Microfabricated Palladium−Silver Alloy Membranes and Their

Jun 25, 2004 - Department of Chemical Engineering and Chemistry, Eindhoven University of Technology,. Eindhoven, The Netherlands, and Aquamarijn ...
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Ind. Eng. Chem. Res. 2004, 43, 4182-4187

Microfabricated Palladium-Silver Alloy Membranes and Their Application in Hydrogen Separation H. D. Tong,*,† F. C. Gielens,‡ J. G. E. Gardeniers,† H. V. Jansen,† C. J. M. van Rijn,§ M. C. Elwenspoek,† and W. Nijdam§ MESA+ Research Institute for Nanotechnology, University of Twente, Enschede, The Netherlands, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, Eindhoven, The Netherlands, and Aquamarijn Micro Filtration BV, Zutphen, The Netherlands

A submicron-thick and defect-free palladium-silver (Pd-Ag) alloy membrane is manufactured using microfabrication technology. The microfabrication process creates a robust wafer-scale membrane module, which can easily be integrated into a holder with gastight connections. High separation fluxes of up to 4 mol of H2/m2‚s with a minimal selectivity of 1500 for H2/He at 450 °C and 83 kPa of H2 retentate pressure were obtained with this setup. The developed membrane technology has great potential for hydrogen purification and in applications such as dehydrogenation. Introduction The increased demand for pure hydrogen gas in recent years in many sectors, ranging from petroleum processing to materials treatment and renewable energyrelated applications such as fuel cells, has led to a revival of interest in methods for separation and purification of hydrogen from gas mixtures.1-3 In addition, the depletion of crude oil, natural gas, and fossil fuel in combination with the stricter rules on environmental regulations have made hydrogen a serious candidate as a future alternative clean energy carrier.2,4,5 Nonporous palladium (Pd)-based membranes have been extensively studied, largely because of their unmatched potential as hydrogen-selective membranes for separation or purification and in membrane reactors for (de)hydrogenation reactions. In most cases, Pd is alloyed with silver (Ag) to overcome the well-known problem of hydrogen embrittlement.6,7 In the past decade, a substantial research effort has been carried out to directly deposit thin layers of Pd or Pd alloys on porous supports, thus creating a so-called composite membrane for hydrogen separation or membrane reactors for (de)hydrogenation.6-11 The use of a thin Pd layer not only gives a high separation flux but also allows fabrication of membranes at reasonable costs. To make a separation layer without pinholes and cracks on top of the porous supports is, however, very difficult when the layer thickness is in the submicron range. The commercially available porous supports are seldom defect-free; they are likely to be supplied with (few) imperfections, e.g., particulates on the substrate, nonuniformities in pore size, etc., which causes the thin metal films to not completely cover the support, which may lead to membrane defects.7,9-11 Because the gas molecules of interest are very small, even a few defects with L >0.5 µm‚cm-2 of the membrane surface will * To whom correspondence should be addressed. Tel.: (00 31) 53 489 2805. Fax: (00 31) 53 489 3343. E-mail: T.Hien@ el.utwente.nl. † University of Twente. ‡ Eindhoven University of Technology. § Aquamarijn Micro Filtration BV.

already significantly deteriorate membrane selectivity.12 For instance, Roa et al. deposited a 10-µm-thick PdCu film on porous γ-alumina (nominal pore size of 5-50 nm) and reported that the membrane was not defectfree, most probably because of the imperfections of the initial supports.9 Other research groups also reported that the surface quality of the initial supports is crucial for the production of defect-free membranes. 7,10,11 Microfabrication technology, originally developed for semiconductor devices and circuits and later extended to microelectromechanical systems,13 offers a new approach for the fabrication of thin and defect-free Pd composite membranes.14-16 In this new approach, the Pd alloy films are first deposited on a dense and smooth surface of previously microfabricated supports. Then, the supports are partially etched from their backside to create pathways to the Pd surface for the gases, thus forming the membranes. Because the separation films are now deposited on a dense and smooth surface with almost no imperfection, the films can cover the support completely, leading to defect-free membranes later. Meanwhile, the use of the microfabricated supports allows the fabrication of very thin films. Here, we present a new process to make a robust PdAg membrane module for hydrogen separation, utilizing microfabrication techniques such as thin film sputter deposition, KOH etching of silicon, and anodic wafer bonding. The microfabrication results, the membrane performance with respect to hydrogen separation and selectivity, and the utilization of the membrane are presented and discussed. Experimental Section Microfabrication of a Pd-Ag Membrane Module. A cross section of a Pd-Ag membrane module is shown in Figure 1. The Pd-Ag membrane is microfabricated on a supporting microsieve on a 〈110〉 silicon wafer (Si〈110〉) and then sandwiched between two thick glass wafers to form a membrane module. The process steps to obtain the Pd-Ag membrane are shown in Figure 2 and are as follows: a 3-in., double-sided, polished Si〈110〉 is coated with 0.3 µm of wet-thermal silicon dioxide (SiO2) and 1 µm of low-stress silicon-rich

