Nanostructured Metal Foams: Synthesis and Applications · Nanostructured Metal Foams: Synthesis and...

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Nanostructured Metal Foams: Synthesis and Applications E Luther, B Tappan, A Mueller, B Mihaila, A Cardenas, H Volz, P Papin, J Veauthier, M Stan Abstract Fabrication of monolithic metallic nanoporous materials is difficult using conventional methodology. Here we report a relatively simple method of synthesizing monolithic, ultralow density, nanostructured metal foams utilizing self-propagating combustion synthesis of novel metal complexes containing high nitrogen energetic ligands. Nanostructured metal foams are formed in a post flame-front dynamic assembly with densities as low as 0.011 g/cc and surface areas as high as 270 m 2 /g. We have produced metal foams via this method of titanium, iron, cobalt, nickel, zirconium, copper, palladium, silver, hafnium, platinum and gold. Microstructural features vary as a function of composition and process parameters. Applications for the metal foams are discussed including hydrogen absorption in palladium foams. A model for the sorption kinetics of hydrogen in the foams is presented. Introduction The introduction of the synthesis of aerogels by Kistler in 1931 marked the beginning of the fabrication of low-density, nanoporous monolithic materials. 1 The synthesis of corresponding metal foams has received attention only more recently. Metal foams with densities from 0.04-0.08 g/cm 3 are reported in the literature; however, these foams are relatively low surface area magnesium and aluminum and contain cells on the millimeter length-scale. 2,3 A silver sponge was reported with pore sizes on the order of a few microns and a surface area of 0.5 m 2 /g and a similar gold sponge with a surface area of 1 m 2 /g have been produced, however, no density was reported. 4 A hybrid dealloying/filter-casting approach to address diffusion limitations has recently been developed for Au monoliths. In this approach, filter-cast microsphere-templated Au/Ag alloys are dealloyed to produce nanoporous gold monoliths with a hierarchal porosity that have densities as low as 0.28 g/cm 3 and surface areas of about 1.5 m 2 /g. 5 Dendritic platinum three- dimensional foam-like nanostructures were synthesized in an aqueous surfactant but these are limited to very small clusters ranging in size from 6 to 200 nm. 6 An excellent reference discussing the synthesis of macrostructured metal foams is also available; 7 however, until reported by Tappan et al., 8 no process had been available to synthesize bulk, nanostructured foams. In this paper, we will discuss the synthesis of various transition metal nanofoams as well as potential applications. The synthesis of monolithic metal foams has been performed by the rapid decomposition of energetic materials. The process is unique in the formation of a bulk material with nanoscale features in a time scale of seconds. In addition, the chemistry of the process can be modified to yield numerous compositions including titanium, zirconium, iron, cobalt, nickel, palladium, platinum, copper, silver, and gold. The microstructural features of the metal foams varies significantly with composition and processing conditions. In the case of iron, extremely high 1 S.S. Kistler, Nature, 1931, 127, 741. 2 L. Gibson, Annu. Rev. Mater. Sci., 2000, 30, 191. 3 H. Kanahashi, T. Mukai, Y. Yamada, K. Shimojima, M. Mabuchi, T.G. Nieh, K. Higashi, Mater. Sci. Eng., 2000, A280, 349. 4 Biener, J., Hodge, A.M., Hamza, A.V., Hsiung, L.L., Satcher, J.H. J. Appl. Physic., 2005, 97, 1 5 Nyce, G.W., Hayes, J.R., Hamza, A.V., Satcher, Jr. J.H., Chem. Mater. 2007, 19, 344‐346 6 D. Walsh, L. Arcelli, I. Toshiyuki, J, Tanaka, S. Mann, Nature Mater. 2003, 2, 386. 7 M. Ashby, A Evans, N. Fleck, L. Gibson, J. Hutchinson, H. Wadley, Metal Foams: A Design Guide, Butterworth-Heinemann, Woburn, MA, 2000. 8 B. C. Tappan, M. H. Huynh, M. A. Hiskey, D. E. Chavez, E. P. Luther, J. T. Mang, S. F. Son, J. Am. Chem. Soc. 2006, 128, 6589-6594.

