Proton conductivity, water permeability and diffusivity, hydrogen permeability, and electro-osmotic drag of Nafion™ membranes for fuel cell applications are presented in this section. State of the art measurements and proceedings are summarized and discussed in order to give a global idea of where the technology stands and the shortcomings of the current methods. Here we attempt to show that the interfaces play a bigger role than attributed to them by disentangling their effects from existing results and why it is important to consider them in fuel cell engineering.
3.1. Proton Conductivity
In PEM analysis, membrane properties are usually discussed in terms of water content,
λ, a quantity expressed as the molar ratio of water molecules to sulfonate groups (–SO
3−). When referring to proton conductivity it should be noted that charge transport happens through a hydrated membrane, that is, through the water held by a polymer matrix. Hence, the mechanism is not the same as in bulk water because of the additional forces exerted by the polymer matrix and sulfonate groups [
2,
8,
18,
19]. Nevertheless, to understand proton transfer in acidic hydrated membranes, such as Nafion™ in PEM fuel cells, it is important to firstly understand the transfer mechanisms in bulk water. In general, there are two mechanisms that describe this phenomenon, namely structure diffusion and vehicle diffusion. Their relative prevalence in bulk water significantly differs from that in membranes albeit that it also depends on the water content.
The structure diffusion of protons, also known as the Grotthuss mechanism, refers to the transfer of protons by tunneling from one water molecule to the next via hydrogen bonding, which is not an actual movement of the ion through the solvent but a rearrangement of atoms; this mechanism is often referred to as “proton hopping” [
2,
12,
20]. On the other hand, it should be noted that water has a high self-diffusion coefficient which has a contribution on the total proton conductivity as protonated water molecules, in the form of H
3O
+ or H
9O
4+; this phenomenon is known as vehicle diffusion and it has a contribution of approximately 22% to the total conductivity assuming that the diffusion coefficients of H
2O and H
3O
+ are the same at Standard Temperature and Pressure (STP) conditions [
2,
21].
In a hydrated acidic polymer, the ionomer material most used for PEM fuel cells, two types of domain can be recognized: hydrophobic domains constituting the polymer backbone that grant the membrane its morphological stability; and hydrophilic domains that allow the proton conduction and consist of protonated sulfonate groups (–SO
3H). This domain is described as well-connected through nanochannels even at a low water content. Hence, percolation in these membranes is very good because there are almost no dead-end pockets [
2,
22,
23]. Moreover, a transition region has been identified between the hydrophobic and hydrophilic domains which is considered to be the consequence of the side-chain architecture of Nafion™. This region is believed to confer Nafion™ with its swelling characteristic as it has been suggested that there is a progressive side-chain unfolding with increasing water content.
Water content can be seen as the hydration of the –SO
3− groups and can be related to widening of the nanochannels and increasing conductivity as the membrane becomes more hydrated. At medium to high values of hydration, ~10 <
λ < 22, the excess protons are located in the center of the nanochannels where the water is bulk-like and, thus, the proton transfer is similar to the phenomena described above for aqueous solutions with structure diffusion prevalently occurring. However, as the degree of hydration decreases, the concentration of protons increases, which generates more proton-donor than acceptor sites; this fact creates a bias of the hydrogen bonds in the electrostatic field which in turn suppresses structure diffusion. Hence, at low water content the transport of protons is mostly due to vehicular diffusion [
2].
The characterization of proton conductivity can be done by either creating a faradaic current, i.e., where there is mass transfer, or by inducing a non-faradaic current, i.e., no mass transfer; in the former case, a redox couple is used to generate electrons as in the case of running electrochemical cells, and in the latter, charge is induced at the electrode interface by an external electric field as it is done in techniques such as NMR or Electrochemical Impedance Spectroscopy (EIS). Commonly, proton conductivity is assessed by EIS, a technique that determines the resistance of a membrane by applying an oscillating electric potential and varying its frequency [
11,
12,
13,
23,
24,
25,
26,
27,
28,
29,
30]. However, properties determined by EIS are averaged quantities and its interpretation usually involves assuming isotropy of the material. The conductance of a membrane can be quantified by performing experiments in different configurations, namely in-plane [
11,
12,
13,
23,
24,
26,
27,
28,
29,
30] and through-plane measurements [
25]. In-plane measurements quantify the conductance in the length of the membrane, while through-plane measurements do so across its thickness. Studies have shown that in-plane measurements are preferred over through-plane measurements as it will be discussed later.
