Water dynamics in rigid ionomer networks

Polymers decorated by ionic groups are in the core of numerous technologies where selective and timed transport is a key to their function. These polymers are incorporated in a large number of applications ranging from clean energy generation^1,2 and storage³ to biotechnology.^4,5 Of particular interest are ionomers, where in contrast to polyelectrolytes, their overall conformation is determined by a balance between electrostatic interactions and the effect of the backbone rigidity. Ionomers are in the core of numerous current technologies such as hydrogen fuel cells,^6–8 sensors,^9,10 water purification,¹¹ and drug delivery.^12,13 Striving to enhance current technologies and controlling selective timed transport has driven a large number of studies to resolve the three prong correlations of the polymer: chemical structure, phase structure, and transport.

Among the most studied ionomers are Nafion™ ^14–21 and sulfonated polystyrene (SPS).^22,23 These flexible and semi-flexible polymers form networks where the ionic groups tend to associate into clusters. The size and shape of these aggregates depend on a large number of parameters including the chemistries of the ionic groups, their distribution along the backbone as well as the polymer topology. These ionic clusters play contradicting roles, where on one hand, they serve as physical cross links, enhancing stability and concurrently forming transport pathways, where hydrophilic solvents such as water and alcohols accumulate. The dynamics within ionic-polymeric networks including the motion of the polymer backbone and that of the ionic moieties and solvents, determine the transport ability of these macromolecules and their mechanical stability.^24,25 As such, the topography of the backbone and its rigidity constitute a critical control over the dynamics of ionic polymer networks.

Here using quasi-elastic neutron scattering (QENS), we probe the dynamic processes within one ionic polymer network that consists of macromolecules with a rigid backbone^26–29 whose structure is shown in Figure 1(a). The backbone of sulfonated poly-phenylene (SPP) is significantly more rigid than most common ionomers including sulfonated polystyrene (SPS)³⁰ and Nafion®.³¹ Small-angle neutron scattering (SANS) studies have shown that SPP molecules form a rather extended conformation in dilute solutions as is visualized in the SPP image captured by molecular dynamics simulations are presented in Figure 1(b). Details of these simulations, carried out under a limited number of molecules for visualization only, are presented in the supplementary material. The rigidity of its backbone leads to the formation of bundles that serve as the building blocks of the ionic structure as shown in the schematic presented in Figure 1(c). This schematic was derived from previous SANS²⁷ and NMR³² studies.

When hydrated, the water molecules associate with the ionic groups of the ionomers and often induce phase transformations. The local dynamics of the water molecules was found to be strongly coupled with macroscopic proton transport.^17,33–35 The significance of water transport in polymeric membrane has driven numerous studies to probe the dynamics within ionomers, where QENS was able to capture the local motion of both segmental motion and that of guest molecules. Volino and co-workers reported fast and slow modes of water dynamics in hydrated Nafion membranes, with bulk like diffusion at length scale smaller than 10 Å.¹⁴ Similar results were observed by Pivovar and Pivovar³⁶ who resolved a jump-exchange between the different sites. Further, using molecular dynamic simulation, Devanathan et al.³⁴ have shown multiple water environments for water including bound, weakly bound, and unbound water in Nafion membranes, which increase with increasing hydration levels.³⁷ The mobility of the solvents, ions, and the polymer backbone determines the stability and transport in these ionic networks, spanning a broad range of dynamical process whose characterization requires a conjunction of technique.

The time and length scales over which solvent dynamics takes place as well as some segmental dynamics are captured by QENS. For organic materials, QENS predominantly follows the incoherent scattering of hydrogen. The inherently large difference in the scattering cross section between proton (H, $σ=80.26$ b) and deuterium (D, $σ=2.05$ b) makes QENS the technique of choice to study segmental dynamics of ionomers^38,39 as well as that of water in confinement.^40–42 Here, using QENS, we explore the effects of chain rigidity on the local dynamics in membranes that consist of substituted polyphenylene backbone with sulfonated ionic groups shown in Figure 1. We find that similar to other ionomers, water occupies multiple sites with a different degree of association and displays fast and slow dynamic modes; however, the distribution of the molecules is strongly affected by the bundle structure arising from the chain rigidity. The paper is organized as follows: experimental details will be first presented followed by results on the dynamics of the polymer networks themselves. Results for water confined in these ionic networks will be then presented.