Transcript of Nanostructured Metal Foams: Synthesis and Applications · Nanostructured Metal Foams: Synthesis and...

Page 1: Nanostructured Metal Foams: Synthesis and Applications · Nanostructured Metal Foams: Synthesis and Applications E Luther, B Tappan, A Mueller, B Mihaila, A Cardenas, H Volz, P Papin,

Nanostructured Metal Foams: Synthesis and Applications E Luther, B Tappan, A Mueller, B Mihaila, A Cardenas, H Volz, P Papin, J Veauthier, M Stan Abstract Fabrication of monolithic metallic nanoporous materials is difficult using conventional methodology. Here we report a relatively simple method of synthesizing monolithic, ultralow density, nanostructured metal foams utilizing self-propagating combustion synthesis of novel metal complexes containing high nitrogen energetic ligands. Nanostructured metal foams are formed in a post flame-front dynamic assembly with densities as low as 0.011 g/cc and surface areas as high as 270 m2/g. We have produced metal foams via this method of titanium, iron, cobalt, nickel, zirconium, copper, palladium, silver, hafnium, platinum and gold. Microstructural features vary as a function of composition and process parameters. Applications for the metal foams are discussed including hydrogen absorption in palladium foams. A model for the sorption kinetics of hydrogen in the foams is presented. Introduction The introduction of the synthesis of aerogels by Kistler in 1931 marked the beginning of the fabrication of low-density, nanoporous monolithic materials.1 The synthesis of corresponding metal foams has received attention only more recently. Metal foams with densities from 0.04-0.08 g/cm3 are reported in the literature; however, these foams are relatively low surface area magnesium and aluminum and contain cells on the millimeter length-scale.2,3 A silver sponge was reported with pore sizes on the order of a few microns and a surface area of 0.5 m2/g and a similar gold sponge with a surface area of 1 m2/g have been produced, however, no density was reported.4 A hybrid dealloying/filter-casting approach to address diffusion limitations has recently been developed for Au monoliths. In this approach, filter-cast microsphere-templated Au/Ag alloys are dealloyed to produce nanoporous gold monoliths with a hierarchal porosity that have densities as low as 0.28 g/cm3 and surface areas of about 1.5 m2/g.5 Dendritic platinum three-dimensional foam-like nanostructures were synthesized in an aqueous surfactant but these are limited to very small clusters ranging in size from 6 to 200 nm.6 An excellent reference discussing the synthesis of macrostructured metal foams is also available;7 however, until reported by Tappan et al.,8 no process had been available to synthesize bulk, nanostructured foams. In this paper, we will discuss the synthesis of various transition metal nanofoams as well as potential applications. The synthesis of monolithic metal foams has been performed by the rapid decomposition of energetic materials. The process is unique in the formation of a bulk material with nanoscale features in a time scale of seconds. In addition, the chemistry of the process can be modified to yield numerous compositions including titanium, zirconium, iron, cobalt, nickel, palladium, platinum, copper, silver, and gold. The microstructural features of the metal foams varies significantly with composition and processing conditions. In the case of iron, extremely high 1 S.S. Kistler, Nature, 1931, 127, 741. 2 L. Gibson, Annu. Rev. Mater. Sci., 2000, 30, 191. 3 H. Kanahashi, T. Mukai, Y. Yamada, K. Shimojima, M. Mabuchi, T.G. Nieh, K. Higashi, Mater. Sci.

