Why do proton conducting polybenzimidazole phosphoric acid membranes perform well in high-temperature PEM fuel cells?

Abstract

Transport properties and hydration behavior of phosphoric acid/(benz)imidazole mixtures are investigated by diverse NMR techniques, thermogravimetric analysis (TGA) and conductivity measurements. The monomeric systems can serve as models for phosphoric acid/poly-benzimidazole membranes which are known for their exceptional performance in high temperature PEM fuel cells. ¹H- and ³¹P-NMR data show benzimidazole acting as a strong Brønsted base with respect to neat phosphoric acid. Since benzimidazole's nitrogens are fully protonated with a low rate for proton exchange with phosphate species, proton diffusion and conduction processes must take place within the hydrogen bond network of phosphoric acid only. The proton exchange dynamics between phosphate and benzimidazole species pass through the intermediate exchange regime (with respect to NMR line separations) with exchange times being close to typical diffusion times chosen in PFG-NMR diffusion measurements (ms regime). The resulting effects, as described by the Kärger equation, are included into the evaluation of PFG-NMR data for obtaining precise proton diffusion coefficients. The highly reduced proton diffusion coefficient within the phosphoric acid part of the model systems compared to neat phosphoric acid is suggested to be the immediate consequence of proton subtraction from phosphoric acid. This reduces hydrogen bond network frustration (imbalance of the number of proton donors and acceptors) and therefore also the rate of structural proton diffusion, phosphoric acid's acidity and hygroscopicity. Reduced water uptake, shown by TGA, goes along with reduced electroosmotic water drag which is suggested to be the reason for PBI–phosphoric acid membranes performing better in fuel cells than other phosphoric-acid-containing electrolytes with higher protonic conductivity.

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Introduction

Neat phosphoric acid (H₃PO₄) is the compound with the highest intrinsic proton conductivity,¹ and it is the main constituent of proton conducting membranes for high temperature polymer electrolyte membrane (PEM) fuel cells operating in the T = 130–160 °C range. Such membranes comprise a basic polymer, such as poly-benzimidazole^2–8 forming an adduct with phosphoric acid. The high conductivity of the pure acid is mainly the consequence of its “frustrated” hydrogen bond network (there is a severe imbalance of potential proton donors and acceptors) and the strength of its highly polarizable hydrogen bonds. The underlying proton conduction mechanism (structural diffusion) comprises very rapid intermolecular proton transfer and hydrogen bond formation reactions within the highly viscous environment of pure phosphoric acid as revealed by a recent ab initio molecular dynamics study.⁹ The proposed mechanism explains in a natural way that for the series phosphoric acid – phosphonic acid – phosphinic acid decreasing viscosity goes along with decreasing proton conductivity.¹⁰ This striking observation is at odds with the so-called Walden rule¹¹ relating viscosity and equivalent conductivity and underlines the peculiar nature of proton conductivity in neat phosphoric acid. It also questions viscosity arguments for explaining conductivity trends in phosphoric acid based systems.¹² Relative to the very high conductivity of the neat acid, the conductivity of phosphoric acid's complexes with poly-benzimidazole (PA–PBI) is significantly reduced even for high acid concentrations,^2–8 which raises the question why they still perform so well in high temperature PEM fuel cells. In the present work, we show that most of the conductivity reduction is a consequence of the chemical interaction between the two constituents, and that is also the reason why mixtures of phosphoric acid and (benz)imidazole can serve as models for phosphoric acid/poly-benzimidazole membranes. For these model systems, we clarify whether the protic sites of (benz)imidazole participate in proton diffusion trajectories (as suggested before^5,12,13) and in which way acid/base interactions affect proton conductivity in this system. We also elucidate to which extent and why these interactions affect the system's hygroscopicity. This is of particular interest because PA–PBI membranes are exposed to varying relative humidity in fuel cells, and water is the only additive which is known to increase phosphoric acid's high conductivity.^13–15

A recent study of the nature of this conductivity increase disclosed that hydrogen bond network “frustration” decreases with the addition of water through proton transfer from phosphate to aqueous species.¹⁶ Hydrogen bonding between phosphate and aqueous species is strong for low water contents but weakens rapidly with hydration level leading to a progressive decoupling of the diffusion of aqueous species (H₂O, H₃O⁺) from that of phosphate species. In addition, the acidity of phosphoric acid is significantly increased at low water contents. As a consequence, fast diffusion of a high concentration of protonated aqueous species (vehicle mechanism¹⁷) accounts for the increasing ionic conductivity with increasing water content. Since this emerging conductivity contribution is on the expense of phosphoric acid's genuine structural diffusion of protons, any effect of phosphoric acid's affinity towards water also effects the nature of its ionic conductivity (which is in contrast to recent claims^18,19). Finally, we will demonstrate that this has important implications for the use of such materials as electrolyte in high temperature PEM fuel cells, and we explain why PA–PBI is performing well despite its aforementioned reduced conductivity.

