Benzophenone is a mutagen, carcinogen, and endocrine disruptor. Its presence in food products or food packaging is banned in the United States. Under California Proposition 65, there is no safe harbor for benzophenone in any personal care products, including sunscreens, anti-aging creams, and moisturizers. The purpose of this study was to determine if (a) benzophenone was present in a wide variety of commercial SPF/sunscreen products and (b) whether benzophenone concentration in the product increased over time, and (c) the degradation of octocrylene was the likely source for benzophenone contamination. Benzophenone concentration was assayed in 9 commercial sunscreen products from the European Union and 8 from the United States (in triplicate), including two single ingredient sources of octocrylene. These same SPF items were subject to FDA-accelerated stability aging protocol for 6 weeks. Benzophenone was measured in the accelerated-aged products. Sixteen octocrylene-containing product lines that were recently purchased had an average concentration of 39 mg/kg benzophenone, ranging from 6 mg/kg to 186 mg/kg. Benzophenone was not detectable in the product that did not contain octocrylene.

After subjecting the 17 products to the FDA-accelerated stability method, the 16 octocrylenecontaining products had an average concentration of 75 mg/kg, ranging from 9.8 mg/kg to 435 mg/kg. Benzophenone was not detectable in the product that did not contain octocrylene.

Benzophenone was detected in the pure octocrylene manufactured ingredient. Octocrylene generates benzophenone through a retro-aldol condensation. In vivo, up to 70% of the benzophenone in these sunscreen products may be absorbed through the skin. U.S. FDA has established a zero-tolerance for benzophenone as a food additive. In the United States, there were 2,999 SPF products containing octocrylene in 2019. The safety of octocrylene as a benzophenone-generator in SPF or any consumer products should be expeditiously reviewed by regulatory agencies.

Introduction

Octocrylene (CAS# 6197-30-4) is one of 14 U.S. Food and Drug Administration active ingredients approved for use in SPF (sun-protection factor) over-the-counter drugs which include sunscreens, moisturizers, lip-balms, and anti-aging products. In March of 2019, 2,999 SPF products that were registered for sale in the United States contained octocrylene 1 . Octocrylene is also used in non-SPF labeled personal care products such as shampoos, hair sprays, tanning oils, and conditioners.

The personal care product industry has known for some time that octocrylene is contaminated with benzophenone (CAS# 119-61-9). When purchasing raw octocrylene for sunscreen or personal care product manufacturing, industry admits that benzophenone is a contaminant found in octocrylene, and for some reason, "cannot be removed by its entirety when octocrylene is being processed…" [START_REF] Rodan | Frequently asked questions: benzophenone & octocrylene California Prop 65 ingredients[END_REF][START_REF]Superior Court of California[END_REF] . Furthermore, industry members have also stated that the concentration of benzophenone in octocrylene manufactured-ingredients and consumer products is "negligible" [START_REF] Rodan | Frequently asked questions: benzophenone & octocrylene California Prop 65 ingredients[END_REF] .

Benzophenone is associated with a wide range of toxicities, including genotoxicity, carcinogenicity, and endocrine disruption. Benzophenone and its common metabolites, benzhydrol and p-hydroxybenzophenone, were positive mutagens in the Ames Test platforms (strain TA102) in the SOS/Umu mutagenicity platform [START_REF] Robinson | Studies in detoxication. 74. The metabolism of benzhydrol, benzophenone and p-hydroxybenzophenone[END_REF][START_REF] Takemoto | Genotoxic activation of benzophenone and its two metabolites by human cytochrome P450s in SOS/umu assay[END_REF][START_REF] Wang | Evaluation by the Ames Assay of the mutagenicity of UV filters using benzophenone and benzophenone-1[END_REF][START_REF] Zhao | Substituent contribution to the genotoxicity of benzophenone-type UV filters[END_REF] . Benzophenone was also demonstrated to induce thymine dimerization and double-stranded DNA break formation in the presence of UV light [START_REF] Charlier | Photochemical reactions of aromatic ketones with nucleic acids and their components -III. Chain breakage and thymine dimerization in benzophenone photosensitized DNA[END_REF] .

Benzophenone is an established carcinogen [9][START_REF]Toxicology and carcinogenesis studies of benzophenone (CAS No. 119-61-9) in F344/N rats and B6C3F1 mice (feed studies[END_REF][START_REF] Rhodes | Carcinogenesis studies of benzophenone in rats and mice[END_REF] . Signs of this pathology induced by benzophenone were first observed in the liver of Guinea pig [START_REF] Dutta | Toxicological impacts of benzophenone on the liver of guinea pig (Cavia Porcellus)[END_REF] . In mice, oral ingestion of benzophenone resulted in significant manifestations of hepatocellular adenoma, hepatocellular carcinoma, hepatoblastoma (male mice) and histiocytic sarcoma (female mice). Benzophenone also induced the incidence of mononuclear-cell leukemia and renal tubule adenoma in male rats, while female rats saw an increase in histiocytic sarcoma [START_REF]Toxicology and carcinogenesis studies of benzophenone (CAS No. 119-61-9) in F344/N rats and B6C3F1 mice (feed studies[END_REF][START_REF] Rhodes | Carcinogenesis studies of benzophenone in rats and mice[END_REF] .

A preponderance of evidence indicates that benzophenone and its metabolites are potential endocrine disruptors with diverse axis impacts [START_REF] Kawamura | Estrogenic and antiandrogenic activities of benzophenones in human estrogen and androgen receptor mediated mammalian reporter gene assays[END_REF][14][START_REF] Suzuki | Estrogenic and antiandrogenic activities of 17 benzophenone derivatives used as UV stabilizers and sunscreens[END_REF] . Recent evidence indicated that benzophenone could alter thyroid-hormone balances. In an in vitro rat thyroid follicular cell line, benzophenone up-regulated the sodium/iodide symporter and thyroid globulin genes, while down-regulating thyroid peroxidase gene [START_REF] Lee | Thyroid hormone disrupting potentials of major benzophenone in two cell lines (GH3 and FRTL-5) and embryo-larval zebrafish[END_REF] . In an in vitro pituitary cell line, benzophenone downregulated the thyroid stimulation hormone β-subunit gene, the thyrotropin releasing hormone receptor gene, and the thyroid receptor β-subunit gene [START_REF] Lee | Thyroid hormone disrupting potentials of major benzophenone in two cell lines (GH3 and FRTL-5) and embryo-larval zebrafish[END_REF] .

para-Hydroxybenzophenone, a metabolite of benzophenone, exhibits estrogenic activity both in vitro and in vivo, as demonstrated by uterotrophic assays [START_REF] Kawamura | Estrogenic and antiandrogenic activities of benzophenones in human estrogen and androgen receptor mediated mammalian reporter gene assays[END_REF][START_REF] Nakagawa | Metabolism and toxicity of benzophenone in isolated rat heptatocytes and estrogenic activity of its metabolites in MCF-7 cells[END_REF][START_REF] Nakagawa | Benzophenone-induced estrogenic potency in ovariectomized rats[END_REF] . p-Hydroxybenzophenone was also shown in vitro to induce anti-androgenic activity [START_REF] Kawamura | Estrogenic and antiandrogenic activities of benzophenones in human estrogen and androgen receptor mediated mammalian reporter gene assays[END_REF][START_REF] Suzuki | Estrogenic and antiandrogenic activities of 17 benzophenone derivatives used as UV stabilizers and sunscreens[END_REF] . Subcutaneous injection into female, juvenile rats with p-hydroxybenzophenone resulted in the proliferation of uterine luminal epithelium cells and cornified vaginal epithelium cells, as well as increased uterine weight 14 . Besides direct interaction with hormone receptors, benzophenone was demonstrated to induce the expression of a number of cytochrome P450 isoforms in male rat livers. This cytochrome P450 induction seems to be elicited by activating both the pregnane X receptor and the steroid receptor coactivator 1 [START_REF] Mikamo | Endocrine disruptors induce cytochrome P450 by affecting transcriptional regulation via pregnane X receptor[END_REF] . There is some evidence, though not rigorously studied, that benzophenone-exposure resulted in a gross-morphological pathology; mature male rats exhibited small seminal vesicles which were at an immature stage of development, as well as testicular hypoplasia [START_REF]Toxicology and carcinogenesis studies of benzophenone (CAS No. 119-61-9) in F344/N rats and B6C3F1 mice (feed studies[END_REF] .

Based on litigation and MSDS/literature provide by manufacturers of octocrylene, it could easily be perceived that benzophenone is a contaminant from the manufacturing synthesis of octocrylene, and that current manufacturing clean-up processes are unable to purify octocrylene to less than 1 mg/kg [START_REF] Rodan | Frequently asked questions: benzophenone & octocrylene California Prop 65 ingredients[END_REF][START_REF]Superior Court of California[END_REF] . Another possibility is that benzophenone is created from the degradation of octocrylene. If this possibility is true, then octocrylene products potentially pose a serious health hazard because benzophenone concentration would increase over time in that product. Under the State of California Proposition 65, there is no "safe harbor" or allowable level of benzophenone contamination in a product [START_REF]Office of Environmental Health Hazard Assessment, Proposition 65 No Significant Risk Levels for Carcinogens and Maximum Allowable Dose Levels for chemicals causing reproductive toxicity[END_REF] . This lack of forbearance is consistent with the danger of dermal absorption of benzophenone; 70% of the benzophenone in a dermatological product would be absorbed through skin and into the body [START_REF] Bronaugh | In vivo percutaneous absorption of fragrance ingredients in rhesus monkeys and humans[END_REF] . Dermal absorption of other benzophenones (e.g., oxybenzone) and octocrylene are a serious public health conundrum, finally recognized by the U.S. FDA [START_REF] Matta | Effect of sunscreen application under maximal use conditions on plasma concentration of sunscreen active ingredients: a randomized clinical trial[END_REF][START_REF] Matta | Effect of sunscreen application on plasma concentration of sunscreen active ingredients[END_REF] .

Octocrylene is quickly becoming the dominant UV-sunscreen environmental contaminant, found in coastlines, rivers, and lakes all over the world [START_REF] Gago-Ferrero | First determination of UV filters in marine mammals. Octocrylene levels in Franciscana dolphins[END_REF][START_REF] Picot-Groz | Diurnal variations in personal care products in seawater and mussels at three Mediterranean coastal sites[END_REF][START_REF] Gadelha | Persistent and emerging pollutants assessment on aquaculture oysters (Crassostrea gigas) from NW Portuguese coast (Ria De Averiro)[END_REF] Most environmental surveys look for this common sunscreen compound, but few environmental or biomonitoring studies examine metabolites or degradation products [START_REF] Stien | Metabolomics reveal that octocrylene accumulates in Pocillopora damicronis tissues as fatty acid conjugates and triggers coral cell mitochondrial dysfunction[END_REF][START_REF] Bury | Urinary metabolites of the UV filter octocrylene in humans as biomarkers of exposure[END_REF] . Benzophenone has been seen in some surveys, but its inclusion into methodical target-analyte surveys has largely been ignored because its presence was assumed to be negligible or non-existent. If octocrylene does give rise to benzophenone, then environmental and public health surveys should actively include benzophenone as a targeted analyte [START_REF] Rodrigues-Gómez | Determination of benzophenone-UV filters in human milk samples using ultrasoundassisted extraction and clean-up with dispersive sorbents followed by UHPLC-MS/MS analysis[END_REF] .

