Possible Repair Mechanism for Hydrocarbon-Based Ionomers Following Damage by Radical Attack

Polymer electrolyte fuel cell (PEFC) membranes are subject to radical-induced degradation. Antioxidant strategies for hydrocarbon-based ionomers containing aromatic units can focus on intermediates that are formed upon attack by hydroxyl radicals (HO · ). Among the different intermediates, the cation radical P · + is the most promising target for repair, for example by cerium(III). For the “ repair ” reaction of Ce(III) with radicals of a poly( α -methylstyrene sulfonate) oligomer we determined an activation energy of (9 ± 2) kJ mol − 1 and a rate constant of 1.6 · 10 8 M − 1 s − 1 at 80 °C by pulse-radiolysis. For the reduction of Ce(IV) by hydrogen peroxide the activation energy was determined by stopped- ﬂ ow as (30 ± 1) kJ mol − 1 with a rate constant of 4.8 · 10 6 M − 1 s − 1 at 80 °C. These parameters are fed into a kinetics model to estimate the ef ﬁ cacy of the cerium (III)/(IV) redox couple as a catalytic repair agent in hydrocarbon-based fuel cell membranes. While cerium can mitigate polymer degradation, repair ef ﬁ cacy depends on the polymer degradation pathway and the nature and lifetime of the intermediates.

Fuel cells have reached a certain degree of technical and economic maturity with application space in the range of residential and mobile sectors. Nevertheless, there is growing need of further development for significant market penetration, especially in the transportation sector. Japan's New Energy and Industrial Technology Development Organization (NEDO) has put forward challenging targets for automotive fuel cell systems by 2040, specifically a single cell voltage of 0.85 V at a current density of 4.4 A cm −2 and a temperature of 120°C. 1 Today's polymer electrolyte fuel cell (PEFC) technology is still largely based on materials that have been around for decades, such as perfluroalkylsulfonic acid (PFSA) ionomers in the membrane and catalyst layers, and carbon-supported nano-sized noble metal based particles as electrocatalyst. Gradual and steady advances have been made over the past two and a half decades. For the proton exchange membrane (PEM), it has been the introduction of reinforced materials, 2 end-group stabilization, 3 short side-chain ionomers, 4,5 a reduction of thickness, 6 and doping with radical scavengers. 7,8 For the ionomer in the catalyst layer, there is a trend towards PFSA based materials with higher oxygen permeability. 9 For the electrocatalyst, in particular for the sluggish oxygen reduction reaction (ORR), the main improvements have been the use of Pt-alloys with improved activity, 10,11 high surface area carbon supports for improved nanoparticle dispersion, 12 and engineering of the carbon porosity to minimize oxygen transport losses. 13 Reaching the aforementioned NEDO targets may require a drastic technological step in the form of next-generation fuel cell materials and cell engineering. Hydrocarbon-based PEMs are often proposed as replacements for PFSA membranes. 14 This class of materials encompasses a wide range of different polymers, most of which contain aromatic units in their main chain. 15 Scheme 1 illustrates a generic structure of such an aromatic unit, where "X" is a linking unit, such as-(chemical bond), -O-(ether), -(C=O)-(ketone), or -(SO 2 )-(sulfone). The sulfonic acid group may be located on either the main chain or a side chain, which itself can be aromatic (Ar), aliphatic (R), or a mixture thereof. The key advantages of polyaromatic membranes are the expected lower cost, lower permeability of hydrogen and oxygen, and better mechanical robustness at temperatures above 90°C. 16,17 In fact, until 2007, hydrocarbon membranes were used in the stack of Honda FCX hydrogen fuel cell demonstration vehicles. 18 Their use, however, was discontinued and PFSA membranes were re-introduced. It appears that the stability and durability of these materials were considered insufficient. 19 A further related challenge associated with hydrocarbon-based PEMs is their diminished performance under reduced relative humidity conditions, due to poor conductivity. With an adequate polymer architecture, such as multi-block copolymers, this short-coming can be somewhat mitigated. 20 Hydrocarbon-based membranes have a much lower gas permeability than PFSA membranes and, therefore, have shown an improved chemical stability under accelerated stress test conditions in open circuit voltage (OCV) hold tests in many cases. 21,22 However, if combined with relative humidity cycling, they typically show much lower durability. 14 This is a result of both higher water uptake and stiffness of the material and an embrittlement caused by crosslinking, which is triggered by oxidation of the polymer chain. 23 Recent results have shown that a tenfold increase in wet-dry cycling durability of an aromatic PEM can be achieved when mechanically reinforced. 24 Nevertheless, gradual oxidative chain degradation is still expected to take place.
