Accelerating SAXS Data Interpretation: A Comparative Assessment of Backbone-Dependent Morphology in Radiation-Grafted Anion-Exchange Membranes

Abstract

Anion exchange membranes (AEMs) are key components in electrochemical energy devices, where nanoscale morphology governs water and ionic transport and overall performance. In the growing interest toward radiation-grafted AEMs, the influence of polymer backbones on properties remains insufficiently explored. Here, we investigate how differences in backbone chemistry between ethylene tetrafluoroethylene (ETFE) and low-density polyethylene (LDPE) affect the AEMs bearing identical functional groups. Small-angle X-ray scattering (SAXS) is combined with ex situ characterization to provide an overview of bulk properties. LDPE-based membranes show ∼30 percentage points higher water uptake and swelling compared to ETFE films, which is consistent with the typically reported crystallinity for LDPE relative to ETFE and the correspondingly greater chain mobility of its matrix. The d-spacing values extracted from SAXS profiles (22−35 nm) do not always mirror bulk hydration behavior: higher degrees of functionalization of LDPE membranes show greater swelling yet reduced spacing, demonstrating that bulk and nanoscale structural responses are decoupled. Additionally, to reduce the barrier to adopting SAXS in the membrane community, we developed TRAMA. This Jupyter Notebook-based platform guides researchers through the data analysis workflow without prior expertise. This work highlights the critical role of the polymer backbone in determining AEM morphology and the value of SAXS as a characterization tool, providing an accessible means of processing scattering data.

1. Introduction

Electrochemical energy conversion devices that operate using ion-exchange membranes (IEMs) are central to the green energy transition, with a wide range of fuel cells, electrolyzers, and batteries making use of the solid polymer electrolyte’s ability to provide rapid ion transport and to mediate electrode reactions while separating anode and cathode compartments. The performance and durability of such devices depend on IEM properties that are profoundly governed by its nanoscale morphology, as it controls the rate and selectivity of ion transport, viscoelastic and chemo-thermal stability, as well as water and gas permeability - all of which have to be carefully balanced. One characterization method that provides insights into the internal structure of IEMs is small-angle X-ray scattering (SAXS). SAXS probes structural features on length scales from approximately 1–100 nm, capturing morphological periodicity and interdomain correlations, such as lamellar stacking and ionic cluster spacing. Unlike imaging techniques, which provide information on surface features, SAXS can provide insights into the bulk morphology of a polymer film under study. More specifically, features present in scattering patterns reflect electron-density fluctuations and thus correlate with characteristic length scales, making it particularly powerful for correlating backbone effects with nanoscale domain organization and degree of order in polymeric membranes. This information is paramount for understanding phase separation, domain spacing (d-spacing), and the distribution of aqueous-ionic domains within a given material. When supplemented by hydration and swelling ratio measurements and resistivity evaluations, it enables a holistic understanding of the internal morphology of an ion-exchange membrane.

Among IEMs, the perfluorosulfonic acid (PFSA)-based Nafion is arguably the most studied and best understood material, having been at the center of technological advances in energy conversion devices for decades. It has been demonstrated in Nafion and other PFSA-type polymers that backbone-driven organization strongly influences the formation of ionic clusters and hydrated domains, which are responsible for the characteristic peaks observed in SAXS profiles, as shown by Kreuer and Portale. , Beyond PFSA systems, block copolymer ion-exchange membranes provide an important model platform for disentangling backbone effects: their ability to form well-ordered morphologies such as gyroids, cylinders, and lamellae enables systematic evaluation of how nanoscale domain architecture controls ion and water transport. , These structured polymer electrolytes reveal that ionic conductivity depends sensitively on morphological order, domain connectivity, and the chemical environment of ionic segments, as demonstrated in recent studies on self-assembled block copolymer electrolytes with varied side-chain chemistry. ,

Moreover, some studies have applied SAXS to commercial and commercially relevant anion-exchange membranes (AEMs), providing initial insights into their nanoscale organization, with broad scattering peaks reported in the q range of approximately 0.03–0.3 Å⁻¹. However, in many works, the influence of the backbone is not highlighted. Luo et al. examined both commercial FAA-3 and poly­(arylene piperidinium)-type membranes in multiple counteranion forms, comparing dry and water-equilibrated samples at 25 °C. Only weak, broad peaks were observed for both membrane types, with no appreciable change upon hydration, heating, or counteranion exchange. Marino et al. measured the stacked FAA-3 membrane layers in bromide and hydroxide forms across a wide range of water volume fractions. A clear dependence of the scattering profile on both counterion type and hydration level was demonstrated. Mazumder et al. studied a series of poly­(arylene piperidinium) copolymers in the hydroxide form after equilibration in water at room temperature. They reported well-defined ionomer peaks attributed to microphase separation between hydrophilic ionic clusters and the hydrophobic backbone.

