Evaluation of water states in thin proton exchange membrane manufacturing using terahertz time-domain spectroscopy

A


Introduction
Proton exchange membrane fuel cells (PEMFCs) are hydrogenfuelled electrochemical devices for clean energy conversion.Given their distinctive characteristics such as low temperature operation, high power density and compactness, PEMFCs have been recognised as a promising zero-emission power source for portable, mobile, and stationary applications [1].PEMFCs incorporate a solid electrolyte, known as the proton exchange membrane (PEM), which selectively conducts protons and water between the electrodes, while preventing electron transport and reactant mixing.The most common electrolyte materials for PEMFCs are perfluorinated sulfonic-acid ionomers (PFSAs) [2], which represents a class of synthetic polymers with ion-conducting properties whose chemical structure consists of a chemically inert and hydrophobic polytetrafluoroethylene backbone with side groups terminated with hydrophilic sulfonate groups.Proton conduction in PFSAs is highly dependent on its degree of hydration [3] and the mechanisms, such as Grötthuss hopping, electro-osmosis and back diffusion are related to the nature of water present [4].Depending on the degree of hydrogen bonding to the polymer's hydrophilic sulfonic groups, there are three main water states: bound water (strongly hydrogen-bonded and predominately bound to the hydrophilic domain containing the sulfonate groups [4,5]), bulk water (weakly hydrogen-bonded, exhibiting co-operative reorganisation of hydrogen bonds and the least interaction with the polymer backbone [5,6]) and free water (not hydrogen-bonded [7,8]).Increase in bulk water presence is generally associated with the formation of channels of weakly hydrogen-bonded water, which can combine isolated hydrophilic domains containing hydrated protons and sulfonate ions resulting in a continuous network.These in turn promote water diffusion and enhance proton conduction [9,10].To reduce the overall transport resistances for improving PEMFC performance, there has been a growing focus to decrease membrane thicknesses while incorporating inorganic fillers or additives (e.g.SiO 2 [11], TiO 2 [12], ZrO 2 [13], clays [14] and zeolite [15]) and reinforcements (e.g.expanded polytetrafluoroethylene (ePTFE) [16]) to produce chemically and mechanically stable composite membranes.These modifications are, however, known to affect membrane water properties [16][17][18][19] and therefore understanding this performance durability trade-off is crucial for optimisation.
To probe hydration in PFSA-based PEMs, various techniques have been demonstrated, for example gravimetric-based dynamic vapour sorption (DVS) [20], neutron scattering and imaging [21][22][23][24], microwave dielectric relaxation spectroscopy [4], Raman spectroscopy [25], Fourier transform infrared spectroscopy and variants [10], differential scanning calorimetry (DSC) [26][27][28], nuclear magnetic resonance spectroscopy [29,30], X-ray scattering [31] and more recently, terahertz time-domain spectroscopy (THz-TDS) [6,32,33].The terahertz portion of the electromagnetic spectrum (between 0.1 and 3 THz) is interesting because the dielectric response of water in this frequency range contains information on the reorientation dynamics of bulk relaxation peak at approximately 20 GHz [4] and free/fast water relaxation [6,34].In general, THz-TDS is an efficient technique for the coherent generation and detection of broadband terahertz radiation: a femtosecond pulsed near-infrared laser is focused onto a terahertz emitter (semiconductor photoconductive antenna or nonlinear crystal), where each optical pulse results in the excitation of sub-picosecond pulses with a bandwidth spanning from several hundred GHz to a few THz.The emitted terahertz pulses interacts with the sample and the resulting terahertz electric fields are measured through a coherent detection scheme either by means of photoconduction or electro-optical detection.The advantage of this approach is that the amplitude and phase of a terahertz pulse can be resolved with an excellent signal-to-noise ratio, which can be used to extract the sample's dielectric response in the form of complex refractive index, an intrinsic property of the material that includes both the refractive index and absorption coefficient at the terahertz spectral range.Advances made in THz-TDS have opened up many exciting industrial applications [35][36][37][38][39] where compared to aforementioned methods in PEMs testing, THz-TDS has been demonstrated to probe molecular water states non-destructively, without specialised sample preparation and without physical contact, producing data consistent with microwave dielectric relaxation spectroscopy [32] and water retention [6].Due to Fabry-Pérot reflections, however, acquired waveforms are analysed using numerical optimisation techniques [40][41][42][43][44][45][46] for parameter extraction.The dielectric response of hydrated PEMs are then fitted with double Debye model to quantify the water contributions [5,6,32,47,48].As prior work has focused on Nafion 117 (160-180 μm thickness) [6,32], we propose to use THz-TDS in this study to evaluate water content inside industrially relevant thin membranes (13-70 μm) prepared under different processing conditions and reinforcement loadings.In particular, we propose a parametric-based algorithm based on the double Debye model [6] to analyse our measurements and validate our analysis against literature [33] and complementary DVS measurements.By tracking the contributions of the relaxations, we examine the bulk, free and bound water contributions during a water desorption process for membranes prepared under various processing conditions.

