Article pubs.acs.org/JPCC
Asymmetric Hysteresis in Nanoscopic Single-Metal Hydrides: Palladium Nanorings Christoph Langhammer,*,†,§ Elin M. Larsson,†,‡,§ Vladimir P. Zhdanov,†,⊥ and Igor Zorić† †
Division of Chemical Physics, Department of Applied Physics, Chalmers University of Technology, S-412 96 Göteborg, Sweden Competence Center for Catalysis, Chalmers University of Technology, S-412 96 Göteborg, Sweden § Insplorion AB, Stena Center 1C, S-412 92 Göteborg, Sweden ⊥ Boreskov Institute of Catalysis, Russian Academy of Sciences, Novosibirsk 630090, Russia ‡
ABSTRACT: Using direct nanoplasmonic sensing (DNPS), we have studied hydrogen sorption in Pd nanorings with a constant average inner diameter of 240 nm and varying wall thickness. As the main finding we observe an unusual feature above a critical wall thickness in the appearance of a double plateau in the hydrogenation coexistence curve, whereas a single plateau is seen during dehydrogenation for all wall thicknesses. This is the first experimental observation of asymmetric hysteresis in a single metal system. We explain this effect by structural defect-related sample heterogeneity and the interplay of strain-dependent hydrogenation thermodynamics and kinetics.
1. INTRODUCTION The hydride formation in metals (M) is one of the best examples of a first-order phase transition in a solid. The ubiquitous lattice strain, induced by the volume difference between the two phases, influences both thermodynamics and kinetics of the phase transformation. Typically, the pressure− concentration (p−C) isotherms for a H2/M system reflect the presence of an α-phase in the low p−C range (hydrogen atoms form an interstitial dilute solution) followed by a “plateau” region, signaling the onset of hydride phase formation (βphase) and the coexistence of the two phases over a wide hydrogen concentration range. At higher pressure, a pure βphase exists and is characterized by a p−C curve with a steep slope. The plateau pressure of the H2/M system is determined by the requirement of thermodynamic equilibrium between the three phases in coexistence (i.e., hydrogen in the gas phase, αphase, and β-phase) and thus primarily by the enthalpy and entropy of hydride formation. The ubiquitous lattice strain, caused by the volume expansion upon hydride phase formation, is responsible for a difference in free energy change during hydride formation and decomposition, which is giving rise to a hysteresis loop in sorption isotherms characterized by two plateaus corresponding to absorption and desorption, respectively. In more complex metal alloy systems, hydride sorption isotherms showing two plateaus during absorption and two plateaus during desorption have been observed,1 indicating the presence of two different hydride types in these systems.2−4 The observation of such “multiplateaus” has been accounted for by introducing hydrogen sorption sites with different enthalpies and entropies of hydride formation.5 The presence of such sites was experimentally confirmed.1 Even more complicated © 2012 American Chemical Society
asymmetric isotherms were reported for some bulk metallic alloy systems. One type exhibited a single plateau during absorption and a double plateau during desorption experiments.6−8 For a second type of alloy, i.e. CeNi1−xCox, an opposite behavior was found, that is, a double plateau during absorption and a single plateau for desorption.9 These, together with numerous other experimental1,10−12 and theoretical studies,13 have led to a general agreement that the presence of the two different hydride phases causes the double plateau structure during absorption or desorption. However, the reasons behind asymmetric hysteresis with a double plateau in only one of the respective absorption or desorption branches are still not clear. In this work, we report for the first time the presence of asymmetric p−C isotherms during the hydrogenation of a nanostructured single metal system (in contrast to the bulk twoor three-component alloys where asymmetric hysteresis was observed before) and explain the asymmetric hysteresis effect by a combination of sample heterogeneity and the interplay of strain-dependent thermodynamics and kinetics. In the experimental part of our study, we investigate Pd nanorings made by colloidal lithography-based nanofabrication on a glass support, for optical measurements of the hydrogen concentration.14 The nanometer-sized Pd rings investigated in the present work are a good example of a nanostructured model system, which we use here to scrutinize how geometry and/or internal structure and defects influence the thermodynamics of hydride formation in nanoentities. Specifically, the studied system Received: June 16, 2012 Revised: August 29, 2012 Published: September 19, 2012 21201
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Figure 1. (first row) Schematic depictions of the sacrificial Pd films with increasing thickness t as thermally evaporated through the colloidal mask. t = 20 (a), 40 (b), 60 (c), 80 (d), and 100 nm (e). We note that we use this thickness of the sacrificial Pd layer as identifier/name for the samples studied in this work but that the latter does not directly translate into (but directly relates to) the wall thickness of the fabricated Pd nanorings. The SEM micrographs show a top-view (second row) and tilted-view (third row) on single and an ensemble of respectively Pd nanoring(s) with increasing nominal wall thickness from left to right. Clearly, not only an increasing wall thickness can be observed but also the overall appearances is changing from a homogeneous and rather smooth one for the thinnest walls to a more heterogeneous shape for the thickest walls, where two different regions clearly are seen. The bottom row comprises optical absorbance spectra for the different Pd nanoring systems.