10.1021/ie034293r CCC: $27.50 © 2004 American Chemical Society Published on Web 06/25/2004

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Figure 1. Cross section of the separation membrane module. Only two membrane/microsieve frames are drawn for illustration.

Figure 2. Fabrication process of the Pd-Ag membrane module.

silicon nitride (SiN) by means of low-pressure chemical vapor deposition.17 Parallellogram-shaped structures of 600 × 2600 µm are aligned and imprinted on the backside of the wafer by standard photolithography, followed by a dry CHF3 + O2 reactive ion etching of SiN and a wet etching of the oxide layer, using a buffered oxide etch (BHF; step 2a). A detailed design of the parallelogram-shaped structure that can be etched by potassium hydroxide (KOH) into Si〈110〉 can be found in ref 18. The wafer is immersed in a 25% KOH solution at 75 °C to etch the silicon until the SiO2 layer is reached, thus forming an array of suspended bilayer SiN/SiO2 membranes (step 2b). The dimensions of the suspended SiN/SiO2 membranes depend on that of the parallelogram-shaped structures previously imprinted on the backside of the Si wafer18 and are ca. 600 × 1900 µm in this membrane design. Afterward, standard lithography and dry etching of SiN are carried out on the frontside of the Si wafer to pattern a microsieve19 with circular sieves of 5 µm on the suspended SiN/SiO2 membranes. The SiN dry etching process is controlled to stop on the SiO2 layer, thus forming a microsieve on top of the SiO2 membrane (step 2c). At this stage, alloy films of Pd-Ag are deposited by simultaneous (dual) sputtering from pure targets of Pd and Ag (5 N; Materials Target Co.) on the flat side of the SiO2 membrane, using titanium (Ti) as an adhesion layer. The detailed dual-sputtering procedure and the properties of the as-deposited layer were reported earlier.15 In the current work, we deposited a 500 nm Pd-Ag film with a Ag content of 23 wt %. Next, SiO2 and Ti are removed in BHF through the openings of the sieves to partially reveal the back surface of the Pd-Ag film, thus forming a Pd-Ag membrane. Parts a-c of Figure 3 are scanning electron microscopy (SEM) images of a ca. 500-nm-thick Pd-Ag membrane on a SiN supporting microsieve. As shown, the fabricated Pd-Ag membrane is uniform in thickness, has a smooth surface, and seems to be defect-free.