In this work, we investigate the class of radiation-grafted (RG) anion-exchange membranes, which are particularly promising for use in AEM-based fuel cells and other devices, yet pose a challenge for describing their internal structure. − This is related to the RG AEM preparation method, which involves grafting of vinyl monomers onto an existing base film, creating polymer brushes on top of the existing backbone scaffold that are later converted to highly ionic moieties. To elucidate the influence of base film backbone chemistry on the internal morphology of an RG AEM, we have chosen the semicrystalline polymers ethylene-tetrafluoroethylene (ETFE) and low-density polyethylene (LDPE) as base membrane platforms. The presence of fluorine atoms (C–F) in the ETFE backbone, in contrast to the purely aliphatic (C–H) LDPE structure, is expected to result in greater backbone rigidity and a distinct hydrophobic/hydrophilic balance, thereby influencing grafting behavior and water transport. Radiation-grafted vinyl pendants functionalized with identical quaternary ammonium (QA) groups are compared to isolate the influence of the base film backbone. To date, research on radiation-grafted AEMs has been limited to a few studies, with no particular focus on the nanoscale structure of the base film or its dependence on the chemical origin of the backbone. − Structural studies on the more extensively studied radiation-grafted cation-exchange membranes have shown that the base film nanostructure is largely conserved upon grafting and that the lamellar spacings initially grow, reaching full saturation with increasing grafting. − In this work, we take an in-depth look into the characteristics of the selected representative AEMs to show the decoupling of the nanoscale and bulk structural response in relevant hydrated and electrolyte-saturated conditions. Additionally, we introduce TRAMA, a Jupyter Notebook-based script that enables SAXS data analysis, accommodating various backbone-structure implications and accounting for potential sample anisotropy that standard SAXS instrument software, developed for high-crystallinity samples, does not automatically account for. A survey of SAXS characterization across the AEMs literature reveals that the majority of studies rely on instrument-bundled commercial software or beamline-specific pipelines for data reduction, followed by self-developed scripts for parameter extraction, an approach that is difficult to reproduce across research groups. ,,, Where a shared open-source tool appears, SasView is the sole example, yet even within this community, it is employed exclusively for d-spacing extraction. This reflects both the absence of a community-standard analysis workflow and the fact that d-spacing is the operationally central parameter for IEM characterization, as also demonstrated by this study. Rather than adding analytical complexity, TRAMA establishes a portable, standardized workflow that makes SAXS characterization of ion-exchange membranes accessible to a broader research community.

2. Results and Discussions

2.1. Membrane Preparation and Characterization

Radiation-grafted membrane samples with varying degrees of grafting (DoG) and attached vinyl units were fabricated independently (ETFE-based from PSI, Switzerland; LDPE-based from the Institute of Energy and Nuclear Research (IPEN), Brazil). For each, two types of membranes with lower and higher grafting degrees are compared. Membrane samples in the manuscript are labeled based on three parameters: backbone chemistry, DoG, and counterion form. For example, E74-OH represents the ETFE backbone, 74% DoG, and the hydroxide form, or L38-HCO3 stands for LDPE, 38% DoG, and the bicarbonate form. The listed ionic forms, as well as KOH and KHCO₃ electrolyte solutions, are frequently encountered in AEM applications. ,, Functionalization was carried out heterogeneously via submersion of membranes in trimethylamine solution to substitute chloride on the vinyl unit with charged quaternary ammonium groups (QA), as shown in Figure .

1.

Functionalization step schematics of radiation-grafted membrane preparation: (A) ETFE-based sample and (B) LDPE-based sample. Structures are shown with a potential ether linkage, which is to be assumed given the peroxidation of irradiated samples stored under air.

Quaternization was confirmed by Fourier-transform infrared spectroscopy (FT-IR) (Figure S1), where the appearance of a characteristic band at 1635 cm⁻¹ (C–N stretch) and a band at 3375 cm⁻¹, assigned to O–H stretching and bound water, indicated successful functionalization, which, for the calculation of theoretical IEC, was assumed to be near-quantitative, and is supported by the agreement between titrated and theoretical IEC for the high-DoG samples. , Table shows the IEC values obtained via acid−base titrations for each membrane; these values correlate well with the calculated theoretical IEC for ETFE-74 and LDPE-76, with deviations below 10%. Low-DoG samples show higher deviations, as can be expected for a higher fraction of vinylbenzyl chloride (VBC) pendants that remain inaccessible during amine substitution. Films with a lower degree of grafting, such as ETFE-42 and LDPE-38, exhibit a lower ion-exchange capacity because fewer grafted sites are available for incorporation of the cationic QA functional group, making the correlation between DoG and IEC straightforward and independent of the backbone structure.

1. Ex Situ Characterization Summary Table.

Backbone	DoG (%)	Form	IECt (mmol g–1)	IEC (mmol g–1)	WUgravimetric (%)	λ	SRt (%)	SRa (%)	σ (mS cm–1)
ETFE	42	OH−	1.80	1.39 ± 0.19	45.3 ± 8.4	18.0	32.7 ± 3	22.2 ± 2.8	133.7 ± 57.5
		HCO3 −	1.66	1.31	25.8 ± 4.8	10.9	9.5 ± 1.9	16.8 ± 1.5	19.2 ± 8.3
	74	OH−	2.50	2.45 ± 0.03	70.1 ± 9.1	15.9	32.7 ± 2.5	41.1 ± 6.6	265.4 ± 58.4
		HCO3 −	2.26	2.21	36.4 ± 4.7	9.2	9.1 ± 1.1	17.9 ± 8.5	53.9 ± 13.8
LDPE	38	OH−	1.68	1.44 ± 0.08	43.3 ± 4.3	16.7	10.9 ± 0.5	35.4 ± 1.8	46.7 ± 8.1
		HCO3 −	1.57	1.35	31.4 ± 1.5	12.9	8.7 ± 1.2	18.1 ± 1.9	3.8 ± 0.1
	76	OH−	2.54	2.30 ± 0.06	101.7 ± 0.6	24.5	23.1 ± 1.2	64.5 ± 0.7	221.8 ± 16.8
		HCO3 −	2.28	2.09	58.5 ± 4.5	15.5	14.4 ± 1.7	34.7 ± 2.6	55.0 ± 1.5

^aIEC determined on Cl⁻ form membranes; values for OH⁻ form and HCO₃ ⁻ form are converted to the mass basis of the respective ionic form.

^bConductivity measured in respective electrolyte solutions: 1 M KOH (OH⁻ form) and 1 M KHCO₃ (HCO₃ ⁻ form).

