SILICON-BASED PROTON EXCHANGE MEMBRANE (PEM) AND METHOD OF MAKING A SILICON-BASED PEM

A silicon-based proton exchange membrane for a membrane electrode assembly comprises a silicon wafer including a back side, a front side, and a membrane region therebetween, where the membrane region includes a plurality of channels extending from openings in the front side of the silicon wafer through the membrane region to openings in the back side of the silicon wafer. Walls of the channels include active sites to which a molecular species may be attached. Each of the front side and the back side of the silicon wafer includes a porous capping layer thereon. The capping layer comprises a plurality of through-thickness apertures contiguous with at least a portion of the channels of the membrane region.

DETAILED DESCRIPTION

A silicon-based inorganic-organic membrane that offers a number of advantages over Nafion—including higher proton conductivity, lack of volumetric size change, and membrane electrode assembly (MEA) construction capabilities—is described. Key to achieving these advantages is fabricating a silicon membrane with a high density of high aspect ratio nanoscale pores, adding a self-assembled molecular monolayer on the pore surface, and capping the pores with a layer of porous silica. The silica layer reduces the diameter of the pores and ensures their hydration, resulting in a proton conductivity of 2-3 orders of magnitude higher than that of Nafion at low humidity. A MEA constructed with this proton exchange membrane can deliver an order of magnitude higher power density than that achieved previously with a dry hydrogen feed and an air-breathing cathode.

FIG. 1provides a schematic of an exemplary silicon-based proton exchange membrane100for a membrane electrode assembly.

The membrane100is formed from a silicon wafer105having a front side105a,a back side105b,and a membrane region105ctherebetween. The membrane region105cincludes a plurality of proton-conducting channels (through-thickness pores)110that extend from openings110ain the front side105aof the silicon wafer105through the membrane region105cto openings110bin the back side105bof the silicon wafer105. The channels110may include active sites on the walls110cfor attachment to molecular species. It may be advantageous for at least about 10%, or preferably at least about 50%, of the active sites on the walls110cto include a molecular species115attached thereto, in order to achieve a high surface coverage of molecules comprising a desired functional group. For example, the surface coverage may be as high as several molecules per square nanometer of channel wall area. Preferably, the molecular species115in each channel110form a self-assembled monolayer (SAM) over substantially all of the channel wall.

The channels110, which may be interconnected130, may be formed in a membrane100composed of crystalline or amorphous silicon. Molecular species that may be attached to the active sites include molecules having an appropriate functional group, such as a —SH end group. A suitable molecule is (3-mercaptopropyl)trimeth-oxysilane (MPTMS), SH—(CH2)3—Si—(OCH3)3. After functionalization, the —SH end group of the molecule may be oxidized to —SO3H, which may exist as a sulfonate salt, depending on the pH. A suitable sulfonate is 3-(trimethoxysilyl)propane-1-sulfonate, Si(OCH3)3—(CH2)3—SO3.

To enable maintenance of high conductivity at low humidity, an ultra-thin conformal layer of an insulating material may be deposited at the opening of each of the larger channels, creating small apertures. Referring again toFIG. 1, a thin porous capping layer120is disposed on the front side105aand on the back side105bof the silicon wafer105over the membrane region105c.Each porous capping layer120includes a plurality of through-thickness apertures125contiguous with at least a portion of the channels110of the membrane region105c.The apertures125may also include molecular species115attached to active sites on the aperture walls125a,125b.Using the Kelvin equation, ln RH=−2γV/rRT, one can calculate that a 1 nm diameter water meniscus can be stable at10% humidity, which is lower than the humidity level in most practical applications of fuel cells. Although the specific conductivity of the capping layer can be relatively low, its overall contribution to total membrane resistance is negligible. In contrast to prior art membranes, this membrane construct maintains hydration without detrimentally decreasing proton conductivity.

The channels110extending through the membrane region105cmay have a diameter of between about 2 nm and about 10 nm. For example, the diameter may lie between about 4 nm and about 8 nm prior to adding the molecular species115that further reduce the diameter of the channels110. (The term “diameter” is used broadly to refer to the average lateral size of the channels110; the channels110are not required to have a circular lateral cross-section.) If the channel diameter is too large, then water may be lost by evaporation and the total channel density in the membrane may be undesirably decreased. At diameters that are too small, however, the proton conductivity may drop due to the reduced size of the passageways. Advantageously, the diameter of the channels is between about 5 nm and about 7 nm. Once functionalized, the diameter may be effectively reduced to between about 2 nm and about 5 nm.