Reported conductivity data in the literature is often difficult to assess as results vary from laboratory to laboratory depending on experimental conditions. Studies have shown that conductivity measurements are influenced by the technique employed and the geometry of the conductivity cell [
11,
12,
13]. In the first, conductivity values might be extracted by extrapolating the imaginary part of the measured impedance in the low frequency region [
11,
12,
13,
23,
25,
26,
27,
28,
30] or extracted from fitting values for the components of an equivalent circuit [
12,
13]. In the latter, different geometries of the conductivity cell include a 2-probe [
10,
12,
13,
23,
25,
26,
27,
28] or 4-probe cell [
12,
13] where the distance between the measuring probes also plays a role. A summary of the possible configurations for EIS measurements is shown in
Figure 1.
In the 2-probe configuration, the voltage measuring electrodes also carry the current. Under an alternating electric field and particularly at low frequencies, a certain amount of ions reaches the electrode before the reversal of polarity which results in charge build up at the interfaces and, thus, lowers the electric field in the bulk of the membrane; this phenomenon is often referred to as electrode blocking [
12,
13]. On the other hand, carrying out the impedance measurements using four probes helps diminish the effect of charge build up near the current carrying electrodes by using different electrodes sufficiently far away from the charge build-up region to measure the voltage across the bulk membrane material [
12,
13]. The voltage measuring electrodes are connected through a high impedance device so that the current flowing through them is negligible [
12,
13].
Conductivity measurements using the 4-probe method are appropriate for ionic conducting materials with low resistivity as the interfacial effects are diminished, whereas the 2-probe measurement is appropriate for high-resistance materials since other impedances present in the circuit can be neglected [
12]. Furthermore, and regardless of the geometry of the cell, the subsequent analysis of the obtained data must be manipulated in order to retrieve the conductivity values. This is done either by extrapolating the obtained semicircle to its intercept with the real axis at low frequencies and taking this value as the bulk resistivity of the membrane; or, conversely, by fitting the obtained data to an equivalent circuit. In the latter, it is possible to disentangle the effects of the interfaces from those of the bulk material [
12,
13].
An important aspect that is often overlooked in the assessment of membranes is that the faradaic conductivity and the non-faradaic conductivity differ when the ionic species do not play the same role. In the case of conductivity measurements involving charge transfer at electrodes—in the faradaic setting—some ions are current carrying and others are blocked. Hence, it is possible to have excellent values for non-faradaic conductivity (no mass transfer) and extremely bad values in a faradaic setting (with mass transfer). For the present case of proton conducting membranes with anions fixed to the membrane, this is not expected to play a role as there is only one charge carrier which is also involved in the charge transfer at the electrodes.
Despite the various different techniques with expected differing outcomes, it is found in the literature that conductivity measurements are done in many instances with disregard to the above mentioned potential errors. As a consequence, the lack of a standard measurement method and data analysis technique leads to varying results and imprecise estimations of the proton conductivity, which ultimately hinders the development of effective PEMs. In
Figure 2 an example of different conductivity values for a bare Nafion™ 117 membrane found in the literature is presented. Even though the experiments were performed at different temperatures, it is evident that the values follow different trends for different measurement cell geometries. Zawodinski et al. [
23,
24] measured the proton conductivity at 30 °C in a 2-probe, in-plane set-up and later Springer et al. [
10,
18,
30] correlated Zawondinski’s values for the water content and temperature according to
The data and correlation from Zawodinski and Springer, respectively, have been widely used ever since as a benchmark [
12]. Lee et al. [
12] performed a systematic investigation on the effect of using two or four probes to measure conductivity in-plane at 60 °C. Their results showed a clear difference between the two methods indicating the nature of the contact effects as shown separately in
Figure 2. However, their measured values are much lower than those of Zawodinski even though Lee et al. performed them at higher temperatures. This fact clearly shows the discrepancy found in the experimental results and the difficulty of assessing them properly. Reasons for this variability include the irreproducibility of the membranes, where no two samples are equal, e.g., different thickness, different pre-treatment method, in addition to the largely irreproducible effects of contacts or interfaces. This indeed calls for the necessity of standard measurement methods.