As mentioned above, depositing the film on the planar surface of the sacrificial layer (SiO2 in our case) and releasing it later seems to be the key point obtaining such good submicron films. Additional advantages such as a low gas transfer resistance to be used in hydrogen separation will be discussed in a separating section. In the current design, the porosity of the supporting microsieve, and therefore the porosity of the Pd-Ag film in the microsieve, is about 20%, but it may be increased to 50%.19 Finally, the silicon wafer is bonded between two thick glass wafers (Borofloat; Schott Co.) by a four-electrode anodic bonding technique.15 Before the bonding procedure, powder blasting20 was used to create a flow channel of 200 µm depth and a buffer zone of 1000 µm on the glass wafers. The bonding process resulted in a tight seal between each glass wafer and the silicon wafer. Furthermore, the bonding process as it was performed here creates a membrane module that is robust enough for practical use; e.g., in this form it could be integrated in a stainless steel membrane holder to have connections to a gas manifold and a measurement setup.15 The mechanical strength of the membranes was tested before carrying out a separation experiment. Tests showed that the 500-nm-thick Pd-Ag/microsieve membrane broken at pressure differences of 4 ( 0.5 bar over the membrane was measured with the setup described by Rijn et al.19 This membrane strength is sufficient for the membrane to be used in hydrogen separation. Although not discussed in detail here, it should be mentioned that stronger membranes can be fabricated by studying the membrane design parameters; e.g., reducing the width Lsf or Lm (see Figure 2e) will create stronger membranes.15,19 Testing Setup for Hydrogen Separation Characterization. The permeability of the membrane was determined for H2 and helium (He) with the experimental setup shown in Figure 4. Nitrogen (N2) was used as a sweep gas at the permeate side. All feed flow rates were measured and controlled with mass flow controllers (Bronkhorst High-Tec, EL-FLOW). The permeate pressure was measured and controlled with an absolute pressure controller (Bronkhorst High-Tec, EL-PRESS). The transmembrane pressure, the pressure drop over the permeate side, and the pressure drop over the retentate side were also measured (Hottinger Baldwin Messtechnik, PD1). A temperature-controlled oven was used to ensure isothermal operation. The H2 and He concentrations in the permeate were measured by a gas chromatograph (GC) equipped with a thermal conductivity detector (TCD) and a 5 Å molecular sieve column. Argon (Ar) was used as the carrier gas, which gives the TCD a high sensitivity to H2 and He and a poor sensitivity to N2. The purity of all gases used was 5 N. The membrane module was placed in a stainless steel holder,15 which was installed in an oven for isothermal operation. The H2/He feed and sweep gases were preheated in spiral channels placed in the same oven. The feed flow was varied between 300 and 1000 mL/min, and the H2 molar fraction was varied from 0.1 to 0.9 mol/mol. The sweep gas flow was kept constant at 300 mL/min. The experimental setup was controlled by a PLC. A PC with Labview handled the data acquisition at 100 Hz. The setup was running fully automatically 24 h/day and could handle 100 recipes without user

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Figure 3. SEM pictures of the microfabricated membrane. (A) An overview of the membrane on Si〈110〉. Pd-Ag film on the SiN microsieve: (B) as seen from the top of part A; (C) as seen from the bottom of part A. Note that, to make the illustration in part C, the wafer membrane was broken and then one part of the Pd-Ag film was peeled off from the supporting microsieve with the aid of an adhesive tape.

Figure 4. Schematic drawing of the hydrogen separation setup.

intervention. For each recipe, 4 samples/h were taken of the permeate and analyzed by GC. Results and Discussion Separation Flux. The hydrogen flow rate through the 500 nm Pd-Ag membrane versus the duration of the experiment is given in Figure 5. The flux is defined as the molecular hydrogen flow through the membrane divided by the free Pd-Ag area (mol of H2/m2‚s). Noted that, in conventional membranes where ceramic porous materials are used to support the membranes, fluxes are often normalized to the entire surface area. At a membrane temperature of 723 K and a hydrogen partial

pressure of 83 kPa at the retentate, a high hydrogen flux of ca. 4 mol of H2 /m2‚s was measured. This flux is at least 5-10 times higher than the fluxes reported in the literature.6-11,21 The reasons for obtaining such high fluxes may be that a thin Pd-Ag membrane (500 nm) with high composition control and nanostructures15 was used. Most importantly, such a membrane has a very low resistance to mass transfer because virtually no support layer is present. It is known that the mass-transfer resistance associated with viscous flow (Hagen-Poiseuille type) or diffusion through the porous support could be very significant in the composite membrane.21

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Figure 5. Hydrogen flow rate through the membrane as a function of time at 723 K and a hydrogen pressure of 83 kPa in the retentate. Note that after measurement for ca. 125 h the permeate flow rate was increased from 300 to 400 mL/min, corresponding with the increase of the hydrogen separation flux from ca. 4 to 4.2 mol of H2/m2‚s.