due to refractive index changes19 as well as to electronic and volume changes of the plasmonic particle itself, such as hydride formation or other solid-state reactions.17,20
consists of Pd nanorings with identical inner diameters but systematically varied wall thickness resulting, additionally and as discussed below, also in different microstructure. From our previous work on similar nanostructures (Pd nanodisks,15−17 Pd nanorings with thin walls,17 and Pd nanoparticles in the sub10 nm size range18), we know that these systems are characterized by phase diagrams showing single-plateau structure for both absorption and desorption runs. Here, however, for Pd nanoring structures with walls nominally thicker than the ones investigated in ref 17, asymmetric hysteresis with a double plateau for hydrogenation and a single plateau with identical equilibrium pressure for dehydrogenation is observed for a wall thickness above a certain threshold. The p−C experiments were carried out by exploiting our direct nanoplasmonic sensing (DNPS) scheme17 where the nanostructure of interest functions as nanoplasmonic sensor and hydride forming entity at the same time. During the DNPS experiment structural and electronic changes, induced in the nanoparticle by hydrogen sorption and linearly linked to variation of the hydrogen concentration in the nanostructure,17 are detected by reading out, in real time, the localized surface plasmon resonance (LSPR) response, e.g., spectral peak shifts (Δλmax), of the hydrogenated nanoparticles. LSPR is a collective excitation of the electrons confined in a metallic nanoparticle, which leads to a strong interaction of light with the latter. The resonance wavelength of this oscillation is very sensitive to events occurring in the particle nanoenvironment
2. NANORING FABRICATION AND STRUCTURAL/OPTICAL CHARACTERIZATION The Pd nanorings in this work were prepared on borofloat glass substrates using colloidal lithography, as described in detail elsewhere.21,22 In brief, polystyrene (PS) colloidal particles (240 nm mean diameter, sulfonate latex, IDC Corporation) were deposited, as sacrificial polymer masks, in a dispersed layer onto the glass substrates using electrostatic self-assembly, which yields an amorphous PS particle array with typically about 10% particle surface coverage. Subsequently, a 20−100 nm thick sacrificial Pd film (determines the wall thickness of the nanorings after the last fabrication step, as described below) was thermally evaporated through the colloidal mask (Figure 1a−e, first row). The substrate holder was water cooled during the evaporation process at the base pressure 2.0 × 10−6 mbar and an evaporation rate of 1 Å/s. Using this thickness of the sacrificial Pd layer as identifier/name for the samples studied, we should emphasize that it does not directly translate into the true wall thickness of the final Pd nanorings (see below). In the next fabrication step, a collimated argon ion beam was used to etch away the sacrificial Pd layer and, through secondary sputtering of material, create a ring-shaped Pd “shell” around 21202
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the undersides of the PS particles. After removal of the remains of the PS particles with UV-ozone treatment, free-standing ring-like Pd structures were obtained on the glass surface as shown in the scanning electron microscope (SEM) pictures in Figure 1 (these pictures were obtained after the hydrogenation experiments). We note that a layer of (surface) oxide that probably formed during the ozone treatment is easily reduced upon the first exposure to hydrogen. As clearly seen in the micrographs, by increasing the thickness of the sacrificial Pd film from 20 to 100 nm, the shape of the ring walls is changed and their thickness can be significantly increased. The bottom row in Figure 1 shows normalized optical absorbance spectra of the Pd nanoring structures obtained in vacuum and at room temperature by shining monochromatic light on the sample (illuminated area diameter ca. 5 mm) and by scanning the wavelength. The measurements reveal the LSPR as a well-defined absorbance maximum in the NIR spectral range. Interestingly, the LSPR line shape becomes systematically narrower as the wall thickness of the nanorings increases. The “shoulder-like” feature, which is seen at shorter wavelengths than the dipolar plasmon peak, is most likely caused by a quadrupolar mode,23 which can be excited, despite the normal incident of the light, due to the inherent structural asymmetry of the rings. We now turn to a discussion of the specific microstructures of the Pd nanorings to be able to correlate structure to the hydrogenation specifics discussed below. As becomes clear from the side-view SEM pictures in Figure 1, an increase of the sacrificial Pd layer gives rise to (i) an increase of the average wall thickness but also to (ii) a drastic change of the general appearance of the nanorings for initial Pd sacrificial layers with thicknesses >40 nm (note that 40 nm is the same sample as used in ref 17). While nanorings with thin walls have a