To begin to address this issue of the relationship between octocrylene and benzophenone, we sought evidence for whether (a) benzophenone was present in a wide variety of commercial SPF/sunscreen products and (b) whether benzophenone concentration in the product increased over time, and (c) the degradation of octocrylene was the likely source for benzophenone contamination.

Materials and Methods

Sunscreen Product Samples

The following products were purchased in triplicate from retail stores in both France and the United States. Product names, sunscreen actives/UV absorbers, ingredient labeling, lot numbers and expiration dates, are presented in Testing of benzophenone contamination in manufactured octocrylene for use in commercial formulated products were:

(1) Symrise Neo Heliopan 3030 (Octocrylene), Product # 600154. www.symrise.com.

Code:0978, Impurities = 200 ppm benzophenone.

(2) TRI-K Galsorb Octocrylene, Lot S/3006. http://www.tri-k.com/wp-content/uploads/2016/02/GalSORB-Octocrylene-Specifications-v2.pdf. Accessed June 1, 2020.

All commercial sunscreens were sampled for testing after being purchased directly from stores and represent products stored under normal conditions of use.

The same products were retested after being stored for six weeks in a 40 º C incubator (Cincinnati Sub-Zero Model STH-24.25-H/AC StableClomate II Temperature/humidity Stability Chamber; U.S.A) with 75% relative humidity and represents accelerated aging of one-year at room temperature. These test conditions are commonly used to evaluate the stability of product formulations for over-the-counter drug stability in the United States of America [START_REF]Guidance for industry. Drug stability guidelines[END_REF] .

Chemical Analysis

A set of four standard solutions of acetonitrile containing known benzophenone concentrations of 0, 1, 5, and 25 µg/mL was prepared by successive dilutions from a stock solution at 233 µg/mL benzophenone. Sunscreens were analyzed in a random order. Four samples of each sunscreen were weighted in four 2-mL Eppendorf tubes (≈ 100 mg per each, measured accurately with a 0.1 mg accuracy Mettler Toledo XP204 balance). The different acetonitrile solutions (1 mL) were added, each one in one Eppendorf tube. The mixtures were sonicated for 30 min in the sweep mode, and then centrifuged at 23,000 g for 10 min [START_REF] Quiñones | Integrating elemental analysis and chromatography techniques by analyzing metal oxide and organic UV absorbers in commercial sunscreens[END_REF] . For each tube, the supernatant (20 µL) was collected and diluted in acetonitrile (980 µL) in an HPLC vial. For every seven sunscreens, a control analysis (no sunscreen in the Ependorf tubes) was conducted similarly.

The HPLC/MS instrument and method were described by Stien et al. ( 2019) with modifications [START_REF] Stien | Metabolomics reveal that octocrylene accumulates in Pocillopora damicronis tissues as fatty acid conjugates and triggers coral cell mitochondrial dysfunction[END_REF] . Here the gradient was 5 % B 3 min before injection, then from one to 12 min, a linear gradient increase of B up to 100 %, followed by 100 % B for 6 min in which A was water with 0.1 % formic acid and B was acetonitrile with 0.1 % formic acid. The column was a Phenomenex Kinetex F5 150×2.1 mm, 1.7 µm. The flow was diverted (not injected into the mass spectrometer) before injection, up to 1 min after injection. With this method, benzophenone was eluted at ≈ 8.3 min. Eventually, another chromatographic method was also used to shorten the analysis time. In this case, the gradient was 5 % B 3 min before injection, then from 1 to 8 min, a linear gradient increase of B up to 100 %, followed by 100 % B for 5 min. With this method, benzophenone was eluted at ≈ 7.5 min.

In ThermoFisher FreeStyle software, the ion at m/z 183.0804 corresponding to the protonated molecular ion of benzophenone was extracted from the UHPLC-MS profiles at 5 ppm mass tolerance. The chromatographic peak was integrated automatically using the Genesis algorithm with the following parameters: percent of highest peak 10.0, minimum peak height 1.0, S/N threshold 1.0, with valley detection disabled. The extracted ion peak was clearly detected for each run, and the integrations were repeatable. In order to assure an optimal quality control, blanks and control samples were analyzed to check carryover, background noise, precision and accuracy of the detection. Selectivity, specificity, accuracy, precision, linearity, range, limit of detection (LOD), limit of quantification (LOQ) for benzophenone are listed in Table S1 (supporting information). The integration values were reported in an Excel sheet for linear regression calculation. The linear regression equation was in the form: Benzophenone ( BP ) Peak Area = a.m added _ BP + b where m added_BP was the mass of benzophenone added to the sunscreen samples with the different solution of benzophenone in acetonitrile (0, 1, 5, and 25 µg). The equation provided the mass of benzophenone (µg) in the sunscreen product ( ) as follows:

-This value was corrected by the amount of benzophenone ( BP ) in the corresponding blank analysis:

A blank of the same day as the analysis was used for correction. When several blanks were available, the "most advantageous" one (i.e., the highest ) was used for correction. Finally, the concentration of benzophenone ( BP ) in the sunscreen product was calculated as for being:

, and was expressed in mg/kg. The results are provided in Table 2.

Results

Benzophenone was detected in all of the octocrylene-containing commercial products, while it was not present in significant or detectable quantities in the only non-octocrylene product that was tested (third column from the left, indicated as "Baseline", Table 2).

Product samples were subjected to a U.S. FDA accelerated-stability testing protocol for six weeks; this duration is supposed to reflect a single year shelf-life. In the E.U. samples, the increase in benzophenone concentrations after the 6-week accelerated stability incubation ranged from a geometric mean of 38.7% to 199.4% (Table 2). The lowest concentration of benzophenone in a product was Uriage Age Protect SPF30 (GM of 6.3 mg/kg), but whose concentration increased to a geometric mean of 38.6 mg/kg after the accelerated-stability incubation (GM of 38.6 mg/kg). L'Oreal Age Perfect FPS 20 had the highest concentration of benzophenone for both the starting material (GM of 64.6 mg/kg) and accelerated-stability incubated (GM of 193.4 mg/kg). It should be noted that the E.U. and France do not require the concentrations of octocrylene or other sunscreen active ingredients on their label, so starting concentration of octocrylene is unknown.

In the U.S. Samples, benzophenone concentrations at the end of the 6-week acceleratedstability incubation ranged from a geometric mean of 14.5% to 134.4% (Table 2). The lowest concentration of benzophenone in a product was Banana Boat Clear UltraMist SPF30 (GM of 11.1 mg/kg), but whose concentration increased to a geometric mean of 17.7 mg/kg after the accelerated-stability incubated. It should be noted that Banana Boat Clear UltraMist contained only 5% octocrylene, one of the lowest octocrylene concentration formulations. Coppertone Sport Clear SPF30 had the highest concentration of benzophenone for both the starting material (GM of 185.45 mg/kg) and accelerated-stability incubated (GM of 434.85 mg/kg). Surprisingly, Coppertone Sport Clear SPF30 only contained 6% octocrylene. Symrise Neo Heliopan 3030 octocrylene contained 151 mg/kg benzophenone. TRI-K Galsorb Octocrylene contained 47.7 mg/kg benzophenone.

Discussion

The presence of octocrylene in a commercial product implies a threat of considerable contamination by benzophenone. Octocrylene is a 2-cyano cinnamic ester that can be synthesized by aldol condensation of benzophenone with 2-ethylhexyl 2-cyanoacetate [START_REF] Jing | Process for the manufacture of substituted 2cyano cinnamic esters. Patent Application No[END_REF] . The aldol condensation is catalyzed either by acidic or basic conditions and whose rate can be accelerated by protic solvents, such as water [START_REF] Aerts | Is unsubstituted benzophenone a potential screening agent to detect photocontact allergy to octocrylene?[END_REF] . The aldol condensation is reversible, and both the aldol and the retro-aldol condensation rates accelerate under these conditions (Figure 1). Our work unambiguously establishes that octocrylene does undergo a slow retro-aldol condensation reaction that gives rise to benzophenone. This process occurred in all commercial sunscreens tested that contain octocrylene, resulting in the concomitant increase of the benzophenone concentration upon aging the product.

The source of benzophenone in a product arises from two main sources: (a) benzophenone contamination in the octocrylene used to manufacture the commercial product and (b) accumulation of benzophenone from the degradation of octocrylene as the product ages. All of the products we tested from the retail stores had benzophenone contamination, violating the State of California Proposition 65. If industry is to continue to use octocrylene in its formulas, it would need to better purify octocrylene from its benzophenone contaminant before selling it to personal care product manufacturers and develop a "safe" stabilizer that prevents the retro-aldol condensation reaction resulting in the formation of benzophenone (Figure 1). Our results did indeed demonstrate that the rate of benzophenone concentration increase depends more on the product formulation than on the initial octocrylene concentration (e.g., Banana Boat Clear UltraMist SPF30 vs. Coppertone Sport Clear SPF30).

Benzophenone and its structurally related compounds (e.g., benzophenone-1, benzophenone-3) are notorious for inducing dermatological pathologies, including contact dermatitis, erythema, urticaria, and photo-induced dermatitis [START_REF] Ramsay | Allergic reaction to benzophenone. Sumultaneous occurrence of urticarial and contact sensitivities[END_REF][START_REF] Knobler | Photoallergy to benzophenone[END_REF][START_REF] Cook | Report of 19 cases of photoallergic contact dermatitis to sunscreens seen at the Skin and Cancer Foundation[END_REF][START_REF] Nedorost | Facial erythema as a result of benzophenone allergy[END_REF][38] . Dermatological pathologies from benzophenone occur not just from personal care product exposure, but also from noncosmetic products that come into direct and prolonged contact with the skin [START_REF] Melé-Ninot | Photoallergic contact dermatitis due to benzophenone contained in swimming goggles[END_REF][START_REF] Tanahashi | Three cases of photoallergic contact dermatitis induced by benzophenone in amusement park wristbands[END_REF] . Benzophenoneinduced dermatitis could also arise from prolonged exposure to paper packaging material, plastics, and food that was in contact with these paper packaging materials 41,42 .

Signs of liver morbidity and homeostatic distress when exposed to benzophenone were often recognized in guinea pig, rat, and mouse models, but the risks have been underestimated in both toxicology journal papers and organizational reports [START_REF] Rhodes | Carcinogenesis studies of benzophenone in rats and mice[END_REF][START_REF] Silano | Safety of benzophenone to be used as flavouring[END_REF][START_REF]Scientific Opinion of EFSA prepared by the Panel on food contact materials, enzymes, flavourings and processing aids (CEF). Toxicological evaluation of benzophenone[END_REF] . This is unfortunate because the earliest reports regarding benzophenone toxicology in a whole organism study concluded that a 15-day exposure to benzophenone induced changes resembling chronic hepatitis 45 . Cellular necrosis was "prominent in different parts of the liver" and that histopathological examination in non-necrotizing cells indicated the presence of "double-nucleated cells." In both guinea pigs and rats, benzophenone-exposure induced significant increases in liver weight [START_REF]Toxicology and carcinogenesis studies of benzophenone (CAS No. 119-61-9) in F344/N rats and B6C3F1 mice (feed studies[END_REF][START_REF] Silano | Safety of benzophenone to be used as flavouring[END_REF] . Significant increases in alanine aminotransferase level are consistent with hepatotoxic necrosis [START_REF]Toxicology and carcinogenesis studies of benzophenone (CAS No. 119-61-9) in F344/N rats and B6C3F1 mice (feed studies[END_REF][START_REF] Silano | Safety of benzophenone to be used as flavouring[END_REF] . Furthermore, increased mitotic divisions of biliary epithelial cells with reduced glycogen reserves and increased glycolysis activity in proximate hepatocytes is an environment conducive to potential carcinogenic transformation. This liver pathology is consistent with the conclusion that benzophenone is a carcinogen by creating both mutagenic events, as well as localized unstable cellular/histological environment that could promote carcinogenesis 46 .

