WO2001066217A1

WO2001066217A1 - Low pore volume electrodes with flow-through capacitor and energy storage use and method

Info

Publication number: WO2001066217A1
Application number: PCT/US2001/007295
Authority: WO
Inventors: Marc D. Andelman
Original assignee: Andelman Marc D
Priority date: 2000-03-06
Filing date: 2001-03-05
Publication date: 2001-09-13

Abstract

This invention relates to a low pore volume electrode wherein less than 50 % of its pores volume comprises macropores, and wherein a capacitance containing active layer is bonded to an integral current collector. The low pore volume electrode material acts as the active layer and may be comprised of a low pore volume carbon material. The integral current collector may be comprised of graphite foil and should be between 0.0001 and 0.1 inches thick. This low pore volume electrode may be used in a flow-through capacitor to purify concentrated solutions and to store energy.

Description

LOW PORE VOLUME ELECTRODES WITH FLOW-THROUGH CAPACITOR AND ENERGY STORAGE USE AND METHOD Reference to Prior Application

This application is based on and claims priority from U.S. Provisional Patent Application Serial No. 60/187,351, filed March 6, 2000, and is hereby incorporated by reference.

Background of the Invention Surface area materials, especially those containing carbon, between 30 meters per gram Brunauer Emmett Teller method (BET) up to 3000 meters per gram or more BET, are commonly used for double layer capacitors. Carbons may take the form of fibers, powders, aerogels, or nanotubes. Pore volume comes associated with the surface area necessary for high capacitance, high performance electrodes. This pore volume gets larger directly proportional to the amount of macro versus meso and micropores. Lowering the surface area lowers the pore volume, but, for a given material, also lowers capacitance. Between electrode materials, selecting for a preponderance of micro and meso versus macropores allows for more useful surface area. Therefore, due to better surface area utilization, even though surface area is lowered, capacitance is still high. Since less surface area is required for a given capacitance, pore volume is also decreased for a given capacitance. Pore volume is deleterious and especially bad for use in a flow-through capacitor, but also for an energy storage capacitor. During the regeneration or desorption cycle, salts remain trapped in the pores and are not released from the pore volume into the space between the electrodes. During the subsequent purification or absorption cycle, these pore volume salts are repurified from the pores and thereby create an inefficiency. This pore volume inefficiency sets an upper limit on the solution concentration that it is possible to purify with a flow-though capacitor. For example, sales literature on the Sabrex Web site, http: //www. sabrex-tx . com/ , has listed limits of 2500 ppm obtainable with the flow-through capacitor. It would be highly desirable to be able to purify more concentrated solutions over 2500 ppm, including sea water, which is 35,000 ppm. In addition to making possible the purification of concentrated solutions, low pore volume, high capacitance electrodes can more efficiently, with respect to energy, flow rate, recovery, and waste volume, purify solutions of any concentration, including solutions less than 2500 ppm. Energy usage can be less than 20 watts hours per gallon, depending upon the solution concentration. Typically, energy usage is much lower, e.g., less than 5 watt hours per gallon. U.S. Patent No. 5,150,283, describes metal foil current collectors with activated carbon attached by binders. Selecting these activated carbons for low pore volumes, e.g., below 1 cc/gram, and preferably, below .8 cc/gram would suit the purposes of this invention. However, metal foils tend to corrode and also have a high Schottky barrier, which causes a contact resistance intrinsic to the dissimilar carbon and metal materials . A graphite foil current collector would overcome this problem when used as an integral, current collector bonded with similar carbon-containing active electrode materials. U.S. Patent No. 5,620,597, issued April 15, 1997, shows such an electrode in Figs. 13A through 13D and describes, in column 11, line 45 to column 12, line 3, a carbonaceous graphite foil current collector that is a better match with adhered carbon electrode layers. None of the prior art describes use of a low pore volume, high capacitance electrode material in order to treat concentrated solutions. The prior art does not describe low pore volume materials that are simultaneously attached or bonded to an integral current collector for use in flow- through capacitors meant to purify concentrated solutions, nor for energy storage purpose capacitors.

