Neutron scattering study on the structure-property relationship of radiation-grafted proton exchange membranes

. The partial scattering function (PSF) analysis through the contrast variation small-angle neutron scattering technique was used to determine the exact structure of the hydrated radiation-grafted proton-exchange membranes, made of poly(styrene sulfonic acid)-grafted poly(ethylene-co-tetrafluoroethylene) (ETFE-g-PSSA) with a high ion exchange capacity of 2.5 mmol/g. The membrane was treated as a three-component system composed of ETFE base polymer, PSSA graft polymer, and absorbed water. The analysis on PSF self-terms gave the exact structure of individual components and that on PSF cross-terms explored the correlation between two components to establish their locations. The characterization was performed in multiple length scales, and the mechanistic insights into membrane conductivity and structure correlations were provided.


Introduction
Radiation-grafted proton exchange membranes (PEMs), made of poly(styrenesulfonic acid)-grafted poly(ethylene-co-tetrafluoroethylene) (ETFE-g-PSSA), are promising alternatives to Nafion® membranes for electrochemical applications such as electrodialysis and fuel cells.They offer the advantages of a potentially low-cost fabrication technique, and the adaptability of both improving membrane ionic conductivity by PSSA graft polymers and maintaining the excellent mechanical/thermal properties of ETFE base polymer [1][2][3].To the current stage of research, challenges remained to overcome are the relatively low proton conductivity of ETFE-g-PSSA under reduced relative humidity and long-term stability, which need thorough understanding of structure-property relationships [1][2][3][4][5][6][7][8][9].
It is known that in hydrated ETFE-g-PSSA PEMs, the sulfonic acid (SA, -SO3H) groups absorb water and form hydrophilic ionic channels that phase segregate from the hydrophobic polymer matrix.Thus, the proton conductivity is strongly controlled by the morphology and connectivity of ion channels [4][5][6][7][8][9].As one of the most essential techniques to understand the nano-scaled structure of a hydrated material, small-angle neutron scattering (SANS) technique has been employed in the previous studies.However, the conventional scattering analysis is based on the scattering intensity profile that contains contributions of all components in the system such as the hydrophobic polymer, hydrophilic polymer, ions, and water molecules, and fails to provide the detailed structure of the individual components.This undesirable original data problem was recently solved by partial scattering function (PSF) analysis, which is * Corresponding author: zhao.yue@qst.go.jp the quantitative decomposition of a series of intensity profiles obtained through contrast-variation SANS (CV-SANS) experiments [10][11][12].PSF analysis was applied to polymer nanocomposites in early studies [10], and recently was developed by us for Nafion and ETFE-g-PSSA PEMs with moderate ion exchange capacity (IEC) of 1.0 ~ 2.0 mmol/g [11,12].
In this article, we extended the application of this PSF analysis to determine the detailed structure of ETFE-g-PSSA PEMs with a high IEC of 2.5 mmol/g (denoted as ETFE-g-PSSA_2.5).The unique capability that PSF analysis provides to understanding structure correlations can result into new insights on the role of the polymer micro-/nano-structure and water in the emergence of the ion conduction.This in turn can help in the design of high-performing PEMs for a wide range of energy conversion applications.

Materials
The ETFE base film with a thickness of 50 µm (mass density, dBP = 1.75 g/cm 3 , crystallinity = 0.32) were purchased from Asahi Glass Co. Ltd, Japan.ETFE-g-PSSA_2.5 membrane with a grafting degree (GD) of 60% and an IEC of 2.5 mmol/g was prepared according to our previous report [13].The water uptake (WU) was estimated to be ~65% at room temperature, which is defined by  =

CV-SANS measurements
CV-SANS measurements were performed on KWS-2 SANS diffractometer operated by Juelich Centre for Neutron Science (JCNS) at the neutron source Heinz Maier-Leibnitz (FRM II reactor) in Garching, Germany [14].The incident neutron beam was monochromatized with a velocity selector to have an average wavelength (λ) of 5 Å with a wavelength resolution of 20%.Measurements were performed on ETFE-g-PSSA_2.5 PEMs equilibrated in H2O/D2O mixtures with eight different volume fractions of D2O (fD2O= 100, 90, 80, 70, 60, 50, 40, 0%) at room temperature.The scattering patterns were collected using a two-dimensional scintillation detector and circularly averaged to scattering intensity profiles, I(q)s, as a function of scattering vector, q.The final I(q)s were corrected for the background, the electronic noise, detector sensitivity, and incoherent scattering.
According to incompressibility assumption, I(q) can be described by three PSF self-terms Sii(q) as follows, where Sii is PSF self-term of the i component (i = BP, GP and W), representing its structural information.
CV-SANS experiments are performed with m different contrast by using H2O/D2O mixtures, the obtained I(q)s are a group of linear equations of Eq (2), Thus, three PSF self-terms of SBP-BP(q), SGP-GP(q) and SW-W(q) on the right side of Eq. ( 2) can be mathematically determined through the simultaneous equations of I(q) [11,12].
The PSF cross-term Sij (i ≠ j) contains information about the interaction between the i and j components and can be deduced from Sii using Eqs (3)-( 5) below.