The SPP polymers were synthesized by Diels-Alder polymerization as described by Fujimoto et al.^26,43 with the average molecular weight of 70,000 g/mol and polydispersity index of 2.2. Specifically, the polymers were synthesized from 1,4-bis(2,4,5-triphenylcyclopendienone) benzene and 1,4-diethynylbenzene followed by sulfonation with chlorosulfonic acid. Membranes were made by evaporating a 10 wt. % solution of SPP in N,N-dimethylacetamide (DMAc) from a flat glass container and the solvent was allowed to evaporate at ambient condition. The ion exchange capacities (IECs) of the SPP polymers were measured by titration with 0.01M NaOH. IEC corresponds the reciprocal mass equivalent of the polymer between adjacent ionic groups. This quantity is a measure of the degree of decoration with ionic groups. It determines the ability of the dry SPP membranes to exchange ions. Two polymers of IECs 1.6 and 2.2 with a corresponding sulfonation level of 22.0% and 33.3% were studied. Table I summarizes the characteristics of the membranes studied. Deuterium oxide, D₂O (99.9%), was purchased from Cambridge Isotope Laboratories. The protonated membranes were kept in vacuum overnight at room temperature.

Samples were studied in ambient and saturated conditions. Ambient here corresponds to membranes kept at room temperature (295 K) and humidity. Membranes were dried under vacuum for 72 h and then exposed to H₂O/D₂O depending on the experiment. The experimental cell was first flushed with nitrogen followed by exposure of the samples to saturated vapors. The weight of the membranes was measured periodically. In parallel, the water NMR signal (for samples with equal dimensions and processing history) was measured and its intensity integrated to follow the uptake. We find that in ambient conditions, the samples absorb water instantaneously and hardly any further changes take place after several minutes. The samples of IEC of 1.6 and 2.2 absorbed 4-4.8 wt. % of water with small variations between samples. Saturated samples were exposed to boiling water for 5 min. IEC of 1.6 absorbed 50 wt. % and IEC of 2.2 absorbed 140 wt. % of water. Differential Scanning Calorimetry (DSC) measurements were carried out with an effort to reveal distinctive possible states of water. Conclusive results could not be obtained because of the presence of multiple water containing sites.

The dynamics processes in SPP ionomer membranes were measured on two QENS spectrometers. Membranes saturated with D₂O were measured on NG-2 high flux backscattering spectrometer⁴⁴ (HFBS) at National Institute of Standards and Technology (NIST). Wavelength of neutron beam used was, $λ0=6.27$ Å, corresponding to an energy E₀ = 2.08 meV. Sixteen Si (111) analyzer crystal detectors covering Q ranges of 0.25 Å⁻¹ to 1.74 Å⁻¹ were used with an instrument dynamic energy range of ±$11μeV$ and $0.8μeV$ energy resolutions. Membranes saturated by H₂O were studied on the backscattering spectrometer (BASIS)⁴⁵ at the Spallation Neutron Source, Oak Ridge National Laboratory. A band of polychromatic incident neutrons was used; the wavelength of the detected neutrons was $λ0=6.267$ Å, as selected by Si (111) Bragg reflection at 88°. Data were obtained from a dynamic range of −100 to + 100 $μeV$ with an overall energy resolution of $3.5μeV$⁠. This value provides the average of the resolution at the Q range covered. The data from multiple detectors were binned into nine Q values to cover the Q range of 0.20 Å^$−$1 to 1.85 Å^$−$1.

Data were collected on both instruments for 10 h at different temperatures using a standard top loading closed cycle refrigerators with helium gas as the refrigerant. All data were reduced and analyzed using the DAVE⁴⁶ software package.