The viscous flow with flux J through the porous support may be calcualated as22

J)

 r2 P ∆P 8ητ RTL m

(1)

with J the flux through the porous support, the driving force ∆p ) P1 - P2,  the porosity, τ the tortuosity, r the average pore diameter, L the thickness of the porous medium, η the viscosity of the gases, and the mean pressure Pm ) 0.5(P1 + P2), where P1 and P2 are the pressures at the inlet and outlet of the porous support, respectively. Applying eq 1, Ward and Dao estimated that to have a viscous H2 flow of 10-3 mol/cm-2‚s at 673 K through a 1-mm-thick porous support with a porosity of 50%, a tortuosity of 3, and an average pore diameter of 5 µm would require a H2 pressure drop of approximately 0.4 bar within the support, assuming P2 ) 0 and no other mass-transfer resistance.21 Apparently, the presence of the porous supports in the conventional membrane construction significantly reduces the driving force across the Pd layer. However, for the microfabricated membrane construction (Figures 1 and 3), the same H2 flow would only have to travel through a thinner support of 0.4 mm with much larger pores of 600 µm to access the Pd-Ag surface, thus requiring a much smaller pressure drop. Computer simulations (using flow solver CFX4.2) gave a pressure drop of less than 5% from the inlet to the membrane surface.23As a result of lowering the pressure drop, the present membrane will obtain a higher flux in comparison with the conventional composite membrane type if the other conditions are taken to be the same. Figure 5 also shows that the flux is rather stable; it was first increased from ca. 3.6 to 4 mol of H2/m2‚s over a period of about 50 h and then became stable. The increase of the flux in the first measuring period may be explained by an increase in the Pd grain size, as was supposed by Lin.24 However, the increase of the flux in the current report is much less than that observed by Lin. After measurement for a period of ca. 120 h, the retentate flow rate was increased about 50% from 600 to 900 mL/min to investigate the flux change. However, there was only a very small increase of the separation flux, suggesting that the previous separation flux of about 4 mol/m2‚s is a stable value in this measurement condition.

Additionally, to investigate the membrane stability, one membrane was measured for a relatively long period of ca. 1000 h, during which period the membrane experienced changes in gas type and concentration as well as temperature cycles between 300 and 723 K. The measured results showed no significant reduction in the membrane flux or the membrane selectivity, suggesting excellent membrane stability. In the case of direct deposition of the metal films on the porous supports to form a membrane, probably strong interactions between metal and supports took place, especially when the top layer on the support has very small pores, leading to instability of the membrane in terms of both the separation flux and the selectivity.10,25 However, in the microfabricated membrane construction (Figures 2e and 3), the Pd-Ag film is free-standing with a period of the sieve diameter (5 µm in our case) on SiN and SiO2, materials of which are both well-known as good antidiffusion barriers in IC technology. Therefore, in the typical range of temperatures in which hydrogen separation is performed (up to 500 °C), there is almost no diffusion of the metals (Pd, Ag, or Pd-Ag) into the support, contributing to the good stability of the membrane. Because hydrogen separation through a Pd film occurs via a solution/diffusion mechanism, it is worth knowing which step is governing the separation process. The equation for the hydrogen flux is written in terms of Fick’s first law as follows:6,7,21,25

J)

Q n (P - Pnpermeate) h retentate

(2)

where J is the flux of hydrogen, Q is the permeability, h denotes the thickness of the membrane layer, n n and Ppermeate stand for the hydrogen partial Pretentate pressure in the retentate and permeate, respectively, and n is the hydrogen pressure exponent. When diffusion through the bulk metal is the rate-limiting step and hydrogen atoms form an ideal solution in the metal (Sievert’s law of hydrogen solubility dependence), n is equal to 0.5. A value of n greater than 0.5 may result when surface processes influence the permeation rate or when Sievert’s law is not followed. It is expected that, as the membrane thickness decreases to the submicron range, the diffusion time of the hydrogen atom becomes extremely fast. Therefore, the n value will be close to 1.6-10,21,25 To determine which step limits the H2 transport rate, experiments were carried out with varying H2 concentrations in the feed from 18 to 83 kPa at 723 K. In Figure 6, the measured fluxes are plotted against the difference in H2 partial pressures in retentate and permeate, which gives a value of n close to 1 for a 500 nm thin Pd-Ag membrane. This n value indicates that the influence of surface processes is dominant in the whole separation process, which is consistent with the common observation for submicron-thick Pd-based membranes.6-8,10,21,25 Currently, more experiments such as the influences of CO, CO2, or steam on the membrane performance are ongoing. We believe that a better understanding of the membrane properties will help us to fabricate membranes with a lower surface resistance, leading to even higher hydrogen separation fluxes. Membrane Selectivity. Possible membrane leaks during the permeation experiment can be detected by measuring the He concentration at the permeate side. However, no He was found during the experiments.