Hydrocarbon based ionomers are inherently susceptible to radical induced degradation, which leads to oxidation, material embrittlement, and polymer chain fragmentation. Under the operating conditions of a PEFC, the radical species HO · , H · and HOO · form as a result of reactions of H 2 and O 2 with the noble metal catalyst. 25 The hydroxyl radical (HO · ) is particularly harmful, as it attacks aromatic units with rate constants close to the diffusion limit, i.e. on the order of 10 9 to 10 10 M -1 s -1 . 26 In contrast, in PFSA ionomers HO · attack is three to four orders of magnitude slower (∼10 6 M -1 s -1 27 ) and limited to weak links in the chain. In fact, in a PEFC with PFSA membrane, most of the hydroxyl radicals are expected to react with dissolved H 2 to form H · which in turn react with O 2 to produce HOO · , which is much less detrimental than HO · . 28 The resulting average lifetime of HO · in PFSA ionomers is in the range of microseconds. This, therefore, allows for effective scavenging of HO · by transition metals, such as cerium-ions and oxides thereof, at concentrations in the range of 0.01 to 0.1 M. 29 A key feature of HO · scavenging in PFSA ionomers by cerium-ions is the catalytic mechanism. This is a consequence of redox cycling between Ce(III) and Ce(IV): upon scavenging of HO · by Ce(III), Ce (IV) is formed. Ce(IV) reacts with H 2 O 2 , which is present in the fuel cell, and regenerates Ce(III). 30 The known sources of H 2 O 2 in the PEFC are two-electron reduction of oxygen to hydrogen peroxide and reaction of O 2 crossed-over from the cathode with hydrogen adsorbed on the Pt catalyst. 25 Hydrocarbon ionomers react much faster with HO · radicals than PFSA ionomers: almost all of the hydroxyl radicals formed will react with the aromatic units of the polymer. The estimated lifetime of HO · is three orders of magnitude lower than in a PFSA ionomer, i.e. around 1 ns, which prevents effective scavenging by cerium-ions at practical concentrations. 28 Under these circumstances, and in analogy to biology, antioxidant action cannot be based on damage prevention but must focus instead on repair and inhibition of damage propagation. 31 This may be possible if intermediates formed upon radical attack are sufficiently long-lived. 23

Radical Attack and Chemical Degradation Mechanism
The attack by HO · on aromatic units of a polymer P, the followup reactions, and the fate of the compound are described by a generic mechanism (Scheme 2). Evidently, the exact mechanism and kinetics depend on many variables, such as the chemistry of the aromatic units, the type of linking groups, substituent pattern, steric effects, temperature, oxygen concentration, etc. Initially, the HO · reacts with the aromatic group, reaction (1), predominantly by addition, yielding the OH-adduct, i.e. a cyclohexydienyl radical, · P-OH. The rate of reaction between HO · and most aromatic compounds is (close to) diffusion controlled and, thus, does not vary significantly with different substituents. 32 Subsequently, irreversible damage can be inflicted on the polymer according to Path A degradation, reaction (2). This can occur, for example, through hydroxylation via addition of O 2 and elimination of HOO · . 33 The formed phenol is oxidized more easily than the parent compound. This can lead to accelerated permanent damage by successive oxidative reactions, ring opening or by crosslinking intermediates via Michael-addition. 34 Additional crosslinking reactions can occur through recombination of different radical centres (intra-chain or inter-chain). The observed embrittlement of hydrocarbon membranes in the fuel cell over time is consistent with this mechanism of crosslink formation and stiffening of the polymer. 16 At sufficiently low pH, · P-OH will undergo acid promoted water elimination, reaction (3), to form the cation radical P ·+ . 35 From this intermediate a number of harmful reactions are conceivable (degradation Path B, reaction (4)) such as chain scission and, if the aromatic ring is sulfonated, desulfonation. 36 Cation radicals are strongly electron withdrawing. The protons of the C-H bonds in α-position to aromatic cation radicals are, therefore, acidified and deprotonate readily to form benzyl radicals. 37 Another important reaction to consider is the nucleophilic addition of water to P ·+ , reaction (-3), the rate of which strongly depends on the substituent pattern of the ring. 38 The ultimate fate of the polymer, therefore, strongly depends on the equilibrium between the OH-adduct and the cation radical, given by the reactions 3 and -3, and the rate of path A and path B degradation reactions.
Recently, we have shown that Ce(III) can react with "aromatic cation radicals" and thereby potentially act as repair agent in sulfonated hydrocarbon-based ionomers, reaction (5). 39 In this article, we extend the study to elevated temperatures relevant for fuel cell application (∼80°C).
If sufficiently fast, reaction (5) prevents irreversible damage to both the cyclohexadienyl and the cation radicals, reactions (2) and (4). Essentially, the effectiveness of this antioxidant strategy depends on the concentration of Ce(III) as the "repair agent" and the rate constant of reaction (5), k 5 , in relation to the rate constants associated with reactions (2) and (4). Additionally, we study the kinetics of the regeneration reaction of Ce(III), reaction (6), also as a function of temperature. Conceptually, the combination of reactions (5) and (6) enables a catalytic repair mechanism of the hydrocarbon ionomer in the fuel cell, Scheme 2. The standard reduction potential of the cerium couple is E°(Ce(IV)/Ce(III)) = 1.44 V. 40 The potential E°(P ·+ /P) is in the range of 2.0-2.4 V for an aromatic ring with intermediate electron density. 32 The efficacy of the repair reaction also depends on the concentration ratio of Ce(III) to Ce(IV) under steady-state conditions. This will be estimated in the kinetic simulation section. The half-cell reaction HOO · + H + + e − → H 2 O 2 has a standard electrode potential of E°(HOO · , H + /H 2 O 2 ) = 1.46 V at pH 0. 41 Therefore, the repair reaction (5) and the regeneration reaction (6) should be thermodynamically favorable. Scheme 1. Schematic structure of sulfonated hydrocarbon-based ionomer. X is a linking group (e.g., sulfone) or a bond.

Scheme 2.
