accepted: 08/22/2023] [Indexed: 09/05/2023]
Abstract
4-Nitrophenol is a widely used emerging pollutant in various industries, including the production of agrochemicals, drugs, and synthetic dyes. Due to its potential environmental harmful effects, there is a need to study its reuse and removal from wastewater. This study used electrodialysis technology to separate 4-nitrophenol ions using a four-compartment stack. The effects of supporting electrolyte concentration, pH, voltages, and current density on the performance of electrodialysis for separating 4-nitrophenol were investigated. A high extraction percentage of 77% was achieved with low energy consumption (107 kWh kg-1) when high 4-nitrophenol flows and transport numbers were reached.
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Affiliation(s)
- Manuel Lopez
- Instituto de Investigaciones en Catálisis y Petroquímica, Universidad Nacional del Litoral, CONICET, Facultad de Ingeniería Química, Santiago del Estero 2829, Santa Fe, S3000AOM, Argentina
| | - Laura María Cornaglia
- Instituto de Investigaciones en Catálisis y Petroquímica, Universidad Nacional del Litoral, CONICET, Facultad de Ingeniería Química, Santiago del Estero 2829, Santa Fe, S3000AOM, Argentina
| | - Laura Beatriz Gutierrez
- Instituto de Investigaciones en Catálisis y Petroquímica, Universidad Nacional del Litoral, CONICET, Facultad de Ingeniería Química, Santiago del Estero 2829, Santa Fe, S3000AOM, Argentina
| | - María Laura Bosko
- Instituto de Investigaciones en Catálisis y Petroquímica, Universidad Nacional del Litoral, CONICET, Facultad de Ingeniería Química, Santiago del Estero 2829, Santa Fe, S3000AOM, Argentina.
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Pismenskaya N, Rybalkina O, Solonchenko K, Butylskii D, Nikonenko V. Phosphates Transfer in Pristine and Modified CJMA-2 Membrane during Electrodialysis Processing of Na xH (3-x)PO 4 Solutions with pH from 4.5 to 9.9. MEMBRANES 2023; 13:647. [PMID: 37505013 PMCID: PMC10386648 DOI: 10.3390/membranes13070647] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2023] [Revised: 06/27/2023] [Accepted: 07/03/2023] [Indexed: 07/29/2023]
Abstract
Phosphate recovery from different second streams using electrodialysis (ED) is a promising step to a nutrients circular economy. However, the relatively low ED performance hinders the widespread adoption of this environmentally sound method. The formation of "bonded species" between phosphates and the weakly basic fixed groups (primary and secondary amines) of the anion exchange membrane can be the cause of decrease in current efficiency and increase in energy consumption. ED processing of NaxH(3-x)PO4 alkaline solutions and the use of intense current modes promote the formation of a bipolar junction from negatively charged bound species and positively charged fixed groups. This phenomenon causes a change in the shape of current-voltage curves, increase in resistance, and an enhancement in proton generation during long-term operation of anion-exchange membrane with weakly basic fixed groups. Shielding of primary and secondary amines with a modifier containing quaternary ammonium bases significantly improves ED performance in the recovery of phosphates from NaxH(3-x)PO4 solution with pH 4.5. Indeed, in the limiting and underlimiting current modes, 40% of phosphates are recovered 1.3 times faster, and energy consumption is reduced by 1.9 times in the case of the modified membrane compared to the pristine one. Studies were performed using a new commercial anion exchange membrane CJMA-2.