Water uptake (WU) results complement these observations, showing that doubling the DoG roughly doubles the WU of the LDPE-based membranes (2.3-fold in the OH form), whereas the increase is less pronounced for ETFE-based films (1.5-fold), indicating that the rigid fluorinated scaffold limits osmotic pressure-driven expansion. Additionally, due to the larger hydration shell of hydroxide ions and their strong polarization of the surrounding water, membranes in the OH form exhibit significantly increased WU and directional (both through- and in-plane) swelling, regardless of DoG. At the same time, the bulkier and less solvated bicarbonate ion does not cause either a substantial increase in absorbed water or domain expansion. When evaluating the hydration number, it becomes clear that the backbone chemistry plays a significant role: the more rigid ETFE backbone appears to better withstand the osmotic swelling pressure in the wet state, even at high IEC and in the strongly solvated hydroxide ion form, as hydration numbers for ETFE samples are very similar at low and high IEC. Conversely, in the LDPE samples, a significant increase of almost 50% in the hydration number - especially in the hydroxide form - is seen when comparing low- to high-IEC samples. Differences in base-polymer crystallinity between these systems contribute to differences in chain mobility, free volume, and WU. Franklin et al. demonstrated that an increase in the high-density polyethylene membrane crystallinity starting from 57−60% to above 81% increased the crystalline domain sizes and lamella width distributions, while reducing the orientational order of the lamellae which resulted in increased WU. At the same time, Sproll et al., using ETFE base films with 33.5% and 36% crystallinity, showcased that the bulk value alone does not describe the material sufficiently and crystallite size and number density play a role in evaluating the uptake results. When comparing materials with different backbone densities more closely, it is important to note that DoG alone does not provide an unbiased comparison basis, because ETFE and LDPE have significantly varied repeat-unit masses and density; identical DoG values correspond to different graft densities per backbone repeat unit (or per volume), as can be seen in Table . Notably, the volumetric graft concentration of ETFE-42 matches that of LDPE-76 despite the difference in DoG. The membranes in this study are therefore compared at a matched IEC of the final membrane, as the application-relevant quantity. Different ways can be applied to compare the present samples, e.g., by expressing charge density volumetrically, as shown in Table . In a simple approximation, using the water density (1 g mL^–1), the dry densities of the polymers can be derived by comparing gravimetric WU and volumetric swelling. Using high-DoG samples in their hydroxide form for this (to make use of large swelling and uptake values for this rough estimation) approximated effective polymer densities (grafted LDPE, approximately 1.00 g mL^–1; grafted ETFE, approximately 1.25 g mL^–1), and then allowed the calculation of the water volume fractions (ϕ _W , given in vol %) and the volumetric ion-exchange capacity for each material. These values are rough estimates sufficient for the comparative purpose here and are consistent with the expectations from the base film densities, diluted by the graft component. On this basis, ETFE-74 and LDPE-76 in their hydroxide forms, which, by gravimetric WU, appear to differ significantly, with lower ETFE-74 WU values of around 30 percentage points, in fact exhibit similar water volume fractions in the swollen state (47−50%), indicating comparable hydrated morphologies (Figure S2). Crucially, wet volumetric IEC is higher for ETFE (1.67 mmol mL^–1, compared to LDPE-76, 1.26 mmol mL^–1), indicating greater ionicity in the swollen state. This helps explain why membranes with similar water contents can still differ in conductivity and why hydration number λ values should not be interpreted in isolation when comparing different material classes.

2. Grafting Level and Ion-Exchange Capacity of the AEMs, Normalized per Mass, per Backbone Repeat Unit, and per Volume (in the Hydroxide Form).

Backbone	DoG (%)	Grafted VBC (mmol g–1 base film)	Graft concentration (mmol mL–1 base film)	Grafts per repeat unit	IECt (mmol g–1)	IECV (dry) (mmol mL–1)	ϕW (vol %)	IECV(wet) (mmol mL–1)
ETFE	42	2.75	4.7	0.35	1.80	2.25	36	1.44
	74	4.85	8.2	0.62	2.50	3.13	47	1.67
LDPE	38	2.49	2.3	0.07	1.68	1.68	30	1.17
	76	4.98	4.6	0.14	2.54	2.54	50	1.26

^aGrafted VBC given per gram and per volume of pristine base film (ρ = 1.70 and 0.92 g mL^–1 for ETFE and LDPE, respectively).

^bIEC_t is calculated based on the hydroxide form.

^cVolumetric IEC and water volume fraction ϕ _W are calculated with effective membrane densities of 1.25 (ETFE) as estimated in the text.

^dVolumetric IEC and water volume fraction ϕ _W are calculated with effective membrane densities of 1.00 g mL^–1 (LDPE) as estimated in the text.

^eWet values refer to the hydroxide form samples swollen in water.

Ionic conductivity measured in the corresponding electrolyte solutions displays a similar trend seen above, with conductivities in the bicarbonate solution matching well with previously reported data. Slightly elevated conductivity values in hydroxide solution may be accounted for by an excess of KOH in either the swollen membranes (as the uptake) or the excess liquid electrolyte during measurement but are within expectations. Generally, hydroxide-ion mobility, which is approximately 5 times that of HCO₃ ⁻, accounts for the higher conductivity of samples measured in an alkaline solution.

2.2. X-ray Scattering Characterization

All samples were evaluated in the dry state, in fully hydrated (submerged in water) hydroxide and bicarbonate forms, and in 1 M KOH and 1 M KHCO₃ electrolytes. The Mylar (biaxially oriented polyethylene terephthalate) film was used as windows for the custom sample contraption because of its minimal scattering, which is essential for reducing background noise.

Before collecting data on the samples of interest, Nafion membranes were used as a well-characterized reference material to validate and optimize the measurement methodology, as summarized in Figure . Counterion form, collection time, and sample thickness were varied under hydrated conditions to determine the optimal measurement configuration.

2.

SAXS profiles of Nafion NR212 showing the qualitative optimization of measurement parameters: (A) counterion influence; (B) collection time; and (C) sample thickness. Measurements were performed in water at room temperature.