uniform shape and a rather smooth surface, the ones with thicker walls develop a distinct two-component structure, consisting of a “bottom” part (resembling a foundation block) and a smoother “top” part (resembling more the thin walled ring structures seen for the thinner sacrificial layers). The reason for the appearance of this two-part structure is not completely clear but may, speculatively, be related to the relaxation of the ring structure (a process expected to introduce defects) for larger nominal wall thicknesses due to the increasing total mass of Pd in the system. In Figure 2, transmission electron microsocope (TEM) pictures (Philips CM200 FEG 200 TEM at 200 keV acceleration voltage) for a 40 nm (left column, a−d) and a 100 nm Pd (right column, e−h) ring sample, fabricated on a TEM grid, are shown. From these images it becomes clear that the microstructure of the rings is rather complex and inhomogeneous. For example, quite significant differences in grain size within the rings become apparent and clearly the wall thickness varies/decreases significantly from the bottom to the top of the ring. Furthermore, recalling the specific mechanism of nanoring fabrication, that is, secondary sputtering of Pd in an Ar-ion miling process, implies that structural defects are quite abundant.
Figure 2. TEM micrographs of Pd nanorings made from a 40 nm (left column) and 100 nm (right column) thick Pd sacrificial layer: [(a) and (e)] overview images illustrating the quasi-random distribution of the rings on the substrate surface; [(b) and (f)] top-view images of single rings; [(c) and (g)] single Pd nanorings at a tilt angle of 35°; and [(d) and (h)] the corresponding zoom-ins on the ring walls.
sorption was then detected by reading out spectral peak shifts (Δλmax) of the LSPR peak obtained from an optical transmission measurement through the measurement chamber using a Varian Cary 5000 spectrophotometer. Prior to every experiment, the measurement chamber was pumped overnight at 80 °C. Thereafter, the sample was catalytically cleaned by two subsequent oxygen−hydrogen cycles and structurally stabilized by repeated hydriding−dehydriding cycles, until the signal was reversible for completed cycles. p−C isotherms were then measured by stepwise increasing the hydrogen pressure in the chamber. The typical time scale for reaching equilibrium was in the few to few tens of seconds range depending on both temperature and position in the phase diagram. In our
3. HYDROGENATION EXPERIMENTS The DNPS hydrogenation experiments were carried out in a heated stainless steel chamber with two windows, whereof one was the sample (Figure 3a). The chamber was connected to a vacuum pump and a gas inlet connected to hydrogen gas (6 N purity). The optical response of the Pd nanorings to hydrogen 21203
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two absorption plateaus even more clear (Figures 3e and 4), whereas the slope is more or less the same. Moreover, the total width of the hysteresis for both plateaus is increased. Finally, for the 100 nm sample, the relative weight of the two absorption plateaus is now shifted toward the second one and accompanied by an even further increase of the total width of the hysteresis. In Figure 4, the phase diagrams for the different nanorings are summarized for hydrogenation (left column) and dehydrogenation (right column). Specifically, the Δλmax signals of the individual measurements are normalized with their value at 1000 mbar H2 in order to directly compare the general shapes of the isotherms. Furthermore, Figures 4b,d comprise a zoom-in on the plateau region with a linear (not logarithmic) H2 pressure axis. As already indicated above, several striking features become very clear. (i) A double plateau appears exclusively on the absorption branch for nominal thicknesses t > 40 nm. On the contrary, the “center of mass” of all desorption plateaus is at the exact identical pressure. (ii) The slope on sorption and desorption plateaus increases significantly for decreasing wall thickness. Notably, identical (in terms of size distribution) PS particles were used for the fabrication of all samples, ruling out sample inhomogeneity on the global level as the origin of slope. Furthermore, based on the SEM and TEM analysis discussed above, the thinner-walled rings appear to be structurally more homogeneous, eliminating structural inhomogeneity at the level of particle shape as potential factor. (iii) The width of the hysteresis decreases systematically with decreasing nominal wall thickness. Notably, the hysteresis is basically absent for the 20 nm sample. Moreover, a higher sorption plateau pressure exclusively accommodates the change in width of the hysteresis. The equilibrium pressure for dehydrogenation is constant and coincides perfectly with the value for bulk-like Pd measured in our earlier work using the identical Pd source.17 An additional observation that can be made in Figure 4 is an apparent stabilization of the α- and β-phase on the cost of a shrinking two-phase coexistence region. Similar observations have been made for