Perfluorinated Sulfonic Acid-Based Ionomers: Current State and Prospects.

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Learn more: PMC Disclaimer | PMC Copyright Notice Polymers (Basel) . 2026 Mar 31;18(7):848. doi: 10.3390/polym18070848 Search in PMC Search in PubMed View in NLM Catalog Add to search Perfluorinated Sulfonic Acid-Based Ionomers: Current State and Prospects Valeriy A Kozlov Valeriy A Kozlov 1 Prokhorov General Physics Institute of the Russian Academy of Sciences, Vavilov Str. 38, 119991 Moscow, Russia; [email protected] (V.A.K.); [email protected] (S.M.K.); [email protected] (S.V.G.) 2 Department of Fundamental Sciences, Bauman Moscow State Technical University, 5 2nd Baumanskaya St., 105005 Moscow, Russia Find articles by Valeriy A Kozlov 1, 2 , Barry W Ninham Barry W Ninham 3 Materials Physics (Formerly Department of Applied Mathematics), Research School of Physics, Australian National University, Canberra, ACT 2600, Australia; [email protected] Find articles by Barry W Ninham 3 , Sergey M Kuznetsov Sergey M Kuznetsov 1 Prokhorov General Physics Institute of the Russian Academy of Sciences, Vavilov Str. 38, 119991 Moscow, Russia; [email protected] (V.A.K.); [email protected] (S.M.K.); [email protected] (S.V.G.) Find articles by Sergey M Kuznetsov 1 , Sergey V Gudkov Sergey V Gudkov 1 Prokhorov General Physics Institute of the Russian Academy of Sciences, Vavilov Str. 38, 119991 Moscow, Russia; [email protected] (V.A.K.); [email protected] (S.M.K.); [email protected] (S.V.G.) 2 Department of Fundamental Sciences, Bauman Moscow State Technical University, 5 2nd Baumanskaya St., 105005 Moscow, Russia Find articles by Sergey V Gudkov 1, 2 , Nikolai F Bunkin Nikolai F Bunkin 2 Department of Fundamental Sciences, Bauman Moscow State Technical University, 5 2nd Baumanskaya St., 105005 Moscow, Russia Find articles by Nikolai F Bunkin 2, * Editor: Chengji Zhao Author information Article notes Copyright and License information 1 Prokhorov General Physics Institute of the Russian Academy of Sciences, Vavilov Str. 38, 119991 Moscow, Russia; [email protected] (V.A.K.); [email protected] (S.M.K.); [email protected] (S.V.G.) 2 Department of Fundamental Sciences, Bauman Moscow State Technical University, 5 2nd Baumanskaya St., 105005 Moscow, Russia 3 Materials Physics (Formerly Department of Applied Mathematics), Research School of Physics, Australian National University, Canberra, ACT 2600, Australia; [email protected] * Correspondence: [email protected] Roles Chengji Zhao : Academic Editor Received 2026 Feb 23; Revised 2026 Mar 22; Accepted 2026 Mar 25; Collection date 2026 Apr. © 2026 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license . PMC Copyright notice PMCID: PMC13074565  PMID: 41977599 Abstract This review summarizes the current state of research on perfluorinated sulfonic acid (PFSA) ionomers, including both classic Nafion and a wide range of alternative chemical modifications, as well as new-generation composite and stabilized membranes. The accumulation of a large body of experimental and modeling data in recent years highlights the need to rethink the differences between traditional ionomers and their modern counterparts, which is especially relevant in light of the development of new materials and their expanding applications. PFSA ionomers have a rich research history, playing a key role in the development of polymer-electrolyte fuel cell technologies and other electrochemical systems. At the same time, these materials have become a unique interdisciplinary platform, stimulating the development of new methods of characterization, modeling, and analysis. In PFSA research, technological progress is closely intertwined with fundamental science, encompassing electrochemistry, polymer physics, mechanics, chemistry, and multiscale modeling. The data we collected allowed us to identify new structural and functional patterns, analyze the behavior of ionomers in various states—from thin films and interfaces to bulk membranes—and summarize numerous previously fragmented relationships. Keywords: perfluorinated sulfonic acid ionomers, phase separation, proton conductivity, proton-exchange membrane fuel cell, Nafion, hydrophobic backbone, hydrophilic ionic fragments, small-angle X-ray scattering, small-angle neutron scattering, fuel cells, equivalent weight, heat treatment, Schroeder’s paradox 1. Introduction Perfluoro sulfonic acid ionomers (PFSAs) are one of the most studied and sought-after classes of ion-conducting materials, and have driven progress in electrochemical technology over the past few decades. First introduced in the 1960s and 1970s, PFSAs quickly gained a prominent position in applications such as polymer electrolyte fuel cells (PEFCs), water electrolyzers, electrodialysis systems, and membrane separators. Their ability to simultaneously exhibit high proton conductivity, chemical inertness, resistance to extreme conditions, and stable mechanical structure makes PFSAs a unique class of materials with no direct counterparts in terms of their combined properties. Their functionality is based on the specific organization of their macro- and nanostructures. A classic example is Nafion, developed by DuPont [ 1 ]. It is a copolymer of polytetrafluoroethylene with perfluorinated side chains terminated by sulfonic acid groups. The contrast between the hydrophobic backbone and the hydrophilic ionic fragments leads to the formation of a phase-separated morphology that includes ion channels and domains of various sizes. These domains are filled with water and facilitate the transport of protons, while the polymer matrix maintains mechanical stability and prevents the transfer of cations and unwanted gas impurities. The complex interactions between structural units at different length scales contribute to the unique combination of transport, mechanical, and chemical properties of PFSAs. Over the past two decades, research on PFSAs has expanded beyond the description of chemical composition and standard performance properties. The development of advanced diagnostic and modeling techniques, such as small-angle X-ray and neutron scattering (SAXS, SANS), molecular dynamics, positron annihilation lifetime spectroscopy (PALS), quasi-elastic neutron scattering (QENS), and X-ray imaging, has significantly deepened our understanding of their intramolecular dynamics, water configuration, and structural–functional correlations. These techniques have revealed the complex nature of hydration in PFSAs, including the transitions between bound and free water, cluster formation, domain percolation, and long-range relaxation processes that govern membrane behavior under a wide range of external conditions. In parallel with the progress in diagnostics, the chemistry of the ionomers themselves has actively developed. In addition to Nafion, PFSAs with short side chains (SSC), multi-acid structures, modified variants with altered acidity or hydrophilicity, as well as composite membranes incorporating reinforcement layers, fillers, or stabilizing additives, have been developed. These developments aim to enhance PFSAs mechanical stability, reduce membrane thickness, improve conductivity in low-humidity conditions, and expand their operating temperature range. It has become evident that even small changes in equivalent weight, side chain chemistry, or thermal treatment protocol can significantly impact their morphology and functional characteristics. Recent studies have also revealed the importance of kinetic aspects: PFSAs exhibit pronounced long-term relaxation effects that are dependent on temperature, humidity, and pre-treatment, leading to slow changes in domain size, water content, conductivity, and mechanical properties. These processes significantly impact the interpretation of experimental data and require careful consideration when comparing the results of different studies. Finally, the expansion of the range of PFSAs’ applications has led to the need to study the behavior of ionomers not only in the traditional form of thick membranes, but also in thin-film states, composite structures, and interfaces with other materials. PFSA thin films (less than 100 nm thick), which are widely used in cathode and anode layers of PEMFCs, exhibit significantly different behavior than bulk membranes: altered morphology, different kinetics of adsorption and desorption, enhanced surface effects and a different balance of mechanical stresses. All of the above facts are confirmed by the growing interest of researchers and the number of published publications and search queries on relevant topics, especially over the past ten years. Figure 1 shows an infographic showing the number of articles that can be found using these keywords, as well as a comparison of the number of search queries for various keywords on the Internet. Figure 1. Open in a new tab Number of articles published with the specified keywords in the PubMed database ( left and center graphs), comparison of the number of search queries for various keywords according to Google ( right graph). Thus, the current research on PFSAs is an interdisciplinary field that includes polymer chemistry, soft matter physics, electrochemistry, materials science, and numerical modeling. Their relevance is determined by the needs of the new energy industry, which requires more productive, durable and stable membranes. The systematization of accumulated data, the identification of key structural and functional dependencies, and the integration of new approaches to chemical modification and characterization are becoming the most important tasks in the current research, which form the basis for the further development of these materials. 2. Overview of Research in PFSA Ionomers Nafion is a statistical copolymer consisting of an electrically neutral semi-crystalline polymer base (polytetrafluoroethylene (PTFE)) and randomly binding side chains with the side ionic group SO 3 − (vinyl ester of polysulfonyl fluoride, which is bound to a specific counterion, for example, SO 3 − + H + → SO 3 H). The dissimilar nature of the covalently bonded side group and the main chain leads to a natural phase separation, which is enhanced by solvation when water or solvent molecules are introduced into the volume of the polymer matrix. It is this phase-separated morphology that endows PFSAs with their unique ion and solvent transport capabilities. Thus, PFSAs are, in fact, multifunctional polymers with transport and mechanical functions regulated by the morphology of PFSAs in the presence of electrostatic interaction. However, this morphology also depends on various interactions and the balance between the mechanical (deformation) energy associated with the hydrophobic backbone and the chemical (entropic) energy associated with the hydration of the hydrophilic ionic groups of their side chains. This balance can be controlled, and it is influenced by a wide range of environmental and material parameters that determine the relationship between the structure and properties of PFSAs. Improving the overall performance of a membrane for its specific application requires an understanding of how various factors (e.g., mechanical, electrochemical, and environmental) affect the ionomer. Any efforts to improve transportation functions and performance can undermine the mechanical stability and durability of the device. Therefore, the task of improving the quality of ion transfer without compromising mechanical integrity is important, and its solution requires optimization of the phase-separated morphology of the polymer matrix structure. Figure 2 shows, along with the general chemical formula of PFSA ionomers with various modifications, the key chemical and structural parameters that determine the phase-separated morphology and properties of the ionomers. Figure 2. Open in a new tab General chemical formula for PFSA ionomers of various forms ( left ), as well as key chemical and structural parameters that determine the phase-separated morphology and properties of the ionomers ( right ). In the ( right ) panel we schematically show the generation of new nanophases: crystalline phase, amorphous phase, ionic phase, hydration shell, bound and free water. These phases are spatially separated in the process of hydration. Ionomeric chemistry techniques are the most effective way to control morphology. PFSAs can be characterized by the following: The equivalent weight (EW) of the dry polymer per ionic group, i.e., g p o l y m e r / m o l i o n i c − g r o u p , which is inversely proportional to the ion exchange capacity (IEC); Chemical composition and side chain length. The equivalent weight is directly dependent on the number of m blocks of tetrafluoroethylene in the backbone, EW = 100 m + MW, where MW is the molecular weight of the side chain. Thus, the length of the side chain and the length of the backbone ( m ) control the equivalent weight and the chemical structure of the PFSA ionomer, as well as its behavior during swelling in water. Additionally, the counterion that neutralizes the SO 3 − group is crucial in determining the structure of the ionomer. Despite the unquestioned dominance of Nafion in published studies, PFSAs and IECs with short side chains have received significant attention in an attempt to optimize functionality. In particular, these ionomers include polymers from 3M, Solvay Specialty Polymers (i.e., Aquivion, formerly known as Dow SSC ionomer from Dow Chemical Company), and Asahi Glass (Flemion), as well as reinforced composite PFSAs from W.L. Gore and Associates. With the same chemical composition of the main chain, these PFSA ionomers are classified based on the length of their side chain and EW. For example, Aquivion PFSA is commonly classified as a short side chain (SSC) PFSA, while Nafion can be considered a long side chain (LSC) PFSA. This terminology is less common, and in general, the classification of side chains based on their length may vary depending on the context. For instance, 3M’s PFSA ionomer has a shorter side chain compared to Nafion, but it is not considered an SSC, unlike PFSA Dow or Aquivion. PFSA ionomers with shorter side chains and higher IECs are increasingly being studied [ 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 ] due to their enhanced transport properties and high performance in devices [ 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 ]. Not only the length of the side chain, but also its chemical composition determines the properties of a PFSA, which may be even more relevant and important when studying ionomers in a dispersed state or the interfaces they form with other materials (e.g., thin films or electrode structures). Another trend is that the thickness of PFSA membranes is decreasing, which is due to the need to reduce the overall resistance of ion transport, but this tends to accelerate gas leakage, which subsequently reduces the efficiency of molecular hydrogen generation in the system [ 18 ]. This trend is particularly noticeable in polymer electrolyte fuel cells (PEMFCs), where there is a need for thinner but stable ionomers that can withstand harsh chemical and environmental conditions while meeting the target durability requirements for commercialization [ 1 , 19 ]. The most comprehensive review on Nafion was published by Mauritz and Moore in 2004 [ 1 ]. This article provides an extensive overview of the literature on Nafion at that time, covering the chemical structure of Nafion, morphological descriptions based on small- and wide-angle X-ray scattering (SAXS, WAXS), microscopic studies, the behavior of water and solvents within the membrane, conductivity, and molecular structure based on molecular dynamics simulations. Most studies conducted before 2005 used Nafion 117, with a thickness of 175 μm (or a similar generation of N11x with a different thickness). In the last decade, there has been a shift towards the development of dispersion-cast Nafion membranes (NR-21x) with a thickness ranging from 25 to 50 μm, as well as stabilized membranes that offer various functional capabilities, particularly in terms of ion transport and mechanical properties. For these Nafion membranes, the “ x ” designation represents the thickness in mils (1/1000 of an inch, equivalent to 0.0254 mm or 25.4 μm). For example, N112, x = 2 mils, with a nominal thickness of 50 μm. Thus, the extensive collection of newer PFSA studies can be classified as follows: New modeling and diagnostic studies of Nafion; New PFSA ionomers; New applications outside of PFSA chemistry with different ionomer behavior. Over the past two decades, a vast amount of research on Nafion has been conducted, which has significantly improved our understanding of its morphology and the relationship between its structural and functional properties. For example, special reviews have been published on its chemical structure in the context of other sulfonated ionomers [ 20 ] or PFSAs [ 8 ], as well as its transport mechanisms [ 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 ], morphology [ 28 , 29 , 30 ], modeling [ 21 , 30 , 31 ], polyacid ion effects [ 32 , 33 , 34 , 35 ], ultrathin film interface effects [ 36 , 37 ], and the use of nanofillers and durability [ 18 , 19 , 30 ] from the perspective of PEMFCs. The establishment of “dynamic crosslinks” between the particles of the nanofiller and the Nafion side groups may improve the mechanical properties of Nafion-based hybrid membranes, stabilize their system, and inhibit swelling in the hydrophilic domains of the Nafion host, reducing water uptake. Kusoglu and Weber have made significant contributions to the analysis of PFSA data by summarizing the current state of ionomer research [ 38 ]. It is interesting to note that the changing themes and focus of these reviews reflect the growing interest in PFSA ionomers for various applications. The increasing body of literature has also led to the emergence of reviews on very specific topics that were not of much interest twenty years ago (e.g., alternative membranes, stabilizers, and advanced on-site diagnostics). Consequently, while our understanding of PFSAs is evolving with an ever-expanding database of properties, the evolving requirements and applications are constantly presenting new challenges, resulting in a highly dynamic field of research. When discussing “alternative membranes” and “other sulfonated ionomers,” it is important to compare PFSAs with other materials to optimize performance (e.g., in order to improve conductivity in low humidity conditions). In this regard, it is worth mentioning a recent review that discusses the progress of research on sulfonated poly(ether ether ketone) (SPEEK) and its composite membranes in proton exchange membrane fuel cells (PEMFCs) [ 39 ]. SPEEK is a perspective material for replacing traditional perfluorosulfonic acid membranes due to its excellent thermal stability, mechanical properties, and tunable proton conductivity. By adjusting the degree of sulfonation (DS) of SPEEK, the hydrophilicity and proton conductivity of the membrane can be controlled, while also balancing its mechanical, thermal, and chemical stability. We can conclude that “alternative membranes”, including non-PFSA ionomers like SPEEK, have shown promise in enhancing PEMFC performance under low-humidity conditions, as reviewed in [ 39 ]. Since the early 2000s, several new topics have emerged, including an understanding of the quasi-equilibrium states of PFSA ionomers, the importance of thermal and manufacturing history, and the study of PFSAs from the perspective of thin-film physics. Recent advancements include the influence of side chains and fragments, surface characterization, a deeper understanding of Schroeder’s paradox [ 40 ], the impact of casting and solvent, the introduction of additives and stabilizers to reduce degradation, time-dependent conductivity and mechanical properties, thin films (thickness < 100 nm), the effect of stretching and compression, additional diagnostic methods such as QENS, PALS, neutron and X-ray imaging, BES, and SAXS with sliding fall (GISAXS), as well as more detailed molecular dynamics simulations. Interestingly, research and focus have shifted from more traditional methods (macroscopic water absorption and transport, SAXS, differential scanning calorimetry) to more advanced techniques that can study the structural–transport correlations of PFSAs at various time and length scales. As a result, PFSAs have become widely used as reference materials in new research and the implementation of advanced characterization methods for fundamental science. The above-mentioned studies need to be critically compared and contrasted so that general trends and conclusions can be identified, which will be done in this comprehensive review. In addition, we will also provide a new perspective on the structural and functional relationships of PFSAs by comparing different datasets on adsorption, transport, measurements of mechanical properties, and morphological features for both Nafion and related PFSA substances. 