Summary of the Invention The invention relates to a low pore volume electrode, flow-through capacitor and energy storage use and method. Therefore, an electrode with a low pore volume, capacitance- containing active layer would be desirable for use in a flow- through capacitor. The capacitance-containing active layer is the material layer which contains most of the capacitance. Preferably, this electrode should contain an integral current collector bonded to the active, high capacitance electrode layers. This current collector should preferably be matched to the materials used in the active, high capacitance, low pore volume electrode layers, such as carbon-containing active layers and graphite foil current collectors. Such an electrode would also be useful in an energy storage capacitor. In order to achieve this, a low pore volume electrode material is desirable. Such a material may be any surface area material. Typically, such a material will be between 100 square meters per gram and 3000 square meters per gram. These materials need to be selected for pore volumes that are 1 cc/gram or less, preferably, 0.8 cc/gram or less. In order for the electrode to have desirable low series resistance, the low pore volume, high capacitance material may be bonded to an integral current collector or it should have an integral current collector bonded to it. The current collector should be thin, so as not to take up excessive space. Ideally, it should be between 0.0001 and 0.1 inches thick, preferably 0.001 to 0.03 inches thick.

The invention comprises a low pore volume electrode material wherein less than 50% of its pore volume comprises macropores, with a capacitance-containing active layer bonded to an integral current collector. This is an electrical bond which may be made by compression, mechanical or chemical means .

The current collector, which may be a film material, may be any conductive metal, conductive polymer, composite, carbon material filled into a polymer, or conductive ceramic material. Graphite foil is a preferred embodiment, because it is a close materials match to preferred carbonaceous high capacitance materials used that comprise the active electrode layers. Therefore, graphite has a low Schottky barrier and a low junction resistance with the preferred carbon-containing materials including: graphite; glassy carbon, carbon particles; fiber; carbon aerogel; carbon foam; nanotube; or aligned nanotube, active electrode materials. One especially advantageous embodiment of the invention is the use of materials with a preponderance of micropores and mesopores compared to macropores. Macropores, as defined by. the IUPAC (International Union of Pure and Applied Chemistry) , are pores with diameters greater than 50 nanometers. A preferred embodiment is a material with greater than 30% of the pore volume representing pores with diameters of less than 50 nanometers, to enable efficient purification of concentrated solutions over 2500 ppm with such materials, typically, to provide a high capacitance to pore volume ratio, ideally, greater than 20 farads per cubic centimeter of pore volume. Examples of materials with high capacitance to pore volume ratios, including selected pyrolized polymers, carbon fibers, aerogels, and carbon foams are selected for pore volumes less than 1 cc/gram, and preferably 0.8 cc/gram or less. For the purpose of a flow-through capacitor, such materials may be used in flow-through capacitors of any design, with or without a current collector, as in any of the following patents: U.S. Patent Nos . 5,192,432, issued March 9, 1993; 5,196,115, issued March 23, 1993; 5,200,068, issued April 6, 1993; 5,360,540, issued November 1, 1994; 5,415,768, issued May 16, 1995; 5,538,611, issued July 23, 1996; 5,547,581, issued August 20, 1996; 5,620,597, issued April 15, 1997; 5,748,437, issued May 5, 1998; 5,779,891, issued July 14, 1998; Japanese Patent Application No. 18004/1993, filed January 9, 1993; PCT International Application No. US92/11358, filed December 31, 1992; PCT International Application No. US95/01653, filed February 9, 1995; Japanese Patent Application No. 521326/1995, filed February 9, 1995; PCT International Application No. US94/05364, filed May 12, 1994; and PCT International Application No. US96/16157, filed October 9, 1996; and Japanese Patent Application No. Toku-gan- hei 10-253706, all incorporated herein by reference. In order to achieve fast flow rate, the capacitor made from low pore volume materials must have low series resistance, for example, 0.01 ohms or less. Highly conductive current collectors are used in the industry in order to provide a conductive backing to the high resistance, active electrode layer materials. According to this invention, it is desirable that the active layer be low in pore volume, so as to be useful for efficient purification, flow-through capacitors. U.S. Patent No. 5,150,283 describes metal foil current collectors with activated carbon attached by binders. Selecting these activated carbons for low pore volumes, e.g., below 1 cc/gram, and preferably, below 0.8 cc/gram, would suit the purposes of this invention. However, metal foils tend to corrode and also have a high Schottky barrier, which causes a contact resistance intrinsic to the dissimilar carbon and metal materials. In U.S. Patent No. 5,620,597, issued April 15, 1997, Figs. 13A through 13D, and column 11, line 45 to column 12 line 3, describe a carbonaceous graphite foil current collector that is a better materials match with adhered carbon electrode layers. Addition of low pore volume yet high capacitance materials of the invention would further enhance the properties of this electrode for use in a flow- through capacitor. Therefore, a need exists for the use of a low pore volume material in a flow-through capacitor. A further need exists for a low pore volume electrode with an integral current collector, where the current collector is graphite foil and the active layer is low pore volume carbon. Generally, low pore volume materials have less resistance, e.g., less than 30 ohm cm, due to greater bulk material density, for example, 30% or more solids. The solids may have a density of 0.7 grams per cubic centimeter or greater. Therefore, low pore volume, high capacitance materials allow for improved capacitors of the energy storage type as well.