The intensity, $I(Q,E)$⁠, of the QENS spectra is given by

where $A(Q)$ and $p1(Q)$ are scaling factor and contribution of elastic scattering, respectively. The elastic scattering is captured by $δ(E)$⁠, a Dirac delta function. The quasi-elastic scattering function $S(Q,E)$ contains the dynamic information; the background is described by $B(Q,E)$ and $R(Q,E)$ is the instrument resolution function.

Inelastic cross section of hydrogen is significantly higher than that of the other elements that constitute most soft materials. The coherent and incoherent scattering cross sections of the atoms that constitute SPP are⁴⁷ $σcoh(H)$ = 1.76 b, $σinch(H)$ = 80.26 b, $σcoh(D)$ = 5.59 b, $σinch(D)$ = 2.04 b, $σcoh(C)$ = 5.56 b, $σinch(C)$ = 0 b, $σcoh(S)$ = 1.02 b, and $σinch(S)$ = 0.007 b. In SPP membranes, the dominant incoherent scattering originates from the protons on the aromatic rings and residual water.

QENS spectra of SPP membranes dry and saturated with D₂O, as a function of temperature at representative Q values, are shown in Figure 2. As mentioned above, the signal arises predominantly from incoherent scattering of protons, thus the observed signals correspond to the polymer network. The spectra, obtained from the membranes for two ionic levels over the Q range that corresponds to potential segmental motion, do not exhibit any dynamics signature as evident by the overlap of the signal with a vanadium standard for all measured Q values. Lack of broadening, in comparison to a vanadium standard, is a clear indication that on the time and length scales captured by the instrument, the polymer molecules hardly move. Lack of dynamics on the time and length scales detected by QENS for the dry membranes is consistent with the high glass transition (T_g) of SPP which is ca. 400 K. The much faster vibrational dynamics expected in organic networks is outside the range of energies detected by the backscattering spectrometer.

The membranes were kept below their glass transition temperature and were hydrated with D₂O. The temperature was not raised above T_g to avoid any processing impacts to the direct environment of the water molecules. Surprisingly, the membranes, saturated with D₂O, did not exhibit any signature of network dynamics in all measured Q and E values. These results show that even though these membranes are saturated with water, the polymeric network remained rigid and displayed a glassy behavior. These characteristics are rationalized in terms of the bundle structure of SPP²⁷ that persists across a broad humidity range. The lack of dynamics on the length and time scales of QENS suggests that the water molecules hardly penetrate the densely packed bundles of SPP and therefore T_g of these nano-domains is not affected even though water occupies inter bundle sites. From the I(Q) spectrum in Figure 3, we conclude that the incoherent scattering does not dominate the QENS signal only below Q = 0.5 Å⁻¹.

The dry membranes were then hydrated with H₂O. As the measurements of the polymer in D₂O did not reveal any dynamics of the network, the incoherent scattering measured for the hydrated samples consists of contributions from the polymer and the water. As the measurements of the polymer in D₂O did not reveal any dynamics of the network and, the quasi-elastic spectra broadening arise from the incoherent signal of the water, membranes exposed to two humidity conditions were probed: ambient and saturated. Measurements were carried out over a Q range of 0.20 Å^$−$1 to 1.85 Å^$−$1 corresponding to distances in real space of ∼31 Å to 4 Å. QENS spectra of SPP (IEC = 1.6) membranes measured at Q = 1.0 Å^$−$1 at the two hydration levels are shown in Figure 4.

Data at additional Q values are presented in Figure 2S of the supplementary material. For both hydration conditions, at all Q ranges, the lines broaden with increasing temperature, revealing increasing mobility of water molecules. It is notable that even for limited numbers of water molecules present under ambient conditions, they remain dynamic. This indicated that the water molecules are only loosely bound to the polymer network. Certain amount of water might be associated with the polymer network, but it is hard to quantify the amount and the position of such water. Qualitatively, water dynamics appear similar as a function of water content as illustrated in Figure 5, where the spectra at 233 K and 343 K at Q = 1.0 Å^$−$1 are presented. Detailed analysis however, discussed below, distinguishes different dynamics. The spectra at other Q values are given in Figure 3S of the supplementary material.