The apertures125defined by the capping layers120that overlie the membrane region105cmay be tapered; specifically, they may have a diameter (average lateral size) that decreases with distance away from the membrane region105c.Consequently, the porous capping layers120serve to shrink the size of the openings110a,110bto the channels110. This may be advantageous to maintain hydration of the channels110without diminishing proton conductivity. In one example, the size of the aperture openings120a,120bmay lie between about 1 nm and about 4 nm. The porous capping layers, which may be formed of silica or another hydrophilic and electrically insulating material, such as other oxides, nitrides (e.g., SiN), or oxynitrides, may have a thickness of between about 1 nm and about 5 nm each. In contrast, the silicon membrane region105chas a much greater thickness that typically lies between about 10 microns and about 40 microns and may be between about 20 microns and about 30 microns.

Given the small diameter of the proton-conducting channels compared to the thickness of the membrane through which they pass, the channels have a large aspect ratio (length-to-width). The aspect ratio of the channels may range from about 1,000 to about 20,000 for example. The aspect ratio may also lie between about 5,000 and 15,000. Despite this high aspect ratio, the inventors are able to form a self-assembled monolayer over a large portion (or substantially all) of the channel walls by using a continuous flow method of attaching molecular species to the active sites, as described in detail below. Preferably, substantially all of the active sites on the walls of the channels include a functional group. In addition, molecular species may be attached to active sites on walls of the apertures of the porous capping layers.

It is possible, by way of the fabrication method described below, to produce a high density of relatively straight proton-conducting channels through the membrane. Proton conductivity may be enhanced at higher channel densities due to the increased number of pathways for protons to traverse. Channel or pore density can quantified in terms of the spacing between adjacent channels, where smaller spacings generally correlate with higher channel densities. It may be advantageous for the channels to have an average center-to-center spacing of about twice the diameter of the channels or less. For example, the average center-to-center spacing may be between about 4 nm and about 20 nm. The average center-to-center spacing may also lie between about 8 nm and about 16 nm, or between about 10 nm and about 14 nm.

In one example, the silicon-based membrane is fabricated to have about 5-7 nm diameter silicon channels with MPTMS (SH—(CH2)3—Si—(OCH3)3) molecules assembled on the modified surface of the channels. After functionalization, the —SH end group of MPTMS is oxidized to —SO3H. The thickness of the resulting self-assembled monolayers (SAMs) of MPTMS on silicon oxide is 0.8±0.1 nm. An increase in the size of the head group after oxidation increases the SAMs thickness to around 1 nm. The overall size, then, of the channels after self-assembly reduces to between about 3 nm and about 5 nm.

Anodization can be employed to create the channels in the silicon membrane. However, using a typical two-cell anodization process in which the wafer is installed between two electrolyte baths, the pores may not extend through the entire thickness of the membrane and a layer of nonporous silicon may remain on the backside. To open up the pores on the backside, the remaining silicon layer is generally etched using a plasma (e.g., Freon plasma). Due to variations in the thickness of the remaining silicon layer on a single membrane and over different membranes as well as the pore penetration depth (FIG. 3(b)), the silicon layer gets etched from some areas, exposing porous silicon, which is then etched at a much faster rate (3-5 times) than the nonporous silicon. This results in localized thinning of the membrane and makes fabrication of thin membranes impractical. In addition to the thickness issue, analysis of the composition of silicon membranes fabricated in this manner using time-of-flight secondary ion mass spectroscopy (ToF-SIMS) shows a significant rise in fluorine presence, particularly towards the backside of the membrane.

In order to overcome these issues, a new fabrication method has been developed that leads to production of membranes with uniform open-ended channels in a single step. The process is summarized here in reference toFIG. 2and described in greater detail below. Once the porous membranes are formed, the high aspect ratio channels may be functionalized to include a self-assembled monolayer over the channel walls, and porous capping layers may be formed on the front side and back side of the membrane.