3. The Effect of Equivalent Mass (EW) and Side Chain Chemistry As noted above, EW is a critical parameter affecting the behavior of an ionomer and its ionic conductivity. However, the question remains of how they affect other transport properties of the ionomer, as well as its dynamic behavior, mechanical properties, surface, and structure in the case of a thin film. EW is measured using acid–base titration, elemental analysis, or infrared spectroscopy. There is a large variation (~10%) in the measured EWs, which may be due to differences between batches and morphological difficulties of a dispersive nature [ 41 ]. The EWs of PFSA ionomers studied in the literature range from 600 to 1500 g/mol, with 1100 g/mol being the most common for Nafion. EW plays a crucial role in balancing transport and stability. For example, 3M ionomers begin to significantly lose their hardness in water and act as a gel when their EW drops below 800 g/mol [ 9 , 10 , 12 ]. Despite the fact that the most frequently studied PFSA is Nafion (its EW = 1100), which dominates published property datasets, the effect of EW on membrane properties and structure has always been of interest for a wide range of EW studies among commercially available PFSAs. Earlier studies conducted by DuPont researchers reported properties of Nafion with various EWs, including its nanostructure, crystallinity, water absorption, and conductivity. They were followed by similar studies on the effect of EW on PFSA swelling and the relationship between structure and properties [ 42 , 43 , 44 ], including PFSA membranes with a shorter side chain (SSC Dow) [ 44 , 45 , 46 , 47 , 48 ]. Relatively recent studies of the effects of EW and side chains have included studies of water absorption [ 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 ], morphology [ 56 , 57 , 58 , 59 , 60 , 61 , 62 ], conductivity, ion diffusion, and other properties affecting ionic conductivity [ 63 , 64 , 65 , 66 , 67 , 68 , 69 , 70 , 71 ], thermal and mechanical properties [ 72 , 73 , 74 , 75 , 76 , 77 ], as well as molecular modeling [ 78 , 79 , 80 , 81 , 82 , 83 , 84 ]. For example, the authors of [ 49 ] demonstrated that membranes with low EW show higher water absorption, while with increasing hydration or temperature, the mechanical properties of the membranes deteriorate. Note that in a recent paper [ 85 ], it was experimentally shown that ionic conductivity is completely controlled by the equivalent weight of PFSA membranes. It was shown in [ 59 ] that with a decrease in EW, there is an improvement in the microphase separation of hydrophilic and hydrophobic domains: membranes with low EW exhibit a narrower distribution of hydrophilic domains. In addition, short side chains (C2 structures in Aquivion ionomers) create dense packing, while long side chains (C4 structures in 3M) form a sparser structure [ 59 ]. As for links with thermal and mechanical properties, tests of a membrane with a low EW at elevated temperatures showed a lower degree of degradation and better mechanical stability than membranes with higher EWs [ 14 ]. This high thermal stability is due to the denser packing of the side chains. Thus, a large number of studies show that the above parameters are closely interrelated and their optimization is critically important for achieving high-quality membranes in fuel cells. More recent studies have advanced towards the study of alternative chemical compositions of PFSAs, such as multiacid ionomers containing several acid groups on the side chain, for example, based on aromatic sulfonic acids (orthobiscids) or perfluorinated side chains (perfluorimidic acids) [ 86 , 87 , 88 , 89 , 90 , 91 , 92 ]. Due to certain peculiarities of the chemical composition of EW and side chains, the chemical and mechanical properties of PFSAs are determined by their phase-separated morphology. Gas transport through PFSA ionomers involves both hydrophilic and hydrophobic pathways, and the relative contribution of each varies with hydration level. At low water content, gas transport through the hydrophobic backbone phase becomes significant. Improvements in membrane chemistry have paved the way for thinner membranes that are chemically and mechanically stable. This can be seen in the continuous decrease in the thickness of commercial PFSA membranes; unlike N117 with a thickness of 175 microns, which was widely studied in the 90s and early 2000s and discussed in [ 1 ], many recent studies have studied thinner PFSA ionomers, membranes with thicknesses of 25 microns or thinner (N211, ionomers 3M, Aquivion, etc.), as well as Nafion XL and Gore-Select, with a thickness of about 5 microns. 4. Effects of Heat Treatment It is well known that the morphology and properties of PFSA membranes (extruded or cast) strongly depend on their heating protocol and on heat treatment processes such as pre-boiling (also known as expanded form) in liquid water or heating at higher temperatures to cause annealing (i.e., to give crystallinity) [ 93 , 94 , 95 , 96 , 97 , 98 , 99 , 100 ], which significantly improve the performance of fuel cells [ 101 , 102 , 103 , 104 , 105 , 106 , 107 , 108 , 109 , 110 , 111 , 112 , 113 , 114 , 115 ]. PFSA membranes are prone to contamination and may exhibit continuous changes in structure and properties over time (for example, the phenomenon of physical aging). Thus, it is common practice to pretreat the membrane by boiling it in peroxide reagents (purification), sulfuric acids (reprotonation), and water (boiling-induced rehydration) with a precisely specified duration and concentration, varying from one study to another, although with similar end states. Such heat treatment processes have shown that they can change the following parameters: Water absorption [ 116 , 117 , 118 , 119 , 120 , 121 , 122 ]; Transfer coefficients (e.g., diffusion coefficient) [ 112 , 117 ]; Density [ 102 , 123 ]; Ionic permeability [ 120 , 124 , 125 ]; Ionic conductivity [ 124 , 125 , 126 , 127 , 128 , 129 , 130 ]; Selectivity [ 129 , 131 ]; Mechanical properties [ 132 , 133 , 134 , 135 , 136 , 137 , 138 , 139 ]; Thermal stability [ 111 , 140 , 141 , 142 , 143 , 144 , 145 , 146 , 147 ]; Phase nanostructure and/or crystallinity [ 147 , 148 , 149 , 150 , 151 ]; The topology of the surface [ 109 , 110 , 152 ]. Such changes make it difficult to compare studies in the literature if their preprocessing conditions have not been described in detail. For example, the surface ionic activity of extruded Nafion membranes is lower in annealed form, but it increases when processed in acidic solutions [ 93 , 116 ]. In addition, experiments with small-angle X-ray scattering have shown that pre-boiling of a PFSA membrane increases water absorption and sets the distance between the water domains to the maximum value compared to the annealed membranes [ 111 , 121 , 153 ]. In general, there is a consensus that the appropriate preprocessing process establishes a quasi-equilibrium state. However, even with new dispersion-cast and/or stabilized membranes with a decrease in their equivalent mass, factors such as the nature of the solvent, casting, additives, and post-annealing processes still need to be studied and optimized, as they strongly affect the properties of the membrane and are controlled by physicochemical interactions and morphology. 5. Determination of Quasi-Equilibrium State and Long-Term Effects When the ionomer is in equilibrium, there is a balance between chemical and mechanical energies that change continuously over time as a result of the complex nanophase separation of the semi-crystalline backbone and ion-rich aqueous domains. The total relaxation or equilibrium times measured for many PFSA properties are much longer than typical experimental observation times. Changes in water absorption and morphology were observed after balancing for several weeks, months, or even years [ 154 , 155 , 156 , 157 ]. It has been shown that mechanical relaxation depends on time, temperature, and humidity [ 158 ]. Thus, even after the PFSA membrane reaches a steady state, it is not in true thermodynamic equilibrium and may, at best, be in quasi-equilibrium, depending on pretreatment and measurement conditions. Slow, continuous changes in properties were observed over longer time scales (up to days and years), which were accompanied by morphological changes. This prolonged relaxation of the polymer matrix leads to possible additional water absorption, and the associated reorganization affects the structure and connectivity of hydrophilic networks. Time-dependent relaxation processes in PFSAs affect ionic conductivity [ 153 , 154 , 155 , 156 , 157 , 158 , 159 , 160 ], mechanical properties of membranes [ 161 , 162 ], the modulus of elasticity [ 163 , 164 , 165 , 166 , 167 ], and the stretching of the polymer base [ 168 , 169 ]. Based on studies of small-angle X-ray scattering [ 170 , 171 ], dielectric measurements [ 172 , 173 , 174 , 175 ], and dynamic mechanical analysis, relaxation phenomena during morphological changes were discussed for several weeks. When the polymer relaxes, the restrictions imposed on the water domains in the polymer volume are also weakened by reduced pressure and swelling. This leads to a change in the chemical and mechanical balance and to an increase in swelling processes. As a result, an additional increase in the amount of water during absorption was observed even after the membrane seemed to have reached quasi-equilibrium [ 168 , 176 ]. This was accompanied by changes in the nanostructure, albeit at a very slow pace, over several weeks [ 155 , 156 , 157 ]. Relaxation phenomena similar to electrostatic interactions reflect and combine the unique properties of PFSA ionomers: ion transport, morphology, and thermomechanical reaction. For example, it has been shown that the ionic conductivity of PFSAs changes over time [ 159 , 161 ], and it changes depending on the pressure applied during measurement [ 160 ]. Thus, the interpretation of the measured time-dependent response is quite intriguing, since it is probably regulated by a combination of chemicals, mechanical and structural factors. To account for relaxation, a time-dependent change in the value of ψ ( t ) can be defined as ψ t = ψ ∞ + ∑ r a r e x p − t τ r β r , (1) where ψ ∞ is the final quasi-equilibrium value, a r and β r are the fitting parameters, and τ r is the process constant r of the relaxation time. When β r = 1, the function has the form of regular exponential decay. Values of β r < 1 indicate a slowly decreasing exponential function. It should be noted that many mechanisms are involved in the relaxation process ( r > 1); a characteristic time constant for PFSAs cannot be identified, especially when these processes and time constants also vary with temperature and humidity. The real problem with the definition of τ r is that in most cases the actual relaxation time is longer than the experimental time for observing the properties of τ exp . The relations for these times are determined by the Deborah numbers ( De ). Interestingly, De for PFSAs has not been studied in detail, although it was mentioned in [ 168 , 177 ]. If the process is diffusive, then the Deborah number can be written as D e ≡ τ r τ e x p = τ r e l a x a t i o n τ d i f f u s i o n = τ r e l a x a t i o n L 2 / D . (2) If De << 1, then the relaxation process is not dominant, whereas a high De indicates processes for which relaxation becomes relevant and important. Based on many years of experiments in the literature, time constants for relaxation processes have been calculated: about 10 3 –10 4 s for conductivity [ 159 ], 10 4 to 10 5 s for water absorption [ 154 ], 10 5 to 10 6 s for the distance between water domains [ 155 , 156 , 157 ], and 10 3 –10 7 s for mechanical relaxation [ 158 , 167 , 178 ]. It is clear that there is a huge gap among the measured values, mainly due to the limited observation time. The observation time limit can be overcome by increasing the temperature. Therefore, low De can be associated with a more viscous (mechanical) reaction and transient (diffusive) behavior, while high De relates to elastic (mechanical) response and steady mutual diffusion. It is quite possible that this is caused by slow leakage or rearrangements of/fusion of trapped nanobubbles, containing dissolved gas. 6. Effects of Casting Most ionomers are currently molded with the possibility of switching to a smaller thickness and ease of inclusion of additives and/or reinforcing materials. The casting of PFSA ionomers in terms of shape is an interesting task, especially for thin films in complex electrode structures [ 179 , 180 , 181 , 182 , 183 , 184 ]. PFSAs do not form a true solution, but rather exhibit dispersion behavior with rod–shaped cylindrical aggregates, the nature of which is influenced by the properties of the cast membranes [ 185 , 186 , 187 , 188 , 189 , 190 , 191 , 192 ]. Some polymeric materials conduct electric current, and their conductivity can be due to the presence of a cylinder-like sub-structure of the polymeric matrix. These cylinders must have an aqueous helical core of nanoscale diameter, surrounded by sulfonate groups, and should be connected to one another. Both randomly connected and ordered conducting nanometer-sized cylinders are geometrically possible. These will be similar to single-phase conducting cylindrical nanostructures formed by cationic microemulsions of water, alkanes and didodecyldimethylammonium surfactants. For such mixtures, depending on component ratios and the type of counterion, conductivity can vary by 10 orders of magnitude, and viscosity can vary by at least 5 orders of magnitude. It is known that very strong long-range non-additive forces result from ionic spatial fluctuation between parallel conducting cylinders. These are probably also operating in the effects of casting and can be expected to result in some extraordinary phenomena, see Refs. [ 193 , 194 , 195 , 196 , 197 , 198 , 199 ]. When creating membranes, for example, based on the Aquivion ionomer, the ionomer can be mixed with sulfonated polystyrene [ 183 ] and reinforced with fiberglass to give them the required mechanical characteristics. At the same time, it is critically important to accurately observe the temperature regime, uniform distribution of components, and control of the glass fiber content (25 wt. % to ensure mechanical stability) and correct phase inversion during solvent evaporation [ 183 ]. It was also shown in [ 183 ] that the addition of sulfonated polystyrene increases water absorption and ionic conductivity, and the ratio of components affects the overall electrical conductivity. The authors of this work synthesized membranes that demonstrated thermal stability similar to that of Nafion membranes. At the same time, the resulting membranes were capable of increasing the absorption of water. It was shown in [ 200 ] that casting PFSAs from a high-boiling liquid led to improved membrane properties. At the same time, the types of liquid dispersion and heat treatment in the ionomeric structure were of great interest. Casting from various solvents changes their conductivity [ 201 , 202 ]. Casting at higher temperatures usually leads to a more tangled network of polymer chains, higher crystallinity, better resistance to solvents, and improved overall mechanical properties [ 148 , 179 ]. In [ 179 ], the use of more than 25 liquids in the spigot systems was demonstrated, in which the mechanical viscosity (inversely proportional to the brittleness) of the molded PFSA membrane is regulated by the critical concentration of gelation of the spigot liquid along the entanglement chain that occurs during evaporation, rather than by crystallinity with additional effects that can be caused by heat treatment of the liquid at high pressure. It is clear that casting conditions and solvents can significantly affect the overall properties and performance of the membrane, and this is currently being actively investigated [ 203 , 204 , 205 ]. 7. Durability Issues and New Developments In the last decade, significant efforts have been made to improve ionomers’ ability to withstand chemical and mechanical stresses when creating hybrid composite membranes with chemical and mechanical stabilizers. The latter was achieved by combining a strong hydrophobic reinforcing layer in a PFSA ionomer to improve its stability during hydration (for example, GORE-SELECT membranes). Attempts have also been made to compensate for wear and mechanical stability in PFSA ionomers with a lower equivalent mass. For example, in [ 14 ], it was shown for 3M membranes that low EW and short side chains, creating a denser package, provide better resistance to mechanical deformation, and the optimal combination of EW and mechanical properties is achieved at an EW of about 700–900 g/mol. At the same time, an excessive decrease in EW can lead to excessive swelling and deterioration of mechanical properties. Over the decades, other strategies have emerged to mitigate degradation, whether mechanical and/or chemical, as well as the development of stronger PFSA membranes. Such strategies include (but are not limited to) the following actions: Impregnation of the ionomer with radical scavengers such as cerium or cerium oxide to prevent the formation of radicals; Impregnation with inorganic fillers to improve water retention, especially at higher temperatures and lower humidity; Impregnation with chemically inert hydrophobic mechanical support layers, such as polytetrafluoroethylene mesh, to improve mechanical properties and stability in response to changes in humidity. This functional role is distinct from durability enhancement and deserves mention in a comprehensive review of PFSA ionomers. Thus, an ionomer filled with particles can be considered a composite membrane. However, given that PFSA ionomers have a phase-separated morphology, the inclusion of additional particles or support layers creates an even more complex multiphase material, where the interactions of the newly added particles, as well as the hydrophilic and hydrophobic phases of the ionomer, become crucial for controlling not only the effectiveness of the hybrid structure, but also the overall functionality of the membrane. It should be noted that in this case, we are not considering the issue of durability outside the context of polymer membranes, i.e., in this case, the scope is limited to membrane durability. Note also that in catalyst layer applications, a primary purpose of incorporating hydrophobic additives into the ionomer phase is to create gas transport pathways and reduce local oxygen transport resistance. 