Based on the dermal absorption studies of benzophenone and its structurally similar sunscreen active ingredients of oxybenzone and avobenzone, benzophenone that is associated with octocrylene products suggests that parts per million exposures and absorption of benzophenone could be expected [START_REF] Bronaugh | In vivo percutaneous absorption of fragrance ingredients in rhesus monkeys and humans[END_REF][START_REF] Matta | Effect of sunscreen application under maximal use conditions on plasma concentration of sunscreen active ingredients: a randomized clinical trial[END_REF][START_REF] Matta | Effect of sunscreen application on plasma concentration of sunscreen active ingredients[END_REF] . Besides use of sunscreen for sun exposure, sunscreen marketing and advertising claims encourage daily and constant use of sunscreen to protect against the "perceived" dangers of "blue light" induced-dermal damage from LCD displays from computers and other persona devices, as well as from light transmission through building and car windows [START_REF] Cook | Could your computer be damaging your skin? Harper's Bazaar[END_REF][START_REF] Buscemi | Should we wear sunscreen to protect our skin from blue light damage? Huffington Post[END_REF][START_REF] Gohara | Sunscreen for computer monitors: yes, you need it![END_REF][START_REF] Saunders | Do you need to wear sunscreen inside? Experts weigh in[END_REF] . If dermatologist and marketing propaganda are to be taken seriously, consumers would be using octocrylene-based sunscreens every day, with multiple reapplications through the day, throughout the entire year. Unlike the claims made by various propaganda sources in response to the two studies by Matta and co-workers, that their exposure-design in their two studies were unrealistic, benzophenone exposure concentration may easily exceed the 100 mg/kg/day [START_REF] Wong | Sunscreens in your blood?? That FDA study[END_REF][52][START_REF] Wong | More sunscreens in your blood??! The new FDA study[END_REF] .

As with other chemicals in mass-produced personal care products, benzophenone can be a potential "emerging contaminant of concern." It can enter environmental systems from at least three routes of contamination: swimmer discharges (sunscreen and fragrances), sewage discharges (sunscreen, cosmetics and fragrances), garbage and debris leachate (personal care products, paper and plastic packaging). Environmental contamination surveys are costly and human resource extensive, requiring ample justification to survey and monitor for a target analyte. This work gives ample justification for launching studies to determine if benzophenone is a significant environmental contaminant, and whether it poses an untenable risk when it contributes to a plume mixture of other contaminants that are known to pose potential ecological threats, such as octocrylene, oxybenzone, avobenzone, and octinoxate.

There are few ecotoxicological studies regarding benzophenone. A marine copepod chronically exposed to benzophenone exhibited decreased egg viability and hatching success, as well as exhibiting significant genomic DNA methylation, raising concerns for potential intraand trans-generational evolutionary effects [START_REF] Wong | More sunscreens in your blood??! The new FDA study[END_REF] . In rainbow trout, benzophenone binds to the trout estrogen receptor and induces vitellogenin mRNA in liver slices [START_REF] Serrano | Metabolism of cyclic phenones in rainbow trout in vitro assays[END_REF] . A more fascinating historical examination of benzophenone is that the first patents on benzophenone were for its herbicidal properties. In 1954, the Monsanto Chemical Company patented benzophenone for its "valuable herbicidal compositions and methods of destroying or preventing plant growth 56 ." In 1976, benzophenone and a number of its derivatives were patented by the Rohm and Haas Company as pre-emergent and post-emergent herbicides 57 . In 1978, benzophenone and benzhydrols were patented for their ability to control "undesirable growth of suckers in tobacco plants" 58 . This small amount of information regarding its use and toxicities is a concern for marine and aquatic ecological integrity, from coral reefs and seaweed forests to river and lake systems.

Octocrylene products that contain benzophenone may pose a threat to the public health, and even ecological health [START_REF] Bury | Urinary metabolites of the UV filter octocrylene in humans as biomarkers of exposure[END_REF][START_REF] Rodrigues-Gómez | Determination of benzophenone-UV filters in human milk samples using ultrasoundassisted extraction and clean-up with dispersive sorbents followed by UHPLC-MS/MS analysis[END_REF][START_REF] Cho | Nonpersistent endocrine disrupting chemicals and reproductive health of women[END_REF] . Safety evaluations done in the past were limited, and in-depth studies need to be conducted to ascertain the full range of toxicity of octocrylene and benzophenone products, so that a more appropriate threat evaluation can be conducted to preserve public health. Mixed xenobiotic exposure-effect studies need to be conducted using chemicals that are commonly found with octocrylene/benzophenone products. Octocrylene by itself is an endocrine disruptor, a developmental toxicant and a metabolic stressor, both to mammal receptor models, but also to various wildlife models, including fish and coral [START_REF] Stien | Metabolomics reveal that octocrylene accumulates in Pocillopora damicronis tissues as fatty acid conjugates and triggers coral cell mitochondrial dysfunction[END_REF][START_REF] Blüthgen | Accumulation and effects of the UV-filter octocrylene in adult and embryonic zebrafish (Danio rerio)[END_REF][START_REF] Zhang | Assessment of multiple hormone activities of a UV-filter (octocrylene in zebrafish (Danio rerio)[END_REF][START_REF] Gu | Urinary concentration of personal care products and polycystic ovary syndrome: a case-control study[END_REF][START_REF] Yan | Reproductive toxicity and estrogen activity in Japanese medaka (Oryzia latipes) exposed to environmentally relevant concentrations of octocrylene[END_REF] . Preliminary evidence potentially suggests that octocrylene may have a role in the behavior of tumorigenesis and carcinogenesis [START_REF] Blüthgen | Accumulation and effects of the UV-filter octocrylene in adult and embryonic zebrafish (Danio rerio)[END_REF][START_REF] Zdravković | In vitro study of the influence of octocrylene on a selected metastatic melanoma cell line[END_REF] . What is the danger of being exposed to a product that simultaneously contains oxybenzone, octinoxate, or homosalate, as well as octocrylene and benzophenone?

Based on the final decision by the E.U. to allow benzophenone as a flavor agent, and the U.S. FDA making no ruling regarding the contamination of over-the-counter SPF drugs, the decisions regarding public health safety regulatory thresholds can be argued to be unjustified and irresponsibly reckless [START_REF]Superior Court of California[END_REF][START_REF] Burdock | Safety evaluation of benzophenone[END_REF][START_REF] Serrano | Metabolism of cyclic phenones in rainbow trout in vitro assays[END_REF] . Both examples, when examined closely, can be argued to be reminiscent of the debacle of beryllium and the U.S. Occupational Safety and Health Administration [START_REF] Michael | Beryllium's public relations problem: protecting workers when there is no safe exposure level[END_REF] . Whether benzophenone and octocrylene products should be allowed for public consumption should not be decided "in the back seat of a taxi by industry consultants" (taxicab standard), but by careful and meticulous review of the literature and publicly available data [START_REF] Zdravković | In vitro study of the influence of octocrylene on a selected metastatic melanoma cell line[END_REF][START_REF] Eisenbud | An environmental odyssey: people, pollution, and politics in the life of a practical scientist[END_REF] .

There is enough scientific literature to make an argument that octocrylene/benzophenone products can pose a threat to individual and public health. Several jurisdictions, including the Republics of Palau and the Marshall Islands, as well as the U.S. Virgin Islands, have banned octocrylene in sunscreen and cosmetic products, effective in January 2020. It is agreeable that there needs to be a more refined and rigorously produced, unbiased data regarding exposure and toxicity of both these chemicals, and the products that contain them. Consideration must be given to the responsible regulatory response to prohibit the manufacture and sale of these octocrylene/benzophenone formulated products until industry can prove beyond a reasonable doubt that chronic exposure does not cause harm over any aspect of the life history of the receptor model or in public health clinical trials. An alternative to this current system of regulatory laissez faire would be a cogent and detailed prescriptive argument for a Precautionary Principle framework whose goal is the protection of public health [START_REF] Sandin | Phenoxyethanol, Butylene Glycol, Cetyl Alcohol, Parfum (Fragrance), CI 77891 (Titanium Dioxide), Chlorphenesin, Polyacrylate-13, Acrylates/C10-30 Alkyl Acrylate Crosspolymer, Tetrasodium EDTA, Caesalpinia Spinosa Fruit Extract, Mica, Polyisobutene, Ascorbyl Tetraisopalmitate, o-Cymen-5-ol, Tocopheryl Acetate, Xanthan Gum, Retinyl Palmitate, Kappaphycus Alvarezii Extract, Adenosine, Sodium Hyaluronate, Polysorbate-20, Croton Lechleri Resin Extract, Sorbitan Isostearate, Theobroma Cacao (Cocoa) Seed Extract, Tin Oxide, BHT, Tocopherol LaRoche-Posay SPF 50 Homosalate Octocrylene Octisalate Avobezone Ethylhexyl Triazone Tinosorb S Mexoryl XL Ecamsule/Mexoryl SX Titanium Dioxide TiO2 (Nano) Aqua/Water, Homosalate, Silica, Octocrylene, Ethylhexyl Salicylate, Butyl Methoxydibenzoylmethane, Ethylhexyl Triazone, Bis-Ethylhexyloxyphenol Methoxyphenyl Triazine, Drometrizole Trisiloxane, Aluminum Starch Octenylsuccinate, Glycerin, Pentylene Glycol, Styrene/Acrylates Copolymer, Potassium Cetyl Phosphate, Dimethicone, Perlite, Propylene Glycol, Acrylates/C10-30 Alkyl Acrylate Crosspolymer, Aluminum Hydroxide, p-Anisic Acid, Caprylyl Glycol, Disodium EDTA, Inulin Lauryl Carbamate, Isopropyl Lauroyl Sarcosinate, PEG-8 Laurate, Scutellaria Baicalensis Extract, Scutellaria Baicalensis Root Extract, Silica Silylate, Stearic Acid, Stearyl Alcohol, Terephthalylidene Dicamphor Sulfonic Acid, Titanium Dioxide, Titanium Dioxide (Nano)/Titanium Dioxide, Tocopherol, Triethanolamine, Xanthan Gum, Zinc Gluconate, Parfum/Fragrance LaRoche-Posay SPF 50 Spray Homosalate Octocrylene Ethyhexyl Salicylate Avobenzone Drometizole Trisiloxane Ethylhexyl Triazone Butane, Aqua/Water, Homosalate, Dicaprylyl Ether, Octocrylene, Ethylhexyl Salicylate, Dimethicone, Styrene/Acrylates Copolymer, Butyl Methoxydibenzoylmethane, Drometizole Trisiloxane[END_REF]

Declaration of competing financial interests

One Laboratoire de Biodiversité et Biotechnologies Microbiennes project is financed in the context of the Pierre Fabre Skin Protect Ocean Respect action. The work reported in this manuscript was not supported by Pierre Fabre Laboratories. The interpretation and views expressed in this manuscript are not those of the company. Haereticus Environmental Laboratory has received funding from the U.S. Environmental Protection Agency and the U.S. Department of Interior, but this funding did not contribute and is in no way associated with this study. Table 2. List of products, product lot number, product expiration date, the concentration of benzophenone (mg/kg; parts per million) at the baseline sampling, the concentration of benzophenone after the 6-week FDA accelerated stability incubation, and the percent increase of the geometric mean (GM) of benzophenone concentration for each product set between the baseline sampling and the 6-week accelerated stability sampling. The Nivea Sun SPF 50+ is the only commercial product that does not contain octocrylene in its active ingredients.