Materials
Membranes used include commercial Nafions (117, 212 and 211) (Fuel Cell Store, TX, USA), ionomers A and B, which were prepared at different conditions (heat application, temperature, heat treatment duration) as summarised in Table 1 (Johnson Matthey, UK) and at different proportions of ePTFE reinforcement relative to a fixed ionomer equivalent weight i.e. effective equivalent weight (EEW).
A small design of experiment (DoE) was performed to systematically understand the effect of process parameters as summarised in Table 2.In particular, we investigated the application of heat treatment, their duration, temperature and the method of heat delivery.Owing to the commercially sensitive nature of the treatment, limited details can be disclosed.Membrane thicknesses were measured using a confocal microscope (Olympus LEXT OLS5000) with a 400-420 nm wavelength laser, assuming a refractive index of 1.36 [49].After removing the protective films, the samples were thoroughly rinsed with deionised water (Res: 18 MΩ cm) prior to measurement to remove impurities.For desorption measurements, the JMFC samples were hydrated from water vapour inside a home-made glass hydration chamber with 100% relative humidity (RH) for 24 h.This method of hydration is used to minimise sample surface water, which can cause significant measurement uncertainty [6,50].For direct comparison against literature [6,33], Nafion samples were soaked in DI water for 24 h, and excess surface water was removed with lint-free paper wipes.With the exception to Nafions, for each of the ionomer specimens investigated in Table 2 there were three repeats.

Experimental setup 2.2.1. Dynamic vapour sorption
DVS measurements were performed using a commercial analyser (Q5000SA, TA Instruments).Approximately 5-10 mg of the same sample used for THz-TDS were placed in an open quartz metal coated pan.The sample was equilibrated at 26 • C at 90% RH and an isotherm was recorded for 300 min.The RH was then set at 80% and the change of weight was monitored for another 30 min.Weight profiles were normalised at the end of the isothermal step from which, the rate of change of the profiles was calculated with the peak representing the maximum rate of change corresponding to the maximum driving force from 90 to 80% RH.The water adsorption isotherms were fitted with Park's multimode adsorption model [51] to extract water population associated to the mechanisms of Langmuir adsorption at low water activity, non-specific adsorption in accordance with Henry's law and clustering  at high water activity.Fitting details can be found in the SI.

Terahertz time-domain spectroscopy
We performed transmission terahertz spectroscopy using a commercial THz-TDS setup (TERA K15, Menlo Systems, Germany) as shown in Fig. 1.The hydrated Nafions and Ionomers A were measured during a 25 min water desorption process at ambient conditions (T = 26 • C, RH = 41%) while Ionomers B were measured under the same conditions for 15 min due to a reduced thickness.Terahertz waveforms were recorded every 1 min interval from 5 averages.Oven dried membranes (60 • C for 24 h) were also measured with THz-TDS.As a standard routine to all our measurements, a reference measurement was always acquired without the sample being present and taken immediately before the sample measurement to remove potential baseline drift.The acquired waveform of the terahertz electric field for both the sample and the reference were then converted to the frequency domain by fast Fourier transformation.

