Patent Publication Number: US-2020280070-A1

Title: High capacity hard carbon materials comprising efficiency enhancers

Description:
BACKGROUND 
     Technical Field 
     The present invention generally relates to novel polymeric materials, hard carbon materials derived therefrom, and methods for making the same and devices containing the same. 
     Description of the Related Art 
     Lithium-based electrical storage devices have potential to replace devices currently used in any number of applications. For example, current lead acid automobile batteries are not adequate for next generation all-electric and hybrid electric vehicles due to irreversible, stable sulfate formations during discharge. Lithium ion batteries are a viable alternative to the lead-based systems currently used due to their capacity, and other considerations. Carbon is one of the primary materials used in both lithium secondary batteries and hybrid lithium-ion capacitors (LIC). The carbon anode typically stores lithium in between layered graphite sheets through a mechanism called intercalation. Traditional lithium ion batteries are comprised of a graphitic carbon anode and a metal oxide cathode; however such graphitic anodes typically suffer from low power performance and limited capacity. 
     Hard carbon materials have been proposed for use in lithium ion batteries, but the physical and chemical properties of known hard carbon materials are not optimized for use as anodes in lithium-based batteries. Thus, anodes comprising known hard carbon materials still suffer from many of the disadvantages of limited capacity and low first cycle efficiency. Hard carbon materials having properties optimized for use in lithium-based batteries are expected to address these deficiencies and provide other related advantages. 
     While significant advances have been made in the field, there continues to be a need in the art for improved hard carbon materials for use in electrical energy storage devices (e.g., lithium ion batteries), as well as for methods of making the same and devices containing the same. The present invention fulfills these needs and provides further related advantages. 
     BRIEF SUMMARY 
     In general terms, the current invention is directed to novel polymeric materials, and novel hard carbon materials derived therefrom which exhibit optimized lithium storage and utilization properties. The novel polymeric materials are organic in nature and comprise efficiency enhancers, for instance phosphorus. The novel carbon materials find utility in any number of electrical energy storage devices, for example as electrode material in lithium-based electrical energy storage devices (e.g., lithium ion batteries). Electrodes comprising the carbon materials display high reversible capacity, high first cycle efficiency, high power performance or any combination thereof. The present inventors have discovered that such improved electrochemical performance is related, at least in part, to the carbon materials&#39; physical and chemical properties such as surface area, pore structure, crystallinity, surface chemistry, chemical composition and other properties as discussed in more detail herein. Specific modulation of the final carbon properties can be achieve through fine control of the initial polymeric material and/or through modification of the carbonization process. Furthermore, certain electrochemical modifiers can be incorporated on the surface of and/or in the carbon material to further tune the desired properties. 
     Accordingly, in one embodiment the present invention provides novel polymeric materials based on poly[(phenol glycidyl ether)-(co-formaldehyde)] and phosphoric acid, which react initially upon mixing and that when heated exhibit an exothermic event at about 250 C, and upon further heating in the presence of non-oxidizing atmosphere produces a novel pyrolzyed carbon material. In one embodiment, the novel carbon material has a surface area of less than 50 m 2 /g and greater than 1 wt % phosphorous wherein the carbon material has a first cycle efficiency of greater than 50% and a reversible capacity of at least 200 mAh/g when the carbon material is incorporated into an electrode of a lithium based energy storage device. In some specific embodiments, the lithium based electrical energy storage device is a lithium ion battery or lithium ion capacitor. 
     In other embodiments, the invention provides a carbon material comprising a surface area of less than 50 m 2 /g and a specific lithium uptake capacity of greater than 1.4:6. For example, in some embodiments the specific surface area is less than 25 m 2 /g or even less than 10 m 2 /g. 
     In some of the foregoing embodiments, the carbon material comprises from 1% to 4% phosphorous by weight relative to total weight of all components in the carbon material. For example, in some embodiments the carbon material comprises from 4% to 20% phosphorous by weight relative to total weight of all components in the carbon material. 
     In other embodiments, the carbon material comprises a total pore volume from 0.001 to 0.1 cm 3 /g. In different embodiments, the carbon material comprises a tap density from 0.3 to 0.9 g/cm 3 . In further embodiments, the carbon material comprises a phosphorous content from 1% to 20%, a total pore volume from 0.001 to 0.1 cm 3 /g and a tap density from 0.3 to 1.0 g/cm 3 . 
     In more embodiments of the foregoing, the first cycle efficiency of a lithium based energy storage device is greater than 80%, greater than 85% or greater than 90% when the carbon material is incorporated into an electrode of the lithium based energy storage device. 
     In even more embodiments of the foregoing carbon material at least 80% of the total pore volume comprises pores less than 100 nm in diameter. In different embodiments, at least 50% of the total pore volume comprises pores less than 1 nm in diameter. 
     In still other embodiments, the total concentration of all elements having an atomic number from 11 to 92 in the carbon material is below 200 ppm as measured by proton induced X-ray emission. In further embodiments, at least 50% of the total pore volume comprises pores less than 1 nm and wherein the total concentration of all elements having an atomic number from 16 to 92 is below 200 ppm as measured by proton induced X-ray emission. 
     In some other embodiments, the carbon material comprises an electrochemical modifier. For example, in some embodiments the electrochemical modifier is selected from phosphorous, iron, tin, silicon, nickel, aluminum and manganese. In other embodiments, the electrochemical modifier comprises silicon, for example, in some embodiments the electrochemical modifier comprising silicon comprises 80-95% of the carbon material. In other embodiments, the electrochemical modifier comprises tin. 
     In some embodiments, the carbon material comprises Al 2 O 3 . 
     In various different embodiments, the carbon material comprises organic functionality as determined by FTIR analysis. In some different embodiments, the carbon material comprises less than 10% crystallinity. In more embodiments, the carbon material comprises an L a  ranging from 20 nm to 30 nm as determined by RAMAN spectroscopy analysis. In still more embodiments, the carbon material comprises an R ranging from 0.60 to 0.90 as determined by RAMAN spectroscopy analysis. 
     In various different embodiments of the foregoing carbon materials, the carbon material comprises a total of less than 200 ppm of all elements having atomic numbers ranging from 11 to 92, excluding any intentionally added electrochemical modifier, as measured by proton induced x-ray emission. 
     In some embodiments, the carbon material comprises a pyrolyzed 3 dimensional polymer network. In other embodiments, the carbon material has a ratio of intercalation storage to pore storage ranging from 2:1 to 1:2. In various embodiments, the lithium content and lithium location within the carbon structure can be measured with a FIB and SEM. 
     In some other different embodiments, the carbon material comprises a lithium plating potential between −5 mV and −15 mV versus lithium metal. 
     In various embodiments, the carbon material exhibits less than 10% capacity decrease when the current density is raised from an initial value to 40 times the initial value. In other embodiments, the carbon material exhibits less than 5% capacity decrease when the current density is raised from an initial value to 30 times the initial value. In yet other embodiments, the carbon material exhibits less than 2% capacity decrease when the current density is raised from an initial value to 20 times the initial value. 
     In other different embodiments, the carbon material exhibits from 0 to 2% capacity increase when the current density is raised from an initial value to 10 times the initial value. In other embodiments, the carbon material exhibits from 0 to 5% capacity increase when the current density is raised from an initial value to 5 times the initial value. In more embodiments, the carbon material exhibits from 0-7% capacity increase when the current density is raised from an initial value to 40 times the initial value. 
     In some embodiments, the carbon material comprises graphite, and the carbon material exhibits end of life evidenced by a voltage (V) vs Li/Li+ of 5% of maximum voltage at a depth of discharge of 75% or less. In different embodiments, the carbon material exhibits end of life evidenced by a voltage (V) vs Li/Li+ of 5% of maximum voltage at a depth of discharge of 85% or less. In more embodiments, the carbon material exhibits end of life evidenced by a voltage (V) vs Li/Li+ of 10% of maximum voltage at a depth of discharge of 75% or less. In other embodiments, the carbon material exhibits end of life evidenced by a voltage (V) vs Li/Li+ of 10% of maximum voltage at a depth of discharge of 85% or less. In some of the foregoing embodiments the graphite content ranges from 80 to 85%. 
     Other embodiments are directed to electrodes comprising the disclosed carbon materials and optional binders as well as electrical energy storage devices comprising the carbon materials (e.g., in the form of an electrode). For example, some embodiments are directed to an electrical energy storage device comprising: 
     a) at least one anode comprising a hard carbon material; 
     b) at least cathode comprising a metal oxide; and 
     c) an electrolyte comprising lithium ions; 
     wherein the electrical energy storage device has a first cycle efficiency of at least 50%, for example at least 70% and a reversible capacity of at least 200 mAh/g with respect to the mass of the hard carbon material. In some embodiments, the hard carbon material is a carbon material according to any carbon materials described herein. In other embodiments of the electrical energy storage device, the first cycle efficiency is greater than 80%, greater than 85% or greater than 90%. 
     In other embodiments, the electrical energy storage device has a gravimetric capacity of greater than 400 mAh/g or greater than 500 mAh/g based on total mass of active material in the electrical energy storage device. 
     In different embodiments, the electrical energy storage device has a gravimetric capacity ranging from 550 mAh/g to 750 mAh/g based on total mass of active material in the electrical energy storage device. 
     In more embodiments, the electrical energy storage device has a ratio of intercalation storage to pore storage ranging from 2:1 to 1:2. In other different embodiments, the electrical energy storage device has a lithium plating potential between −5 mV and −15 mV versus lithium metal. 
     In other embodiments, the invention provides a co-polymer gel (e.g., a condensation co-polymer gel) comprising an epoxy containing phenol-formaldehyde co-polymer, the co-polymer gel comprising phosphorous-containing cross links, a phosphorous content of at least 1%, at least 4% or at least 10% by mass of the dry weight of the co-polymer and an optional solvent. 
     In further embodiments of the foregoing co-polymer gel, a dopant phosphorous-containing compound is bound covalently with the co-polymer. In other embodiments, the aldehyde is formaldehyde, the phenolic compound is phenol, resorcinol, or combinations thereof, the optional solvent system comprises water and acetone, and the dopant phosphorous-containing compound is in the form of phosphoric acid. In still more embodiments, the aldehyde is formaldehyde, the phenolic compound is phenol, resorcinol, or combinations thereof, the optional solvent system comprises water and acetone, and the dopant phosphorous-containing compound is in the form of a salt where the cation is comprised of ammonium, tetraethylammonium, tetramethylammonium or combinations thereof, and wherein the anion if comprised of phosphate, phosphite, phosphide, hydrogen phosphate, dihydrogen phosphate, hexafluorophosphate, hypophosphite, polyphosphate, or pyrophosphate ions, or combinations thereof. In yet other further embodiments, the dopant phosphorous-containing compound is ammonium phosphate. 
     In other embodiments, the invention provides a polymer gel (e.g., a condensation polymer gel) comprising monomers derived from an aldehyde compound, an alcohol compound and a phosphoric acid compound, wherein the phosphorous content is at least 1% by mass of the dry weight of the condensation polymer. In some embodiments, of any of the foregoing polymer gels, the polymer gel is in the form of particles having a volume average particle size ranging from 1 to 25 mm. In other embodiments, the polymer gel is in the form of particles having a volume average particle size ranging from 10 to 1000 um. In other embodiments, the polymer gel exhibits an exotherm upon heating to a temperature between about 200 C and 300 C. 
     These and other aspects of the invention will be apparent upon reference to the following detailed description. To this end, various references are set forth herein which describe in more detail certain background information, procedures, compounds and/or compositions, and are each hereby incorporated by reference in their entirety. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the figures, identical reference numbers identify similar elements. The sizes and relative positions of elements in the figures are not necessarily drawn to scale and some of these elements are arbitrarily enlarged and positioned to improve figure legibility. Further, the particular shapes of the elements as drawn are not intended to convey any information regarding the actual shape of the particular elements, and have been solely selected for ease of recognition in the figures. 
         FIG. 1  depicts pore size distribution of exemplary carbon materials. 
         FIG. 2  presents particle size distributions of exemplary carbon materials. 
         FIG. 3  depicts RAMAN spectra of exemplary carbon materials. 
         FIG. 4  is a plot of an x-ray diffraction pattern of exemplary carbon materials. 
         FIG. 5  shows an example SAXS plot along with the calculation of the empirical R value for determining internal pore structure. 
         FIG. 6  presents SAXS of three exemplary carbon materials. 
         FIG. 7A  presents FTIR spectra of exemplary carbon materials. 
         FIG. 7B  shows electrochemical performance of exemplary carbon materials. 
         FIG. 8  shows FTIR spectra of neat epoxy resin, in green, diluted phosphoric acid, in pink, and cured epoxy-P resin, in red. 
         FIG. 9  shows the spectra from  FIG. 8 , sized to highlight the fingerprint region. 
         FIG. 10  shows the FTIR spectra of the neat epoxy resin, in red, cured epoxy-P resin with 5% acid, in light blue, 10% acid, in green, 20% acid, in purple, and 40% acid, in dark blue. The viewing area of the spectra is sized to illustrate the epoxide bending absorbance band at ˜910 cm-1. 
         FIG. 11  shows example TGA data for polymer resin comprising phosphoric acid demonstrating an exothermic event at about 250 C. 
         FIGS. 12 and 13  illustrate carbon electrochemical performance. 
         FIG. 14  is a graph showing superior capability to monitor EOL as hard carbon percentage is increased. 
     
    
    