While considering the influence of the counterion on the charged groups of the ion-exchange membrane, two factors should be accounted for. In the presence of such an ion near the polymer’s charged site, the electron density distribution exhibits a degree of inhomogeneity, with detectable local contrast (difference between the electron density of the polymer backbone and that of the ion), which enhances scattering. Additionally, ionic domain spacing and aggregation are influenced by the presence of counterions due to the ion-dependent hydration and swelling of the charged polymer. These considerations apply to a dry measurement of the polymer film in SAXS; however, when the measurement is performed in water, the hydration of the polymer film sample plays a larger role, hence the ion that ensures a higher hydration number (more water molecules around the charged site of the polymer) would also ensure a better contrast and consequently better scattering. ,, As can be seen from Figure A, the sample ion-exchanged into its proton form displayed a stronger scattering response, resulting in a curve with distinct features corresponding to the expected ionic domain spacing of a Nafion membrane. This is consistent with the ionomer peak position reported in the literature at q = 1.4 nm⁻¹, whereas our measurement yields q = 1.5 nm⁻¹, obtained from a Gaussian fit of the peak as described in Section . At the same time, the Cs-doped sample had significantly more dispersed scattering, resulting in a curve with no traceable peaks characteristic of Nafion's charged groups. Despite the higher electron density of Cs⁺, which would in principle enhance electron density contrast, the reduced hydration of Cs⁺ relative to H⁺ leads to less swollen ionic clusters, diminishing the structural contrast that drives the characteristic scattering features. Conversely, H⁺ counterions promote a larger hydration shell, preserving the nanoscale contrast and yielding the well-resolved scattering profile typically observed for Nafion. This suggests that the trade-off where the heavier counterion can potentially provide a better contrast vs the ionic form of the polymer that would result in more hydrated charged clusters has to be considered carefully when conducting SAXS measurements on IEMs.

The primary rationale for optimizing the collection time is to improve the signal-to-noise ratio. Because X-rays have inherently low intensities at small angles, longer exposure to the beam allows the prolonged collection of scattered photons, which improves data accuracy, enabling more reliable structure-factor fitting and the detection of weaker features. As shown in Figure B, the collection time was varied between 1, 5, and 30 min, with the latter two yielding better-defined profiles due to improved counting statistics.

The optimization of the sample thickness via layering was conducted for the specific X-ray beam energy and the desired q range (Figure C). The scattered intensity is proportional to the amount of material the beam interacts with. This is especially pronounced in the case of thin polymer samples with weak nanoscale heterogeneities. A sample with ahigh volume (a layered membrane sample to increase thickness) would provide more detectable features along the beam path, enhancing the visibility of characteristic SAXS peaks. A single-layer sample of 55 μm has resulted in a less defined profile, while 5 layers (275 μm) and 10 layers (550 μm) show a significant improvement. At the same time, beyond 275 μm, the improvement in signal quality becomes marginal as further gains in scattering volume are offset by increased X-ray self-absorption.

Once this optimization methodology was established using Nafion, the same approach was applied to ETFE- and LDPE-based AEMs, yielding an optimal collection time of 20 min and a sample thickness of 50−80 μm. Both hydroxide and bicarbonate counterion forms were found to provide adequate scattering contrast and were therefore used for all samples. With these parameters established, SAXS intensity profiles, I(q), as a function of the scattering vector magnitude, q, were collected. Resulting curves are presented in Figure for the OH⁻ and HCO₃ ⁻ ionic forms of each membrane in dry and fully hydrated states. The profiles are vertically shifted for clarity. All profiles display a broad, ill-defined scattering shoulder in the low-q region (q = 0.01–0.04 Å⁻¹), indicative of a nanoscale organization between hydrophilic and hydrophobic domains within the membrane matrix, while a secondary scattering feature at higher q (q = 0.04–0.08 Å⁻¹) is exclusively observed in the LDPE-based membranes.

3.

SAXS intensity profiles I(q) as a function of scattering vector q for dry and water-submerged membranes: (A) LDPE-based membranes in the OH⁻ form. (B) LDPE-based membranes in the HCO₃ ⁻ form. (C) ETFE-based membranes in the OH⁻ form. (D) ETFE-based membranes in the HCO₃ ⁻ form.

For the ETFE-based membranes, the single shoulder is consistent with the lamellar periodicity of the semicrystalline matrix, as reported for analogous radiation-grafted ETFE membranes. , The shoulder shifts toward lower q upon immersion in water, reflecting the expansion of the amorphous layer as water is absorbed into the regions where the graft chains and ion-conducting groups reside. Notably, the low-q shoulder is more defined in the ETFE-based membranes than in the LDPE-based membranes, suggesting a higher degree of structural organization in the ETFE matrix, consistent with its more regular semicrystalline lamellar architecture.

For the LDPE-based membranes, the primary shoulder shifts similarly to a lower q upon hydration. The secondary higher-q feature, absent in the pristine polyethylene substrate and arising only after grafting and quaternization, is attributed to the characteristic interdomain spacing between the ionic domains, formed by QA groups, counterions, and associated water, and the surrounding hydrophobic matrix. , In contrast to the primary shoulder, the secondary feature shows minimal sensitivity to the hydration state and DoG, with the corresponding d-spacing remaining nearly constant across all LDPE samples, ranging narrowly between 10 and 10.7 nm.