8. Applications This section describes a number of applications of PFSA ionomers and their analogs, which are characterized by good performance and durability and which have become the industry standard for fuel cells [ 18 , 59 , 75 , 206 , 207 , 208 , 209 ]. A block diagram listing the main application areas is shown in Figure 3 . Figure 3. Open in a new tab A block diagram showing the various applications of PFSA ionomers. The main functions of ionomers used in energy devices are ionic conductivity, use as a bonding component for combining electrode elements, and ensuring interaction between active materials [ 208 ]. The authors of this work identify some promising applications, such as the creation of new types of ionomers with improved characteristics, the development of composite materials, the optimization of the microstructure of electrode layers, and the improvement of mass transfer of reagents. Special attention in such developments is paid to the study of interactions of ionomers with electrode surfaces on the micro- and mesoscale, which is critically important for optimizing the operation of energy devices [ 208 ]. The constant increase in cost and durability targets for commercial applications is forcing improvements in PFSA functionality and/or the development of alternative membranes. Since 2004, Nafion and related PFSA ionomers, due to their attractive electrochemical and thermal properties, pronounced phase-separated structure and high proton conductivity [ 210 , 211 , 212 , 213 ], have attracted increasing interest for devices that require high ion and water transfer rates and improved mechanical and chemical properties. Despite the gaps in the current state of understanding and modeling their ion transport structure, PFSA ionomers continue to be reference materials, especially for low-temperature PEMFCs. Their success in polymer-electrolyte fuel cells as an electrolyte or separator [ 214 , 215 , 216 , 217 , 218 ] has made them interesting for other solid-state energy conversion and storage devices, such as flow batteries [ 219 , 220 , 221 ], solar generators and electrolyzers [ 222 , 223 , 224 , 225 , 226 , 227 , 228 , 229 , 230 ], for which the behavior and functionality of the ionomer will vary ( Table 1 ). In addition, they are used in other applications such as microfluidic devices and soft actuators [ 231 , 232 , 233 , 234 , 235 , 236 ], humidifiers [ 237 , 238 , 239 ], dehumidifying membranes for moisture removal [ 240 , 241 ], as a chlorine-resistant gas separation membrane [ 242 , 243 ], for electrodialysis, and in water and air purification systems [ 138 , 244 , 245 , 246 ]. These applications take advantage of various membrane properties, such as conductivity, water transport, and chemical stability, as well as other properties (such as improved transport properties compared to lower mechanical stability). Therefore, it is important to demonstrate control over these properties and optimize the structure depending on its functionality in a particular application. Table 1. Applications of PFSA ionomers. Application or System Role Functionality for Transport Functionality for Stability Optimization for Applications, Key Parameters Fuel cells, PEMFCs Ion-conducting electrolyte, separator Ionic conductivity, water transport, low reagent crossover selectivity Mechanical strength, chemical stability Thin stable membranes with low gas crossover Catalytic layers Binding material for Pt, electrolyte Ionic conductivity, gas permeability Pt/C coating, stability Coating of catalyst particles, kinetics of oxidation Chlor-alkali systems Ion exchange membrane Selective ion exchange Chemical stability Concentration of solutions, transport Passive transfer of water vapor Humidifier membrane Water permeability, gas tightness Chemical stability, gas barrier properties High water permeability Desalination and water purification Membrane with selective permeability Water permeability, limited ion permeability Chlorine resistance, durability Selectivity Shape memory devices Shape-memory material Reversible thermomechanical deformation Restoration of shape under thermal influences Thermal history, mechanical properties Ion–metal composites Actuator, sensor Deformation under the action of an electric field Membrane stability Flexural stiffness, strain maintenance, and hydration Biomimetic pumps Soft drive Reversible strain under stress Flexibility and mechanical strength Optimal hydration to maintain swelling Flowing batteries Electrolyte membrane Selective ionic conductivity Mechanical integrity Selectivity Solar generators Electrolyte membrane Gas separation, ion exchange Photostability, chemical stability Optical transparency, a balance between blocking and gas conduction Open in a new tab For example, while actuators use swelling-induced deformation of the membrane under stress [ 233 ], shape memory applications focus on thermomechanical properties that can be controlled by deformation and heat treatment [ 247 ]. All these studies have provided new data sets and have expanded the ability to understand and improve the dependence of a structure on the properties of PFSA membranes. Traditional PFSA membrane production methods (extrusion and casting) have significant drawbacks, such as the risk of pore formation. The authors of [ 243 ] propose an alternative method for obtaining PFSA membranes through electroforming nanofibers, which can potentially solve many problems and improve the characteristics of the material, in particular, its resistance to aggressive media, including chlorine. 9. Solvent Adsorption and Absorption As noted above, the adsorption behavior of PFSA ionomers is the most important phenomenon affecting their phase separation morphology and, consequently, their general transport and structural characteristics. Thus, the starting point for any characteristic of a PFSA is to determine its ability to absorb water or any other solvent. Although general concepts and modeling approaches are applicable to other solvents, further emphasis will be placed on water, and only then will there be a discussion of other solvents. The amount of water in a hydrated membrane can be quantified in several ways, all of which are interrelated, although the most commonly used value—water content λ = mol H2O /mol SO3 is defined as the number of water molecules per mole of sulfonic acid, which was introduced for the first time in the article by Springer et al. [ 248 ]. The concept of quantifying water locally at sites, while also accounting for the presence of clusters of water molecules, is already present in previous works [ 76 , 143 , 249 ]. The water content λ is related to water absorption and the equivalent mass of the EW membrane λ ≡ n H 2 O n S O 3 = ∆ M H 2 O M P E W M ¯ H 2 O , (3) where the fraction in parentheses corresponds to solvent absorption. Here ∆ M H 2 O is the molar mass of absorbed water, M P is the molar mass of the dry polymer, and M ¯ H 2 O is the molar mass of water. Note that the terminology “ λ ” is now ubiquitously used in PFSA research; it was introduced by researchers working at the University of California, Berkeley, and Los Alamos National Laboratory around 1990. The water content may also be related to the volume fraction of water φ w and the concentration c w through the following formulas: c w = λ λ V ¯ w + V ¯ p , φ w = c w V ¯ w = λ V ¯ w λ V ¯ w + V ¯ p , (4) where V ¯ w and V ¯ p are the molar volumes of water and dry polymer, respectively. The above-mentioned ratios are stored as averages for the entire membrane (i.e., not locally) and assume the additivity of molar volumes for the total volume of the membrane. In most experiments, the change in membrane weight is measured gravimetrically, with controlled water vapor activity a w (or relative humidity) at a given temperature. This weight change can be used to bind λ and a w to produce an adsorption isotherm. The water absorption pattern of the Nafion 1100 EW membrane has been studied for many decades, and more than a hundred articles have been published on this topic since the 1980s, showing the appearance of isotherms that are similar in shape but differ in absolute values. For the dependence λ = f ( RH ), the observed differences in some cases have explanations—the effects of pretreatment and thermal history (as mentioned earlier). It should be noted that there is a significant difference depending on whether it is a vapor phase or a liquid phase. The water absorption of the PFSA membrane decreases with an increase in the equivalent mass of EW [ 111 , 143 , 250 , 251 , 252 ], a decrease in the polarity of the solvent [ 253 , 254 ] (for example, alcohol [ 255 ]), an increase in the heat treatment temperature [ 102 , 110 , 112 , 119 , 154 , 256 ], aging and contamination [ 114 , 237 , 257 , 258 , 259 ] and mechanical compression [ 260 ]. Despite their seeming irrelevance, all these factors are fundamentally the result of changes in the chemical and mechanical energy balance in the separable phases of the ionomer nanostructure. In this sense, all the listed effects can be considered to increase the resistance of the structure to deformation (for example, crystallization, compression, etc.) or its tendency to dissolution (for example, a decrease in EW). For example, it is known [ 259 ] that cyclic changes in humidity lead to fluctuations in the water content in the membrane, which in turn causes the formation of cracks, micro-holes and additional stresses in the material and, in general, mechanical fatigue in the structure. Chemical pollution is manifested through the formation of aggressive media (for example, hydrogen peroxide, reactive oxygen species) [ 259 ]. Reactive oxygen species (ROS) are useful indicators of a polymeric structure. Such species are activated by mechanical shaking, see Ref. [ 261 ]. We turn to biology for illumination. For example, enzyme reactions occur as follows. The enzyme has a particular nanostructured hydrophobic cavity with geometry determined by a specific divalent ion, like Mg ++ , Mn ++ or Ni ++ . When an enzyme and substrate come together, the effect of cavitation occurs, and the chemical energy produced by this cooperative event releases ROS, hydrogen peroxide and free radicals that accomplish the required catalysis, e.g., cutting of the phosphate bond. It is a universal cooperative mechanism of reaction by which Nature harnesses weak physical forces to produce chemical energy. The mechanism is universal and not confined to enzymes, see Refs. [ 199 , 262 ]. In this connection, we should remind you of some information about the endothelial surface layer. The endothelial surface layer (ESL) is a universal nanostructured coating on all biological cells and tissues made up of sulfated hydrocarbon polymers, predominantly Heparan, Chondroitin sulphates, and very hydrophilic hyaluronan. The ESL is the analog of the Exclusion Zone of Nafion (see the monograph [ 263 ] for more details about the Exclusion Zone), albeit on a smaller scale. The ESL, having a thickness of about 1000 nm, teases out Glycocalyx (GC; its thickness of 50 nm) from the bulk, see Ref. [ 262 ]. It is essential to all life forms and has a dynamic nanostructure mimicking that of Nafion, with connected random helical nanotubes, through which blood electrolytes pass. It also allows the passage of glucose, oxygen/nitrogen and CO 2 nanobubbles. This nanostructured biological smart material (ESL-GC) is maintained in a fit condition by insulin. ESL unravels, lines and maintains the structure of aqueous sulfated tubes and medium. A second observation concerns both the Exclusion Zone of Nafion and a certain analog of the Exclusion Zone that is created by the ESL. There are extensive studies that have reported on the swelling of Nafion to form its Exclusion Zone, with different cations, see Ref. [ 199 ]. The swelling of Nafion in water, accompanied by a teasing out of Nafion polymer threads from the polymer matrix towards the liquid bulk, is dramatically different for sodium, potassium and lithium at all concentrations. Equally interesting, it varies, again dramatically, with and without deuterium in water; for more details, see Section 22 , which is devoted to the characteristics of Nafion’s swelling in water depending on its deuterium content. These are remarkable phenomena—illustrating the effects of specific ions and of deuterium—which are probably the key to some forms of chirality. Together with the insulin example, they provide clear strategies to manufacture, maintain and improve the properties of a swollen polymer. It is important to note that it is the synergistic effect of the combined action of mechanical and chemical factors that is key in the aging process of membranes. At the same time, increased water absorption acts as a catalyst for accelerated destruction of the material under the influence of aggressive media. This chemical–mechanical balance has long been a key aspect of equilibrium in ionomer modeling, albeit with many different approaches and formulations, starting with early studies by Eisenberg [ 264 ], Mauritz et al. [ 265 ], Dreyfus et al. [ 266 ], revised by Choi et al. [ 267 , 268 ], Weber [ 269 ], Freger [ 270 , 271 ], Kusoglu et al. [ 111 , 272 , 273 ] and Kreuer [ 274 ], and correlations related to the structure and transport properties of PFSAs [ 275 , 276 ], as well as to their swelling and mechanical reactions [ 272 , 277 ]. In addition, this balance also changes qualitatively with cations [ 278 , 279 ] due to electrostatic interactions that change not only the chemical properties, but also the mechanical response of the material. The process of swelling or adsorption in a PFSA ionomer membrane is a multi-stage, multiscale phenomenon regulated by complex interactions between water, hydrophilic ionic parts, and a hydrophobic polymer matrix, resulting in high nonlinearity in the water absorption profile. The water absorption process is determined by the solvation energy of ionic groups and the chemical potential that controls the attachment of external water molecules to hydrophilic ionic membrane fragments, which are balanced by the deformation of the hydrophobic matrix of the ionomer (the chemical and mechanical energy balance). In the hydration process, the first water molecule (H 2 O) is ionized and is associated with the acidic sulfonate group via hydrogen bonds, with the formation of hydronium ions. The initial water molecules continue the solvation of ionic fragments by forming a stable hydrate shell, which leads to the dissociation of bound counterions; such water is called bound water. This is due to the fact that the enthalpy of hydration of the proton is much higher than that of the conjugate base (SO 3 ). Thus, water can form hydrate shells around cations, not just around bound sulfonic acid groups, and such cation-dependent hydration can affect the interactions and properties of PFSAs. When the membrane absorbs water, the protons H + in the process of dissociation pass into the bulk of water from the sulfonate sites, SO 3 becomes solvated (forming ions such as H 9 O 4+ ), and the enthalpy of hydration through additional adsorption of water decreases. The process of water solvation is associated with a decrease in the enthalpy of hydration due to the exothermic process of water adsorption [ 274 , 280 , 281 ]. The enthalpy change is maximal in the range λ = 1–2, which corresponds to the ionization of SO 3 H with water at δH s = −20–−25 kJ/mol [ 255 , 274 , 280 , 282 , 283 , 284 ]. Water molecules enhance phase separation and form hydrophilic, ion-rich domains in the basic matrix [ 285 , 286 , 287 , 288 , 289 , 290 , 291 , 292 , 293 ]. This process is schematically demonstrated in Figure 4 . When two or more water molecules are adsorbed, an interconnected network of domains is formed, which marks the percolation threshold, providing the membrane with its ion and water transport functions. The adsorption process continues to 5–6 water molecules, forming several solvate shells around a fixed sulfonic acid center (SO 3 H + ), and after dissociation, the H 3 O + ion arrives. At higher relative humidity, additional water molecules cause further growth and connectivity in hydrophilic domains ( Figure 4 ), which eventually leads to a more voluminous water region where water molecules move freely. In this mode ( λ > 6), the enthalpy of hydration reaches a plateau from 40 to 45 kJ/mol [ 255 , 274 , 280 , 282 , 283 , 284 ] and approaches the heat of condensation of water (40 kJ/mol). Thus, the total water content in the ionomer for a given water activity a w and T can be expressed as λ a w = λ 0 + λ B a w + λ F a w , (5) where the first term corresponds to residual water (primary solvation), the second to bound water, and the third to free water. In this case, the residual water is a tightly bound water molecule in primary hydrate shells, which can only be removed at elevated temperatures, i.e., λ 0 = 1–2 at 120 °C [ 96 , 111 , 112 , 119 , 294 , 295 ], with small traces of water, possibly remaining up to 200 °C [ 295 , 296 , 297 , 298 , 299 ] before decomposition of SO 3 begins. The existence of a strongly bound water molecule also corresponds to single stationary water, which was determined by studies of quasi-elastic neutron scattering [ 300 , 301 , 302 , 303 , 304 , 305 , 306 ]. Figure 4. Open in a new tab Shapes of adsorption isotherms for the PFSA ionomer ( top ), as well as the balance of chemical/mechanical energy in a phase-separated nanostructure ( bottom ). Figure S1 summarizes the data from the literature on water absorption by Nafion membranes, demonstrating the characteristic features of the adsorption isotherm. The curves in the left graph represent a polynomial expression from the work of Springer et al. [ 248 ], as well as the lower and upper bounds from the models of Kusoglu et al. [ 111 , 260 , 272 ] and Weber and Newman [ 269 ]. The solid lines are based on a polynomial that best describes all the points on the graph. The lines represent the results of simulation from [ 111 , 260 ]: a —liquid water; b and c —saturated water vapor for cases of increased and decreased absorption with temperature, respectively. For simplicity, when constructing these data, residual water is not taken into account (i.e., λ 0 = 0 in Equation (5)), the non-zero value of which is discussed only in limited studies, usually in connection with the effects of drying [ 96 , 111 , 302 ]. Although only data on adsorption (wetting) are presented, PFSA membranes exhibit comparable adsorption and desorption in terms of absorption, λ [ 284 , 303 , 304 ], albeit with rather different kinetics. Despite the fact that the data plotted on the graph show some variation, partly due to the different experimental devices and techniques used, they show similar trends. Moreover, a close examination of the membranes used in these studies shows that pre-boiled membranes tend to absorb more water than annealed (or pre-dried) membranes, especially at relative humidity above 60%, indicating the important role of thermal history and membrane pretreatment. At higher relative humidity, the N21x membranes absorb slightly more water than the N11x membranes of the previous generation, which may be due to processing effects. It is worth noting that increased humidity, through which thermal and technological effects are manifested in the controlled adsorption capacity of the membrane, also corresponds to the transition from bound water to a free regime (according to Equation (5)). Thus, at relative humidity ranging from 50 to 60%, the absorption of water by the membrane is mainly regulated by the Langmuir adsorption of water molecules that create hydrate shells around the ionic group. This creates a local swelling at the nanoscale, which seems to depend less on the length of the side chain, the equivalent mass of EW, and the thermal history of the membrane. It is only in the free-water mode that these parameters begin to play a role. This is due to the accommodation of absorbed water molecules in growing hydrophilic domains, which deform the phase-separated morphology, resulting in swelling at several length scales, where crystallinity, thermal history, and processing effects become more influential. It has been shown that increasing the equivalent mass reduces the water absorption capacity and alters the growth of the isotherm, especially at high hydration levels (from 75% relative humidity in liquid water), where the absorption of free water molecules is controlled by the resistance of the polymer matrix, which increases the equivalent mass (for this side chain). There is little information in the literature on the behavior of the adsorption isotherm at elevated temperatures, which is explained by the difficulties in obtaining an accurate measurement value at high temperatures or in conditions of high humidity. For this membrane, almost all studies report the same water absorption at 70% relative humidity, regardless of temperature (from 25 to 90 °C) [ 112 , 256 , 274 , 307 ]. However, in steam conditions, especially close to saturation, the water content decreases with increasing temperature [ 118 , 119 , 305 , 308 , 309 ], with a notable exception in the studies of Kreuer [ 274 ], who reported a tendency for a temperature decrease with relative humidity at λ < 80% and a temperature increase at λ < 80%. In fact, purely from the point of view of mechanics, with a temperature increase in the moment of inertia in the polymer matrix, the pressure on the growing water domains decreases, i.e., the matrix absorbs more water molecules. Thus, a temperature decrease in water absorption at high relative humidity may be due to chemical interactions that prevent water absorption in the vapor phase. The temperature decrease in swelling has been discussed in many studies and is explained by a change in hydrophilicity due to surface interaction [ 114 , 119 , 122 ] and a change in the entropy of water upon interaction with the polymer [ 111 , 112 , 260 , 310 , 311 ]. Small temperature changes with values of λ below 70% are associated with the exothermic nature of hydration in this regime, where chemical interactions persist [ 274 ]. At the same time, the phenomena underlying the decrease in water absorption at elevated temperatures have not yet been definitively explained for PFSA membranes; this has been observed for other polymers and is being discussed in the context of cross-linking or water retention (or release) through controlled condensation (or evaporation), depending on the size of the nanodomain [ 161 , 275 ]. 