     DETAILED DESCRIPTION 
     In the following description, certain specific details are set forth in order to provide a thorough understanding of various embodiments. However, one skilled in the art will understand that the invention may be practiced without these details. In other instances, well-known structures have not been shown or described in detail to avoid unnecessarily obscuring descriptions of the embodiments. Unless the context requires otherwise, throughout the specification and claims which follow, the word “comprise” and variations thereof, such as, “comprises” and “comprising” are to be construed in an open, inclusive sense, that is, as “including, but not limited to.” Further, headings provided herein are for convenience only and do not interpret the scope or meaning of the claimed invention. 
     Reference throughout this specification to “one embodiment” or “an embodiment” means that a particular feature, structure or characteristic described in connection with the embodiment is included in at least one embodiment. Thus, the appearances of the phrases “in one embodiment” or “in an embodiment” in various places throughout this specification are not necessarily all referring to the same embodiment. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. Also, as used in this specification and the appended claims, the singular forms “a,” “an,” and “the” include plural referents unless the content clearly dictates otherwise. It should also be noted that the term “or” is generally employed in its sense including “and/or” unless the content clearly dictates otherwise. 
     Definitions 
     As used herein, and unless the context dictates otherwise, the following terms have the meanings as specified below. 
     “Carbon material” refers to a material or substance comprised substantially of carbon. Carbon materials include ultrapure as well as amorphous and crystalline carbon materials. Examples of carbon materials include, but are not limited to, activated carbon, pyrolyzed dried polymer gels, pyrolyzed polymer cryogels, pyrolyzed polymer xerogels, pyrolyzed polymer aerogels, activated dried polymer gels, activated polymer cryogels, activated polymer xerogels, activated polymer aerogels and the like. 
     “Hard Carbon” refers to a non-graphitizable carbon material. At elevated temperatures (e.g., &gt;1500° C.) a hard carbon remains substantially amorphous, whereas a “soft” carbon will undergo crystallization and become graphitic. 
     “First cycle efficiency” refers to the percent difference in volumetric or gravimetric capacity between the initial charge and the first discharge cycle of a lithium battery. First cycle efficiency is calculated by the following formula: (F 2 /F 1 )×100), where F 1  and F 2  are the volumetric or gravimetric capacity of the initial lithium insertion and the first cycle lithium extraction, respectively. 
     “Electrochemical modifier” refers to any chemical element, compound comprising a chemical element or any combination of different chemical elements and compounds which enhances the electrochemical performance of a carbon material. Electrochemical modifiers can change (increase or decrease) the resistance, capacity, efficiency, power performance, stability and other properties of a carbon material. Electrochemical modifiers generally impart a desired electrochemical effect. In contrast, an impurity in a carbon material is generally undesired and tends to degrade, rather than enhance, the electrochemical performance of the carbon material. Examples of electrochemical modifiers within the context of the present disclosure include, but are not limited to, elements, and compounds or oxides comprising elements, in groups 12-15 of the periodic table, other elements such as silicon, tin, sulfur, phosphorus, boron, and tungsten and combinations thereof. For example, electrochemical modifiers include, but are not limited to, phosphorus, boron, tin, silicon, tungsten, silver, zinc, molybdenum, iron, nickel, aluminum, manganese and combinations thereof as well as oxides of the same and compounds comprising the same. 
     “Efficiency enhancer” refers to a sub-class of electrochemical modifier that can increase the first cycle efficiency of a carbon material. The potency of an efficiency enhancer typically is dependent of the method of its incorporation into the carbon material. 
     “Group 12” elements include zinc (Zn), cadmium (Cd), mercury (Hg), and copernicium (Cn). 
     “Group 13” elements include boron (B), aluminum (Al), gallium (Ga), indium (In) and thallium (Tl). 
     “Group 14” elements include carbon (C), silicon (Si), germanium (Ge), tin (Sn) and lead (Pb). 
     “Group 15” elements include nitrogen (N), phosphorous (P), arsenic (As), antimony (Sb) and bismuth (Bi). 
     “Amorphous” refers to a material, for example an amorphous carbon material, whose constituent atoms, molecules, or ions are arranged randomly without a regular repeating pattern. Amorphous materials may have some localized crystallinity (i.e., regularity) but lack long-range order of the positions of the atoms. Pyrolyzed and/or activated carbon materials are generally amorphous. 
     “Crystalline” refers to a material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern. Examples of crystalline carbon materials include, but are not limited to, diamond and graphene. 
     “Synthetic” refers to a substance which has been prepared by chemical means rather than isolated from a natural source. For example, a synthetic carbon material is one which is synthesized from precursor materials and is not isolated from natural sources. 
     “Impurity” or “impurity element” refers to an undesired foreign substance (e.g., a chemical element) within a material which differs from the chemical composition of the base material. For example, an impurity in a carbon material refers to any element or combination of elements, other than carbon, which is present in the carbon material. Impurity levels are typically expressed in parts per million (ppm). 
     “PIXE impurity” or “PIXE element” is any impurity element having an atomic number ranging from 11 to 92 (i.e., from sodium to uranium). The phrases “total PIXE impurity content” and “total PIXE impurity level” both refer to the sum of all PIXE impurities present in a sample, for example, a polymer gel or a carbon material. Electrochemical modifiers are not considered PIXE impurities as they are a desired constituent of the carbon materials. For example, in some embodiments an element may be added to a carbon material as an electrochemical modifier and will not be considered a PIXE impurity, while in other embodiments the same element may not be a desired electrochemical modifier and, if present in the carbon material, will be considered a PIXE impurity. PIXE impurity concentrations and identities may be determined by proton induced x-ray emission (PIXE). 
     “XPS” or “X-ray photoelectron spectroscopy” is a quantitative spectroscopic technique that measures the elemental composition, empirical formula, chemical state and electronic state of the elements that exist within a material. 
     “tXRF” or “Total X-ray fluorescence” is a quantitative method for measuring elemental composition of a material. In this method, an air-cooled X-ray tube with molybdenum target generates an X-ray beam, which is reduced to a narrow energy range by a multi-layer monochromator. The fine beam impinges on a polished sample carrier at a very small angle)(&lt;0.1° and is totally reflected. The characteristic fluorescence of the sample is emitted and measured in an energy-dispersive X-ray detector. Due to the short distance to the carrier, the fluorescence yield is very high and the absorption by air is very low. 
     “Ultrapure” refers to a substance having a total PIXE impurity content of less than 0.050%. For example, an “ultrapure carbon material” is a carbon material having a total PIXE impurity content of less than 0.050% (i.e., 500 ppm). 
     “Ash content” refers to the nonvolatile inorganic matter remaining after subjecting a substance to a high decomposition temperature. Herein, the ash content of a carbon material is calculated from the total PIXE impurity content as measured by proton induced x-ray emission, assuming that nonvolatile elements are completely converted to expected combustion products (i.e., oxides). 
     “Polymer” refers to a macromolecule comprised of two or more structural repeating units. 
     “Synthetic polymer precursor material” or “polymer precursor” refers to compounds used in the preparation of a synthetic polymer. Examples of polymer precursors that can be used in certain embodiments of the preparations disclosed herein include, but are not limited to, aldehydes (i.e., HC(═O)R, where R is an organic group), such as for example, methanal (formaldehyde); ethanal (acetaldehyde); propanal (propionaldehyde); butanal (butyraldehyde); glucose; benzaldehyde and cinnamaldehyde. Other exemplary polymer precursors include, but are not limited to, phenolic compounds such as phenol and polyhydroxy benzenes, such as dihydroxy or trihydroxy benzenes, for example, resorcinol (i.e., 1,3-dihydroxy benzene), catechol, hydroquinone, and phloroglucinol. Important functionality includes alcohols, epoxides, carboxylic acids, ureas and carbamates. Mixtures of two or more polyhydroxy benzenes are also contemplated within the meaning of polymer precursor. 
     “Monolithic” refers to a solid, three-dimensional structure that is not particulate in nature. 
     “Sol” refers to a colloidal suspension of precursor particles (e.g., polymer precursors), and the term “gel” refers to a wet three-dimensional porous network obtained by condensation or reaction of the precursor particles. 
     “Polymer gel” refers to a gel in which the network component is a polymer; generally a polymer gel is a wet (aqueous, non-aqueous or solvent free) three-dimensional structure comprised of a polymer formed from synthetic precursors or polymer precursors. 
     “Sol gel” refers to a sub-class of polymer gel where the polymer is a colloidal suspension that forms a wet three-dimensional porous network obtained by reaction of the polymer precursors. 
     “Polymer hydrogel” or “hydrogel” refers to a subclass of polymer gel or gel wherein the solvent for the synthetic precursors or monomers is water or mixtures of water and one or more water-miscible solvent. 
     “Melt processed” refers to a system where mixing and reactions happen above the melting point of one or more of the components and where the system is generally considered solvent free (less than 15% solvent). 
     “Solid state processed” refers to a system comprised of solid components wherein reactions occur in the vicinity of the melting point or other analogous thermal event of one or more component in the system. The system is generally considered solvent free (for instance less than 15% solvent). 
     “Acid” refers to any substance that is capable of lowering the pH of a solution. Acids include Arrhenius, Brønsted and Lewis acids. A “solid acid” refers to a dried or granular compound that yields an acidic solution when dissolved in a solvent. The term “acidic” means having the properties of an acid. 
     “Base” refers to any substance that is capable of raising the pH of a solution. Bases include Arrhenius, Brønsted and Lewis bases. A “solid base” refers to a dried or granular compound that yields basic solution when dissolved in a solvent. The term “basic” means having the properties of a base. 
     “Miscible” refers to the property of a mixture wherein the mixture forms a single phase over certain ranges of temperature, pressure, and composition. 
     “Catalyst” is a substance which alters the rate of a chemical reaction. Catalysts participate in a reaction in a cyclic fashion such that the catalyst is cyclically regenerated. The present disclosure contemplates catalysts which are sodium free. The catalyst used in the preparation of a ultrapure polymer gel as described herein can be any compound that facilitates the polymerization of the polymer precursors to form an ultrapure polymer gel. A “volatile catalyst” is a catalyst which has a tendency to vaporize at or below atmospheric pressure. Exemplary volatile catalysts include, but are not limited to, ammoniums salts, such as ammonium bicarbonate, ammonium carbonate, ammonium hydroxide, and combinations thereof. 
     “Solvent” refers to a substance which dissolves or suspends reactants (e.g., ultrapure polymer precursors) and provides a medium in which a reaction may occur. Examples of solvents useful in the preparation of the gels, ultrapure polymer gels, ultrapure synthetic carbon materials and ultrapure synthetic amorphous carbon materials disclosed herein include, but are not limited to, water, alcohols and mixtures thereof. Exemplary alcohols include ethanol, t-butanol, methanol and mixtures thereof. Such solvents are useful for dissolution of the synthetic ultrapure polymer precursor materials, for example dissolution of a phenolic or aldehyde compound. In addition, in some processes such solvents are employed for solvent exchange in a polymer hydrogel (prior to freezing and drying), wherein the solvent from the polymerization of the precursors, for example, resorcinol and formaldehyde, is exchanged for a pure alcohol. In one embodiment of the present application, a cryogel is prepared by a process that does not include solvent exchange. 
     “Dried gel” or “dried polymer gel” refers to a gel or polymer gel, respectively, from which the solvent, generally water, or mixture of water and one or more water-miscible solvents, has been substantially removed. If the polymer is made without the inclusion of a solvent the initial polymer can be considered a “dried gel” or “dried polymer gel?. 
     “Pyrolyzed dried polymer gel” refers to a dried polymer gel which has been pyrolyzed but not yet activated, while an “activated dried polymer gel” refers to a dried polymer gel which has been activated. 
     “Carbonizing”, “pyrolyzing”, “carbonization” and “pyrolysis” each refer to the process of heating a carbon-containing substance at a pyrolysis dwell temperature in an inert atmosphere (e.g., argon, nitrogen or combinations thereof) or in a vacuum such that the targeted material collected at the end of the process is primarily carbon. “Pyrolyzed” refers to a material or substance, for example a carbon material, which has undergone the process of pyrolysis. 
     “Dwell temperature” refers to the temperature of the furnace during the portion of a process which is reserved for maintaining a relatively constant temperature (i.e., neither increasing nor decreasing the temperature). For example, the pyrolysis dwell temperature refers to the relatively constant temperature of the furnace during pyrolysis, and the activation dwell temperature refers to the relatively constant temperature of the furnace during activation. 
     “Pore” refers to an opening or depression in the surface, or a tunnel in a carbon material, such as for example activated carbon, pyrolyzed dried polymer gels, pyrolyzed polymer cryogels, pyrolyzed polymer xerogels, pyrolyzed polymer aerogels, activated dried polymer gels, activated polymer cryogels, activated polymer xerogels, activated polymer aerogels and the like. A pore can be a single tunnel or connected to other tunnels in a continuous network throughout the structure. 
     “Pore structure” refers to the layout of the surface of the internal pores within a carbon material, such as an activated carbon material. Components of the pore structure include pore size, pore volume, surface area, density, pore size distribution and pore length. Generally the pore structure of activated carbon material comprises micropores and mesopores. 
     “Pore volume” refers to the total volume of the carbon mass occupied by pores or empty volume. The pores may be either internal (not accessible by gas sorption) or external (accessible by gas sorption). 
     “Mesopore” generally refers to pores having a diameter between about 2 nanometers and about 50 nanometers while the term “micropore” refers to pores having a diameter less than about 2 nanometers. Mesoporous carbon materials comprise greater than 50% of their total pore volume in mesopores while microporous carbon materials comprise greater than 50% of their total pore volume in micropores. 
     “Surface area” refers to the total specific surface area of a substance measurable by the BET technique. Surface area is typically expressed in units of m 2 /g. The BET (Brunauer/Emmett/Teller) technique employs an inert gas, for example nitrogen, to measure the amount of gas adsorbed on a material and is commonly used in the art to determine the accessible surface area of materials. 
     “Electrode” refers to a conductor through which electricity enters or leaves an object, substance or region. 
     “Binder” refers to a material capable of holding individual particles of a substance (e.g., a carbon material) together such that after mixing a binder and the particles together the resulting mixture can be formed into sheets, pellets, disks or other shapes. Non-exclusive examples of binders include fluoro polymers, such as, for example, PTFE (polytetrafluoroethylene, Teflon), PFA (perfluoroalkoxy polymer resin, also known as Teflon), FEP (fluorinated ethylene propylene, also known as Teflon), ETFE (polyethylenetetrafluoroethylene, sold as Tefzel and Fluon), PVF (polyvinyl fluoride, sold as Tedlar), ECTFE (polyethylenechlorotrifluoroethylene, sold as Halar), PVDF (polyvinylidene fluoride, sold as Kynar), PCTFE (polychlorotrifluoroethylene, sold as Kel-F and CTFE), trifluoroethanol and combinations thereof. 
     “Inert” refers to a material that is not active in the electrolyte of an electrical energy storage device, that is it does not absorb a significant amount of ions or change chemically, e.g., degrade. 
     “Conductive” refers to the ability of a material to conduct electrons through transmission of loosely held valence electrons. 
     “Current collector” refers to a part of an electrical energy storage and/or distribution device which provides an electrical connection to facilitate the flow of electricity in to, or out of, the device. Current collectors often comprise metal and/or other conductive materials and may be used as a backing for electrodes to facilitate the flow of electricity to and from the electrode. 
     “Electrolyte” means a substance containing free ions such that the substance is electrically conductive. Electrolytes are commonly employed in electrical energy storage devices. Examples of electrolytes include, but are not limited to, solvents such as propylene carbonate, ethylene carbonate, butylene carbonate, dimethyl carbonate, methyl ethyl carbonate, diethyl carbonate, sulfolane, methylsulfolane, acetonitrile or mixtures thereof in combination with solutes such as tetralkylammonium salts such as LiPF 6  (lithium hexafluorophosphate), LiBOB (lithium bis(oxatlato)borate, TEA TFB (tetraethyl ammonium tetrafluoroborate), MTEATFB (methyltriethylammonium tetrafluoroborate), EMITFB (1-ethyl-3-methylimidazolium tetrafluoroborate), tetraethylammonium, triethylammonium based salts or mixtures thereof. In some embodiments, the electrolyte can be a water-based acid or water-based base electrolyte such as mild aqueous sulfuric acid or aqueous potassium hydroxide. 
     “Elemental form” refers to a chemical element having an oxidation state of zero (e.g., metallic lead). 
     “Oxidized form” form refers to a chemical element having an oxidation state greater than zero. 
     “Skeletal density” refers to the density of the material including internal porosity and excluding external porosity as measured by helium pycnometry 
     “Lithium uptake” refers to a carbon&#39;s ability to intercalate, absorb, or store lithium as measured as a ratio between the maximum number of lithium atoms to 6 carbon atoms. 
     “TGA” or “thermogravimetric analysis” refers to the measurement of heat flow and mass of a material as a function of time, temperature, and/or environment (i.e., carrier gas). 
     A. Carbon Materials 
     As noted above, traditional lithium based energy storage devices comprise graphitic anode material. The disadvantages of graphitic carbon are numerous in lithium ion batteries. For one, the graphite undergoes a phase and volume change during battery operation. That is, the material physically expands and contracts when lithium is inserted between the graphene sheets while the individual sheets physically shift laterally to maintain a low energy storage state. Secondly, graphite has a low capacity. Given the ordered and crystalline structure of graphite, it takes six carbons to store one lithium ion. The structure is not able to accommodate additional lithium. Thirdly, the movement of lithium ions is restricted to a 2D plane, reducing the kinetics and the rate capability of the material in a battery. This means that graphite does not perform well at high rates where power is needed. This power disadvantage is one of the limiting factors for using lithium ion batteries in all-electric vehicles. 
     Although hard carbon anodes for lithium-based devices has been explored, these carbon materials are generally low purity and the known devices still suffer from poor power performance and low first cycle efficiency. The presently disclosed hard carbon materials comprise properties which are optimized for use in lithium-based devices which exceed the performance characteristics of other known devices. 
     1. Hard Carbon Materials 
     As noted above, the present disclosure is directed to hard carbon materials useful as anode material in lithium-based (or sodium-based) and other electrical storage devices. While not wishing to be bound by theory, it is believed that the purity profile, chemical composition, polymer precursors, surface area, porosity and other properties of the carbon materials are related, at least in part, to its preparation method, and variation of the preparation parameters may yield carbon materials having different properties. Accordingly, in some embodiments, the carbon material is a pyrolyzed dried polymer gel. 
     The disclosed carbon materials improve the properties of any number of electrical energy storage devices, for example the carbon materials have been shown to improve the first cycle efficiency of a lithium-based battery. Accordingly, one embodiment of the present disclosure provides a carbon material, wherein the carbon material has a first cycle efficiency of greater than 50% when the carbon material is incorporated into an electrode of a lithium based energy storage device, for example a lithium ion battery. For example, some embodiments provide a carbon material having a surface area of less than 50 m 2 /g, wherein the carbon material has a first cycle efficiency of greater than 50% and a reversible capacity of at least 200 mAh/g when the carbon material is incorporated into an electrode of a lithium based energy storage device. In other embodiments, the first cycle efficiency is greater than 60%. In some other embodiments, the first cycle efficiency is greater than 70%. In yet other embodiments, the first cycle efficiency is greater than 80%. In still other embodiments, the first cycle efficiency is greater than 85%. In other embodiments, the first cycle efficiency is greater than 90%, greater than 95%, greater than 98%, or greater than 99%. In some embodiments of the foregoing, the carbon materials also comprise a surface area ranging from about 0.01 m 2 /g to about 50 m 2 /g or a pore volume ranging from about 0.0001 to about 0.03 cc/g or both. For example, in some embodiments the surface area ranges from about 1 m 2 /g to about 15 m 2 /g or the surface area is about 7 m 2 /g. 
     The properties of the carbon material (e.g., first cycle efficiency, capacity, etc.) can be determined by incorporating into an electrode and testing electrochemically between upper and lower voltages of 3V and −20 mV versus lithium metal, respectively. Alternatively, the carbon materials are tested at a current density of 40 mA/g with respect to the mass of carbon material. 
     The first cycle efficiency of the carbon anode material can be determined by comparing the lithium inserted into the anode during the first cycle to the lithium extracted from the anode on the first cycle. When the insertion and extraction are equal, the efficiency is 100%. As known in the art, the anode material can be tested in a half cell, where the counter electrode is lithium metal, the electrolyte is a 1M LiPF 6  1:1 ethylene carbonate:diethylcarbonate (EC:DEC), using a commercial polypropylene separator, though other similar electrolytes and separators can be used to yield similar performance results. 
     In some embodiments, the operating voltage for the anode material ranges from about −20 mV to about 3 V versus lithium metal. In other embodiments, the operating voltage for the anode material ranges from about −20 mV to about 2 V versus lithium metal, from about −5 mV to about 2 V versus lithium metal, from about 0 V to about 3 V versus lithium metal, from about 0 V to about 2V versus lithium metal, or from about 0.05 V to about 2.7 V versus lithium metal. 
     In another embodiment the present disclosure provides a carbon material, wherein the carbon material has a volumetric capacity (i.e., reversible capacity) of at least 500 mAh/cc when the carbon material is incorporated into an electrode of a lithium based energy storage device, for example a lithium ion battery. In other embodiments, the volumetric capacity is at least 550 mAh/cc. In some other embodiments, the volumetric capacity is at least 600 mAh/cc. In yet other embodiments, the volumetric capacity is at least 650 mAh/cc. In still other embodiments, the volumetric capacity is at least 700 mAh/cc. In other embodiments, the volumetric capacity is at least 800 mAh/cc, and in other embodiments, the volumetric capacity is at least 900 mAh/cc. 
     In another embodiment the present disclosure provides a carbon material, wherein the carbon material has a gravimetric capacity (i.e., reversible capacity) of at least 300 mAh/g when the carbon material is incorporated into an electrode of a lithium based energy storage device, for example a lithium ion battery. In other embodiments, the gravimetric capacity is at least 350 mAh/g. In some other embodiments, the gravimetric capacity is at least 400 mAh/g. In yet other embodiments, the gravimetric capacity is at least 450 mAh/g. In still other embodiments, the gravimetric capacity is at least 500 mAh/g. In other embodiments, the gravimetric capacity is at least 600 mAh/g, and in other embodiments, the gravimetric capacity is at least 700 mAh/g, at least 800 mAh/g, at least 900 mAh/g, at least 1000 mAh/g, at least 1100 mAh/g or even at least 1200 mAh/g. In yet other embodiments, the gravimetric capacity is between 1200 and 3500 mAh/g. In some particular embodiments the carbon materials have a gravimetric capacity ranging from about 450 mAh/g to about 550 mAh/g. Certain examples of any of the above carbons may comprise an electrochemical modifier as described in more detail below. 
     The volumetric and gravimetric capacity can be determined through the use of any number of methods known in the art, for example by incorporating into an electrode half cell with lithium metal counter electrode in a coin cell. The gravimetric specific capacity is determined by dividing the measured capacity by the mass of the electrochemically active carbon materials. The volumetric specific capacity is determined by dividing the measured capacity by the volume of the electrode, including binder and conductivity additive. Methods for determining the volumetric and gravimetric capacity are described in more detail in the Examples. 
     Due to structural differences, lithium plating may occur at different voltages. The voltage of lithium plating is defined as when the voltage increases despite lithium insertion. This can occur at a slow current rate, for example a rate corresponding to less than 40 mA/g, for example less than 20 mA/g. In one embodiment the voltage of lithium plating of the carbon collected in a half-cell versus lithium metal at a current density of 20 mA/g is 0V. In another embodiment the voltage of lithium plating of the carbon collected in a half-cell versus lithium metal at a current density of 20 mA/g is between 0V and −5 mV. In yet another embodiment the voltage of lithium plating of the carbon collected in a half-cell versus lithium metal at a current density of 20 mA/g is between −5 mV and −10 mV. In still yet another embodiment the voltage of lithium plating of the carbon collected in a half-cell versus lithium metal at a current density of 20 mA/g is between −10 mV and −15 mV. In still another embodiment the voltage of lithium plating of the carbon collected in a half-cell versus lithium metal at a current density of 20 mA/g is between −15 mV and −20 mV. In yet another embodiment the voltage of lithium plating of the carbon collected in a half-cell versus lithium metal at a current density of 20 mA/g is below −20 mV. In yet another embodiment the voltage of lithium plating of the carbon collected in a half-cell versus lithium metal at a current density of 20 mA/g is below −40 mV. 
     In some embodiments of the foregoing, the carbon materials also comprise a surface area ranging from about 0.1 m 2 /g to about 30 m 2 /g or a pore volume of at least about 0.00001 cc/g or both. For example, in some embodiments the surface area ranges from about 1 m 2 /g to about 15 m 2 /g or about 7 m 2 /g. In other embodiments, the pore volume ranges from about 0.00001 to about 0.002 cc/g. 
     In still other embodiments the present disclosure provides a carbon material, wherein when the carbon material is incorporated into an electrode of a lithium based energy storage device the carbon material has a volumetric capacity at least 10% greater than when the lithium based energy storage device comprises a graphite electrode. In some embodiments, the lithium based energy storage device is a lithium ion battery. In other embodiments, the carbon material has a volumetric capacity in a lithium based energy storage device that is at least 5% greater, at least 10% greater, at least 15% greater than the volumetric capacity of the same electrical energy storage device having a graphite electrode. In still other embodiments, the carbon material has a volumetric capacity in a lithium based energy storage device that is at least 20% greater, at least 30% greater, at least 40% greater, at least 50% greater, at least 200% greater, at least 100% greater or at least 150% greater than the volumetric capacity of the same electrical energy storage device having a graphite electrode. 
     While not wishing to be bound by theory, the present applicants believe the superior properties of the disclosed carbon materials is related, at least in part, to its unique properties such as surface area, purity, pore structure, chemical composition, crystallinity and surface chemistry, etc. For example, in some embodiments the surface area ranges from about 0.01 m 2 /g to about 50 m 2 /g for example from about 1 m 2 /g to about 25 m 2 /g. In other particular embodiments, the surface area ranges from about 5 m 2 /g to about 10 m 2 /g for example the surface area may be about 7 m 2 /g. In other embodiments, the specific surface area is less than about 5 m 2 /g have also been found to have good first cycle efficiency (e.g., &gt;80%). Certain embodiments which comprise low surface area (&lt;20 m2/g) have been found to have high gravimetric capacity (e.g., &gt;400 mAh/g) and high skeletal density (&gt;1.9 g/cc) and tap density (&gt;1 g/cc). 
     The surface area may be modified through activation. The activation method may use steam, chemical activation, CO 2  or other gasses. Methods for activation of carbon material are well known in the art. 
     The carbon material may be doped with lithium atoms, wherein the lithium is in ionic form and not in the form of lithium metal. These lithium atoms may or may not be able to be separated from the carbon. The number of lithium atoms to 6 carbon atoms can be calculated by techniques known to those familiar with the art: 
       #  Li=Q× 3.6× MM /( C  %× F )
 