The d-spacing values extracted from the primary low-q shoulder are presented in Figure as a function of the DoG and membrane state. For LDPE-based membranes, d-spacing values range from 25.6 to 35.3 nm, while ETFE-based membranes display a range of approximately 21.6–33.5 nm across all ionic forms and hydration states. A supplementary data set for the ETFE-based samples is presented in Table S2 (Supporting Information). ETFE- and LDPE-based membranes show opposite trends with increasing DoG (Figure A): d-spacing increases in ETFE, consistent with progressive expansion of the amorphous lamellar layer as graft chains are accommodated within it, while it decreases in LDPE, likely reflecting structural reorganization of the less constrained polyethylene backbone under increasing graft density and cross-linking. This decrease is particularly noteworthy given that the higher-DoG LDPE sample simultaneously exhibits significantly greater WU and swelling ratio, demonstrating that water absorption and domain spacing are not directly correlated and cannot be used interchangeably as proxies for hydration-driven structural changes. Upon immersion in water, d-spacing increases for all samples regardless of the base polymer, ionic form, or DoG (Figure B,C), confirming that hydration drives the swelling of the hydrophilic domains in both membrane families, in agreement with the positive WU and swelling ratio values reported in Table . Immersion in a 1 M electrolyte solution produces a further increase in d-spacing for LDPE-based membranes in both ionic forms. ETFE-based membranes respond differently: the low-DoG sample is largely unaffected by the electrolyte, while the high-DoG sample shows a significant and ionic form-dependent response. For these samples, d-spacing increases further in KOH but decreases in KHCO₃, which might indicate a larger importance of the hydration carried by the counterion in more hydrophobic materials, such as ETFE. The contrasting structural behavior of the two membrane families in the OH⁻ form is further highlighted in Figure S4, where d-spacing and hydration number are plotted as a function of IEC_v(wet). In ETFE-based membranes, higher DoG results in a larger d-spacing but a lower hydration number, suggesting that the fluorinated backbone maintains its lamellar order upon grafting, allowing modest domain expansion while distributing water less efficiently per functional group. In LDPE-based membranes, the trend is reversed: a higher DoG yields a smaller d-spacing alongside a larger hydration number, consistent with grafting-induced reorientation of the more mobile polyethylene crystalline domains, which, despite reducing the channel size, enables more efficient water coordination per quaternary ammonium group.

4.

Values of d-spacing extracted from the low-q shoulder as a function of DoG and hydration state. (A) The d-spacing as a function of DoG for ETFE- and LDPE-based membranes in both ionic forms, comparing dry and hydrated states. (B) Evolution of d-spacing across dry, hydrated, and electrolyte-immersed states for OH⁻ form membranes. (C) Evolution of d-spacing across dry, hydrated, and electrolyte-immersed states for HCO₃ ⁻ form membranes.

2.3. Data Processing Workflow

Despite the established utility of SAXS for polymer membrane characterization, existing software packages employ general-purpose approaches designed for diverse material systems, requiring researchers to configure workflows and select appropriate analytical methods manually. , No specialized tool has yet been developed to guide scientists working with ion exchange membranes through the complete SAXS analysis workflow in an accessible manner. This is particularly relevant for IEM characterization, where the amorphous and poorly ordered nanostructure typical for these materials produces broad and ill-defined scattering features that are susceptible to overfitting when complex models are applied, making d-spacing the most directly extractable and reproducible structural parameter from I(q) profiles. To address this, we developed TRAMA v1.0 (Tool for Rapid Analysis of Membrane Architecture). This Jupyter Notebook-based platform implements a strictly sequential pipeline from raw scattering data to d-spacing extraction with methodological annotations embedded at each step to guide the user through parameter selection and result interpretation, as illustrated by the three interactive widgets shown in Figure .

5.

SAXS analysis notebook workflow scheme. Key components of the notebook widgets are shown as a reference; this schematic does not represent the complete user interface. (A) Experimental parameter validation in the data loading interface. (B) Azimuthal integration with masking of noninformative regions from I(q) profiles. (C) Comparison tool for overlaying multiple I(q) profiles.

The first widget (Figure A) validates the experimental parameters and prepares data for quantitative analysis. Users load a SAXS image file (.edf, .ebf, .tiff) and an optional background measurement (essential for accurate structural quantification). The widget automatically extracts metadata (pixel size, sample-to-detector distance, and X-ray wavelength) from the file header. Note that TRAMA has been tested exclusively with .edf files, and compatibility with other formats cannot be guaranteed. The 2D scattering pattern is displayed with adjustable zoom controls for visual quality assessment, and an integrated centering workflow corrects beam center misalignment without requiring measurement repetition. Note that plotting artifacts may appear at high zoom levels (a window size of <300 pixels) but do not affect the underlying data or subsequent analysis. Users should verify that extracted metadata values match logbook entries and are in the correct units, as these parameters directly determine the accuracy of reciprocal space conversion and domain spacing calculations. The widget also calculates the maximum scattering angle and maximum accessible q value required for downstream analysis, as well as trims the data set around the scattering area.

The second widget (Figure B) generates I(q) profiles through azimuthal integration of the scattering pattern. First, module edges within detector arrays and other invalid regions are masked and excluded. Next, a Cartesian-to-polar coordinate transformation is performed, then the widget maps every pixel to a normalized radial distance and azimuthal angle relative to the beam center. User-defined radial (r-range) and angular (θ-range) bounds are applied to restrict integration to regions containing structural information. For anisotropic samples, angular sector selection restricts integration, preventing dilution of the structural signal by regions with no scattering, which would otherwise broaden peaks in the I(q) profile. Azimuthal integration is performed by averaging the intensity of valid pixels within logarithmically spaced radial shells, with an adaptive minimum pixel threshold per shell to ensure statistical reliability. When a background measurement is available, a scaling factor is derived from the average intensity of the direct beam region, where background transmission exceeds sample transmission, and applied uniformly before subtraction. The raw and background profiles are independently processed by an outlier removal function that identifies and interpolates anomalous intensity spikes, commonly arising from hot pixels (pixels registering anomalously high intensity) and dead pixels (pixels always reading zero), both of which are common artifacts in SAXS detectors. Both background subtraction and outlier removal are active by default and can be deactivated by the user. Finally, normalized radial coordinates are converted to physical scattering vector magnitudes. To extract characteristic domain spacings, the I(q) profile is transformed into q ²·I(q) vs q, enhancing broad structural shoulders; peak positions are identified and fitted with a multi-Gaussian model, and domain spacings are calculated from each peak position.