Simplified reaction pathway of aromatic compounds considered in this study. Attack by HO · forming the OH-adduct, · P-OH (reaction 1), which can undergo irreversible degradation (reaction 2) or acid promoted water elimination to form the cation radical, P ·+ (reaction 3). The backward reaction is reaction-3. P ·+ can undergo irreversible degradation (reaction 4) or a reduction reaction with Ce(III) (reaction 5), which repairs the aromatic unit to the starting compound. The produced Ce(IV) reacts with H 2 O 2 to restore Ce(III) (reaction 6).
We use a poly(α-methylstyrene sulfonate) (PAMSS) oligomer as a hydrocarbon ionomer model compound in this study. It is a continuation of our earlier work on the effects of radical attack on styrene based oligomers. 33,36,39,42 We anticipate that the results obtained largely characterize the generic behaviour of hydrocarbon ionomers. Conceptually, we analyze how modifications to the polymer chemistry can influence the degradation behavior. Experimental work is combined with modelling in order to explore the prospect of mitigating radical induced degradation of polymers containing aromatic units through repair of the cation radical intermediate. With this approach we hope to gain a basis for improvements of membranes to be tested on the device level.

Methods-Experimental
Many of the reactions measured and discussed are of second order but, under our conditions, pseudo-first order. With reaction (3) as example, we use the following notation: with k 3 and k −3 the "real" forward and backward rate constants, k 3 ′ and k −3 ′ the pseudo-first order rate constants at the given conditions (here pH and water concentration), K 3 = k 3 /k −3 the equilibrium constant and K 3 ′ = k 3 ′/k −3 ′ the position of the equilibrium under the given conditions. All errors given represent standard deviations, not confidence intervals. The suppliers and purity of the chemicals used are given in the Supporting Information, section 1.
Kinetics measurements.-In order to measure k 5 , the unstable cation radical P ·+ has to be produced in high enough concentrations that its reaction can be followed with time-resolution in the microsecond range. To achieve this, we applied the pulse-radiolysis technique using the setup at ETH: 43 samples are exposed to short pulses of ionizing radiation, here fast electrons, to ionize material. The setup is similar to laser flash photolysis. Instead of a pulse of light (2-6 eV photon energy), a pulse of high-energy radiation (2 MeV) is applied. 44 In liquids, ionization will eventually form solvated electrons and products of the initially formed cation radicals. Ionization occurs in mass-proportional manner and in dilute solution, therefore, initially only solvent radicals and electrons are formed. Product concentrations are proportional to the applied dose and known for water. 45 We used an oligomer of PAMSS for our studies. The oligomer had a mass average molecular weight of 14'600 Da, a polydispersity index of <1.06, and a degree of sulfonation of >95% (PSS Polymer Standards Service, Mainz, Germany). This corresponds to a degree of polymerization of around 60.
The rate constant of reaction (6) was measured by mixing H 2 O 2 and Ce(IV) under pseudo first-order conditions in an Applied Photophysics SX18 stopped-flow apparatus (Leatherhead, UK). In stopped-flow the content of two syringes are forced by high pressure through a mixer coupled to a measurement cell and subsequently into a product syringe. The mixing is stopped when the product syringe hits a stop-block, and this is "time zero." The reaction is then followed in time resolved manner, usually by absorption spectroscopy. 46 When Ce(IV) was used in excess, five single traces were acquired per reaction condition and subsequently evaluated separately (Appendix B and SI). In the controls (H 2 O 2 in excess), five single traces were averaged per reaction condition. The averages were then analyzed using a first-order decay model to obtain the observed pseudo-first order rate constant k 6,obs .
Importantly, peroxide solutions become increasingly unstable at elevated temperatures, which limits the measurement range and the accuracy of data at temperatures above 60°C in certain experiments. This is true for both pulse radiolysis and stopped flow experiments. The experimental conditions suffer additional constraints and are, therefore, a result of optimization and compromise, Appendix A. Please see Appendices A and B also for more details on the pulse radiolysis and stopped flow experiments, respectively.

Methods-Kinetics Model
Our simplified kinetics model describes the main reaction pathways initiated by the reaction of HO · with the polymer, based on our earlier work. 25,29 In analogy to our recent conference proceedings, 47 we assume a constant rate of radical formation and their attack of the polymer, reaction (1), which describes the constant bombardment of the membrane by HO · in an operating fuel cell. We use a value of r HO · = 10 −6 Ms −1 here, cf. Supporting Information for explanations how this value was obtained. However, the qualitative outcome of the model does not depend on the initial rate of attack of the polymer, because we are looking at the probability of certain degradation pathways and relative changes compared to a scenario without antioxidants. By extension, the actual membrane lifetime in the fuel cell is not of primary interest, but rather the relative lifetime improvement.
We assume that the attack of the polymer P by HO · leads to the formation of intermediates P*, which then undergo further reactions. We describe the degradation by a "lumped" effective first-order rate constant k eff , which embodies a combination of different reactions, as indicated in Scheme 2 and reaction (8).
In the simulation we assume a steady state, i.e., a constant concentration of intermediates [P*] with equal rates of formation r HO · and decay k eff · [P*]. The detailed analysis of the kinetic scheme and derivation of expressions given in this section can be found in Appendix C. The parameter values used in the simulation are listed in Table I.
