Humidity effect on temperature behavior of proton diffusion coefficient in sulfonated co-polynaphthoyleneimide membranes measured by 1H NMR diffusometry

Proton diffusion in the co-PNIS85/15 membrane was investigated in the temperature range from 200 to 363 K at different water contents (4 ≤ λ ≤ 21) using 1H SFG NMR diffusometry. At high hydration values, above the threshold value λ0 = 10.5, the ln(DNMR(1/T)) dependences show two different activation modes, separated by a crossover point Tcr ≈ 250–260 K. At temperatures above Tcr, the activation energy is Ea ~ 0.20 eV, which is close to the value for bulk water (Ea ~ 0.17 eV). At temperatures below the crossover point, the ln(DNMR(1/T)) dependences for different water contents merge together into one straight line characterized by a much higher Ea = 0.46 eV. At low hydration values λ < λ0, the activation energies for the high-temperature and low-temperature modes converge, so that at λ = 4, the dependence ln(DNMR(1/T)) is described by one straight line throughout the studied temperature range with Ea = 0.38 eV. A model is proposed that phenomenologically describes the diffusion in the co-PNIS membrane at different moisture contents λ.

Water diffusivity is one of the most important characteristics of the proton exchange membrane for PEMFC operation, because in addition to the water produced at the cathode by the electrochemical reaction, the migrating proton also transports 3 to 5 water molecules by the electroosmotic mechanism under the influence of the electric field [20,21]. Thus, a water concentration gradient is created in the membrane with an excess at the cathode and a deficit at the anode. This can lead both to a decrease in proton conductivity and to a slowing down of the electrochemical reaction at the cathode as a result of its flooding.
Humidity control is very important for the correct operation of the PEMFC, since with decreasing humidity, not only the transport characteristics of the membrane, but also the capacity of PEMFC based on it, decrease. Moreover, since the dependence of transport characteristics of proton exchange membranes on humidity is nonlinear, at humidity less than 50%, this effect is observed both for membranes based on sulfonated hydrocarbon polymers and on perfluorinated ones [22]. Authors in [23,24] discuss strategies for effectively controlling and managing the amount of water during fuel cell operation.
The equalization of the H 2 O concentration occurs due to the reverse flux, which requires a high diffusion coefficient for optimal PEMFC performance. Thus, determining the self-diffusion coefficient of water in these polymers is an important task.
In addition to interest in applied science, the study of diffusion coefficients in hydrocarbon polymers is of undoubted interest from a fundamental point of view. Water in these membranes is in a confined state with characteristic pore sizes of ~ 2-50 nm [25][26][27][28]. The study of diffusion processes in systems with water in a confined state is important also for fundamental understanding of processes in biology, mineralogy, oil and gas industry, etc., when water is enclosed in confinements of similar size. 1 H NMR diffusometry using a static or pulsed magnetic field gradient is one of the established methods of determining diffusion coefficients of protons. It allows studies in a wide temperature range and at different moisture content in the sample, which in proton exchange membranes is usually described by the number of water molecules per sulfonic group λ = N H2O /N SO3 [29][30][31][32].
Several NMR studies of Nafion proton exchange membranes show that the diffusion coefficient (D NMR ) at a fixed temperature has a strongly nonlinear dependence on λ: when the membrane is saturated at 100% humidity, corresponding to values of λ between 7 and 25, depending from the wetting time, D NMR (λ) has a weak and almost linear dependence on λ. For a polymer saturated at low humidity (RH less than 80%), when the corresponding λ values vary between 4 and 6, a change in the slope of the D NMR (λ) dependence is observed. In the case of saturation at even lower humidity, when λ ≤ 3, a sharp, several orders of magnitude drop in D NMR is observed when λ changes from 3 to 1 [29][30][31][32].
This D NMR behavior correlates with the assumption that there are three types of water states in Nafion (depending on the interaction with the polymer matrix) [33][34][35]: • Bulk-like water in the center of the channels that is not bound to the polymer • Water weakly bound to the polymer • Water strongly bound to sulfonic groups (SO 3 ) of polymer side chains (near wall water) At high moisture content, the probability of finding a proton in a water molecule is 28 times higher than in any ionic states of H + [28]. Therefore, the 1 H D NMR diffusion coefficient measured at λ ≥ 6 can be associated with the selfdiffusion coefficient of water molecules in the central part of the channel. At low (λ ≤ 3) and intermediate (4 ≤ λ ≤ 6) moisture content, the contribution to diffusion from intermediate near-wall regions should become more noticeable.