Pd clusters in the sub-10 nm size range24 and are usually attributed to the increasing relative importance of (sub)surface sites in small structures. In our case here, it is more debatable to what extent this argument can be applied since it is very difficult to obtain reliable quantitative information about the true wall thickness of the ring structures. Nevertheless, we believe that it is reasonable to assume that for the thinnest rings at least the top part of the structure is 10 nm or thinner. Therefore, tentatively, the made observation could have the same origin as in clusters. As the next step in our analysis, in Figure 5a, a series of three isotherms obtained at different temperatures (30, 55, 80 °C) for the rings with thickest walls (sample 5 made with a 100 nm Pd sacrificial layer) are shown. A similar analysis for 40 nm wall thickness was presented in ref 17. Notably, at all three temperatures the double plateau structure is clearly seen and occurs only during absorption, while a single plateau is observed during dehydrogenation. Furthermore, we also note that the size of the hysteresis is, as expected, diminishing as one approaches the critical point in the phase diagram. The corresponding Van’t Hoff plots are shown in Figure 5b where the logarithm of the plateau pressure is plotted as a function of 1/T. The slope of the plots reveals the enthalpies for hydride formation and hydride decomposition. Interestingly, the obtained values for hydride formation (−40 and −38 kJ/mol
Figure 3. (a) Schematic depiction of the experimental setup and the DNPS optical readout principle. (b−f) Optical hydrogenation isotherms for Pd nanorings with different nominal wall thickness obtained at 55 °C. The SEM picture insets show a top view on a single nanoring with respective dimensions. The main observations are the appearance of a “double plateau” upon hydrogenation together with an increasing width of the hysteresis and decreasing plateau slope for increasing wall thicknesses.
experiments, at least three wavelength scans (each taking ca. 1 min each) were taken for each pressure to make sure that two subsequent scans were falling perfectly on top of each other (indicating that the sample had reached the new equilibrium). Thus, each data point for the isotherm was taken in equilibrium or, more specifically, in apparent equilibrium on the time scale of at least 2 min. Figure 3b shows a DNPS isotherm measured at 55 °C for the 20 nm Pd sample with the thinnest walls. Clearly, both absorption and desorption plateau exhibit a significant slope and hysteresis is almost absent. For the next nominal thickness, 40 nm Pd, a decrease in slope on the coexistence plateau together with an increased width of the hysteresis is evident from Figure 3c. When further increasing the nominal thickness of the rings to 60 nm Pd (Figure 3d), a striking new feature appears in the absorption isotherm as a second plateau with significantly higher plateau pressure. Furthermore, seemingly, the slope on the first absorption and on the desorption plateau is even further reduced compared to the first two samples with thinner walls. Increasing the thickness to 80 nm makes the presence of 21204
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Figure 4. Series of 55 °C isotherms for the different nanorings for optical signals Δλmax normalized with their value at 1000 mbar H2 for direct comparison of general isotherm shape. The hydrogenation branches at logarithmic (a) and linear (b) hydrogen pressure scale clearly illustrate an increasing plateau pressure and decreasing slope for increasing ring wall thickness between 20 and 60 nm. Above these values the slope remains basically unchanged. The dehydrogenation branches at logarithmic (c) and linear (d) hydrogen pressure scale illustrate a constant equilibrium pressure for all samples, while the slope of the plateau increases for decreasing wall thickness up to 60 nm. Note also widening α- and β-phase regions for decreasing nominal wall thickness. The dashed black lines indicate, for comparison, bulk plateau pressures measured for Pd nanodisks by Zoric et al.17
these details. Under such circumstances, one can hardly give a full-scale interpretation of the observed asymmetric hysteresis. For these reasons, our analysis below is kept on the generic conceptual level. With the reservation above, we start by recalling that the hydride formation in metals represents an example of a firstorder phase transition in a solid. According to general theory of such phase transitions, the standard thermodynamic condition for the coexistence of dilute dissolved hydrogen (α phase) and hydride (β phase) is represented as
H2 for the lower and higher plateau, respectively) are slightly lower than the corresponding values for the nanorings with thin (40 nm) walls (−42.4 kJ/mol) reported by us in an earlier work.17 The analogous Van’t Hoff analysis for the desorption plateau yields an enthalpy for hydride decomposition of −44 kJ/mol H2 for the 100 nm thick-walled sample, comparing to a value of −47.3 kJ/mol H2 for the 40 nm thin-walled nanorings.