Eng., 2000, A280, 349. 4 Biener, J., Hodge, A.M., Hamza, A.V., Hsiung, L.L., Satcher, J.H. J. Appl. Physic., 2005, 97, 1 5 Nyce, G.W., Hayes, J.R., Hamza, A.V., Satcher, Jr. J.H., Chem. Mater. 2007, 19, 344‐346 6 D. Walsh, L. Arcelli, I. Toshiyuki, J, Tanaka, S. Mann, Nature Mater. 2003, 2, 386. 7 M. Ashby, A Evans, N. Fleck, L. Gibson, J. Hutchinson, H. Wadley, Metal Foams: A Design Guide,

Butterworth-Heinemann, Woburn, MA, 2000. 8 B. C. Tappan, M. H. Huynh, M. A. Hiskey, D. E. Chavez, E. P. Luther, J. T. Mang, S. F. Son, J. Am.

Chem. Soc. 2006, 128, 6589-6594.

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surface areas (~270 m2/g) and extraordinarily low densities (0.011 g/cm3) have been achieved.7 Numerous applications are suggested by the favorable combinations of materials properties offered by metal foams. The high surface area combined with the inherent high electrical conductivity of metals is attractive for electrode applications in batteries, fuel cells and supercapacitors. The high surface area and nanoporosity suggests applications in catalysis. The high surface area and high thermal conductivity suggests use in hydrogen storage. In this paper we briefly discuss possible applications for several interesting metal foam compositions. We then describe more closely study the hydrogen uptake in palladium nanofoams. Experimental Note: This work involves the use of energetic materials and proper precautions should be taken. Energetic materials synthesized in this laboratory are routinely tested for explosive sensitivity to impact, friction and spark and are considered acceptable to handle if values are less than or equal to that of the explosive standard pentaerythritol tetranitrate (PETN). The generalized synthesis method for metal foams consists of the decomposition of metal complexes of the energetic ligand bistetrazolamine (BTA) under inert environments. Several methods have been reported for the synthesis of the BTA ligand;9,10 however, in this study, the method of Naud et al.11 was used. Dicyanamide salt was reacted with an azide salt and acidified to a pKa of less than 1. The bi(tetrazolato)amine metal complexes were synthesized in an aqueous solution by reaction of the monohydrated bi(tetrazolato)amine, or ammonium bi(tetrazolo)amine and a metal salt as described elsewhere.12 The metal complex is dried under inert atmosphere or in a vacuum oven and collected as a fine powder. The nano-porous palladium produced in this work resulted from the decomposition of palladium complexes of the energetic ligand bistetrazolamine (BTA) under inert environments. The bi(tetrazolato)amine metal complexes were synthesized in an aqueous solution by reaction of the ammonium bi(tetrazolo)amine ((NH4)2BTA) and a metal salt of palladium consisting of either K2PdCl4 or PdCl2(CH3CN)2. A portion of (NH4)2BTA (2 eq) was dissolved in water with heating and K2PdCl4 (1 eq) or PdCl2(CH3CN)2 (1 eq) were dissolved in water and warmed. This was added to the (NH4)2BTA solution to give a white or beige precipitate and pale-yellow solution. This mixture was stirred overnight at room temperature and the precipitate filtered and washed with ethanol for a yield of 90-92%.

Water or CH3CN

NN

NN

NN

NN

NH4 NH4

HN

Pd(II)-saltN

N

NN

NN

NN H

N

Pd

NN

NN

NN

NN

NH

2-

2.0

Heats of formation of certain complexes used to make nanofoams were measured and adiabatic

9 Norris, W. P.; Henry, R. A. J. Org. Chem. 1964, 29, 650. 10 Highsmith, T. K.; Hajik, R. M.; Wardle, R. B.; Lund, G. K.; Blau, R. J.

U.S. Patent 5,468,866, 1995. 11 Naud, D. L.; Hiskey, M. A. U.S. Patent 6,570,022, 2003. 12 Chavez, D. E.; Hiskey, M. A.; Naud, D. L. J. Pyrotech. 1999, 10, 17.

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flame temperatures calculated, Table 1. (Foams made from some of the complexes listed are not discussed in this paper.) These measurements provide interesting insight into the mechanism of formation of the metal monoliths in the combustion front, as even the complexes with the highest adiabatic temperatures are still below the melting point of the metal.