The third widget (Figure C) enables comparison of SAXS profiles by accumulating data sets and presenting both graphical and tabular outputs. Users progressively save data sets using the “Save Data” function, generating overlaid I(q) plots for visual comparison. Labels and plot titles are customizable, while a “Reset Storage” option clears accumulated data when initiating a new analysis series. Consistent visual comparison requires that all data sets be processed using identical q-ranges during azimuthal integration. The widget displays extracted structural parameters, such as d-spacing (d) and correlation length (ξ), enabling direct numerical assessment of trends across samples or processing conditions. Accumulated data sets and parameters can be exported to the CSV format and reimported in subsequent sessions. An additional model-fitting widget (Figure S5D), currently under active development, is available for users requiring physical model-based extraction of structural parameters from I(q) profiles. A full description of its capabilities and usage is provided in the Supporting Information.

3. Conclusion

In this work, we investigated how differences in backbone architecture influence the internal morphology of radiation-grafted AEMs bearing identical functional groups, correlating SAXS-derived structural parameters with bulk hydration and transport properties. SAXS is an essential tool for resolving such backbone-dependent morphological differences, probing structural features from ionic-cluster spacing to crystalline or semicrystalline packing in the polymer matrix. However, extracting meaningful structural parameters from raw scattering data requires a multistep analytical workflow that remains inaccessible to researchers without dedicated data processing expertise. To address this, we developed TRAMA, a Jupyter Notebook-based platform that guides users through the complete SAXS analysis workflow, from experimental parameter validation to d-spacing extraction, without requiring programming experience. Using this tool, the influence of the backbone on membrane properties was clearly demonstrated: LDPE-based samples exhibit a general trend toward higher WU and swelling, which can be attributed to greater chain mobility that facilitates structural reorganization to accommodate hydration water. In contrast, ETFE-based samples show better dimensional stability and lower WU at comparable degrees of grafting, owing to the high hydrophobicity of the fluorine-containing backbone that hinders water absorption and imparts greater structural rigidity. At the nanoscale, however, the d-spacing trends do not simply mirror bulk hydration behavior: the higher-DoG LDPE sample simultaneously exhibits significantly greater WU and swelling ratio yet reduced domain spacing, demonstrating that water absorption and domain spacing are not directly correlated and that bulk swelling measurements alone may not fully capture nanoscale structural reorganization.

4. Experimental Methods

4.1. Materials

N,N-Dimethylacetamide (DMAc, 99.9%, water <0.1%), supplied by VWR Chemicals, was purchased from Avantor. Methanol (99.9%, water <0.1%), trimethylamine (TMA) solution (31−35 wt % in ethanol, 4.2 M, containing toluene as a stabilizer), and cesium chloride (99.9%) were supplied by Sigma-Aldrich. Potassium hydroxide (KOH, ≥ 85%), supplied by Supelco, and potassium bicarbonate (KHCO₃, ≥85%), supplied by J.T. Baker, were purchased from Avantor. Nafion NR212 was purchased from Ion Power, Inc. All aqueous solutions were prepared using Milli-Q ultrapure water (UPW) (18.2 MΩ cm^–1 at 25 °C).

4.2. Membrane Grafting

Ethylene-tetrafluoroethylene (ETFE) films grafted with VBC were prepared in-house at PSI, Switzerland, similar to the procedure described elsewhere. ETFE films (Nowofol, Germany, 50 μm) were irradiated with a dose of 50 kGy using an EBLab 200 (COMET, 200 kV, 12 m min^–1 speed, 3 mA, air gap of 10 mm). Irradiated films were stored at −80 °C before use. An alumina-type inhibitor remover (Sigma-Aldrich) was used to prepare VBC (Sigma-Aldrich, 90% purity, containing 500 ppm tert-butylcatechol as inhibitor) for grafting and used directly afterward. Grafting reactors contained (by volume) 20% VBC, 1% surfactant (1-octyl-2-pyrrolidon, Sigma-Aldrich, 98% purity), and 79% isopropyl alcohol. Reactors were loaded with preirradiated films and purged with nitrogen for at least 1 h before being sealed and inserted into preheated sleeves (70 °C). Reactions were run for 1−7 h before being quenched and grafted films were extracted, washed, and sonicated in toluene multiple times to remove residual monomer and formed homopolymer. Finally, grafted films were dried at 80 °C in a convection oven and stored. Low-Density Polyethylene (LDPE), also grafted with VBC, was provided by IPEN, Brazil. The films (Goodfellow, 50 μm) were irradiated with doses of 30 and 100 kGy at low temperatures, as described elsewhere. The films were irradiated in a Dynamitron Continuous Electron Beam Unit from RDI-Radiation Dynamics Inc., USA, model DC 1500/25/4JOB 188 with a maximum energy of 1.5 MeV. For the grafting process, a mixture of 3- and 4-VBC was used as the monomer. More specifically, the grafting was carried out through the preparation of a solution containing 96.5% (v/v) of UPW, 1% (v/v) of the surfactant 1-octyl-pyrroline (98%, Sigma-Aldrich), and 2.5% of VBC (90%, Sigma-Aldrich), which was deoxygenated with N₂ for 30 min. In a sequence, the preirradiated film was immersed in the solution, which was deoxygenated for another 30 min. The N₂ flow was then stopped, and the reactor was immediately sealed and heated at 50 °C for 5 h under stirring. After the reaction ended, abundant acetone and toluene were used for washing the LDPE-grafted film, ensuring complete elimination of any homopolymer and residual impurities. The samples were dried at room temperature for 5 h in a vacuum oven and stored.