Methodology

A combination of proton nuclear magnetic resonance (¹H-NMR) techniques offers the unique possibility to characterize systems comprising of two differently diffusing subsystems exchanging protons at a certain rate. Diffusion coefficients and exchange processes are actually related in that the latter affects not only the shape of NMR spectra in the so-called intermediate and fast exchange regimes^20,21 but also the apparent diffusion coefficients as obtained by pulsed field gradient (PFG) NMR.^22,23 Analysis of the NMR lineshape is an established technique to determine the exchange rate of protons between different chemical sites,^20,21 while only a few examples exist employing PFG-NMR to quantify exchange rates between two subsystems with known diffusion coefficients.^24,25 In this study, NMR lineshape analysis and PFG-NMR are combined to obtain accurate diffusion coefficients of protons in the phosphoric acid part (PA) of mixtures consisting of phosphoric acid and (benz)imidazole.

In a PFG-NMR experiment, the diffusion coefficient D is usually determined from the dependence of the echo attenuation

on the strength of the field gradient pulses G.^26,27 The value b(G) in eqn (1) depends on the choice of the PFG-NMR sequence; is obtained for a stimulated-echo sequence with rectangular gradient pulses of length δ and strength G. The diffusion time Δ is given by the separation of the leading edges of the gradient pulses and γ denotes the gyromagnetic ratio of the proton.

PFG-NMR has been widely used for determining proton diffusion coefficients in systems containing phosphorus oxoacids (neat phosphoric,^16,28 phosphonic,²⁹ and phosphinic acid,¹⁰ di-phosphoric acid,^16,30 phosphoric acid/water mixtures,^16,19,31 PA–PBI at various water contents^32,33 and phosphoric acid-containing gels³⁴). In some cases the effects arising from proton exchange between species of different diffusion coefficient are not critical, or the information, which is lost through these effects, is regained by measuring the diffusion coefficient of different types of nuclei (e.g.³¹P and ¹⁷O in the case of phosphoric acid–water mixtures¹⁶). For instance, the reactants of condensation and hydrolysis reactions in phosphoric acid systems (e.g. H₄P₂O₇, H₃PO₄) are so long-lived³⁵ that their separate ³¹P-NMR lines allow for a separate determination of the diffusion coefficient of each species (low exchange limit).^16,30,31 In this case, the echo attenuation for each line is measured separately by PFG-NMR. On the other hand, very fast proton exchange in the same systems gives rise to a single ¹H-NMR line which is generally used to determine an average proton diffusion coefficient (fast exchange limit).^16,19,31

At intermediate exchange rates, the decay of echo intensity contains additional information on the populations of both subsystems, the diffusion coefficients in these systems and the exchange rate between them. In the present work we consider the exchange of protons between H₃PO₄ (PA) and protons attached to benzimidazole's nitrogen atoms (BI) with mean residence times τ_PA and τ_BI. The corresponding rate denotes the transfer from PA to BI and that from BI to PA. There is a detailed balance between protons on PA with population p_PA and protons on BI with population p_BI yielding for the ratio of the mean residence time at PA and at BI.

If the values for the mean time of residence in both phases are of the same order of magnitude as the diffusion time Δ (in the range of milliseconds), the simple eqn (1) is no longer applicable. The generalized description of the echo decay in a system of two subsystems with different diffusion coefficients is given by Kärger's equations:^22–24

This complex decay of the echo amplitude with G² depends on populations (p_PA, p_BI), mean life times (τ_PA, τ_BI), and diffusion coefficients of the protons in the subsystems (PA, BI) and is quasi double-exponential. This behavior is not always immediately evident from the experimental data and can be easily overlooked. For low or a large difference between the diffusion coefficients, for example, the decay will appear almost mono-exponential, as the onset of the second exponential is disguised in signal noise, or the maximum gradient strength G is not high enough to observe the onset of the second exponential decay. In such cases, apparent diffusion coefficients obtained from mono-exponential fits of the Stejskal–Tanner equation (eqn (1)) strongly depend on experimental settings, e.g., the diffusion time Δ and particularly the maximum gradient strength G_max, and a simple analysis of the recorded echo intensities may yield highly inaccurate values for the diffusion coefficients (see ESI†).

Intermediate exchange effects are also observable in NMR spectra if the exchange rates are similar to the difference of the resonance frequencies of protons at PA and BI. At low temperature, i.e., low exchange rate, those lines are clearly separated with Δν > 0.5 kHz and their intensity ratio allows for determination of the population ratio . At higher temperatures, when the exchange rate increases, the lines coalesce and the shape of the spectrum depends on the exchange rates and the proton populations.²¹ In this work, exchange rates have been obtained for all samples through analysis of the coalescing ¹H-NMR spectra using a two-site exchange model (MEXICO 3.0 routines).²⁰

Obtaining population and exchange rate from spectral analysis, actually reduces the 4 independent parameters in the Kärger equation (eqn (2)) to two parameters . Additionally in the system (benz)imidazole–phosphoric acid the benzimidazole diffusion coefficient is obtained from the echo decay of non-exchanging C–H proton resonances, which further reduces the number of parameters in the Kärger equation to one free parameter (). This fitting parameter, the diffusion coefficient of protons in the phosphoric acid part of the mixture , can thus be obtained at high accuracy (see Experimental). It needs to be emphasized that the described way of reducing the number of free parameters in the Kärger equations is only feasible as the intermediate exchange regimes in spectral analysis and PFG-NMR overlap. This overlap is a special case, as in both experiments the occurrence of intermediate exchange effects depend on independent parameters: the frequency difference Δν for the spectral analysis and the diffusion time Δ for PFG-NMR.