The method of forming the porous membrane entails depositing two metal layers (e.g., a first metal layer made of chromium (Cr) and a second metal layer made of gold (Au)) on the backside of a silicon wafer that includes a thinned membrane region. The first and second metal layers extend over the membrane region10. A plurality of channels are formed in the front side of the silicon wafer20and extended through the membrane region to the back side of the wafer, forming a plurality of openings in the back side30. The channels may be formed and grown through the membrane region by anodization, which entails immersing the silicon wafer and a cathode electrode in an electrolyte solution to form an anodization cell, and running an electrical current through the cell to initiate etching of the silicon to form the channels. Once one or more of the channels extends entirely through the thickness of the membrane region and creates one or more openings in the back side of the wafer, portions of the first metal layer exposed by the openings are removed (e.g., by etching)40. This in turn exposes portions of the second metal layer, which are consequently detached or delaminated from the first metal layer50. When this occurs, the self-terminating anodization process is halted locally (in the vicinity of the openings), although etching continues in other parts of the membrane region.

Delamination of the entire second metal layer occurs after substantially all of the channels extend through the membrane region to the back side60and much or all of the first metal layer is removed. After the process is complete, the first metal layer, which may be formed of gold or another noble metal, may be reused since it is not consumed in the process. The etching process proceeds at an extremely high rate, resulting in a porous silicon membrane comprising a plurality of channels or through-thickness pores that are densely packed across the membrane region.

The first metal layer is generally made of a transition metal with good adhesion to silicon, such as chromium, titanium and/or tungsten. A thickness of about 50 nm or less may be suitable. The second metal layer is typically made of a noble metal with good ductility, such as gold or platinum, and may be about 200 nm in thickness or less. Other metals that may be suitable for the second metal layer include palladium or nickel.

After the porous silicon membrane is fabricated, molecular species may be attached to active sites on walls of the through-thickness pores (i.e., the active sites may be functionalized) to form a self-assembled monolayer over substantially all of the channel walls. A continuous flow process that entails introducing a solute-rich solvent into channel openings on one side of the porous silicon membrane while extracting depleted solvent from channel openings on the other side of the porous silicon membrane may be used to carry out the functionalization. The solute-rich solvent may be, for example, a benzene solution comprising (3-mercaptopropyl)trimethoxysilane (MPTMS), and a solute concentration of between about 0.001 mM to about 100 mM. For example, a concentration of between about 1 mM and about 10 mM may be employed. To facilitate the functionalization, it may be advantageous to convert hydrophobic surface species at the active sites to hydrated silica prior to carrying out the continuous flow process. After attaching the molecular species to the active sites, oxidation of the molecular species may be employed to convert —SH end groups to —SO3H.

Before or after functionalization, a porous capping layer may be deposited on the front side and also on the back side of the porous silicon membrane. The porous capping layers include a plurality of through-thickness apertures contiguous with at least a portion of the channels of the porous silicon membrane. Because the through-thickness apertures decrease in diameter (lateral size) in a direction away from the porous silicon membrane, they effectively reduce the size of the channel openings. As mentioned above, the silica layer ensures that the channels remain hydrated, resulting in a proton conductivity of 2-3 orders of magnitude higher than that of Nafion at low humidity. The porous capping layer is generally formed by atomic layer deposition (ALD), physical vapor deposition (e.g., sputtering or evaporation), or chemical vapor deposition (CVD) to have a thickness of about 10 nm or less. Preferably the thickness of the porous capping layer is about 5 nm or less. Molecular species may be attached to active sites on walls of the through-thickness apertures by either the continuous flow process described previously or by a dipping process.

Fabrication of Porous Silicon Membrane

Fabrication of the silicon membranes may begin with KOH etching of a p-doped <100> silicon wafer. A 0.8 μm thick LPCVD nitride layer is used as a protection mask in KOH solution. First, the nitride layer on the backside of the membrane is patterned and etched using a Freon plasma. The exposed silicon areas are then etched in KOH until a membrane thickness of 24±2 μm is reached. The nitride layer on the frontside of the membrane is subsequently patterned and etched to expose silicon. In membranes with an additional metal layer on the frontside, the patterning step is followed by wet etching of the metal layer and then Freon plasma etching of the nitride layer.