10. Comparison of Adsorption from Steam and Liquid The water content at saturation is of great interest. At the maximum state of hydration, depending on whether the water is located at the membrane bordering the vapor or liquid, these states are, respectively, called vapor- and liquid-balanced. However, the water molecules inside these domains are always in a condensed state or in a liquid-like phase. A similar effect is observed upon absorption from different solvents [ 312 , 313 ]. The reason for the difference between λ measured in saturated steam and in liquid, i.e., Δ λ liq − vap = λ liq − λ vap , is the subject of long–term disputes, since the membrane is in thermodynamic equilibrium in both cases, i.e., a w = 1. Therefore, a nonzero value of Δ λ liq − vap indicates an anomaly with the assumption of a single-phase system. This phenomenon is called the “Schroeder’s paradox”, described in the work of Schroeder [ 314 ], who showed that gelatins swell more in liquid water than in saturated steam. This has been the subject of much debate regarding the swelling of gels and other related polymer networks [ 40 , 312 , 315 , 316 ] and remains an intriguing problem in both theoretical (thermodynamics of phase equilibrium) and experimental (achieving true liquid–vapor equilibrium) research. The Schroeder paradox for the PFSA community has stimulated a number of systematic studies that have attempted to provide solutions through simulation [ 260 , 269 , 271 , 317 , 318 , 319 ] based on experimental work [ 40 , 155 , 312 , 320 , 321 ]. Although previous modeling approaches used various methods to redefine thermodynamic equilibrium through interphase effects and morphological changes, experimental studies have investigated the issue of membrane saturation in true equilibrium (kinetic effects), as well as the reversibility of the paradox [ 121 , 122 , 155 , 156 ] through the study of the membrane surface and morphological changes between vapor and liquid [ 156 , 320 , 322 , 323 ]. The specific sources of this change in vapor/liquid conditions are still not fully understood or satisfactorily explained, although significant progress has been made, leading to new research on membranes. It is believed that the main causes of the liquid/vapor interaction are of interphase or thermal nature, where the first factor induces a different morphology at the interface, and the second one induces it throughout the volume. As for the latter, the fact is that a pre-dried membrane means that it absorbs the same amount of water, regardless of whether it is in saturated steam or liquid water ( λ vap ≈ λ liq ≈ 14 ± 1), while there is no such effect for a pre-boiled membrane ( λ vap = 14 ± 1 < λ liq = 22 ± 1) [ 121 , 122 , 154 , 312 ]. Some studies have concluded that the difference is a matter of balance or lack thereof. However, since the paradox has a thermodynamic origin, the main focus should be on the membrane, the state of which is closer to quasi-equilibrium, which is performed for a pre-boiled membrane, for which the difference is “vapor/liquid” Δ λ liq − vap > 0. For example, it is known that as the temperature of liquid water increases, its content increases and approaches the value for a pre-boiled membrane for both Nafion [ 121 , 124 , 153 , 154 , 324 , 325 , 326 ] and other PFSA ionomers [ 118 , 119 , 123 ]. For a membrane that has not been pre-boiled (for example, annealed), its λ in water increases with temperature [ 121 , 122 , 292 , 327 , 328 ]. However, if the membrane is pre-boiled, its water absorption does not change with temperature [ 102 , 111 , 121 , 153 , 329 ], which indicates that the membrane is already in a quasi-equilibrium state. Thus, the observed increase in the sorption capacity of membranes (annealed or heat-treated) with temperature is related to their morphology, which can be in a kinetically trapped state, which is consistent with a longer balancing time. In [ 95 , 154 ], the authors showed that it took up to 200 h to achieve equilibrium in pre-dried membranes, and the higher the pre-drying temperature, the longer the equilibrium time was. This indicates that heat treatment sets a limited morphology even at temperatures below the cluster transition. In fact, it has been shown that as the pre-drying temperature of the membrane increases, subsequent water absorption decreases in steam [ 112 , 119 , 154 , 256 ] and liquid water [ 112 , 119 , 256 , 330 ], which also affects the corresponding transport properties. In an attempt to elucidate the origin and nature of Schroeder’s paradox, Freger [ 271 ] conducted a systematic study of Nafion’s water absorption at a w < 1 using polyelectrolyte solutions (polyvinylsulfonic acid salts) as an osmotic stress factor, which made it possible to measure isopiesthetic adsorption isotherms in vapor- and liquid-balanced regimes. Their findings demonstrated that Schroeder’s paradox is not an anomaly at 100% relative humidity, but occurs in water at up to 50% relative humidity, confirming the difference between vapor and liquid equilibrium. This difference is related to the morphology of the membrane, especially on the surface. The surface of the PFSA membrane changes with hydration, which has been verified through contact angle (wetting angle) [ 152 , 322 , 331 ], atomic force microscopy [ 91 , 327 , 328 , 329 , 331 , 332 , 333 , 334 ], electrochemical mass transfer measurements [ 335 ] and X–ray studies [ 56 , 336 ]. Bass and Freger [ 322 , 323 ] investigated the morphology of the Nafion membrane and showed that the surface morphology is hydrophobic in nature in vapors, but becomes hydrophilic in liquid. Later, the authors of Kusoglu et al. [ 155 ], using time-resolved MPR (SAXS), showed that the distance d of the membrane reaches a steady state in seconds in liquid water, but in steam this distance does not reach a steady state even after a month, and it is even lower than in liquid. Gebel et al. [ 156 ] reported similar morphological differences and kinetic effects between vapor and liquid using small-angle neutron scattering (SANS). They also showed that the peak of the ionomer in vapor equilibrium changed even after a year, with a linear dependence of the d-interval on the logarithm of time, which implies a slow constant reorganization and relaxation of the water network [ 156 , 157 ]. Therefore, an accurate characterization of water absorption by a membrane requires an understanding of its surface morphology, thermal history, and long-term adsorption behavior, as well as its relaxation phenomena. Significant structural and morphological changes are observed during hydration of the PFSA membrane (using the example of Nafion [ 334 ]). The morphology of the surface shows the appearance of random bumps ranging in size from tens to hundreds of nanometers. At low relative humidity (up to 25%), the relief height is relatively small (up to 10 nm), and with an increase in humidity above 45%, there is a significant increase in surface roughness (up to 40–60 nm). The observed morphological differences in the vapor and liquid phases have not only improved the current understanding of PFSAs but have also provided compelling evidence for surface changes under saturated vapor/liquid conditions and their key role in describing Schroeder’s paradox. It should be noted that it is difficult to determine the true specific activity of steam ( a w = 1) during liquid-water condensation on the surface, since this changes the state of the membrane. Finally, it should be noted that experiments investigating the absorption of different vapor and liquid solvents show a pronounced tendency toward the fact that the more polar the solvent [ 255 , 308 , 337 ], the greater the discrepancy between liquid and vapor [ 253 , 254 , 338 ]. This means that the surrounding interactions have a similar effect on the morphology of the membrane and, consequently, on solvent absorption. 11. Size Change upon Swelling A direct consequence of adsorption in PFSA membranes is a change in their size, i.e., swelling. In this way, the membrane adapts to the absorbed water molecules, and this, as described in Section 9 mainly occurs in anhydrous absorption mode. A volume change can be defined as a volumetric swelling deformation, which can be decomposed into swelling deformations in three directions (in the plane, along the x and y axes, and in thickness, z ): ε V s w = Δ V w V p d r y = 1 + ε x s w 1 + ε y s w 1 + ε z s w − 1 . (6) This may be related to water absorption as follows (assuming isotropic swelling and constant molar volumes): L s λ L d r y = 1 + Δ V w V p d r y 1 3 ε s w e ≈ 1 3 V ¯ w V ¯ p λ = β s w e λ , (7) where L S and L dry are the swollen and dry (initial) size (length), respectively, and λ ref is the reference water content. Size changes usually begin at λ ref ≥ 2. A simplified expression for swelling deformation ε swe can also be written as a linear function of λ , where the calculated coefficient between swelling and expansion β swe = 0.009 ± 0.002 agrees well with experimental data taken from various sources [ 339 , 340 , 341 ]. Similarly, the coefficient of thermal expansion α T can be determined to relate thermal deformation to temperature variation: ε the = α T δT . Studies on resizing PFSA membranes can be roughly classified into moisture-dependent swelling deformation at constant temperature [ 301 , 334 , 335 , 336 , 337 , 338 , 339 , 340 ] and swelling in liquid water at different temperatures, with an emphasis on anisotropic swelling, i.e., greater swelling in thickness than in the plane [ 324 , 342 , 343 , 344 , 345 , 346 , 347 , 348 , 349 , 350 ]. Although PFSAs exhibit noticeable anisotropy in terms of thickness from swelling in the plane, there is reason to believe that swelling in thickness may be higher than swelling in one of the directions in the plane, albeit slightly [ 163 , 253 , 339 , 340 , 343 ]. In addition, membranes reinforced with foamed polytetrafluoroethylene have a 10-fold decrease in swelling in the plane (i.e., at lower β swe ), since swelling in the plane is difficult due to reinforcement in favor of swelling in thickness [ 118 , 340 , 344 , 351 , 352 ]. As discussed earlier, pretreatment can have a significant effect on swelling deformation measured in liquid water as a result not only of the effects of thermal history but also of changing the reference length depending on whether the membrane is pre-dried and then moistened or pre-boiled. In these cases, the swelling was calculated after the membrane had dried. Anisotropic swelling occurs in the following cases: Extrusion of PFSA membranes, which swell less in the direction of extrusion (in the longitudinal direction), as a result of which the coefficient of longitudinal/transverse swelling is in the range ε TD swe / ε MD swe = 1.1 … 1.4 [ 118 , 343 , 345 , 349 ]; Pre-stretching [ 353 , 354 ]; Compression-drying, which causes reversible heating and an increase in the swelling coefficient in thickness and (or) length from 1.4 to 5.8 [ 349 ]. There is little information about the swelling of PFSAs of various chemical compositions, with the notable exceptions of Aquivion [ 61 , 77 ] and 3M [ 11 ] samples, which showed higher swelling (still directly proportional to the water content) than the Nafion membrane. According to [ 61 ], Nafion, as a representative of long-chain monomers, exhibits the lowest swelling in the range of 14–21%. At the same time, short-chain ionomers—Aquivion and 3M Ionomer—show higher swelling values (18.2–24.6%). It is noteworthy that the untreated thermal version of Nafion exhibits extremely high swelling, exceeding 51%. Finally, the coefficient of thermal expansion α T in PFSA membranes is significantly less than the coefficient of expansion of swelling, and does not depend on the usual operating conditions of a device (i.e., at < 100 °C). The existing literature provides information indicating that α T = 0.0001–0.0005 [ 123 , 167 , 355 ] for temperatures below T g , and α T = 0.003–0.009 [ 356 ] for temperatures above T g , which also varies depending on different cationic forms [ 123 ]. In addition, it was shown in [ 59 ] that an excessive decrease in EW can lead to excessive swelling (as in the case of Aquivion 720 membranes). 12. Density and Free Volume in Membranes During Water Absorption The density of a hydrated PFSA ionomeric membrane can be found using its density in a dry state and the proportion of water according to the mixing rule: ρ p ϕ w , E W = ϕ w ρ p d r y E W + ϕ w ρ w , (8) where ϕ w = 1 − ϕ p and dry density ρ dry p = 2.05 ± 0.05 g/cm 3 for most PFSA membranes, which varies with equivalent mass (EW), as shown in [ 143 , 281 , 357 , 358 ]. The density of a hydrated PFSA membrane decreases with water absorption and approaches 1.5 for a liquid-balanced membrane ( φ w ≈ 0.5). The density is also related to the free volume of the PFSA ionomer. This free volume was studied using positron annihilation lifetime spectroscopy (PALS) based on positron annihilation during interaction with electrons. By examining the lifetimes of positrons (–Ps) in various states, it is possible to determine the radius of the holes of the free volume, since short lifetimes indicate smaller volumes [ 359 , 360 ]. The size of the free volume in the Nafion as a function of temperature and humidity is shown based on PALS data [ 360 ]. An increase in the free volume with the temperature of thermal expansion indicates a beta transition, which is a process of sub-glass transition relaxation, often representing local movement of side groups or short chain segments, typically occurring below the main glass transition temperature, see, e.g., [ 361 ]. This transition is usually observed for the so-called beta temperatures (of about 20 °C), at which a change in the slope of the coefficient of thermal expansion is detected. However, in K + and Na + forms, PFSAs do not demonstrate this transition due to a shift in their beta temperature [ 362 ]. A gradual decrease in free volume with increasing humidity, especially after 60% (around a bound-free water crossing), is accompanied by greater positron annihilation in the aqueous phase due to high water absorption [ 360 ]. This free volume is key for transport processes such as gas permeability, as it provides pathways for molecular jumps [ 360 ]. The free volume of dry Nafion 212 detected by the PALS method was in the range of 0.175 … 0.219 nm 3 [ 359 , 360 , 362 ], which is less than that of polytetrafluoroethylene (PTFE, 0.297 nm 3 ) [ 360 ]. It is interesting to note that the proportion of the total free volume in all polymer cavities is approximately 0.028 (i.e., 2.8%) [ 360 ], and this is a rather small value compared to the general indicators of macroscopic volume change in a membrane. Therefore, despite the imperfect mixing caused by the solvation of ions by bound water at the beginning of the hydration stage and related to the nanoscopic free volume, the hydration behavior of the PFSA membrane and the overall volume change for high λ (or relative humidity) can be approximated on a macroscopic scale due to the additivity of the molar volumes of water and polymer. 13. The Behavior of Water in Membranes During Freezing Adsorption isotherms measured at subzero temperatures show the same behavior as at room temperature, although with lower total water absorption due to less free water [ 363 , 364 ]. A smaller amount of free water at subzero temperatures is the result of a change in the energy balance in the membrane due to an increase in the modulus of the polymer chain [ 365 ]. However, the adsorption of bound water in the membrane does not change at subzero temperatures, as these water molecules do not freeze due to their strong electrostatic interaction with ionic groups. Unlike free water molecules, which freeze, bound water molecules turn out to be non-freezing. Thus, the behavior of ionomers at subzero temperatures is commonly used to identify and study bound and free water molecules in a system. Using information from dynamic scanning calorimetry (DSC), it is possible to connect the amount of freezing (free) water λ F in a hydrated membrane with the total water content: λ = λ F + λ N F , (9) where λ N F ≈ λ B . Further relationships can be established based on the dependence of the total amount of water on free (freezing) water, based on values where the intersection point gives a rough estimate λ NF ≈ λ B : λ = 1.7 λ F + 4.75 . (10) It should be noted that the above expression quantifies the measured data and simplifies the state of the water into two different states. DSC studies of frozen water indicate a third type of “semi-free” water, which is bound but can still freeze, occupying the outer solvate shells of the polymer –SO 3 •H 3 O + [ 328 , 366 , 367 ]. In fact, this type of water is sensitive to the nature of the cations in PFSAs, which not only affects the amount of total and frozen water, but also the intermediate states of the water [ 250 , 328 , 366 , 367 , 368 ]. The terahertz spectroscopy method makes it possible to quantify the proportion of each type of water in the membrane and track their changes with changes in humidity [ 368 ]. At the same time, there is a correlation between the water content by volume and the proton conductivity of the material. Nevertheless, the fact that the adsorption isotherm at subzero temperatures approaches the Langmuir-type adsorption curve for bound water carriers suggests that non-freezing water can be considered to be bound water. Finally, although freezing and non-freezing water can be distinguished, the water in PFSA ionomers is a continuous condensed phase with different properties depending on the molecular interactions of the polymer chain, rather than the phase composition of the system. Due to non-freezing mobile water molecules, transfer in the membrane is possible even at temperatures below zero (which is expected due to the concentrated ionic solution) [ 369 ]. The water content, transport, thermal, and mechanical properties of PFSA ionomers at temperatures below 0 °C were studied using various techniques, including adsorption [ 282 , 363 , 370 ], dynamic scanning calorimetry (DSC) [ 282 , 363 , 371 , 372 , 373 , 374 , 375 , 376 ], dynamic mechanical analysis (DMA) [ 76 , 282 , 363 ], and nuclear magnetic resonance (NMR) [ 363 , 364 , 373 , 377 ], not only with H + but also with other counterions (K + , Na + , Li + ) [ 250 , 328 , 363 , 366 , 367 ]. In DSC studies, an endothermic peak of about 0 °C due to the melting of water is observed with a high water content (saturated or liquid). With a decrease in the initial value λ , the peak becomes wider, shifting towards lower temperatures, which indicates a decrease in the freezing point [ 71 , 282 , 372 , 378 ]. Thus, the higher the water content, the closer the temperature of the water is to 0 °C, and thus to the occurrence of phase transition [ 71 , 369 , 372 ]. The maximum amount of water that can be absorbed also decreases with decreasing temperature, from λ = 15 at 0 °C to λ = 8 at 15 °C and up to λ = 6 at 35 °C, while the limit value is reached regardless of the initial water content [ 364 , 370 , 372 ]. The formation of ice with subsequent desorption was confirmed by morphological studies using X-rays [ 379 , 380 , 381 ]. Thus, a constant decrease in temperature below 0 °C not only reduces the total amount of water (causes desorption) but also reduces the amount of free water (leads to freezing), thereby limiting transport functionality. Despite the presence of non-freezing water molecules at temperatures up to −50 °C, significantly slower mobility is observed using NMR, with a decrease in one order of magnitude in the coefficient of tracer diffusion of water [ 364 , 373 , 377 ]. Consequently, water molecules exhibit greater coordination with ionic centers at these temperatures, which leads to limited mobility [ 71 , 364 , 369 , 372 , 373 ]. In addition, compared with the ambient temperature, PFSAs at subzero temperatures exhibit a higher activation energy of conductivity [ 71 , 126 , 325 ], a higher modulus of elasticity [ 365 , 382 ] and a slight change in the coefficient of electroosmosis [ 370 ]. All these changes are traditionally associated with a decrease in the freezing point due to the interaction of water with ions in nanodomains [ 369 ]. Based on the study of water behavior and related transport mechanisms, quantitative assessment of freezing/non-freezing water is used to study various factors such as mechanical stretching [ 354 ], degradation [ 383 ], nanostructure studies [ 379 , 381 , 384 ], as well as transport properties [ 71 , 250 , 320 , 325 , 369 , 370 , 377 ]. X-ray [ 379 , 381 ] and neutron [ 384 ] studies based on water crystallization and changes in the peak of the PFSA ionomer, which determines the size of domains, below 0 °C, have shown that water is desorbed without freezing in the membrane and becomes glassy at temperatures from −53 to −60 °C [ 379 , 381 , 384 , 385 , 386 , 387 , 388 ]. Moreover, water remains amorphous even at λ = 22 or a domain size of ~3 nm, crystallizing only at λ = 50 (hyper-swollen state) and/or a domain size of 5 nm [ 381 ]. Thus, a drop in the freezing point is associated with the closure and acidity of the nanodomains of water in hydrated PFSAs [ 369 , 372 , 381 , 384 ]. In addition, the closure effect is also confirmed by an increase in the proportion of non-freezing water in PFSAs when stretched, which creates less entangled and smaller domains [ 354 ]. The nature of water in a mixed state, i.e., intermediates, can be better described by studying its transport properties. Such an attempt was made in [ 372 ], where, as a result of a systematic study of the electrical conductivity and DSC of Nafion at temperatures up to −50 °C during heating/cooling cycles, a phase diagram of water/Nafion was constructed, which is similar to the molecular acid/aqueous mixture diagram. In general, the water domains in “frozen” PFSAs contain an ice core surrounded by concentrated acid, an aqueous solution. It is limited by liquid and solid phase compositions, which are dependent on λ . The formation of ice cores in hydrophilic domains does not significantly affect their percolation or, consequently, their conductivity. Rather, they help to stabilize a network where mobile water molecules push through and bind through unfrozen domain walls and junction pathways. Due to these morphological differences and the state of the water, freezing and dehydration cannot be considered to be controlled by the same phenomena, even under the same conditions. Based on the Poisson–Boltzmann models, the differences between conductivity and calorimetry are explained by proton concentration gradients. This leads to a proton-depleted nucleus in hydrated domains, which freeze first and make a minimal contribution to conductivity. However, such models do not take into account solvation and other changes in the chemical potential of water and protons. 