     Wherein Q is the lithium extraction capacity measured in mAh/g between the voltages of 5 mV and 2.0V versus lithium metal, MM is 72 or the molecular mass of 6 carbons, F is Faraday&#39;s constant of 96500, C % is the mass percent carbon present in the structure as measured by CHNO or XPS. 
     The material can be characterized by the ratio of lithium atoms to carbon atoms (Li:C) which may vary between about 0:6 and 2:6. In some embodiments the Li:C ratio is between about 0.05:6 and about 1.9:6. In other embodiments the maximum Li:C ratio wherein the lithium is in ionic and not metallic form is 2.2:6. In certain other embodiments, the Li:C ratio ranges from about 1.2:6 to about 2:6, from about 1.3:6 to about 1.9:6, from about 1.4:6 to about 1.9:6, from about 1.6:6 to about 1.8:6 or from about 1.7:6 to about 1.8:6. In other embodiments, the Li:C ratio is greater than 1:6, greater than 1.2:6, greater than 1.4:6, greater than 1.6:6 or even greater than 1.8:6. In even other embodiments, the Li:C ratio is about 1.4:6, about 1.5:6, about 1.6:6, about 1.6:6, about 1.7:6, about 1.8:6 or about 2:6. In a specific embodiment the Li:C ratio is about 1.78:6. 
     In certain other embodiments, the carbon materials comprise an Li:C ratio ranging from about 1:6 to about 2.5:6, from about 1.4:6 to about 2.2:6 or from about 1.4:6 to about 2:6. In still other embodiments, the carbon materials may not necessarily include lithium, but instead have a lithium uptake capacity (i.e., the capability to uptake a certain quantity of lithium). While not wishing to be bound by theory, it is believed the lithium uptake capacity of the carbon materials contributes to their superior performance in lithium based energy storage devices. The lithium uptake capacity is expressed as a ratio of the atoms of lithium taken up by the carbon per atom of carbon. In certain other embodiments, the carbon materials comprise a lithium uptake capacity ranging from about 1:6 to about 2.5:6, from about 1.4:6 to about 2.2:6 or from about 1.4:6 to about 2:6. 
     In certain other embodiments, the lithium uptake capacity ranges from about 1.2:6 to about 2:6, from about 1.3:6 to about 1.9:6, from about 1.4:6 to about 1.9:6, from about 1.6:6 to about 1.8:6 or from about 1.7:6 to about 1.8:6. In other embodiments, the lithium uptake capacity is greater than 1:6, greater than 1.2:6, greater than 1.4:6, greater than 1.6:6 or even greater than 1.8:6. In even other embodiments, the Li:C ratio is about 1.4:6, about 1.5:6, about 1.6:6, about 1.6:6, about 1.7:6, about 1.8:6 or about 2:6. In a specific embodiment the Li:C ratio is about 1.78:6. 
     Different methods of doping may include chemical reactions, electrochemical reactions, physical mixing of particles, gas phase reactions, solid phase reactions, liquid phase reactions. 
     In other embodiments the lithium is in the form of lithium metal. 
     Since the total pore volume may partially relate to the storage of lithium ions, the internal ionic kinetics, as well as the available carbon/electrolyte surfaces capable of charge-transfer, this is one parameter that can be adjusted to obtain the desired electrochemical properties. Some embodiments include carbon materials having low total pore volume (e.g., less than about 0.1 cc/g). In one embodiment, the total pore volume of the carbon materials is less than about 0.01 cc/g. In another embodiment, the total pore volume of the carbon materials is less than about 0.001 cc/g. In yet another embodiment, the total pore volume of the carbon materials is less than about 0.0001 cc/g. 
     In one embodiment, the total pore volume of the carbon materials ranges from about 0.00001 cc/g to about 0.1 cc/g, for example from about 0.0001 cc/g to about 0.01 cc/g. In some other embodiments, the total pore volume of the carbon materials ranges from about 0.001 cc/g to about 0.01 cc/g. 
     In other embodiments, the carbon materials comprise a total pore volume less than or equal to 0.6 cc/g, for example less than 0.5 cc/g, for example less than 0.4 cc/g, for example less than 0.3 cc/g, for example less than 0.2 cc/g, for example less than 0.1 cc/g, for example less than 0.05 cc/g, for example less than 0.01 cc/g, for example less than 0.001 cc/g. In other embodiments, the carbon materials comprise a total pore volume ranging from about 0.1 cc/g to about 0.6 cc/g. In some other embodiments, the total pore volume of the carbon materials ranges from about 0.01 cc/g to about 0.1 cc/g. In some other embodiments, the total pore volume of the carbon materials ranges from about 0.1 cc/g to about 0.2 cc/g. In some other embodiments, the total pore volume of the carbon materials ranges from about 0.2 cc/g to about 0.3 cc/g. In some other embodiments, the total pore volume of the carbon materials ranges from about 0.3 cc/g to about 0.4 cc/g. In some other embodiments, the total pore volume of the carbon materials ranges from about 0.4 cc/g to about 0.5 cc/g. In some other embodiments, the total pore volume of the carbon materials ranges from about 0.5 cc/g to about 0.6 cc/g. 
     The present invention also includes hard carbon materials having high total pore volume, for example greater than 0.6 cc/g. In some other embodiments, the total pore volume of the carbon materials ranges from about 0.6 cc/g to about 2.0 cc/g. In some other embodiments, the total pore volume of the carbon materials ranges from about 0.6 cc/g to about 1.0 cc/g. In some other embodiments, the total pore volume of the carbon materials ranges from about 1.0 cc/g to about 1.5 cc/g. In some other embodiments, the total pore volume of the carbon materials ranges from about 1.5 cc/g to about 2.0 cc/g. 
     The carbon materials may comprise a majority (e.g., &gt;50%) of the total pore volume residing in pores of certain diameter. For example, in some embodiments greater than 50%, greater than 60%, greater than 70%, greater than 80%, greater than 90% or even greater than 95% of the total pore volume resides in pores having a diameter of 1 nm or less. In other embodiments greater than 50%, greater than 60%, greater than 70%, greater than 80%, greater than 90% or even greater than 95% of the total pore volume resides in pores having a diameter of 100 nm or less. In other embodiments greater than 50%, greater than 60%, greater than 70%, greater than 80%, greater than 90% or even greater than 95% of the total pore volume resides in pores having a diameter of 0.5 nm or less. 
     In some embodiments, the tap density of the carbon materials may be predictive of their electrochemical performance, for example the volumetric capacity. In yet some embodiments, the carbon materials comprise a tap density greater than about 0.5 g/cc. In some other embodiments, the carbon materials comprise a tap density ranging from about 0.5 g/cc to about 2.0 g/cc. In some other embodiments, the carbon materials comprise a tap density ranging from about 0.5 g/cc to about 1.0 g/cc. In some embodiments, the carbon materials comprise a tap density ranging from about 0.5 g/cc to about 0.75 g/cc. In some embodiments, the carbon materials comprise a tap density ranging from about 0.75 g/cc to about 1.2 g/cc, for example from about 0.8 g/cc to about 1.0 g/cc. In some embodiments of the foregoing, the carbon materials comprise a low, medium or high total pore volume. 
     The density of the carbon materials can also be characterized by their skeletal density as measured by helium pycnometry. In certain embodiments, the skeletal density of the carbon materials ranges from about 1 g/cc to about 3 g/cc, for example from about 1.5 g/cc to about 2.3 g/cc. In other embodiments, the skeletal density ranges from about 1.5 cc/g to about 1.6 cc/g, from about 1.6 cc/g to about 1.7 cc/g, from about 1.7 cc/g to about 1.8 cc/g, from about 1.8 cc/g to about 1.9 cc/g, from about 1.9 cc/g to about 2.0 cc/g, from about 2.0 cc/g to about 2.1 cc/g, from about 2.1 cc/g to about 2.2 cc/g or from about 2.2 cc/g to about 2.3 cc/g. 
     As discussed in more detail below, the surface functionality of the presently disclosed carbon materials may be altered to obtain the desired electrochemical properties. One property which can be predictive of surface functionality is the pH of the carbon materials. The presently disclosed carbon materials comprise pH values ranging from less than 1 to about 14, for example less than 5, from 5 to 8 or greater than 8. In some embodiments, the pH of the carbon materials is less than 4, less than 3, less than 2 or even less than 1. In other embodiments, the pH of the carbon materials is between about 5 and 6, between about 6 and 7, between about 7 and 8 or between 8 and 9 or between 9 and 10. In still other embodiments, the pH is high and the pH of the carbon materials ranges is greater than 8, greater than 9, greater than 10, greater than 11, greater than 12, or even greater than 13. 
     Pore size distribution may be important to both the storage capacity of the material and the kinetics and power capability of the system. The pore size distribution can range from micro to meso to macro (see e.g.,  FIG. 1 ) and may be either monomodal, bimodal or multimodal (i.e., may comprise one or more different distribution of pore sizes. Micropores, with average pore sizes less than 1 nm, may create additional storage sites as well as lithium (or sodium) ion diffusion paths. Graphite sheets typically are spaced 0.33 nm apart for lithium storage. While not wishing to be bound by theory, it is thought that large quantities of pores of similar size may yield graphite-like structures within pores with additional hard carbon-type storage in the bulk structure. Mesopores are typically below 100 nm. These pores are ideal locations for nano particle dopants, such as metals, and provide pathways for both conductive additive and electrolyte for ion and electron conduction. In some embodiments the carbon materials comprise macropores greater than 100 nm which may be especially suited for large particle doping. 
     Accordingly, in one embodiment, the carbon material comprises a fractional pore volume of pores at or below 1 nm that comprises at least 50% of the total pore volume, at least 75% of the total pore volume, at least 90% of the total pore volume or at least 99% of the total pore volume. In other embodiments, the carbon material comprises a fractional pore volume of pores at or below 10 nm that comprises at least 50% of the total pore volume, at least 75% of the total pore volume, at least 90% of the total pore volume or at least 99% of the total pore volume. In other embodiments, the carbon material comprises a fractional pore volume of pores at or below 50 nm that comprises at least 50% of the total pore volume, at least 75% of the total pore volume, at least 90% of the total pore volume or at least 99% of the total pore volume. 
     In another embodiment, the carbon material comprises a fractional pore surface area of pores at or below 100 nm that comprises at least 50% of the total pore surface area, at least 75% of the total pore surface area, at least 90% of the total pore surface area or at least 99% of the total pore surface area. In another embodiment, the carbon material comprises a fractional pore surface area of pores at or greater than 100 nm that comprises at least 50% of the total pore surface area, at least 75% of the total pore surface area, at least 90% of the total pore surface area or at least 99% of the total pore surface area. 
     In another embodiment, the carbon material comprises pores predominantly in the range of 100 nm or lower, for example 10 nm or lower, for example 5 nm or lower. Alternatively, the carbon material comprises micropores in the range of 0-2 nm and mesopores in the range of 2-100 nm. The ratio of pore volume or pore surface in the micropore range compared to the mesopore range can be in the range of 95:5 to 5:95. 
     In some embodiments, the median particle diameter for the carbon materials ranges from 1 to 1000 microns. In other embodiments the median particle diameter for the carbon materials ranges from 1 to 100 microns. Still in other embodiments the median particle diameter for the carbon materials ranges from 1 to 50 microns. Yet in other embodiments, the median particle diameter for the carbon materials ranges from 5 to 15 microns or from 1 to 5 microns. Still in other embodiments, the median particle diameter for the carbon materials is about 10 microns. Still in other embodiments, the median particle diameter for the carbon materials is less than 4, is less than 3, is less than 2, is less than 1 microns. 
     In some embodiments, the carbon materials exhibit a median particle diameter ranging from 1 micron to 5 microns. In other embodiments, the median particle diameter ranges from 5 microns to 10 microns. In yet other embodiments, the median particle diameter ranges from 10 nm to 20 microns. Still in other embodiments, the median particle diameter ranges from 20 nm to 30 microns. Yet still in other embodiments, the median particle diameter ranges from 30 microns to 40 microns. Yet still in other embodiments, the median particle diameter ranges from 40 microns to 50 microns. In other embodiments, the median particle diameter ranges from 50 microns to 100 microns. In other embodiments, the median particle diameter ranges in the submicron range &lt;1 micron. In certain embodiments, the particle size distribution can be monomodal, bimodal, or multimodal, e.g., see  FIG. 2  for example particle size distributions. 
     In other embodiments, the carbon materials are microporous (e.g., greater than 50% of pores less than 1 nm) and comprise monodisperse micropores. For example in some embodiments the carbon materials are microporous, and (Dv90−Dv10)/Dv50, where Dv10, Dv50 and Dv90 refer to the pore size at 10%, 50% and 90% of the distribution by volume, is about 3 or less, typically about 2 or less, often about 1.5 or less. 
     In other embodiments, the carbon materials are mesoporous (e.g., greater than 50% of pores less than 100 nm) and comprise monodisperse mesopores. For example in some embodiments, the carbon materials are mesoporous and (Dv90−Dv10)/Dv50, where Dv10, Dv50 and Dv90 refer to the pore size at 10%, 50% and 90% of the distribution by volume, is about 3 or less, typically about 2 or less, often about 1.5 or less. 
     In other embodiments, the carbon materials are macroporous (e.g., greater than 50% of pores greater than 100 nm) and comprise monodisperse macropores. For example in some embodiments, the carbon materials are macroporous and (Dv90−Dv10)/Dv50, where Dv10, Dv50 and Dv90 refer to the pore size at 10%, 50% and 90% of the distribution by volume, is about 3 or less, typically about 2 or less, often about 1.5 or less. 
     In some other embodiments, the carbon materials have a bimodal pore size distribution. For example, the carbon materials may comprise a population of micropores and a population of mesopores. In some embodiments, the ratio of micropores to mesopores ranges from about 1:10 to about 10:1, for example from about 1:3 to about 3:1. 
     In some embodiments, the carbon materials comprise pores having a peak height found in the pore volume distribution ranging from 0.1 nm to 0.25 nm. In other embodiments, the peak height found in the pore volume distribution ranges from 0.25 nm to 0.50 nm. Yet in other embodiments, the peak height found in the pore volume distribution ranges from 0.75 nm to 1.0 nm. Still in other embodiments, the peak height found in the pore volume distribution ranges from 0.1 nm to 0.50 nm. Yet still in other embodiments, the peak height found in the pore volume distribution ranges from 0.50 nm to 1.0 nm. 
     In some embodiments, the carbon materials comprise pores having a peak height found in the pore volume distribution ranging from 2 nm to 10 nm. In other embodiments, the peak height found in the pore volume distribution ranges from 10 nm to 20 nm. Yet in other embodiments, the peak height found in the pore volume distribution ranges from 20 nm to 30 nm. Still in other embodiments, the peak height found in the pore volume distribution ranges from 30 nm to 40 nm. Yet still in other embodiments, the peak height found in the pore volume distribution ranges from 40 nm to 50 nm. In other embodiments, the peak height found in the pore volume distribution ranges from 50 nm to 100 nm. 
     The present inventors have found that the extent of disorder in the carbon materials may have an impact on the electrochemical properties of the carbon materials. For example, the data in Table 4 (see Examples) shows a possible trend between the available lithium sites for insertion and the range of disorder/crystallite size. Thus controlling the extent of disorder in the carbon materials provides a possible avenue to improve the rate capability for carbons since a smaller crystallite size may allow for lower resistive lithium ion diffusion through the amorphous structure. The present invention includes embodiments which comprise both high and low levels of disorder. 
     Disorder, as recorded by RAMAN spectroscopy, is a measure of the size of the crystallites found within both amorphous and crystalline structures (M. A. Pimenta, G. Dresselhaus, M. S. Dresselhaus, L. G. Can ado, A. Jorio, and R. Saito, “Studying disorder in graphite-based systems by Raman spectroscopy,” Physical Chemistry Chemical Physics, vol. 9, no. 11, p. 1276, 2007). RAMAN spectra of exemplary carbon are shown in  FIG. 3 . For carbon structures, crystallite sizes (L a ) can be calculated from the relative peak intensities of the D and G Raman shifts (Eq 1) 
         L   a  (nm)=(2.4×10 −10 )λ 4   laser   R   −1   (1)
 