Complex Name Chemical Formula

Molecular Weight

Heat of Formation

kJ/mol

Density g/cm3

Adiabatic Flame

Temperature K**

Ammonium tris(bi(tetrazolato)ammine)amine Fe(III)

C6H15N30Fe 563.23 767.8 1.847 1219.3

Ammonium bis(bi(tetrazolato)ammine)amine Ni(II)

C4H10N20Ni 396.95 -10.4 1.734 621.4

Ammonium tris(bi(tetrazolato)ammine)amine Co(III)

C6H15N30Co 566.32 781.8 1.856 1237.2

Copper(II) bis-(1(2)H-tetrazol-5-yl)amine Diammonia

C2H7N11Cu 248.70 52.6 1.767 708.0

Ammonium bis(bi(tetrazolato)amine Pd(II)

C4H10N20Pd 444.68 336.7 * *

Ammonium bis(bi(tetrazolato)amine Pt(II)

C4H10N20Pt 533.34 -109.2 * *

*Data Unavailable **Calculated at 1.01bar

The data suggests that melting does not occur during formation of the foam, but rather that foam assembly occurs by rapid sintering or localized surface melting in a highly non-equilibrated state. (Because Pd and Pt are not in the product libraries for the thermoequilibrium code used for the data, the adiabatic flame temperature for the combustion of these two complexes could not be determined. However, from the heats of formation, similar molecular weights and chemical formulas, the adiabatic flame temperatures are expected to be well below the melting point of these metals.) The complexes were pressed into 6.35 mm by 6.35 mm pellets in a uniaxial press. The density of the pellets was determined volumetrically. In most cases, fully dense pellets were desired and were pressed to approximately 95% of theoretical maximum density. In some cases, less dense pellets were desired if the precursor did not support a stable burn front. These were pressed at correspondingly lower pressure. For example, the PdBTA complexes were pressed to approximately 65% density with a gauge pressure of 60 kPa. The pellets were loaded into a 2 liter combustion chamber under N2 or Ar gas. Ignition was accomplished either by means of a resistively heated nickel-chromium wire or a 10.6 µm CO2 laser. Metal foams were studied by electron microscopy. Scanning electron microscopy (SEM) images were obtained using a Strata DB235 Dual Beam Focused Ion Beam SEM using the through the lens detector, or with a LEO 1525. Transmission electron micrographs (TEM) were taken by a JEOL JEM-1200EXII electron microscope operation at 120 kV. The supporting grids were Formvar-covered, carbon-coated, 200-mesh copper grids. Powder X-ray diffraction scans were recorded with a Bruker-AXS, Inc. (Madison, WI) D8 Advance, in Bragg-Brentano geometry. The radiation used was from a Cu K sealed tube source (=1.5418 Å). The detector was a scintillation counter equipped with a diffracted beam graphite monochromator.

Hydrogen sorption studies were conducted on a Hiden Intelligent Gravimetric Analyzer. Prior to

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hydrogen adsorption studies, foams were conditioned by heating to 300˚C under 100 mbar of H2. Static isotherms were then taken to 0.1 MPa (1000 mbar) H2. Isotherms were alternated between the temperature of interest and a higher temperature (80˚C) isotherm in order to bring the material to a “standard state”. Gold Nanofoams Gold is usually considered a catalytically inactive metal due to its completely filled 5d orbital and high first ionization energy;13 however, nanostructured gold has been shown to be catalytic. Some examples of gold used for catalysis are are the epoxidation of propenes;14 and recently, growth of single- and multi-walled carbon nanotubes by chemical vapor deposition.15 The low-/room-temperature oxidation of CO to CO2