14. Modeling of Water Absorption Despite a large number of experimental studies on PFSA water absorption, the modeling of their adsorption behavior has been less studied. On average, the authors of every tenth paper with data on water absorption try to model and explain these data by using well-known theoretical foundations, but these foundations, in our opinion, are badly flawed due to sins of omission and commission. The problem here is fundamental. Properties like osmotic and oncotic pressure, viscosity, activities, interfacial tension, pH, buffers and anion deficiency are all based on models of electrolyte chemistry, which allow only electrostatic interactions between ions, and between ions and surfaces. Water is considered an incompressible continuum liquid with bulk properties. In our opinion, it is a very primitive model; see Ref. [ 389 ] for more details. We will not, however, examine in detail the shortcomings of existing theoretical approaches in this review. Various approaches to modeling water absorption and transport in ion-exchange membranes are being considered. Among the models, we can single out the cluster-channel model, which describes the membrane structure as a system of clusters and channels formed by the interaction of hydrophilic and hydrophobic components, as well as the two-phase membrane structure, which includes a hydrophobic base (hydrocarbon or perfluorinated chains), hydrophilic functional groups, and a system of pores of different sizes. Table 2 lists some of the modeling studies, as well as some experimental studies in which analysis was performed; see the Refs in the table. For example, using the TEAM-potential method of molecular dynamics, it was found that the water domains in PFSA ionomers have a spherical shape [ 390 ]. The average radius of water clusters depends mainly on their water content, and varies from 12 Å at λ = 12 to 7 Å at λ = 22. Modeling in this work also showed that almost all hydrated ions in PFSAs are located near the surface of water clusters, and acid groups are located only in the surface water layer (3–6 Å from the surface of the cluster) [ 390 ]. Table 2. Description of some studies on modeling phenomena related to sorption in PFSA ionomers. A Source Method and Approach What Predicts/Analyzes Eikerling and co-authors [ 276 , 391 , 392 ] A random porous network with idealized pores having surface and volume characteristics and electroelasticity, with pore size distribution Adsorption, conductivity, aging Gavish and co-authors [ 393 ] Phase flow model, Kahn–Hillard functionalization Adsorption, morphology Wu and Paddison [ 83 , 88 ] Dissipative particle dynamics, coarse-grained mesoscale model Morphology and transport Hwang and co-authors [ 394 ] Bimodal porous domains + MD (canonical Monte Carlo method) Adsorption, conductivity Weber and Newman [ 269 ] Macrouniform membrane model Sorption, transportation Kusoglu and co-authors [ 111 , 395 ] Micro-homogeneous model based on inter-domain distance data (SAXS) Adsorption, compression effects Li and co-authors [ 396 ] Free energy perturbation using density functional theory Adsorption, diffusion Voth and co-authors [ 397 , 398 , 399 , 400 ] Coarse-grained model with smoothed particle hydrodynamics for capturing morphology and transport based on chemical potential with morphologies (cluster, cylindrical, lamellar) Macroscopic transport and conductivity, electrostatic interactions, and the effect of ion group distribution on transport Gostick and Weber [ 401 ] A network model of resistors and pores with mesoscale domain distribution Effective conduction and percolation Daly and co-authors [ 402 ] Molecular dynamics with thermodynamic and transport models λ (RH, T), the role of water-sulfonate interactions Open in a new tab It should be noted that most modeling studies are not aimed at predicting absorption by solving basic physical equations. Instead, they use the analysis of other properties and phenomena. Despite remarkable attempts to create a unified model, none of them has yet yielded satisfactory results and a complete explanation of sorption phenomena, including such effects as thermal history (annealing, pre-drying), equivalent mass (EW), vapor–liquid transition, multiscale swelling, morphological changes, etc. Since the water content is a critical variable for transport and other properties, and it describes in detail the condition of the membrane, attempts have been made to predict λ based on measured properties and environmental conditions (for example, humidity). Most efforts are aimed at using thermodynamics; however, it is worth highlighting an approach based on the equilibrium of the energy balance to explain the phenomenon of adsorption based on the contribution of elastic forces and electrostatic interactions [ 312 , 363 , 403 , 404 , 405 , 406 ]. These models usually assume nanoscale morphology. Adsorption isotherms have been analyzed or modeled using empirical curves [ 119 , 248 , 278 ], Henry’s law [ 357 , 407 , 408 ], adsorption isotherms [ 312 , 317 , 407 , 409 , 410 ], the Flory–Huggins theory [ 267 , 272 , 305 , 309 , 408 ] and/or the equilibrium between water in the membrane and steam [ 226 , 269 , 317 , 410 , 411 , 412 ]. Due to the different physico-chemical processes that each model represents, usually only a specific phase of PFSA water absorption is modeled, which has prompted researchers to combine the models or modify them to take into account the very complex nature of PFSA water absorption. A commonly used approach is to model bound and free water separately and then linearly overlay solutions to predict total water absorption or continue the adsorption model to account for swelling pressure [ 111 , 260 , 267 , 268 , 274 , 278 , 305 ]. Multiscale multiphysical phenomena complicate the task of developing a comprehensive, consistent model that would explain all the aspects discussed above. Thus, early models based on the thermodynamic equilibrium of hydrated PFSAs have been modified or expanded over the years to take into account the electrostatic interactions of the ionomer and bound water, matrix deformation, and swelling pressures, as well as phase-separated nanostructure (growth of water nanodomains). Despite the differences, a common framework can still be outlined for many of these models. Before proceeding to a detailed modeling of the water absorption of PFSA membranes, it should be noted that many models use a polynomial expression for the isotherm of Nafion adsorption [ 248 ]: λ a w = λ R H 100 = b 3 a w 3 + b 2 a w 2 + b 1 a w + b 0 , (11) where b i represents the coefficients of the polynomial. Due to its simplicity, this expression is not predictive for the conditions outside of which the measurements were carried out. It is possible to determine a more general set of coefficients from a single polynomial’s correspondence: b 3 = 36.00 ± 2.45, b 2 = −42.8 ± 2, 4 or b 1 = 20.45 ± 0.65, b 3 = 0.05 ± 0.20, (see [ 248 ]), where the largest and smallest values of b i correspond to the obtained and pre-boiled membranes, respectively. 15. Modeling Equations The equilibrium swelling of the membrane in the environment at a given water activity a w is determined by the chemical potential of the membrane, ∆ μ p w , and the environmental factors surrounding the membrane, such as humid air: ∆ μ e w = μ e w μ e 0 = RT ∙ln a w , where μ e 0 is the chemical potential of the reference state (usually a unit of activity). The change in the chemical potential of water in the membrane relative to the reference value is expressed as follows: Δ μ w p = μ w p − μ r e f p = R T ln a p + V ¯ w P s , (12) where T is the absolute temperature, R is the universal gas constant, a p is the water activity in the membrane, and P s is the swelling pressure (or osmotic stress) that occurs in the polymer matrix as it deforms and the domains swell. Thermodynamics states that the chemical potential of water, both internal and external to the ionomer, must be the same, i.e., Δ μ w e = R T l n a w Δ μ w p = R T l n a p + V ¯ w P s → ln a w − l n a p = V ¯ w P s R T . (13) This expression is commonly used to describe the equilibrium point of PFSA ionomer swelling. Alternatively, the equilibrium can be expressed in terms of the total change in free energy relative to the reference state: Δ G = Δ G s + Δ G e ; Δ μ w a p = 𝜕 𝜕 n w Δ G p , T , (14) where the first term refers to swelling (osmosis), and the second term refers to the elastic energy associated with the elastic deformation of the matrix that opposes swelling. The factor that causes the models to deviate is the description of the a p value. The simplest expression for a p is the mole fraction of water in the hydrophilic domains: a p = λ /(1+ λ ), which, however, does not take into account molecular interactions. Specific expressions can be adopted to describe a p or ∆ μ p w , depending on the physical chemistry of the adsorption phenomenon. As discussed earlier, due to the different nature of free and bound water molecules in the ionomer, it is advisable to treat and model these modes separately. Therefore, the model water content was adopted as λ ( a w )∙ λ B ( a w ) + λ F ( a w ). This approach does not consider water as a separate thermodynamic phase, but acknowledges that the water continuum exhibits different properties due to its local conditions of ion concentrations, dielectric constant, etc. The isotherm regions for bound and free water can be predicted using the modeling approaches presented below. For bound water, the Langmuir isotherm is commonly used [ 267 , 305 , 317 , 413 , 414 , 415 ], which is well-suited for describing the process of monomolecular adsorption, where water molecules form a single layer on the ionomer surface [ 413 ]. The Langmuir adsorption of the first water molecule at a given partial pressure p w is expressed in terms of the surface (monolayer) coverage fraction θ: θ 1 w = K e q , 1 ω p w 1 + K e q , 1 ω p w , (15) where K w e q ,1 p w is the equilibrium constant for the adsorption reaction of the first water molecule that forms a solvate shell. In the case of the adsorption of bound water molecules λ B on ionic groups in PFSAs, the following expression is valid: λ B a w = ∑ i = 1 v λ i B a w = ∑ i = 1 v ∏ j = 1 i θ j w θ j w = K j w a p 1 + K j w a p , K j w = exp − Δ G j R T , (16) where △ G j is the hydration (solvation) energy of reaction stage j and v is the total number of equilibrium stages or the number of bound water molecules ( μ = 4–5). The above equation represents the multilayer adsorption of water molecules in clustering on the primary monolayer based on the Brunauer–Emmett–Teller (BET) theory [ 416 ], which gives the following expression in terms of water concentration: c w = C m A s a w 1 − a w 1 − C m − 1 a w , (17) where a w = R H 100 , C m is the sorption capacity of the monolayer, and A s is related to the difference in sorption heat between the first monolayer ( j = 1) and all other layers, which are the same as those of the pure liquid H L , i.e., A S ∝ e ( H 1− HL )/ RT [ 416 ]. Assuming that the interaction energy for the first step, K 1 , decreases, a modified form of the PFSA equation was proposed in [ 267 , 268 , 317 ]: c w = C m A s a w 1 − a w 1 − C m − 1 a w , (18) where a w = R H 100 . Thus, the sorption (or solubility) of a water molecule (or any other molecule) can also be related to its hydration enthalpy ∆ H s , through S ∝ S 0 exp( H s / RT ), as described in studies [ 274 , 280 , 282 , 283 , 417 ]. The sorption enthalpy ∆ H s decreases with lower humidity (0 < λ < 7), indicating an exothermic reaction with the largest enthalpy change occurring for the first two water molecules, reflecting the high hydrophilicity of PFSAs [ 281 , 417 , 418 , 419 ]. Thus, the hydration enthalpy also depends on the cation: the most negative H + and Li + combine with PFSAs, and an increase in the cation charge leads to less swelling [ 417 , 419 ]. These models have been shown to be applicable for analyzing the water absorption of PFSAs when exchanged with other cations, whose interaction (and energy) can be related to changes in swelling [ 278 , 279 ]. For the free water part of the absorption isotherm ( λ > 6), a Flory–Huggins-based approach is commonly used, which is traditionally used to study the thermodynamics of mixing and swelling in gels [ 420 ]: ln a p = ln 1 − ϕ p + 1 − V ¯ w V ¯ p ϕ p + χ ϕ p 2 , (19) where the mixing entropy is combined with the interaction enthalpy through the Flory–Huggins interaction parameter X , which is related to the polymer solubility δ p and water solubility δ w as follows: χ = V ¯ w R T δ w 2 − δ p 2 . (20) Thus, as the water solubility approaches the polymer solubility, X decreases, which means that the enthalpic interactions that resist mixing become weaker and swelling becomes more favorable. Equation (12) can be rewritten in terms of the processes that drive mixing (the left-hand side of the equation) and those that resist it (the right-hand side of the equation): ln a w − ln 1 − ϕ p − 1 − 1 V ¯ p / V ¯ w ϕ p = χ ϕ p , T ϕ p 2 + V ¯ w R T P s ϕ p , T . (21) It is also assumed here that the interaction parameter and pressure vary with temperature and swelling ( ϕ p ). Therefore, the tendency of water nanodomains to swell due to favorable interactions between water and ionic groups is represented by the chemical energy of solvation and hydration (the left-hand side of Equation (21)), which is opposed by the deformation of the hydrophobic backbone, which acts against swelling (i.e., the mechanical energy on the right-hand side of Equation (21)). Thus, it is common practice to interpret the equilibrium of swelling as a balance between the entropic forces that lead to swelling and the exergonic effects, including the mechanical deformation of the backbone, that act as a resistance that creates swelling pressure. The Flory–Huggins models can successfully predict the swelling of cross-linked gels in the absence of electrostatic interactions, which are abundant in PFSA ionomers. Therefore, the Flory–Huggins theory may be applicable, at best, to the swelling of the membrane by free water. However, a complete model should take into account the nature of the water, i.e., whether it is free or bound. For this reason, the volume fraction of the polymer in the Flory–Huggins equation is typically modified to include bound water, which is strongly associated with ionic fragments [ 305 , 317 , 421 ]: ϕ p = V ¯ p + λ B V ¯ w V ¯ p + λ V ¯ w . (22) It is clear that as the water activity increases, the contribution from Langmuir adsorption to the sorption isotherm decreases in favor of the accumulation of free water [ 111 , 267 , 274 , 407 ]. Similarly, the fraction of hydrophilic domains in ionic water can be calculated as φ h f = φ SO 3 + φ w = φ p φ dry SO 3 + φ w , where the volume fraction of the SO 3 group in the dry polymer is approximately φ dry SO3 = V SO3 / V p ≈ 40.94 cm 3 /mol [ 143 ]. 16. Swelling Pressure The swelling pressure in Equations (12) and (13) is directly related to the modulus of elasticity of the polymer matrix acting against swelling. The concept of deformation of the polymer base by swelling of aqueous nanodomains has been discussed both from the point of view of modeling and structural characteristics [ 185 , 260 , 269 , 270 , 274 , 403 , 421 ]. Thus, it is quite obvious that the formulas for swelling pressure should include the modulus of elasticity of the polymer, but the deformation of the matrix is quite difficult to calculate. The simplest approach connects deformation with a macroscopic change in volume, although it is doubtful that the deformation of the matrix at the nanoscale can be represented in macroscopic terms [ 265 , 274 , 317 ], given that the nanoscopic swelling of water domains differs from the macroscopic swelling of the membrane, i.e., nonaffinity swelling. Therefore, formulas for swelling pressure include microscopic [ 270 , 271 ] and nanoscopic [ 111 , 272 ] swelling. In both models, the swelling pressure calculated for the case of nonaffinity swelling is higher than for affinity. Although formulas for swelling pressure exist in classical theories, they give a finite pressure at zero swelling, as discussed by Freger in [ 270 ], who developed an alternative expression based on the nonaffinity swelling of a phase-separated PFSA network. It relates the swelling pressure to the shear modulus G of the dry polymer network: P s ϕ p = 2 3 G ϕ p 1 / 3 − ϕ p 7 / 3 . (23) In [ 111 , 272 ], the authors proposed another expression for swelling pressure based on the deformation of the hydrophobic backbone (modulus E b ) contracting between the growing water domains (diameter d and the distance between the domains d w ) with hydration, i.e., P S ∝ E b × ( d w − d ): P s T , ϕ w = E b T × b b d r y − 1 b ϕ w b d r y = d w ϕ w − 2 r w ϕ w d d r y − 2 r d r y = d w ϕ w d d r y 1 − ϕ w 1 / n − 1 1 − ϕ d r y 1 / n , (24) where b and b dry are the thickness of the substrate in the swollen and dry state, respectively, between the water regions, which can be related to the distance d w and radius r w of the hydrophilic domain. Both distances increase with hydration ( φ w ), as shown in Figure S2 . This concept is consistent with changes in the wall thickness of the polymer substrate [ 143 , 422 ]. The advantage of this approach is that it includes the domain size as a deformation parameter, which can be measured using the small-angle X-ray scattering (SAXS) technique. Therefore, it provides a flexible model that predicts lower water absorption due to annealing, compression, and higher equivalent mass. All these factors increase either the swelling pressure or the modulus of elasticity of the polymer matrix, or create additional deformation in the matrix, which is confirmed by the SAXS studies [ 111 , 260 , 272 , 395 ]. The above expressions give comparable trends, although they are obtained using different approaches. Consequently, despite the idealization of the disordered morphology of PFSAs and the simplification of the complex multiscale swelling process, structural models of thermodynamic equilibrium can help analyze and explain the measured absorption data. However, the true nature of the water inside the ionomer has not yet been fully elucidated due to its complex interactions with the spatial distribution of ions, retention effects, and the role of penetrant suspension side chains. 