       where 
         R=I   D   /I   G   (2)
 
     The values for R and L a  can vary in certain embodiments, and their value may affect the electrochemical properties of the carbon materials, for example the capacity of the 2 nd  lithium insertion (2 nd  lithium insertion is related to first cycle efficiency since first cycle efficiency=(capacity at 1 st  lithium insertion/capacity at 2 nd  lithium insertion)×100). For example, in some embodiments R ranges from about 0 to about 1 or from about 0.50 to about 0.95. In other embodiments, R ranges from about 0.60 to about 0.90. In other embodiments, R ranges from about 0.80 to about 0.90. L a  also varies in certain embodiments and can range from about 1 nm to about 500 nm. In certain other embodiments, La ranges from about 5 nm to about 100 nm or from about 10 to about 50 nm. In other embodiments, La ranges from about 15 nm to about 30 nm, for example from about 20 nm to about 30 nm or from about 25 nm to 30 nm. 
     In a related embodiment, the electrochemical properties of the carbon materials are related to the level of crystallinity as measured by X-ray diffraction (XRD). While Raman measures the size of the crystallites, XRD records the level of periodicity in the bulk structure through the scattering of incident X-rays (see e.g.,  FIG. 4 ). The present invention includes materials that are non-graphitic (crystallinity &lt;10%) and semi-graphitic (crystallinity between 10 and 50%). The crystallinity of the carbon materials ranges from about 0% to about 99%. In some embodiments, the carbon materials comprise less than 10% crystallinity, less than 5% crystallinity or even less than 1% crystallinity (i.e., highly amorphous). In other embodiments, the carbon materials comprise from 10% to 50% crystallinity. In still other embodiments, the carbon materials comprise less than 50% crystallinity, less than 40% crystallinity, less than 30% crystallinity or even less than 20% crystallinity. 
     In a related embodiment, the electrochemical performance of the carbon materials are related to the empirical values, R, as calculated from Small Angle X-ray Diffraction (SAXS), wherein R=B/A and B is the height of the double layer peak and A is the baseline for the single graphene sheet as measured by SAXS. 
     SAXS has the ability to measure internal pores, perhaps inaccessible by gas adsorption techniques but capable of lithium storage. In certain embodiments, the R factor is below 1, comprising single layers of graphene. In other embodiments, the R factor ranges from about 0.1 to about 20 or from about 1 to 10. In yet other embodiments, the R factor ranges from 1 to 5, from 1 to 2, or from 1.5 to 2. In still other embodiments, the R factor ranges from 1.5 to 5, from 1.75 to 3, or from 2 to 2.5. Alternatively, the R factor is greater than 10. The SAXS pattern may also be analyzed by the number of peaks found between 10° and 40°. In some embodiments, the number of peaks found by SAXS at low scattering angles are 1, 2, 3, or even more than 3.  FIGS. 5 and 6  present representative SAXS plots. 
     In certain embodiments, the organic content of the carbon materials can be manipulated to provide the desired properties, for example by contacting the carbon materials with a hydrocarbon compound such as cyclohexane and the like. Infra-red spectroscopy (FTIR) can be used as a metric to determine the organic content of both surface and bulk structures of the carbon materials (see e.g.,  FIG. 7A .). In one embodiment, the carbon materials comprise essentially no organic material. An FTIR spectra which is essentially featureless is indicative of such embodiments (e.g., carbons B and D). In other embodiments, the carbon materials comprise organic material, either on the surface or within the bulk structure. In such embodiments, the FTIR spectra generally depict large hills and valleys which indicates the presence of organic content. 
     The organic content may have a direct relationship to the electrochemical performance ( FIG. 7B ) and response of the material when placed into a lithium bearing device for energy storage. Carbon materials with flat FTIR signals (no organics) often display a low extraction peak in the voltage profile at 0.2 V. Well known to the art, the extract voltage is typical of lithium stripping. In certain embodiments, the carbon materials comprise organic content and the lithium stripping plateau is absent or near absent. 
     The carbon materials may also comprise varying amounts of carbon, oxygen, hydrogen and nitrogen as measured by gas chromatography CHNO analysis. In one embodiment, the carbon content is greater than 98 wt. % or even greater than 99.9 wt % as measured by CHNO analysis. In another embodiment, the carbon content ranges from about 10 wt % to about 99.9%, for example from about 50 to about 98 wt. % of the total mass. In yet other embodiments, the carbon content ranges 90 to 98 wt. %, 92 to 98 wt % or greater than 95% of the total mass. In yet other embodiments, the carbon content ranges from 80 to 90 wt. % of the total mass. In yet other embodiments, the carbon content ranges from 70 to 80 wt. % of the total mass. In yet other embodiments, the carbon content ranges from 60 to 70 wt. % of the total mass. 
     In another embodiment, the nitrogen content ranges from 0 to 90 wt. % based on total mass of all components in the carbon material as measured by CHNO analysis. In another embodiment, the nitrogen content ranges from 1 to 10 wt. % of the total mass. In yet other embodiments, the nitrogen content ranges from 10 to 20 wt. % of the total mass. In yet other embodiments, the nitrogen content ranges from 20 to 30 wt. % of the total mass. In another embodiment, the nitrogen content is greater than 30 wt. %. 
     In still other embodiments, the nitrogen content is greater than 1% or ranges from about 1% to about 20%. In some more specific embodiments, the nitrogen content ranges from about 1% to about 6%, while in other embodiments, the nitrogen content ranges from about 0.1% to about 1%. In certain of the above embodiments, the nitrogen content is based on weight relative to total weight of all components in the carbon material 
     The carbon and nitrogen content may also be measured as a ratio of C:N (carbon atoms to nitrogen atoms). In one embodiment, the C:N ratio ranges from 1:0.001 to 0.001:1 or from 1:0.001 to 1:1. In another embodiment, the C:N ratio ranges from 1:0.001 to 1:0.01. In yet another embodiment, the C:N ratio ranges from 1:0.01 to 1:1. In yet another embodiment, the content of nitrogen exceeds the content of carbon, for example the C:N ratio can range from about 0.01:1 to about 0.1:1 or from 0.1:1 to about 0.5:1. 
     In still other embodiments, the phosphorous content is greater than 1% or ranges from about 1% to about 20%. In some more specific embodiments, the phosophsorous content ranges from about 3% to about 15%, while in other embodiments, the phosphorous content ranges from about 0.1% to about 1%. In certain of the above embodiments, the phosphorous content is based on weight relative to total weight of all components in the carbon material. 
     The carbon materials may also comprise varying amounts of carbon, oxygen, nitrogen, Cl, and Na, to name a few, as measured by XPS analysis. In one embodiment, the carbon content is greater than 98 wt. % as measured by XPS analysis. In another embodiment, the carbon content ranges from 50 to 98 wt. % of the total mass. In yet other embodiments, the carbon content ranges 90 to 98 wt. % of the total mass. In yet other embodiments, the carbon content ranges from 80 to 90 wt. % of the total mass. In yet other embodiments, the carbon content ranges from 70 to 80 wt. % of the total mass. In yet other embodiments, the carbon content ranges from 60 to 70 wt. % of the total mass. 
     In other embodiments, the carbon content ranges from 10% to 99.9%, from 10% to 99%, from 10% to 98%, from 50% to 99.9%, from 50% to 99%, from 50% to 98%, from 75% to 99.9%, from 75% to 99% or from 75% to 98% of the total mass of all components in the carbon material as measured by XPS analysis 
     In another embodiment, the nitrogen content ranges from 0 to 90 wt. % as measured by XPS analysis. In another embodiment, the nitrogen content ranges from 1 to 75 wt. % of the total mass. In another embodiment, the nitrogen content ranges from 1 to 50 wt. % of the total mass. In another embodiment, the nitrogen content ranges from 1 to 25 wt. % of the total mass. In another embodiment, the nitrogen content ranges from 1 to 20 wt. % of the total mass. In another embodiment, the nitrogen content ranges from 1 to 10 wt. % of the total mass. In another embodiment, the nitrogen content ranges from 1 to 6 wt. % of the total mass. In yet other embodiments, the nitrogen content ranges from 10 to 20 wt. % of the total mass. In yet other embodiments, the nitrogen content ranges from 20 to 30 wt. % of the total mass. In another embodiment, the nitrogen content is greater than 30 wt. %. 
     The carbon and nitrogen content may also be measured as a ratio of C:N by XPS. In one embodiment, the C:N ratio ranges from 0.001:1 to 1:0.001. In one embodiment, the C:N ratio ranges from 0.01:1 to 1:0.01. In one embodiment, the C:N ratio ranges from 0.1:1 to 1:0.01. In one embodiment, the C:N ratio ranges from 1:0.5 to 1:0.001. In one embodiment, the C:N ratio ranges from 1:0.5 to 1:0.01. In one embodiment, the C:N ratio ranges from 1:0.5 to 1:0.1. In one embodiment, the C:N ratio ranges from 1:0.2 to 1:0.01. In one embodiment, the C:N ratio ranges from 1:0.001 to 1:1. In another embodiment, the C:N ratio ranges from 1:0.001 to 0.01. In yet another embodiment, the C:N ratio ranges from 1:0.01 to 1:1. In yet another embodiment, the content of nitrogen exceeds the content of carbon. 
     In some embodiments, the phosphorus content in the carbon material is between 0.01% and 75%, for example between 0.1% and 50%, for example between 1% and 25%, for example between 2% and 15%, for example between 3% and 10%. In other embodiments, the phosphorus content in the carbon material is between 1% and 5%. In other embodiments, the phosphorus content in the carbon material is between 5% and 10%. In other embodiments, the phosphorus content in the carbon material is between 10% and 15%. In other embodiments, the phosphorus content in the carbon material is between 15% and 20%. 
     The carbon and nitrogen phosphorous content may also be measured as a ratio of C:P by XPS. In one embodiment, the C:P ratio ranges from 0.001:1 to 1:0.001. In one embodiment, the C:P ratio ranges from 0.01:1 to 1:0.01. In one embodiment, the C:P ratio ranges from 0.1:1 to 1:0.01. In one embodiment, the C:P ratio ranges from 1:0.5 to 1:0.001. In one embodiment, the C:P ratio ranges from 1:0.5 to 1:0.01. In one embodiment, the C:P ratio ranges from 1:0.5 to 1:0.1. In one embodiment, the C:P ratio ranges from 1:0.2 to 1:0.01. In one embodiment, the C:P ratio ranges from 1:0.001 to 1:1. In another embodiment, the C:P ratio ranges from 1:0.001 to 0.01. In yet another embodiment, the C:P ratio ranges from 1:0.01 to 1:1. In yet another embodiment, the content of phosphorus exceeds the content of carbon. 
     In some embodiments, the carbon contains an electrochemical modifier from Group 13 (B, Al, Ga, In, Tl), Group 14 (Si, Ge, Sn, Pb), Group 15 (N, P, As, Sb) or Group 16 (0, S, Se) and the content in the carbon material is between 0.01% and 75%, for example between 0.1% and 50%, for example between 1% and 25%, for example between 2% and 15%, for example between 3% and 10%. In other embodiments, the electrochemical modifier content in the carbon material is between 1% and 5%. In other embodiments, the electrochemical modifier content in the carbon material is between 5% and 10%. In other embodiments, the electrochemical modifier content in the carbon material is between 10% and 15%. In other embodiments, the electrochemical modifier content in the carbon material is between 15% and 20%. 
     The carbon and electrochemical modifier (EM) content may also be measured as a ratio of C:EM by XPS. In one embodiment, the C:EM ratio ranges from 0.001:1 to 1:0.001. In one embodiment, the C:EM ratio ranges from 0.01:1 to 1:0.01. In one embodiment, the C:EM ratio ranges from 0.1:1 to 1:0.01. In one embodiment, the C:EM ratio ranges from 1:0.5 to 1:0.001. In one embodiment, the C:EM ratio ranges from 1:0.5 to 1:0.01. In one embodiment, the C:EM ratio ranges from 1:0.5 to 1:0.1. In one embodiment, the C:EM ratio ranges from 1:0.2 to 1:0.01. In one embodiment, the C:EM ratio ranges from 1:0.001 to 1:1. In another embodiment, the C:EM ratio ranges from 1:0.001 to 0.01. In yet another embodiment, the C:EM ratio ranges from 1:0.01 to 1:1. In yet another embodiment, the content of electrochemical modifier exceeds the content of carbon. 
     The carbon material can include both sp3 and sp2 hybridized carbons. The percentage of sp2 hybridization can be measured by XPS using the Auger spectrum, as known in the art. It is assumed that for materials which are less than 100% sp2, the remainder of the bonds are sp3. The carbon materials range from about 1% sp2 hybridization to 100% sp2 hybridization. Other embodiments include carbon materials comprising from about 25% to about 95% sp2, from about 50%-95% sp2, from about 50% to about 75% sp2, from about 65% to about 95% sp2 or about 65% sp2. 
     The carbon materials may also comprise an electrochemical modifier (i.e., a dopant) selected to optimize the electrochemical performance of the carbon materials. The electrochemical modifier may be incorporated within the pore structure and/or on the surface of the carbon material or incorporated in any number of other ways. For example, in some embodiments, the carbon materials comprise a coating of the electrochemical modifier (e.g., Al 2 O 3 ) on the surface of the carbon materials. In some embodiments, the carbon materials comprise greater than about 100 ppm of an electrochemical modifier. In certain embodiments, the electrochemical modifier is selected from iron, tin, silicon, nickel, aluminum and manganese. 
     In certain embodiments the electrochemical modifier comprises an element with the ability to lithiate from 3 to 0 V versus lithium metal (e.g. silicon, tin, sulfur). In other embodiments, the electrochemical modifier comprises metal oxides with the ability to lithiate from 3 to 0 V versus lithium metal (e.g. iron oxide, molybdenum oxide, titanium oxide). In still other embodiments, the electrochemical modifier comprises elements which do not lithiate from 3 to 0 V versus lithium metal (e.g. aluminum, manganese, nickel, metal-phosphates). In yet other embodiments, the electrochemical modifier comprises a non-metal element (e.g. fluorine, nitrogen, hydrogen). In still other embodiments, the electrochemical modifier comprises any of the foregoing electrochemical modifiers or any combination thereof (e.g. tin-silicon, nickel-titanium oxide). 
     The electrochemical modifier may be provided in any number of forms. For example, in some embodiments the electrochemical modifier comprises a salt. In other embodiments, the electrochemical modifier comprises one or more elements in elemental form, for example elemental iron, tin, silicon, nickel or manganese. In other embodiments, the electrochemical modifier comprises one or more elements in oxidized form, for example iron oxides, tin oxides, silicon oxides, nickel oxides, aluminum oxides or manganese oxides. 
     In other embodiments, the electrochemical modifier comprises iron. In other embodiments, the electrochemical modifier comprises tin. In other embodiments, the electrochemical modifier comprises silicon. In some other embodiments, the electrochemical modifier comprises nickel. In yet other embodiments, the electrochemical modifier comprises aluminum. In yet other embodiments, the electrochemical modifier comprises manganese. In yet other embodiments, the electrochemical modifier comprises Al 2 O 3 . In yet other embodiments, the electrochemical modifier comprises titanium. In yet other embodiments, the electrochemical modifier comprises titanium oxide. In yet other embodiments, the electrochemical modifier comprises lithium. In yet other embodiments, the electrochemical modifier comprises sulfur. In yet other embodiments, the electrochemical modifier comprises phosphorous. In yet other embodiments, the electrochemical modifier comprises molybdenum. 
     In addition to the above exemplified electrochemical modifiers, the carbon materials may comprise one or more additional forms (i.e., allotropes) of carbon. In this regard, it has been found that inclusion of different allotropes of carbon such as graphite, amorphous carbon, diamond, C60, carbon nanotubes (e.g., single and/or multi-walled), graphene and/or carbon fibers into the carbon materials is effective to optimize the electrochemical properties of the carbon materials. The various allotropes of carbon can be incorporated into the carbon materials during any stage of the preparation process described herein. For example, during the solution phase, during the gelation phase, during the curing phase, during the pyrolysis phase, during the milling phase, or after milling. In some embodiments, the second carbon form is incorporated into the carbon material by adding the second carbon form before or during polymerization of the polymer gel as described in more detail herein. The polymerized polymer gel containing the second carbon form is then processed according to the general techniques described herein to obtain a carbon material containing a second allotrope of carbon. 
     Accordingly, in some embodiments the carbon materials comprise a second carbon form selected from graphite, amorphous carbon, diamond, C60, carbon nanotubes (e.g., single and/or multi-walled), graphene and carbon fibers. In some embodiments, the second carbon form is graphite. In other embodiments, the second form is diamond. The ratio of carbon material (e.g., hard carbon) to second carbon allotrope can be tailored to fit any desired electrochemical application. 
     In certain embodiments, the ratio of hard carbon to second carbon allotrope in the carbon materials ranges from about 0.01:1 to about 100:1. In other embodiments, the ratio of hard carbon to second carbon allotrope ranges from about 1:1 to about 10:1 or about 5:1. In other embodiments, the ratio of hard carbon to second carbon allotrope ranges from about 1:10 to about 10:1. In other embodiments, the ratio of hard carbon to second carbon allotrope ranges from about 1:5 to about 5:1. In other embodiments, the ratio of hard carbon to second carbon allotrope ranges from about 1:3 to about 3:1. In other embodiments, the ratio of hard carbon to second carbon allotrope ranges from about 1:2 to about 2:1. 
     In certain embodiments, the ratio of hard carbon to second allotrope ranges from 0.01 to 0.5. For example, in some embodiments the ratio of hard carbon to second allotrope ranges from 0.1 to 0.4. In other embodiments, the ratio of hard carbon to second allotrope ranges from 0.15 to 0.3. For example, the ratio of hard carbon to second allotrope ranges from 0.15 to 0.25 in various embodiments. In still more embodiments, the ratio of hard carbon to second allotrope ranges from 0.17 to 0.25. In certain other embodiments, the second allotrope is graphite, and the ratio of hard carbon to graphite ranges from 0.01 to 0.5, for instance from 0.1 to 0.4, for instance 0.15 to 0.3, for instance 0.17 to 0.25. In certain embodiments, the second allotrope is graphene, and the ratio of hard carbon to graphene ranges from 0.01 to 0.5, for instance from 0.1 to 0.4, for instance 0.15 to 0.3, for instance 0.17 to 0.25. 
     The electrochemical properties of the carbon materials can be modified, at least in part, by the amount of the electrochemical modifier in the carbon material. Accordingly, in some embodiments, the carbon material comprises at least 0.10%, at least 0.25%, at least 0.50%, at least 1.0%, at least 5.0%, at least 10%, at least 25%, at least 50%, at least 75%, at least 90%, at least 95%, at least 99% or at least 99.5% of the electrochemical modifier. For example, in some embodiments, the carbon materials comprise between 0.5% and 99.5% carbon and between 0.5% and 99.5% electrochemical modifier. The percent of the electrochemical modifier is calculated on weight percent basis (wt %). In some other more specific embodiments, the electrochemical modifier comprises iron, tin, silicon, nickel and manganese. 
     In certain instances, the electrochemical modifier comprises silicon. The electrochemical modifier comprising silicon can be various species known in the art, such as elemental silicon, silicon oxide, silicon dioxide and the like. The elemental silicon, silicon oxide, silicon dioxide, or other electrochemical modifier comprising silicon can be in amorphous and/or crystalline form. In some embodiments, the carbon materials comprise between 0.5% to 99.5% electrochemical modifier comprising silicon, for example 10 to 95%, for example 20% to 95%, for example 50% to 95%, for example 75% to 95%, for example 80-95%, for example 85-95%, for example about 90%. 
     The hard carbon materials have purities not previously obtained with hard carbon materials. While not wishing to be bound by theory, it is believed that the high purity of the hard carbon materials contributes to the superior electrochemical properties of the same. In some embodiments, the carbon material comprises low total PIXE impurities (excluding any intentionally included electrochemical modifier). Thus, in some embodiments the total PIXE impurity content (excluding any intentionally included electrochemical modifier) of all other PIXE elements in the carbon material (as measured by proton induced x-ray emission) is less than 1000 ppm. In other embodiments, the total PIXE impurity content (excluding any intentionally included electrochemical modifier) of all other PIXE elements in the carbon material is less than 800 ppm, less than 500 ppm, less than 300 ppm, less than 200 ppm, less than 150 ppm, less than 100 ppm, less than 50 ppm, less than 25 ppm, less than 10 ppm, less than 5 ppm or less than 1 ppm. 