Computer simulations of proton dynamics in Nafion indicate that at low moisture contents (λ ≤ 3), dissociation of water molecules on sulfonic groups occurs, leading to additional proton injection into the water cluster [36]. Thus, it is expected that the contribution of H + and/or H 3 O + ions to the 1 H diffusion measured by SFG NMR should increase with decreasing moisture content. This argument is partially supported by the fact the diffusion coefficient at λ ≤ 3 calculated from the proton conductivity D σ data practically coincides with the D NMR values, i.e., D NMR /D σ ≈1 [29,30,35].
At intermediate humidity (4 ≤ λ ≤ 6) in Nafion-type membranes, the influence on diffusion of weakly bound

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water and bulk-like water in the central part of the channel increases. In this regard, one can assume that the D NMR data correspond to the transition region (crossover) from proton H + diffusion to bulk-like H 2 O self-diffusion. Indeed, such a kink in the D NMR (λ) dependences at a fixed temperature was observed in [31,32]. The behavior of mobile water molecules and the proton diffusion coefficient in Nafion 117 as a function of temperature at different water contents were analyzed in [37]. The authors suggested that at temperatures below 0 °C, the water molecules are bound, but are unable to form an ice phase because part of their hydrogen bonds is occupied by the oxygen of the sulfonate group and the H + cation [37]. For hydrocarbon co-PNIS x/1−x membranes, it was found that the D NMR (T) dependences for the compositions 60/40, 70/30, and 85/15 at 100% humidity show qualitatively similar behavior among themselves over a wide temperature range [16,17]. For all three compositions, two temperature intervals, separated by a crossover point around T cr ≈ 250-260 K, have been observed with activation energy E a ≈ 0.19 eV above and 0.46 eV below this point [16,17]. It is important to note two important features found in co-PNIS: 1. At temperatures below the crossover point, the ln(D NMR (1/T)) dependences coincide (within the experimental error) for all three compositions. 2. At temperatures above the crossover point, the D NMR diffusion coefficients for co-PNIS 60/40 and co-PNIS 70/30 also practically coincide, whereas for the co-PNIS 85/15 composition, the diffusion coefficient values are ca. 2.3 times higher than for co-PNIS 60/40 and co-PNIS 70/30 .
The morphology of hydrocarbon membranes is similar to that of Nafion [25][26][27][28] and can also be described by a system of nanoscale channels where three main water states can be assumed at high water content: bulk-like water in the central part of the channel, weakly bound (transition layer) water, and strongly bound (near wall) water. The volume fraction of these fractions will depend on the ratio of hydrophobic and hydrophilic blocks and the fraction of near-wall water on the concentration of sulfonic SO 3 2− groups. Measurements of the IEC value, which characterizes the concentration of sulfonic groups, show that this parameter is almost the same for all compositions studied [28] and is at a level of 2.5, so we can assume that for all compositions, the fraction of nearwall water is approximately the same. Therefore, these data allow one to assume that at low temperatures, the water in the center of the channels freezes. Below, the crossing point (which depends on the fraction of bulk-like water) proton diffusion thus only occurs in a thin non-freezable interfacial layer, where the thickness of this layer does not depend on the composition 14 . If this assumption is correct, then a decrease in moisture content should also lead to an increase in the contribution of near-wall diffusion and, consequently, an increase in the activation energy to values of ~ 0.46 eV.
The goal of this work was to investigate the temperature dependences of D NMR in hydrocarbon co-PNIS membranes at different moisture contents and to clarify the micro-mechanism of the diffusion process and the water management conditions during its operation in PEMFC. The study has been done using co-PNIS 85/15 membrane, which has a higher diffusion coefficient at room temperature, allowing the diffusion to be traced to lower moisture content values.

Methods
Details of the synthesis of co-PNIS 85/15 membranes were presented earlier [17]. For NMR studies, 4 × 8 mm 2 membrane samples were prepared, stacked 1 mm thick and tightly inserted into 5-mm NMR ampoules flattened to 1 mm from the end. The samples were dried at 150 °C in a vacuum oven at 1 mbar for 2 h. By weighing the sample on an analytical scale and knowing the weight of the NMR ampoule, the weight of the dry sample (m dry ) was determined. The ampoules with the membrane samples were then sealed over cuvettes of distilled water, avoiding direct contact between the water and the membrane. Periodically, the NMR sample ampoules were weighed (m wet ). Moisture saturation of the membranes was carried out until the desired values of λ were reached, using Eq. (1): where μ = 18 g/mol is the molar mass of water, IEC = 2.66 meq/g is ion exchange capacity of the co-PNIS, and n = 0.575 relative fraction of mobile protons, excluding protons contained in the aromatic matrix of a hydrocarbon polymer. The details of determining these parameters are presented in [17], and a general characterization of membranes is presented in [14,15].
