While not an extensive review of the field, the work described here shows the critical role that neutron techniques play in the research and development of PEM fuel cells. Interestingly, neutron techniques can serve researchers at several points along the process of developing a working and high-performance PEM fuel cell. At the earliest stages, neutron scattering can inform chemists of the structures that develop given the choices made in molecular architecture. In turn, it can then be determined how these structures may impact important materials properties such as water and ion transport. Finally, state-of-the-art neutron methods can be used to monitor and analyse operating PEM fuel cells and aid in determining operating conditions for optimum fuel-cell performance. Therefore, researchers have the tools necessary to correlate materials chemistry and structure to overall device perfor­mance. This can deliver critical information and serve as a powerful tool to a chemist or materials developer, by providing them with a general set of fundamental design parameters with which they can move forward in membrane development. It is reasonable to consider that neutron-based techniques will continue to serve the PEM fuel-cell community by aiding in the characterization and establishment of fundamental membrane structure-property-performance relationships.

1 To ensure that the total internal resistance (electrolyte + electrodes) of a fuel cell is sufficiently small, the target value for the areal specific-resistivity of the electrolyte is set at 0.15 Xcm2. Oxide films can be reliably produced using conventional ceramic fabrication routes at thicknesses down to * 15 im. It follows that the specific conductivity of the electrolyte must exceed 0.01 Scm^1 [1].

[1] Mineral Commodities Summary 2008, United States Geological Survey (2008); later versions

(2009-2012) do not give a number for In reserves.

[3] A difference is marked in the literature between “stacked” and “tandem” PVs. The former refers to the case of layers made from the same material, whereas in the latter there are two different materials.

[4] Calculations based on standard semi-local, hybrid or meta functionals lead to a repulsive PES, i. e. no minimum is found. The combination of hybrid and meta contributions in PBE1KCIS is presently adequate for treating weak interactions. For reliability, detailed benchmark calculations were made for several non-bonded systems and are reported in [20—22] (and references therein). It is worthwhile to note that DFT-based methods can nowadays be improved in an efficient way like wave function-based approaches [23].

[5] The quantitative fragment-orbital approach and a symmetry-adapted linear combination of the HOMOs of the two HAT6 molecules are used. The corresponding computational procedure [24, 25] can be summarized as follows: Molecular orbitals (MOs) are firstly calculated for each single HAT6 forming the dimer in the specific orientation. Subsequently, MOs of the two stacked molecules are then expressed as a linear combination of the MOs of the monomer HAT6 (frag­ment), фi, leading to the overlap matrix S, the eigenvector matrix C, and the eigenvalue vector E. The relation hKS = SCEC-1 provides CTIs, < фі|ЬК5|ф/ > . This procedure allows exact and direct calculations of J as the diagonal elements of the Kohn-Sham Hamiltonian hKS. A second approach is adopted to estimate J, which is called the dimer approach and is based on a zero spatial overlap assumption and can be used in some limited cases where the overlap between the interacting individual units forming a stacked system is negligible. It consists of the use of the half energy splitting between the HOMO and HOMO-1 to get, qualitatively, the effective CTI.

[6] Results of the fragment approach are compared to those obtained using the dimer approach. There is a significant difference between the methods due to the non-zero overlap neglected in the latter.

[7] Neutron powder diffraction on HAT6 and HAT6D was performed using the D16 diffractometer at the Institut Laue Langevin in France, using wavelength of 4.54 A to get a good compromise between d-spacing range and angular resolution.

[8] The MD force field employed is COMPASS which is a second-generation force field that generally achieves higher accuracy by including cross terms in the energy expression to account for such factors as bond, angle, or torsion distortions caused by nearby atoms. A periodic hex­agonal super-cell consisting of 72 HAT6D molecules (10,368 interacting atoms) was used. The 72 molecules were arranged in 12 columns, each column consisting of 6 molecules (Fig. 6.11c).

[9] The dynamics on the picosecond timescale were determined by directly comparing the QENS spectra of the two MD models TWIST25 and TWIST60 with the experiments [27]. QENS has the advantage that neutrons follow both the temporal and spatial characteristics of atomic motion via a well-characterized interaction with the atomic nuclei. Consequently, it is fairly straightforward to calculate the expected spectral profiles by using the atomic trajectories from the MD simulations. If these are in acceptable agreement with the observed spectra, the time scales of motion can be assigned to the underlying mechanisms. Further details about the experiment and the theoretical basis can be found in reference [27].

[10] A skeletal density of 1.08 ± 0.01 g cm 3 is observed for HAT6D-TNFD, corresponding to an increase in density of about 7 % with respect to HAT6.

[11] Research exists in conversion-alloying electrodes of Li containing compounds, but this chapter is focused on the insertion materials.

[12] tG = (Ra + Ro)//2(Rb + RO), where RA is the ionic radius of the A ion, RB is the ionic radius of the B ion, and RO is the ionic radius of oxygen [25].

[13] Assuming that the two-state model is true and the proton spends an average time, t1, in the defect — free region and a time in a trap, tj + t0, then the diffusivity is scaled by a factor, tj/(tj + t0) [32]. Increasing the concentration of traps then leads to a decrease of t1. It implies that in the two-state model the diffusivity depends on the concentration of traps but not on the activation energy.