17. Effects of Limitation and Compression In most cases, ionomeric membranes are in a compressed state due to the nature of the design and geometry of the multicomponent system (for example, fixing the membrane electrode to seal and ensure minimal resistance contact). In addition, there may be other internal limitations that occur in the membrane during the manufacturing process. For example, extruded or stretched membranes exhibit structural anisotropy due to their preferential orientation during processing [ 163 , 423 , 424 ]. Moreover, membranes macroscopically reinforced with foamed polytetrafluoroethylene have almost insignificant superficial swelling and excellent mechanical properties [ 343 , 344 ]. These internal limitations lead to effects inherent to the properties of the membrane. For example, reinforcing a membrane with a stiffer material creates additional internal swelling resistance in the reinforcement direction. This effect is similar, at least theoretically, to the action of an external containment membrane, which is not reinforced in one direction, allowing it to hydrate; it swells less in limited directions compared to an unlimited direction. Changes in the water content in Nafion during compression were observed using neutron imaging of a polymer-electrolyte fuel cell [ 425 , 426 ] and subsequent compression tests [ 260 , 282 , 427 ]. These tests showed that the change in water content is insignificant when compressed, unless the membrane is in liquid water and is compressed by more than 4 MPa; at the same time, a decrease of λ by 10% was reported in [ 260 , 282 , 427 ]. The pressure in the hydrated ionomer membrane, measured using compression devices, ranges from 30 to 100 Mpa [ 249 , 282 , 427 ]. Such high values were attributed to the swelling pressure in the swollen membrane domains at the nanoscale [ 265 , 270 , 272 ]. Unlike hydrogels, ionomeric membranes require high pressure to lose free water (25 MPa is required to reduce λ by 50%) due to their own partially crystalline morphology, high concentration of ion domains, and strong electrostatic interaction. The compression effect was studied using macrouniform models [ 260 , 395 , 428 , 429 ]. The model of Kusoglu et al. [ 260 ] took into account the deformation of nanodomains during compression using SAXS and used it to determine changes in swelling pressure, chemical potential equilibrium, and water content [ 260 ]. Conceptually, the compression effect can be realized at the swelling equilibrium if Equation (5) [ 260 , 428 ] is supplemented: Δ μ w e = Δ μ w p = Δ μ w p , c ⇒ R T Δ ln a w = R T Δ ln a w + V ¯ w Δ P s = R T Δ ln a p + V ¯ w Δ P s c , (25) where ∆ μ p , c w and P s are the chemical potential and the swelling pressure of the compressible and constricted membrane, respectively. It should be noted that if the hydrated membrane is subjected to hydrostatic pressure p , its volume will also decrease by dV = p / K b ( λ ); this affects the molar volume of the membrane ( K b is the volume modulus, depending on λ ). 18. Interaction Parameter and Solubility The key parameter characterizing interactions in the Flory–Huggins model (see Equation (26)) is X , the value of which goes beyond the model due to its relationship with solubility. With a decrease in the solvent–polymer network interaction parameter, solvent assimilation becomes more favorable. The value X can be determined either by the measured solubility [ 253 , 254 , 430 ], or by selecting the sorption isotherm using the Flory–Huggins expression [ 111 , 267 , 272 , 309 , 430 ], or predicted using ab initio calculations [ 83 , 87 , 88 ]. The interaction parameters X calculated on the basis of molecular dynamics modeling and determined on the basis of absorption data are summarized in Table 3 . Table 3. Interaction parameters X for Nafion, 3M and SSC PFSA *. Interacting Pair Interaction Parameters X 3M [ 88 ] SSC PFSA [ 87 ] Nafion [ 83 ] Backbone—side chain −0.03 0.15 1.23 Backbone—CF 2 SO 3 H·3H 2 O 7.07 6.86 7.44 Backbone—6H 2 O 3.30 3.28 3.36 Side chain—CF 2 SO 3 H·3H 2 O 7.04 6.24 2.70 Side chain—6H 2 O 3.47 3.15 1.53 CF 2 SO 3 H·3H 2 O—6H 2 O 1.53 1.24 1.48 Open in a new tab * In all cases, the molecular backbone has structure 6(CF 2 ), and the side chains are CF 2 CF(OCF 2 CF 2 CF 2 ) for 3M, CF 2 CF 2 CF 2 CF(OCF 3 ) for SSC PFSA, OCF 2 C(CF 3 )FOCF 2 for Nafion. Most of these studies agree that hydration depends on the interaction parameter (which consists of various independent individual interactions), as shown in the graph showing the range from 0.9–2.5 [ 254 , 309 , 421 ]. The interaction parameter decreased with hydration, which is described by the expression X ≈ φ p 1.5 or φ p , [ 111 , 267 , 309 ]. The data for plotting the parameter X as a function of the proportion of solvent (and water), as collected from the literature, fall between two trends with φ p 1 and φ p 2 . At the same time, the exponents capture swelling quite well in the steam-water regime, which was discussed in the works of Kusoglu et al. [ 111 , 260 ]. In addition, X is expected to decrease with increasing temperature [ 420 ], which favors the thermodynamics of mixing (swelling), which has been observed for other polymers [ 311 , 431 ]. However, in water vapor, an increase in temperature can decrease λ at very high relative humidity. In the context of this discussion, this implies that X increases with temperature, which is consistent with other studies [ 112 , 309 ]. The resulting expression for the interaction parameter can be written as [ 111 , 260 ]. χ ϕ p , T = χ s ϕ p 1.5 + χ T 1 − T r e f T , (26) where the parameter X T (and its sign) is determined by the polymer–solvent interaction resulting from changes in the phase of water and the morphology of membranes with a thermal history [ 114 , 121 , 122 , 154 , 313 ]. In liquid water, the opposite trend is observed, i.e., a higher value of λ and a lower value of X with increasing temperature. This fact suggests that either the interaction parameter cannot be derived from the classical Flory–Huggins theory for vapor-balanced PFSAs at higher temperatures (for example, due to the very small amount of free water), or its behavior is controlled by increasing morphological differences between steam and a temperature-balanced liquid. In the latter case, the interaction parameter can provide an interesting connection between ∆ λ liq − vap and pair interactions between water and PFSA parts, including surface interactions that could be used to explain Schroeder’s paradox. Another interesting relationship is observed for temperature-dependent water absorption: while temperature reduces the modulus of elasticity of the polymer base and, consequently, its resistance to swelling, this leads to a higher value of λ , and the positive dependence of X on temperature tends to decrease λ . Thus, once again, equilibrium absorption is regulated by mechanical and chemical energy with an intriguing effect of temperature on interactions. However, it is still unclear how the interaction parameter changes depending on certain thermodynamic variables such as pressure, which is an active area of research. However, in liquid solvents, the absorption values vary significantly depending on the solvent (its polarity and dielectric constant) [ 253 , 254 , 338 , 413 , 414 ]. In general, the solvent absorption capacity of PFSAs seems to correlate with the dielectric constant or solvent parameters, although universal trends exist with higher solvent absorption, which usually leads to increased conductivity [ 253 , 432 , 433 ]. These dependences of solvent absorption on solubility create a “swollen envelope” controlled by two PFSA solubility values: one for its hydrophobic base δ ≈ 10 (cal·cm −3 ) 1/2 and the other for binding to hydrophilic ionic groups δ ≈ 17 (cal·cm −3 ) 1/2 , as discussed in [ 434 ]. At the same time, all data are limited by the solubility of PTFE and pure water, which explains the origin of the two different solubility values for PFSAs. Gebel and his colleagues [ 253 ] published a detailed study of the swelling of Nafion 117 membranes in various solvents and reported that it correlates better with the solvent donor number than with the dielectric constant and solubility. Doyle et al. later presented a similar correlation, where PFSAs swell more strongly in polar solvents [ 253 , 432 , 435 ], which was confirmed by the applicability of the group contribution theory [ 435 ]. The solvent has been reported to affect the absorption of PFSAs [ 253 , 254 , 255 , 338 , 435 , 436 ], as well as their conductivity [ 255 , 338 , 433 ] and domain spacing [ 188 , 189 , 437 ]. Studies of vapor absorption in other solvents are rather limited [ 255 , 436 ]. A study by Zhao and co-authors showed that the Nafion swelling stress is higher in ethanol and methanol compared to water, despite the fact that the number of solute molecules in water is greater than in alcohols [ 255 ]. 19. Morphology and Its Variations Despite the strong connection between sorption and transport properties, they are usually modeled separately from each other, seemingly in disparate areas that try to combine them with little effort [ 269 , 274 , 276 , 394 , 397 , 402 ]. While sorption models for water absorption are interpreted as “equilibrium”, transport models include water absorption and mobility and other factors (e.g., conductivity), sometimes even a time dependence (e.g., for diffusion capacity). An effective approach to connect the phenomena of water absorption and transport is carried out through phase separation morphology (discussed in Section 20 ) using the sizes, shapes and connectivity of hydrophilic domains. In such models, a membrane nanostructure (usually a spherical or cylindrical “pore” representing a hydrophilic domain) is usually assumed, and dependent properties are predicted. This geometric idealization of water regions is usually used to interpret data for SAXS with a wide peak and a measured distance between domains, which can be used to estimate parameters such as the diameter and size of the domain and the number of ion cells per domain, depending on the water content. Although the interpretation of morphology is useful for modeling purposes, such approaches lack the nuances of the actual structure and its response to changes, because, in fact, phase-separated nanodomains and their geometric features change as a result of moisture. It should be noted that various morphological descriptions have been accepted in the literature: from spherical clusters to locally flat morphologies. However, the domain can still be defined as the smallest observed repeating structural unit on the nanoscale. Historically, the domain has often been associated with a spherical cluster due to the cluster geometry of the network adopted in early studies; however, the current state of the understanding of PFSA morphology requires a more general description without prescribed geometric shapes. In addition, due to the evolution of phase separation during sorption, it is impossible to specify a specific morphology and geometry of PFSA ionomers. In fact, these morphological changes have been discussed and used in model studies to explain the unique sorption properties of PFSA ionomers. Inspired by an idealized two-phase morphology, such as the cluster network model, a similar geometric description has been adopted to explain or model the nanostructure based on available SAXS data [ 111 , 272 , 286 , 293 , 365 ] for swelling pressure and sorption [ 111 , 265 , 272 ], sorption and transport properties [ 267 , 269 , 391 ], or the pore network ensemble [ 276 , 391 , 394 ]. The pore network model assumes either idealized rigid pores [ 276 , 394 ], or uses a pore size distribution [ 392 , 401 ]. One of the disadvantages of idealizing water domains as rigid voids and the phenomenon of pore wetting is the lack of nanosetting and deformation of the polymer base, which does not necessarily reflect the true nature of PFSAs, for which hydrophilic domains grow and which may merge through water absorption and deformation of hydrophobic domains. In addition, the shape and connectivity of domains, regardless of whether they are spherical or cylindrical, have been discussed in combination with these models: Weber and Newman proposed that spherical domains become cylindrical in liquid water, which explains the vapor-to-liquid transition [ 269 ]. Similarly, but using a different approach, Kusoglu et al. showed that the measured dependence of hydration on water absorption and mechanical properties can be reproduced better, especially at higher humidity, if randomly located cylindrical domains are used in the nanostructure [ 111 , 260 ]. It has been shown that using such idealized regions, the actual absorption of water by the membrane is limited to that of a hypothetical membrane with completely spherical and cylindrical domains [ 111 , 260 , 272 , 286 ]. In [ 422 ], it was concluded that only locally flat regions are consistent with several sources of experimental data, the description of which is consistent with recent results of cryo-electron tomography of hydrated Nafion [ 438 ]. Unlike the above-mentioned models, the models in [ 84 , 86 , 270 , 271 ] use an expression for the free energy of the system and minimize it among possible geometries in order to obtain a description of a hydrophilic domain nanostructure. Thus, they predict the environmental impact of water swelling and provide a domain distribution that can be used to run simulations of transport properties. The vapor–liquid transition is also explained using this type of model, but using changes in surface energies [ 271 ]. Therefore, the basic idea of all models is that thermodynamic equilibrium is determined by the mechanico-chemical energy balance, through which the sulfonic acid fragments could dissolve, but this is prevented by the polymer base and hydrophobic fragments, which create swelling pressure [ 270 , 272 ]. As noted earlier, most models try to explain Schroeder’s paradox by stating that the membrane undergoes a morphological transition from vapor to liquid equilibrium, especially at the beginning, accompanied by specific surface phenomena [ 276 , 317 , 318 , 439 ]. This interpretation eliminates the “paradox” by adopting different structures, even when the activity of water is a w = 1 (similar to the phase transitions of liquid and vapor). Early models were based on the assertion that the PFSA membrane has a hydrophobic surface when saturated with steam, but becomes hydrophilic upon contact with liquid water, which was confirmed by observations based on experimental data on the contact angle [ 152 , 322 , 331 ] and measurement of the mass of transport [ 335 ], and more recently by water sorption [ 274 , 313 , 323 ], atomic force microscopy (AFM) [ 440 , 441 ], SAXS [ 155 , 322 ] and grazing-incidence small-angle X-ray scattering (GISAXS) [ 322 , 442 ]. Also, in a pair, the hydrophobicity of the PFSA surface decreases with increasing relative humidity [ 291 , 332 , 443 , 444 , 445 , 446 ], which is accompanied by higher ionic activity [ 332 , 333 , 440 ]. Inspired by these observations, researchers proposed representing the swelling pressure in thermodynamic models with a member that is present in the vapor phase due to the “hydrophobic skin” on the membrane surface, but is absent in models with liquid water, thereby reducing the back pressure [ 274 , 276 , 440 , 441 ]. As a result of a decrease in the swelling pressure on the surface, the water absorption capacity of the membrane increases with the same level of water activity. In one approach, an additional term has been proposed for the resulting capillary effect in pores, which is quantified by adding a pore capillary pressure term representing water domains to the normal pressure in the polymer matrix, which is positive due to the hydrophobicity of the surface [ 267 , 276 , 317 ]. Eikerling and Berg [ 276 ] used models of a pore ensemble that included the effects of capillary, osmotic, and elastic pressure, which could explain the reorganization of surface charge density and link pore swelling to macroscopic absorption through pore filling. Their model also solved Schroeder’s paradox by using capillary arguments that change the pressure equilibrium inside the pores. However, with the help of capillary pressure and pore wetting, the question of the mechanisms of water nanodomains on the surface remains controversial due to their energy instability [ 310 ]. In another approach [ 312 , 439 ], the modified Laplace pressure is added to the energy term of the surface, which exists for vapor equilibrium but disappears for liquid equilibrium. Although the first approach relates the term capillary pressure to the inner polymer matrix and the external environment, the latter energy approach forms a connection between the inner liquid and the polymer matrix. Both approaches are mathematically different, but they are conceptually similar and use a thermodynamic force to balance swelling, which changes with the phase of the outer water, thereby resolving the paradox. Freger [ 271 ] proposed another term G L , which adds to the free energy, ∆ G + ∆ G L , to take into account the interfacial energy at the interface of the ion aggregate/polymer matrix and determine the chemical potential by minimizing the total energy per ionic group g with respect to λ : g = g s + g e + γ σ → μ w λ = 𝜕 g 𝜕 λ σ = μ s λ + υ p e λ + υ p L λ , σ , (27) where the additional term is related to the surface tension y , and the values σ and υ are, respectively, the surface area and volume of the polymer per ionic group. Then the chemical potential of water is represented as the sum of the following terms: swelling and two osmotic conditions that counteract swelling: the usual swelling pressure p e , which occurs during elastic deformation of the matrix, and the Laplace pressure p L , which includes interfacial and elastic contributions. In vapor equilibrium, the membrane surface is covered by a polymer matrix/vapor interface with a nonzero Laplace pressure. However, in liquid water, this term for interfacial pressure disappears, thereby releasing pressure by the amount of excess pressure p L , which leads to greater swelling. This phenomenon has been proposed to explain Schroeder’s paradox. According to this approach, high pressure develops around the domains of the membrane balanced in the vapor phase, which limits the absorption of water in it. 20. Morphological Features The phase of hydrated PFSAs is divided at the nanoscale into various disordered complex morphologies that use mesoscale connectivity to form a hydrophilic ion-conducting phase and a hydrophobic, non-conducting phase, controlling mechanical properties. Hydrophilic domains are used to describe a region with solvent and cations, although in some studies, they are described as clusters or aggregates in molecular models. Morphological features of sulfonated polymers have been extensively studied over the past few decades using small- and wide-angle X-ray and neutron scattering (i.e., SAXS, WAXS and SANS) [ 447 , 448 , 449 , 450 , 451 , 452 , 453 , 454 ]. X-ray scattering has historically been a useful tool for studying the morphology of dry and hydrated PFSAs and similar random copolymers. The most commonly used information from scattering is a single wide ionomeric peak, which corresponds to the structural correlation length for hydrophilic domains and is interpreted as the distance between water domains. Additional information that can be extracted from the entire q -range: the second scattering maximum, often referred to as the “matrix knee” (the distance between intercrystalline domains) at a lower q (larger scales), the Porod regime (Porod’s law, discovered by Günther Porod, describes the asymptote of scattering intensity) at a higher q (lower scales), which is related to the internal structure (surface-to-volume ratio S/V), crystallinity at the highest q (diffraction mode), related to atomic distances. In general, due to the relatively random separation of phases, peaks are often quite wide, and therefore, data interpretation (for example, the behavior of the peak during humidification) is a difficult task that researchers have been actively looking for in recent decades, but the results have often been interpreted differently and have not been definitive. The analysis is also complicated by the fact that scattering methods provide data in Fourier space, the transformation of which into real space for three-dimensional morphology is interpreted ambiguously, especially for disordered polymers such as PFSAs. This is overcome due to the extensive amount of structural data obtained using SAXS and WAXS (wide-angle X-ray scattering), as well as SANS and QENS. Such data helps to understand the influence of factors such as time, humidity, temperature, crystallinity, mechanical loads, and, to a certain extent, film thickness and ion exchange capacity on the behavior of the ionomer peak and associated macroscopic water absorption and conductivity. In addition, these methods remain reliable and powerful tools for elucidating and comparing structural features of PFSAs, especially with advances in on-site diagnostics. However, debates about the exact nanostructure and connectivity of these domains and their interactive role in ion transport are still ongoing, partly due to the desire to improve and optimize the functional characteristics of the material (e.g., conductivity and stability) through understanding the relationship between transport mechanisms and morphological behavior. The key to this understanding is also the local environment, which has been studied by various spectroscopic methods [ 8 , 32 , 368 ]. Such spectroscopic methods have been used to study PFSAs since the 1980s, initially using techniques in [ 47 , 455 , 456 , 457 ], and then using Raman spectroscopy [ 173 , 292 , 350 , 458 , 459 , 460 , 461 ], Fourier spectroscopy, attenuated total reflection spectroscopy [ 462 , 463 , 464 , 465 , 466 , 467 , 468 , 469 , 470 ] and solid-state NMR [ 258 , 376 , 471 , 472 , 473 , 474 , 475 , 476 ]. When studying the effect of hydration on membrane thickness during swelling in [ 61 ], Raman spectroscopy was analyzed in the confocal mode, which made it possible to obtain accurate and reproducible results without mechanical action on the sample. In [ 184 ], the presence of various functional groups, especially sulfonic groups responsible for proton conductivity, was studied using attenuated total internal reflection IR spectroscopy. The main vibrations were attributed to spectral lines, and additional weak peaks were found for the sample obtained by processing spent fuel cell membranes, which could be associated with the presence of carbon nanoparticles. Attributing bands of IR spectra to specific molecular interactions is the key to their analysis [ 292 , 350 , 456 , 466 , 470 ]. In these studies, the characteristic IR peaks of PFSAs are associated with polymer chains (bands for C–O–C and CF 2 from 950 to 1425 cm −1 ), ionic groups SO 3 − with symmetric (SO 3 ) s ~1060 cm −1 and antisymmetric (SO 3 ) as ~1130 cm −1 and S–O stretching modes, as well as vibrations (SO 3 H) around 2200–2720 cm −1 [ 286 , 292 , 455 , 457 , 477 ], and with interacting and free water H–O–H in the range of 1620–1740 cm −1 and stretching (O–H) in the range of 3000–3450 cm −1 [ 286 , 292 , 455 , 457 , 466 , 467 , 477 , 478 ]. The latter bands, attributed to changes in the local water environment, are used to analyze the water absorption characteristics [ 286 , 292 , 456 , 462 , 479 , 480 , 481 ]. Thus, PFSA spectroscopic analysis provides information related to proton dissociation from the SO 3 groups and hydration changes in sulfonate water affecting conductivity [ 9 , 173 , 383 , 462 ], diffusion [ 168 , 463 , 464 , 482 ], sorption [ 286 , 296 ], cation interaction with sulfonate groups [ 94 , 456 , 472 , 478 , 480 , 483 , 484 ], annealing [ 110 , 116 , 147 , 464 , 485 ], and conformational changes in the backbone in the context of the semicrystalline PTFE chain [ 9 , 286 , 471 , 474 ]. For example, the oscillatory mode SO 3 is influenced by the local chemical environment, where strong cationic interactions polarize the S–O dipole, from which interaction energies can be determined [ 480 ]. For this reason, spectroscopy is commonly used to elucidate the substructure of water in many phenomena, from aging and cationic fouling [ 237 , 257 , 258 , 478 , 484 , 486 , 487 ] to the interaction of inorganic fillers with the main ionomer matrix [ 466 , 488 , 489 , 490 ]. 