Experimental

Sample preparation

Nominally dry phosphoric as obtained by centrifuging crystalline phosphoric acid (Aldrich, >99.999%)^16,28 and dry benzimidazole (Fluka, purum > 98%) or imidazole (Merck, >99%) powder were mixed by weight in a glovebox under dry nitrogen atmosphere. The samples were mixed under slight heating (50–80 °C) in closed glass viols. The resulting viscous liquids were either filled in a Teflon crucible for thermogravimetric analysis, impedance cells for conductivity measurements, or in 5 mm NMR tubes with screw lids (Deutero Duran S300). Dead volume above the sample was filled with a glass filler and the NMR tube was closed with its lid inside the nitrogen atmosphere and subsequently heat sealed outside the glove box.

Thermo-gravimetrical analysis (TGA)

Equilibrium thermo gravimetric analysis (TGA) was carried out by using a balance (Mettler AT20) magnetically coupled (Rubotherm) to a PTFE crucible containing the sample. This technique allowed for weighing even at high temperature T and high and very low relative humidity RH, as described before.³⁶ Changes of the buoyancy were compensated by a two parameter (temperature of sample and humidifier) baseline correction. Equilibration times of up to several days (especially at low T and RH) were chosen in order to ensure thermodynamic equilibrium. Reversibility was cross-checked through comparing the weights recorded during heating and cooling runs which also allowed excluding the uptake and release of species other than water. Nominally dry phosphoric acid (crystalline ortho-phosphoric acid) was used for mixtures with benzimidazole, and their weights were taken as reference (λ = 3). TGA crucibles were filled with such mixtures (1 g) under dry nitrogen atmosphere before transferring to the balance under the same dry gas.

Impedance spectroscopy

Temperature-dependent dc-conductivities were derived from impedance spectra measured by a HP-ac-impedance analyzer (4192A LF) in the frequency range 10 Hz – 1 MHz. A closed conductivity cell made from glass (Duran, sample volume 0.3–0.6 ml) with platinum electrodes (diameter ∼ 6 mm), as previously described,¹⁶ has been used for measuring conductivities in the temperature range T = 20–160 °C. The maximum temperature was limited by the reactivity of phosphoric acid with glass. Heating and cooling runs were performed to ensure reversibility. The cell constant was determined by calibration with standard KCl solutions of different normalities (0.1 N and 0.01 N CertiPUR® Merck).

NMR spectroscopy

NMR measurements have been performed with a Bruker Avance III 400 spectrometer equipped with a diff60 gradient probe in the temperature range T = 70 to 160 °C.

³¹P-NMR spectra clearly resolve H₃PO₄, H₄P₂O₇ and H₅P₃O₁₀ lines^16,31,37,38 and the molar concentrations x_i of the phosphoric acid (P1: H₃PO₄, H₂PO₄⁻, H₄PO₄⁺; P2: H₃P₂O₇⁻; P3: H₃P₃O₁₀²⁻) and aqueous (aq: H₂O, H₃O⁺) species are calculated from peak intensities as described previously.¹⁶

Diffusion coefficients of the different species are measured by ³¹P PFG-NMR. For this, the stimulated echo PFGSTE sequence with spoiler gradients,³⁹ sinoidal gradient shape, effective gradient time δ = 1 ms to and a diffusion time Δ = 20 ms were used,^26,40 for which .^40–42 The obtained diffusion coefficient were found to be independent of the diffusion time Δ which was varied in the range Δ = 20–40 ms.

At low temperature, ¹H-NMR spectra show clearly resolved lines for H₃PO₄, protons attached to (benz)imidazole nitrogens atoms (N–H) and (benz)imidazole benzene ring protons (C–H). At higher temperature the first two lines coalesce, indicating exchange of protons on the millisecond timescale. Exchange life-times and proton populations of N–H and H₃PO₄ were analyzed through fits with the MEXICO 3.0 fitting routine.^20,21

The parameters describing proton distribution between benzimidazole and phosphoric acid (populations and life times) together with diffusion coefficients of (benz)imidazole obtained from ¹H-PFG-NMR of C–H protons are then used as input parameter for fitting the echo attenuation of the common ¹H signal of N–H and O–H protons in PFG-NMR experiments (256 gradient steps, maximum gradient of G_max = 29 T m⁻¹, sinoidal gradient shape, diffusion time Δ = 20 and 40 ms, and effective gradient duration δ = 1 ms). For this, the Kärger equation for intermediate exchange (eqn (2)) is used with the diffusion coefficient of protons within the phosphoric acid phase as the only free parameter. This diffusion coefficient is not affected by contributions from the diffusion of benzimidazole protons exchanging with protons in the phosphoric acid phase. It is this diffusion coefficient which is the used for discussing proton conduction mechanisms.