Figure and Table Legends

Figure 1 .

 1 Figure 1. The retro aldol condensation reaction between octocrylene and benzophenone.

Table 1 .

 1

	Products purchased in France in December 2019 (Supplemental Figure S1): Nivea Sun
	Protect & Hydrate SPF 50+ (does not contained octocrylene). The remaining products all
	identified OC in the ingredient labeling -Garnier Ambre Solaire Resisto Enfant FPS 50+;
	Bioderma Photoderm AR SPF 50+ Teinte Naturelle; Uriage Age Protect Fluide Multi-Actions
	SPF 30; LaRoche-Posay Sans Traces Blanches SPF 50+; LaRoche-Posay 50+ SPF Brume
	Invisible/Transparentes Spray; Cosmia Sun BB Creme SPF 50 Haute Protection; Cosmia Sun
	Haute-High Protection SPF 30; and L'Oreal Age Perfect Soin Rose Re-Fortifiant FPS 20.
	Products purchased in the United States of America in January 2020 (Supplemental
	Figure S2): Coppertone Kids Sport SPF 50 Spray; Coppertone Sunscreen Lotion Defend & Care
	Face Oil Free 50 Lotion; Coppertone Sunscreen Spray Water Babies 50, Coppertone Clear
	Sunscreen Sport Clear 30; Banana Boat Clear UltraMist Sport Performance 30; Banana Boat
	Sport Performance Sunscreen Lotion 50+; Neutrogena Beach Defense Sunscreen Spray 100;
	Neutrogena Beach Defense Sunscreen Lotion 70. All products identified OC at levels between
	4.5% and 10% in the active ingredients section of the drug facts labeling.

  .

	Authors
	Joseph DiNardo -Vesuvius, Virginia, 24484, United States; ORCID ID 0000-0001-8823-9814
	Didier Stien -Sorbonne Université, CNRS, Laboratoire de Biodiversité et Biotechnologies
	Microbiennes, USR3579, Observatoire Océanologique, 66650, Banyuls-sur-mer, France; ORCID
	ID 0000-0002-9950-5361
	Alice M.S. Rodriguez -Sorbonne Université, CNRS, Laboratoire de Biodiversité et
	Biotechnologies Microbiennes, USR3579, Observatoire Océanologique, 66650, Banyuls-sur-
	mer, France; ORCID ID 0000-0001-7671-1261
	Philippe Lebaron -Sorbonne Université, CNRS, Laboratoire de Biodiversité et Biotechnologies
	Microbiennes, USR3579, Observatoire Océanologique, 66650, Banyuls-sur-mer, France; ORCID
	ID 0000-0002-8520-9078
		ASSOCIATED CONTENT

Table 1

 1 Dimethyl Ether, Aloe Barbadensis Leaf Juice, C12-15 Alkyl Benzoate, Neopentyl Glycol, Diheptanoate, Butylene Glycol, Styrene/Acrylates Copolymer, VP/Eicosene Copolymer, 1,2-Hexanediol, Hydroxyacetophenone, Fragrance, Tocopherol, Acrylates/C10-30 Alkyl Acrylate Crosspolymer, Potassium Hydroxide, Disodium EDTA , avobenzone, homosalate, octisalate, octocrylene SPF 30 = SD Alcohol 40-B (60.3% v/v), Dicaprylyl Ether, Ethylhexyl Isononanoate, PVP, Dimethicone/Vinyl Dimethicone Crosspolymer, Polyester-27, Silica Dimethicone Silylate, Beeswax, Acrylates/C12-22 Alkyl Methacrylate Copolymer, Fragrance, Silica, avobenzone, homosalate, octocrylene Cetearyl Alcohol, Stearyl Alcohol, Glycerin, Phenoxyethanol, Acrylates C12-22 Alkyl Methacrylate Copolymer, Caprylyl Glycol, Cetyl Alcohol, Carbomer, Ceteth-10 Phosphate, Dicetyl Phosphate, Coco-Glucoside, Methylparaben, Xathan Gum, Propylparaben, Sodium Hydroxide, Disodium EDTA, Lauryl PEG-8 Dimethicone, Methyl Dihydroabietate, Phenylisopropyl Dimethicone, Polyglyceryl-3 Stearate/Isostearate/Dimer Dilinoleate Crosspolymer, Sodium Ascorbyl Phosphate, Tocopheryl Acetate, Aloe Barbadensis Leaf Juice, avobenzone, homosalate, octisalate, octocrylene, oxbenzone Styrene/Acrylates Copolymer, Dimethicone, Potassium Cetyl Phosphate, Benzyl Alcohol, Silica, Diethylhexyl 2,6-Naphthalate, Dimethicone/PEG-1-/15 Crosspolymer, Trisiloxane, Cetyl Dimethicone, Beeswax, Ethylhexylglycerin, Sodium Polyacrylate, Xanthan Gum, Ethylhexyl Stearate, Acrylates/C12-22 Alkyl Methacrylate Copolymer, Behenyl Alcohol, Trideceth-6, Disodium EDTA, Glyceryl Stearate, PEG-100 Stearate, Caprylyl Glycol, Chlorphensin, Fragrance, avobenzone, homosalate, octisalate, octocrylene, oxybenzone

	Product	Active Ingredients	Ingredients
	French Products
	Nivea Sun SPF 50+	Homosalate	Aqua, Homosalate, Glycerin, Alcohol Denat., Butyl
		Avobenzone	Methoxydibenzoylmethane (Avobenzone), Bis-
	Control Sample -	Tinosorb S	Ethylhexyloxyphenol Methoxyphenyl Triazine (Tinosorb S),
	No Octocrylene	Octisalate	Ethylhexyl Salicylate (Octisalate), Dibutyl Adipate, Ethylhexyl
		Ethylhexyl Triazone	Triazone, Copernicia Cerifera Cera, Panthenol, VP/Hexadecene
		Ensulizole	Copolymer, Phenylbenzimidazole Sulfonic Acid (Ensulizole),
			Tocopheryl Acetate, Tetrasodium Iminodisuccinate, Cellulose
			Gum, Acrylates/C10-30 Alkyl Acrylate Crosspolymer.
			Microcrystalline Cellulose, Xanthan Gum, Butylene Gylcol
			Dicaprylate/Dicaprate, Polyglyceryl-4
			Diisostearate/Polyhydroxystearate/Sebacate, Sucrose
			Polystearate, Sodium Stearoyl Glutamate, Hydrogenated
			Polyisobutene, Trisodium EDTA, Sodium Hydroxide, Sodium
			Chloride, Ethylhexylglycerin, Phenoxyethanol, Linalool,
			Limonene, Benzyl Alcohol, Alpha-Isomethyllonone,
			Citronellol, Geraniol, Parfum
	Garnier Ambre	Homosalate	Aqua/Water, Glycerin, Alcohol Denat., Homosalate,
	Solaire FPS 50	Octisalate	Ethylhexyl Salicylate (Octisalate), Butyl
		Avobenzone	Methoxydibenzoylmethane, Styrene/Acrylates Copolymer,
		Octocrylene	Octocrylene, Diisopropyl Sebacate, Dicaprylyl Carbonate,
		Ethylhexyl Triazone	Ethylhexyl Triazone, Dimethicone, Polyester-5, Bis-
		Tinosorb S	Ethylhexyloxyphenol Methoxyphenyl Triazine,
		Ecamsule/Mexoryl	Parfum/Fragrance, Drometrizole trisiloxane (Mexoryl XL),
		SX	Tocopherol, PEG-8 Laurate, Ethylenediamine/Stearyl Dimer
			Dilinoleate Copolymer, Triethanolamine, Pentaerythrityl Tetra-
			Di-T-Butyl Hydroxyhydrocinnamate (Tinogard® TT), Caprylyl
			Glycol, Acrylates Copolymer, Terephthalylidene Dicamphor
			Sulfonic Acid (Ecamsule/Mexoryl SX), Disodium EDTA,
	Bioderma Photoderm	Octocrylene	Aqua/Water/Eau, Dicaprylyl Carbonate, Octocrylene,
	AR SPF 50+	Tinosorb M (nano)	Dipropylene Glycol, Methylene bis-benzotriazolyl
		Avobenzone	tetramethylbutylphenol (Tinosorb M -nano), Butyl
		Tinosorb S	Methoxydibenzoylmethane, Cylcopentasiloxane, Bis-
		Titanium Dioxide	Ethylhexyloxyphenol Methoxyphenyl Triazine, Hydroxypropyl
		(77891),	Dimethicone Behenate, Potassium Cetyl Phosphate, Glyceryl
			Stearate, PEG-100 Stearate, Glycyrrhetinic Acid, Gingo Biloba
			Leaf Extract, Tocopheryl Acetate, Ectoin, Mannitol, Xylitol,
			Rhamnose Fructooucosaccharides, Laminaria Ochroleuca
			Extract, Glycerin Soja (Soybean) Germ Extract, Propylene
			Glycol, Silica, Hydrogenated Vegetable Oil, Ammonium
			Acryloyldimethyltaurate/VP Copolymer, Xanthan Gum, Citric
			Acid, Trilinolein, Trilinoleinin, Triolein, Tripalmitin,
			Caprylic/Capric Triglyceride, Tristrin, Iron Oxides (77492),
			Iron Oxides (77491), Iron Oxides (77499), Titanium Dioxide
			(77891), Disodium EDTA, Phenoxyethanol, Chlorphenesin
	Uriage Age Protect	Octinoxate	Aqua (Water, Eau), Ethylhexyl Methoxycinnamate
	SPF 30	Octisalate	(Octinoxate), Ethylhexyl Salicylate, Butyl
		Avobenzone	Methoxydibenzoylmethane, Octocrylene, Polymethyl
		Octocrylene	Methacrylate, Isononyl Isononanoate, Propanediol, Glycerin,

ACKNOWLEDGEMENTS

We would like to thank the four anonymous reviewers for the constructive comments and their time and effort in improving the manuscript.

Supporting Information

The Supporting Information is available free of charge at


P Knauth

L Pasquini

R Narducci

E Sgreccia

R.-A Becerra-Arciniegas

M L Di Vona

Effective ion mobility in anion exchange ionomers: relations with hydration, porosity, tortuosity, and percolation

Keywords: Anion exchange membranes, Ionic conductivity, Polysulfone, Poly(2,6-dimethyl-1,4-phenylene)oxide, Ion pairs

ABSTRACT

The effective mobility of hydroxide, chloride and fluoride ions is reported in various anion exchange membranes (AEM) with a backbone of polysulfone (PSU) or poly(2,6-dimethyl-1,4-phenylene)oxide (PPO). The concentration dependence of the effective mobility is used to derive the porosity (π), tortuosity (τ), and percolation thresholds and to plot the ionic conductivity vs the hydration number. Semi-logarithmic plots of the effective ion mobility u(i) vs the square root of concentration √c(i) for hydroxide, fluoride and chloride ions in various PSU-and PPO-based ionomers at 25 and 60 °C show linear relations, from which the ratio π/τ can be determined. This existence of linear u(i)=f(√c(i)) plots is related to the very particular boundary conditions experienced by mobile ions, migrating in close vicinity to the immobile grafted counter-ions placed at the interfaces between polymer domains and electrolyte solution. The π/τ values for PSU-QA (0.29) and PPO-QA (0.38) are consistent with a relatively low hydrophilic-hydrophobic nanophase separation, which leads to channels with low diameter and high tortuosity. The tortuosity determined from a Bruggeman-type relation is 1.9 for PSU-QA and 1.6 for PPO-QA. The percolation thresholds , determined from the universal percolation equation near and above , are at a water volume fraction of 0.07 for PSU-TMA and 0.03 for PPO-QA indicating that these AEM have a two-dimensional structure of the hydrated domains. The prefactor, which should represent a good indication as to the maximum achievable ionic conductivity, is slightly below 100 mS/cm for both PSU-TMA and PPO-based ionomers. Plots of experimental and computed hydroxide and chloride ion conductivities as function of the hydration number () show a maximum ionic conductivity for a value of the hydration number around 60, corresponding to optimal hydration conditions. At λ = 100, the ratio of conductivity between PSU-QA (OH form) and PPO-QA (Cl -form) indicates that the degree of dissociation of ion pairs is about 30% lower for hydroxide than for chloride ions, which is consistent with the effective ionic radii of Cl -and OH -.