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Figure 6. Dependence of hydrogen fluxes on the driving force through the membrane at 723 K. Note that an average flux for a period of about 100 h was used for each measurement point in this graph.

Therefore, to calculate a minimum selectivity of H2 over He, the detection limit of GC for He is used as the maximum He concentration. In this way, a minimal separation factor of 1500 for H2 to He (or equivalent to about 4000 for H2 to N2) is calculated. This high selectivity indicates that the microfabricated membrane is most likely defect-free. We believe that depositing the Pd-Ag separation layer on a very smooth and clean silicon oxide layer and preparing the membrane in a dust-poor clean room environment were the key parameters to get to this result. Vos and Verweij claimed that the use of a clean room reduced the average concentration of particles of 0.5 µm from 18 million m-3 in normal laboratory air to less than 100 m-3 in a class 100 clean room, where our membranes are prepared.12 Without clean-room conditions, the number of defects caused by particles from the air was estimated to be at least 5 defects of L > 0.5 µm‚cm-2 of the membrane surface. This number dropped to ,1 when our clean-room conditions were applied. Membrane Utilization Although the thickness of the Pd-Ag membrane has been reduced to submicron thickness, the membrane costs are probably still high in comparison to those of composite membranes,26 because the microfabricated membrane has to be produced in a clean-room environment using clean-room techniques. The main retail costs seem to be clean-room expenses as well as silicon and glass substrates,27 not the Pd films, as is the case for conventional membranes. However, following the general trends in semiconductor technology, we expect that the total membrane costs will be significantly reduced when membranes can be batch-produced. Considering the high hydrogen separation flux as well as high selectivity, the present membrane seems to be suited for small-scale purification units that supply high-quality hydrogen for applications such as fuel cells, semiconductor materials processing, or laboratory use.1-5,28,29 For example, several manufacturers are proposing to produce fuel cell power systems to produce 1 kW of electricity for residential use.9,30 Production of 1 kW of electricity would require approximately 600 standard liters per hour (SLPH) of high-purity hydrogen. This amount of hydrogen can be purified by using a Pd-Ag membrane made on the 6 in. silicon wafer with a feasible membrane porosity of 25%.

The present technology would allow the construction of a larger module, in which the larger (and thicker) glass plates are used to house a number of membrane wafers, thus obtaining a large Pd area for separation. Additionally, this larger module can be operated in a parallel mode, thus using the principle of “numbering up” instead of scaling up to increase hydrogen throughput. The proposed unit may find application in an onsite hydrogen production system, where small, natural gas based reformers, being developed for a distributed fuel cell power system, could potentially be used to generate hydrogen-rich reformate streams.31 Purification is an essential step to remove impurities in the reformate that may poison the storage unit or fuel cell and to remove non-hydrogen species that can dramatically increase the size of the on-site and on-board storage system.31 The numbering-up principle has certain advantages over conventional scale-up. Conventional scale-up entails going from laboratory scale to a single large unit through a series of costly laboratory experiments, simulations, and pilot plan testing.32 While, because each microfabricated-based membrane would behave exactly alike, individually and in replicated units, numbering up would be considerably shorter and less expensive, allowing for faster transfer time to the market. We think that in certain applications the advantages provided by numbering up of microfabricated membranes may override the economies of conventional large plants. The fabricated membrane may be used as a membrane reactor for dehydrogenation reactions to synthesize high-value products,33,34 although the applicability may be limited because hydrogenation reactions are normally carried out at much higher pressures as tested here, nominally at several tens of bars. Nevertheless, the membrane design can be changed to obtain stronger membranes.27 Furthermore, the present technology here may be used to fabricate other kinds of thin but strong and defect-free membranes to set up new applications; for instance, an ultrathin SiN membrane has been made for nanosieve membrane formation.35 Conclusions Thin but strong Pd-Ag alloy membranes were fabricated with microfabrication technology and tested. Pd-Ag films were sputtered onto a planar surface support (SiO2/SiN microsieve) and released later, creating defect-free, submicron-thick Pd-Ag films. The fabrication method also created a robust membrane module, which is important for practical use. The microfabricated membranes achieved high permeation rate and high hydrogen selectivity; flow rates of ca. 4 mol of H2 /m2‚s are measured with a selectivity above 1500 for H2/He. In addition, the membranes possessed a good stability in performance. The utilization of the reported membranes at different scales was presented and discussed. The present technology seems to be suitable for fabricating small-scale membrane units for hydrogen purification from gas mixtures. Also, the present membrane may be used as a membrane reactor for hydrogenation/dehydrogenation. Acknowledgment Financial support from the STW foundation, ABB Lummus Global Inc., DSM, and Aquamarijn is kindly acknowledged. Our thanks are also due to Erwin Ber-

