--- title: "Size-dependent hydrogen uptake behavior of Pd nanoparticles revealed by photonic crystal surface waves" authors: ["Valery N. Konopsky", "Dmitry V. Basmanov", "Elena V. Alieva", "Sergey K. Sekatskii", "Giovanni Dietler"] affiliation: "Institute of Spectroscopy, Russian Academy of Sciences, Fizicheskaya, 5, Troitsk, Moscow region, 142190, Russia" journal: "Applied Physics Letters" year: 2012 volume: "100" issue: "8" article_number: "083108" pages: "" doi: "10.1063/1.3690085" type: journal-article site_group: "Surface plasmons and photonic bandgaps" url_abstract: "" url_pdf: "https://valery.konopsky.com/kvnlocal/APL2012.pdf" language: en source_tex: "Z:\\ValeryData\\Valery_New\\my_articles\\APL2012\\APL\\Konopsky2APL.tex" source_pdf: "Z:\\ValeryData\\Valery_New\\my_articles\\APL2012\\APL\\Published\\APL2012.pdf" --- ## Abstract A new optical method of study of nanoparticle properties using photonic crystal surface waves is presented. Palladium nanoparticles were deposited on a surface of a 1D photonic crystal, which supports the propagation of {\sl p}\,-polarized optical surface waves. The changes in the nanoparticle properties, such as its dimension and refractive index, were monitored through angle interrogation of the photonic crystal surface waves. The interaction of palladium nanoparticles with hydrogen was detected with this method. The size-different hydrogen uptake behavior by 2\,nm and 6\,nm diameter Pd nanoparticles results in qualitatively different response of the optical signal, viz. in the different signs of such a response. This not only confirms the absence of the $\alpha$- to $\beta$-phase transformation for the smallest palladium nanoparticles, but is a plausible indication that hydrogen donates its electrons to a collective electron band of the metal. y41 Institute of Spectroscopy, Russian Academy of Sciences, Fizicheskaya, 5, Troitsk, Moscow region, 142190, Russia Laboratoire de Physique de la Matière Vivante, Institut de Physique des Systèmes Biologiques, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland Nanometer sized materials are of great scientific and technological interest, because their physical and chemical properties are often size-dependent and different from their bulk counterpart. The palladium-hydrogen system can be considered as a model system for such studies for several reasons. Firstly, due to the noble character of $Pd$, its nanoparticles have only a very thin oxide surface film (about one atomic monolayer [1]) that can be removed in the initial exposure to $H_2$. [2] Secondly, the behavior of bulk palladium under hydrogen exposure has been thoroughly investigated both experimentally and theoretically. [3, 4] Palladium hydride, $Pd H_x$, exhibits two distinct phases, denoted as $\alpha$ and $\beta$ phases (the latter is sometimes referred to in literature as $\alpha'$ phase). In the $\alpha$ phase, at low hydrogen concentration, the hydrogen atoms are incorporated into the $Pd$ crystal structure and occupy interstitial sites in the lattice and at the grain boundaries. This leads to internal strain and a slight expansion of the face-centered cubic (fcc) $Pd$ lattice. This expansion is approximately linear in a [$Pd$ lattice constant]-[$H_2$ pressure] dependence. When the hydrogen concentration increases further, a first-order phase transition occurs. For some metals there is a structural phase transformation of the metal lattice in passing from the $\alpha$ to $\beta$ phase, however, in palladium there is only a change in the lattice constant of the fcc lattice. In this $\beta$ ($\alpha'$) phase the palladium hydride may be considered as an interstitial alloy, where the hydrogen atoms occupy the octahedral lattice sites of the fcc Pd lattice, forming a defective rock-salt ($NaCl$) structure. The $\alpha$-$\beta$ phase transformation results in the large increase of the Pd lattice constant by 3.54% that corresponds to a 11% volume increase. This sharp, nonlinear increase on the [$Pd$ lattice constant]-[$H_2$ pressure] curve corresponds to the well-known plateau (miscibility gap) on a pressure-composition isotherm, i.e., on a [$H_2$ pressure]-[$x$] (from $PdH_x$) curve. The modification of this bulk $Pd$ behavior at the nanoscale has been extensively studied over the past decade. [5, 6, 7, 8, 9] It was found that in palladium nanoclusters the miscibility gap is narrowed and practically disappears for clusters smaller than 3 nm. [10] Theoretical simulations of hydrogen uptake in small $Pd$ nanoparticles also confirm the disappearance of the miscibility gap and $\alpha$-$\beta$ phase transformation. [11] For $Pd$ nanoparticles less than 3 nm in size, the discontinuity in the [$Pd$ lattice constant]-[$H_2$ pressure] curve, which is specific for the $\alpha$-$\beta$ transition, disappears and this curve becomes approximately linear in this region. [12] Nevertheless some residual features of the $\alpha$-$\beta$ phase transition, such as a small hysteresis on the pressure-composition isotherm, still occur even for the smallest $Pd$ nanoparticles. [13, 12] There is a wide range of tools available to detect the presence of the hydrogen in an environment under study. In such hydrogen sensors, a palladium film is commonly used as the selective layer, in conjunction with a range of transducers, such as thin film resistors [14] or nanoparticle resistors. [17] However, the number of instruments, able to distinguish between the $\alpha$ and $\beta$ phase response of $Pd$ nanoparticles upon hydrogen injection is limited. As a rule, detailed study of $Pd$-hydrogen interaction involves either, a gas-loading gravimetric Sartorius micro-balance measurements, or measurements of pressure change due to hydrogen absorption/release in Sievert’s reactor (a closed system with constant volume). Then, the $\alpha$ and $\beta$ phase response are determined from correspondent parts of the pressure-composition isotherm. In this Letter we show that Photonic Crystal Surface Waves (PC SWs) can be used as a sensitive measurement tool of hydrogen uptake by $Pd$ nanoparticles. Moreover, a peculiarity of the sensing system *“$Pd$ nanoparticles on the PC surface”* results in different signs of the optical response of this system, depending on the phase of palladium. PC SWs are excitation of optical modes, which can exist on the external surface of a photonic crystal in its band gap region. Sometimes these PC SWs are also called Bloch surface waves [28] or optical Tamm states. [29] In recent years, PC SWs have been used in ever-widening applications in the field of optical sensors. [35, 36, 37, 38, 39, 40, 41] ![.Changes in the propagation constant ΔρSW of the PC SW in response to hydrogen injection for different experimental arrangements.](media/APL2012/fig2.eps) *.Changes in the propagation constant ΔρSW of the PC SW in response to hydrogen injection for different experimental arrangements.* The experimental results are shown in Fig. 2. The response of the uncoated, bare 1D PC on the injection of 0.5% $H_2$ was just a result of the change of the RI of the external gas medium. At normal conditions, RI of the nitrogen is $n_\mathrm{N_2}=1.000297$, while RI of the hydrogen is $n_\mathrm{H_2}=1.000139$. Therefore, the change of RI due to injection of 0.5% $H_2$ is about $\Delta n \simeq -0.8\times 10^{-6}$. From Fig. 2 (top-left) one can see that the propagation constant $\rho_\mathrm{SW}$ changed to approximately this value, as expected. From top-right and bottom-right parts of Fig. 2, it is seen that the signs of $\Delta\rho$ in response to injection of 0.5% $H_2$ differ for the 2 nm and 6 nm nanoparticle layers. The response of the continuous 8 nm thick $Pd$ film at the $\alpha$-$\beta$ phase transition is also shown in Fig. 2 (bottom-left) for comparison. A small hysteresis is present at experiments with $Pd$ of all sizes. From these data one can see that for 2 nm $Pd$ NPs, where the $\alpha$-$\beta$ phase transformation does not occur, the sign of $\Delta\rho$ is negative. While for 6 nm $Pd$ NPs, where the $\alpha$-$\beta$ phase transition takes place, the sign of $\Delta\rho$ is positive. Below we give our interpretation of these experimental results. The propagation constant $\rho_\mathrm{SW}$ and, therefore, the excitation angle $\theta_0$ of the PC SW may undergo a change due to two reasons: a change of an “effective thickness” of the layer of $Pd$ nanoparticles and a change