Different forms of low pore volume carbon may be adhered to the graphite foil electrode. For example, activated glassy carbons and procedures for activating glassy carbon electrodes that have a nearly ideal low pore volume yet high capacitance, have been described in "X-ray Scattering and Adsorption Studies of Thermally Oxidized Glassy Carbon"; Braun et al, Journal of Non-Crystalline Solids , 260 (1999), pp. 1-14, and "Thick Active Layers of Electrochemically Modified Glassy Carbon, Electrochemical Impedance Studies"; Sullivan et al, Journal of the Electrochemical Society, 147 (1) , pp. 308-317

(2000) . For optimal use in an efficient flow-through capacitor, such glassy carbons should have an electrode planar area capacitance of 0.2 farads/square cm or greater, and a pore volume of 0.8 cc/gram or less, a weight specific capacitance of 20 farads per gram or greater, and a volumetric capacitance of 20 farads per cc or greater, as measured in concentrated H₂S0₄. Thickness of the glassy carbon layer, deposited upon the graphite foil current collector, should be between 0.2 and 200 mils. However, for thicknesses much over 0.4 mils, surface stresses tend to crack the glassy carbon coating. To alleviate these stresses and facilitate manufacturing, it is desirable to incorporate x-y or radial grids of naked, bare electrode. This can be achieved by masking the graphite foil, applying the glassy carbon precursor on top of the mask, and pyrolyzing.

Alternatively, a low carbon-containing blocking agent, for example, wax or any other ablatable compound, may be painted on the graphite foil in the desired grid pattern. The glassy carbon precursor is painted, doctor bladed, sprayed, or otherwise deposited on top, but does not adhere to the wax or blocking agent. The precursor, such as, but not limited to any of the glassy carbon precursors, may include phenolic resin, furfural alcohol, mesophase pitch, polyimide, etc. Upon pyrolyzing, this blocking agent ablates away, thereby leaving a grid of naked graphite foil. As the thick layers of glassy carbon shrink during firing, the grid patterns can shrink along with the overall electrode, thereby relieving stresses and preventing cracking during manufacture. The graphite foil layer should be between 2 mils and 50 mils, and preferably 3 to 13 mils.

Brief Description of the Drawings Fig. 1A is a top plan view of a glassy carbon electrode; Fig. IB is a side view of the glassy carbon electrode of Fig. 1A; and

Fig. 2 is a schematic illustration composed of a nanolithic electrode of aligned nanotubes attached to a graphite foil. Description of the Embodiments

Figs. 1A and IB illustrate a glassy carbon electrode with embossed lines to prevent stress cracking during manufacture, which is prepared by masking and pyrolyzing or plasma etching of graphite foil.

An alternative to low pore volume glassy carbons, high capacitance materials are conductive polymers, as described in U.S. Patent No. 5,733,683, issued March 31, 1998, and incorporated by reference. Optionally, these may be applied as a coating to a thin metal foil or graphite current collector. The precursor is pyrolized in an oven to glassy carbon. The glassy carbon is subsequently electrochemically or thermally activated to a BET level of 1000 or higher.