Prior to anodizing the silicon wafer, metal films may be deposited on the back side by using a magnetron sputtering system at 5×10−2Torr pressure and 300 W DC power in argon gas. The resulting backside Cr/Au layer may be wired directly to the anode electrode to provide an electrical path for the electrons to exit the silicon membrane once the pores penetrate to the backside of the membrane. When the pores open up at any location, the Cr layer gets etched at that location and the Au layer delaminates, resulting in a local electrical discontinuity and thereby anodization termination at that location. Since the Au layer does not get etched, it ensures electrical connectivity of the rest of the membrane to the circuit. The Au delamination process occurs gradually over the entire wafer until the pores on all membranes are opened. This event appears as a sudden rise in process voltage, as shown inFIG. 2c. The reason behind a finite increase in voltage is continuation of the anodization process beyond the edges of the membrane into the bulk silicon. Interestingly, the Au layer left outside the membrane can be used as the anode electrode. The cathode electrode is also a Cr/Au layer deposited on the frontside of the wafer prior to etching the nitride layer (both Cr/Au and nitride layers are etched in one patterning step).

Hydroxylation of Pore Walls

After the anodization process, the membrane may be left in de-ionized (DI) water for a few hours to clean the anodization electrolyte from the pores. As the Fourier Transfer Infrared (FTIR) spectra of the membrane (FIG. 4(a)) suggests, the pore wall is covered with SiHx(x=1-3) hydrophobic surface species (the absorption bands were assigned by Glass et al.,Surf. Sci.348 (1996) 325-334). To successfully conduct silane-based self-assembly within the membrane, the surfaces of the pores may be converted to hydrated silica. This can be achieved in two steps. First, the membrane may be partially oxidized at low temperature (300° C.) in an oxygen environment (e.g., O2furnace). Although close to 600° C. may be required to desorb surface hydride species, processing at such a temperature level is not practical due to significant changes in membrane morphology and membrane fracturing. The morphology of porous silicon is known to change at temperatures above 350-450° C. due to changes in crystalline dimensions (i.e., coarsening of the porous silicon texture). These changes may result in a significant decrease in the specific surface area. However, no distinct texture coarsening is observed at 300° C. The oxidized membrane spectrum shows that all Si—H2vibrational stretch modes have shifted to 2260 cm−1with a low intensity tail extending towards lower frequencies, suggesting that the backbone of the Si atoms are targeted by oxygen and the maximum degree of oxidation to —O3SiH (corresponding to absorption at 2260 cm−1frequency) has occurred. The lower frequency tail also indicates the presence of a relatively small population of —OySiHxsurface species. Leaving the membrane in DI water, after the oxidation step, results in insertion of oxygen into Si—H bonds and creation of SiOH surface species. As a result, the 2260 and 876 cm−1absorption bands associated with —O3SiH stretching and bending modes, respectively, disappear and absorption at 3743 cm−1, assigned to isolated SiOH species, intensifies along with the Si—O asymmetric stretching vibrations at 1200 to 1000 cm−1assigned to the siloxane network. The broad absorption band centered at around 3500 cm−1corresponds to the overlapping of the0-H stretching bands of hydrogen-bonded water (H—O—H . . . H) and SiO—H stretching of surface silanols hydrogen-bonded to molecular water (SiO—H H2O). These results suggest the creation of a well hydrated silica pore surface as desired for the subsequent self-assembly step.

Functionalization of Pore Walls

Due to the large surface area and high aspect ratio of the pores, a reactor was constructed (FIG. 5(a)) to continuously supply an approximately 1 mM solution of MPTMS to one end of the pores and extract the solvent from the opposite end.

The membrane die is installed within a fixture between the top and bottom compartments of the functionalization setup. This arrangement allows extraction of the depleted solvent from the bottom of the membrane pores continuously while the solute-rich solvent is supplied over the membrane. A typical process run involves evacuating the chamber and purging with helium multiple times to remove condensed water from the pores. Excess water results in self-polymerization of the MPTMS molecules and clogging of the pores (note that surface adsorbed water remains on the surface). Then, MPTMS in benzene solution is supplied to the solution reservoir on top of the membrane. While the top chamber was charged with helium and the vacuum and helium lines connected to it were closed, the lines connected to the bottom compartment were opened slightly to maintain a slow flow of dry helium. The process was continued until the top reservoir was emptied from solution.

This procedure enabled uniform functionalization of the hydroxyl groups within the membrane (estimated to be ˜5 sites/nm2) as confirmed by ToF-SIMS with depth profiling (shown inFIG. 4b). The —SH end group of the MPTMS molecule was then oxidized to —SO3H in dilute nitric acid, and finally, the membrane was maintained in a large volume of DI water for 24 hrs to diffuse out the nitric acid and hydrate the pores.