¹H T₁ relaxation times were measured by inversion recovery to set the re-magnetization times. Their temperature dependence exhibits clear BPP behavior with a 1/T₁ maximum in the investigated temperature range.⁴³ A detailed analysis of the data together with data from quasi-elastic neutron scattering (QENS) will be presented in a separate publication.

Results and discussion

Phosphoric acid–benzimidazole: a model system for PA–PBI

Let us first prove that phosphoric acid–benzimidazole is a suitable model system for studying transport in PA–PBI adducts. For this, we compare the ionic conductivity decrease for identical ratio of phosphoric acid per equivalent benzimidazole for the monomeric and the polymeric system AB-PBI.^44–47 For the monomeric model system, such data have been measured in the present work, but for PA–PBI adducts, conductivity data are recorded for given relative humidity RH only.⁴⁵

However, hydration isotherms measured in this work (Fig. 1) allow identifying values for RH which correspond to certain water contents λ. The nominally dry complex 3PA·1BI (λ = 3) exists at RH ∼ 12% almost independent of temperature. We therefore compare the conductivity of 3PA·1BI with the conductivity of 3PA·1ABPBI recorded at RH = 12%⁴⁵ (Fig. 2). For both cases the conductivity decrease compared to the high conductivity of pure phosphoric acid is similar (more than an order of magnitude). Obviously, the detrimental effect on conductivity is essentially the consequence of the chemical interaction of the benzimidazole unit with phosphoric acid rather than steric effects associated with the polymeric nature of PBI. These chemical effects can be studied more easily for the monomeric system, and for this the hygroscopicity is significantly reduced compared to the very high hygroscopicity of pure phosphoric acid (Fig. 1). Since hygroscopicity and enhanced acidity of pure phosphoric acid are most likely related to hydrogen bond network frustration,^16,43 this observation points towards a reduction of network frustration. This will be discussed in the following section followed by the central sections on transport discussing the implications on proton diffusion and conductivity including the underlying transport mechanisms.

Fig. 1 Hydration number λ = [H₂O]/[P₂O₅] for neat H₃PO₄ and mixtures of H₃PO₄ and benzimidazole (9PA1BI = 9 mol H₃PO₄ per 1 mol benzimidazole; 3PA1BI = 3 mol H₃PO₄ per 1 mol benzimidazole). The water uptake at constant relative humidity (RH) is reduced with increasing benzimidazole content.

Fig. 2 Ionic conductivity of nominally dry phosphoric acid (H₃PO₄), liquid 3PA·1BI and polymeric AB-PBI–phosphoric acid membranes with the same PA/BI ratio (recorded at RH = 12%,⁴⁵ see text). The conductivity reduction of the monomeric system almost compasses the one observed for the polymeric membrane. Note that the ionic conductivity of the liquid 3PA·1BI has some contribution from the diffusion of benzimidazolium H–BI⁺ (see below).

Proton distribution between benzimidazole and phosphoric acid

OH groups which accept a hydrogen bond from a proton donor while being prevented from donating its covalently bound hydrogen to another proton acceptor within frustrated hydrogen bond networks constitute local high energy states.^9,16,30 These reactive states tend to relax if adequate pathways are available. In the case of pure ortho-phosphoric acid (H₃PO₄) frustration of the hydrogen bond network relaxes through condensation reactions:

3H₃PO₄ ⇌ H₃P₂O₇⁻ + H₄PO₄⁺ + H₂O (3)

3H₃P₂O₇⁻ + H₃PO₄ ⇌ 2H₃P₃O₁₀²⁻ + H₄PO₄⁺ + H₂O (4)

which reduce the ratio of the number of proton donors versus acceptor sites. This is thought to be the reason for the presence of a significant concentration of condensation products (di-phosphoric acid P2, tri-phosphoric acid P3, higher phosphates and aqueous species) in nominally dry phosphoric acid. In fact, the mole fraction x_P1 of P1 species (H₃PO₄, H₂PO₄⁻ and H₄PO₄⁺) in neat phosphoric acid is only about 0.92 at T = 350 K further decreasing with increasing temperature (Fig. 3).

Fig. 3 Mole fraction x_P1 of ortho-phosphoric acid species (P1: H₃PO₄, H₂PO₄⁻, H₄PO₄⁺) in nominally dry phosphoric acid benzimidazole mixtures increases with the addition of the Brønsted base. The corresponding concentrations of di-phosphoric acid (P2: H₃P₂O₇⁻) and aqueous species (aq: H₂O, H₃O⁺) decrease (see reactions (3) and (4) and text). Mole fraction x_P1 in nominally dry phosphoric acid imidazole mixtures are virtually identical (see ESI†).