     In addition to low content of undesired PIXE impurities, the disclosed carbon materials may comprise high total carbon content. In some examples, in addition to carbon, the carbon material may also comprise oxygen, hydrogen, nitrogen and an optional electrochemical modifier. In some embodiments, the material comprises at least 75% carbon, 80% carbon, 85% carbon, at least 90% carbon, at least 95% carbon, at least 96% carbon, at least 97% carbon, at least 98% carbon or at least 99% carbon on a weight/weight basis. In some other embodiments, the carbon material comprises less than 10% oxygen, less than 5% oxygen, less than 3.0% oxygen, less than 2.5% oxygen, less than 1% oxygen or less than 0.5% oxygen on a weight/weight basis. In other embodiments, the carbon material comprises less than 10% hydrogen, less than 5% hydrogen, less than 2.5% hydrogen, less than 1% hydrogen, less than 0.5% hydrogen or less than 0.1% hydrogen on a weight/weight basis. In other embodiments, the carbon material comprises less than 5% nitrogen, less than 2.5% nitrogen, less than 1% nitrogen, less than 0.5% nitrogen, less than 0.25% nitrogen or less than 0.01% nitrogen on a weight/weight basis. The oxygen, hydrogen and nitrogen content of the disclosed carbon materials can be determined by combustion analysis. Techniques for determining elemental composition by combustion analysis are well known in the art. 
     The total ash content of a carbon material may, in some instances, have an effect on the electrochemical performance of a carbon material. Accordingly, in some embodiments, the ash content (excluding any intentionally included electrochemical modifier) of the carbon material ranges from 0.1% to 0.001% weight percent ash, for example in some specific embodiments the ash content (excluding any intentionally included electrochemical modifier) of the carbon material is less than 0.1%, less than 0.08%, less than 0.05%, less than 0.03%, than 0.025%, less than 0.01%, less than 0.0075%, less than 0.005% or less than 0.001%. 
     In other embodiments, the carbon material comprises a total PIXE impurity content of all other elements (excluding any intentionally included electrochemical modifier) of less than 500 ppm and an ash content (excluding any intentionally included electrochemical modifier) of less than 0.08%. In further embodiments, the carbon material comprises a total PIXE impurity content of all other elements (excluding any intentionally included electrochemical modifier) of less than 300 ppm and an ash content (excluding any intentionally included electrochemical modifier) of less than 0.05%. In other further embodiments, the carbon material comprises a total PIXE impurity content of all other elements (excluding any intentionally included electrochemical modifier) of less than 200 ppm and an ash content (excluding any intentionally included electrochemical modifier) of less than 0.05%. In other further embodiments, the carbon material comprises a total PIXE impurity content of all other elements (excluding any intentionally included electrochemical modifier) of less than 200 ppm and an ash content (excluding any intentionally included electrochemical modifier) of less than 0.025%. In other further embodiments, the carbon material comprises a total PIXE impurity content of all other elements (excluding any intentionally included electrochemical modifier) of less than 100 ppm and an ash content (excluding any intentionally included electrochemical modifier) of less than 0.02%. In other further embodiments, the carbon material comprises a total PIXE impurity content of all other elements (excluding any intentionally included electrochemical modifier) of less than 50 ppm and an ash content (excluding any intentionally included electrochemical modifier) of less than 0.01%. 
     The amount of individual PIXE impurities present in the disclosed carbon materials can be determined by proton induced x-ray emission. Individual PIXE impurities may contribute in different ways to the overall electrochemical performance of the disclosed carbon materials. Thus, in some embodiments, the level of sodium present in the carbon material is less than 1000 ppm, less than 500 ppm, less than 100 ppm, less than 50 ppm, less than 10 ppm, or less than 1 ppm. In some embodiments, the level of magnesium present in the carbon material is less than 1000 ppm, less than 100 ppm, less than 50 ppm, less than 10 ppm, or less than 1 ppm. In some embodiments, the level of aluminum present in the carbon material is less than 1000 ppm, less than 100 ppm, less than 50 ppm, less than 10 ppm, or less than 1 ppm. In some embodiments, the level of silicon present in the carbon material is less than 500 ppm, less than 300 ppm, less than 100 ppm, less than 50 ppm, less than 20 ppm, less than 10 ppm or less than 1 ppm. In some embodiments, the level of phosphorous present in the carbon material is less than 1000 ppm, less than 100 ppm, less than 50 ppm, less than 10 ppm, or less than 1 ppm. In some embodiments, the level of sulfur present in the carbon material is less than 1000 ppm, less than 100 ppm, less than 50 ppm, less than 30 ppm, less than 10 ppm, less than 5 ppm or less than 1 ppm. In some embodiments, the level of chlorine present in the carbon material is less than 1000 ppm, less than 100 ppm, less than 50 ppm, less than 10 ppm, or less than 1 ppm. In some embodiments, the level of potassium present in the carbon material is less than 1000 ppm, less than 100 ppm, less than 50 ppm, less than 10 ppm, or less than 1 ppm. In other embodiments, the level of calcium present in the carbon material is less than 100 ppm, less than 50 ppm, less than 20 ppm, less than 10 ppm, less than 5 ppm or less than 1 ppm. In some embodiments, the level of chromium present in the carbon material is less than 1000 ppm, less than 100 ppm, less than 50 ppm, less than 10 ppm, less than 5 ppm, less than 4 ppm, less than 3 ppm, less than 2 ppm or less than 1 ppm. In other embodiments, the level of iron present in the carbon material is less than 50 ppm, less than 20 ppm, less than 10 ppm, less than 5 ppm, less than 4 ppm, less than 3 ppm, less than 2 ppm or less than 1 ppm. In other embodiments, the level of nickel present in the carbon material is less than 20 ppm, less than 10 ppm, less than 5 ppm, less than 4 ppm, less than 3 ppm, less than 2 ppm or less than 1 ppm. In some other embodiments, the level of copper present in the carbon material is less than 140 ppm, less than 100 ppm, less than 40 ppm, less than 20 ppm, less than 10 ppm, less than 5 ppm, less than 4 ppm, less than 3 ppm, less than 2 ppm or less than 1 ppm. In yet other embodiments, the level of zinc present in the carbon material is less than 20 ppm, less than 10 ppm, less than 5 ppm, less than 2 ppm or less than 1 ppm. In yet other embodiments, the sum of all other PIXE impurities (excluding any intentionally included electrochemical modifier) present in the carbon material is less than 1000 ppm, less than 500 pm, less than 300 ppm, less than 200 ppm, less than 100 ppm, less than 50 ppm, less than 25 ppm, less than 10 ppm or less than 1 ppm. As noted above, in some embodiments other impurities such as hydrogen, oxygen and/or nitrogen may be present in levels ranging from less than 10% to less than 0.01%. 
     In some embodiments, the carbon material comprises undesired PIXE impurities near or below the detection limit of the proton induced x-ray emission analysis. For example, in some embodiments the carbon material comprises less than 50 ppm sodium, less than 15 ppm magnesium, less than 10 ppm aluminum, less than 8 ppm silicon, less than 4 ppm phosphorous, less than 3 ppm sulfur, less than 3 ppm chlorine, less than 2 ppm potassium, less than 3 ppm calcium, less than 2 ppm scandium, less than 1 ppm titanium, less than 1 ppm vanadium, less than 0.5 ppm chromium, less than 0.5 ppm manganese, less than 0.5 ppm iron, less than 0.25 ppm cobalt, less than 0.25 ppm nickel, less than 0.25 ppm copper, less than 0.5 ppm zinc, less than 0.5 ppm gallium, less than 0.5 ppm germanium, less than 0.5 ppm arsenic, less than 0.5 ppm selenium, less than 1 ppm bromine, less than 1 ppm rubidium, less than 1.5 ppm strontium, less than 2 ppm yttrium, less than 3 ppm zirconium, less than 2 ppm niobium, less than 4 ppm molybdenum, less than 4 ppm, technetium, less than 7 ppm rubidium, less than 6 ppm rhodium, less than 6 ppm palladium, less than 9 ppm silver, less than 6 ppm cadmium, less than 6 ppm indium, less than 5 ppm tin, less than 6 ppm antimony, less than 6 ppm tellurium, less than 5 ppm iodine, less than 4 ppm cesium, less than 4 ppm barium, less than 3 ppm lanthanum, less than 3 ppm cerium, less than 2 ppm praseodymium, less than 2 ppm, neodymium, less than 1.5 ppm promethium, less than 1 ppm samarium, less than 1 ppm europium, less than 1 ppm gadolinium, less than 1 ppm terbium, less than 1 ppm dysprosium, less than 1 ppm holmium, less than 1 ppm erbium, less than 1 ppm thulium, less than 1 ppm ytterbium, less than 1 ppm lutetium, less than 1 ppm hafnium, less than 1 ppm tantalum, less than 1 ppm tungsten, less than 1.5 ppm rhenium, less than 1 ppm osmium, less than 1 ppm iridium, less than 1 ppm platinum, less than 1 ppm silver, less than 1 ppm mercury, less than 1 ppm thallium, less than 1 ppm lead, less than 1.5 ppm bismuth, less than 2 ppm thorium, or less than 4 ppm uranium. 
     In some embodiments, the carbon material comprises undesired PIXE impurities near or below the detection limit of the proton induced x-ray emission analysis. In some specific embodiments, the carbon material comprises less than 100 ppm sodium, less than 300 ppm silicon, less than 50 ppm sulfur, less than 100 ppm calcium, less than 20 ppm iron, less than 10 ppm nickel, less than 140 ppm copper, less than 5 ppm chromium and less than 5 ppm zinc as measured by proton induced x-ray emission. In other specific embodiments, the carbon material comprises less than 50 ppm sodium, less than 30 ppm sulfur, less than 100 ppm silicon, less than 50 ppm calcium, less than 10 ppm iron, less than 5 ppm nickel, less than 20 ppm copper, less than 2 ppm chromium and less than 2 ppm zinc. 
     In other specific embodiments, the carbon material comprises less than 50 ppm sodium, less than 50 ppm silicon, less than 30 ppm sulfur, less than 10 ppm calcium, less than 2 ppm iron, less than 1 ppm nickel, less than 1 ppm copper, less than 1 ppm chromium and less than 1 ppm zinc. 
     In some other specific embodiments, the carbon material comprises less than 100 ppm sodium, less than 50 ppm magnesium, less than 50 ppm aluminum, less than 10 ppm sulfur, less than 10 ppm chlorine, less than 10 ppm potassium, less than 1 ppm chromium and less than 1 ppm manganese. 
     In another embodiment of the present disclosure, the carbon material is prepared by a method disclosed herein, for example, in some embodiments the carbon material is prepared by a method comprising pyrolyzing a polymer gel as disclosed herein. The carbon materials may also be prepared by pryolyzing a substance such as glucose, chitosan or other naturally occurring macromolecules. The carbon materials can be prepared by any number of methods described in more detail below. 
     Electrochemical modifiers can be incorporated into the carbon materials at various stages of the sol gel process. For example, electrochemical modifiers can be incorporated during the polymerization stage, into the polymer gel or into the pyrolyzed or activated carbon materials. In certain embodiments, the electrochemical modifer is phosphorus. In certain embodiments, the phosphorus can be introduced into the polymer gel in the form of elemental phosphorus, for instance red phosphorus. In certain other embodiments, the phosphorus can be introduced into the polymer gel in the form of phosphoric acid. In certain other embodiments, the phosphorus can be introduced into the polymer gel in the form of a salt, wherein the anion of the salt comprises one or more phosphate, phosphite, phosphide, hydrogen phosphate, dihydrogen phosphate, hexafluorophosphate, hypophosphite, polyphosphate, or pyrophosphate ions, or combinations thereof. In certain other embodiments, the phosphorus can be introduced into the polymer gel in the form of a salt, wherein the cation of the salt comprises one or more phosphonium ions. The non-phophate containing anion or cation pair for any of the above embodiments can be chosen for those known and described in the art. In the context, exemplary cations to pair with phosphate-containing anions include, but are not limited to, ammonium, tetraethylammonium, and tetramethylammonium ions. In the context, exemplary anions to pair with phosphate-containing cations include, but are not limited to, carbonate, dicarbonate, and acetate ions. 
     In certain embodiments, the phosphorus containing polymer gel when heated undergoes an exothermic even between about 100 and 500 C, for example, between 150 and 350 C, for example between 200 and 300 C, for example between 240 C and 260 C. In certain further embodiments, upon further heating under non-oxidizing atmosphere, a pyrolzyed carbon is produced wherein the phosphorus-containing carbon exhibits unprecedented high levels of capacity and first cycle efficiency when the carbon material is incorporated into an electrode of a lithium based energy storage device. 
     In some cases this heating is rate is fast (50° C./hr, 100° C./hr or faster). In other cases this heating is slow (10° C./hr, 5° C./hr, or slower). In other cases the heating is performed in a stepwise fashion with variable rates at different temperatures. Is some cases the dwell time at the reaction temperature is long and in other cases it is short. 
     In certain other embodiments, the phosphorus containing polymer gel does not exhibit an exothermic event upon heating between 200 and 300 C, for example does not exhibit an exothermic event upon heating between 240 and 360 C. In certain other further embodiments, upon further heating under non-oxidizing atmosphere, a pyrolzyed carbon is produced wherein the phosphorus-containing carbon exhibits markedly lower levels of capacity and/or lower first cycle efficiency (as compared to the embodiment described above for the case where the exothermic event was observed for the polymer gel) when the carbon material is incorporated into an electrode of a lithium based energy storage device. 
     Methods for preparation of carbon materials from the polymer materials are described in more detail below. 
     2. Polymer Gels Polymer gels are intermediates in the preparation of the disclosed carbon materials. As such, the physical and chemical properties of the polymer gels contribute to, and are predictive of, the properties of the carbon materials. Polymer gels used for preparation of the carbon materials are included within the scope of certain aspects of the present invention. 
     B. Preparation of Carbon Materials 
     Methods for preparing the carbon materials are not known in the art. For example, methods for preparation of carbon materials are described in U.S. Pat. Nos. 7,723,262 and 8,293,818; and U.S. patent application Ser. Nos. 12/829,282; 13/046,572; 13/250,430; 12/965,709; 13/336,975 and 13/486,731, the full disclosures of which are hereby incorporated by reference in their entireties for all purposes. Accordingly, in one embodiment the present disclosure provides a method for preparing any of the carbon materials or polymer gels described above. The carbon materials may be synthesized through pyrolysis of either a single precursor (such as chitosan) or from a complex resin, formed using a sol-gel method using polymer precursors such as phenol, resorcinol, urea, melamine, etc in water, ethanol, methanol, etc with formaldehyde. The resin may be acid or basic, and possibly contain a catalyst. The pyrolysis temperature and dwell time may be optimized as described below. 
     In some embodiments, the methods comprise preparation of a polymer resin by a sol gel process followed by pyrolysis of the polymer gel. In other embodiments the polymer is formed by a solution state or melt state process. In another embodiment the polymer is formed by a solid state process. In some cases the polymer resin is a high molecular weight polymer. In other cases the polymer gel is a low molecular weight dimmer, trimer or oligomer. The polymer gel may be dried (e.g., freeze dried) prior to pyrolysis; however drying is not required and in some embodiments is not desired. The polymerization process provides significant flexibility such that an electrochemical modifier can be incorporated at any number of steps. In one embodiment, a method for preparing a polymer gel comprising an electrochemical modifier is provided. In another embodiment, methods for preparing pyrolyzed polymer gels are provided. Details of the variable process parameters of the various embodiments of the disclosed methods are described below. 
     1. Preparation of Polymer Resins The polymer resin may be prepared by a sol gel process, condensation process or crosslinking process involving two existing polymers and a crosslinking agent or a single polymer and a crosslinking agent. For example, the polymer gel may be prepared by co-polymerizing one or more polymer precursors in an appropriate solvent. In one embodiment, the one or more polymer precursors are co-polymerized under acidic conditions. In some embodiments, a first polymer precursor is a phenolic compound and a second polymer precursor is an aldehyde compound. In one embodiment, of the method the phenolic compound is phenol, resorcinol, catechol, hydroquinone, phloroglucinol, or a combination thereof; and the aldehyde compound is formaldehyde, acetaldehyde, propionaldehyde, butyraldehyde, benzaldehyde, cinnamaldehyde, or a combination thereof. In a further embodiment, the phenolic compound is resorcinol, phenol or a combination thereof, and the aldehyde compound is formaldehyde. In yet further embodiments, the phenolic compound is resorcinol and the aldehyde compound is formaldehyde. Other polymer precursors include nitrogen containing compounds such as melamine, urea and ammonia. 
     In certain embodiments, an optional electrochemical modifier is incorporated during the above described polymerization process. For example, in some embodiments, an electrochemical modifier in the form of metal particles, metal paste, metal salt, metal oxide or molten metal can be dissolved or suspended into the mixture from which the gel resin is produced. 
     In some embodiments, the metal salt dissolved into the mixture from which the gel resin is produced is soluble in the reaction mixture. In this case, the mixture from which the gel resin is produced may contain an acid and/or alcohol which improves the solubility of the metal salt. The metal-containing polymer gel can be optionally freeze dried, followed by pyrolysis. Alternatively, the metal-containing polymer gel is not freeze dried prior to pyrolysis. 
     The polymerization process is generally performed under catalytic conditions. Reaction conditions may be acidic or basic. Accordingly, in some embodiments, preparing the polymer gel comprises co-polymerizing one or more polymer precursors in the presence of a catalyst. In some embodiments, the catalyst comprises a basic volatile catalyst. For example, in one embodiment, the basic volatile catalyst comprises ammonium carbonate, ammonium bicarbonate, ammonium acetate, ammonium hydroxide, or combinations thereof. In a further embodiment, the basic volatile catalyst is ammonium carbonate. In another further embodiment, the basic volatile catalyst is ammonium acetate. 
     In other cases the co-polymer is further reacted with a crosslinker or an electrochemical modifier, here to referred to as a reactant. In some cases this reactant is an acid and in other cases this reactant is a base. Examples of acids in this context include, but are not limited to aliphatic organic acids such as formic acid, acetic acid, oxalic acid, malonic acid, succinic acid and the like, acids containing nitrogen functionality such as amino acids and the like, hydroxy-containing acids such as lactic acid and the like, unsaturated aliphatic acids such as sorbic acid and the like, aromatic acids and the like, and other acids known in the art. The acid can have one, two, three or more carboxy groups. The acid can be inorganic or organic in nature; in a preferred embodiment, the acid is an organic acid. Examples of bases in this context include, but are not limited to ammonium salts such as ammonium carbonate, ammonium bicarbonate, ammonium hydroxide, ammonium acetate and the like, amino containing compounds such as ammonia, methylamine, ethylamine, dimethylamine, diethylamine, hexamethylenetetramine, phenylamine and the like, imidazoles and the like, and other bases known in the art. The base can be inorganic or organic in nature; in preferred embodiments, the base is organic in nature. 
     In some embodiments this reactant contains phosphorous. In certain other embodiments, the phosphorus is in the form of phosphoric acid. In certain other embodiments, the phosphorus can be in the form of a salt, wherein the anion of the salt comprises one or more phosphate, phosphite, phosphide, hydrogen phosphate, dihydrogen phosphate, hexafluorophosphate, hypophosphite, polyphosphate, or pyrophosphate ions, or combinations thereof. In certain other embodiments, the phosphorus can be in the form of a salt, wherein the cation of the salt comprises one or more phosphonium ions. The non-phophate containing anion or cation pair for any of the above embodiments can be chosen for those known and described in the art. In the context, exemplary cations to pair with phosphate-containing anions include, but are not limited to, ammonium, tetraethylammonium, and tetramethylammonium ions. In the context, exemplary anions to pair with phosphate-containing cations include, but are not limited to, carbonate, dicarbonate, and acetate ions. 
     In some cases the crosslinker is important because of its chemical and electrochemical properties. In other cases the crosslinker is important because it locks in the polymer geometry. In other cases both polymer geometry and chemical composition are important. 