Formation of Porous Capping Layers

In order to create a thin hydrophilic silica aperture at the mouth of the pores, plasma-directed atomic layer deposition (PD-ALD) may be employed. Unlike conventional ALD, in PD-ALD, a remote plasma instead of water vapor exposure is used to activate the surface. Because both the plasma Debye length and the radical mean free path greatly exceed the pore diameter, surface activation and silica deposition are confined to the immediate external surface of the membrane pores with no deposition on internal pores. Successive oxygen plasma and tetramethyl orthosilicate (TMOS) exposures using an Ar carrier gas resulted in an approximately 2nm thick silica layer. The interiors of the pores within the silica layer were then functionalized with MPTMS. The maximum diameter of the pores at the two surfaces of the membrane is approximately 2 nm as estimated from SEM and analysis of water adsorption isotherms (FIG. 6).

Fabrication of Membrane Electrode Assembly (MEA)

The last fabrication stage of the MEA was spray painting the anode and cathode catalysts on the membrane (FIG. 6(d)). A catalyst ink with an 18 wt % ratio of Nafion ionomer 1100 EW (from Solution Technology, Inc.) to platinum black (from Alfa Aesar Co.) was prepared in de-ionized (DI) water and isopropyl alcohol (IPA). Direct spray painting of the catalyst ink on the membrane was straight forward since the membrane did not swell and wrinkle as the catalyst solution came in contact with the membrane surface. The membrane was set on a hot plate at 85° C. during spraying. As mentioned previously, and shown inFIG. 3(d), Cr/Au layers already deposited on both sides of the die are used as current collectors. The catalyst layer overlaps with the Cr/Au electrode around the edges of the membrane and provides electrical connectivity. The platinum loading in the catalyst layers was 7 mg/cm2.

Characterization of MEA

All tests were conducted on the MEA in a configuration most relevant to MFCs, where no auxiliary equipment for conditioning the membrane as well as the supply gases is desired, i.e. dry hydrogen is supplied to the anode and the cathode is air-breathing at room temperature (−25° C.). The test package (FIG. 6(e)) was left in an environmental chamber to simulate different ambient humidity levels (uncertainty in humidity measurement was ±2%). The membrane proton conductivity was measured using the four-probe technique (using Solartron 1287). The results (MEA-1) are compared (FIG. 7)with another silicon-based MEA but without the PD-ALD-deposited silica layers (MEA-2) as well as a MEA based on DuPont Nafion PFSA NRE-211membrane (MEA-3) with a nominal thickness of 25 microns. This MEA has been fabricated through sandwiching Nafion between two stainless steel (SS) foils with 2×2 mm2square openings aligned during adhesive bonding of the layers together. The exposed 2×2 mm2Nafion membrane was subsequently brush painted with catalyst. Before discussing various differences between the developed membrane and Nafion, it should be mentioned that adding the silica layer has resulted in approximately 25% decline in the maximum conductivity of the PS-PEM, from about 0.11 S/cm to 0.08 S/cm. This significant decline is most likely due to the closure of some of the smaller membrane pores after the PD-ALD and the subsequent self-assembly processes rather than impeded proton mobility at the smaller entrance and exit of the pores, considering the small thickness of the silica layers.

Aside from this observation, the results show that conductivity of the MEA-1membrane is almost constant down to approximately 20% humidity and then starts to significantly decline. A similar trend is seen in the case of MEA-2membrane, but with a decline at a higher humidity level (50-60%). This difference is expected between the two membranes, since smaller pore diameter allows the water meniscus to remain stable at a lower humidity ambient. Decline in humidity levels beyond this thermodynamic equilibrium condition leads to the partial dryout of the pores, and an increase in crossover as evidenced by a drop in OCP (FIG. 7(b)). Overall, the data suggest a nearly humidity-independent conductivity as long as the vapor pressure at the membrane/ambient interface remains below the ambient saturated vapor pressure, so that the ambient vapor condenses within the pores keeping them filled with water. This fundamentally different attribute of the Si-based membrane over that of Nafion in which pores shrink at low ambient humidity, is a major factor responsible for the difference in conductivity of these two membranes. When the Nafion pores shrink, the amount of bulk-like water at the center of the pores sharply declines. Shrinkage along with reduction in interconnectivity of the water clusters is responsible for the exponential decay in Nafion conductivity.