Introduction

The ionic conductivity of ion exchange membranes is a critical property for their application as separators in various electrochemical energy technologies, such as fuel cells, electrolysers, or redox flow batteries [START_REF] Varcoe | Anion-exchange membranes in electrochemical energy systems[END_REF][START_REF] Kreuer | Ion Conducting Membranes for Fuel Cells and other Electrochemical Devices[END_REF][START_REF] Smitha | Solid polymer electrolyte membranes for fuel cell applicationsa review[END_REF][START_REF] Doan | Recent development of polymer membranes as separators for all-vanadium redox flow batteries[END_REF]. A low ion conductivity increases the area specific resistance of the devices and the Ohmic drop of the electrochemical cell and reduces the energy conversion efficiency by heat production [START_REF] Dekel | Review of cell performance in anion exchange membrane fuel cells[END_REF][START_REF] Gottesfeld | Anion exchange membrane fuel cells: Current status and remaining challenges[END_REF].

Generally, the ionic conductivity is the sum of the partial conductivities of various ions that depend on three factors: the charge of the ion (equal to the Faraday constant F for molar quantities and a singly charged ion), the ion concentration and the ion mobility. The case of ion exchange polymers is peculiar, because only one type of ion is mobile in the internal electrolytic solution, whereas the counterions are grafted on the polymer backbone and immobile [START_REF] Kreuer | On the development of proton conducting polymer membranes for hydrogen and methanol fuel cells[END_REF][START_REF] Kreuer | Transport in proton conductors for fuel-cell applications: Simulations, elementary reactions, and phenomenology[END_REF][START_REF] Bauer | Anion-Exchange Membranes with Improved Alkaline Stability[END_REF]. The ion concentration can be modified by a change of the ion exchange capacity (IEC) of the ionomer and/or a change of its hydration [START_REF] Peckham | Main-chain, statistically sulfonated proton exchange membranes: the relationships of acid concentration and proton mobility to water content and their effect upon proton conductivity[END_REF][START_REF] Kreuer | On the development of proton conducting materials for technological applications[END_REF][START_REF] Zawodzinski | Water-Uptake by and Transport Through Nafion 117 Membranes[END_REF].

The mobility of a single monovalent ion u(i) is defined according to equation 1 by the ionic conductivity σ(i) (expressed in mS/cm) and the ion concentration c(i) (expressed in mol/L):

The ion mobility is a complex parameter in an ionomer, given that it reflects the conditions of ionic motion in the restricted area of nanometric ion conduction channels present in the hydrated ionomers, but also the particular electrostatic conditions, where the mobile ions migrate inside channels with immobile counterions grafted on the channel walls [START_REF] Mauritz | State of understanding of Nafion[END_REF][START_REF] Gierke | THE MORPHOLOGY IN NAFION PERFLUORINATED MEMBRANE PRODUCTS[END_REF][START_REF] Yeager | Cation and water diffusion in nafion ion-exchange membranes -influence of polymer structure[END_REF]. This situation reduces the ion mobility by electrostatic interactions. Furthermore, the ionic transport depends on the percolation of the hydrated channels and their tortuosity [START_REF] Epstein | On tortuosity and the tortuosity factor in flow and diffusion through porous-media[END_REF][START_REF] Wernert | Influence of Molecule Size on Its Transport Properties through a Porous Medium[END_REF].

The percolation threshold is reached when the hydrated clusters become interconnected and long-range ionic conduction is possible [START_REF] Hsu | ION PERCOLATION AND INSULATOR-TO-CONDUCTOR TRANSITION IN NAFION PERFLUOROSULFONIC ACID MEMBRANES[END_REF]. The cross-section available for ionic conduction is proportional to the effective size of the hydrated channels; it is only a fraction of the total cross-sectional area of the ionomer, expressed phenomenologically by the "porosity" π (0 < π < 1) [START_REF] Diat | Proton channels[END_REF][START_REF] Gebel | Structural evolution of water swollen perfluorosulfonated ionomers from dry membrane to solution[END_REF][START_REF] Gebel | Structure of Membranes for Fuel Cells: SANS and SAXS Analyses of Sulfonated PEEK Membranes and Solutions[END_REF]. Moreover, not all pores have the same transport efficiency: the "tortuosity" τ is also a phenomenological parameter, which describes the complex interconnected pore network with irregular shapes and cross sections (τ > 1) [START_REF] Wernert | Influence of Molecule Size on Its Transport Properties through a Porous Medium[END_REF]. 1/τ is the fraction of pore volume having the same efficiency for transport as the bulk electrolyte [START_REF] Epstein | On tortuosity and the tortuosity factor in flow and diffusion through porous-media[END_REF]. The percolation threshold, porosity and tortuosity are a function of the nanophase separation, which is associated to the hydrophilicity of the ionic groups and the hydrophobicity of the polymer backbone [START_REF] Peckham | Relationships of acid and water content to proton transport in statistically sulfonated proton exchange membranes: Variation of water content via control of relative humidity[END_REF]. Phase-separated morphologies are also related to the temperature and the solvent-polymer and polymer-polymer interactions, described by the Flory-Huggins theory [START_REF] Flory | Statistical mechanics of cross-linked polymer networks II Swelling[END_REF].

Various authors have investigated the effective ion mobility dependence on the ion concentration for proton-conducting ionomers [START_REF] Peckham | Main-chain, statistically sulfonated proton exchange membranes: the relationships of acid concentration and proton mobility to water content and their effect upon proton conductivity[END_REF][START_REF] Kreuer | On the development of proton conducting materials for technological applications[END_REF][START_REF] Peckham | Relationships of acid and water content to proton transport in statistically sulfonated proton exchange membranes: Variation of water content via control of relative humidity[END_REF][START_REF] Telfah | Formation and mobility of protonic charge carriers in methyl sulfonic acid-water mixtures: A model for sulfonic acid based ionomers at low degree of hydration[END_REF][START_REF] Zawodzinski | A Comparative Study of Water-Uptake by and Transport Through Ionomeric Fuel-Cell Membranes[END_REF][START_REF] Paddison | The modeling of molecular structure and ion transport in sulfonic acid based ionomer membranes[END_REF][START_REF] Paddison | The nature of proton transport in fully hydrated Nafion (R)[END_REF][START_REF] Paddison | Theoretically computed proton diffusion coefficients in hydrated PEEKK membranes[END_REF][START_REF] Hickner | Water-mediated transport in ion-containing polymers[END_REF]. We have previously reported the proton mobility dependence on concentration in various sulfonated aromatic polymers (SAP) and perfluorinated sulfonic acid (PFSA) polymers [START_REF] Knauth | Water Activity Coefficient and Proton Mobility in Hydrated Acidic Polymers[END_REF][START_REF] Di Vona | Crosslinked sulfonated aromatic ionomers via SO2 bridges: Conductivity properties[END_REF][START_REF] Knauth | Proton Mobility in Sulfonated PolyEtherEtherKetone (SPEEK): Influence of Thermal Crosslinking and Annealing[END_REF][START_REF] Di Vona | Organic-inorganic hybrid membranes based on sulfonated polyaryl-ether-ketones: Correlation between water uptake and electrical conductivity[END_REF] and deduced percolation thresholds and tortuosity values [START_REF] Knauth | Water Activity Coefficient and Proton Mobility in Hydrated Acidic Polymers[END_REF][START_REF] Di Vona | Crosslinked sulfonated aromatic ionomers via SO2 bridges: Conductivity properties[END_REF][START_REF] Knauth | Sulfonated aromatic ionomers: Analysis of proton conductivity and proton mobility[END_REF].

For anion exchange membranes (AEM), the groups of Kreuer [START_REF] Marino | Hydroxide, halide and water transport in a model anion exchange membrane[END_REF], Dekel [START_REF] Amel | Bicarbonate and chloride anion transport in anion exchange membranes[END_REF],

Benziger [START_REF] Yan | Ion and water transport in functionalized PEEK membranes[END_REF] and Hickner [START_REF] Amel | Bicarbonate and chloride anion transport in anion exchange membranes[END_REF][START_REF] Disabb-Miller | Ion Motion in Anion and Proton-Conducting Triblock Copolymers[END_REF] reported anion conductivity data and discussed their relevance. Paddison and coworkers published mesoscale simulations of AEM [START_REF] Sepehr | Mesoscale Simulations of Anion Exchange Membranes Based on Quaternary Ammonium Tethered Triblock Copolymers[END_REF]. Wu et al.

discussed the hydroxide ion mobility in poly(ether ether ketone) based AEM [START_REF] Yan | Ion and water transport in functionalized PEEK membranes[END_REF][START_REF] Wu | Enhancement of hydroxide conductivity by the di-quaternization strategy for poly(ether ether ketone) based anion exchange membranes[END_REF]. In the case of AEM, the dissociation of ion pairs [START_REF] Stolwijk | What Can We Learn from Ionic Conductivity Measurements in Polymer Electrolytes? A Case Study on Poly(ethylene oxide) (PEO)-NaI and PEO-LiTFSI[END_REF] is incomplete, reminiscent of the so-called "Manning condensation" in polyelectrolytes [START_REF] Manning | Counterion binding in polyelectrolyte theory[END_REF].

In this paper, we report the effective mobility of hydroxide, chloride and fluoride ions in various ionomers with a backbone of polysulfone (PSU) or poly(2,6-dimethyl-1,4phenylene)oxide (PPO) and quaternary ammonium (QA) groups. The concentration dependence of the effective mobility is applied to derive the tortuosity and percolation parameters and to establish the relation between conductivity and hydration number. The relevance of these data for practical applications of AEM as ion-conducting separators in electrochemical devices is also discussed.

Experimental

Products

PSU (MW = 55500 g/mol) was purchased from Solvay. PPO (MW = 50000 g/mol),

Ionomer synthesis

The synthesis of the various ionomers was described in the following references: PSU-TMA and PSU-DABCO [START_REF] Di Vona | Anion-conducting ionomers: Study of type of functionalizing amine and macromolecular cross-linking[END_REF], PPO-DABCO with long side chain [START_REF] Becerra-Arciniegas | Model Long Side-Chain PPO-Based Anion Exchange Ionomers: Properties and Alkaline Stability[END_REF]. In short, PSU-TMA and PSU-DABCO were prepared by the chloromethylation route. Different degrees of chloromethylation were obtained varying the reaction time. Chloromethylated PSU samples (PSU-CH 2 Cl) reacted with TMA and DABCO via nucleophilic substitution (quaternization).