Another preferred embodiment of the invention is aligned nanotubes grown directly upon graphite foil. These may be grown in a tube furnace or by plasma CVD, and are well- described in various scientific papers, including, but not limited to: "Single Wall Nanotubes Produced by Metal Catalyzed Disproportionation of Carbon Monoxide"; Hongjie Dai et al, Chemical Physics Letters , 260, pp. 471-475; "Growth of Highly Oriented Carbon Nanotubes by Plasma-Enhanced Hot Filament Chemical Vapor Deposition"; Z.P. Huang et al, Applied Physics Letters, Volume 23, No. 2628, December 1998; "Large Arrays of Well-Aligned Carbon Nanotubes"; Z.F. Ren et al, Proceedings of the 13th Interna tional Winter School on Electronic Properties of Novel Ma terials, Feb 27 to March 6, 1999, Kirchberg/Tirol, Austria; and "Synthesis of Large Arrays of Well-Aligned Carbon Nanotubes on Glass"; Z.F. Ren et al, Science, 6 November 1998, Volume 282, pp. 1105-1107.

Fig. 2 is an illustration of aligned nanotubes grown and extending substantially perpendicularly from a graphite foil collector to provide a nanolithic electrode with an integral current collector. The aligned nanotube, graphite foil collector of Fig. 2 has the flow-through capacitor or energy storage device employing nanotube-graphite foil electrodes and may have nanotubes which are hemogeneous or inhomogeneous in respect to diameter, length, material, or wall thickness. The nanotubes may be subsequently treated, e.g., thermally or chemically, as to enhance surface area, such as by acid treatment. One advantage of nanotubes is that the ionic conductive path is relatively straight down through the nanotubes. This lessens the pore resistance that occurs in activated carbon and similar pore systems which present labyrinthine pathways for the ions to work through. The nanotubes may be preferentially attached more or less perpendicular to the current collector. Aligned nanotubes, as may be grown in a tube furnace, require a substrate to support the nanotube catalyst. This is shown on the Web site http: //buckv5.wustl . edu/Science/Nanofiber Growth .html .

However, no prior art teaches dual use of a substrate as both a catalyst support and an electrode current collector. For the purpose of this invention, the catalyst supporting substrate/current collector may be any metal foil. A preferable embodiment is graphite foil, since this has a similar material composition to the nanotubes, and therefore, offers a lower Schottky barrier.

The catalyst may be any metal, metal-containing compound, such as: iron; nickel molybdenum; etc., that is used to catalyze the growth of nanotubes . In order to ensure that the nanotubes are tightly adhered to the substrate, the catalyst may be applied with a mixture of phenolic resin, mesophase pitch, furfural I alcohol, or other carbon-containing adhesive mixture. This mixture is pyrolized, either prior to or during nanotube formation, thereby firmly adhering catalyst microparticles, in a carbon or glassy carbon matrix, onto the surface of the substrate material. Nanotubes formed from this adhered catalyst are better adhered to the integral current collector substrate material for optimum performance as a capacitor electrode, whether for a flow-through capacitor or energy storage use. The nanotubes should be grown onto an intrinsic, integral graphite foil current collector to enhance the surface area, and therefore the capacitance, yet retain low pore volume. The nanotubes should also be thin, e.g., less than 200 nm in diameter. Surface area increases exponentially with thinness, but only linearly with the length of the nanotubes. Preferentially, the nanotubes should be less than 50 nm in diameter. The nanotubes may be any length up to 500 microns. However, to improve the capacitance to pore volume ratio, the nanotubes should be much thinner than taller, e.g., in a ratio of 1 to 100 or greater. For example, nanotubes 100 microns tall should be 200 nm thin or less.

Example 1

Graphite foil, 3 mils thick, is coated with glassy carbon to a thickness of between 0.2 to 10 mils, either single or double-sided coated. The glassy carbon is subsequently activated by thermal oxidation until it has a surface area as measured by BET of over 1000. Pore volume is measured at 50%. Capacitance is over 0.2 farads per electrode plane area square centimeter, providing for a high capacitance, low series resistance capacitor with a series resistance of less than 0.1 ohm. UCAR graphite foil, 3 mils thick, is coated with 20 mils of glassy carbon on each side in an x-y grid pattern, similar to the one shown in Fig. 1, where the grid lines are 0.1 mm wide and the grid rectangles are 0.5 cm x 1 cm. The glassy carbon is subsequently potassium hydroxide-activated to a surface area of 2000 BET. Porosity ratio is greater than 50% micro - mesopores to macropores, and electrode plane area capacitance is approximately 1 farad per square centimeter. Macropores should comprise less than 50% of the total pore volume. Total pore volume is 0.6 cc/gram of active layer. This electrode is incorporated into a 1000 farad, flow-through capacitor containing 10 anode/cathode pairs of four by four inch sheets, separated by a 0.01 inch thick open screen netting material spacer defining a flow path. The capacitor is incorporated in a PVC, box-shaped cartridge holder provided with an inlet and an outlet. An oily waste mixture containing suspended oil droplets in concentrated brine of 10,000 ppm salt is passed through the capacitor at 100 mis/minute and purified to a level of 1000 ppm salt in a batch recycle loop mode. This breaks the colloidal suspension, allowing the oil droplets to coalesce together and separate from the water. The oil is then skimmed off from the water and recovered.