A delta function was used to account for the contributions from polymer chains and residual water molecules whose dynamics remain outside the range of the experiment resolution. A flat background was also introduced to take account of any vibrational motion that falls outside the instrument dynamics range (⁠$±100μeV$⁠). After convolution with the instrument resolution, water dynamics was followed through the analysis of $S(Q,E)$⁠, given by Equation (1).

In an effort to analyze the water dynamics, we have tested common models often used including stretched exponential,⁴⁸ Gaussian dynamics,⁴⁹ and single Lorentzian.^41,50,51 These models were not able to capture the dynamics in the system. We attribute this to the unusual water dynamics in physical nano-confinement, originated from the rigid bundle structure of the SPP membranes providing both inter- and intra-bundle sites. Confined water dynamics depend on the nature of the confining matrices and their geometrics. A number of different models have been used to understand the dynamics of confined water in different media, including Nafion from QENS experiments.⁴¹ Especially for Nafion, a variety of models, such as diffusion inside a sphere,⁵² a single Lorentzian,³⁶ and a Gaussian model,⁵³ have been used to extract the length scale and time scale of water dynamics in hydrated membranes. In SPPs, the backbone and bundle are rigid compared to Nafion, the membrane form non-conforming structures that remain rigid in presence of water, forming larger vacancies compared with Nafion and polystyrene sulfonate.

Further insight is obtained from the dynamics susceptibility, $χ(Q,E)$⁠. It provides a measure of temperature-induced dynamic fluctuations and accounts for experimentally multipoint correlator that identifies the dynamic heterogeneities. $χ(Q,E)$ is obtained by converting $S(Q,E)$ using Bose occupation factor⁵⁴ that accounts for the energy difference between species occupying different sites and the temperature. Practically, it helps to separate the contribution coming from different dynamics processes, manifested in different peaks. The presence of a minimum in the susceptibility of both ambient and saturated membranes as a function of energy transfer suggests the presence of two peaks, one at low energy transfer and another at higher energy transfer, as shown by arrows, thus indicating two different relaxation processes at two different time scales. Note that the data contain the onset of the second peak, limited by the signal to noise of the system. In order to capture those separate dynamic processes, a sum of two Lorentzian functions representing a differentcharacteristics time was essential to capture the dynamics in the entire measured range. Therefore, $S(Q,E)$ is modeled as

where $Γ1(Q)$ and $Γ2(Q)$ correspond to the HWHM of two Lorentzians, with the broader one describing the faster dynamics and the narrower, the slower one, respectively.

The relative weights of the fast and slow components of the overall dynamics are given by $p2(Q)$ and $(1−p2(Q))$⁠, respectively. The best fits obtained for $S(Q,E)$ incorporating the elastic component and the resolution function are described by the solid lines in Figures 4 and 5. $Γ1(Q)$ and $Γ2(Q)$ extracted from the best fits at ambient and saturated conditions are presented as a function of Q² in Figure 6. For a simple Fickian diffusion, $Γ(Q)=DQ2$ where D is the translational diffusion coefficient. Both $Γ1(Q)$ and $Γ2(Q)$ initially increase with Q at all measured temperatures, where $Γ1(Q)$ is significantly higher than $Γ2(Q)$⁠. However, $Γ1(Q)$ is not a linear function of Q², diverting from simple Fickian diffusion. We find a fast increase of $Γ1(Q)$ for low Q, which crosses over to a plateau at ∼7 Å (Q = 1 Å^$−$1) for all measured temperatures. This Q-temperature dependence is typical of jump diffusion.^55,56

$Γ2(Q)$ exhibits similar behavior at low Q and becomes rather random at high Q. The slow component is attributed to bound water that is impacted by small structural changes that take place with increasing temperature.²⁷ The changes in $Γ1(Q)$ and $Γ2(Q)$ for the fully hydrated membranes are shown in Figure 6(b). Both $Γ1(Q)$ and $Γ2(Q)$ for the saturated membrane are higher than the values at ambient conditions (Figure 6(a)) but show a similar trend as a function of temperature. These results show that though water molecules in saturated membranes are significantly more dynamic, they occupy similar sites to those in ambient conditions. In saturated membrane, HWHM at certain Q (high Q) values is at the edge of the resolution, and therefore a large error is associated with their values.