21. Nanomorphology Since the early works of SAXS [ 42 , 143 , 144 , 150 , 288 , 296 ] reported on the moisture-dependent peak of the ionomer associated with a phase-separated nanostructure, a large number of studies have used SAXS/SANS to determine the morphological features of PFSAs. Such works include studies of the influence of many factors: Hydration [ 289 , 290 , 291 , 447 , 491 , 492 ]; Temperature and thermal history [ 148 , 149 , 157 , 171 , 186 , 227 , 422 , 493 ]; Freezing [ 97 , 381 , 384 , 487 , 494 , 495 , 496 , 497 ]; Mechanical loads, stretching, and orientation [ 423 , 424 , 448 , 450 , 453 , 498 , 499 , 500 ]; Time [ 155 , 156 , 157 , 285 , 501 ]; Cations [ 143 , 149 , 171 , 279 , 437 ]; Solvents [ 189 , 437 , 502 , 503 , 504 , 505 ]; The dispersion state of PFSAs [ 181 , 185 , 186 , 188 , 189 , 190 , 191 , 192 ]; Addition of nanofillers [ 489 , 492 , 506 , 507 , 508 , 509 ]. Early studies used thermodynamic models to predict the formation of hydrophilic domains in a hydrophobic matrix based on the energy balance between electrostatic interactions and deformation of the surrounding matrix [ 144 , 266 , 403 , 500 ]. Although the energy of dipole interactions favors the aggregation of hydrophilic ionic centers, the main chain of the polymer prevents this. Other works include interpretation based on scattering theory [ 291 , 422 , 447 , 449 , 491 , 510 ], simulation studies to reproduce experimental observations [ 398 , 451 , 511 , 512 , 513 ], direct imaging using transmission electron microscopy [ 438 ], and nanostructure-based macroscopic models for sorption determination [ 111 , 269 , 272 , 514 ], transport [ 269 , 391 , 395 , 514 ] and mechanical properties [ 515 , 516 , 517 , 518 , 519 , 520 , 521 ]. Despite the fact that it is not difficult to determine the distance between domains (their correlation length) from the SAXS peak, the same cannot be said about the shape, structure, or connectivity of domains. In [ 181 ], using the methods of SAXS and pH-metry, it was shown that the structure of aggregates in PFSA dispersion determines the behavior of the material under tension: dense secondary aggregates form, domains align parallel to the substrate surface, and the distance between them also varies depending on the chemical composition of the side chains. The degree of orientation of the domains correlates with the water content in the dispersion. The authors of [ 181 ] also found that solvent composition significantly affects morphology. Namely, aqueous solutions help to improve proton conductivity and change the structure of aggregates, while alcohol components affect the processes of hydrophobic interactions, the state of aggregation of the ionomer, and its mechanical properties. Based on structural idealizations, a hydrophobic “wall” of 2 to 3 nm thickness has been estimated that separates hydrophilic primary domains of 2 to 4 nm in size, which are interconnected by secondary domains (0.5 to 1 nm) [ 289 , 291 , 293 , 422 , 423 , 522 , 523 ], although these values depend on the domain shape (spherical or cylindrical) specified in the calculations and become ambiguous when quantifying secondary bonds and other morphological representations (e.g., locally flat regions). However, they are in reasonable agreement with similar analyses performed by porosimetry [ 524 , 525 , 526 ] and cryoporometry [ 151 ], which suggest that most of the water in hydrated Nafion is located within domains of 1 to 3 nm, but larger (>5 nm) domains in the size distribution were also found in [ 524 , 525 , 526 ]. As noted, domain shape is usually assumed to perform the analysis, and commonly used geometries (i.e., spherical, cylindrical, and lamellar) and their possible connectivity have been evaluated and discussed in studies by Gebel and co-workers [ 185 , 447 , 510 ] and recently by Kreuer et al. [ 422 ] (see Figure S3 ). Although the structures are expected to provide some information, direct visualization is required due to the confounding issues with the data discussed above. This image demonstrates a locally flat, highly branched structure at full hydration. However, quantitatively assessing the morphology with an accurate geometric representation of the domains, their shape, distribution, and connectivity, particularly in terms of water content, remains challenging. The effect of hydration on the structure and morphology of PFSA membranes was studied in detail using the example of Nafion and Aquivion in [ 287 ]. During the study, it was found that hydration has a significant effect on the structural characteristics of membranes, and this effect manifests itself in different ways for samples with different side chain lengths. During humidification, the intercluster distances in the ion domains increase: for Nafion, this indicator increases by 2.5 nm (from 3.4 to 5.9 nm), while for Aquivion, the increase is 1.5 nm (from 3.1 to 4.6 nm). The flexible long side chains of Nafion ensure more efficient restructuring of the structure during hydration and the formation of ordered crystalline regions, while the short rigid chains of Aquivion limit the mobility of the polymer chain and prevent the formation of crystalline domains. Changes are also observed in the crystalline domains: the distance between crystallites in Nafion increases by 0.8 nm (from 11 to 11.8 nm), and in Aquivion by 1.5 nm (from 17.3 to 18.8 nm). At the same time, the degree of crystallinity of Nafion (11.5%) is significantly higher than that of Aquivion (5.3%) [ 287 ]. It is noteworthy that both materials exhibit increased plasticity during hydration, but their structural responses to moisture differ due to the peculiarities of their molecular architecture. Temperature effects also play an important role: Aquivion exhibits a higher sensitivity to temperature changes, while Nafion retains a well-developed structure of ionic domains even at low temperatures, which is due to the mobility features of its polymer chain. An integral component of morphological studies is the structure of PFSAs in a dispersed state, the study of which dates back to the late 80s. It is generally accepted that PFSAs are not a real solution in dispersion (although this term is still used), but rather a colloidal suspension due to the strong role of polymer/solvent interactions [ 515 ]. In a series of SAXS/SANS studies of PFSAs in various solvents and cations [ 188 , 189 , 190 , 191 ], the authors developed a morphological picture of aggregated PFSA colloids in polar solvents (see Figure S2 ). The size of aggregates is determined by the elastic energy required to form a rod-like structure and the interphase energy associated with the polymer–solvent interaction, which tends to decrease while minimizing the surface area [ 185 , 189 , 190 , 191 ]. The size scales of such units are shown schematically in Figure 5 . The study used SANS data for the solutions to extract: Bragg distances of aggregates using the ionomer peak; Radii of scattering particles using Guinier analysis; Information about the particle interface by studying the asymptotic behavior (for a large value of q at Porod’s limit) [ 454 ]. Figure 5. Open in a new tab Schematic representation of the size scales of aggregated PFSA colloids. In the low- q regime, the intensity ( I ) scales with q −1 , indicating elongated objects [ 447 , 449 , 450 , 527 ], whereas in the asymptotic regime, I scales as q −4 , indicating that the aggregates represent a well-defined interface with the solvent [ 185 , 189 , 190 , 191 , 447 , 449 ]. Thus, in dilute solutions of polar solvents, rod-shaped elongated aggregates with a radius of 20 to 25 Å and a persistent length l p = 3–5 nm [ 191 ]. Moreover, an increase in the solvent permittivity promotes the existence of local order but does not have a strong effect on the rod radius [ 203 , 204 ]. An increase in the size or valence of the counterion significantly reduces the electrostatic repulsions between particles and promotes interparticle aggregation. Compared with LSC ionomers, the radius in PFSAs with a short side chain was found to be slightly smaller due to the lower EW: 15–17 Å versus 20–25 Å. The effect of the nature of the terminal ionic group was found to be insignificant [ 191 ]. All these studies of PFSAs from membrane to dispersed form make significant contributions to the current understanding of morphology. A number of morphological models have been proposed, starting with the cluster network model proposed by Gierke, Hsu, and co-workers [ 143 , 144 ], in which water attached to ionic groups forms interconnected spherical hydrophilic clusters with diameters ranging from 4 to 6 nm that are distributed in a polymer network. The studies of Gebel and colleagues on PFSAs from the dry state to the solution phase have combined several features of previous models. They concluded that the interconnected network of domains is transformed into a rod-like polymer structure in colloidal solution with an inversion of the structure due to excessive swelling of the water domains [ 185 , 188 , 191 , 290 , 454 ]. Later, Rollet, Rubatat and co-workers described the morphology of PFSAs as elongated polymer rod-like aggregates with water reservoirs located among them [ 447 , 449 , 510 ], expanding on previous studies by the same group [ 191 , 454 ]. According to their model, the scattering peak is related to the interaggregate distance, and hydration is interpreted as dilution of these aggregates without structural reorganization [ 447 , 449 ]. Since then, alternative descriptions of the morphology of hydrated PFSAs have been proposed [ 522 , 524 , 525 , 526 , 528 , 529 , 530 , 531 , 532 ], including a sandwich model where water is embedded in the polymer matrix [ 491 ], a disordered network of polymer chains and water pools [ 285 ], a plate–ribbon structure of polymer domains with ionic centers on their surfaces [ 511 ], parallel cylindrical water channels embedded in a semicrystalline polymer matrix [ 512 ], and a bicontinuous network of ionic clusters in a matrix of fluorocarbon chains [ 451 ]. However, the structure at full hydration is close to ribbons, i.e., locally planar, hydrophilic domains interspersed among the backbone crystallites [ 422 , 449 ]. Although the structure at different hydration levels is not fully known, a more discontinuous cluster-like behavior at very low water contents is possible. This picture is also consistent with surface morphology studies (e.g., AFM), which suggest that the fluorocarbon-rich surface is dependent on humidity within a worm-like network of elongated [ 533 ] or locally flat [ 64 ] domains. A similar structural interpretation of the SAXS data comes from the Porod regime, which yields polymer–water interface S/V values ranging from ~600 to 400 m 2 /cm 3 [ 422 , 523 , 534 , 535 ]. While Kong et al. [ 535 ] explained this trend in the S/V dependence on φ w in the two regimes by arguing for a transition from spherical domains in the dry state to ribbons in the hydrated state, Kreuer [ 422 ] argues that local flattening is still energetically more favorable than cylinders or spheres as long as the separated charges are not completely shielded by the high-dielectric solvent. This allows PFSAs to adopt a rod-like morphology in the dispersed state due to very high hydration levels. In [ 399 ], the authors examined the large-scale morphology of PFSAs and found that their bundle structure flattens into ribbons, thereby creating a locally flat model that fits the transport data better than lamellar and random models. They also found that the hydrophobic–hydrophilic interface is key to transport phenomena, with smaller surface areas (S/V) exhibiting higher H + diffusion coefficients. Later studies of different solutions and counterion forms showed that PFSA dispersions form primary aggregates at low PFSA concentrations, followed by secondary aggregates with increasing concentration, resulting in more disordered chain segments that do not participate in the formation of cylindrical rods; the number and length of molecular chains in the rod, as well as the rod size, decrease with increasing concentration [ 536 ]. Overall, these studies suggest a transition with increasing PFSA concentration from a helical disordered aggregate structure, in which ionic interactions are still preserved, to more ordered rod-like aggregates with secondary ionic clusters [ 536 , 537 , 538 ]. The phase separation of the aggregates is controlled by the compatibility of the solvent with the PFSA backbone, where this is favorable, and electrostatic interactions also influence their interaggregate distance [ 539 ]. 22. The Role of Isotopic Effects in the Soaking of Polymer Membranes In a number of works, the features of swelling in the proton-exchange polymer membrane of Nafion in water and aqueous solutions of salts with deuterium content in the range of 1–10 6 ppm were investigated. In fact, in these works, the entire possible range of deuterium concentrations in water and aqueous solutions was investigated, see [ 540 , 541 ], and the polymer membrane studied was that of Nafion N117. The relevance of these studies is due to the fact that proton exchange membranes are used in hydrogen fuel cells and in electrolyzers for the production of molecular hydrogen. One of the key performance indicators of a hydrogen fuel cell and a hydrogen generator is the proton conductivity of its ionomeric polymer membrane. Developments aimed at increasing the proton conductivity of membranes in hydrogen production plants have developed in three directions: increasing the temperature of the liquid, increasing the liquid content in the nanoscale channels of the membrane, and introducing organic and inorganic nanoparticles into the polymer matrix. Such particles affect the local lyophilic properties of the membrane and increase the membrane’s ability to retain liquid in a loosely bound state inside the nanoscale channels of the membrane over a wide temperature range. In these works, the possibility of increasing the proton conductivity of solid-state ionomeric polymer membranes by changing the isotopic composition of water and aqueous solutions used in the generation of molecular hydrogen was investigated. As is known, the concentration of deuterium in natural deionized water is 157 ppm; water with such a deuterium content is traditionally used in electrolyzers. The studies were conducted using various experimental techniques. In experiments on photoluminescent spectroscopy at a wavelength of 369 nm, the surface of a polymer membrane was irradiated in a sliding incidence geometry with the possibility of shifting the membrane surface by a distance X relative to the optical axis. At a certain distance X , the pump radiation in the sliding drop scheme stops hitting the membrane surface, and there is no luminescence signal. In these experiments, it was found that during the swelling process, polymer fibers are unwound into a volume of liquid without completely detaching from the membrane surface. Figure 6 shows the photoluminescence spectra of dry (a) and swollen Nafion in water with a deuterium content of 157 ppm (b) as a function of the distance X between the optical axis and the surface of the Nafion. Figure 6. Open in a new tab Photoluminescence spectra of dry ( a ) and swollen Nafion in water with a deuterium content of 157 ppm ( b ) as a function of the distance X between the optical axis and the surface of the Nafion. In the case of dry Nafion ( Figure 6 a), the luminescence signal disappears at a distance of X = 150 microns between the optical axis and the membrane surface. This is due to the divergence of the pump radiation coming out of the multimode fiber. Based on the results obtained for dry Nafion, the hardware function of the photoluminescence spectroscopy installation was determined, taking into account the divergence of the pump radiation and the mechanical features of the installation. As follows from the graphs on panel (b), when Nafion swells in water with a deuterium content of 157 ppm, the luminescence signal does not disappear up to distances of X = 700 microns. It was concluded that when Nafion is soaked in water, polymer fibers are effectively unwound into a volume of liquid, and this effect is controlled by the deuterium content and is most pronounced at 10 2 < C < 10 3 ppm. Based on experimental data of the type shown in Figure 6 b, the inverse problem of finding the size of the region X 0 that is occupied by unwound polymer fibers, depending on the deuterium content, was solved; see Figure 7 . Figure 7. Open in a new tab Dependence of the size of the region in the volume of liquid occupied by unwound polymer fibers on the deuterium content. As follows from the graph in Figure 7 , there is no unwinding effect in water with a deuterium content of 1 ppm (deuterium depleted water, DDW), while in natural water with a deuterium content of 157 ppm this effect is manifested, and the area occupied by unwound fibers reaches 300 microns; with a further increase in the deuterium content, the size of the area occupied by unwound fibers decreases. Thus, we are dealing with a non-monotonic dependence on the deuterium content. The theoretical basis for this experimental result is the data from quantum chemical modeling. It is shown that the swelling of the polymer membrane in water is accompanied by unwinding of polymer fibers into the volume of the surrounding liquid, and the unwinding effect is controlled by the deuterium content in the water in which the membrane swells. The pH value on the surface of Nafion was also measured during soaking in water, depending on the deuterium content; the parameter of these dependencies is the soaking time. See Figure 8 , as well as [ 542 ]. Figure 8. Open in a new tab Dependence of the pH value on the deuterium content in water near the surface of the Nafion; the parameter of these dependences is the soaking time τ. As is known, the pH value decreases as it is soaked in water due to the dissociation of sulfonate groups at the ends of polymer fibers due to the reaction R—SO 3 H + H 2 O ⇔ R—SO 3 − + H 3 O + . It was shown that the pH