Self-diffusion coefficients were measured using 1 H static field gradient (SFG) NMR diffusometry [38], which allows for higher gradient strengths and shorter T 1 and T 2 spin relaxation times as compared to the pulsed field gradient analog and, thus, enables measurements of samples at low temperatures with smaller diffusivities. To probe the fluctuations of the resonance frequencies arising from the diffusion process in magnetic field gradient, the three-pulse stimulated-echo (STE) experiments have been applied, which involve two evolution times t p separated by the variable mixing time t m [17]. The measurements were conducted at a resonance frequency of 173 MHz and two gradients of the magnetic field The length of the 90° pulses was 0.7 μs. The temperature was set with an accuracy of ± 1 K in the range from 200 to 363 K and stabilized to ± 0.2 K using a N 2 flow cryostat.
To avoid effects, like polarization transfer among mobile and framework protons and spin relaxation, which, in addition to molecular diffusion, may result in a damping of the observed echo amplitude S in experimental practice, we used an approach, which takes into account exchange between fast and slow proton species. It was initially proposed in [39,40] and proved to be well suited for SFG NMR studies of diffusion in co-PINS systems with protonated framework as we presented in the previous work [17].
In order to successfully apply this model to SFG NMR diffusometry, it is necessary to perform several STE experiments with different evolution times and gradient strengths. Exemplary, STE decays obtained for co-PNIS 85/15 at T = 260 K and λ = 6.6, for evolution times t p of 50 and 100 μs and two field gradients G and g, show not only the expected dependence on the evolution time and the gradient strength but also allow to estimate additional parameters, like relaxation times and exchange rates among mobile and immobile protons (Fig. 2).

Results and discussion
The results for diffusion in the co-PNIS 85/15 membrane at different moisture contents from 21 to 4 are shown in Fig. 3 as an Arrhenius plot. It can be seen that at λ values between 21 and 11.6, the ln(D NM R(1/T)) dependences have two modes with different activation energies, and a crossover point at T cr . At temperatures above the crossover point, the temperature dependences of ln(D NMR (1/T)) are almost parallel with a slight increase in activation energy from 0.19 to 0.22 eV while decreasing λ from 21 to 11.6.
In this case, the activation energy of diffusion for the co-PNIS 85/15 membrane is close to the activation energy of 0.17 eV of bulk water [41]. Consequently, in this membrane, like in Nafion, the diffusion coefficient at high λ values can be associated with self-diffusion of water molecules. In the co-PNIS 85/15 membrane, this behavior is observed at λ higher than 11.6, while in Nafion, it sets in already at lower λ, starting from 6 [29,42]. This difference in moisture content required to achieve the bulk-like behavior of D NMR probably indicates wider transport channels in co-PNIS 85/15 compared to those in Nafion, since it takes more water to fill them. Figure 3 also shows that at temperatures below the crossover point and moisture contents of λ ≥ 11.6, the ln(D NMR (1/T)) dependences for the co-PNIS 85/15 membrane practically coincide and are characterized by an activation energy of ~ 0.46 eV. Similar behavior of the ln(D NMR (1/T)) dependences is observed for Nafion at T ≤ 263 K and λ in the range from 4 to 12 (6-21% by weight) [42]. The Girke cluster-channel model assumes that below the crossover point, some of the water freezes, while some remains in the liquid state [42]. From the coincidence of the dependences ln(D NMR (1/T)) below the crossover point, the assumption was made that regardless of the initial value of λ, the same amount of supercooled water remains, and the rest of the water freezes inside the hydrophilic areas of the membrane [42]. Some evidence for this assumption could be obtained by studying D NMR (T) in Nafion at low-humidity content (λ ≤ 4), but such measurements have not been carried out in [42]. We performed this study on the co-PNIS 85/15 membrane to establish the proton diffusion behavior at lower hydration level.  At λ ≈ 8.8, the ln(D NMR (1/T)) dependence also shows two temperature regimes with different activation energies. However, the high-temperature regime is characterized by higher (0.25 eV) and the low-temperature regime by lower (0.40 eV) activation energies than for samples with λ ≥ 11.6 (Fig. 3). The low-temperature regime/mode no longer coincides with the regime at λ ≥ 11.6. The trend toward equalization of the activation energies for the high-temperature and low-temperature regimes continues as the moisture content decreases further, so that, at λ ≈ 4.0, the crossover point becomes indistinguishable and the ln(D NMR (1/T)) dependence is described by one line with an activation energy of 0.38 eV (Fig. 3). Similarly, it was observed for water in silica pores with diameters d > 2 nm that a water fraction in the pore center freezes and substantially affects the diffusion of the non-freezable water fraction near the pore walls, which is characterized by an activation energy of ~ 0.4 eV below the freezing point [43].