In order to extract the heterogeneous dynamics of water molecules at different length and time scales, the dynamics reflected in $Γ1(Q)$ and $Γ2(Q)$ were analyzed using the random jump diffusion model⁵⁷ given by Equation (3), the simplest exchange model between two different sites. This model has been used to capture water dynamics in heterogeneous environments including ionomers membrane³⁶ and porous media.⁵⁵ It assumes that water molecules oscillate around an equilibrium position for an average time $τo$⁠, before jumping a distance L to another equilibrium position. $Γi(Q)$ for site i = 1 and 2 for the jump model are correlated with the translational diffusion coefficient, D and the residence time, $τo$⁠, as described in the following equation:⁵⁸ 

and the jump length, $L$ is described by the following:

We find that $Γ1(Q)$ extracted from this model was well behaved across the entire measured Q range where $Γ2(Q)$ deviated at larger Q for both hydration levels. The jump diffusion constants extracted from the fit for ambient and saturated hydration levels are presented in Table II and the results for the jump length are given in Table III. The jump diffusion constants for both fast and slow dynamics for the saturated membranes are larger than for those at ambient conditions.

SPP membrane structure has been previously studied using SANS and x-ray scattering experiments.²⁷ The structure at high Q, where chain packing is reflected, exhibits one broad line centered around 4.6 Å which slightly broadens with hydration and shifts to higher dimensions. The linewidths, however, are rather broad and no quantitative information can be extracted. In higher dimensions, where bundles and ion clustering have been traditionally detected, SANS revealed the presence of larger domains of ∼35-60 nm in dry membranes. With increasing water content, this line becomes slightly pronounced, indicating the penetration of water into hydrophobic regions. The water penetration is attributed to the presence of ionic groups within the bundles. At ∼32 Å, a temperature insensitive peak attributed to hydrophilic/ionic domain is observed. Therefore, the higher values of water diffusivity in saturated membrane are attributed to the increase in the size of the hydrophilic domain, forming a less constraint environment. This is further corroborated by the jump length extracted from the analysis as shown in Table III. The jump length increases with increasing temperature and hydration levels of the SPP membranes. The jump lengths are 2-5 times larger than the bulk water values (1.3 Å), which is commonly observed for water molecules in confinement,⁵⁹ except for the slow component at 343 K in saturated membrane, where it is large. This data point is clearly affected by some ambiguity due to internal structure changes.

The diffusion coefficients increase with increasing temperature for both ambient and saturated hydration levels. The jump diffusion constants for the slow component are smaller than the fast components in both hydration levels at a given temperature. At 343 K, uncharacteristically high values are obtained for $Γ1(Q)$ which are higher than those obtained for $Γ2(Q)$⁠, and the slow-fast model breaks down. At this temperature, structural changes take place where the bundle structure itself is affected, allowing penetration of the water into the bundles themselves as shown by He et al.²⁷ The direct correlation of the structure and dynamics of these saturated membranes at high temperatures though remain an open question. We found that water remains dynamic below its freezing point in this ionomer membrane due to their confined geometry that does not allow the formation of hydrogen bonds that often promote crystallization. Similar phenomena have been observed in water in confined geometry.^41,60

Here the measured value of diffusion coefficients is slightly higher than that of bulk water.⁵⁰ Similar type of higher value for water diffusion in confinement has been previously reported^61,62 and rationalized through the breaking of highly regular hydrogen bonding for water confined to small pores. With increasing temperature, more sulfonate groups migrate to the interface, disturbing much of the bulk hydrogen bonding, and may facilitate water diffusivity in SPP membranes. This high value of diffusivity is local and does not propagate across the sample and remains confined on some length scale that may be larger than the lowest Q of the QENS experiment. Therefore, leveling off of the low Q data is not detectable.