     The crosslinker can react at either low or high temperatures. In some cases a portion of the reaction will occur at low temperatures with the rest of the reaction occurring at higher temperatures. Both extent of crosslinking and reaction kinetics can be measured by a variety of chemical techniques (TGA, FTIR, NMR, XRD, etc.) and physical techniques (indentation, tensile testing, modulus, hardness, etc.). 
     In some cases it will be favorable to have the electrochemical modifier and/or crosslinker evenly distributed throughout the initial co-polymer—a homogenous mixture. In other cases it is important to have an uneven distribution of crosslinker and/or electrochemical modified throughout the initial co-polymer. 
     The molar ratio of catalyst to polymer precursor (e.g., phenolic compound) may have an effect on the final properties of the polymer gel as well as the final properties of the carbon materials. Thus, in some embodiments such catalysts are used in the range of molar ratios of 5:1 to 2000:1 phenolic compound:catalyst. In some embodiments, such catalysts can be used in the range of molar ratios of 10:1 to 400:1 phenolic compound:catalyst. For example in other embodiments, such catalysts can be used in the range of molar ratios of 5:1 to 100:1 phenolic compound:catalyst. For example, in some embodiments the molar ratio of catalyst to phenolic compound is about 400:1. In other embodiments the molar ratio of catalyst to phenolic compound is about 100:1. In other embodiments the molar ratio of catalyst to phenolic compound is about 50:1. In other embodiments the molar ratio of catalyst to phenolic compound is about 10:1. 
     The reaction solvent is another process parameter that may be varied to obtain the desired properties (e.g., surface area, porosity, purity, etc.) of the polymer gels and carbon materials. In some embodiments, the solvent for preparation of the polymer gel is a mixed solvent system of water and a miscible co-solvent. For example, in certain embodiments the solvent comprises a water miscible acid. Examples of water miscible acids include, but are not limited to, propionic acid, acetic acid, and formic acid. In further embodiments, the solvent comprises a ratio of water-miscible acid to water of 99:1, 90:10, 75:25, 50:50, 25:75, 10:90 or 1:90. In other embodiments, acidity is provided by adding a solid acid to the reaction solvent. 
     In some other embodiments of the foregoing, the solvent for preparation of the polymer gel is acidic. For example, in certain embodiments the solvent comprises acetic acid. For example, in one embodiment, the solvent is 100% acetic acid. In other embodiments, a mixed solvent system is provided, wherein one of the solvents is acidic. For example, in one embodiment of the method the solvent is a binary solvent comprising acetic acid and water. In further embodiments, the solvent comprises a ratio of acetic acid to water of 99:1, 90:10, 75:25, 50:50, 25:75, 20:80, 10:90 or 1:90. In other embodiments, acidity is provided by adding a solid acid to the reaction solvent. In other embodiments the solvent is neutral and the acid is a polymer precursor. In other embodiments the polymer is formed under neutral conditions. 
     In some embodiments the polymer precursor is itself a polymer. In these cases the polymer has some additional functionality that can react with itself or with another precursor material. In some embodiments the starting polymer is a novolac and in other embodiments the starting polymer is a resol. In still other embodiments the starting polymer is an acrylate or a styrene rubber or a nylon. In some embodiments the secondary functionality is an acid group. In some cases the acid is an organic acid other cases it is an inorganic acid. In other cases is it an amine or an isocyanate or an epoxide. 
     In some embodiments, an optional electrochemical modifier is incorporated into the polymer gel after the polymerization step, for example either before or after and optional drying and before pyrolyzing polymer gel. In some other embodiments, the polymer gel (either before or after and optional drying and prior to pyrolysis) is impregnated with electrochemical modifier by immersion in a metal salt solution or suspension or particles. In some embodiments, the particle is micronized silicon powder. In other embodiments, the particle is nano silicon powder. In some embodiment, the particle is tin. In still other embodiments, the particle is a combination of silicon, tin, carbon, or any oxides. The metal salt solution or suspension may comprise acids and/or alcohols to improve solubility of the metal salt. In yet another variation, the polymer gel (either before or after an optional drying step) is contacted with a paste comprising the electrochemical modifier. In yet another variation, the polymer gel (either before or after an optional drying step) is contacted with a metal or metal oxide sol comprising the desired electrochemical modifier. 
     In some embodiments of the methods described herein, the molar ratio of phenolic precursor to catalyst is from about 5:1 to about 2000:1 or the molar ratio of phenolic precursor to catalyst is from about 20:1 to about 200:1. In further embodiments, the molar ratio of phenolic precursor to catalyst is from about 25:1 to about 100:1. In further embodiments, the molar ratio of phenolic precursor to catalyst is from about 5:1 to about 10:1. In further embodiments, the molar ratio of phenolic precursor to catalyst is from about 100:1 to about 5:1. 
     In the specific embodiment wherein one of the polymer precursors is resorcinol and another polymer precursor is formaldehyde, the resorcinol to catalyst ratio can be varied to obtain the desired properties of the resultant polymer gel and carbon materials. In some embodiments of the methods described herein, the molar ratio of resorcinol to catalyst is from about 10:1 to about 2000:1 or the molar ratio of resorcinol to catalyst is from about 20:1 to about 200:1. In further embodiments, the molar ratio of resorcinol to catalyst is from about 25:1 to about 100:1. In further embodiments, the molar ratio of resorcinol to catalyst is from about 5:1 to about 10:1. In further embodiments, the molar ratio of resorcinol to catalyst is from about 100:1 to about 5:1. 
     Polymerization to form a polymer gel can be accomplished by various means described in the art and may include addition of an electrochemical modifier. For instance, polymerization can be accomplished by incubating suitable polymer precursor materials, and optionally an electrochemical modifier, in the presence of a suitable catalyst for a sufficient period of time. The time for polymerization can be a period ranging from minutes or hours to days, depending on the temperature (the higher the temperature the faster, the reaction rate, and correspondingly, the shorter the time required). The polymerization temperature can range from room temperature to a temperature approaching (but lower than) the boiling point of the starting solution. For example, in some embodiments the polymer gel is aged at temperatures from about 20° C. to about 120° C., for example about 20° C. to about 100° C. Other embodiments include temperature ranging from about 30° C. to about 90° C., for example about 45° C. or about 85° C. In other embodiments, the temperature ranges from about 65° C. to about 80° C., while other embodiments include aging at two or more temperatures, for example about 45° C. and about 75-85° C. or about 110-140° C. 
     In some embodiments the starting polymer precursors are processed in a solution. In other embodiments the polymer precursors are processed in a melt or solid state. In some cases the polymer precursor is a small molecule. In other cases the polymer precursor is a medium molecular weight oligomer or a high molecular weight polymer. In some cases the polymer precursor materials are similar in molecular weight. In other cases the polymer precursor materials are different in molecular weight. 
     The structure of the polymer precursors is not particularly limited, provided that the polymer precursor is capable of reacting with another polymer precursor or with a second polymer precursor to form a polymer. Exemplary polymer precursors include amine-containing compounds, alcohol-containing compounds and carbonyl-containing compounds, for example in some embodiments the polymer precursors are selected from an alcohol, a phenol, a polyalcohol, a sugar, an alkyl amine, an aromatic amine, an aldehyde, a ketone, a carboxylic acid, an ester, a urea, an acid halide and an isocyanate. 
     The polymer precursor materials as disclosed herein include (a) alcohols, phenolic compounds, and other mono- or polyhydroxy compounds and (b) aldehydes, ketones, and combinations thereof. Representative alcohols in this context include straight chain and branched, saturated and unsaturated alcohols. Suitable phenolic compounds include polyhydroxy benzene, such as a dihydroxy or trihydroxy benzene. Representative polyhydroxy benzenes include resorcinol (i.e., 1,3-dihydroxy benzene), catechol, hydroquinone, and phloroglucinol. Mixtures of two or more polyhydroxy benzenes can also be used. Phenol (monohydroxy benzene) can also be used. Representative polyhydroxy compounds include sugars, such as glucose, and other polyols, such as mannitol. Aldehydes in this context include: straight chain saturated aldeydes such as methanal (formaldehyde), ethanal (acetaldehyde), propanal (propionaldehyde), butanal (butyraldehyde), and the like; straight chain unsaturated aldehydes such as ethenone and other ketenes, 2-propenal (acrylaldehyde), 2-butenal (crotonaldehyde), 3 butenal, and the like; branched saturated and unsaturated aldehydes; and aromatic-type aldehydes such as benzaldehyde, salicylaldehyde, hydrocinnamaldehyde, and the like. Suitable ketones include: straight chain saturated ketones such as propanone and 2 butanone, and the like; straight chain unsaturated ketones such as propenone, 2 butenone, and 3-butenone (methyl vinyl ketone) and the like; branched saturated and unsaturated ketones; and aromatic-type ketones such as methyl benzyl ketone (phenylacetone), ethyl benzyl ketone, and the like. The polymer precursor materials can also be combinations of the precursors described above. 
     In some embodiments, one polymer precursor is an alcohol-containing species and another polymer precursor is a carbonyl-containing species. The relative amounts of alcohol-containing species (e.g., alcohols, phenolic compounds and mono- or poly-hydroxy compounds or combinations thereof) reacted with the carbonyl containing species (e.g. aldehydes, ketones or combinations thereof) can vary substantially. In some embodiments, the ratio of alcohol-containing species to aldehyde species is selected so that the total moles of reactive alcohol groups in the alcohol-containing species is approximately the same as the total moles of reactive carbonyl groups in the aldehyde species. Similarly, the ratio of alcohol-containing species to ketone species may be selected so that the total moles of reactive alcohol groups in the alcohol containing species is approximately the same as the total moles of reactive carbonyl groups in the ketone species. The same general 1:1 molar ratio holds true when the carbonyl-containing species comprises a combination of an aldehyde species and a ketone species. 
     In other embodiments, the polymer precursor is a urea or an amine containing compound. For example, in some embodiments the polymer precursor is urea or melamine. Other embodiments include polymer precursors selected from isocyanates or other activated carbonyl compounds such as acid halides and the like. 
     The total solids content in the solution or suspension prior to polymer gel formation can be varied. The weight ratio of resorcinol to water is from about 0.05 to 1 to about 0.70 to 1. Alternatively, the ratio of resorcinol to water is from about 0.15 to 1 to about 0.6 to 1. Alternatively, the ratio of resorcinol to water is from about 0.15 to 1 to about 0.35 to 1. Alternatively, the ratio of resorcinol to water is from about 0.25 to 1 to about 0.5 to 1. Alternatively, the ratio of resorcinol to water is from about 0.3 to 1 to about 0.35 to 0.6. 
     Examples of solvents useful in the preparation of the polymer gels disclosed herein include but are not limited to water or alcohols such as, for example, ethanol, t butanol, methanol or combinations thereof as well as aqueous mixtures of the same. Such solvents are useful for dissolution of the polymer precursor materials, for example dissolution of the phenolic compound. In addition, in some processes such solvents are employed for solvent exchange in the polymer gel (prior to freezing and drying), wherein the solvent from the polymerization of the precursors, for example, resorcinol and formaldehyde, is exchanged for a pure alcohol. In one embodiment of the present application, a polymer gel is prepared by a process that does not include solvent exchange. In some embodiments no solvent is used for in the synthesis of the polymer gel. 
     Suitable catalysts in the preparation of the polymer gels include volatile basic catalysts that facilitate polymerization of the precursor materials into a monolithic polymer. The catalyst can also comprise various combinations of the catalysts described above. In embodiments comprising phenolic compounds, such catalysts can be used in the range of molar ratios of 5:1 to 200:1 phenolic compound:catalyst. For example, in some specific embodiments such catalysts can be used in the range of molar ratios of 5:1 to 10:1 phenolic compound:catalyst. 
     Accordingly, in some embodiments, the invention provides a method for preparing a condensation polymer gel, the method comprising; 
     a) forming crosslinked polymer gel particles having a volume average particle size ranging from 0.01 to 25 mm from an epoxy containing phenolic-aldehyde in an optional solvent system; and 
     b) crosslinking the polymer gel particles with a dopant phosphorous containing compound under conditions sufficient to associate at least 1% by mass of the dry weight of the co-polymer of the dopant phosphorous containing compound to bind covalently with the co-polymer gel. 
     In some embodiments, the volume average particle size ranges from 1 to 25 mm. In other embodiments, the volume average particle size ranges from 10 to 1000 um. 
     In some embodiments, the aldehyde is formaldehyde, the phenolic compound is phenol, resorcinol, or combination thereof, and the optional solvent comprises water and acetic acid. In some embodiments, the method further includes use of a volatile basic salt catalyst, for example the catalyst may be selected from ammonium carbonate, ammonium bicarbonate, ammonium acetate, and ammonium hydroxide, and a combination thereof. In some embodiments, the dopant phosphorous containing compound is phosphoric acid or a phosphoric acid-containing compound. 
     In different embodiments, the invention provides a method for preparing a condensation polymer gel, the method comprising; 
     a) forming crosslinked polymer gel particles having a volume average particle size ranging from 0.01 to 25 mm from an epoxy containing phenolic-aldehyde in an optional solvent system; and 
     b) crosslinking the polymer gel particles with a dopant nitrogen containing compound under conditions sufficient to associate at least 1% by mass of the dry weight of the co-polymer of the dopant nitrogen containing compound to bind covalently with the co-polymer gel. 
     In some embodiments, the volume average particle size ranges from 1 to 25 mm. In other embodiments, the volume average particle size ranges from 10 to 1000 um. 
     In some embodiments, the aldehyde is formaldehyde, the phenolic compound is phenol, resorcinol, or combination thereof, and the optional solvent comprises water and acetic acid. In some embodiments, the method further includes use of a volatile basic salt catalyst, for example the catalyst may be selected from ammonium carbonate, ammonium bicarbonate, ammonium acetate, and ammonium hydroxide, and a combination thereof. In some embodiments, the dopant nitrogen-containing compound is urea, melamine, ammonia, or combination thereof 
     2. Creation of Polymer Gel Particles 
     A monolithic polymer gel can be physically disrupted to create smaller particles according to various techniques known in the art. The resultant polymer gel particles generally have an average diameter of less than about 30 mm, for example, in the size range of about 1 mm to about 25 mm, or between about 1 mm to about 5 mm or between about 0.5 mm to about 10 mm. Alternatively, the size of the polymer gel particles can be in the range below about 1 mm, for example, in the size range of about 10 to 1000 microns. Techniques for creating polymer gel particles from monolithic material include manual or machine disruption methods, such as sieving, grinding, milling, or combinations thereof. Such methods are well-known to those of skill in the art. Various types of mills can be employed in this context such as roller, bead, and ball mills and rotary crushers and similar particle creation equipment known in the art. Include extruders, mixers, etc. 
     In other embodiments, the polymer gel particles are in the range of 0.1 microns to 2.5 cm, from about 0.1 microns to about 1 cm, from about 1 micron to about 1000 microns, from about 1 micron to about 100 microns, from about 1 micron to about 50 microns, from about 1 micron to about 25 microns or from about 1 microns to about 10 microns. In other embodiments, the polymer gel particles are in the range of about 1 mm to about 100 mm, from about 1 mm to about 50 mm, from about 1 mm to about 25 mm or from about 1 mm to about 10 mm. 
     In an embodiment, a roller mill is employed. A roller mill has three stages to gradually reduce the size of the gel particles. The polymer gels are generally very brittle and are not damp to the touch. Consequently they are easily milled using this approach; however, the width of each stage must be set appropriately to achieve the targeted final mesh. This adjustment is made and validated for each combination of gel recipe and mesh size. Each gel is milled via passage through a sieve of known mesh size. Sieved particles can be temporarily stored in sealed containers. 
     In one embodiment, a rotary crusher is employed. The rotary crusher has a screen mesh size of about ⅛ th  inch. In another embodiment, the rotary crusher has a screen mesh size of about ⅜ th  inch. In another embodiment, the rotary crusher has a screen mesh size of about ⅝ th  inch. In another embodiment, the rotary crusher has a screen mesh size of about ⅜ th  inch. 
     Milling can be accomplished at room temperature according to methods well known to those of skill in the art. Alternatively, milling can be accomplished cryogenically, for example by co-milling the polymer gel with solid carbon dioxide (dry ice) particles. 
     3. Soaking or Treatment of Polymer Gels 
     The polymer gels described above, can be further soaked or treated for the inclusion of an optional electrochemical modifier. The inclusion of the electrochemical modifier may change both the electrochemical properties of the final product when used in a lithium battery and/or change the physical/chemical properties of the material. 
     In some embodiments, the optional electrochemical modifier is added through a liquid phase soaking or solvent exchange. The solvent used may be the same or different than that used in the polymer gel process. Generally, for soaking, wet polymer gels are weighed and placed into a larger container. A solution containing a solvent and a precursor for electrochemical modification is combined with the wet polymer gel to form a mixture. The mixture is left to soak at a set stir rate, temperature and time. Upon completion, the excess solvent is decanted from the mixture. In other embodiments, the optional electrochemical modifier is added through a vapor phase. 
     In some embodiments, the precursor may be soluble in the solvent. For precursors that are soluble in the chosen solvent, in some embodiments, the solution may be unsaturated, saturated, or super saturated. In other embodiments, the precursor may be insoluble and therefore suspended in the solvent. 
     In some embodiments, the soak temperature ranges from 20 to 30° C. In other embodiments, the soak temperature ranges from 30 to 40° C. In yet other embodiments, the soak temperature ranges from 40 to 50° C. In yet other embodiments, the soak temperature ranges from 50 to 60° C. In yet other embodiments, the soak temperature ranges from 60 to 70° C. In yet other embodiments, the soak temperature ranges from 70 to 80° C. In yet other embodiments, the soak temperature ranges from 80 to 100° C. 
     In some embodiments, the soak time (the period of time between the combination of the wet polymer gel and the solution and the decanting of the excess liquid) is from about 0 hours to about 5 hours. In other embodiments, the soak time ranges from about 10 minutes to about 120 minutes, between about 30 minute and 90 minutes, and between about 40 minutes and 60 minutes. In yet other embodiments, the soak time is between about from about 0 hours to about 10 hours, from about 0 hours to about 20 hours, from about 10 hours to about 100 hours, from about 10 hours to about 15 hours, or from about 5 hours to about 10 hours. 
     In some embodiments, the stir rate is between 0 and 10 rpm. In other embodiments, the stir rate is between 10 and 15 rpm, between 15 and 20 rpm, between 20 and 30 rpm, between 30 and 50 rpm, between 50 and 100 rpm, between 100 and 200 rpm, between 200 and 1000 rpm, or greater than 1000 rpm. In yet other embodiments, the mixture undergoes no artificial agitation. 
     The optional electrochemical modifier may fall into one or more than one of the chemical classifications listed in Table 1. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Exemplary Electrochemical Modifiers 
               