Membrane samples in the paper are addressed based on three parameters: backbone chemistry, DoG, and counterion form. For example, E74-OH stands for the ETFE backbone, 74% DoG, and hydroxide form, or L38-HCO3 stands for LDPE, 38% DoG, and bicarbonate form.

4.3. Membrane Functionalization

Both VBC-grafted ETFE and VBC-grafted LDPE were functionalized to prepare AEMs via nucleophilic substitution with a tertiary amine, forming positively charged quaternary ammonium (QA) ion-conducting groups. The reaction was carried out heterogeneously by submerging VBC-grafted precursor polymer films in a 1:2 (v/v) solution of TMA in DMAc at 60 °C overnight. A large molar excess of TMA relative to the available chloromethyl groups was deployed to ensure complete QA substitution on each available grafted site. The resulting AEMs were thoroughly washed with UPW and methanol to remove residual TMA, followed by storage in UPW. To confirm a successful functionalization of membranes, attenuated total reflectance (ATR)–FTIR spectra were recorded from 550 cm⁻¹ to 4000 cm⁻¹ using a PerkinElmer Spectrum Two FT-IR Spectrometer. After quaternization, membranes were converted to either hydroxide or bicarbonate form by submersion in 1 M KOH (aq.) or 1 M KHCO₃ (aq.) overnight, followed by rinsing with UPW to remove excess ions, followed by storage in UPW.

4.4. Gravimetric Water Uptake and Swelling Ratio

Water uptake (WU) (eq ), through-plane swelling ratio SR_t, and in-plane swelling ratio SR_A (eq and eq ) measurements were performed on at least 3 AEM samples of 3 cm × 1 cm size. Wet weight m _wet and thickness t _wet were measured with a Mettler Toledo AE200 Analytical Balance (0.1 mg readability) and Mitutoyo Digimatic Micrometer (0.001 mm readability), respectively, immediately after removing the samples from UPW to minimize evaporation and blotting them with a filter paper. For drying, membranes were again blotted, placed between folded filter paper sheets secured with tape to prevent rupture from shrinkage, and heated at 60 °C in the oven overnight. Dry weight m _dry and thickness t _dry measurements were taken immediately after removing samples from the oven to minimize atmospheric moisture uptake. The membrane’s dry area, A _dry, was determined by placing the samples between two polypropylene sheets, scanning them with an EPSON Perfection V39II and analyzing the images with ImageJ. For wet area measurements, A _wet, surface water was left to preserve the hydration state.

$$\mathrm{W}\mathrm{U}=\frac{m_{\mathrm{w}\mathrm{e}\mathrm{t}}-m_{\mathrm{d}\mathrm{r}\mathrm{y}}}{m_{\mathrm{d}\mathrm{r}\mathrm{y}}}\times 100$$ 1

$$\mathrm{S}{\mathrm{R}}_{\mathrm{t}}=\frac{t_{\mathrm{w}\mathrm{e}\mathrm{t}}-t_{\mathrm{d}\mathrm{r}\mathrm{y}}}{t_{\mathrm{d}\mathrm{r}\mathrm{y}}}\times 100$$ 2

$$\mathrm{S}{\mathrm{R}}_{\mathrm{A}}=\frac{A_{\mathrm{w}\mathrm{e}\mathrm{t}}-A_{\mathrm{d}\mathrm{r}\mathrm{y}}}{A_{\mathrm{d}\mathrm{r}\mathrm{y}}}\times 100$$ 3

4.5. Ion Exchange Capacity

Ion exchange capacity (IEC) was determined using the potentiometric method using acid−base titration. The Orion Star T940 all-in-one titrator was calibrated with an Orion ROSS 8102 glass pH electrode using pH 7 and pH 10 buffer solutions. At least 3 membrane samples were preconditioned in 1 M KOH solution overnight, thoroughly rinsed with water to remove excess hydroxide ions, and stored overnight in 0.1 M NaCl to promote ion exchange. For the measurement, the electrode was immersed in 0.1 M NaCl solution along with the membrane to ensure that any remaining OH⁻ ions trapped in the membrane would be released during the experiment. A solution of 0.1 M HCl (aq.) was added incrementally in 0.01 mL steps until the equivalence point was reached. The exact volume corresponding to a neutral pH was identified from the pH vs volume plot, and the IEC was calculated using eq , where V _ep is the volume of titrant used at the equivalence point, c is the concentration of the titrant, and m _dry is the dry mass of the membrane sample, in its chloride form. Measured values were converted to the respective mass basis of the discussed ionic forms. ,

$$\mathrm{I}\mathrm{E}\mathrm{C}=\frac{V_{\mathrm{e}\mathrm{p}}\times c}{m_{\mathrm{d}\mathrm{r}\mathrm{y}}}$$ 4

Theoretical IEC was calculated as a function of the DoG, using eq , where M is the molar mass of the indicated species. Complete functionalization of the VBC groups was assumed.

$${\mathrm{I}\mathrm{E}\mathrm{C}}_{\mathrm{t}}=\frac{1}{\frac{M_{\mathrm{V}\mathrm{B}\mathrm{C}}}{\mathrm{D}\mathrm{o}\mathrm{G}}+M_{\mathrm{V}\mathrm{B}\mathrm{C}}+M_{{{\mathrm{N}({\mathrm{C}\mathrm{H}}_3)}_3}^{+}}}$$ 5

4.6. Hydration Number

Hydration number λ represents the number of water molecules per ionic group and was calculated from the ratio of moles of water, n _H2O, per dry mass of polymer, m _dry, with respect to the IEC as shown by eq .

$$\lambda =\frac{n({\mathrm{H}}_2\mathrm{O})}{\mathrm{I}\mathrm{E}\mathrm{C}\times m_{\mathrm{d}\mathrm{r}\mathrm{y}}}$$ 6