Under the conditions of this study [Ce(III)] ≈ [Ce] (see Results). In order to quantify the efficacy of repair reaction (5) compared to Path B degradation, reaction (4), we define the mitigation factor μ B of degradation Path B. This is in analogy to our earlier conceptual study. 47  [8] Journal of The Electrochemical Society, 2021 168 054514 Overall, degradation Path A must also be considered. The analysis of the kinetic framework (see Appendix C), considering both degradation pathways, yields the total mitigation factor μ A+B , ′ characterizes the position of the equilibrium between the OHadduct, · P-OH, and the cation radical, P ·+ (cf. Methods-Experimental). For large values of μ B and μ A+B ? 1, the two mitigation factors differ by a factor f B , the fraction of Path B degradation.

Results
The results of the pulse radiolysis study on PAMSS are presented first. Rate constants for the repair reaction (5) and the pseudo firstorder rate constant for degradation along Path B, reaction (4) (Scheme 2), were determined. Then, stopped-flow results on reaction (6) are described. Subsequently, these data are used together with literature data to explore the prospects and limitations of polymer repair in a hydrocarbon fuel cell membrane doped with cerium-ions.
Kinetics measurements.-When a deaerated (Ar saturated) solution of 0.1 mM PAMSS, 10 mM K 2 S 2 O 8 and 1 mM H 2 SO 4 is pulse-irradiated with a dose of 30 Gy, we expect the formation of approximately 6 μM SO 4 ·− . These in turn oxidize the polymer to form P ·+ , reaction (7), which can be observed by a corresponding absorption build-up at 560 nm. 36 Water radiolysis results in direct formation of 8 μM HO · that reacts with PAMSS to produce · P-OH, reaction (1). We observed a decay of the 560 nm band over several milliseconds, Fig. 1, which is tentatively attributed to fragmentation reactions according to Path B, Scheme 2. If 0.2 mM Ce(III) was added to the solutions, the observed maximum absorption decreased because of the competition between PAMSS and Ce(III) for the oxidant radicals, HO · and SO 4 ·− . Importantly, in the presence of 0.2 mM Ce(III) the observed decay rate of the polymer intermediate increased by two orders of magnitude, which is visible in the drastically reduced half-life, inset of Fig. 1 (see also Figs. S1 and S2 (available online at stacks.iop.org/JES/168/054514/mmedia)). This effect is interpreted in terms of reaction (5).
In order to establish the rate constants and the activation energy of reaction (5), solutions with 0.1, 0.3 and 1 mM Ce 2 (SO 4 ) 3 and 0.1, 0.3 and 1 mM PAMSS, respectively, were pulse-irradiated; k 5,obs was derived from the slope of the plot k obs vs [Ce(III)], with k obs being the pseudo first-order rate constant associated with the observed absorption decay at 560 nm (Fig. S3). Measurements were repeated at different temperatures, Table II. At high enough [Ce(III)], reaction (5) outcompetes Path A and Path B. But even then the observed decay, i.e. reaction (5, obs), is influenced by preequilibrium (3), Scheme 2. Briefly, k 5,obs , is a function of K 3( Appendix A) and represents a low limit of the real value, k 5 . Therefore, also the slope of the plot ln(k 5,obs )·R vs 1/T, Fig. S5, represents the activation energy of the overall reaction. We derive an overall activation energy of E a,5obs = 9 ± 2 kJ mol −1 if all individual measurements are used for its calculation. If E a,5obs is derived from the averages of the measurements at each given temperature, we find   E a,5obs = 8 ± 1 kJ mol −1 , the value displayed in Fig. 2. For the calculation of repair efficacy, the latter value represents the conservative low limit and is therefore used.
In principle, the intercept in a plot of k obs vs [Ce(III)] represents the rate constant for Path B degradation. However, the associated uncertainty precludes such determination of k PathB . An independent determination of k PathB was carried out by pulse irradiation of 0.1 mM PAMSS in the absence of cerium (Fig. S2). For Path B we find E a,PathB = 63 ± 2 kJ mol −1 (cf. Appendix A and Fig. S5).
The rate constant k 6 was measured by stopped-flow: two solutions, one containing Ce(IV) and one containing H 2 O 2 , were mixed and the decay of Ce(IV) was followed by absorption spectroscopy at 320 nm (Fig. S10). The measurements were carried out at pH 1 (100 mM H 2 SO 4 ) under pseudo first-order conditions (see Appendix B for details). With Ce(IV): H 2 O 2 ≈ 10: 1, and covering a concentration range of one order of magnitude between 30 μM and 290 μM Ce(IV) (Table B·I), we carried out experiments at 10°C, 25°C, 50°C and 74°C (Fig. S11). The obtained rate constants are listed in Table II (see also  Fig. S12, was not used in our calculations. Kinetics simulation.-The simulation of the degradation kinetics of the polymer according to Scheme 2 is based on the rate constants listed in Table III, with the model parameters given in Table I. Our model is a simplification of a complex reaction framework and is used to gain an overview and identify a starting point for improvement strategies. It is known that polymer degradation will take place from the cyclohexadienyl ( · P-OH, Path A) as well as from the cation radical (P ·+ , Path B). Exact mechanisms are not known at this point. Modelling, however, requires mathematical values, k 2 and k 4 , for the calculation. These values describe the stability of the polymer in the absence of additives. The more intuitive radical persistence shows the timescale in which repair reaction (5) has to occur and is given by the half-lives τ 0.5 ( · P-OH) = ln(2)/k 2 and τ 0.5 (P ·+ ) = ln(2)/k 4 (Fig. 2, right axis). We derive estimates of these values from data published or measured here.