            
           
           
               
               
               
            
               
                   
                 Chemical Classification 
                 Example Precursor Materials 
               
               
                   
                   
               
               
                   
                 Group 13 
                 Moieties comprising B, Al, 
               
               
                   
                   
                 Ga, In, and/or Tl 
               
               
                   
                 Group 14 
                 Moieties comprising Si, Ge, 
               
               
                   
                   
                 Sn, and/or Pb 
               
               
                   
                 Group 15 
                 Moieties comprising N, P, 
               
               
                   
                   
                 As, and/or Sb 
               
               
                   
                 Group 16 
                 Moieties comprising O, S, 
               
               
                   
                   
                 and/or Se 
               
               
                   
                 Saccharides 
                 Chitin 
               
               
                   
                   
                 Chitosan 
               
               
                   
                   
                 Glucose 
               
               
                   
                   
                 Sucrose 
               
               
                   
                   
                 Fructose 
               
               
                   
                   
                 Cellulose 
               
               
                   
                 Biopolymers 
                 Lignin 
               
               
                   
                 Proteins 
                 Gelatin 
               
               
                   
                 Amines and Ureas 
                 Urea 
               
               
                   
                   
                 Melamine 
               
               
                   
                 Halogen Salts 
                 LiBr 
               
               
                   
                   
                 NaCl 
               
               
                   
                   
                 KF 
               
               
                   
                 Nitrate Salts 
                 NaNO 3   
               
               
                   
                   
                 LiNO 3   
               
               
                   
                 Carbides 
                 SiC 
               
               
                   
                   
                 CaC 2   
               
               
                   
                 Metal Containing Compounds 
                 Aluminum isoproproxide 
               
               
                   
                   
                 Manganese Acetate 
               
               
                   
                   
                 Nickel Acetate 
               
               
                   
                   
                 Iron Acetate 
               
               
                   
                 Hydrocarbons 
                 Propane 
               
               
                   
                   
                 Butane 
               
               
                   
                   
                 Ethylene 
               
               
                   
                   
                 Cyclohexane 
               
               
                   
                   
                 Methane 
               
               
                   
                   
                 Benzene 
               
               
                   
                   
                 Ethane 
               
               
                   
                   
                 Hexane 
               
               
                   
                   
                 Octane 
               
               
                   
                   
                 Pentane 
               
               
                   
                 Alcohols 
                 Isopropanol 
               
               
                   
                   
                 Ethanol 
               
               
                   
                   
                 Methanol 
               
               
                   
                   
                 Butanol 
               
               
                   
                   
                 Ethylene Glycol 
               
               
                   
                   
                 Xylitol 
               
               
                   
                   
                 Menthol 
               
               
                   
                 Phosphorous containing 
                 H 3 PO 
               
               
                   
                 compounds 
                 NH 4 H 2 PO 3   
               
               
                   
                   
                 Na 3 PO 3   
               
               
                   
                   
                 and other examples 
               
               
                   
                   
                 described herein 
               
               
                   
                 Ketones 
                 Acetone 
               
               
                   
                   
                 Ethyl Methyl Ketone 
               
               
                   
                   
                 Acetophenone 
               
               
                   
                   
                 Muscone 
               
               
                   
                   
               
            
           
         
       