Results of PSF analysis
I(q) profiles are plotted as a function of q in Figure 1 for representative fD2O in the CV-SANS measurements.They show typical scattering features in that a small-q upturn and two scattering maxima in three q-regions.In region I at q < 0.12 nm −1 , the small-q upturn follows a power-law relationship with an exponent of about −2.4.
In Region II at 0.12 < q < 1.7 nm −1 , a shoulder-like scattering peak appears at q1 ~ 0.17 nm −1 , corresponding to a d-spacing (=2π/q1) ~ 36.9 nm.In Region III at q > 1.7 nm −1 , the second scattering peak, so-called "ionomer peak", appears at q2 = 2.6 nm −1 , with a d-spacing (=2π/q2) of 2.4 nm.The self-terms of PSFs including SBP-BP, SGP-GP, and SW-W were calculated based on section 3.1 and plotted as a function of q in Figure 2. In Region I, all Sii exhibit an upturn with a power-law exponent of about −2.4.In Region II, all Sii shows a shoulder-like scattering maximum with a centre position close to the peak observed in I(q) profiles in Figure 1.In Region III, SGP-GP and SW-W show a peak with a centre position close to the ionomer peak, and the peak in SGP-GP is broader than that in SW-W.On the contrary, SBP-BP in Region III is flat, revealing ETFE BP is structureless at this length scale.With these three Sii, all reconstructed I(q) profiles (solid lines) using Eq (2) via back-substitution are well matched to the experimental profiles (symbols) in Figure 1, evidencing the correctness of Sii.
As mentioned in section 3.1, Sii reflects the concrete structure of the i component, including its arrangement and phase-separated morphology in the membrane.Since Sii show similar features to the previously studied ETFE-g-PSSA PEMs with an IEC of 2.0 mmol/g (denoted as ETFE-g-PSSA_2.0)[12], we reasonably propose the same fitting functions here to interpret Sii: Mass fractal (MF) structure to describe the smallq upturn in Region I, the unified Guinier-exponential function (GE model) to fit the shoulder peak in Region II, and Teubner-Strey (TS) model to describe the local structure in Region III.However, it should be noted that the scattering origin for the two membranes ETFE-g-PSSA_2.0 and ETFE-g-PSSA_2.5 are different.It is the aggregation of individual GP nanodomains in the hydrophobic BP matrix that makes the structure pattern of ETFE-g-PSSA_2.0, while the structure of the ETFEg-PSSA_2.5 is originated from the aggregation of hydrophobic BP nanodomains in the GP matrix.This difference is evidenced by taking account of the volume fraction of BP in the hydrated PEMs, φBP, where dx (x=BP, GP and W) is the mass density of x being approximately 0.55 and 0.3 for ETFE-g-PSSA_2.0 and ETFE-g-PSSA_2.5, respectively.Thus, Sii of ETFE-g-PSSA_2.5 is the sum of the three models given by Sii(q)=C1SMF(q)+C2SGE(q)+C3STS(q)+CB (7) where C1, C2, and C3 are the fitting constants, and CB is the constant background.The first term SMF(q) is expressed as which is the MF function with the gamma function (Γ), MF dimension (Df), and the upper cutoff length of the MF structure (ξ) being roughly estimated as ~150 nm according to the previous report using the Ultra-SAXS method [13].The second term,   (), is proposed to describe the structure of irregularly shaped individual BP nano-domains as expressed below.
where Rg is the radius of gyration of individual BP particle, erf(x) is the error function of x, k is an empirical constant equal to 1.06.P (3 < P < 4) describes the particle's surface fractal dimension, and B is a constant prefactor.The third term,   () , is the scattering function of the TS model describing bicontinuousshaped domains with short-range order as below: where d is the mean separation distance between two domains determined from the peak position, qm ( = 2π/  ), and ε is considered as the dispersion of d (inversely proportional to the peak width).A smaller ε resulted from a broader peak indicates a more disordered bicontinuous structure.The best-fitted curves obtained using Eq. ( 7) are shown together with Sii in Figure 2, and all the fitting parameters are listed in Table 1.
Table 1.Fitting parameters in Eq (7).The PSF cross-terms Sij (i ≠ j) through Eqs.(3)−( 5) reflect cross-correlation between the components i and j.The positive and negative sign of Sij reveals the interaction force between i and j, denoting attractive and repulsive interactions, respectively.The cross-terms of PSFs as a function of q are shown in Figure 3. SBP-GP and SBP-W are always negative, whereas the sign of SGP-W is opposite at q lower and higher than 1.5 nm −1 as shown in the inset, respectively.Fig. 3 PSF cross-terms of the fully hydrated ETFE-g-PSSA_2.5 PEMs.Enlarged plots at q > 1 nm −1 in the inset.