4.7. Wet Volumetric IEC

Volumetric IEC was approximated by combining gravimetric IEC, WU, and geometric swelling of the membrane. First, combining area and through-plane swelling ratios provides the volumetric swelling factor (α), shown in eq .

$$\alpha =(1+\mathrm{S}{\mathrm{R}}_{\mathrm{t}})(1+\mathrm{S}{\mathrm{R}}_{\mathrm{A}})$$ 7

Assuming a water density of 1.0 g mL^–1 and attributing all volume expansion to absorbed WU, the wet volumetric IEC_V,wet was then calculated for a basis of 1 g dry membrane using the titrated IEC according to eq .

$${\mathrm{I}\mathrm{E}\mathrm{C}}_{\mathrm{V},\mathrm{w}\mathrm{e}\mathrm{t}}=\mathrm{I}\mathrm{E}\mathrm{C}\times \frac{\alpha -1}{\alpha }\times \frac{1}{\mathrm{W}\mathrm{U}/100}$$ 8

4.8. Ionic Conductivity

Conductivity measurements were performed using a two-compartment cell with nickel-perforated plate electrodes (2.5 cm × 2.5 cm). Since the membrane samples were cut to 3 cm × 1 cm in the dry state, PTFE gaskets were adapted to define an active measurement area of 0.9 cm × 0.9 cm. The membrane samples were presoaked in 1 M KOH (aq.) or 1 M KHCO₃ (aq.) solutions at room temperature overnight. The through-plane resistance of the membrane was determined at room temperature using electrochemical impedance spectroscopy (EIS) with a Gamry Reference 3000 instrument. The resistance R was taken as Z _re at Z _im = 0 Ω, and the conductivity (σ) was calculated as shown in eq , where t and A are the electrolyte-saturated thickness and surface area of the membrane, respectively.

$$\sigma =\frac{t}{R\times A}$$ 9

4.9. Small-Angle X-ray Scattering

SAXS measurements were performed on a Xenocs Xeuss 3.0 Pro instrument equipped with a Cu source (λ = 1.542 Å, flux = 100 Mph s^–1), a two-slit collimation system (S1 = 0.4 mm, S2 = 0.25 mm), an Eiger 4 M single-photon counting detector (DECTRIS), and a 0.9 m sample-to-detector distance in a vacuum chamber. Detector calibration was performed using silver behenate (AgBeh) as a positional standard, as detailed in the Supporting Information (Table S1). Flat-field correction was automatically applied by the Dectris detector firmware. Samples were tested under dry, fully hydrated, and electrolyte-saturated conditions, using 1 M KOH (aq.) or 1 M KHCO₃ (aq.). Preliminary tests using a Nafion membrane were conducted to assess the impact of exposure time, sample thickness, and counterion type on data quality. To perform the experiment under the desired conditions, a custom sample holder was used (Figure S3). The holder consists of two brass plates, two Mylar windows, and an O-ring to seal the membrane and liquid. This design ensures reliable sealing for SAXS measurements of samples submerged in water or electrolyte under vacuum. Data processing was carried out with a custom Jupyter Notebook TRAMA, which converts the 2D scattering patterns into one-dimensional intensity profiles via a multistep process described in Section . The scattered intensity is recorded as a function of the scattering wavevector q, whose magnitude is calculated with eq , where λ is the X-ray wavelength and θ the scattering angle, yielding the final I(q) profile in the range q = 0.05–2.5 nm⁻¹. In ion-exchange membranes, such contrast arises from the nanoscale phase separation between hydrophobic polymer backbones and hydrophilic ionic domains.

$$q=\frac{4\pi \sin \theta }{\lambda }$$ 10

The magnitude of q is inversely related to real-space length scales through eq , which is derived by substituting eq into Bragg’s law. The latter strictly describes the repeat distance in ordered periodic structures. In less ordered systems exhibiting only short-range correlations, such as the ionic domain morphology typical of AEMs, the same relation is applied, but d-spacing represents an average interdomain spacing, for instance, the mean distance between adjacent ionic clusters, rather than a true lattice periodicity.

$$d‐\mathrm{s}\mathrm{p}\mathrm{a}\mathrm{c}\mathrm{i}\mathrm{n}\mathrm{g}=\frac{2\pi }{q}$$ 11

Correlation length ξ complements the d-spacing by quantifying the spatial extent over which the average periodicity remains coherent. In practice, ξ is extracted from the width of the ionomer peak. A broader, more diffuse peak corresponds to a shorter correlation length and indicates that ionic domains are poorly organized, losing positional correlation over distances of only a few repeat units, whereas a narrower peak signals more persistent, longer range domain order.

4.10. Generative Artificial Intelligence Tools

TRAMA Jupyter Notebook scripts for SAXS data processing and analysis were developed with the assistance of Claude 3.5 Sonnet (Anthropic, accessed January 2025). Specific code segments generated by the AI were subsequently reviewed, adapted, and integrated by the authors, who verified the accuracy and reproducibility of all of the analytical outputs.

Jupyter Notebook TRAMA for data processing can be found at github.com/dtu-energy-polymer-research/TRAMA.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsmeasuresciau.6c00236.

• Detector geometrical calibration and peak fitting validation; FTIR spectra of membrane samples before and after functionalization, relationship between volumetric IEC and water volume fraction for characterized samples; schematic of a custom sample holder used for SAXS measurements; scatter plot correlation between IEC, hydration number, d-spacing; supplementary data set for ETFE-based samples with d-spacing data; and data processing workflow with the physical model fitting interface widget included and a short description of its functionality (PDF)

Conceptualization, A.K., A.L.; methodology, A.K., L.B., and A.L.; investigation, A.L., T.S., J.E.S.F., L.B.; visualization, A.L. and A.K.; writingoriginal draft, A.K. and A.L.; writingreview and editing, A.L., A.K., T.S., L.B., J.E.S.F., E.L.S.; supervision, A.K., E.I.S.

The authors declare no competing financial interest.