Example 2

Graphite foil, 5 mils thick, is coated with a mixture of an adhesive hydrogel, such as: polyvinyl alcohol; polyvinyl pyrrone; gelatin; and a nanoparticulate metal catalyst, such as molybdenum nanoparticles of less than 20 nanometers in diameter. Alternatively, any nanoparticle colloid or nanoparticle-polyelectrolyte mixture may be applied to form a nanoparticle layer on the graphite foil. Upon heating in the nanotube forming oven, the low carbon- containing hydrogels or polyelectrolytes ablate away. Aligned carbon nanotubes are grown by disproportionation of C0₂ in a tube furnace at 1200°C. The resultant nanotubes are 5 nanometers in diameter and 10 microns tall, with a length to width ratio of 2000 and a BET surface area of the nanotube layer of over 800 square meters per gram, a capacitance of over 0.8 farads per square centimeter of electrode plane area surface, and over 80 farads per gram of the combined electrode current collector material. Pore volume is less than 0.004 cc per each farad capacitance, and inefficiency, due to repurification of pore volume ions, is less than 20% when these electrodes are built into flow- through capacitors, according to the designs in U.S. Patent No. 5,748,437, issued May 5, 1998. This electrode is made into a spiral wound, flow-through capacitor and used to purify a dilute hard water solution of 500 ppm.

Example 3 Graphite foil, 0.003 inches thick, is coated with a metal nanoparticle catalyst, where nanotubes are grown in a 900°C tube furnace. The metal nanoparticles are deposited via ion implantation, sputtering, or onto the graphite foil substrate, in order to form especially small metal nanoparticles, e.g., under 10 nanometers, and nanotubes less than 10 nm wide, in order to produce a high capacitance, low pore volume electrode. This electrode is incorporated into a 3 volt, 10 farad capacitor comprising three cells in series of 1 volt each, for use in CMOS and computer memory circuits with enhanced power usage properties, due to low electrical series resistance (ESR) of the capacitor of below 0.1 ohms.

Example 4

Graphite foil, 0.005 inches thick, is coated with metal nanoparticle catalyst, which is applied by mixing a metal salt solution with an adhesive hydrogel, spraying it onto the graphite foil surface, and air drying. Alternatively, metal nanopowders may be suspended in the air and electrostatically powder-coated onto the graphite foil.

The catalyst-coated graphite foil is put inside a 3 foot diameter tube furnace. Nanotubes, 2 to 40 nanometers in diameter, are grown as in inhomogeneous mixture, with lengths from 5 to 100 microns, in order to produce a high capacitance, low volume electrode with an integral, attached current collector and capacitance greater than 0.2 farads/electrode plane area square centimeter and greater than 10 farads per gram of total electrode material . Example 5

Graphite foil, 3 mils thick, is painted with a mixture of phenolic resin and iron nitride, to form a catalyst-phenolic film layer. This is carbonized in a 1000°C oven to form a 0.0002 inch film of carbon with reduced metal nanoparticles less than 10 nm in diameter. Subsequently, the electrode formed by this process is a substrate on which to grow tightly adhered nanotubes for use as a capacitor electrode with an integral, graphite foil current collector.

Example 6

Carbon cloth with a pore volume of 0.8 grams/cc is used with a graphite foil current collector and a compression contact to build a flat plate, flow-through capacitor. This material is used to remove 90% of the ions from tap water for a home water purification unit of 100 gallons per day, with an energy usage of 5 watt hours per gallon or less.

Claims

ClaimsWhat is claimed is:

Claim 1. A low pore volume electrode material wherein less than 50% of its pore volume comprises macropores, with a capacitance-containing active layer bonded to an integral current collector.

Claim 2. The electrode material of claim 1 wherein the high capacitance layer comprises glassy carbon, and the integral current collector is graphite foil.