The concentration ratio of the two cerium oxidation states can be obtained from the steady state of reactions (5) and (6) (Fig. 2), see also Figs. S4 and S5. b) Effective first-order rate constant (O 2 degradation pathway) at 25°C, cf. Appendix D. This value is used in the simulation. The value at 80°C was calculated assuming an activation energy of 22 kJ mol −1 . c) For anisole at pH <3 the OH addition reaction becomes rate determining and not the reaction with protons, i.e. the protonation is (almost) diffusion controlled. 49 d) Extrapolated using E a = 63 kJ mol −1 (Fig. 2). e) Extrapolated using E a = 8.0 kJ mol −1 (Fig. 2). f) Extrapolated using E a = 28.2 kJ mol −1 (Fig. 2).  Table III). In analogy to PFSA membranes, 30 we considered 1% cerium ions relative to the concentration of membrane sulfonate groups, [P-SO 3 − ], to be the upper concentration limit in a PEM for fuel cells. Based on Eq. 9, Fig. 3a shows the mitigation factor μ B for Path B degradation as a function of temperature for 0.1% and 1% [Ce]/[P-SO 3 − ]. The ratio k 5 /k 4 decreases with increasing temperature because of the different activation energies of reaction (4) and reaction (5), Fig. 2. In other words, high fuel cell temperatures reduce the repair efficacy. At a concentration of 0.1% cerium, reaction (5) outcompetes degradation Path B by a factor of around 800 at ambient temperature, yet this factor drops by more than an order of magnitude at 80°C. With 1% Ce the mitigation factor at 80°C is only 260. Figure 3b shows the required cerium-ion content for a target mitigation factor of μ B = 100. With the rate of radical formation of r HO· = 10 -6 M·s -1 (Table I) used in the simulation, a membrane lifetime of 280 h is obtained in the absence of cerium-ions (cf. Supporting Information, section 5). A mitigation factor of 100, therefore, corresponds to a projected membrane lifetime of 28'000 h.
Indirectly, reaction (5) is also in competition with Path A via the fast equilibrium (3), 38,50 (Table III) (4) and (5). Figure 4 shows reaction rates r 2 (Path A degradation), r 4 (Path B degradation), the total rate of degradation r 2 + r 4 , and the rate of cation radical repair r 5 at a temperature of 80°C. Neither the temperature dependence of K 3 nor thatof the rate constants k 3 and k -3 isknown. For the rate constants we use the values at room temperature as low limits and thereby implicitly assume the temperature dependence of K 3 to be negligible. With the model parameters used (Tables I  and III), K 3 ′ = 5.6, and the ratio a of degradation rates of Paths A and B, a = k 2 /(k 4 ·K 3 ′) = 1.1 (cf. Appendix C). Hence, the rates associated with Path A and Path B are almost identical under the conditions of our model (Fig. 4). In the absence of cerium, the rate of membrane degradation is equal to the rate of HO · attack. Detectable protection of the membrane, via repair reaction (5), begins at a minimum Ce concentration of approximately 0.1 mM. At [Ce] = 1.5 mM (0.1% Ce) degradation is reduced by a factor of μ A+B = 13, and by a factor of μ A+B = 130 at [Ce] = 15 mM (1% Ce), Eq. 10.

Discussion
The degradation of a fuel cell membrane is a complex process that involves many reactions with very different timescales. In this work, we focus on the initiating reactions, explore the possibility of mitigating damage at an early stage, and attempt a mathematical description of potential efficacy of repair. Most importantly, the "full reaction mechanism" (Scheme 2) is a simplification and, given the current knowledge, partly an assumption. Influences of individual reactions in complex reaction schemes are inherently difficult to disentangle and understand. Therefore, we use classes of reactions to describe the overall process in a simplified kinetic framework. In order to achieve this, we need rate constants, some of which are derived by analogy from similar systems and some of which have been published for different conditions, others we have measured ourselves. In the following sections, we discuss the potential of polymer repair and the limitations of our kinetic framework's ability to describe the actual situation in a fuel cell membrane.    Table III. Due to the fast equilibrium on membrane stabilization. At high values of K 3´, degradation follows Path B and repair efficacy can be maximized. The influence of K 3´s hould be seen as a qualitative study indicating a trend.
Limits of accuracy.-We do not take the data of Fig. 5 as quantitative, because k 3 and k -3 were estimated by analogy, k PathB carries systematic uncertainty and the (effective) rate constant k PathA is an estimation, too. Additionally, some of the data collected here rely on assumptions from previous work that have not been confirmed experimentally. Specifically, the rate constant of reaction (5) is determined by following an absorption change in the green part of the visible spectrum during pulse radiolysis. This has been previously interpreted as being caused by the formation of the cation radical, P ·+ , but has not been unambiguously confirmed. Equilibrium 3. There is little information available in the literature on equilibrium (3), we based the values for k 3 and k -3 used here on data of methylated benzenes in a lab-report from Risø National Laboratory (Denmark). 38 The mechanism of the reaction makes perfect chemical sense and is, in principal, known. However, we are cautious about the reported values of the rate constants and we are not aware of any data for phenylsulfonates. While this problem may influence the numbers obtained from our simulation, it does not compromise the overall picture we want to draw and discuss here.
Path B: As explained in Appendix A, k 4 is merely estimated and the value we use represents an upper limit of k 4 relative to k 5 . It is conceivable that the ratio k 4 /k 5 is, therefore, lower and consequently the mitigation factor μ B is larger.