Thus, we can assume that there is some critical value of λ 0 separating two different regimes of the diffusion mechanism. The value can be estimated from analysis of diffusion as a function of λ; see Fig. 4. One can see that for different temperatures above T cr , the D NMR (λ) dependences have a kink at λ 0 ≈ 10.5, which may be an indication of a change in the diffusion micromechanism. At moisture content higher than λ 0 , above the crossover point, the diffusion is comparable to the diffusion of bulk water. At moisture content below λ 0 , the D NMR is characterized by a less pronounced change in the slope at the crossover point or by the absence of this point at all. Below some threshold values of T cr and λ 0 , the activation energy does not change in the entire temperature range studied, indicating that the diffusion micromechanism is identical at different temperatures in samples with low hydration.
The observed evolution of the temperature dependences ln(D NMR (1/T)) in the co-PNIS 85/15 membrane for different λ can be interpreted using the model that assumes the existence of different water states in these polymers [33][34][35]: bulk water in the central part of the channels, strongly bound water on the surface and on the sulfonic groups, and weakly bound water between them. From our NMR experiment, we cannot separate the weakly bound water for the following reasons: the probably small amount of this water, the rapid exchange with other water states, and the polarization transfer among protons, which is inevitable in NMR experiment. Therefore, we will consider a simplified model with two different water states: bulk-like water in the central part of the channels and surface water.
Numerous studies show that at low temperatures in Nafion membranes, the bulk-like water is not in a crystalline, but in a glassy state [32,44], enclosed in channels and in clusters with characteristic sizes of 1-4 nm [45,46]. This fact is in general agreement with the observation that severely confined water undergoes a glass transition in various nanoscaled matrices with sizes below ca. 2 nm [47][48][49][50][51][52][53], while, in slightly larger pores with sizes of a few nanometers, a water fraction forms strongly disordered ice phases, e.g., stacking disordered ice comprising hexagonal and cubic forms, and coexists with a liquid water fraction [54,55]. Assuming co-PNIS membranes, our previous study of the co-PNIS 85/15 revealed no anisotropic and Q-dependent diffusion, indicating homogeneous proton transport in this membrane on a three-dimensional system of transport channels and lack of large cluster areas [17]. Therefore, based on the results obtained in this work (Figs. 3 and 4), the following generalized model of proton diffusion in co-PNIS membranes with varying temperature and/or moisture content can be assumed. The proton transport in these polymers can be considered as migration in a three-dimensional isotropic mesh formed by nanoscaled channels. Figure 5 provides a qualitative view of the cross-section of the nanoscale channel of co-PNIS membranes at different temperatures and moisture contents. In this model, it is assumed that bulklike water is in the center (inner circle), and surface strongly bonded water is on the walls, and it is concentrated near the sulfonic groups (outer circle).
At high hydration levels (λ ≥ 10.5), water exists in both states, but the main mass of water is in the bulk-like state; see Fig. 5a. At temperatures above the crossover point (T > T cr ), protons of H 2 O molecules located in the central part of the pore dominate and determine the self-diffusion coefficient. The degree of filling of the central region of the channel affects the homogeneity of the hydrogen bonding network along which the proton diffusion occurs. The homogeneity of the hydrogen bonding network worsens with decreasing λ, leading to an almost parallel shift downwards of the ln(D NMR (1/T)) dependences (Fig. 3). The bulk-like state of water in the center of the co-PNIS 85/15 nanochannel is not completely identical to that of ordinary bulk water, first, because of volume limitations on the order of a few nanometers, and second, because of the large concentration of injected protons arising from the SO 3 H group dissociation with sufficient water content (λ ≥ 3) [35,36,56,57].
Therefore, when the temperature drops below the crossover point (T < T cr ), water in the central part of the channel does not form an ordered crystal, but rather forms a substantially disordered solid state, which has a very short spin-spin relaxation time T 2 so that it does not contribute to our NMR diffusion measurements. Consequently, the measured diffusion coefficients at temperatures below the crossover point characterize the transport of bound water in the near-wall region, whose movements are hindered, resulting in a higher activation energy than that of bulk water. The thickness of the non-freezable surface water layer hardly depends on the diameter of the channels. Consequently, at high moisture content, when the filled central part of the channel freezes as the temperature decreases, the thickness of the layer of mobile surface water will not change regardless of how much water is frozen in the central part. Therefore, at temperatures below the crossover point and moisture content λ ≥ 10.5, the diffusion process will be characterized by close D NMR and activation energy values, regardless of the initial membrane hydration value (Fig. 5a, T < T cr ), as observed in the experiment (Fig. 3, λ = 21, 15.8 and 11.6).