16 has also been of focus, however recent publications suggest that oxidation of CO to CO2 may have been a result of catalysis by residual silver in the dealloyed gold foam. Counter intuitively the use of nanostructured Au is potentially less costly relative to bulk Pt, Pd, and Rh used in heterogeneous catalysis. Gold foams have been produced by self-propagating high temperature synthesis from two related BTA containing precursors. The two precursors contain different concentrations of volatiles. The burn rate varies by almost an order of magnitude between these materials (1.3 vs. 16 cm/s). A scanning electron microscopy (SEM) image of the fast burning foam is seen in Figure 1. The foam was found to contain ~95 wt% Au by EDX analysis. The surface area as determined by BET analysis was 10.9 m2/g, which is, the highest surface area Au monolith known to us. The slower burning foam is notable because its bulk density of 0.057 g/cm3 is, to our knowledge, the lowest density monolithic gold foam reported to date.17,18 Au nanofoams were annealed under a flow of 40 sccm of a 6% H2 in Ar mixture at 550°C for 4 h. Two-point probe conductivity measurements of the annealed foams revealed a conductivity of ~150 Ω/cm for the slow burning foam but only ~5 Ω/cm for the fast burning foam. Conductivities of the annealed foams were ~106 times higher than the unannealed precursors likely due to an increase in crystallinity and removal of non-conductive impurities. Nickel Nanofoam Nickel is a low cost alternative to precious metal catalysts. The requirement is an electronic band structure that promotes the reaction of interest and high surface area to maximize reagent contact.

13 G. Schmid, Chem. Rev. 1992, 92, 1709-1727. 14 T. Hayashi, K. Tanaka, M. Haruta, J. Catal. 1998, 178, 566. 15 M. Yamada, M.-A. Kawana, M. Miyake, App. Catal. C, 2006, 201-207. 16 M. Haruta, T. Kobayashi, H. Sano, N. Yamada Chem. Lett. 1987, 2, 405 17 J. Biener, G.W. Nyce, A.M. Hodge, M.M. Biener, A.V. Hamza, S. Maier, S. A. Adv. Mater. 2008, 20,

1211–1217. 18 D. J. Bond, J. D. Hares, J. D. Kilkenny, Phys. Rev. Lett. 1980, 45(4), 252-5.

Figure 1 SEM image of gold nanofoam, 1 µm scale bar

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Typically, so called “skeletal catalysts”, “sponge metal catalysts” or Raney nickel are used. These materials are high surface area nickel structures produced by leaching, or dealloying, a nickel aluminum alloy with sodium hydroxide to remove the aluminum leaving a porous material. These catalysts have been used for many organic processes including hydrogenation, ammonolysis, reductive alkylations and dehydrogenation. Porous nickel is also used as an electrode in fuel cells, batteries and hybrid supercapacitors. The higher surface area of a porous material allows the electrolyte access to more of the metal resulting in faster charge/discharge characteristics. Nickel is typically used as the positive electrode being one of few materials that can withstand repeated cycling and the associated volumetric changes. Nickel metal nanofoams were produced via the self-propagating high temperature synthesis method. An SEM image of the resulting foam is seen in Figure 2. This material has a surface area of approximately 36 m2/g. This compares reasonably well with the 20 to 100 m2/g typical of Raney nickel.19 XRD data is seen in Figure 3. As can be seen, a curious result of the synthesis method is the formation of both the typical cubic form of nickel as well as the more unusual hexagonal form. The implications of this result on catalysis have not been evaluated to date. Furthermore, unlike Raney Ni catalysts which can contain up to 25% residual Al, the Ni nanofoams produced from this process are metallically pure Ni (as formed, however, Ni nanofoams contain surface organic impurities which can be removed via heat-treatment or possibly chemical treatments). Titanium Nanofoams Titanium has the highest strength to weight ratio of any metal, is highly corrosion resistant and is considered physiologically inert. This combination of properties makes it widely used in fields from aerospace to medical implants. The fabrication of titanium foams has implications in many fields. In the medical arena, titanium is capable of osseointegration, the direct connection of living bone and structural implant.20 As a lightweight material, titanium is prized. The open structure of a foam has the potential for even lighter weight, stiff structural materials; e.g. in sandwich panels.21

19 J. Freel, W. Pieters, R. Anderson, J. Catalysis, 1968, 14, 247. 20 H. Li, S. Oppenheimer, S. Stupp, D. Dunand, L. Brinson, Mater. Trans., 2004, 45(4), 1124. 21 F. Zok, S. Waltner, Z. Wei, H. Rathbun, R. McMeeking, A. Evans, Int. J. Solids and Structures, 2004,

41, 6249.