4. DISCUSSION In the this section, we primarily focus on discussion of the possible explanation of the striking observation of a double plateau observed during hydrogenation of thick-wall Pd nanorings followed by a single plateau isotherm during the reverse dehydrogenation. As stated in the Introduction, similar asymmetry in absorption/decomposition isotherms has been seen in bulk alloy systems.9 From the outset, we exclude the usual simple two-hydride type arguments since they lead to the double plateau structure in the isotherms for both hydrogenation and dehydrogenation. Instead, we use an approach implying sample heterogeneity, defect-induced strain, and kinetic limitations. To justify our theoretical analysis, we note that the SEM and TEM pictures (Figure 2) clearly show that the thin-walled Pd nanorings, which exhibit a classical symmetric hysteresis curve, are structurally nearly homogeneous. In contrast, the thickwalled (t > 40 nm) nanoring samples exhibiting asymmetric hysteresis are much more heterogeneous. Physically, this heterogeneity appears to be related to the “far from equilibrium” conditions of the fabrication of the nanorings. The details of the microstructure of these nanorings remain, however, obscure despite the SEM and TEM measurements. Unfortunately, there are no other more efficient ways to clarify
μHm = μHh = μH0
μm H
(1)
μhH
where and are the chemical potentials of hydrogen atoms in the former and latter phases, and μ0H is the coexistence potential. At equilibrium between dissolved hydrogen atoms and hydrogen molecules in the gas phase, the chemical potentials of these species are related as 2μH = μH = kBT ln(p) + const 2
(2)
where p is the H2 pressure. The pressure p0 corresponding to the coexistence of α and β phases is defined by the condition 2μH0 = kBT ln(p0 ) + const
(3)
According to eqs 1−3, the H absorption and desorption isotherms should coincide and exhibit a plateau at p = p0. In reality, one can observe various deviations from this prediction due to lattice strain, sample inhomogeneity, and surface-related factors. To explain the kinetic features under consideration from our experiments, we now assume that the sample is heterogeneous and can be divided into two regions (1 and 2). If these regions were structurally perfect and there were no complicating 21205
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Figure 6. Schematic location of the equilibrium plateaus of the H absorption and desorption isotherms for regions 1 and 2: (a) ideal case without hysteresis, (b) ideal case with hysteresis, [(c) and (d)] with the defect-induced lattice strain in region 1. In cases (c) and (d), the matching of the desorption-plateau positions is perfect and nonperfect, respectively.
Figure 5. (a) Three isotherms measured at different temperatures for the ring with thickest walls (sample 5, 100 nm Pd sacrificial layer). In all cases, the double plateau structure occurs only during hydrogenation whereas a single plateau is observed during the dehydrogenation process. Furthermore, the coexistence region and the size of the hysteresis are diminishing as one approaches the critical point in the phase diagram. (b) Van’t Hoff plots showing the logarithm of the plateau pressure as a function of inverse temperature for the lower (1) and upper hydrogenation plateau (2) as well as for the single plateau observed during dehydrogenation. The enthalpies for hydride formation and decomposition obtained from the Van’t Hoff analysis are also given.