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Affiliation(s)
- Natalia Pismenskaya
- Russian Federation, Kuban State University, 149, Stavropolskaya Str., 350040 Krasnodar, Russia
| | - Olesya Rybalkina
- Russian Federation, Kuban State University, 149, Stavropolskaya Str., 350040 Krasnodar, Russia
| | - Ksenia Solonchenko
- Russian Federation, Kuban State University, 149, Stavropolskaya Str., 350040 Krasnodar, Russia
| | - Dmitrii Butylskii
- Russian Federation, Kuban State University, 149, Stavropolskaya Str., 350040 Krasnodar, Russia
| | - Victor Nikonenko
- Russian Federation, Kuban State University, 149, Stavropolskaya Str., 350040 Krasnodar, Russia
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Song Y, Lee YG, Ahn YS, Nguyen DT, Bae HJ. Utilization of bamboo as biorefinery feedstock: Co-production of xylo-oligosaccharide with succinic acid and lactic acid. BIORESOURCE TECHNOLOGY 2023; 372:128694. [PMID: 36731613 DOI: 10.1016/j.biortech.2023.128694] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/28/2022] [Revised: 01/26/2023] [Accepted: 01/28/2023] [Indexed: 06/18/2023]
Abstract
Herein, we investigated the possibility of co-producing xylo-oligosaccharides (XOSs) from bamboo, as value-added products, along with succinic and lactic acids, as platform chemicals. Xylan was extracted from bamboo using the alkali method under mild conditions. From xylan, XOSs were produced by partial enzymatic hydrolysis at a conversion rate of 83.9%, and all reaction conditions resulted in similar degrees of polymerization. Hydrogen peroxide-acetic acid (HPAC) pretreatment effectively removed lignin from NaOH-treated bamboo, and the enzymatic hydrolytic yield of NaOH and HPAC-treated bamboo was 84.3% of the theoretical yield. The production of succinic and lactic acids from the hydrolysate resulted in conversion rates of approximately 63.2% and 91.3% of the theoretical yield using Corynebacterium glutamicum Δldh and Actinobacillus succinogenes, respectively, under facultative anaerobic conditions. This study demonstrates that bamboo has a high potential to produce value-added products using a biorefinery process and is an alternative resource for compounds typically derived from petroleum.
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Affiliation(s)
- Younho Song
- Bio-energy Research Center, Chonnam National University, Gwangju 500-757, Republic of Korea
| | - Yoon Gyo Lee
- Bio-energy Research Center, Chonnam National University, Gwangju 500-757, Republic of Korea
| | - Young Sang Ahn
- Department of Forest Resources, Chonnam National University, Gwangju 500-757, Republic of Korea
| | | | - Hyeun-Jong Bae
- Bio-energy Research Center, Chonnam National University, Gwangju 500-757, Republic of Korea.
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Cournoyer A, Bazinet L. Electrodialysis Processes an Answer to Industrial Sustainability: Toward the Concept of Eco-Circular Economy?-A Review. MEMBRANES 2023; 13:205. [PMID: 36837708 PMCID: PMC9962313 DOI: 10.3390/membranes13020205] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/11/2023] [Revised: 01/25/2023] [Accepted: 01/28/2023] [Indexed: 06/18/2023]
Abstract
Wastewater and by-product treatments are substantial issues with consequences for our society, both in terms of environmental impacts and economic losses. With an overall global objective of sustainable development, it is essential to offer eco-efficient and circular solutions. Indeed, one of the major solutions to limit the use of new raw materials and the production of wastes is the transition toward a circular economy. Industries must find ways to close their production loops. Electrodialysis (ED) processes such as conventional ED, selective ED, ED with bipolar membranes, and ED with filtration membranes are processes that have demonstrated, in the past decades and recently, their potential and eco-efficiency. This review presents the most recent valorization opportunities among different industrial sectors (water, food, mining, chemistry, etc.) to manage waste or by-product resources through electrodialysis processes and to improve global industrial sustainability by moving toward circular processes. The limitations of existing studies are raised, especially concerning eco-efficiency. Indeed, electrodialysis processes can be optimized to decrease energy consumption and costs, and to increase efficiency; however, eco-efficiency scores should be determined to compare electrodialysis with conventional processes and support their advantages. The review shows the high potential of the different types of electrodialysis processes to treat wastewaters and liquid by-products in order to add value or to generate new raw materials. It also highlights the strong interest in using eco-efficient processes within a circular economy. The ideal scenario for sustainable development would be to make a transition toward an eco-circular economy.