of “effective RI” of the $Pd$ nanolayer. The general rules of PC SW response on the changes of a metal film, that can be concluded from the dispersion relation, [42] are: (1) if the thickness of the metal nanolayer increases, the $\rho_\mathrm{SW}$ increases, and (2) if the imaginary part of RI of the metal increases (i.e., the nanolayer becomes “more metallic”), $\rho_\mathrm{SW}$ decreases (i.e., $\rho_\mathrm{SW}$ shifts to the “light line”). The signs of these contributions in $\Delta\rho$ are opposite due to the negative sign of the real part of permittivity of a metal ($\mathrm{Re}(\varepsilon_\mathrm{M}<0$)). The permittivity of a metal $\varepsilon_\mathrm{M}$ in the red and infrared range may be characterized by the Drude model: [43] ``` math \begin{equation} \varepsilon_\mathrm{M} %&=& = \varepsilon_\infty-\frac{\omega_\mathrm{p}^2 }{\omega^2+i\gamma \omega} +\varepsilon_\mathrm{int}(\omega) %\nonumber %\\ \end{equation} ``` ``` math \begin{equation} \mathrm{Re}(\varepsilon_\mathrm{M}-\varepsilon_\mathrm{int}(\omega)) %&=& = \varepsilon_\infty-\frac{\omega_\mathrm{p}^2}{\omega^2+\gamma^2} %\\ \end{equation} ``` ``` math \begin{equation} \mathrm{Im}(\varepsilon_\mathrm{M}-\varepsilon_\mathrm{int}(\omega)) %&=& =\frac{\gamma\omega_\mathrm{p}^2}{\omega(\omega^2+\gamma^2)} \; , %\nonumber \end{equation} ``` where $\omega_{\mathrm p}$ is a plasma frequency, $\gamma$ is collision frequency of electrons, $\varepsilon_\infty$ is the optical constant, and $\varepsilon_\mathrm{int}(\omega)$ is a fitting permittivity which reflects the contribution of bounded electron transitions located in the nearest spectral range. The plasma frequency, in turn, depends on the density of the free electrons in the metal $N_e$: ``` math \begin{equation} \omega_\mathrm{p}^2=\frac{4\pi N_e e^2}{m^*}\; , \end{equation} ``` where $e$ and $m^*$ are the charge and the effective mass of the electrons, respectively. There is general agreement that the electrons of hydrogen atoms become the shared free electrons in the metal, [44] although other interpretations are still discussed. Hereafter, we accept this “shared free electrons” interpretation (possible alternatives will be outlined below). In this case, the plasma frequency of free electrons is changed, while hydrogen atoms donate their electrons to a collective metallic electron band. Therefore, hydrogen uptake by a $Pd$ nanoparticle in the $\alpha$ phase leads to increase in the electron density of the $Pd$ nanoparticle, on the one hand, and to an increase in scattering of the electrons in metal on the other (i.e., protons of hydrogen become additional scattering centers for free electrons in the metal). The first effect increases the plasma frequency (see Eq. 4) and resulting in a more negative real part value of the $Pd$ permittivity (see Eq. 2: $-\mathrm{Re}(\varepsilon_\mathrm{Pd+H})>-\mathrm{Re}(\varepsilon_\mathrm{Pd})$), while the second effect increases the $\gamma$ and the value of the imaginary part of $Pd$ permittivity: (see Eq. 3: $\mathrm{Im}(\varepsilon_\mathrm{Pd+H})>\mathrm{Im}(\varepsilon_\mathrm{Pd})$). Both effects lead to an increase in the value of the imaginary part of palladium RI (i.e., makes the $Pd$ “more metallic” in the $\alpha$ phase): ``` math \begin{equation} \mathrm{Im}(n) = \mathrm{Im}(\sqrt{\varepsilon})=\frac{\sqrt{2}}{2} \sqrt{\sqrt{ \mathrm{Re}(\varepsilon)^2+\mathrm{Im}(\varepsilon)^2 }-\mathrm{Re}(\varepsilon)} \; . %\nonumber \end{equation} ``` As we have mentioned above, it may be shown, from the dispersion relation of PC SW, that the increase of imaginary part of RI of a metal nanolayer in 1D PC leads to decrease of PC SW propagation constant $\rho$, while the increase of the “effective thickness” of the metal nanolayer leads to increase of $\rho$. Therefore, if a $Pd$ nanoparticle is in the $\alpha$ phase, where the thickness increase under hydrogen uptake is small, the “effective RI” effect dominates, and PC SW propagation constant $\rho$ decreases. This is the explanation of the negative sign of $\Delta\rho$ for 2 nm $Pd$ nanoparticles at $H_2$ injections. For 6 nm $Pd$ nanoparticles, the effect of the 3.54% increase on the “effective thickness” (during the $\alpha$-$\beta$ phase transformation) is predominant, and the PC SW propagation constant $\rho$ increases during this transformation. Moreover, the 11% volume increase results in a decrease in the electron density in the $Pd$ nanoparticles during the $\alpha$-$\beta$ phase transition, which also leads to an increase in $\rho$. This explains the positive sign for $\Delta\rho$ for 6 nm $Pd$ NPs. Additionally, one may speculate that a more regular arrangement of hydrogen protons in the octahedral lattice sites in $\beta$ phase leads to less scattering than with a nonregular distribution in the $\alpha$ phase. So, the presented results may be considered as an additional plausible argument that hydrogen donates its electrons to palladium and becomes (at least partially) ionized inside the metal. The negative sign of $\Delta\rho$ for 2 nm $Pd$ nanoparticles, in this case, is the result of an increase in the density of the free electrons $N_e$ (and, therefore, more negative $\mathrm{Re}(\varepsilon_\mathrm{Pd})$) in a nanoparticle. Two possible alternative interpretations seem less probable for the following reasons. The 1st alternative is that the imaginary part of RI (see Eq. 5) increases due to increase of $\mathrm{Im}(\varepsilon_\mathrm{Pd})$, as a result of the increase in scattering. But the scattering in a 2 nm nanoparticle is already strongly increased due to collision-induced scattering of conducting electrons at the walls of the nanoparticle. At optical frequencies, the dampening in nanostructures with the characteristic dimension $L$ is ``` math \begin{equation} \gamma=\gamma_\mathrm{bulk}+\frac{\upsilon_F}{L}\, , \end{equation} ``` where $\gamma_\mathrm{bulk}$ is the damping constant for the bulk sample and $\upsilon_F$ is the electron velocity on the Fermi surface. For a spherical nanoparticle (NP): [45] ``` math %\begin{align} \mathrm{Im}(\varepsilon_\mathrm{M}^\mathrm{NP}-\varepsilon_\mathrm{int}(\omega)) \simeq \frac{\omega_p^2}{\omega^3}\gamma = \frac{\omega_p^2}{\omega^3}\left (\gamma_\mathrm{bulk}+ \frac{3 \upsilon_F}{4r}\right )\, , ``` and ``` math \begin{equation} \mathrm{Im}(\varepsilon_\mathrm{M}^\mathrm{NP}) \simeq \mathrm{Im}(\varepsilon_\mathrm{M}^\mathrm{bulk})+ \frac{3}{4}\frac{\omega_p^2}{\omega^3}\frac{ \upsilon_F}{r}\, , \end{equation} ``` where $r$ is the radius of the sphere. Numerical estimation shows that this addition to the bulk imaginary part is about 60 for 2 nm NPs, while bulk value of $\mathrm{Im}(\varepsilon_\mathrm{Pd})$ itself is about 18 in this spectral range. So, it is a reasonable assumption that the influence of the additional scattering on the hydrogen in 2 nm $Pd$ NPs is relatively small. The 2nd alternative is that the real part of $\mathrm{Re}(\varepsilon_\mathrm{Pd})$ becomes more negative not as a result of $\omega_p^2$ increasing, but rather as a result of decreasing of $\mathrm{Re}(\varepsilon_\mathrm{int}(\omega))$ in Eq. 2. In other words, the $\mathrm{Re}(\varepsilon_\mathrm{Pd})$ is changed due to interaction of hydrogen with bounded electrons in palladium. This alternative cannot be simply excluded, since the interband transitions in infrared range are rather common in transition metals, and palladium does have an interband transition in the range of 800-900 nm. Some additional investigations with different laser wavelengths are needed to clarify this point. Here we assume that this contribution of bounded electrons to $\mathrm{Re}(\varepsilon_\mathrm{Pd})$ at $\lambda\sim 737$ nm is small in comparison with the contribution of free electrons. To summarize: we presented an experimental technique where changes in size and RI of a nanoparticle’s layer are monitored by PC SWs. Deposition of nanoparticles on 1D PC, which support *p* -polarized SWs on its external surface, permits optically investigate even such lossy objects as 2 nm Pd NLs. This technique is able to detect hydrogen uptake in small $Pd$ nanoparticles and to distinguish between the $\alpha$ phase response and $\alpha$-$\beta$ phase transition upon injection. The negative sign of the response of $\alpha$ phase presumably points out that the electrons of hydrogen become shared free electrons in the palladium after injection. ## Acknowledgments This work was financially supported by the Science and Technology Cooperation Programme Switzerland–Russia and by the Russian Foundation for Fundamental Research. 