Analysis algorithm
In order to estimate the macroscopic water content in the PEMs, we use the method in Ref. [6] where an equivalent model of a hydrated membranes arranged as a dry membrane and a layer of water of consistent thickness is assumed.From Beer-Lambert's law, which relates light attenuation across the sample to its material properties, we can calculate water thickness d m according to Equation (1) [6]: where E ref (ω) and E hyd (ω, t) are the frequency dependent fast fourier transforms of the terahertz time-domain pulse of the reference (free space) and sample (hydrated membrane), respectively, α w (ω) and α m (ω) are the absorption coefficients of water and PFSA samples, respectively and d m is the sample thickness.The time dependent macroscopic water content in a weight basis WC(t) is estimated using Equation (2) [6]: where ρ w and ρ m are the density of water (1 g/cm 3 ) and Nafion (1.94 g/ cm3 [6]), respectively.To process measurements from thin membranes, the proposed parametric algorithm examines the total transmitted electromagnetic wave E s (ω) through a dielectric slab with complex refractive index ns = n s (ω) − ik s (ω) at normal incidence in free-space using plane wave approximation in Equation ( 3) [36]: where E s (ω) and E r (ω) are the Fourier transform waveforms of sample and reference signals, respectively, Ĥ(ω) is the transfer function, ω is the angular frequency, n 0 is the refractive index of air, c is the vacuum speed of light, d is the sample thickness.FP(ω) is the Fabry-Pérot from multiple reflections inside the slab given by Ref. [36]: It should be noted that in cases where the sample is sufficiently thick, Fabry-Pérot reflections are temporally separated out from the main pulse in the time-domain and therefore can be removed by a time windowing function resulting in an approximate solution for ns [52].Iterative methods can also extract the optical parameters by minimising the error between modelled transfer function Ĥ(ω) and the measured transfer function [40][41][42][43][44][45][46].The error is commonly known as the objective function g(w) in optimisation [53] which can be expressed as the following The modelled transfer function is determined by intermediate values of complex refractive index, which is initially entered in as guesses, but allowed to gradually converge to the actual values.This approach considers Fabry-Pérot in Equation ( 4) and therefore can additionally determine the sample thickness.Without material a priori information, however, an iterative solver can produce solutions with discontinuities and non-physical artefacts due to multi-modal solutions.To overcome these difficulties, assumptions are made on the material's dielectric properties, i.e. the complex refractive index behaves in accordance with a dispersion model such as Lorentz or Drude, commonly known as parametric based methods [53,54].This is therefore exploited in hydrated membranes, which follow a double Debye response [32,33] and is given by where ε ∞ is infinite dielectric constant, Δε complex refractive index is related to the complex permittivity ε(ω) = ε ′ (ω) − jε ′′ (ω) via Equations ( 7) and ( 8) For the membrane at the dry state, the dielectric response follows a single Debye model [55] with the fits shown in SI.For all the fittings against measurement in this work, we simultaneously fit the real and imaginary part by nonlinear least squares method.To optimise the objective function, a derivative-free particle-swarm solver is used for global optimisation with bounds with initial values taken from the literature [33] and thickness from the confocal microscope measurements.The search range of all the variables were set as ±15% of the initial value.A flowchart of the algorithm and further details can be found in SI.From the extracted dielectric parameters and macroscopic water content, the time dependant proportions of bulk (f bulk ), bound (f bound ) and free (f free ) water states in hydrated membranes during desorption [6] are estimated using Equation ( 9), ( 10) and ( 11) [6].
where Δε 1,bulk and Δε 2,bulk are the values of dielectric strength for pure water [56] and C 0 is the concentration of pure water (55 mol/L).The time dependent density of the hydrated membrane ρ wm (t) and molecular concentration of water in hydrated membranes (C H2O (t)) are obtained from Equations ( 12) and ( 13) where M w is the molecular weight of water (18 g/mol).

Algorithm validation
To test the algorithm, we compare the analysis results of a Nafion 117 against the literature [6] where the extracted values of Δε 2 , ε ∞ and τ 2 are in close agreement, with the values of Δε 1 being higher due to difference in amount of surface water at t = 0 and relative humidity of the environment.The extracted thickness is 172 μm in close agreement to the measured thickness of 170 μm.As THz-TDS is essentially a high frequency extension of microwave dielectric relaxation spectroscopy, our extracted dielectric constants is comparable against Nafion with low water content [32], which previously was validated against the low frequency regime [4].We then applied the algorithm to the Nafions 212 and 211 measurements at approximate thicknesses of 50 μm and 25 μm, respectively and the fitted results are shown in Table 3. Small deviations are due to high frequency noises occurring at frequencies >1 THz.It should be noted that analysis of these thin membrane measurement using non-parametric based analysis did not converge.