Contribution of slow and fast components in the overall dynamics has been determined. The Q dependence of the relative weight of the slow components, 1-p₂(Q), for membranes at both ambient and saturated conditions is presented in Figures 7(a) and 7(b), respectively. In both cases, 1-p₂(Q) decreases as Q increases and levels off at high temperature for higher Q values. The crossover at higher Q values at higher temperatures reflects the capturing of some coherent scattering at smaller length scale. As the temperature increases, the molecular motion of the water molecules increases, leading to an increase in the jump length of the water. In principal, the geometry of water motion can be obtained from the elastic incoherent structure factor of water diffusing translationally in confined geometry. It is however a challenge in highly heterogeneous systems.

Here we showed that water in the ionomer follows two diffusion processes. The temperature dependence of the diffusion coefficients of both populations of water at ambient and saturated condition is illustrated in Figure 8.

The diffusion constants of water extracted for both types of water follow the Arrhenius process of $D=Ae−EaRT$⁠, where $D$ is the self-diffusion coefficient, $A$ is a constant, and $R$ is the universal gas constant. The diffusion coefficients at 233 K for the slow water component could not be included in the Arrhenius fit, reflecting the fact that slow population of water molecules do not show Arrhenius behavior at T ≤ 233 K. The activation energies of the diffusion mechanism at both conditions were calculated and summarized in Table IV. Activation energy of the slow population of water is comparable to the bulk water hydrogen bonding⁶³ but is lower for the fast population. Precaution must be taken while using the activation energies derived for slow moving water population because of the limited number of points that could be included in the Arrhenius fit.

This smaller value of $Ea$⁠, compared to bulk water, is attributed to the presence of bundles of polymers, along with sulfonated groups that accelerate the water diffusion. The activation energy for fast population of water at saturated membrane is smaller than at ambient condition. This smaller value of activation energy corresponds to a lowering of the energy barrier for water diffusion and is consistent with the diffusion in swollen membranes. The interfacial diffusion of water molecules is facilitated by the backbone rigidity giving rise to faster diffusion with smaller activation energy.

Dynamics of water in SPP ionomers membranes was investigated by QENS as a function of water content and temperature. Our study shows that on the time scale of measurement, the polymer molecules are immobile, while the water in the membrane molecules is exchanged between multiple sites resulting in slow and fast dynamics. We attribute the fast components to water molecules that reside predominantly in inter-bundle space and the slow one to water molecules associated with the polar groups. Water dynamics is characterized by jump diffusion for both components. We found that diffusion of both populations of water molecules rises with increasing water content and temperature and is higher than the values reported for Nafion.³⁶ These higher values are attributed to the rigidity of SPP polymer backbone. As in porous materials,⁶⁰ water molecules remain non-frozen even at subzero temperature in SPP ionomer membranes.

See supplementary material for molecular dynamics simulation detail, QENS spectra and dynamics susceptibility plots.

This work was supported by the U.S. Department of Energy under the Contract Nos. DOE-DE-FG02-07ER46456 and DE-FG02-12ER46843. The use of neutron scattering facility at Oak Ridge National Laboratory is supported by the U.S. Department of Energy, Office of Basic Energy Sciences. Travel to Oak Ridge National Laboratory to carry out this work was supported by a Travel Fellowship from the DOE-EPSCoR Grant to the University of Tennessee, DE-FG02-08ER46528. This work utilized facilities supported in part by the National Science Foundation under Agreement No. DMR-0944772. We acknowledge the support of the National Institute of Standards and Technology, U.S. Department of Commerce, in providing the neutron research facilities used in this work. Any mention of commercial products within NIST web pages is for information only; it does not imply recommendation or endorsement by NIST.