28 J. Klikovits, E. Napetschnig, M. Schmid, N. Seriani, author O. Dubay, G. Kresse, and P. Varga, “ Surface oxides on pd(111): Stm and density functional calculations,” ‘\ 12‘\$12 ‘&12‘#12‘1̂2‘\_12‘%12 Phys. Rev. B **76**, 045405 ( 2007)bibitemNoStop C. Sachs, A. Pundt, R. Kirchheim, author M. Winter, M. Reetz, and D. Fritsch, “ Solubility of hydrogen in single-sized palladium clusters,” Phys. Rev. B **64**, 075 408 ( 2001)bibitemNoStop F. A. Lewis, *The Palladium Hydrogen System* ( Academic, London, 1967)bibitemNoStop R. J. Wolf, M. W. Lee, R. C. Davis, author P. J. Fay, and author J. R. 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Konopsky, “ Plasmon-polariton waves in nanofilms on one-dimensional photonic crystal surfaces,” New J. Phys. **12**, 093006 ( 2010)bibitemNoStop W. Vargas, I. Rojas, D. Azofeifa, and N. Clark, title “ Optical and electrical properties of hydrided palladium thin films studied by an inversion approach from transmittance measurements,” Thin Solid Films **496**, pages 189 – 196 ( 2006)bibitemNoStop F. A. Lewis, “ The form of the interaction between palladium and hydrogen,” Platinum Metals Rev. **15**, 21–25 ( 1971)bibitemNoStop C. Bohren and D. Huffman, *Absorption and Scattering of Light by Small Particles* ( Wiley & Sons, New-York, 1983)bibitemNoStop ## References 1. % J. Klikovits, E. Napetschnig, M. Schmid, N. Seriani, O. Dubay, G. Kresse, and P. Varga, Surface oxides on pd(111): Stm and density functional calculations, Phys. Rev. B **76, 045405 (2007)NoStop%. 2. % C. Sachs, A. Pundt, R. Kirchheim, M. Winter, M. Reetz, and D. 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Vinogradov, A. A. Lisyansky, and A. B. Granovsky, Tailoring surfaces of one-dimensional magnetophotonic crystals: Optical Tamm state and Faraday rotation, Phys. Rev. B **79, 125103 (2009)NoStop%. 18. % A. Shinn and W. Robertson, Surface plasmon-like sensor based on surface electromagnetic waves in a photonic band-gap material, Sens. Actuator B-Chem. **105, 360--364 (2005)NoStop%. 19. % V. N. Konopsky and E. V. Alieva, Long-range propagation of plasmon polaritons in a thin metal film on a one-dimensional photonic crystal surface, Phys. Rev. Lett. **97, 253904 (2006)NoStop%. 20. % V. N. Konopsky and E. V. Alieva, Photonic crystal surface waves for optical biosensors, Anal. Chem. **79, 4729--4735 (2007)NoStop%. 21. % V. N. Konopsky and E. V. Alieva, Long-range plasmons in lossy metal films on photonic crystal surfaces, Opt. Lett. **34, 479--481 (2009)NoStop%. 22. % V. N. Konopsky, D. V. Basmanov, E. V. Alieva, D. I. Dolgy, E. D. Olshansky, S. K. Sekatskii, and G. Dietler, Registration of long-range surface plasmon resonance by angle-scanning feedback and its implementation for optical hydrogen sensing, New J. Phys. **11, 063049 (2009)NoStop%. 23. % Y. Guo, J. Y. Ye, C. Divin, B. Huang, T. P. Thomas, J. R. Baker, Jr., and T. B. Norris, Real-time biomolecular binding detection using a sensitive photonic crystal biosensor, Anal. Chem. **82, 5211--5218 (2010)NoStop%. 24. % V. N. Konopsky and E. V. Alieva, A biosensor based on photonic crystal surface waves with an independent registration of the liquid refractive index, Biosens. Bioelectron. **25, 1212--1216 (2010)NoStop%. 25. % V. N. Konopsky, Plasmon-polariton waves in nanofilms on one-dimensional photonic crystal surfaces, New J. Phys. **12, 093006 (2010)NoStop%. 26. % W. Vargas, I. Rojas, D. Azofeifa, and N. Clark, Optical and electrical properties of hydrided palladium thin films studied by an inversion approach from transmittance measurements, Thin Solid Films **496, 189 -- 196 (2006)NoStop%. 27. % F. A. Lewis, The form of the interaction between palladium and hydrogen, Platinum Metals Rev. **15, 21--25 (1971)NoStop%. 28. % C. Bohren and D. Huffman, *Absorption and Scattering of Light by Small Particles (Wiley,&,Sons, New-York, 1983)NoStop% thebibliography. --- Generated: 2026-08-30 from Z:\ValeryData\Valery_New\my_articles\APL2012\APL\Konopsky2APL.tex, validated against Z:\ValeryData\Valery_New\my_articles\APL2012\APL\Published\APL2012.pdf.