Water content (WC)
Fig. 2 shows the terahertz estimated WC for all the samples where exponential decays are observed, consistent with earlier work [20,50], with the exception of Nafion 117, which is outside the drying time window [33].Ionomer A6 also has the highest water uptake >50% from ionomer equivalent weight without any heat treatment.As expected, membrane drying rate is faster in thinner membranes than thicker counterparts.Due to uncertainties related to initial water content (t = 0) from surface water removal and sample mounting time, some water loss can be expected.Therefore, the desorption profiles are represented by the desorption rate taken as the slope of the desorption in the first minute.In particular, we compare against DVS data at RH 90-80% for Ionomers A1-A6 in Fig. 3 where a linear correlation is observed.The choice of 80% over 40% is because there is correlation between 80% and 40% DVS data (see SI) where the instrument is able to record with sufficient fidelity at a lower driving force resulting in a lower rate of change.It should be noted that the DVS data here represents the maximum desorption rate from saturation, while the initial water content from the terahertz data will always be lower due to uncertainties under the measurement configuration.Owning to the time-consuming nature of each DVS measurement (~1.5 days/sample), only a subset of ionomers were tested using DVS.Further details on DVS data are available in SI.
Fig. 4 summarises the effect of the processing conditions investigated as part of the DoE on the desportion rate where Ionomers A1, A2 and A6 results are consistent with DVS (Fig. 2).As expected, Ionomer A6 without heat treatment has a higher desoprtion rate than the heat treated Ionomer A2 due to a greater amount of water being present.Higher water content in turn promotes the formation of water channels thus increasing the water diffusion across the membrane.In contrast, heat treatment has the function to improve the mechanical properties of the membrane at the expense of morphology change thus collapsing the water channels leading to a decrease of water sorption, retention and eventually diffusion [17][18][19]57].Similar trend is observed for both ionomer types when the duration of heat treatment is considered.An increase in desorption, however, is observed for increased in treatment temperature in Ionomers B1-3 contrary to what is expected [58].This is possibly due to a different approach being used to administer heat to ionomers B, which is also observed between Ionomers B4 and B3.Methods of heat treatment has been shown to induce shape-memory effects in Nafions [59] resulting in changes polymers' properties such as water uptake, tensile modulus and counter-elasticity [60,61].The fact that there a contrast shown by THz-TDS highlights the sensitivity of the technique for future investigation.

Molecular water states
Fig. 5 shows the extracted water states for all samples without heat treatment where the following trend can be observed: bulk water contribution generally dominates inside the membrane followed by bound and free water at the start of the experiment -Nafions in particular with a hydration number ~12-13 resulting in more bulk than bound [2,4,6]; bulk water becomes the main source of water loss with bound water becoming the dominant over time signified by a cross-over point where bulk and bound contributions are the same; stabilisation of bulk water at approximately 30-40% sufficient for proton conduction [62].The Nafion 117 data is a notable exception to these trends because of a comparatively longer drying time, but generally is in agreement (Table 3) though with a lower desorption due to a higher measurement RH and temperature [6].Another trend observed is that thinner membranes generally encounter this crossover faster, which is expected that given that bulk water molecules are considered the ones at the centre of the pores of the membranes, it is reasonable to assume that thinner membranes will have comparatively less space for bulk-water networks to form [63,64].It should also be noted that this crossover is also affected by initial water, which for thin membranes are prone to dry out quicker than thicker counterparts due to the ambient nature of the measurement used.Fig. 6 shows the corresponding water states for the heat treated ionomers where like the un-treated counterparts in Fig. 5, similar trends are observed.However, key difference being that the removal of the crossover point between bulk and bound water desorption profiles.This could be due to the lowering of the initial bulk water uptake as a result of having a greater amount of heat induced crystalline domains in the polymer chain resulting in a structure with reduced water cluster domains [65].As the non-specific adsorbing water corresponds to water with the highest mobility, which correlates to non-freezable water [51], Fig. 7 compares the non-specific adsorbing water against terahertz bulk water contributions at t = 0 with an estimated water activity between ~0.8-0.9 and at t = 25 with water activity ~0.4 for Ionomers A1-6 where similarities between the trends can be observed.However, there are some discrepancies, e.g.Ionomer A5 at t =0, Ionomer A1 and A6 at t = 25, but these are relatively small compared to the changes at t = 0 between Ionomers A1, A2 and A3-A6.These discrepancies could be due to uncertainties associated with membrane water activity, and the fact that single point measurement is taken in THz-TDS as opposed to over an entire membrane by DVS.
Fig. 8 summaries the desorption profiles as a function of the processing conditions, highlighting the effect of heat treatment on the water states.In particular, comparing Ionomer A6 against the heat treated Ionomer A2 at t = 0 shows that bulk water has reduced.As bulk water is related to proton conduction [66], this reduction agrees with prior works where proton conductivity is reduced with heat treatment at the trade-off of better mechanical properties [67,68].The data also shows an opposing trend between Ionomers A and B, for example at the wet state (t = 0), Ionomers A generally has higher bulk water than Ionomers B but that trend is reversed at the end of measurement (t = 15) indicating a greater bulk water retention between different ionomer types.Furthermore, heat duration has the effect of increasing initial bulk water in Ionomers A than B while temperature presents a nonlinear effect on Ionomers B where an optimum retention is seen for the B2 sample.Minor differences at wet conditions can be observed for the water states thus suggesting the change of water content may be due to additional effects such as hydrophobic nanometre thick skin layers forming at membrane air interface than just ionomer structural changes [69][70][71].Owing to the complexity of the process, it also highlights the need to interpret water content (e.g.Fig. 3) in conjunction with other information such as water states, complementary techniques at different scale e. g.Neutron scattering [72,73] in order to comprehensively infer on the morphological changes induced in a manner similar to Ref. [74].
To further explore the effect of ePTFE reinforcement across all the ionomers, Fig. 9 shows the water states contributions when ePTFE proportion is accounted for across Ionomers A1-A6.In particular, the EEW = 963 g/mol data point is taken as the average between Ionomers A1, A2.Inclusion of other ionomers to this particular EEW is possible though would unlikely to change the trend observed due to similarities in values.This is necessary as EEW is used to account for the ionomer dilution to ensure the trend is not an artefact.Here bulk water decreases with increasing ePTFE proportion implying water domains have been disrupted under reinforcements thus decreasing the ability of ionomers to accommodate water, consistent with prior observations made where proton conductivities were also reduced in membranes with hydrophobic ePTFEs [75,76].This trend occurs for both initial (t = 0) and end of measurement (t = 15) and supports water disruption hypothesis.The extent of the decrease is also accentuated by the initial water uncertainty, which becomes more dominant for thinner ionomers.Even though there is a general agreement between the presented results against independent DVS analysis and literature findings, practioners of the technique should generally be aware of the following in addition to those pointed out previously [6,33,50]: 1) manual surface water removal during sample preparation will inevitably introduce measurement uncertainty especially pertinent for thin membranes and therefore vapour humidification is suggested; 2) the exact values on the proportion of water states will likely be few percent lower (<5%) where this baseline would correspond to the extracted proportions from fitting the double Debye model to a completely dry sample.As such, what is being presented is the relative proportions of water states; 3) as the sample is not in a closed chamber where the local environment can be varied significantly, the extracted water states are at constant room temperature thus not directly comparable to the water states extracted at other environmental conditions e.g. at low temperatures with nitrogen flow using DSC [77].Improving the proposed technique with THz-TDS inside a closed chamber to cater for a variety of environmental conditions is therefore the subject on future investigation for unambiguous comparisons.Our data in this study has demonstrated the sensitivity of THz-TDS to the molecular water states inside membranes prepared under various treatement strategies where measurements and analysis can be performed rapidly, without physical contact using table-top instruments, thus opening up opportunities for practical manufacturing parameter space investigation for future product optimisation.