Figure 3 presents the differences in proton conductivity results obtained by the different geometries of the measuring cell. The data were fitted to an average function in both cases and the mean-square and root-mean-square errors were calculated; additionally, the percentage error was averaged over the whole range (see
Section 4). A comparison of the 2-probe and 4-probe method yields an error of 34.6%, while the effect of the plane in which the measurement is done shows an error of 32.8%. These errors are a representation of the variability between measurements and support the hypothesis that the interfaces play a much more important role than is usually attributed to them. These effects are particularly notorious when comparing the results between the 2-probe and the 4-probe case, where the effect of the interfaces are known to play a role. At higher water content, where the Grotthuss mechanism of transport is dominant, the proton conductivity was lower for the 2-probe case due to other impedances present in the system apart from that of the bulk membrane. All the same, when comparing the plane in which the measurement was carried out, through-plane measurements yielded lower values which can be related to the fact that the interfaces, or area over which the current is being transported, is larger; hence, having a bigger contribution on the overall resistance. This fact is supported by studies performed at Scribner Associates Inc. labs where the contact resistance’s effect or “cell resistance” was eliminated by extrapolating the resistance at high frequencies to zero membrane thickness in a through-plane configuration. By doing this correction, they found that the membrane conductivity was the same for in- and through-plane measurements. This also provides evidence for the intrinsic isotropy of the material although this fact holds only for bare or untreated membranes as MEA (membrane electrode assembly) preparation processes such as hot-pressing may induce structural changes that affect charge transport in different directions [
7].
3.2. Water Permeability
Water transport in proton-conducting membranes is of the most importance as water is mainly responsible for the transport of charges across the membrane. Therefore, the permeability of the membrane to water molecules and their diffusivity are properties that have been extensively studied [
1,
8,
9,
22,
23,
24]. The water permeation process through a membrane can be expressed in terms of three different steps, namely (i) sorption of water into the membrane at the sorption side; (ii) diffusion of water across the membrane; and (iii) desorption of water from the membrane at the dry side [
8,
9]. The sorption and desorption steps represent interfacial resistances to mass transport and have been studied by several authors [
1,
8,
9]. From their permeation studies, they have reported that reasons for this resistance to be significant include the membrane’s surface being hydrophobic to water vapor and hydrophilic to liquid water. This has been proven by SAXS (Small Angle X-ray Scattering) experiments that corroborated structural changes of the membrane’s interface according to the medium it was in contact with [
8]. Majsztrik et al. reported that the rate limiting step in permeation experiments was water desorption at the membrane/gas interface [
9].
There are various methods to estimate water permeability and diffusivity (see next subsection) through a membrane [
8] and unfortunately literature results are found to vary with the measuring technique. Zhao et al. and Majsztrik et al. have reviewed them and shown that results for permeability and diffusivity vary up to three orders of magnitude [
8,
9]. Water permeability is typically measured with a simple permeation experiment where two water-filled chambers are separated by the membrane and a total pressure difference is applied. The change in volume in the lower pressure chamber is measured with a capillary and related to the permeability of the membrane [
2,
31]. Alternatively, water diffusivity through the membrane can be measured by NMR [
1,
8,
9,
22,
24] and then related to the permeability using the following argument.