The addition of the strong Brønsted base (benz)imidazole to phosphoric acid provides another direct pathway for reducing the proton concentration within the frustrated hydrogen bond network of the ortho-phosphate species by simple proton transfer to the basic species as evidenced by IR spectroscopy:^48,49

BI + H₃PO₄ → H–BI⁺ + H₂PO₄⁻ (5)

Of course, this reaction reduces the driving force for phosphate condensation, i.e., the alternative pathway for the elimination of highly reactive frustrated OH groups. This effect is clearly visible in the evolution of the mole fraction of ortho-phosphate species x_P1 with the addition of benzimidazole BI (Fig. 3), i.e., addition of BI reduces the concentration of condensation products (P2, P3) while the concentration of ortho-phosphate species (P1) increases.

In a recent ab initio molecular dynamics simulation⁵⁰ of a 2 : 1 phosphoric acid imidazole (2PA1Imi) mixture imidazole was fully protonated without any proton exchange events taking place on the ps time scale of the simulation. The present NMR study, however, clearly shows that there are very rare proton exchange events between BI and PA which lead to coalescing ¹H-NMR lines for NH and OH protons (Fig. 4a). For the mixture 9PA1BI, e.g., the NMR lines of NH (δ ∼ 10.5 ppm) and OH protons (δ ∼ 9.2 ppm) are well separated (∼1.3 ppm corresponding to 520 Hz) at T = 320 K with the expected intensity ratio for full nitrogen protonation but start to coalesce with increasing temperature (Fig. 4a). Coalescence occurs when the rate of proton exchange between the two chemically different environments is close to the spectral separation of the two ¹H-NMR signals Δν ∼ 600 Hz. Therefore, proton exchange between benzimidazole and phosphoric acid must be very slow with a rate about nine orders of magnitude lower compared to the THz scale where proton exchange reactions within the phosphoric acid part take place. While previous reports have argued that exchange of protons between benzimidazole and phosphoric acid might occur on fast timescales relevant for proton conductivity,^5,12,13 this observation indicates that exchanging protons are virtually trapped at benzimidazole's nitrogen with very rare excursions to phosphate species limiting the rate of successful proton exchange events. Average populations and exchange rates are quantified through fits with MEXICO 3.0 routines²⁰ confirming full protonation of benzimidazole's nitrogen (100% within the error bars of about ±4%) and exchange rates on the kHz scale which are compiled in Fig. 5 as a function of temperature for different PA/BI ratios.

Fig. 4 (a) ¹H-NMR spectra of 9PA·BI as a function of temperature showing the coalescing lines of NH (δ = 10.5 ppm) and OH (δ = 9.2 ppm) protons. (b) Example of a fit with MEXICO 3.0 routines from which populations and exchange rates (see Fig. 5) are obtained.

Fig. 5 Exchange rate k_BI and lifetime τ_BI of protons exchanging between (benz)imidazole and phosphoric acid. Note, that life times are of the same order as diffusion times typically chosen for PFG-NMR experiments.

The observed proton distribution has several important implications in the context of the present work. Benzimidazole's nitrogen sites are strong traps for protons, which reduces frustration within phosphoric acid's hydrogen bond network, and excludes the nitrogen sites from any fast proton diffusion pathway. (Previously proposed proton exchange between different benzimidazole molecules is effectively suppressed by the full protonation of benzimidazole, i.e., a lack of proton accepting sites. In fact, proton transport between NH sites through the structural diffusion mechanism of pure heterocycles,⁵¹ has already been shown to break down upon addition of acid.^52,53 Exchange of protons between benzimidazole and phosphoric acid is too slow to contribute to any fast proton diffusion or structural conductivity.) However, proton exchange between phosphoric acid and benzimidazole is still fast enough for inducing mixing of NH (BI) and OH (PA) ¹H-NMR signals. As will be shown in the next section this effect needs to be included into the quantitative evaluation of PFG-NMR data, from which diffusion coefficients of protons in the phosphoric acid part are reliably obtained.

The effects of acid/base interaction on ionic diffusion and conductivity

The strong acid/base interaction between benz(imidazole) and phosphoric acid is expected to have severe implications for transport within the system. Proton transfer from phosphoric acid to benz(imidazole) (reaction (5)) leads to the formation of additional ionic species (H–BI⁺ and H₂PO₄⁻) and reduces frustration within phosphoric acid's hydrogen bond network. The increased ionicity may increase viscosity, reduce local dynamics and the diffusion coefficient of PA and BI species while the number of ionic charge carriers may increase. In which way these combined effects affect vehicular transport of protons is not clear. The most relevant question, however, is to what extent the reduced network frustration and retarded dynamics reduces the rate of proton structural diffusion. For neat phosphoric acid structural diffusion is the dominant proton transport mechanism, i.e., proton diffusion is significantly faster than phosphate diffusion and structural diffusion accounts for 97% of the total ionic conductivity.^16,28 Therefore, the severe reduction of proton conductivity in PA/BI mixtures must be closely related to the retardation of structural diffusion within the phosphoric acid part of the system.