At intermediate moisture values below the boundary value λ < λ 0 , but still high enough to fill the entire wall area, the bulk-like water share in the channel center becomes less than the surface water share, and the bulk-like water contribution to diffusion decreases. This leads to an increase in the activation energy at temperatures above T cr (Fig. 5b, T > T cr ). As the temperature decreases, the freezing of the water remaining in the central part of the channel will no longer have a significant effect on the measured diffusion coefficient, determined mainly by surface water and water strongly bound to sulfonic groups (Fig. 5b, T < T cr ). Therefore, the temperature dependences of ln(D NMR (1/T)) will have a milder kink, as seen in Fig. 3, for λ = 8.8 and λ = 6.5.
With further decrease in moisture content, λ ≤ 4, the thickness of the surface water layer begins to decrease and it may be interrupted. Then, over the entire temperature range, the diffusion coefficient is determined only by the mobility of surface water, which leads to the disappearance of the kink in the ln(D NMR (1/T)) dependence. The activation energy increases due to the strong interaction of water molecules with sulfonic groups; see Figs. 3 (λ = 4.0) and 5c.
An interesting point is the higher activation energy below T cr for samples with higher moisture content (at λ = 4, E a = 0.38 eV whereas at λ > 11.5, E a = 0.46 eV). According to the proposed model, at low temperatures, the activation energy characterizes diffusion in a thin layer on the walls, the thickness of which does not depend significantly on the moisture content. We assume that at high λ values, water freezing in the central part of the channel increases its volume and thus creates additional pressure on the channel walls. This leads to difficulty of diffusion in the near-wall region and, accordingly, to increase of activation energy.

Conclusion
The temperature dependences of proton diffusion in the co-PNIS 85/15 membrane were investigated at different moisture contents λ, ranging from 4 to 21. It was found that at λ > 10.5, there is a crossover in the ln(D NMR (1/T)) dependences at T cr ≈ 250-260 K characterizing the change in the diffusion micromechanism. Schematic representation of the states of water in the co-PNIS membrane channel above and below crossover temperature T cr at different water contents Above the crossover point, the activation energy E a ~ 0.2 eV is close to the activation energy of self-diffusion of H 2 O molecules in bulk water (~ 0.17 eV [41]). At temperatures below T cr , the ln(D NMR (1/T)) dependences for = 11.6, 15.8, and 21 coincide in one common line with an activation energy of ~ 0.46 eV. It should be noted that similar diffusion coefficient dependencies were observed for co-PNIS x/1−x membranes when varying the ratio of hydrophilic to hydrophobic blocks [17]. Such behavior of the diffusion coefficient suggests that above the crossover point, the measured diffusion coefficient corresponds to bulk-like water in the central part of the transport channel. At temperatures below the crossover point, this bulk-like water freezes and diffusion occurs only in the near-surface region of the transport channels, where water is strongly bound to sulfonic groups. In this case, the mobile near-surface water layer has almost the same thickness regardless of the moisture content, if it is above a certain value. This leads to coincidence of the dependences ln(D NMR (1/T)) at low temperatures. Consistent with these arguments, previous work on water in silica pores [51] reported that D NMR becomes independent of the pore diameter when water fractions in the pore center freeze and restrict diffusion to a narrow layer of non-freezable water at the pore wall.
Analysis of D NMR in dependence on the moisture content at fixed temperatures showed that this scenario holds up to a limit value of λ 0 ≈ 10.5, which seems to correspond to the lower limit of bulk-like water presence in the sample. The existence of different types of water in proton conducting polymers has been also previously suggested [33][34][35].
At lower moisture content 4 < λ < λ 0 , the ln(D NMR (1/T)) dependences retain the crossover point with the two regions having different activation energies, but this difference is much smaller than at λ ≥ λ 0 . At the lowest studied value of λ ≈ 4, the crossover point disappears, and the diffusion coefficient is described by one activation energy over the entire temperature range. Thus, for water content λ < λ 0 , the measured diffusion coefficient can be related to the transport of surface protons bound to SO 3 2− groups.

Declarations
Ethical approval The publication has no ethnic issues applicable to both human and/ or animal studies.

Competing interests
The authors declare no competing interests.
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