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Affiliation(s)
| | - Laurent Bazinet
- Department of Food Sciences, Laboratoire de Transformation Alimentaire et Procédés ÉlectroMembranaires (LTAPEM, Laboratory of Food Processing and ElectroMembrane Processes), Institute of Nutrition and Functional Foods (INAF), Dairy Research Center (STELA), Université Laval, Quebec, QC G1V 0A6, Canada
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Zhou H, Ju P, Hu S, Shi L, Yuan W, Chen D, Wang Y, Shi S. Separation of Hydrochloric Acid and Oxalic Acid from Rare Earth Oxalic Acid Precipitation Mother Liquor by Electrodialysis. MEMBRANES 2023; 13:162. [PMID: 36837666 PMCID: PMC9964671 DOI: 10.3390/membranes13020162] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/30/2022] [Revised: 12/29/2022] [Accepted: 01/13/2023] [Indexed: 06/18/2023]
Abstract
In this study, the hydrochloric acid from rare earth oxalic acid precipitation mother liquor was separated by electrodialysis (ED) with different anion exchange membranes, including selective anion exchange membrane (SAEM), polymer alloy anion exchange membrane (PAAEM), and homogenous anion exchange membrane (HAEM). In addition to actual wastewater, nine types of simulated solutions with different concentrations of hydrochloric acid and oxalic acid were used in the experiments. The results indicated that the hydrochloric acid could be separated effectively by electrodialysis with SAEM from simulated and real rare earth oxalic acid precipitation mother liquor under the operating voltage 15 V and ampere 2.2 A, in which the hydrochloric acid obtained in the concentrate chamber of ED is of higher purity (>91.5%) generally. It was found that the separation effect of the two acids was related to the concentrations and molar ratios of hydrochloric acid and oxalic acid contained in their mixtures. The SEM images and ESD-mapping analyses indicated that membrane fouling appeared on the surface of ACS and CSE at the diluted side of the ED membrane stack when electrodialysis was used to treat the real rare earth oxalic acid precipitation mother liquor. Fe, Yb, Al, and Dy were found in the CSE membrane section, and organic compounds containing carbon and sulfur were attached to the surface of the ACS. The results also indicated that the real rare earth precipitation mother liquor needed to be pretreated before the separation of hydrochloric acid and oxalic acid by electrodialysis.
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Affiliation(s)
- Hengcheng Zhou
- College of Resources and Environment, Nanchang University, Nanchang 330031, China
- Ganjiang Innovation Academy, Chinese Academy of Sciences, Ganzhou 341119, China
- Jiangxi Province Key Laboratory of Cleaner Production of Rare Earths, Ganzhou 341119, China
| | - Peihai Ju
- Ganjiang Innovation Academy, Chinese Academy of Sciences, Ganzhou 341119, China
- Jiangxi Province Key Laboratory of Cleaner Production of Rare Earths, Ganzhou 341119, China
| | - Shaowei Hu
- Technology Center of Angang Steel Co., Ltd., Anshan 114009, China
| | - Lili Shi
- College of Resources and Environment, Nanchang University, Nanchang 330031, China
- Ganjiang Innovation Academy, Chinese Academy of Sciences, Ganzhou 341119, China
- Jiangxi Province Key Laboratory of Cleaner Production of Rare Earths, Ganzhou 341119, China
| | - Wenjing Yuan
- Ganjiang Innovation Academy, Chinese Academy of Sciences, Ganzhou 341119, China
- Jiangxi Province Key Laboratory of Cleaner Production of Rare Earths, Ganzhou 341119, China
| | - Dongdong Chen
- Ganjiang Innovation Academy, Chinese Academy of Sciences, Ganzhou 341119, China
- Jiangxi Province Key Laboratory of Cleaner Production of Rare Earths, Ganzhou 341119, China
| | - Yujie Wang
- Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China
| | - Shaoyuan Shi
- College of Resources and Environment, Nanchang University, Nanchang 330031, China
- Ganjiang Innovation Academy, Chinese Academy of Sciences, Ganzhou 341119, China
- Jiangxi Province Key Laboratory of Cleaner Production of Rare Earths, Ganzhou 341119, China
- Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China
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Maitz S, Wernsperger L, Kienberger M. Isolation of Carboxylic Acids and NaOH from Kraft Black Liquor with a Membrane-Based Process Sequence. MEMBRANES 2023; 13:92. [PMID: 36676899 PMCID: PMC9863791 DOI: 10.3390/membranes13010092] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/12/2022] [Revised: 01/05/2023] [Accepted: 01/06/2023] [Indexed: 06/17/2023]
Abstract
In kraft pulping, large quantities of biomass degradation products dissolved in the black liquor are incinerated for power generation and chemical recovery. The black liquor is, however, a promising feedstock for carboxylic acids and lignin. Efficient fractionation of black liquor can be used to isolate these compounds and recycle the pulping chemicals. The present work discusses the fractionation of industrial black liquor by a sequence of nanofiltration and bipolar membrane electrodialysis units. Nanofiltration led to retention of the majority of lignin in the retentate and to a significant concentration increase in low-molecular-weight carboxylic acids, such as formic, acetic, glycolic and lactic acids, in the permeate. Subsequent treatment with bipolar membrane electrodialysis showed the potential for simultaneous recovery of acids in the acid compartment and the pulping chemical NaOH in the base compartment. The residual lignin was completely retained by the used membranes. Diffusion of acids to the base compartment and the low current density, however, limited the yield of acids and the current efficiency. In experiments with a black liquor model solution under optimized conditions, NaOH and acid recoveries of 68-72% were achieved.