Path A: As was shown in Fig. 5, Path A has a strong influence on the overall rate of degradation. Unfortunately, k pathA is not known for elevated temperatures. Previously, Dockheer et al. and Nolte et al. have measured the oxygen-dependent part of Path A at room temperature. 25,33 However, it is difficult to measure at elevated temperature since the solubility of oxygen in water is strongly temperature dependent and it is not certain that we have full equilibrium conditions in our solution during the experiment.
Here, instead, we use an effective rate constant k 2 characterizing degradation in the presence of oxygen, based on literature values (Appendix D). The room temperature value of k PathA = 1.4·10 4 s −1 is extrapolated to 80°C using an activation energy of 22 kJ mol −1 (Table III, see also Fig. S5), which represents an educated guess based on the temperature dependence of the self-decay of · P-OH. This approach is admittedly crude, yet can be justified in view of the lack of experimental data. To probe the influence of the variation of k PathA , we carried out a sensitivity analysis, changing its value at 80°C by a factor of 10. If k PathA is decreased by a factor of 10 (k PathA = 5.6·10 3 s −1 ) μ A+B increases by a factor of 2, approximately, at a cerium content of 1%. If the rate constant is increased by a factor of 10 (k PathA = 5.6·10 5 s −1 ), μ A+B approximately decreases by a factor of 6. If k 2 were substantially larger than expected, Path A would be the dominant degradation route and polymer repair by Ce(III) as proposed here will be ineffective.
Cerium-ions in fuel cell membranes.-The incorporation of cerium-ions into a proton exchange membrane requires us to consider a number of issues. As previously mentioned, ceriumions replace protons in the membrane. This will have an impact on the conductivity of the membrane, which puts a practical limit on the Ce concentration of about 1% of the sulfonate content. The effectiveness of the repair reaction in the confined environment of an ionomer membrane may be different to the situation of a dilute aqueous solution used in the experiments here. Furthermore, lifetime of intermediates may also be different due to steric restrictions in a membrane. Additionally, cerium-ion diffusivity also needs to be taken into account. The repair action of cerium-ions requires them to be near a "repairable" point of damage, i.e. a cation radical. Since the cation radical is part of the polymer, we consider it to be immobile in a first approximation. Therefore, a cerium-ion needs to be sufficiently close to the location of the cation radical to be able to repair it before irreversible damage occurs. Based on rate constant k 4 and the associated lifetime of P ·+ , we can estimate whether ceriumions at a certain concentration in the membrane can reach all potential points of damage on the polymer. Therefore, the diffusivity of Ce(III) as a function of relative humidity has to be considered. It is shown that at a concentration of 0.01% Ce (0.15 mM), the average spacing of cerium-ions of 22 nm allows cerium-ions to reach P ·+ sites with a probability of more than 99% at 50% r.h. (Appendix E).
The assumption here is that cerium-ions are evenly distributed. However, cerium-ions are mobile and will migrate towards the cathode under the influence of the electric field, 51 so (partial) immobilization may be required. Alternatively, the use of ceria based nano-particles 52 instead of cerium-ions may avoid cerium-ion migration. However, it is questionable if the particles can be sufficiently well dispersed to ensure that points of damage and cerium-ions are close enough for repair. A further issue caused by the degradation of the polymer membrane is that negatively charged ionic species are released (e.g. aromatic sulfonates, sulfates), which can form ion pairs with Ce(III). This inherently will promote the washing out of Ce ions during fuel cell operation, which will contribute to a decrease in concentration of cerium over time, making the repair reaction less and less effective. One possible approach to mitigate this effect is to use covalently bound Ce(III) complexes, based on relatively simple host molecules, such as crown ethers. 53,54 Finally, we have used an oligomer of PAMSS with a low molecular weight of 14.6 kDa in this study. With the corresponding degree of polymerization of around 60 the polyelectrolyte assumes a coiled configuration that also allows for intra-chain interactions, which may be important to stabilize intermediates. 36 In a recent article, we studied the dependence of selected reactions on the degree of polymerization of PAMSS and found that, in general, rate constants for reactions of intermediates somewhat decrease for increasing chain lengths due to intramolecular stabilization. 39 Promising future strategies.-In an operating fuel cell, degradation Path A must be inhibited and the ratio k 4 /k 5 must be minimized. The first requirement may be achieved by engineering a polymer where the cyclohexadienyl radical has a lower propensity to react with oxygen and by changing the pK a of the polymer so that equilibrium (3) lies on the cation radical side. In principle, the properties of the membrane aromatic units can be tuned by functional groups. Electron-withdrawing groups would reduce the electron density of the HO-adduct, and decrease the rate constant of Path A, i.e. the reaction with oxygen. 55 Such a strategy also has disadvantages: electron-withdrawing groups on the aromatic units of the polymer will decrease K 3 and shift the equilibrium towards the HO-adduct as the overall pK a of the cation radical is decreased. Conversely, electron-donating groups increase the pK a of the cation radical and shift the equilibrium towards the cation radical, thus promoting the efficacy of the repair. However, the rate constant k PathA will increase. The net overall effect will depend on the chemistry of the building blocks used.