lattice strain caused by other means than the H-sorption itself. In particular, the Pd lattice in nanosized structures can be strained by surface tension.28 Because of this factor, the isotherms are shifted up, and the scale of this effect can be estimated by using the expression kBT ln(pabs/p0) = 4γv/R, where γ is the surface tension, v is the increase of the lattice volume per absorbed H atom, and R is the radius of curvature. For the H/Pd system, this effect is significant if R ≤ 4 nm. Consequently, in our case, the contribution of surface tension induced lattice strain seems to be minor because the typical sizes of the assumed regions 1 and 2 are expected to be larger, as can be seen from the SEM an TEM pictures. As a third key factor, we note that the lattice strain can also be related to lattice defects. In particular, our nanorings, as already noted, are heterogeneous, i.e., are expected to contain defects created by the peculiarities of the fabrication method or, more specifically, by the lack of thermal annealing. In our analysis, we assume that region 2, which would correspond e.g. to the internal part of the ring is more uniform and neglect defects there, while the main type of defect in region 1, corresponding e.g. to the external part of the ring, is considered to contain vacancies resulting in the formation of tensile lattice strain. Because of this factor, the isotherms associated with region 1 are shifted down on the pressure axis. The scale of this effect can be estimated by using the relations ΔμH2 = 2ΔμH = −2vσii/3, where σii is the trace of the stress tensor.29 In particular, this defect-induced shift of the isotherms is expected to be comparable with that related to the H-induced lattice strain described above. Consequently, if this shift of the isotherms of region 1 nearly compensates the inherent difference of the desorption-plateau positions for regions 1 and 2 (Figure 6c), the system will exhibit the isotherms like those we observe for our thick-walled Pd nanorings, that is, a
factors, the H absorption and desorption would occur at p = p0 in both cases as schematically shown in Figure 6a. Let us now consider step by step the role of likely complicating issues. One of the key factors and the first one considered in our discussion is the H-induced lattice strain. According to the analysis performed by Schwarz and Khachaturyan25,26 for macroscopic samples, this factor results in appreciable hysteresis. In particular, the H absorption should occur at p = pabs > p0, whereas the desorption should take place at p = pdes < p0. Notably, the ratio pabs/pdes (that is basically the width of the hysteresis) can be sizable and up to 1 order of magnitude for, in particular, bulk systems. In our case, however, this ratio is considerably smaller due to the specifics of H absorption and desorption in nanometer-sized structures. In this limit, the ratio pabs/pdes should decrease with decreasing nanostructure size as observed in experiments and predicted by our earlier analysis.27 Let us now consider that the size scale (i.e., the volume) of region 2 in our nanoring system is larger than for region 1. Then, accordingly, the ratio pabs/pdes for region 2 is larger than that for region 1, as schematically shown in Figure 6b. As a second general factor, the H absorption and desorption isotherms can also be influenced by imposed lattice strain, that is, 21206
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double plateau for absorption and a single plateau for desorption, respectively. Of course, the matching of the desorption-plateau positions in regions 1 and 2, due to the shift of the isotherms of region 1, may be nonperfect as schematically shown, e.g., in Figure 6d. Notably, even in this case the system can in principle exhibit isotherms like those we observe provided that regions 1 and 2 correspond to the external and internal parts of the nanoring as, for example, has been assumed above. In this situation, the hydrogen absorption, governed by thermodynamics, will occur first in region 1 and then in region 2. In this case, the hydride formation in region 2 can in principle be limited by H diffusion in region 1, but the apparent kinetics will anyway exhibit the second plateau. According to thermodynamics, the H desorption should first occur from region 2; however, this process may be slow because it can be limited by H diffusion via region 1 which is still in the hydride state. During the measurements of isotherms, the driving force for H absorption and desorption is relatively weak (because the subsequent changes in the pressure are modest), and we cannot exclude that desorption from region 2 is kinetically postponed up to the moment of desorption from region 1. Physically, this situation is similar to that observed during sorption of nitrogen at 77 K in porous solids30,31 where the condensation is fully governed by thermodynamics and occurs in different pores independently, while the desorption from large pores may be controlled by desorption from surrounding small pores and accordingly depends on the desorption pathways and should be described by using the percolation theory.
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5. CONCLUSIONS In summary, we have observed that hydrogenation/dehydrogenation isotherms for nanosized Pd nanorings show features consisting of a double plateau in the coexistence curve during the hydrogenation stage and a single plateau during the reverse dehydrogenation stage. Such an unusual behavior seems to be accounted for by the influence of the H and defect-induced tensile strains present in our structurally inhomogeneous nanorings combined with specifics of the hydrogenation/ dehydrogenation kinetics. Basically, we believe that the observation of a double plateau in our Pd nanostructures during hydrogenation and a single plateau during dehydrogenation is related to the sample heterogeneity and the interplay of thermodynamics and kinetics. This concept is generic and can be applied to alloys as well. Similar arguments can be used to explain a single plateau during hydrogenation and a double plateau during dehydrogenation. The experimentally observed size-dependent hysteresis trends require quantification of this model, which, in view of the limited knowledge of the material nanostructure, is beyond the scope of this work.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We acknowledge Dr. Stefan Gustafsson for the TEM pictures. The work was funded by the SSF project RMA-08, the Formas project 229-2009-772, and the Swedish Research Council project 2010-4041. 21207
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