PPO-DABCO with long side-chain was prepared by benzyl bromination followed by quaternization. Cross-linked AEM (XL-AEM) were synthetized using 5% of chlorosulfonated poly(ether ether ketone) (PEEK-SO 2 Cl) as cross-linker [START_REF] Di Vona | Anion-conducting ionomers: Study of type of functionalizing amine and macromolecular cross-linking[END_REF].

PPO-DABCO was prepared by the chloromethylation route using the following ratio The quaternization was carried out in NMP for 72 h at 70 °C with a ratio between functional groups of PPO-CH 2 Cl and DABCO 1:1.4. After this time, the solution was reduced to a third under low pressure at 80 °C and directly used for the casting procedure. The ion exchange capacity (see Table 1) was measured by Mohr titration [START_REF] Becerra-Arciniegas | Model Long Side-Chain PPO-Based Anion Exchange Ionomers: Properties and Alkaline Stability[END_REF].

Composite AEM

The ionomer composites (see Table 1) were prepared using TiO 2 functionalized with poly(methylhydrosiloxane) [START_REF] Derbali | Composite anion exchange membranes with functionalized hydrophilic or hydrophobic titanium dioxide[END_REF] or layered double hydroxides (LDH) as fillers. The synthesis of Mg/Al LDH was described in reference [START_REF] Di Vona | Anionic conducting composite membranes based on aromatic polymer and layered double hydroxides[END_REF].

Membrane preparation

The membranes were generally prepared by dissolution of the ionomers in NMP, typically 250 mg per 20 mL of solvent, and casting at 100 °C before drying in an oven at 90-100 °C during 48 h.

For composite AEM, the nanometric inorganic filler was added to the ionomer solution before casting (between 5 and 30 wt%) and sometimes DMSO was preferred to NMP to assure a better homogeneity of the samples. The detailed procedures for composites can be found in the following references: PSU-DABCO-TiO 2 [START_REF] Derbali | Composite anion exchange membranes with functionalized hydrophilic or hydrophobic titanium dioxide[END_REF], PSU-TMA-LDH [START_REF] Di Vona | Anionic conducting composite membranes based on aromatic polymer and layered double hydroxides[END_REF] and PSU-DABCO-LDH [START_REF] Di Vona | Anionic conducting composite membranes based on aromatic polymer and layered double hydroxides[END_REF][START_REF] Pizzoferrato | Layered Double Hydroxides Containing an Ionic Liquid: Ionic Conductivity and Use in Composite Anion Exchange Membranes[END_REF]. PPO-DABCO-LDH was obtained by adding 30 wt% of LDH to 20 mL of a 0.05 M solution of PPO-DABCO in NMP. The mixture was evaporated to a half of the initial volume during vigorous stirring and the viscous solution was cast onto a Petri dish and heated in an oven at 100 °C during 48 h.

Determination of the IEC

The IEC (meq/g) is expressed in milliequivalents of ionic groups n per mass of dry polymer m dry :

The ion exchange capacity was determined by acid-base titration or by Mohr titration. For the latter, the ionomer was first ion-exchanged in a 1 M NaCl solution during 24 h and carefully washed in deionized water during 24 h. The polymer dried in a desiccator during 48 h was immersed in Na 2 SO 4 solution and the exchanged Cl -ions were titrated with 0.1 M AgNO 3 solution. 1 mL of 0.25 M K 2 CrO 4 indicator solution was added prior to the titration. At the equivalence point, a red-brown precipitate of Ag 2 CrO 4 appeared.

Water uptake measurements

The water uptake (WU) is determined from the masses of dry and wet polymer (m wet ); it is related to the volumes of water and dry polymer via the dry polymer density ρ dry :

The densities of the electrolytic solutions are approximated as 1 g/cm 3 . Experimental values determined in Nafion are near 1 and the concentration dependence of the electrolyte density is small [START_REF] Alberti | New results on the visco-elastic behaviour of ionomer membranes and relations between T-RH plots and proton conductivity decay of Nafion (R) 117 in the range 50-140 degrees C[END_REF]. We assume that all water molecules reside near ionic groups for thermodynamic affinity reasons (in agreement with the definition of the hydration number) and that the concentration of the internal electrolytic solution is homogeneous throughout the membrane.

Combining equations 2 and 3, one obtains:

The hydration number, which is the number of water molecules per ionic group, is defined as:

M(H 2 O)
is the molar mass of water.

The measurements were made on ionomers in hydroxide, chloride or fluoride forms.

The samples were obtained by ion exchange in 1 M solutions of NaOH (under nitrogen), NaCl or NH 4 F during 24 h. After the ion exchange, the samples were carefully washed in deionized and decarbonated water during 24 h to remove any excess of electrolyte. The hydroxide forms were analyzed immediately or stored in absence of CO 2 to avoid carbonation issues. The mass of wet samples (m wet ) was determined after immersion during 24 h in deionized water and wiping the sample surface with absorbing paper. The mass of dry samples (m dry ) was measured after storing them over P 2 O 5 in a desiccator during 48 h.

Ion conductivity measurements

AEM samples in hydroxide, chloride, or fluoride forms were made as described above.

The fully humidified membranes were immediately placed in Swagelok holders with stainless steel electrodes (through-plane configuration). Electrochemical impedance spectroscopy measurements were performed using a Biologic VSP-300 apparatus. The applied a.c. voltage was 20 mV and the frequency range 1 Hz-6 MHz. The impedance spectra were interpreted by non-linear least-square fitting using a classical Randles circuit (R 1 -R 2 //CPE) or a series of two parallel circuits containing a resistance and a constant phase element (R 1 //CPE 1 -R 2 //CPE 2 ).

The ionic conductivity at partial humidification (65 ≤ RH / % ≤ 95) was measured with inplane configuration using the apparatus described in reference [START_REF] Di Vona | Anionic conducting composite membranes based on aromatic polymer and layered double hydroxides[END_REF].

Results

The chemical formulas of PSU-TMA, PSU-DABCO, PPO-DABCO, and PPO-DABCO with long side-chain are shown in Figure 1.

Table 1 presents the experimental results for IEC, WU and ionic conductivity for the various investigated AEM.

Discussion

The ion concentration in the electrolytic solution inside the ionomer channels, expressed in mol/L, can be calculated from IEC and WU (combining eq. 2-4). c(i) is directly related to the hydration number λ (cf. eq. 5):

Changes of the ion concentration due to an incomplete dissociation or the formation of ion pairs are observed in the effective ion mobility defined by eq. 1.

Figure 2 shows a semi-logarithmic plot of the effective ion mobility at 25 °C vs the square root of concentration for hydroxide and fluoride ions in PSU-TMA and PSU-DABCO ionomers (triangles) as well as chloride ions in PPO-DABCO based ionomers (dots). Figure 3 shows a comparison of hydroxide ion mobilities in PSU-QA ionomers at 25 and 60 °C with literature data for proton-conducting SPEEK [START_REF] Di Vona | Crosslinked sulfonated aromatic ionomers via SO2 bridges: Conductivity properties[END_REF]. We present the data for PSU-DABCO and PSU-TMA with identical symbols in Fig. 3, because there is no significant difference between the two data sets, confirming that the nature of the amine is less important for the anion mobility, as already stated [START_REF] Di Vona | Anion-conducting ionomers: Study of type of functionalizing amine and macromolecular cross-linking[END_REF].

One should mention that the hydroxide ion mobilities at 60 °C (calculated from the data in Table 2) were obtained by in-plane measurements [START_REF] Di Vona | Anionic conducting composite membranes based on aromatic polymer and layered double hydroxides[END_REF][START_REF] Casciola | A critical investigation of the effect of hygrothermal cycling on hydration and in-plane/through-plane proton conductivity of Nafion 117 at medium temperature (70-130 degrees C)[END_REF][START_REF] Casciola | On the decay of Nafion proton conductivity at high temperature and relative humidity[END_REF], which give somewhat higher ionic conductivities, due to a surface segregation of functional groups [START_REF] Casciola | A critical investigation of the effect of hygrothermal cycling on hydration and in-plane/through-plane proton conductivity of Nafion 117 at medium temperature (70-130 degrees C)[END_REF]. Literature values for the activation energy of hydroxide ion migration are between 0.1-0.2 eV [START_REF] Tuckerman | The nature and transport mechanism of hydrated hydroxide ions in aqueous solution[END_REF][START_REF] Agmon | Mechanism of hydroxide mobility[END_REF][START_REF] Marx | Aqueous Basic Solutions: Hydroxide Solvation, Structural Diffusion, and Comparison to the Hydrated Proton[END_REF][START_REF] Pandey | A Highly Hydroxide Conductive, Chemically Stable Anion Exchange Membrane, Poly(2,6 dimethyl 1,4 phenylene oxide)-b-Poly(vinyl benzyl trimethyl ammonium), for Electrochemical Applications[END_REF], but above 0.2 eV for λ < 20 [START_REF] Marino | Hydroxide, halide and water transport in a model anion exchange membrane[END_REF].

This u(i) vs. c(i) 1/2 plot type is selected following the classical square root concentration dependence of the equivalent conductivity of electrolyte solutions ("Kohlrausch law" [START_REF] Kortüm | Treatise on Electrochemistry[END_REF][START_REF] Hamann | Electrochemistry[END_REF][START_REF] Onsager | The motion of ions: principles and concepts[END_REF]). A linear decrease with the square root of concentration is observed for strong electrolytes. In "weak" electrolytes, the concentration dependence of the equivalent conductivity is much stronger, due to the incomplete dissociation, which becomes complete only at infinite dilution [START_REF] Amel | Bicarbonate and chloride anion transport in anion exchange membranes[END_REF][START_REF] Hamann | Electrochemistry[END_REF]. Polyelectrolyte solutions also do not obey the linear limiting law, which is attributed to the high charge density of the polyions and to the flexibility of the polyion chain and its ability to change conformation [START_REF] Halla | Some New Contributions to the Theory of Polyelectrolyte Solutions: Prediction of Polyion Conformation and Interpretation of Some Deviations from Kohlrausch's Law According to the Superposition Principle and the Dielectric Friction Effect[END_REF]. A similar strong concentration dependence is here observed for the electrolyte solutions inside ionomers, including those containing strong sulfonic acids, such as SPEEK (Figure 2) and Nafion [START_REF] Knauth | Water Activity Coefficient and Proton Mobility in Hydrated Acidic Polymers[END_REF][START_REF] Knauth | Sulfonated aromatic ionomers: Analysis of proton conductivity and proton mobility[END_REF]. The very particular boundary conditions experienced by the mobile ions, migrating in close vicinity to the fixed opposite charges of the grafted ionic groups placed at the interfaces between polymer domains and electrolyte solution, leads to a strong concentration dependence of the effective ion mobility. It reflects the concentration-dependent formation of ion pairs or complexes of several ions that break apart only at high water content [START_REF] Marino | Hydroxide, halide and water transport in a model anion exchange membrane[END_REF]. with the proton mobility in SPEEK from reference [START_REF] Di Vona | Crosslinked sulfonated aromatic ionomers via SO2 bridges: Conductivity properties[END_REF].