Claim 3. The electrode material of claim 1 wherein the high capacitance layer comprises nanotubes, and the integral current collector is graphite foil.

Claim 4. The electrode material of claim 3 wherein the nanotubes are less than about 100 microns tall and 200 nanometers wide.

Claim 5. The use of the electrode material of claim 1 in an energy storage capacitor.

Claim 6. The use of the electrode material of claim 1 in a flow-through capacitor for the purpose of purifying fluids.

Claim 7. The use of an electrode material with a pore volume less than about 1 cubic centimeter per gram (1 cc/gram) in a flow-through capacitor.

Claim 8. The use of the electrode material of claim 6 in a flow-through capacitor wherein the electrode material is carbon cloth with a pore volume of about 0.8 cubic centimeters per gram (0.8 cc/gram) or less.

Claim 9. The use of the electrode material in claim 6 in a flow-through capacitor wherein the electrode material comprises generally aligned nanotubes adhered to graphite foil.

Claim 10. The electrode of claim 1 wherein the current collector is graphite foil, and the active high capacitance, low pore volume layer is a coating of glassy carbon, activated to above 1000 Brunauer Emmett Teller method (BET) to form a low pore volume, high capacitance coating of less than 1 cubic centimeter per gram (1 cc/gram) pore volume, greater than about 0 . 2 farads per electrode plane area square centimeter, greater than about 20 farads per gram of electrode material, and greater than about 20 farads per cubic centimeter of electrode material, as measured in concentrated H₂S0.

Claim 11. The electrode of claim 1 wherein the high capacitance material comprises carbon powder.

Claim 12. The electrode of claim 1 wherein the current collector is compression, mechanically, or electrically bonded to the capacitance-containing active layer.

Claim 13. The electrode of claim 1 wherein the ionic conductive path into the pore system is relatively straight and less labyrinthine when compared to activated carbon.

Claim 14. The electrode of claim 1 wherein the high capacitance material has a pore volume of less than 0.8 cubic centimeters per gram (0.8 cc/gm) .

Claim 15. The electrode of claim 1 which has 30 percent (30%) or more solids, and the solids have a density of about 0.7 grams per cubic centimeter (0.7 cc/gm) or greater.

Claim 16. The electrode of claim 9 with a stress relieving x-y grid embossed in the glassy carbon layer.

Claim 17. An electrode for flow-through capacitors or energy storage use satisfying all of the following requirements : a) a pore volume less than 1 cubic centimeter per gram; and b) a surface area of between 30 and 3000 square meters per gram and greater than 30 percent of the pore volume representing pores with diameters less than about 50 nanometers.

Claim 18. The electrode of claim 17 wherein the plane area capacitance is about 0.2 farads per square centimeter or greater .

Claim 19. The electrode of claim 17 wherein a volumetric capacitance of about 20 farads per cubic centimeter or greater .

Claim 20. The electrode of claim 17 with a weight specific capacitance of about 20 farads per gram or greater.

Claim 21. The electrode of claim 17 wherein the current collector is a metal or graphite foil between about 2 and 50 mils thick, wherein the current collector serves as a support for arrays of aligned nanotubes.

Claim 22. The electrode of claim 21 wherein the nanotubes are less than about 200 nanometers in diameter, with a ratio of tallness to thinness of greater than about 100 to 1.

Claim 23. The electrode of claim 17 wherein the low pore volume material is carbon.

Claim 24. The electrode of claim 20 wherein the nanotubes are less than about 30 nanometers in diameter.

Claim 25. The electrode of claim 23 wherein the low pore volume carbon is selected from a group of pyrolized polymers, carbon fibers, aerogels, and carbon foams.

Claim 26. The electrode of claim 17 which comprises low pore volume carbon with a pore volume in the range below 1 cubic centimeter per gram (1 cc/gm) adhered to metal or graphite foil by means of binders.

Claim 27. The electrode of claim 17 which is used in a flow-through capacitor to purify solutions in the range of 2500 ppm.

Claim 28. The electrode of claim 17 with a density of about 0.7 grams per cubic centimeter (0.7 g/cc) or greater.

Claim 29. The electrode of claim 17 with a pore volume of about less than 0.004 cubic centimeter per farad of capacitance.

Claim 30. The method of using the electrode of claim 1 in a low electrical series resistance (ESR) capacitor of below about 0.1 ohms .