There is, at present, no experimental evidence for damage repair by cerium or other compounds in a working fuel cell. There have been, however, reports of improved stability against attack by HO · of aromatic hydrocarbon membranes containing cerium in an ex situ Fenton test. 53,54 The observed improvements in stability have been explained by radical quenching. However, considering the fast reaction of OH · with aromatic compounds, it may well be that the stabilizing effect of cerium is in fact a result of the repair of formed intermediates as presented in this work. Dedicated experimental strategies therefore need to be devised to investigate the role of cerium and potentially other additives in a membrane under fuel cell operating conditions. It is important to be able to distinguish mechanistically and quantify kinetically whether an additive is acting as a scavenger or a repair agent. This can potentially be studied using ionomers of defined chemistry with variations in the substituent pattern. It is, however, important to keep in mind that modification of the polymer chemistry may accelerate other degradation mechanisms, such as desulfonation and crosslinking. We plan to study the influence of cerium-ion doping on the stability of hydrocarbon-based membranes and investigate the influence of the polymer chemistry on reaction patterns with radicals, cerium-ions and potentially other additives.

Conclusions
Cerium(III) may repair aromatic hydrocarbon-based ionomers during fuel cell operation. This is achieved by reducing cation radicals, which are formed along with other intermediates, such as the HO-adduct, as a result of HO · attack on the polymer. The efficacy of repair depends on the lifetime of the cation radical and competing degradation mechanisms that are not amenable to repair. The concentration of the different intermediates can likely be influenced by the substituent pattern of the aromatic units. If degradation via intermediates other than cation radicals is dominant, repair is inefficient. Fine-tuning of the repair agent and polymer chemistry offers the prospect of significantly increased membrane lifetime in the fuel cell.
A.1. Experimental conditions.-As a biradical, oxygen reacts very quickly with a multitude of radicals. To minimize complications, our solutions were, therefore, deaerated.
Radiolysis ionizes matter about mass-proportionally. Therefore, the effect is measured in energy deposited on the sample per mass unit, i.e. the dose: 1 Gy = 1 J kg −1 . With dilute solutions, the energy is quantitatively deposited on the solvent that is ionized. Pulse irradiation of water generates primary species (reaction A·1), with well-known yields. 45 These radiochemical yields are referred to as the G-value and are traditionally given in in number of species created per 100 eV of deposited energy or, modern, in 10 −7 M/Gy radiolysis product. The numbers differ ∼4%, due to the interconversion factor between the old and new units (G(old) = 0.96485 G (new)). Radiolysis concomitantly produces reducing and oxidizing species, reaction (A·1). This complicates the mechanistic and kinetic interpretation of successive reactions. Therefore, experimentalists usually add an excess of chemicals that would, eventually, convert primary species to better controlled starting conditions: oftentimes, buffers are used to maintain the proton concentration, hydrated electrons can be converted into oxidizing species, reactions (A·2) and (A·4), and hydroxyl radicals can be converted to strongly reductive species (no examples given). Not always, however, "clean" starting conditions are achievable: the hydrated electron, for example, is a moderately strong base, pK a (H · ) = 9.1, and its reaction with protons is diffusion controlled.
If fuel cell conditions are to be mimicked, experiments should be carried out under strongly acidic conditions. At acidic pH reaction (A·3) may compete effectively with reaction (A·2), the yield of SO 4 ·− decreases with pH (Fig. A·1). 26 Additionally, in N 2 O-saturated aqueous solutions (24.8 mM at 20°C), the solvated electron e (aq) − can be converted to HO · , reaction (A·4), which, depending on pH and peroxodisulfate concentration, may also compete with reactions (A·2) and (A·3). Therefore, we used argon saturated solutions.
The formed primary species H · will form an adduct with polymer P, according to reaction (A·6). ] ?
[P]. The side product · P-H compromises the determination of the rate constants of the reactions of interest which follow the oxidative damage of the polymer. This puts practical limits to the applicable pH-range, cf. Fig. A·1 and Table SI. 26,57,58 We aimed to limit the yield of side reactions to 10%.
Apart from reacting with the aromatic ring of PAMSS, reaction (1) hydroxyl radicals could, in principle, oxidize the aliphatic or the aromatic subunits, reactions (A·7) and (A·8), but direct oxidation of aromatic subunits is rarely observed (A·8). Hydroxyl radicals, HO · , can abstract H from aliphatic molecules (A·7) but k A-7 is approximately one order of magnitude slower than k 1   reaction (3). This reaction has a low free energy. Consequently, an equilibrium is observed. The speciation of this purportedly fast equilibrium depends on pH. 38 For the relatively electron-deficient, thus very acidic, aromatic sulfonates the pK a,3 is expected to be much lower than the one reported for the more electron rich anisole (pK a ≈ 3). 49 We monitored the decay of the absorption band at 560 nm, perceived to stem from the cation radical P ·+ , to describe reaction (5). The observation of k 5 , however, is only indirect and we rationalize the observations as follows: there is a fast equilibrium K 3 coupled to decay reactions (5) and Path B. To simplify notation, we refer to the reactions associated with the decay of the 560 nm band as reaction (A·10) with rate constant k A-10 .