1E-7 1E-6 1E-5 1E-4 1E-3 0 1 2 3 4 u(X -) / (cm 2 s -1 V -1 ) c(X -) 1/2 / (mol/L) 1/2 PSU-DABCO u(OH-) PSU-TMA u(OH-) PSU-QA u(F-) PPO-DABCO u(Cl-) PPO-DABCO long side chain u(Cl-) PPO-DABCO-LDH u(Cl-) 1E-9 1E-8 1E-7 1E-6 1E-5 1E-4 1E-3 1E-2 0 1 2 3 4 5 u(i) (cm 2 s -1 V -1 ) c(i) 1/2 (mol/L) 1/2 SPEEK u(H+) 25 °C PSU-QA u(OH-) 25 °C PSU-QA u(OH-) 60 °C u(OH -) u(H + ) u(OH -) u(F -) u(Cl -) u(Cl -) u(Cl -) u(OH -) u(OH -)

Porosity and tortuosity

The ratio of porosity and tortuosity can be determined from the renormalisation equation 7 [START_REF] Wernert | Influence of Molecule Size on Its Transport Properties through a Porous Medium[END_REF][START_REF] Di Vona | Crosslinked sulfonated aromatic ionomers via SO2 bridges: Conductivity properties[END_REF][START_REF] Knauth | Sulfonated aromatic ionomers: Analysis of proton conductivity and proton mobility[END_REF][START_REF] Pisani | An analytical model for the conductivity of polymeric sulfonated membranes[END_REF], where u(i)° is the ion mobility at infinite dilution in an aqueous solution not contained in the ionomer matrix.

The proton, hydroxide and chloride ion mobility data at 25 °C are used to extrapolate the ion mobility at infinite dilution, which can be compared with reference literature data. Consistent values for H + (36.2 10 -4 cm 2 s -1 V -1 ), OH -(20.5 10 -4 cm 2 s -1 V -1 ), and Cl -(7.9 10 -4 cm 2 s -1 V -1 ) can be taken from various references [START_REF] Kortüm | Treatise on Electrochemistry[END_REF][START_REF] Hamann | Electrochemistry[END_REF][START_REF] Milazzo | Electrochemistry: Theoretical Principles and Practical Applications[END_REF][START_REF] Weast | Handbook of Chemistry and Physics[END_REF]. Let us recall that although strong ion pairs are formed in AEM, they are totally dissociated at infinite dilution.

Equation 7 is applied to deduce the ratio porosity/tortuosity from Figure 2 for PSU-QA (π/τ = 0.29) and PPO-QA (π/τ = 0.38) and from Figure 3 for sulfonated poly(ether ether ketone) (SPEEK, π/τ = 0.61). Sulfonated aromatic polymers, such as SPEEK, present a lower hydrophilic/hydrophobic nanophase separation than Nafion [START_REF] Peckham | Relationships of acid and water content to proton transport in statistically sulfonated proton exchange membranes: Variation of water content via control of relative humidity[END_REF][START_REF] Mahajan | Atomistic Simulations of Structure of Solvated Sulfonated Poly(ether ether ketone) Membranes and Their Comparisons to Nafion: II. Structure and Transport Properties of Water, Hydronium Ions, and Methanol[END_REF][START_REF] Mahajan | Atomistic Simulations of Structure of Solvated Sulfonated Poly(ether ether ketone) Membranes and Their Comparisons to Nafion: I. Nanophase Segregation and Hydrophilic Domains[END_REF]; two reasons for this difference are that the sulfonic group has a lower acidity and hydrophilicity than the strongly acidic perflurosulfonic group and that the aromatic backbone is less hydrophobic than the perfluorinated polymer backbone (it contains e.g. ether linkages). Other factors, such as chain flexibility, entanglement defects, crystallinity, and the various interaction parameters affect the nanophase separation. AEM with quaternary ammonium groups present an even lower nanophase separation, because the functional groups are less hydrophilic than sulfonic acids [START_REF] Marino | Hydroxide, halide and water transport in a model anion exchange membrane[END_REF][START_REF] Dang | Exploring Different Cationic Alkyl Side Chain Designs for Enhanced Alkaline Stability and Hydroxide Ion Conductivity of Anion-Exchange Membranes[END_REF]. The lower π/τ values for PSU-QA and PPO-QA are consistent with a lower hydrophilic-hydrophobic nanophase separation, which leads to channels with low diameter (low π) and high tortuosity τ (for example more dead-ends [START_REF] Kreuer | Transport in proton conductors for fuel-cell applications: Simulations, elementary reactions, and phenomenology[END_REF]). The lowest value for PSU-QA corresponds to the larger hydrophilicity of the PSU backbone vs. PPO, due inter alia to the presence of sulfone groups, which further reduces the nanophase separation and the porosity/tortuosity ratio, leading to narrower hydrophilic channels and to a larger separation between the functional groups [START_REF] Kreuer | A Critical Revision of the Nano-Morphology of Proton Conducting Ionomers and Polyelectrolytes for Fuel Cell Applications[END_REF].

Phenomenological relations exist between porosity and tortuosity; the best known is the Bruggeman-type expression [START_REF] Pisani | An analytical model for the conductivity of polymeric sulfonated membranes[END_REF]:

 is the universal percolation exponent [START_REF] Knauth | Water Activity Coefficient and Proton Mobility in Hydrated Acidic Polymers[END_REF][START_REF] Staufer | Introduction to Percolation Theory[END_REF]. Assuming three-dimensional percolation (α ≈ 2), one obtains a tortuosity of 1.9 for PSU-QA and 1.6 for PPO-QA, in good agreement with the values reported for PSU-QA (τ = 1.83-1.88 [START_REF] Amel | Bicarbonate and chloride anion transport in anion exchange membranes[END_REF]) and for a PPO-based copolymer (τ = 1.8 [START_REF] Pandey | A Highly Hydroxide Conductive, Chemically Stable Anion Exchange Membrane, Poly(2,6 dimethyl 1,4 phenylene oxide)-b-Poly(vinyl benzyl trimethyl ammonium), for Electrochemical Applications[END_REF]).

Percolation

The ionic conductivity can be written near and above the percolation threshold as a function of the volume fraction of the hydrated domains [START_REF] Hsu | ION PERCOLATION AND INSULATOR-TO-CONDUCTOR TRANSITION IN NAFION PERFLUOROSULFONIC ACID MEMBRANES[END_REF][START_REF] Clerc | The ac Electrical Conductivity of Binary Disordered-Systems, Percolation Clusters, Fractals and Related Models[END_REF]:

The universal percolation exponent α is near 2 for three-dimensional (3D) percolation [START_REF] Knauth | Water Activity Coefficient and Proton Mobility in Hydrated Acidic Polymers[END_REF][START_REF] Staufer | Introduction to Percolation Theory[END_REF]. is the water volume fraction at the percolation threshold and is the prefactor.

By simple mathematical transformation of eq. 9, one can show that a plot σ(i) 1/2 = f( ) should give a straight line; and can be determined from its slope and intercept, respectively.

The volume fraction of water in the wet ionomer is defined and related to WU (cf. eq. 3) by eq. 10:

The volume fraction can be related to the IEC and the ion concentration combining eq. 6

and 10:

The dry density of the polymers is taken as 2.07 g/cm 3 for Nafion [START_REF] Gierke | THE MORPHOLOGY IN NAFION PERFLUORINATED MEMBRANE PRODUCTS[END_REF], 1.34 g/cm 3 for SPEEK [START_REF] Narducci | Cation-conducting ionomers made by ion exchange of sulfonated poly-ether-ether-ketone: Hydration, mechanical and thermal properties and ionic conductivity[END_REF], or by the values for PPO (1.06 g/cm 3 [START_REF] Liang | Poly(phenylene oxide)[END_REF]) and PSU (1.24 g/cm 3 [START_REF] Sastri | Chapter 8 -High-Temperature Engineering Thermoplastics: Polysulfones, Polyimides, Polysulfides, Polyketones, Liquid Crystalline Polymers, and Fluoropolymers[END_REF]). Using experimental values for each membrane might further improve the quality of the fits. Figure 4 shows such a plot for PSU-TMA and PPO-QA and a comparison with SPEEK [START_REF] Di Vona | Crosslinked sulfonated aromatic ionomers via SO2 bridges: Conductivity properties[END_REF] and reference data for Nafion [START_REF] Kreuer | Transport in proton conductors for fuel-cell applications: Simulations, elementary reactions, and phenomenology[END_REF]. The percolation threshold is at a water volume fraction of 0.01 for Nafion and somewhat higher, but not that much for PSU-TMA (0.07) and PPO-DABCO ionomers (0.03), whereas it is much higher for SPEEK (0.21). Indeed, no percolation threshold is observed for PSU-QA in Figure 3, whereas it is clearly visible for SPEEK. The percolation threshold for conduction paths to traverse the ionomer, , is reported in SPEEK at a water volume fraction below 0.3, consistent with a stochastic medium with randomly dispersed spherical hydrated clusters [START_REF] Gebel | Structure of Membranes for Fuel Cells: SANS and SAXS Analyses of Sulfonated PEEK Membranes and Solutions[END_REF][START_REF] Pisani | An analytical model for the conductivity of polymeric sulfonated membranes[END_REF][START_REF] Komarov | Mesoscale simulation of polymer electrolyte membranes based on sulfonated poly(ether ether ketone) and Nafion[END_REF][START_REF] Wu | Differences in Water Sorption and Proton Conductivity Between Nafion and SPEEK[END_REF]. Pisani et al. fit conductivity data for SPEEK with = 0.22, in excellent agreement with our result [START_REF] Pisani | An analytical model for the conductivity of polymeric sulfonated membranes[END_REF]. Lamellar hydrophilic domains, supposed to exist in Nafion, percolate through the hydrophobic matrix at a volume fraction below 0.1 [START_REF] Mauritz | State of understanding of Nafion[END_REF][START_REF] Hsu | ION PERCOLATION AND INSULATOR-TO-CONDUCTOR TRANSITION IN NAFION PERFLUOROSULFONIC ACID MEMBRANES[END_REF][START_REF] Komarov | Mesoscale simulation of polymer electrolyte membranes based on sulfonated poly(ether ether ketone) and Nafion[END_REF][START_REF] Wu | Differences in Water Sorption and Proton Conductivity Between Nafion and SPEEK[END_REF], which is much lower than the value for a completely random system. Pisani et al. take = 0 for the simulation of Nafion conductivity data [START_REF] Pisani | An analytical model for the conductivity of polymeric sulfonated membranes[END_REF].

The low percolation threshold value for PSU-TMA and PPO-DABCO (well below 0.1, like that reported for PEEK-QA [START_REF] Yan | Ion and water transport in functionalized PEEK membranes[END_REF]) seems to indicate that these AEM present also a partly two-dimensional (2D) structure of the hydrated domains, but less pronounced than Nafion ("layered morphologies" [START_REF] Alberti | More on Nafion Conductivity Decay at Temperatures Higher than 80 °C: Preparation and First Characterization of In-Plane Oriented Layered Morphologies[END_REF]). Indeed, SAXS investigations suggested nanometerrange swelling to occur in two dimensions in AEM with polymer chains having a tendency to arrange locally in a parallel fashion [START_REF] Marino | Hydroxide, halide and water transport in a model anion exchange membrane[END_REF]. Mesoscale simulations support this picture of layered morphology [START_REF] Sepehr | Mesoscale Simulations of Anion Exchange Membranes Based on Quaternary Ammonium Tethered Triblock Copolymers[END_REF]. The particularly low percolation threshold for PSU-TMA is consistent with the low nanophase separation in PSU-QA (see above), which leads to narrower hydrophilic channels than in PPO-QA. It is well known that percolation thresholds are displaced to lower volume fractions, when the domain size of the percolating phase decreases (correlation effects) [START_REF] Debierre | Enhanced conductivity in ionic conductor-insulator composites: Experiments and numerical model[END_REF][START_REF] Albinet | Enhanced conductivity in ionic conductor-insulator composites: numerical models in two and three dimensions[END_REF].

