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Thermodynamics of the hybrid interaction of hydrogen with palladium nanoparticles

Abstract

Palladium–hydrogen is a prototypical metal–hydrogen system. It is therefore not at all surprising that a lot of attention has been devoted to the absorption and desorption of hydrogen in nanosized palladium particles. Several seminal articles on the interaction of H with Pd nanocubes and nanoparticles have recently been published. Although each article provides for the first time detailed data on specific aspects of hydrogen in nanoparticles, they individually do not contain enough information to draw firm conclusions about the involved mechanisms. Here, we show that the large body of data available so far in literature exhibits general patterns that lead to unambiguous conclusions about the processes involved in H absorption and desorption in Pd nanoparticles. On the basis of a remarkably robust scaling law for the hysteresis in absorption–desorption isotherms, we show that hydrogen absorption in palladium nanoparticles is consistent with a coherent interface model and is thus clearly different from bulk Pd behaviour. However, H desorption occurs fully coherently only for small nanoparticles (typically smaller than 50 nm) at temperatures sufficiently close to the critical temperature. For larger particles it is partially incoherent, as in bulk, where dilute α-PdHx and high concentration β-PdHx phases coexist.

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Figure 1: Schematic pressure–composition isotherms at three different temperatures.
Figure 2: Enthalpy–entropy correlation for H absorption and desorption in nanosized Pd particles.
Figure 3: Experimental and calculated plateau pressures at 300 K for H in Pd nanocubes and nanoparticles.
Figure 4: Scaling law for the hysteresis.
Figure 5: Pressure–composition isotherms of various Pd samples, comparing model, and experimental data.

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Acknowledgements

We are grateful to J. Urban (Lawrence Berkeley National Laboratory) and A. Baldi (Stanford University) for providing us their original experimental data. We are especially grateful to C. Langhammer, C. Wadell and S. Syrenova (Chalmers University, Gothenburg) for making available pressure–composition isotherms of nanocube ensembles before publication. We also acknowledge enlightening discussions with A. Baldi, S. Syrenova and A. Pundt (University of Göttingen). R.G. was supported by an MPI guest professorship at University of Stuttgart and the MPI for Solid State Research. N.S. and H.G. were supported by the Deutsche Forschungsgemeinschaft (SPP1391, FOR730 and GI 269/11-1), by the Bundesministerium für Bildung und Forschung (13N9048 and 13N10146), by ERC Advanced Grant COMPLEXPLAS, by the Baden-Württemberg Stiftung (Spitzenforschung II) and by the Ministerium für Wissenschaft, Forschung und Kunst Baden-Württemberg (Az: 7533-7-11.6-8).

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R.G. developed the theoretical framework for the enthalpy–entropy correlation and the hysteresis scaling law. N.S. developed the numerical method to calculate the pressure–composition isotherms of nanoparticles consisting of elastically coupled surface shell and core. H.G. coordinated the project. All authors contributed to the writing of the manuscript.

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Correspondence to Ronald Griessen.

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Griessen, R., Strohfeldt, N. & Giessen, H. Thermodynamics of the hybrid interaction of hydrogen with palladium nanoparticles. Nature Mater 15, 311–317 (2016). https://doi.org/10.1038/nmat4480

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