Conclusions
In this study, we have demonstrated the broad applicability of THz-TDS to extract the water states and their retention properties of industrially relevant membranes where previous studies have focused on thicker membranes.In particular, we have developed a parametricbased algorithm to perform the data analysis, where the results have been validated against prior work and complementary measurement.By further evaluating the extracted water states against membranes prepared under various heat treatment conditions, our results have generally agreed with prior understanding and literature demonstrations.Compared to other approaches, THz-TDS is a highly interesting contactless, table-top characterisation technique with clear potential to complement existing methods and to open up new opportunities for future rapid membrane performance testing, enabling a greater material understanding for optimising performance stability trade-off.

Funding sources
The authors acknowledge financial support from the EPSRC (Grant No. EP/R019460/1, H2FC Supergen Flexible Grant EP/P024807/1).Additional data sets related to this publication are available from the Lancaster University data repository https://doi.org/10.17635/lancaster/researchdata/505

Fig. 2 .
Fig. 2. Desorption of macroscopic WC in all samples.The line and shade region in the plots refer to mean and standard deviation data for three repeats.(For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 3 .Fig. 4 .
Fig. 3. Comparison of rate of water desorption for the Ionomers A1-A6 acquired using THz-TDS and DVS.Line is plotted to guide the eye.

Fig. 5 .Fig. 8 .
Fig. 5. Desorption of microscopic water states in the Nafion and non-heat treated JMFC membranes.The line and shade region in the plots refer to mean and standard deviation data for three repeats.(For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 9 .
Fig. 9. Water states at the 0 th minute (a) and 15th minute (b) for the JMFC membranes as a function of EEW.

Table 1
Range of process parameters.

Table 2
Summary of the membranes used in the study.

Table 3
Double Debye parameters at the 0th minute of Nafions.