Figure 2 SEM image of Ni nanofoam, 200 nm scale bar.

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Nanosized titanium dioxide is a critical component of dye sensitized solar cells (DSSC).22 In DSSCs, photogenerated electrons are created by a monolayer of, typically, ruthenium metalorganic dye which is deposited on titanium dioxide nanoparticles. The n-type titanium dioxide carries the electron while the holes are passed to an electrolyte. Titanium BTA complexes were produced by the reaction of Ti[OCH(CH3)2]4 with two

22 L. Schmidt-Mende, U. Bach, R. Humphry-Baker, T. Horiuchi, H. Miura, S. Ito, S, Uchida, M. Gratzel,

Adv. Mater., 2005, 17(7), 813.

Figure 4 SEM image of titanium nanofoam synthesized under inert gas, 500 nm scale bar.

Figure 5 SEM image of titanium dioxide nanofoam synthesized by oxidation of titanium metal nanofoam in air, 1 µm scale bar.

Figure 3 XRD of nickel nanofoam showing cubic (blue) and hexagonal (red) crystallography

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equivalents of BTA in dry alcohol. As seen in Figure 4 titanium nanofoams were successfully produced by the self-propagating high temperature synthesis method. A surface area of 70 m2/g was obtained. In contrast with other metal foams produced by this technique, XRD analysis shows an essentially amorphous structure with a broad peak corresponding to anatase. A further unique feature was the ability to oxidize the foam in air. Unexpectedly, the oxidized material maintained its structural integrity, Figure 5, and crystallized into a mixture of anatase and rutile titanium dioxide as identified by XRD, see Figure 6.

Palladium Nanofoams In contrast with gold, palladium is a well known catalyst in organic synthesis.23 It is considered to be one of the most versatile catalysts for C-C bond formation. Palladium is also well known for its hydrogen permeability. This discovery dates back to the 19th century but invigorated interest came with the advent of hydrogen fuel cells and the need to filter impurities from the hydrogen feed stream. In addition, bulk palladium is also known to reversibly store a remarkable amount of hydrogen, up to 900 times its volume at room temperature; however, in nanosized palladium, desorption is not completely reversible.24 In our research we synthesized a nanostructured palladium foam as a model system to study the adsorption desorption kinetics and reversibility of hydrogen storage with an eye towards improving the kinetics of hydrogen storage in commercially viable hydrogen storage alloys; e.g., LaNi5. A model was also developed to better understand the kinetics of the hydrogen uptake by palladium foam.

23 J Tsuji, ed. Palladium in Organic Synthesis, Springer, 2005. 24 H Kobayashi, M Yamauchi, H Kitagawa, Y Kubota, K Kato, M Takata, J. Am. Chem. Soc, 2008, 130,

1828.

Figure 6 XRD of titanium oxide nanofoam after oxidation

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Palladium foams synthesized by high temperature self-propagating synthesis roughly doubled in volume to very fragile black monoliths. Scanning electron microscopy, Figure 7, shows an extremely fine structure with a poly-modal pore size distribution on the order of 100-200 nm with structural elements of the walls having particle sizes of roughly 10-20 nm. The finer structural features of the walls are better seen in the TEM, as in Figure 8. BET surface areas of Pd foam formed at 3.5 MPa overpressure was 36.5 m2/g. The hydrogen sorption properties of the palladium nanofoams were evaluated by a series of isotherms in static hydrogen to 1000 mbar at various temperatures. Identical isotherms were also performed on palladium foam, powder (~0.5 µm diameter) and sheet (~0.1 mm thick). Figure 9 shows a representative isotherm at 50˚C for the foam compared with palladium powder. As seen in the figure, the kinetics of adsorption for both the powder and foam are quite fast; however,

Figure 7 SEM Image of Pd nanofoam formed at 3.5 MPa nitrogen overpressure, a, scale 10 µm, b, scale 100 nm.