In the following section, we therefore first evaluate ¹H-PFG data (NH and OH ¹H-lines, see above) taking into account the effects of proton exchange between phosphoric acid and (benz)imidazole's nitrogen. With the ¹H-diffusion coefficient in the phosphoric acid part and the hydrodynamic background, also measured through (³¹P, ¹H)-PFG-NMR, the rate of structural proton diffusion is readily obtained. In a separate section we then translate diffusion data into conductivity contributions which are discussed on the background of experimental conductivity data.

Proton diffusion

The proton diffusion coefficient within the phosphate part is buried in the echo attenuation of the combined NH and OH ¹H-NMR signal in PFG-NMR experiments (see above). As expected for the intermediate exchange case (eqn (2)), quasi double exponential decays are observed (Fig. 6), which depend on the proton exchange rate and the proton population of the involved species (PA and BI), the diffusion coefficient of H–BI⁺ (benzimidazolium) as a whole and the diffusion coefficient of rapidly exchanging protons within the PA part. Since benzimidazolium diffusion coefficients are readily obtained by PFG-NMR making use of the C–H proton line (see Fig. 9ff, ESI†), and exchange rates (Fig. 5) and populations are available through the coalescence analysis of the two NMR lines (see above), the proton diffusion coefficient is left as the only free parameter in the expression for the echo-attenuation (eqn (2)). The fact that recorded echo attenuations are well fitted with one parameter only (Fig. 6) and are reproduced for two different diffusion times (Δ = 20 ms and 40 ms) provide confidence in the assumptions and the reliability of the input data. From the proton diffusion coefficients obtained in this way for several PA/BI ratios as a function of temperature (Fig. 7a, the corresponding data for PA/Imi mixtures are shown in Fig. 16a, ESI†) the proton structural diffusion contribution is extracted by subtracting the hydrodynamic background, i.e., proton diffusion stemming from the diffusion of phosphate species as a whole. Since there are not only diffusion contributions from ortho-phosphate species (P1) but also from condensates (P2, P3), especially at higher temperature (see also Fig. 3), we have measured , , and (for reasons of clarity, only is shown in Fig. 7b) the corresponding data for PA/Imi mixtures are shown in Fig. 16b (ESI†). By simply weighing each diffusion coefficient with the concentrations of the diffusing species and the number of protons they are carrying, the effective hydrodynamic background of proton diffusion is obtained (for details see ref. 16).

Fig. 6 Attenuation of normalized echo intensity as recorded by a ¹H PFG-NMR experiment (stimulated echo) with the resonance of protons distributed over NH and OH sites of a 6PA·1BI mixture at T = 313 K (see Experimental). The decay is fitted by the Kärger equation (eqn (2)) with proton populations (p_PA = 17/19, p_BI = 2/19) and exchange rates (τ_NH = 25 ms) obtained from coalescence analysis and diffusion coefficient of benzimidazolium (H–BI⁺) recorded by PFG-NMR of CH protons () leaving the diffusion of rapidly exchanging protons within the phosphate part as only free parameter.

Fig. 7 (a) Diffusion coefficients for protons in the PA part of PA/BI mixtures as obtained from ¹H-PFG NMR (see text) and (b) diffusion coefficient of ortho-phosphate species for the same mixtures (for diffusion coefficients of PA/Imi mixtures and and see ESI†). Insets show the same data as a function of base/acid ratio for T = 127 °C.

As the total proton diffusion coefficient within the phosphate part is reduced with the addition of (benz)imidazole also the hydrodynamic background decreases. In the case of PA/BI mixtures this reduction is even more pronounced, especially at low temperature corresponding to a significant increase of the activation enthalpy which is smaller for the proton diffusion coefficient. The retardation of the hydrodynamic diffusion is also noticed as a severe viscosity increase with the addition of BI(Imi). It may be noted that this effect is smaller for the addition of imidazole compared to benzimidazole.

Since the hydrodynamic contribution of proton diffusion remains small also for the mixtures, proton structural diffusion closely follows the evolution of . Fig. 8 shows for both series of mixtures in order to demonstrate that the reduction of the rate of this transport mode correlates with the number of basic sites subtracting protons from phosphoric acid's hydrogen bond network. The fact that for PA/Imi mixtures is slightly but systematically higher than for the more viscous PA/BI mixtures points towards a small positive effect of increased local dynamics on structural diffusion of protons.

Fig. 8 Structural diffusion coefficient of protons in the phosphoric acid part of (benz)imidazole–phosphoric acid mixtures at different temperatures and mixing ratios. Note, that the data for both types of mixtures are close (see also inset for data at T = 127 °C).

It needs to be emphasized that the proton exchange on the millisecond scale between phosphoric acid and benzimidazole, which necessitated the ¹H PFG-NMR data treatment described above, is also present in PBI–PA membranes for high-temperature fuel cells. In these membranes, benzimidazole is part of a polymer with diffusion coefficient . This special case, in which one of the two diffusion coefficients in eqn (2) is zero, results also in a double exponential decay of the echo intensity, as it has already been discussed by Kärger.²² Implications for measurements of diffusion coefficients in membranes are considered in more detail in the ESI.†

Proton conductivity

Above discussed diffusion coefficients (Fig. 8) are single particle properties (tracer diffusion) their changes directly reflecting changes of the rates of the underlying elementary reactions. In contrast, proton conductivity is a material property which has additional concentration effects. Conductivity is expected to decrease even more than the rate of proton structural diffusion does, since the addition of benzimidazole or imidazole to phosphoric acid not only affects the mobility of protons but also reduces the concentration of exchangeable protons c_OH (combined dilution and proton trapping effect).