Large scale structure
The MF model describes a structure consists of selfsimilar polymer particles within a spatial range.Based on the analysis of Sii in Region I, the schematic picture of the large-scale structure is shown in Figure 4 (a).Note that BP hydrophobic domains are clearly phaseseparated from hydrophilic domains made of GP and water, as evidenced by the repulsive interactions suggested by the negative sign of SBP-GP and SBP-W.All

Middle scale structure
The GE model analysis in Region II shows all domains have a characteristic Rg of ~10.0 nm, which is the average size of the individual building blocks for each component to form the MF structure in Region I. Since GP and water domains coordinatively move, we reasonably conclude that BP nano-domains with a size of Rg = 10 nm are distributed in the homogeneous matrix of GP and water.The power-law relationship in the high-q-regime in Region II allows for the estimation of P, which is an indicative of the surface roughness of the domain.P is in the range 3.1-3.3,smaller than the typical sharp Porod surface (P = 4), indicating a rough domain surface.Based on the above discussion, a schematic of the structure in Region II is shown in Figure 4(b).

Small scale structure
The detailed local structure in a GP/water domain is explained by TS model analysis of SGP−GP and SW−W that shows both components have bicontinuous-like structure with similar d value (2.2−2.3 nm) as schematically shown in Figure 4(c).SGP-W is negative in this region with a molecular length level < 3.7 nm (q > 1.7 nm -1 ), indicating a repulsion between GP and water probably due to the strong repulsive force between PS polymer and water.This result is in good agreement with what we observed in ETFE-g-PSSA_2.0 PEM, and much different from Nafion membrane where the interaction between polymer side chain and water are positive.This considerable difference results in the low swelling of ETFE-g-PSSA_2.5 PEM but high conductivity under low relative humidity conditions, as compared to Nafion.
The detailed structure evolution of ETFE-g-PSSA_2.5 at multiple length scales illustrates the power of PSF analysis to gain insight into structure-property relationships in disordered and bi-continuous systems.

Conclusions
We applied PSF analysis to gain quantitative knowledge of the role of each component in the entire structure of fully hydrated radiation-grafted ETFE-g-PSSA_2.5 PEMs by CV-SANS experiments.Our results suggested three-component domains consisting of ETFE base polymer, PSSA graft polymers and water.PSF selfterms analysis revealed the detailed structure of each component, whereas the cross-terms gave the correlation between two components, leading to the location determination of the components.The entire structure patterns of the hydrated PEM were constructed in Figure 4. PSF analysis provides mechanistic insights concerning structural correlations over a range of length scales, from micro-/nano-meter to molecular scale, which offers the structural guidelines in the design of high-performing PEMs for a wide range of energy conversion applications.

Fig. 1
Fig.1Experimental scattering intensity profiles (symbols) and the reconstructed intensity profiles (solid lines) of the fully hydrated ETFE-g-PSSA_2.5 PEMs equilibrated in water mixtures of D2O and H2O with different ratios.
components show a similar mass fractal structure with a dimension of Df = 2.4, indicating a dense packing of BP nano-domains in space, close to percolating networks.Instead, GP and water domains form the compensative matrix according to Babinet's principle, therefore, SGP-GP and SW-W shows the same MF structure feature as SBP-BP does.In addition, the positive SGP-W indicates that water is closely attached to GP due to the hydrophilic nature of SA groups.Therefore, water domains coordinatively move with GP domains.

Fig. 4
Fig. 4 Schematic of the hierarchical structure of the individual components in the fully hydrated ETFE-g-PSSA_2.5 PEMs at (a) large-scale; (b) middle-scale; and (c) small-scale.