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Liang X, Guo Y. High-efficiency recovery and regeneration of choline-polyol deep eutectic solvent for biorefinery via bipolar membrane electrodialysis and ultrafiltration. BIORESOURCE TECHNOLOGY 2022; 362:127805. [PMID: 36007766 DOI: 10.1016/j.biortech.2022.127805] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2022] [Revised: 08/14/2022] [Accepted: 08/16/2022] [Indexed: 06/15/2023]
Abstract
Deep eutectic solvents (DES) have been widely studied for interesting solvent properties in resources utilization and green conversion of energy. Complex composition of DES and lack of recovery techniques restricts their further scale-up application. Exploring efficient recovery and regeneration methodology of DES in biorefinery could be beneficial for low-carbon circular bioeconomy. Recovery and regeneration of choline-polyol DES (choline chloride-ethylene glycol, ChCl-EG) after biomass pretreatment was studied using bipolar membrane electrodialysis (BMED) with ultrafiltration (UF). UF-BMED treatment worked based on the interception of macromolecular degradation products in pretreatment liquor and regional recovery of Ch+, Cl- with EG. Influence of major parameters on DES recovery performance was studied with emphasis. Maximum recovery ratio of DES reached 97.4% and minimum specific energy consumption of DES recovery approached 6.0 kW·h/kg. Cognition gained from this research revealed an efficient technique for DES recycling after biorefinery.
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Affiliation(s)
- Xiaocong Liang
- School of Energy and Power Engineering, North University of China, Taiyuan 030051, China.
| | - Yongkang Guo
- School of Energy and Power Engineering, North University of China, Taiyuan 030051, China
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Karpenko TV, Kovalev NV, Kirillova KR, Achoh AR, Melnikov SS, Sheldeshov NV, Zabolotsky VI. Competing Transport of Malonic and Acetic acids across Commercial and Modified RALEX AMH Anion-Exchange Membranes. MEMBRANES AND MEMBRANE TECHNOLOGIES 2022. [DOI: 10.1134/s2517751622020056] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Pismenskaya N, Rybalkina O, Moroz I, Mareev S, Nikonenko V. Influence of Electroconvection on Chronopotentiograms of an Anion-Exchange Membrane in Solutions of Weak Polybasic Acid Salts. Int J Mol Sci 2021; 22:ijms222413518. [PMID: 34948329 PMCID: PMC8708104 DOI: 10.3390/ijms222413518] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2021] [Revised: 12/10/2021] [Accepted: 12/13/2021] [Indexed: 12/25/2022] Open
Abstract
Visualization of electroconvective (EC) vortices at the undulated surface of an AMX anion-exchange membrane (Astom, Osaka, Japan) was carried out in parallel with the measurement of chronopotentiograms. Weak polybasic acid salts, including 0.02 M solutions of tartaric (NaHT), phosphoric (NaH2PO4), and citric (NaH2Cit) acids salts, and NaCl were investigated. It was shown that, for a given current density normalized to the theoretical limiting current calculated by the Leveque equation (i/ilimtheor), EC vortex zone thickness, dEC, decreases in the order NaCl > NaHT > NaH2PO4 > NaH2Cit. This order is inverse to the increase in the intensity of proton generation in the membrane systems under study. The higher the intensity of proton generation, the lower the electroconvection. This is due to the fact that protons released into the depleted solution reduce the space charge density, which is the driver of EC. In all studied systems, a region in chronopotentiograms between the rapid growth of the potential drop and the attainment of its stationary values corresponds to the appearance of EC vortex clusters. The amplitude of the potential drop oscillations in the chronopotentiograms is proportional to the size of the observed vortex clusters.
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