These effects are included into the calculation of the proton structural diffusion contribution of the conductivity by the Nernst–Einstein-relationship:

For the Haven ratio H, describing correlation effects, we have chosen a constant value of 1.3 as determined for pure phosphoric acid.¹⁶ The calculated values for σ^D_structural are shown in Fig. 9 together with total conductivity as measured in this work for both series of mixtures. Calculated and measured conductivity values are actually quite close suggesting that structural diffusion remains the prevailing conduction process also in the mixtures. Although there is some unsystematic scatter in the data (in the case of 6PA1BI the calculated conductivity is even slightly higher than the measured one), at high BI(Imi) content, structural diffusion appears to distinctly fall below the total conductivity. Obviously, the hydrodynamic background (vehicle mechanism) decreases less than anticipated from the decrease of the average phosphorus diffusion coefficient only. It could well be that additional H₂PO₄⁻ formed through proton transfer to the heterocycle may act as charge carriers in the hydrodynamic background of the conductivity rather than forming stable contact ion pairs with the (benz)imidazolium cation. The limited precision of the data and missing information about the way correlation effects change with composition leave this to be a speculation only. In any case, the major effect of proton trapping on (benz)imidazole is the sever reduction of proton structural diffusion within the phosphoric acid part.

Fig. 9 Conductivity σ^D_obs (solid lines, see ESI† for data points) and structural conductivity σ^D_structural (dashed lines, points) as calculated from (a) PA–BI (b) PA–Imi (see text).

Implications for the use of PBI–PA membranes in high-temperature PEM-fuel cells

A superficial consideration may suggest that the severe conductivity decrease observed for phosphoric acid when interacting with the basic sites of benzimidazole in PBI–PA membranes is a disadvantage for their use in high-temperature PEM fuel cells. This rational seems to be behind approaches limiting the conductivity decrease by minimizing the polymer part of the membrane (this is possible through the so-called PPA-process^3,7,54,55), or by grafting sulfonic acid groups to the polymer,^3–6,56,57 both measures increasing the membrane's hydrophilicity.^43,58 Water uptake is very well known to increase the conductivity of phosphoric acid based systems, hence such approaches lead to higher conductivity, indeed.^2,12,49 Surprisingly, conductivity increases obtained in these ways do not lead to an increase of fuel cell performance. On the contrary, in some cases like Nafion membranes imbibed with phosphoric acid, the very high conductivity of such membranes stands in stark contrast to their bad performance in PEM fuel cells.^59,60 The latter seems to be related to severe concentration polarization effects which dramatically increase with increasing current density.

Our recent work on the transport properties of phosphoric acid containing extra water clearly indicates that the addition of water severely changes the nature of ionic transport.¹⁶ The high hydrogen bond network frustration of neat phosphoric acid makes it a very strong acid at low water contents. In the presence of small amounts of water (less than about two water molecules per phosphoric acid molecule) there is significant proton transfer from phosphoric acid to water leading to the formation of aqueous protonic charge carriers (H₃O⁺). With increasing water content, these species progressively decouple from the phosphoric acid structure leading to an increasing vehicular conductivity contribution (cooperative diffusion of H₃O⁺ and H₂O¹⁷). Together with the increasing conductivity contribution from H₂PO₄⁻ (formed in the same reaction) this proton transfer explains the conductivity increase with addition of water. At the same time, proton structural diffusion, i.e., the prevailing conduction mechanism of neat phosphoric acid, decreases eventually dying out at a water content of about [H₂O]/[H₃PO₄] = 2.¹⁶

Transference experiments actually showed that each protonic charge carried by vehicle transport is associated with the effective transport of about one water molecule through the combined fluxes of H₃O⁺ and H₂PO₄⁻ where ¹⁷O PFG NMR diffusion data suggest the flux of H₃O⁺ to be significantly higher than the H₂PO₄⁻ flux.¹⁶ In a running fuel cell, these fluxes are expected to lead to water drag from the anode to the cathode. The water flux then should increase with both current density and concentration of excess water. We are not yet able to calculate how the water distribution develops across the membrane, but some water depletion must occur at the anode side. Especially for membranes with additional hygroscopic groups (–SO₃H) in which conductivity is even more hydration dependent,^43,61 this depletion may lead to a resistance increase at the anode side of the membrane limiting the current across the membrane. At the same time, the increasing water concentration at the cathode side may cause irreversible leaching of phosphoric acid out of the membrane.⁶² Consistent with our findings of increased vehicle conductivity, i.e., water transport at higher temperatures leaching has indeed already been shown to also increase with temperature and to occur predominantly at the cathode side.⁶² In any case, enhanced water transport is most likely detrimental for fuel cell performance.^63,64