Therefore, as the decay of PAMSS-radicals is observed, the observed rate constant is not k A-10 but k A-10 · K 3 ′/(1 + K 3 ′). As we do have no literature reports on K 3 , we assume [P*] = [P ·+ ]. This affects both the measurement of k 5 and k Path B : at sufficiently high [Ce(III)] k A-10,obs = k 5,obs and represents the low limit of the associated k 5 = k A-10 which, depending on K 3 ′, might be orders of magnitude higher. This is also true for [Ce(III)] = 0, where k Path B = k A-10 . But here there is an additional problem. Path B should be investigated under conditions where no radical recombination occurs and this requires minimal radical concentration. The observed rate constants are several orders of magnitude slower than repair. It is, therefore best observed at minimal dose, which implies a minimal signal-to-noise ratio: under our conditions we cannot unambiguously pinpoint any second-order contributions to our trace anymore, be it because of their real absence or the limited precision of the detection. Because the influence of equilibrium (3) and possible second order contributions have an opposite effect, we do not exactly know in which way Path B is influenced. It is clear, however, that our data sets a lower limit of k 5 /k PathB and represents, therefore, a conservative estimation for the Ce(III)-related repair efficacy. We assume that the cation radical P ·+ can be repaired by Ce(III), reaction (5), which is in competition with degradation Path B, reaction (4). We are interested which degradation route, Path A or B, is dominant. Therefore, we define the ratio a of the reaction rates representing irreversible degradation:

[ -] [ ] [ · ]
· · ¢ = = = + Therefore, the fraction of Path A degradation is f A = a/(1+a), and the fraction of Path B degradation f B = 1/(1+a) a . At the considered concentration of cerium-ions up to ∼0.01 M in the polymer (∼1% with respect to the content of sulfonate groups), the rapid equilibrium between · P-OH and P ·+ will not be significantly affected (as mentioned above), and the values of f A and f B can be considered constant.
In a first approach, our interest is to assess the efficacy of the repair reaction 5 to reduce the likelihood of degradation along Path B. The reaction between P ·+ and Ce(III) is in competition with Path B degradation, reaction (4). In the absence of cerium, the cation radical P ·+ formed at a rate of r P·+ reacts exclusively along Path B with the same rate r 4,0 : The rate of P ·+ formation r P·+ is largely independent on the presence of cerium owing to the rapid equilibrium 3/-3 (as mentioned above).
In the presence of cerium-ions, the rate of degradation along Path B is lowered. We form the ratio of reaction rates with cerium, r 4 , and without cerium, r 4,0 : In previous work, 25,33 we have identified the following pathway for poly(styrene sulfonate) (PSS) degradation from the OH-adduct: with the room temperature rate constants k D1 = 4.8·10 6 M -1 s -1 , 39 k -D1 = 4.5·10 3 s -1 , 33 and k D2 = 2.7·10 3 s -1 . 60,61 For the simulation in this study, we condense this reaction sequence in Scheme D·1 to degradation Path A, reaction 2 (cf. main text) with the rate expressed as r 2 = k 2 [ · P-OH]. To obtain the rate constant k 2 = k D2,eff , we stipulate steady state concentration of the intermediate · OO-P-OH: where we have assumed an oxygen concentration of 7.5 mM. 25 The temperature dependence of the equilibrium constant K D1 = k D1 /k -D1 can be estimated as follows. At 25°C K D1 = 1. Therefore, with increasing temperature the equilibrium shifts to · P-OH. However, we do not know the temperature dependence of k D2 . In the simulation, the value of 1.4·10 4 s -1 (Eq. D·6) is used at room temperature, and, in lack of a better alternative, extrapolated to 80°C using the activation energy of 22 kJ mol −1 determined from the self-decay of the HO-adduct in the absence of oxygen (rate k 2 , Fig. 2), yielding a value of 5.6·10 4 s -1 . In view of the uncertainty associated with the kinetics of Path A degradation, we performed a study on the effect of the variation of the equilibrium between · P-OH and P ·+ and the fraction of Path A degradation (cf. Fig. 5 and related text).

Appendix E: Spacing and Diffusivity of Cerium-Ions
The cation radicals P ·+ are part of the polymer structure and therefore largely immobilized. For Ce(III) to act as a repair agent, the nearest ions need to be able to diffuse to the location of P ·+ to repair it before it undergoes a detrimental degradation reaction. The available time for a repair to take place is given by the lifetime of the cation radical, which can be calculated from its effective rate constant for first-order decay, k 4 . At 80°C, k 4 = 9·10 3 s −1 (Table III). The time τ α for a fraction α of P ·+ to decay is given by τ α = -ln(1-α)/k 4 . At the same time, within this time span, ceriumions diffuse on average over a distance L given by L D 4 a t = (diffusion length). The diffusion coefficient of Ce(III) in a PFSA membrane has been determined by Coms et al. 63 , at 80°C D = 5·10 −5 cm 2 s −1 at a relative humidity (r.h.) of 100%, and D = 4·10 −7 cm 2 s −1 at 50% r.h. The diffusion length L of Ce(III) for different lifetime values τ α of P ·+ is listed in Table E·I.
The average separation d of cerium-ions in the membrane, assuming homogeneous distribution and a simple cubic lattice, is given by d = ([Ce]·N A ) −1/3 , where N A is the Avogadro constant. Table E·II lists a few values for practical cerium-ion concentrations. Therefore, we see that at practical target concentrations of cerium in the membrane, the spacing of ions is sufficiently small for them to reach a significant fraction of cation radicals P ·+ within their expected lifetime to repair the damage. Scheme D·1. Reaction sequence showing the reversible addition of oxygen to the OH-adduct, · P-OH (reactions D1 and -D1). The formed · OO-P-OH can eliminate HOO · (reaction D2) to yield a hydroxylated product, P-OH.