The prefactor represents mathematically the ionic conductivity when , corresponding to a "bulk" electrolyte experiencing similar electrostatic boundary conditions than in the ionomer. The prefactor σ(i)° depends on the particular conduction mechanism within and between two adjacent clusters, involving interactions among ions, water molecules, and the ionomer [START_REF] Mauritz | State of understanding of Nafion[END_REF]. The prefactor should therefore represent a good indication as to the maximum achievable ionic conductivity in an ionomer. Indeed, σ(i)° is much higher for Nafion (~700 mS/cm) and SPEEK (223 mS/cm) than for PSU-TMA (86 mS/cm) and PPO-DABCO (93 mS/cm) in good accordance with the larger mobility of protons vs. hydroxide ions and the larger tortuosity of AEM.

Hydration dependence of the ionic conductivity

The presence of a solvent with high dielectric constant, especially water, is fundamental for the particular conduction mechanism in ionomers. However, hydration has antagonistic effects on the conductivity, because a large hydration increases the effective ion mobility, but reduces the ion concentration.

Figure 5 shows a plot of the proton, hydroxide and chloride ion conductivity in ionomers as function of the hydration number. The dots correspond to experimental data from Tables 1 and2 or reference [START_REF] Di Vona | Crosslinked sulfonated aromatic ionomers via SO2 bridges: Conductivity properties[END_REF] for SPEEK. The lines are computed from the ion concentrations and effective ion mobilities. These plots show a maximum ionic conductivity for an intermediate value of the hydration number, corresponding to optimal hydration conditions, around 60 for AEM and 80 for SPEEK. The maximum conductivities are still significantly below the prefactors obtained from the percolation approach above, indicating that there is still substantial room for improvement of the ionic conductivity of these ionomers.

Figure 5. Experimental and computed ionic conductivity dependence on the hydration number for protons [START_REF] Di Vona | Crosslinked sulfonated aromatic ionomers via SO2 bridges: Conductivity properties[END_REF], hydroxide and chloride ion-conducing ionomers at 25 °C.

For large hydration numbers, the aqueous channels are fully percolating and the sulfonic acid groups are fully dissociated, but the ion pairs in AEM not necessarily, so that the ion concentration calculated according to eq. 6 is overestimated and the effective mobility calculated is underestimated according to eq. 1. At λ = 100, the ratio of conductivity for SPEEK and PPO-QA amounts to 4.6, whereas the mobility ratio at infinite dilution is 5.3 [START_REF] Kortüm | Treatise on Electrochemistry[END_REF][START_REF] Hamann | Electrochemistry[END_REF]. Assuming that this difference is related only to the incomplete dissociation of ion pairs in PPO-QA would lead to a dissociation degree of 85% for Cl -ions. This value is somewhat higher than the values of around 50% reported by Kreuer et al. for the Cl -dissociation in a related AEM [START_REF] Marino | Hydroxide, halide and water transport in a model anion exchange membrane[END_REF]. Laidler et al. reported a dissociation constant of 28 for tetramethylammonium iodide in acetone solution that would give similar dissociation degrees [START_REF] Adams | Electrical conductivities of quaternary ammonium salts in acetone 1. Pressure and temperature effects[END_REF]. However, there are two major differences with AEM, which have an antagonistic effect on ion pair dissociation: the solvent acetone has a low dielectric constant, but the acetone solution is not contained in an ionomer with its very particular electrostatic situation.

Finally, making a similar comparison of the conductivity ratio of PSU-QA (OH -) and PPO-QA (Cl -), which is 1.8 at λ = 100, and the ratio of the ion mobility of hydroxide and chloride ions at infinite dilution (2.6 [START_REF] Kortüm | Treatise on Electrochemistry[END_REF][START_REF] Hamann | Electrochemistry[END_REF]), the difference might again be attributed to the would be about 30% lower for hydroxide than for chloride ions. This result is consistent with the effective ionic radii of chloride (181 pm [START_REF] Shannon | Revised effective ionic-radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF]) and hydroxide ions (132 pm [START_REF] Shannon | Revised effective ionic-radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF]) given that a lower ion radius increases the strength of ion pairs [START_REF] Onsager | Deviations from Ohm's Law in Weak Electrolytes[END_REF][START_REF] Adams | Electrical Conductivities of Quaternary Ammonium Salts in Acetone 2. Mechanisms of Transport[END_REF][START_REF] Adams | Electrical Conductivities of Quaternary Ammonium Salts in Acetone 3. Ion-Pair Formation[END_REF].

Conclusions

The effective ion mobility in ionomers is a key property in order to reach ionic conductivities high enough to design ionomer separators for electrochemical devices with low area specific resistance. The effective ion mobility is a complex parameter, which depends on the complicated situation encountered by the mobile ions during their migration in the restricted area of ion conduction channels surrounded by a solvent with high dielectric constant and fixed counter-ions grafted on the channel walls. This complexity can be described by several phenomenological parameters, such as porosity and tortuosity, percolation threshold, degree of dissociation of ion pairs.

In this work, we determined and analysed the effective anion mobility in various anion This finding is in agreement with the conclusions of literature SAXS experiments.

The ion conductivity shows a maximum for a hydration number around 60 for AEM, which corresponds to an optimal compromise of anion concentration and effective anion mobility. The ratio of conductivities for chloride and hydroxide ions indicates that the degree of dissociation of ion pairs is about 30% lower for OH -ions. This conclusion is consistent with the lower radius of hydroxide ions, because the strength of ion pairs, due to Coulombic interactions, is related to the inter-ionic distance.

  of reagents PPO:Me 3 SiCl:(CH 2 O) n :SnCl 4 = 1:3:3:0.05. Before the use, chloroform was washed with water to remove ethanol and dried on molecular sieves (3 Å). All the steps were carried out under nitrogen in anhydrous conditions. PPO (41.8 meq) was dissolved in 250 mL of CHCl 3 at RT, then the temperature was increased to 45 °C. At the same time Me 3 SiCl, paraformaldehyde, and SnCl 4 were mixed and heated to 45 °C. After 1 h, a clear solution was obtained. This solution was quickly added to the solution of PPO and the reaction performed at 45 °C for a time in the range 8-17 h in order to obtain different degrees of chloromethylation. After this time, the temperature was reduced to RT and 150 mL of CH 3 OH added until complete precipitation. The PPO-CH 2 Cl was washed with CH 3 OH and dried in the oven at 60 °C for 48 h[START_REF] Becerra-Arciniegas | Alkaline stability of model anion exchange membranes based on poly (phenylene oxide) (PPO) with grafted quaternary ammonium groups: Influence of the functionalization route[END_REF].

Figure 1 .

 1 Figure 1. Chemical formulas of a) PSU-TMA, b) PSU-DABCO, c) PPO-DABCO, and d) PPO-DABCO with long side-chain.

Figure 2 .

 2 Figure 2. Concentration dependence of the effective mobility of hydroxide and fluoride anions in PSU-based ionomers and chloride anions in PPO-based ionomers with quaternary ammonium groups.

Figure 3 .

 3 Figure 3. Square root concentration dependence of the effective mobility of hydroxide anions in PSU-based ionomers with quaternary ammonium groups at 25 and 60 °C and a comparison

Figure 4 .

 4 Figure 4. Determination of the percolation threshold for AEM, SPEEK and Nafion.

  of ion pairs indicating that the degree of dissociation of ion pairs

  exchange membranes with PSU or PPO backbones. Linear semi-logarithmic plots of the effective ion mobility vs. the square root of the ion concentration allowed determining the ratio porosity/tortuosity. The values of AEM (PSU-QA: π/τ = 0.29 and PPO-QA: π/τ = 0.38) are inferior to those of proton exchange membranes (SPEEK, π/τ = 0.61). This finding can be attributed to a lower nanophase separation, due to the minor hydrophilicity of quaternary ammonium groups vs sulfonic acids. The smaller value for PSU-QA with respect to PPO-QA is related to the lower hydrophobicity of the ionomer backbone, due to the more hydrophilic sulfone moieties and the absence of methyl groups.The percolation threshold was determined from linear plots of the square root of ionic conductivity vs. the volume fraction of aqueous domains. The low percolation threshold of AEM (PSU-TMA: = 0.07 and PPO-QA: = 0.03) indicates the existence of 2D arrangements of the ionic domains, which percolate at lower water fractions than 3D domains.

Table 2

 2 shows the IEC, WU and ionic conductivity data of PSU-TMA and PSU-DABCO as well as composites with LDH at 60 °C and 95, 80 or 65% RH.

The values of WU (in %) must be divided by 100 in all equations.

Table 1 .

 1 Ion exchange capacity (IEC), water uptake (WU), and ionic conductivity (σ) of various PSU and PPO-based ionomers at 25 °C.

	Samples	IEC	WU	σ	Samples		IEC	WU	σ
		(meq/g)	(%)	(mS/cm)			(meq/g)	(%)	(mS/cm)
	PSU-based AEM (OH	-form)		PPO-based AEM (Cl	-form)
	DABCO [43]	1.10	33.0 5.3	DABCO		0.88	15.7	0.5
	DABCO [46]	1.25	85.0 5.1	DABCO		0.91	22.1	0.9
	DABCO [47]	1.57	124.3 5.3	DABCO		1.10	22.8	1.1
	DABCO [43]	1.70	504.0 6.7	DABCO		1.48	30.4	1.2
	DABCO-TiO 2 [46]	1.25	56.0 4.3	DABCO		1.60	30.6	2.0
	DABCO-LDH [47]	1.57	25.4 2.2	DABCO long chain [44] 1.30	21.0	1.4
	TMA [43]	0.81	19.0 2.2	DABCO-LDH		0.91	39.5	0.9
	TMA 5% XL* [43]	0.81	26.0 2.3	DABCO-LDH		1.67	36.4	1.0
	TMA 5% XL** [43] 1.19	32.0 2.2	DABCO-LDH		1.69	39.8	1.3
	TMA 5% XL*** [43] 1.19	319.0 4.3
	TMA [43]	1.34	40.0 4.6	PSU-based AEM (F	-form)
	TMA [43]	1.64	53.0 12.0	DABCO (F -form) [50]		1.30	198.0 5.8
	TMA-LDH [47]	1.67	42.1 3.7	TMA (F -form) [50]		1.64	130.0 9.5
	* Cross-linked (XL) ionomer
	** XL ionomer annealed 24 h at 120 °C
	*** Strongly hydrated XL ionomer

Table 2

 2

	Samples	IEC	RH	WU	σ
		(meq/g)	(%)	(%)	(mS/cm)
	TMA	1.67	95	40.0	81.0
			80	36.1	49.6
			65	33.1	28.0
	TMA-LDH	1.67	95	26.2	26.6
			80	22.8	14.7
			65	17.7	7.4
	DABCO	1.57	95	34.8	45.7
			80	29.1	23.0
			65	25.7	8.9
	DABCO-LDH	1.57	95	28.0	30.0
			80	25.1	17.9
			65	19.8	5.5

. Ion exchange capacity (IEC), water uptake (WU), and hydroxide ion conductivity (σ) of PSU-based ionomers at 60 °C and various relative humidity values (RH)

[START_REF] Di Vona | Anionic conducting composite membranes based on aromatic polymer and layered double hydroxides[END_REF]

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