Conductivity of the MEA-1and MEA-2membrane is 3.5 and 4.8 times, respectively, greater than that of the MEA-3at 95% humidity. However, it should be noted that the MEA-3has gone through a 100° C. hot-pressing step (as part of its fabrication process) widely known to adversely affect Nafion conductivity. Our data on MEA-3at high humidity closely matches data on N-117membrane heat-treated at 105° C. provided in a study by Sone et al. (J. Electrochem. Soc.143 (1996) 1254-1259). At low humidity, however, conductivity of the MEA-3membrane is an order of magnitude higher than that of the heat-treated N-117. Data on non-heat-treated N-117membrane from Zawodzinski et al. (J. Electrochem. Soc.140 (1993) 1981-1985) and Sumner et al. (J. Electrochem. Soc.145 (1998) 107-110) are also provided inFIG. 7(a) for further comparison. The data suggest a conductivity of about 0.06 S/cm at 95% humidity for non-heat-treated Nafion that is moderately less than 0.08 S/cm and 0.11 S/cm conductivities associated with MEA-1and MEA-2membranes, respectively. Understanding the reasons behind higher conductivity of the PS-PEM compare to Nafion requires detailed characterization of the PS-PEM as well as a more concrete understanding of the Nafion structure and mechanisms of proton conductivity within its pores. Aside from morphological differences between the two membranes as well as the pores wall properties, difference in number density of the sulfonate groups on the pore wall and the length and chemistry of their pendant groups are among the parameters that can affect proton mobility.

Current-voltage (I-V) performance of the MEA-1at different humidity levels is provided inFIGS. 7(c)-7(d). The MEA delivered a maximum power density of 332 mW/cm2at 70% humidity. However, operation at lower humidity led to a decline in performance primarily due to an increase in activation overpotential losses resulting from an increase in charge transfer resistance within the catalyst layer due to Nafion dryout. Although the greater loss and its effect on the maximum power density was minimal at 55% humidity, further reducing the humidity to 25% resulted in a significant activation loss that led to approximately 30% decline in maximum output power. Operation at high humidity levels also led to performance degradation (FIG. 7(d)) as a result of partial water flooding of the cathode catalyst due to a low water evaporation rate. In addition to I-V performance tests, an MEA was subjected to continuous operation at 150 mA/cm2for 40 hrs. Aside from a 0.018 V drop during the first 5 hrs of operation (FIG. 7(e)), believed to be mainly due to the system reaching steady state, the device showed an additional 0.007 V drop over the rest of the test duration (0.18 mV/hr). To determine if the changes in the membrane proton conductivity were responsible for the observed drop in potential, a second test was conducted in which the membrane conductivity was measured frequently after periods of operation (FIG. 7(f)). The results did not show any statistically significant change in membrane conductivity. Thus, the membrane conductivity does not seem to be responsible for the decline observed in the MEA performance.

The concept of a surface nano-engineered fixed-geometry proton exchange membrane that can enable nearly constant proton conductivity over a wide humidity range with no changes in volume and the fabrication of such a membrane based on silicon have been described. The technology may greatly facilitate manufacturing of membrane electrode assemblies (MEAS) and their further integration with microfabricated elements of MFCs. Due to the many advantages of this PEM/MEA, the inventors believe that this technology can simplify fabrication and operation of small fuel cells.

The fabrication processes developed to create the PS-PEM provide a versatile route to nanostructuring membranes with tailored properties for optimum performance. The ability to modify the surface of this dimensionally stable membrane opens up vast opportunities to fine tune the membrane's characteristics (e.g., water and fuel transport through the membrane) enabling development of better fuel cells. The technologies presented in this work can potentially be used for low crossover membranes for liquid fuels, membranes for above ambient operating temperatures (120-140° C.), anion exchange membranes, etc. In addition, the known geometry of the pores and the ability to systematically control the pore surface chemistry with SAMs provide a unique opportunity to enhance our understanding of the physics of proton transport and its relation to pore size and surface properties.

Although the present invention has been described with reference to certain embodiments thereof, other embodiments are possible without departing from the present invention. The spirit and scope of the appended claims should not be limited, therefore, to the description of the preferred embodiments contained herein. All embodiments that come within the meaning of the claims, either literally or by equivalence, are intended to be embraced therein. Furthermore, the advantages described above are not necessarily the only advantages of the invention, and it is not necessarily expected that all of the described advantages will be achieved with every embodiment of the invention.