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enschot, Meint de Boer, and Rik de Boer for their technical support. Literature Cited (1) Ramachandran, R.; Menon, R. K. An Overview of Industrial Uses of Hydrogen. Int. J. Hydrogen Energy 1998, 23, 593. (2) Steele, B. H. C.; Heinzel, A. Materials for Fuel-Cell Technology. Nature 2001, 414, 338-344. (3) A Review of the National Hydrogen Vision Meeting; United States Department of Energy: Washington, DC, Nov 15-16, 2001. (4) Hoffmann, P. Tomorrow’s Energy; MIT Press: Cambridge, MA, 2001. (5) Dresselhaus, M. S.; Thomas, I. L. Alternative energy technologies. Nature 2001, 414, 332. (6) Shu, J.; Grandjean, B. P. A.; VanNeste, A.; Kaliaguine, J. Catalytic Palladium-Based Membrane Reactors: review. Can. J. Chem. Eng. 1991, 69, 223. (7) Dittmeyer, R.; Hollein, V.; Daub, K. Membrane Reactors for Hydrogenation and Dehydrogenation Processes based on Supported Palladium. J. Mol. Catal. A: Chem. 2001, 173, 35. (8) King, L. Y.; Varma, A. Novel Preparation Technique for Thin Metal-Ceramic Composite Membranes. AIChE J. 1995, 41 (9), 2131. (9) Roa, F.; Way, J. D.; McCormick, R. L.; Paglieri, S. N. Preparation and Characterization of Pd-Cu Composite Membranes for Hydrogen Separation. J. Chem. Eng. 2003, 93, 11. (10) Xomeritakis, G.; Lin, Y. S. CVD Synthesis and Gas Permeation Properties of thin Palladium/Alumina membranes. AIChE J. 1998, 44, 174. (11) Brien, J. O.; Hughes, R.; Hisek, J. Pd-Ag Membranes on porous Alumina Substrates by Unbalanced Magnetron Sputtering. Surf. Coat. Technol. 2001, 142, 253. (12) Vos, R. M.; Verweij, H. High-Selectivity, High-Flux Silica Membranes for Gas Separation. Science 1998, 279, 1710. (13) Wise, K. D.; Najafi, K. Microfabrication Techniques for Integrated Sensors and Microsystems. Science 1991, 254, 1335. (14) Frank, A. J.; Jensen, K. F.; Schmidt, M. A. Palladium Based Membranes for Hydrogen Separation and Hydrogenation/ Dehydrogenation. Proc.sIEEE Micro Electro Mech. Syst. 1999, 382. (15) Tong, H. D.; Berenschot, J. W.; De Boer, M. J.; Gardeniers, J. G. E.; Wensink, H.; Jansen, H. V.; Nijdam, W.; Elwenspoek, M. C.; Gielens, F. C.; Rijn, C. J. M. Microfabrication of PalladiumSilver alloy Membrane for Hydrogen Separation. J. Microelectromech. Syst. 2003, 12, 622-630. (16) Karnik, S. V.; Hatalis, M. K.; Kothare, M. V. Towards a Palladium Micro-Membrane for the Water Gas Shift Reaction: Microfabrication Approach and Hydrogen Purification Results. J. Microelectromech. Syst. 2003, 1, 93. (17) Gardeniers, J. G. E.; Tilman, H.; Visser, C. C. G. LPCVD Silicon-Rich Silicon Nitride Films for Applications in Micromechanics, Studied with Statistical Experimental Design. J. Vac. Sci. Technol., A 1996, 14, 2879. (18) Kendall, D. L. Vertical etching of silicon at very high aspect ratios. Rev. Instrum. Sci. 1979, 9, 373. (19) Rijn, C. J. M.; Wekken, M.; Nijdam, W.; Elwenspoek, M. C. Deflection and Maximum Load of Microfiltration Membrane

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Received for review December 8, 2003 Revised manuscript received May 4, 2004 Accepted May 13, 2004 IE034293R