From Fick’s law, that relates mass flux to the concentration gradient, one obtains an expression in terms of the water diffusivity
Dw as
where
pw is the water vapor pressure in equilibrium with the water in the membrane. The water permeability defined in the previous section is then related to the diffusivity as
Pw =
PV/Vw =
Dw/(
pwVw) assuming that the experiments are done in the absence of hydrogen so that the volume flow only involves water. The water permeability is usually given in mol cm
−1 s
−1 bar
−1 and the diffusivity in cm
2 s
−1.
Data gathered for permeability and diffusivity of water through a Nafion™ 117 membrane are shown in
Figure 4. For comparison, the diffusivity values were converted to permeability using the above argument. The data were fit to an average function to assess the variability among experiments.
The data are spread over several orders of magnitude, indicating underlying phenomena that were not accounted for. The highest values correspond to those measured by NMR for the intra-diffusion coefficient; however, those obtained by permeation experiments are much lower. The data from permeability measurements and the calculated values from diffusivity seem to follow the same trend which is expected from the above argument; nevertheless, at low water contents the trend seems to be different.
Two regimes can be identified in the permeability of the membrane, with a faster increase after a water content higher than 14. However, in the case of diffusivity there seems to be an inflexion point at a lower water content (~4). Zhao et al. [
8] performed diffusivity experiments at different temperatures and the results followed the same trend. The change in regime in both cases suggests an interfacial effect as the resistance to mass transport at the liquid-liquid interface becomes lower with increasing amounts of water in the membrane; with more water the nanochannels swell, thus creating more space for water to move across [
8,
9]. An activation volume has been reported by various authors, where after a certain level of hydration of the membrane, its properties change at a different rate [
22]; this activation volume or percolation threshold has been reported to occur at low water volume fractions (~0.005) [
22]. At this point the membrane has enough water to connect the nanochannels, thus increasing percolation.
3.3. Hydrogen Permeability
One important issue present in proton-conducting membranes for PEM fuel cell applications is their permeability to hydrogen gas. It is important that the membrane is permeable to water as this provides the means for charge transport; however, this also means that hydrogen gas from the anode feed can move through the membrane as it dissolves in water. In turn, this results in fuel losses and hence efficiency losses. Due to this cross-over effect, the hydrogen mass transport properties have been given some attention in the past few decades [
8,
9,
19,
32,
33,
34,
35,
36,
37]. Typical methods for permeability and diffusivity measurements are shown in
Figure 5 (applicable for gases, e.g. oxygen and hydrogen, and water).
The preferred methods for hydrogen transport measurements are chromatography and electrochemical monitoring. Attempts were made by Sakai et al. and Wu et al. to use the Barrer-Dynes time-lag technique [
19,
32] but the diffusion time of hydrogen is too small to be measured by this technique. In order to make the results comparable, the mass transport will be assessed in terms of the permeability (mol cm
−1 s
−1 bar
−1). Permeability and diffusivity results are interchangeable via the solubility of hydrogen in the membrane [
32,
33]; the permeability has been extracted from results reported as permeation flux (mol cm
−2 s
−1) by means of the hydrogen saturation pressure in water.
Figure 6 shows different results from various measuring techniques for hydrogen permeability; for comparison, the points corresponding to a wet and a dry membrane are also shown. In this case, the variability was evaluated between experiments performed by an electrochemical technique [
35] vs. chromatography [
32] as the sample of data is spread over a larger range of water content values. The average relative error in this case was estimated to be ~28%. The higher values are those reported by Broka et al. [
38] who used a volumetric method to measure hydrogen permeability, whereas electrochemical methods presented lower, but varying, values. This difference could be attributed to the presence of electrical interfaces in the electrochemical measurements. In these cases, protons were allowed through the membrane and the current generated was related to the amount of substance through Faraday’s law. Due to the electrical resistances at the interfaces, it is natural to assume electrical losses and thus, the measurements would yield lower values. This effect will be discussed further in the next section.