Figure 8 TEM Image of Pd nanofoam formed at 3.5 MPa nitrogen overpressure, a, scale 0.5 µm, b, scale 50 nm.

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there is a significant difference in the curve profiles. As expected the rate of hydrogen uptake in palladium sheet is significantly longer. The hydrogen uptake in the nanofoam was found to be only about half that of powder or sheet. A decrease in hydrogen capacity was somewhat expected due to the lower purity of the palladium produced by the combustion process. The combustion process leaves residual carbon and nitrogen which is not fully removed by the 300˚C heat treatment under H2. Figure 10 shows an SEM image of the foam after over 20 hydrogen adsorption/desorption cycles. No obvious physical degradation of the foam has taken place. Hydrogen Storage Modeling in Palladium Nanofoams We assume that the hydriding and dehydriding processes are initiated at the surface and progress into the bulk of the sample governed by Fick’s law of diffusion. To understand the hydrogen diffusion in Pd, we use an idealized model representation of the system as a collection of identical spherical aggregates (particles) of radius R. The radius of the particle, R, does not change during the diffusion process. Assuming the hydrogen diffusion occurs only in the radial direction, the hydrogen diffusion equation reads

where D is the diffusion coefficient, r is the radial space coordinate, T is the temperature, t is the time, and C is the hydrogen mass concentration. Assuming the diffusion coefficient, D, has no radial dependence, the diffusion equation becomes

At t=0, the hydrogen concentration of the particle is initially zero, except for r=R. The hydrogen concentration at the surface is kept constant at a concentration Cs during the simulation, i.e. our

Figure 10 SEM Image of Pd nanofoam after numerous hydrogen uptake/release cycles

Powder

Foam

Figure 9 Hydrogen isotherm to 1000 mbar at 50˚C

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choice of boundary conditions is

To compare with the experimental data, we require the time-dependent mass of the particle, which can be calculated at any time, t, as

The parameters D(T) and Cs are optimized by solving numerically the hydrogen diffusion equation in combination with a standard conjugate-gradient method applied to minimizing the standard deviation between model and experimental data. We demonstrate the applicability of the model for the case of a Pd nano-powder sample. In Figure 11, we show a comparison between experimental data and model at T=50oC. We find that a diffusivity, D/R2 =1.77×10-2 sec-1, describes well the dynamics at intermediate and long times, t > 15sec. The time evolution of the hydrogen concentration in the particle, relative to the concentration at the surface, Cs, is illustrated in Figure 12. To capture better the early-time behavior of hydrogen diffusion, a concentration-dependent chemical diffusivity model25 will be considered in future work. Based on our preliminary experimental and modeling work, we find that the temperature dependence of the diffusivity between 40oC and 70 oC obeys the quadratic law depicted in Figure 13.

25 M. Stan, Y.T. Ahu, H. Jiang, and D.P. Butt, J. Appl. Phys, 2004, 95, 3358

Figure 11 Dynamics of the hydrogen absorption model in nano-powder compared to experiment for T=50˚C.

Figure 12 Time-evolution of the radial profile of hydrogen concentration inside the particle.

Figure 13 Temperature dependence of the hydrogen chemical diffusivity derived from the model.

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Conclusions We have explored the synthesis method of Tappan et al.7 and demonstrated its versatility with regard to the synthesis of numerous metal nanofoams. The nanofoams produced have unusual and sometimes unique properties that are attractive for various applications. We have studied the sorption behavior of hydrogen in palladium as a function of palladium structure. No enhanced kinetic sorption characteristics were observed as a function of size or structure. A reduced storage capacity in the nanofoam was noted that is attributed to the relatively low purity of the palladium nanofoam relative to the palladium powder studied. The hydrogen storage model developed to better understand the kinetics agrees reasonably well with the data.