dependence, similar to the size X 0 , occupied by unwound fibers, is not monotonic with respect to the deuterium content in water. Based on the density functional method, which simulates the interaction of a polymer membrane with an aqueous matrix at various deuterium concentrations, the effect of unwinding polymer fibers from the polymer surface into a liquid volume was described at a qualitative level, taking into account isotopic effects [ 543 ]; it was shown that the non-monotonic deuterium content dependencies shown in Figure 7 and Figure 8 are explained within the framework of a model that takes into account the interaction of a network of hydrogen bonds of water molecules with sulfonate groups at the ends of polymer chains of Nafion, and in these interactions, in addition to hydrogen atoms, deuterium atoms must also be taken into account. The effect of unwinding polymer fibers has been studied using various experimental techniques. In addition to the photoluminescence spectroscopy mentioned above, Fourier infrared spectroscopy [ 544 , 545 , 546 ], spectrophotometry [ 547 ], and ultrasonic wave irradiation [ 542 , 548 ] should be noted. It should be noted that the basic technique of studying this effect is photoluminescence spectroscopy [ 262 , 540 , 542 , 543 , 549 , 550 ]. This is due to the fact that, as was shown in [ 199 , 262 , 541 ], the centers of Nafion luminescence are the terminal sulfonate groups in the main polymer chain of tetrafluoroethylene. Polymer fibers unwound into a liquid volume are an object of soft matter; therefore, it becomes possible to control the spatial distribution of these fibers using any external influence. Since sulfonate groups (luminescence centers) are localized at the ends of the unwound fibers, the effect of external influences on the unwinding effect can be studied in experiments using photoluminescence spectroscopy. It turns out that the spatial distribution of polymer fibers unwound into a liquid volume can be effectively controlled by irradiation with ultrasonic waves. In this regard, the experimental photoluminescence spectroscopy facility can be modified in such a way that optical pumping in the near UV range irradiates the polymer surface in a grazing incidence pattern while simultaneously irradiating the polymer surface with one or two ultrasonic waves directed towards each other across polymer fibers unwound into a liquid volume [ 548 ]. In [ 548 ], a theoretical model was created describing the specifics of irradiation of unwound polymer fibers with an ultrasonic wave. It is shown that in this case it is necessary to take into account the possibility of electron transfer from the donor luminescence center to the acceptor luminescence center; in this case, the end sulfonate groups are donors and acceptors. Electron transfer can lead to luminescence quenching, which was observed in experiments on photoluminescence spectroscopy of Nafion when irradiating the membrane with one or two ultrasonic waves. It was shown in [ 548 ] that when irradiating a polymer membrane with ultrasound, it is necessary to take into account the absorption of a longitudinal ultrasonic wave inside the surface layer near the membrane. This layer contains unwound polymer fibers, across which ultrasonic waves propagate. The presence of unwound fibers increases the viscosity inside this layer and causes the absorption of an ultrasonic wave. As is known, when sound attenuates, an ultrasonic wave pulse is transmitted to liquid particles, causing them to move in the direction of the initial sound wave, which leads to the appearance of an acoustic flow. In an experiment with two counter ultrasonic waves, two acoustic fluxes move to the center of the Nafion plate and effectively shift the ends of the unwound polymer fibers to the central part of the Nafion plate, from where luminescence is excited. It was shown in [ 548 ] that when the distance between the luminescence centers decreases, luminescence quenching effects occur due to electron transfer from the donor to the acceptor. In this case, the maximum extinguishing effect is achieved when two opposing acoustic fluxes meet near the center of the polymer membrane, i.e., in the region of luminescence excitation. An estimate of 4 × 10 −5 m/s was obtained for the velocity of these flows. Irradiation of a polymer membrane with one or two oncoming ultrasonic waves formed the basis of a technique for controlling the growth and structure of crystals deposited on polymer substrates from supersaturated aqueous solutions of salts with different isotopic compositions [ 542 , 543 ]. In these studies, it was shown that the effect of unwinding polymer fibers can lead to a change in the syngony of the unit cell of a crystal, which is deposited on a polymer substrate from a saturated aqueous solution with different deuterium content. Since the unwound polymer fibers are perpendicular to the polymer substrate, and the distance between the unwound fibers is of the order of the size of the elementary crystal cell, these fibers actually set the angle between the edges of the elementary crystal cell of the deposited crystal. For example, for copper sulfate crystals precipitated from a supersaturated aqueous solution, the crystal cell has the form of either CuSO 4 × 5H 2 O pentahydrate with triclinic syngony, or CuSO 4 × 3H 2 O trihydrate with monoclinic syngony, and the crystal cell in the form of pentahydrate is more energetically advantageous. In the case of triclinic syngony, the angles between the translational vectors of the elementary crystal cell α = 77.33°, β = 82.27°, γ = 72.57°, i.e., there is no orthogonality between these vectors (the elementary crystal cell is a beveled parallelepiped), and for monoclinic syngony of CuSO 4 × 3H 2 O trihydrate, these angles are α = 90°, β = 97,1°, γ = 90°, i.e., the elementary crystal cell is a rectangular parallelepiped. Since polymer fibers in the case of a solution based on natural water (deuterium content of 157 ppm; the unwinding effect exists), they are unwound perpendicular to the substrate, this is manifested in the syngony of the deposited crystal. Therefore, in the case of a solution based on natural water, a CuSO 4 × 3H 2 O crystal always grows on a polymer substrate, since for this crystal the two angles between the edges of the unit cell are 90°. At the same time, in the absence of the unwinding effect, i.e., when precipitation from a supersaturated DDW-based solution (deuterium content of 1 ppm), a CuSO 4 × 5H 2 O crystal always grows on the polymer substrate. When crystals are deposited on a polymer substrate from supersaturated aqueous solutions in which, due to the isotopic composition, the effect of unwinding of polymer fibers exists, it is possible to control the syngony of the deposited crystals using ultrasonic waves directed along the surface of the substrate. This possibility is due to the fact that, as shown above, when absorbing ultrasonic waves directed across unwound fibers, hydrodynamic flows arise that deflect polymer fibers unwound perpendicular to the substrate. In the absence of ultrasonic irradiation, CuSO 4 × 3H 2 O trihydrate with a monoclinic lattice is formed on a polymer substrate from a supersaturated water-based solution with a deuterium content of 157 ppm, for which the elementary crystal cell is a rectangular parallelepiped. As theoretically shown in [ 543 ], this orientation of the translation vectors is complementary to polymer chains unwound perpendicular to the substrate surface. At the same time, if the CuSO 4 solution is prepared on the basis of DDW, then there is no unwinding effect, and therefore the polymer substrate cannot play the role of a structuring template, and CuSO 4 × 5H 2 O pentahydrate with triclinic syngony is deposited on the substrate, for which the elementary crystal cell is a beveled parallelepiped. It should also be noted that in [ 551 ] it was found that the effects of instantaneous luminescence quenching occur when luminescence centers (terminal sulfonate groups) interact with various biological macromolecules, for example, amino acids, and the quenching modes differ when the luminescence centers are located at the ends of fibers unwound into a liquid volume (swelling occurs in natural water with a deuterium content of 157 ppm) and are rigidly fixed to the membrane surface (swelling occurs in DDW; unwinding is absent). Based on the effect of luminescence quenching by amino acids, a “1–0–1” logic cell was implemented for the first time in the “Nafion membrane—aqueous suspension of glutamic acid—aqueous suspension of lysine” system using a microfluidic chip. In this case, the state “1” corresponds to high-intensity luminescence, and the state “0” corresponds to luminescence quenching, see [ 551 ]. Moreover, in experiments with biological macromolecules, it was shown [ 262 , 551 ] that the Nafion membrane is similar to a cell membrane. This is due to the effect of unwinding of polymer fibers from the membrane surface into the volume of the surrounding fluid; the unwound polymer fibers are similar to the endothelial surface layer adjacent to the cell membrane; for more details, see the review [ 262 ] for more detail. It is necessary to take into account the difference in characteristic scales: the thickness of the endothelial layer is of the order of 1 micron, while the thickness of the layer of fibers unwound from the surface of the polymer membrane is of the order of 300 microns; see the commentary to Figure 7 , where the size of the area occupied by unwound polymer fibers is discussed, with a deuterium content of 157 ppm (natural water). In Fourier transform IR spectrometry experiments [ 544 , 545 , 546 ], it was found that the transmission spectra of water samples with a deuterium content of 3 < C < 10 4 ppm in the spectral range of 1.8 < λ < 2.2 μm are identical within the experimental error for a cuvette with a window distance (cuvette thickness) of 90 μm. At the same time, the transmission spectra of water with a deuterium content in the same range, which is located inside the nanometer pores of Nafion, differ significantly from each other. Thus, in the Fourier transform IR spectroscopy experiments, the “confinement” effect was obtained: the absorption spectrum of water in the nanometer pores of Nafion differs from the absorption spectrum of the same water in a cell about a hundred microns of thickness, see [ 544 ]. Also in these experiments, the dynamics of unwinding of polymer fibers into a volume of water in a cuvette of limited thickness were studied. In this case, initially hydrophobic polymer fibers unwound from the Nafion surface abut the windows of the spectrometer cuvette and expel water molecules from the region near the cuvette windows, forming a liquid-free, gas-filled cavity. It has been shown that the rate of collapse of this cavity is determined by the isotopic composition of the water, as well as the concentration and type of dissolved ions [ 545 , 546 ]. Based on this effect, a new method for studying isotopic and specific ion effects in liquids has been proposed. In spectrophotometric experiments, the absorption spectra of Nafion in the visible range were studied after it was swollen in natural water and in deuterium-free water (DDW) [ 547 ]. It was found that the absorption coefficient of Nafion does not change upon soaking in deuterium-free water, but decreases upon soaking in natural deionized water with a deuterium content of 157 ppm. Since any change in absorption reflects changes in the electronic structure of Nafion, which are interconnected with changes in the nuclear configurations of the polymer matrix, the isotope-dependent decrease in optical density over a relatively wide spectral range observed in this experiment can only be due to a change in the overall conformation of the polymer chains upon unwinding the polymer fibers in the bulk of natural deionized water. The absorption spectrum of Nafion upon soaking in an aqueous solution of methylene blue (MB) was also studied in spectrophotometric experiments. In these experiments, the adsorption of MB onto the Nafion surface during swelling in aqueous MB solutions with different isotopic compositions, as well as the dynamics of water desorption with different isotopic compositions during membrane drying, were studied. A dependence of the membrane swelling and drying rates on the isotopic composition was discovered, and the corresponding diffusion coefficients of MB macromolecules onto the polymer membrane surface were measured for the first time as a function of the isotopic composition of the aqueous MB solution [ 199 ]. Interest in these studies is due to the fact that MB is widely used to treat patients with SARS-CoV-2, and the Nafion polymer membrane is similar to a cell membrane (see above). 23. Conclusions To summarize, the fundamental properties of PFSAs are determined by a complex balance of chemical and mechanical energies that shape their hierarchical morphology. Phase separation, characteristic ionic domains, interfacial zones, and mesoscale network organization jointly govern water sorption, proton transport, gas dissolution, and other transport processes. Despite significant progress, existing morphological models—from cluster-network to two-phase—still do not fully capture transition states and the role of interfaces, especially under high humidity conditions. Issues related to surface layer dynamics, the nature of Schroeder’s paradox, and the interactions between hydrophobic and hydrophilic side chain fragments remain the subject of active research. The transport properties of PFSAs manifest themselves at the nanoscale, but their macroscopic expression is determined by the connectivity of ionic domains and the nature of the network structure. This highlights the need to move from analyzing individual domain elements to describing materials as multiscale systems. Modern molecular dynamics models and coarse-grained approaches are already making it possible to approach such problems, but difficulties remain related to the physical consistency of the models and the lack of data for ionomers other than Nafion. The development of more predictive models that simultaneously describe sorption, transport, and mechanical phenomena represents one of the most promising areas. Studying the durability of PFSAs, including their chemical, mechanical, and electrochemical degradation, remains an important task. Also crucial is monitoring the isotopic composition of the liquids in which PFSAs swell. Many applications require an understanding of ionomer behavior, not only at the start of operation but also under long-term exposure to potentials, temperature cycles, and mechanical stress. In the future, research aimed at identifying the synergies between chemical and mechanical processes that influence stability under real-world operating conditions will be particularly important. Hybrid and composite PFSAs are actively developing, opening up opportunities for both improving membrane performance and conducting fundamental research on the interaction of ionomers with fillers. However, to form a complete picture, it is necessary to combine device-focused and structure-focused approaches, which will allow us to link the observed improvements to specific physicochemical mechanisms. The study of thin-film PFSAs requires special attention, as their confined geometry and interaction with the substrate significantly alter the morphology, chain orientation, transport anisotropy, and relaxation processes. Such systems require a transition from scalar parameters to directional and tensor characteristics, as well as further development of in situ characterization methods. Overall, PFSAs remain benchmark materials for ionic conductivity and stability. The continued expansion of their application areas makes a thorough understanding of the relationships between structure, transport, and mechanical phenomena particularly important. Despite significant progress, researchers still face a wide range of open questions, from developing universal morphological models to creating hybrid materials with targeted functional properties. Solving these challenges will determine the direction of development of ionomer membranes and their role in future electrochemical and energy technologies. Let us finally note that in January 2023, authorities from Denmark, Germany, the Netherlands, Norway and Sweden (the Dossier Submitters) submitted a Registration, Evaluation, Authorization and Restriction of Chemicals (REACH) dossier for a restriction proposal for per- and polyfluoroalkyl substances (PFAS) in the EU to the European Chemicals Agency (ECHA). PFASs are a group of thousands of mainly man-made substances that are used in numerous applications in the EU. The basis for the proposed restriction is the fact that PFASs and their degradation products may persist in the environment for a very long period, longer than any other man-made chemical. Further concerns are their bioaccumulation, mobility, long-range transport potential, accumulation in plants, global warming potential and (eco)toxicological effects. The EU-wide risk arises from the continued emissions of PFASs into the environment during manufacture, the use phase, and the waste stage. This restriction dossier is built on the principle that PFASs are to be substituted where already feasible today, or to become feasible in the foreseeable future. At the same time, it provides the possibility for allowing the continued use of PFASs in certain circumstances, e.g., where there are no suitable alternative substances or technologies available, while still ensuring that emissions into the environment are minimized. Like for all restriction dossiers under REACH, the PFAS dossier includes an assessment of the risk reduction capacity and proportionality to the risk of any proposed restriction option while taking into account the availability of alternatives and their practicability and monitorability. These elements are key considerations in the evaluation of ECHA’s scientific committees for Risk Assessment (RAC) and for Socio-Economic Analysis (SEAC), respectively, and will thereby be reflected in the final consolidated opinion sent to the European Commission. A consultation will be held afterwards on the draft opinion of the SEAC. This will provide an opportunity for all interested third parties to provide relevant information regarding socio-economic aspects to be considered in the final SEAC opinion. The progress of the PFAS restriction so far has been possible through the combined and committed efforts of ECHA and the Dossier Submitters, who are focused on supporting the development of a consolidated opinion from RAC and SEAC. As an additional result of this process, more has become known about the use of PFASs, which has resulted in all parties becoming more aware of the associated concern. Working together with the Dossier Submitters, ECHA aims to provide the European Commission with a transparent, independent, and high-quality RAC and SEAC opinion as soon as possible. The European Commission will ultimately decide on the restriction in consultation with EU Member States. Further information and progress updates can be found via the hyperlink [ 552 ]. Currently, the question of alternatives for some areas of fluoropolymer application, technical and organizational measures to minimize their emissions into the environment, as well as the potential socio-economic consequences of banning their production, market release, and use, is actively discussed. However, in our opinion, such PFSA properties as high ionic conductivity, chemical/thermal stability, mechanical strength, excellent resistance to oxidation/chemical attack, and low gas permeability are most difficult to replicate in non-fluorinated systems. Supplementary Materials The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/polym18070848/s1 . polymers-18-00848-s001.zip (736.4KB, zip) Author Contributions Conceptualization, N.F.B., S.V.G. and B.W.N.; Investigation, S.V.G., V.A.K., S.M.K., and N.F.B.; Writing—original draft preparation, N.F.B., V.A.K. and B.W.N.; Supervision, N.F.B., S.V.G. and B.W.N. All authors have read and agreed to the published version of the manuscript. Institutional Review Board Statement Not applicable. Data Availability Statement No new data were created or analyzed in this study. Data sharing is not applicable to this article. Conflicts of Interest The authors declare no conflicts of interest. Funding Statement This research received no external funding. Footnotes Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. References 1. Mauritz K.A., Moore R.B. State of Understanding of Nafion. Chem. Rev. 2004;104:4535–4586. doi: 10.1021/cr0207123. [ DOI ] [ PubMed ] [ Google Scholar ] 2. Giffin G.A., Haugen G.M., Hamrock S.J., Di Noto V. 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