It may be one of the hidden advantages of PBI/PA membranes that their hygroscopicity is reduced through the interaction of phosphoric acid with the basic nitrogen sites of the polymer (see above and Fig. 1). For a relative humidity of RH = 10%, e.g., the phosphoric acid part of the mixture 3PA1BI is nominally dry (Fig. 1) while pure phosphoric acid retains about 0.6H₂O per H₃PO₄ (Fig. 1). Under these conditions, which may be considered to be close to operation conditions of high temperature PEM fuel cells, the conductivity of the model system is more than an order of magnitude lower than the conductivity of hydrated pure phosphoric acid (for data see ref. 16). But the residual conductivity is still high enough for fuel cell applications (σ ∼ 0.1 S cm⁻¹ at T = 160 °C, see Fig. 9), and proton transport is dominated by structural diffusion, i.e., there is very little transport of aqueous and phosphate species. This is in perfect agreement with the absence of any significant electroosmotic water drag in a PBI/PA membrane as measured by Weng et al.⁶¹ and appears to be a clear advantage of this type of membranes since water drag is known to cause concentration polarization effects limiting the current in a running fuel cell. On the other hand, the significant water content of pure phosphoric acid under these conditions leads to a water drag of about 0.4 water molecule per proton, which is actually very close to the water drag observed for a Nafion/PA membrane.⁶¹ It is worth mentioning that for H₃PO₄·0.6H₂O, the rate of proton structural diffusion is reduced almost by a factor of 1.9, although the total conductivity is a factor of 1.1 higher than the conductivity of “dry” phosphoric acid.

These considerations favor the use of not too high phosphoric acid contents in PBI/PA membranes with good homogeneity maximizing internal acid/base contacts. This is actually different from our earlier approach aiming at stabilizing a phase separated morphology with high conductivity.⁶⁵ The PPA-process provides a unique route for obtaining a favorably high dispersion of phosphoric acid in the final PBI structure, but the phosphoric acid content is generally high. Reducing the phosphoric acid content while keeping the intimate mix of acid and polymer could be a versatile way to further improve this type of membrane.⁶⁶ Additional mechanical stabilization, e.g., through cross-linking, may not only improve the membrane's dimensional stability, it may also reduce phosphoric acid loss as a response to external pressure.⁶⁷ We have already seen several experimental moves in these directions,^55,68–72 the present work on model systems providing additional underpinning for these approaches.

Conclusions

The present work, which relies to a large extent on the accuracy of NMR data, allow for conclusions relevant for the application of PFG-NMR techniques in membrane science per se, it provides insight into the proton conduction mechanism in phosphoric acid – based systems containing basic heterocycles such as benzimidazole, and it explains why PBI/phosphoric acid membranes are performing well in high temperature PEM fuel cells.

(Benz)imidazole clearly acts as a strong Brønsted base with respect to neat phosphoric acid. Benzimidazole's nitrogen sites are virtually fully protonated with a very slow proton exchange rate with phosphoric acid. The dynamics in such systems constitute very rare cases where proton exchange between two subsystems passes through the intermediate exchange regime in terms of ¹H-spectral analysis and is coincidentally close to typical diffusion times chosen in PFG-NMR diffusion measurements (millisecond regime). The resulting effects, described by the Kärger equations (eqn (2)), must then be included into the evaluation of PFG-NMR data for obtaining precise diffusion coefficients.

From the fact that proton exchange between benzimidazole and phosphoric acid is about nine orders of magnitude slower than proton exchange between phosphate species (10³ compared to 10¹² s^{−1 9,50,73}) we clearly exclude any proton diffusion trajectory comprising benzimidazole's nitrogen sites. As in the case of pure phosphoric acid, the dominant proton conduction mechanism is structural diffusion within the hydrogen bond network of the phosphoric acid part. However, the subtraction of protons through (irreversible) proton transfer to benzimidazole reduces the degree of frustration and therefore also the rate of structural diffusion as observed in the phosphoric acid/water system.¹⁶ As opposed to the latter where aqueous species are highly mobile, the hydrodynamic background (vehicle mechanism) in the system PA/BI is retarded, so that structural diffusion remains the prevailing conduction mechanism.

Reduced hydrogen bond network frustration also reduces phosphoric acid's very high acidity and hygroscopicity, i.e., water uptake for given RH/T conditions is reduced. As a consequence, electroosmotic water drag is reduced, and this is suggested to be the reason why, in fuel cells, PBI–phosphoric acid membranes perform better than other phosphoric acid containing electrolytes with higher protonic conductivity.

Acknowledgements

The authors thank Udo Klock for help with the TGA measurements. JPM thanks Prof. Alex Bain (McMaster University, Ontario) for an introduction to the MEXICO 3.0 routine and Igor Moudrakowski for discussions concerning exchange in NMR. We are also grateful to Robert Usiskin for reading the proofs and kindly acknowledge financial support by the Bundesministerium für Bildung und Forschung and Energie Baden Württemberg EnBW (project PSUMEA-2 No. 03SF0473).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6cp05331a

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