     
     4. Pyrolysis of Polymer Gels 
     The polymer gels described above, can be further processed to obtain the desired carbon materials. Such processing includes, for example, pyrolysis. Generally, in the pyrolysis process, wet polymer gels are weighed and placed in a rotary kiln. Pyrolysis may also occur in a stationary kiln such as a tube furnace or a hearth kiln. The temperature ramp, the dwell time and dwell temperature are set according to the needs of the material and the limitations of the equipment; cool down is determined by the natural cooling rate of the furnace. The entire process is usually run under an inert atmosphere, such as a nitrogen environment. However, in certain embodiments, the gas may be a hydrocarbon listed in table 1, such as methane, or ammonia or could be steam. Pyrolyzed samples are then removed and weighed. Other pyrolysis processes are well known to those of skill in the art. 
     In some embodiments, an optional electrochemical modifier is incorporated into the carbon material after pyrolysis of the polymer gel. For example, the electrochemical modifier can be incorporated into the pyrolyzed polymer gel by contacting the pyrolyzed polymer gel with the electrochemical modifier, for example, colloidal metal, molten metal, metal salt, metal paste, metal oxide or other sources of metals. 
     In some embodiments, pyrolysis dwell time (the period of time during which the sample is at the desired temperature) is from about 0 minutes to about 180 minutes, from about 10 minutes to about 120 minutes, from about 30 minutes to about 100 minutes, from about 40 minutes to about 80 minutes, from about 45 to 70 minutes or from about 50 to 70 minutes. 
     Pyrolysis may also be carried out more slowly than described above. For example, in one embodiment the pyrolysis is carried out in about 120 to 480 minutes. In other embodiments, the pyrolysis is carried out in about 120 to 240 minutes. In other embodiments pyrolysis is carried out in about 5 to 24 hours or from 5 to 48 hours. Pyrolysis may also be carried out with varying ramp rates. In some cases the ramp between two temperatures may be fast (20-50° C./min) in other cases the ramp rate might be slow (&lt;20° C.) a minute. Dwell times from 1-4 h may happen throughout the pyrolysis. 
     In some embodiments, pyrolysis dwell temperature ranges from about 500° C. to 2400° C. In some embodiments, pyrolysis dwell temperature ranges from about 650° C. to 1800° C. In other embodiments pyrolysis dwell temperature ranges from about 700° C. to about 1200° C. In other embodiments pyrolysis dwell temperature ranges from about 850° C. to about 1050° C. In other embodiments pyrolysis dwell temperature ranges from about 1000° C. to about 1200° C. 
     In some embodiments, the pyrolysis dwell temperature is varied during the course of pyrolysis. In one embodiment, the pyrolysis is carried out in a rotary kiln with separate, distinct heating zones. The temperature for each zone is sequentially decreased from the entrance to the exit end of the rotary kiln tube. In one embodiment, the pyrolysis is carried out in a rotary kiln with separate distinct heating zones, and the temperature for each zone is sequentially increased from entrance to exit end of the rotary kiln tube. 
     In yet other embodiments, the surface of the hard carbon may be modified during pyrolysis due to the thermal breakdown of solid, liquid or gas precursors. Theses precursors may include any of the chemicals listed in Table 1. In one embodiment the precursors may be introduced prior to pyrolysis under room temperature conditions. In a second embodiment, the precursors may be introduced while the material is at an elevated temperature during pyrolysis. In a third embodiment, the precursors may be introduced post-pyrolysis. Multiple precursors or a mixture of precursors for chemical and structural modification may also be used. 
     The carbon may also undergo an additional heat treatment step to help change the surface functionality. In some embodiments, heat treatment dwell temperature ranges from about 500° C. to 2400° C. In some embodiments, heat treatment dwell temperature ranges from about 650° C. to 1800° C. In other embodiments heat treatment dwell temperature ranges from about 700° C. to about 1200° C. In other embodiments heat treatment dwell temperature ranges from about 850° C. to about 1050° C. In other embodiments heat treatment dwell temperature ranges from about 1000° C. to about 1200° C. In other embodiments heat treatment dwell temperature ranges from about 800° C. to about 1100° C. 
     In some embodiments, heat treatment dwell time (the period of time during which the sample is at the desired temperature) is from about 0 minutes to about 300 minutes, from about 10 minutes to about 180 minutes, from about 10 minutes to about 120 minutes, from about 30 minutes to about 100 minutes, from about 40 minutes to about 80 minutes, from about 45 to 70 minutes or from about 50 to 70 minutes. 
     Pyrolysis may also be carried out more slowly than described above. For example, in one embodiment the pyrolysis is carried out in about 120 to 480 minutes. In other embodiments, the pyrolysis is carried out in about 120 to 240 minutes. 
     In one embodiment the carbon may also undergo a heat treatment under a volatile gas, such as a hydrocarbon listed in Table 1. Wishing not to be bound by theory, the hydrocarbon or volatile gas may decompose or react on the surface of the carbon when exposed to elevated temperatures. The volatile may leave behind a thin layer, such as a soft carbon, covering the surface of the hard carbon. 
     In one embodiment the gas may be piped in directly from a compressed tank. In another embodiment the gas may originate through the heating of a liquid and the mixing of an inert carrier gas using a bubbler technique commonly known in the art. In another embodiment, as solid or liquid may be placed upstream of the sample and decompose into a volatile gas, which then reacts with the carbon in the hot zone. 
     In one embodiment the vapor deposition may be completed under a static gas environment. In another embodiment the vapor deposition may be completed in a dynamic, gas flowing environment but wherein the carbon is static. In yet another embodiment, the vapor deposition may be completed under continuous coating, wherein the gas and the carbon are flowing through a hot zone. In still yet another embodiment the vapor deposition may be completed under continuous coating, wherein the gas and the carbon are flowing through a hot zone, but where the gas is flowing counter current to the solid carbon. In another embodiment the carbon is coated by chemical vapor deposition while rotating in a rotatory kiln. 
     The carbon may also undergo a vapor deposition through the heating of a volatile gas at different temperatures. In some embodiments vapor deposition temperature ranges from about 500° C. to 2400° C. In some embodiments, heat treatment dwell temperature ranges from about 650° C. to 1800° C. In other embodiments heat treatment dwell temperature ranges from about 700° C. to about 1000° C. In other embodiments heat treatment dwell temperature ranges from about 800° C. to about 900° C. In other embodiments heat treatment dwell temperature ranges from about 1000° C. to about 1200° C. In other embodiments heat treatment dwell temperature ranges from about 900° C. to about 1100° C., from about 950° C. to about 1050° C. or about 1000° C. 
     The carbon may also undergo a vapor deposition through the heating of a volatile gas for different dwell times. In some embodiments, vapor deposition dwell time (the period of time during which the sample is at the desired temperature) is from about 0 minutes to about 5 hours, from about 10 minutes to about 180 minutes, from about 10 minutes to about 120 minutes, from about 30 minutes to about 100 minutes, from about 40 minutes to about 80 minutes, from about 45 to 70 minutes or from about 50 to 70 minutes. 
     The thickness of the layer of carbon deposited by vapor deposition of hydrocarbon decomposition can be measured by HRTEM. In one embodiment the thickness of the layer is less than 0.1 nm, less than 0.5 nm, less than 1 nm, or less than 2 nm. In other embodiments the thickness of the carbon layer deposited by vapor deposition of hydrocarbon decomposition measured by HRTEM is between 1 nm and 100 nm. In yet other embodiments the thickness of the carbon layer deposited by vapor deposition of hydrocarbon decomposition measured by HRTEM is between 0.1 nm and 50 nm. In still other embodiments the thickness of the carbon layer deposited by vapor deposition of hydrocarbon decomposition measured by HRTEM is between 1 nm and 50 nm. In still other embodiments the thickness of the carbon layer deposited by vapor deposition of hydrocarbon decomposition measured by HRTEM is between 2 nm and 50 nm, for example between about 10 nm and 25 nm. 
     5. One-Step Polymerization/Pyrolysis Procedure 
     A carbon material may also be synthesized through a one-step polymerization/pyrolysis method. In general, the polymer is formed during the pyrolysis temperature ramp. The precursors are placed into a rotary kiln with an inert nitrogen atmosphere. The precursors will undergo polymerization within the kiln during the temperature ramp. In other embodiments, the precursors and placed in a sagger or other equivalent high-temperature resistant vessel and heated in a stationary kiln, for example an elevator kiln or other kiln described and known in the art. There may or may not be an intermediate dwell time to allow for complete polymerization. After polymerization is complete, the temperature is once again increased, where the polymer undergoes pyrolysis as previously described. 
     In some embodiments the precursors comprise a saccharide, protein, or a biopolymer. Examples of saccharides include, but are not limited to, sucrose, glucose, fructose, chitin, chitosan, and lignin. A non-limiting example of a protein is animal derived gelatin. In certain embodiments, the precursor is comprised of an organic acid. Examples of organic acids in this context include, but are not limited to, oxalic acid, citric acid, mucic acid, and succinic acid. In other embodiments the precursor comprises a multifunctional phenolic molecule. Examples of phenolic molecules in this context include, but are not limited to, phenol, resorcinol, phloroglucinol, bisphenol A, bisphenol F, 2,2′-bipehnol, 4-4′-biphenol, 1-naphthol, and 2-napththol, or combinations thereof, In certain embodiments, the precursor comprises a crosslinking agent. Examples of crosslinking agents in this context include, but are not limited to, formaldehyde, hexamethylenetetramine, or combinations thereof. 
     In other embodiments, the precursors may be partially polymerized prior to insertion into the kiln. In yet other embodiments, the precursors are not fully polymerized before pyrolysis is initiated. 
     The intermediate dwell time may vary. In one embodiment, no intermediate dwell time exists. In another embodiment, the dwell time ranges from about 0 to about 10 hrs. In yet another embodiment, the dwell time ranges from about 0 to about 5 hrs. In yet other embodiments, the dwell time ranges from about 0 to about 1 hour. 
     The intermediate dwell temperature may also vary. In some embodiments, the intermediate dwell temperature ranges from about 100 to about 600° C., from about 150 to about 500° C., or from about 350 to about 450° C. In other embodiments, the dwell temperature is greater than about 600° C. In yet other embodiments, the intermediate dwell temperature is below about 100° C. 
     The material will undergo pyrolysis to form carbon, as previously described. In some embodiments, pyrolysis dwell time (the period of time during which the sample is at the desired temperature) is from about 0 minutes to about 180 minutes, from about 10 minutes to about 120 minutes, from about 30 minutes to about 100 minutes, from about 40 minutes to about 80 minutes, from about 45 to 70 minutes or from about 50 to 70 minutes. 
     Pyrolysis may also be carried out more slowly than described above. For example, in one embodiment the pyrolysis is carried out in about 120 to 480 minutes. In other embodiments, the pyrolysis is carried out in about 120 to 240 minutes. 
     In some embodiments, pyrolysis dwell temperature ranges from about 500° C. to 2400° C. In some embodiments, pyrolysis dwell temperature ranges from about 650° C. to 1800° C. In other embodiments pyrolysis dwell temperature ranges from about 700° C. to about 1200° C. In other embodiments pyrolysis dwell temperature ranges from about 850° C. to about 1050° C. In other embodiments pyrolysis dwell temperature ranges from about 1000° C. to about 1200° C. 
     After pyrolysis the surface area of the carbon as measured by nitrogen sorption may vary between 0 and 500 m 2 /g, 0 and 250 m 2 /g, 5 and 100 m 2 /g, 5 and 50 m 2 /g. In other embodiments, the surface area of the carbon as measured by nitrogen sorption may vary between 250 and 500 m 2 /g, 300 and 400 m 2 /g, 300 and 350 m 2 /g, 350 and 400 m 2 /g. 
     In some embodiments, the invention provides a carbon material prepared by a process comprising:
         1) polymerizing one or more polymer precursors to obtain a polymer gel; and   2) pyrolyzing the polymer gel to obtain the carbon material,       

     wherein a nitrogen containing substance is contacted with the polymer gel during polymerization of the one or more polymer precursors, the nitrogen containing substance is contacted with the polymer gel after polymerization of the polymer gel, the nitrogen containing compound is contacted with the carbon material or polymer gel during pyrolysis or the nitrogen containing compound is contacted with the carbon material after pyrolysis or combinations thereof. 
     In other embodiments, the invention provides a carbon material prepared by a process comprising:
         1) polymerizing one or more polymer precursors to obtain a polymer gel; and   2) pyrolyzing the polymer gel to obtain the carbon material,       

     wherein a phosphorous containing substance is contacted with the polymer gel during polymerization of the one or more polymer precursors, the phosphorous containing substance is contacted with the polymer gel after polymerization of the polymer gel, the phosphorous containing compound is contacted with the carbon material or polymer gel during pyrolysis or the phosphorous containing compound is contacted with the carbon material after pyrolysis or combinations thereof. 
     C. Characterization of Polymer Gels and Carbon Materials 
     The structural properties of the final carbon material and intermediate polymer gels may be measured using Nitrogen sorption at 77K, a method known to those of skill in the art. The final performance and characteristics of the finished carbon material is important, but the intermediate products (both dried polymer gel and pyrolyzed, but not activated, polymer gel), can also be evaluated, particularly from a quality control standpoint, as known to those of skill in the art. The Micromeretics ASAP 2020 is used to perform detailed micropore and mesopore analysis, which reveals a pore size distribution from 0.35 nm to 50 nm in some embodiments. The system produces a nitrogen isotherm starting at a pressure of 10 −7  atm, which enables high resolution pore size distributions in the sub 1 nm range. The software generated reports utilize a Density Functional Theory (DFT) method to calculate properties such as pore size distributions, surface area distributions, total surface area, total pore volume, and pore volume within certain pore size ranges. 
     The impurity and optional electrochemical modifier content of the carbon materials can be determined by any number of analytical techniques known to those of skill in the art. One particular analytical method useful within the context of the present disclosure is proton induced x-ray emission (PIXE). This technique is capable of measuring the concentration of elements having atomic numbers ranging from 11 to 92 at low ppm levels. Accordingly, in one embodiment the concentration of electrochemical modifier, as well as all other elements, present in the carbon materials is determined by PIXE analysis. 
     D. Devices Comprising the Carbon Materials 
     The disclosed carbon materials can be used as electrode material in any number of electrical energy storage and distribution devices. For example, in one embodiment the present disclosure provides a lithium-based electrical energy storage device comprising an electrode prepared from the disclosed carbon materials. Such lithium based devices are superior to previous devices in a number of respects including gravimetric and volumetric capacity and first cycle efficiency. Electrodes comprising the disclosed carbon materials are also provided. 
     Accordingly, in one embodiment, the present disclosure provides an electrical energy storage device comprising: 
     a) at least one anode comprising a hard carbon material; 
     b) at least cathode comprising a metal oxide; and 
     c) an electrolyte comprising lithium ions; 
     wherein the electrical energy storage device has a first cycle efficiency of at least 50% and a reversible capacity of at least 200 mAh/g with respect to the mass of the hard carbon material. In other embodiments, the efficiency is measured at a current density of about 100 mA/g with respect to the mass of the active hard carbon material in the anode. In still other embodiments, the efficiency is measured at a current density of about 1000 mA/g with respect to the mass of the active hard carbon material in the anode. 
     In some embodiments, the capacity of the carbon materials decreases less than 20% as the current density is increased 40-fold. In certain embodiments, the capacity exhibits less than 15% decrease as the current density is increased 40-fold. In certain embodiments, the capacity exhibits 10% decrease as the current density is increased 40-fold. 
     In certain embodiments, the capacity of carbon materials decreases less than 15% as the current density is increased 30-fold. In certain embodiments, the capacity exhibits less than 10% decrease as the current density is increased 30-fold. In certain embodiments, the capacity exhibits less than 5% decrease as the current density is increased 30-fold. 
     In certain embodiments, the capacity of carbon materials decreases less than 10% as the current density is increased 20-fold. In certain embodiments, the capacity exhibits less than 5% decrease as the current density is increased 20-fold. In certain embodiments, the capacity exhibits less than 2% decrease as the current density is increased 20-fold. 
     In certain embodiments, the capacity of carbon materials decreases less than 5% as the current density is increased 10-fold. In certain embodiments, the capacity exhibits less than 1% decrease as the current density is increased 10-fold. In certain embodiments, the capacity exhibits no decrease as the current density is increased 10-fold. In certain embodiments, the capacity exhibits 0-2% increase as the current density is increased 10-fold. 
     In certain embodiments, the capacity of carbon materials decreases less than 5% as the current density is increased 5-fold. In certain embodiments, the capacity exhibits less than 1% decrease as the current density is increased 5-fold. In certain embodiments, the capacity exhibits no decrease as the current density is increased 5-fold. In certain embodiments, the capacity exhibits 0-5% increase as the current density is increased 5-fold. 
     In certain embodiments, the capacity of carbon materials decreases less than 3% as the current density is increased 2-fold. In certain embodiments, the capacity exhibits less than 1% decrease as the current density is increased 2-fold. In certain embodiments, the capacity exhibits no decrease as the current density is increased 2-fold. In certain embodiments, the capacity exhibits 0-7% increase as the current density is increased 2-fold. 
     It is understood that the decrease or increase in capacitance described herein (e.g., above) is relative to the capacitance measured at the initial current density. For example, if the initial current density is X and the capacitance at this current density is Y, then the decrease or increase in capacitance when the current density is increased 5-fold is the difference (typically expressed in percent) between Y and the capacitance at a current density of 5×. Other differences in capacitance are determined in an analogous manner. One skilled in the art will recognize means for testing the capacitance of the carbon materials at different current densities. Exemplary means for testing are provided herein. 
     In some embodiments the properties of the device are tested electrochemically between upper and lower voltages of 3V and −20 mV, respectively. In other embodiments the lower cut-off voltage is between 50 mV and −20 mV, between 0V and −15 mV, or between 10 mV and 0V. Alternatively, the device is tested at a current density of 40 mA/g with respect to the mass of carbon material. 
     The hard carbon material may be any of the hard carbon materials described herein. In other embodiments, the first cycle efficiency is greater than 55%. In some other embodiments, the first cycle efficiency is greater than 60%. In yet other embodiments, the first cycle efficiency is greater than 65%. In still other embodiments, the first cycle efficiency is greater than 70%. In other embodiments, the first cycle efficiency is greater than 75%, and in other embodiments, the first cycle efficiency is greater than 80%, greater than 90%, greater than 95%, greater than 98%, or greater than 99%. In some embodiments of the foregoing, the hard carbon material comprises a surface area of less than about 300 m 2 /g. In other embodiments, the hard carbon material comprises a pore volume of less than about 0.1 cc/g. In still other embodiments of the foregoing, the hard carbon material comprises a surface area of less than about 300 m 2 /g and a pore volume of less than about 0.1 cc/g. 
     In another embodiment of the foregoing electrical energy storage device, the electrical energy storage device has a volumetric capacity (i.e., reversible capacity) of at least 400 mAh/cc. In other embodiments, the volumetric capacity is at least 450 mAh/cc. In some other embodiments, the volumetric capacity is at least 500 mAh/cc. In yet other embodiments, the volumetric capacity is at least 550 mAh/cc. In still other embodiments, the volumetric capacity is at least 600 mAh/cc. In other embodiments, the volumetric capacity is at least 650 mAh/cc, and in other embodiments, the volumetric capacity is at least 700 mAh/cc. 
     In another embodiment the device, the device has a gravimetric capacity (i.e., reversible capacity, based on mass of hard carbon) of at least 150 mAh/g. In other embodiments, the gravimetric capacity is at least 200 mAh/g. In some other embodiments, the gravimetric capacity is at least 300 mAh/g. In yet other embodiments, the gravimetric capacity is at least 400 mAh/g. In still other embodiments, the gravimetric capacity is at least 500 mAh/g. In other embodiments, the gravimetric capacity is at least 600 mAh/g, and in other embodiments, the gravimetric capacity is at least 700 mAh/g, at least 800 mAh/g, at least 900 mAh/g, at least 1000 mAh/g, at least 1100 mAh/g or even at least 1200 mAh/g. In some particular embodiments the device has a gravimetric capacity ranging from about 550 mAh/g to about 750 mAh/g. 
     Some of the capacity may be due to surface loss/storage, structural intercalation or storage of lithium within the pores. Structural storage is defined as capacity inserted above 50 mV vs Li/Li while lithium pore storage is below 50 mV versus Li/Li+ but above the potential of lithium plating. In one embodiment, the storage capacity ratio of a device between structural intercalation and pore storage is between 1:10 and 10:1. In another embodiment, the storage capacity ratio of a device between structural intercalation and pore storage is between 1:5 and 1:10. In yet another embodiment, the storage capacity ratio of a device between structural intercalation and pore storage is between 1:2 and 1:4. In still yet another embodiment, the storage capacity ratio of a device between structural intercalation and pore storage is between 1:1.5 and 1:2. In still another embodiment, the storage capacity ratio of a device between structural intercalation and pore storage is 1:1. The ratio of capacity stored through intercalation may be greater than that of pore storage in a device. In another embodiment, the storage capacity ratio of a device between structural intercalation and pore storage is between 10:1 and 5:1. In yet another embodiment, the storage capacity ratio of a device between structural intercalation and pore storage is between 2:1 and 4:1. In still yet another embodiment, the storage capacity ratio of a device between structural intercalation and pore storage is between 1.5:1 and 2:1. 
     Due to structural differences, lithium plating may occur at different voltages. The voltage of lithium plating is defined as when the voltage increases despite lithium insertion at a slow rate of 20 mA/g. In one embodiment the voltage of lithium plating of a device collected in a half-cell versus lithium metal at a current density of 20 mA/g is 0V. In another embodiment the voltage of lithium plating of a device collected in a half-cell versus lithium metal at a current density of 20 mA/g is between 0V and −5 mV. In yet another embodiment the voltage of lithium plating of a device collected in a half-cell versus lithium metal at a current density of 20 mA/g is between −5 mV and −10 mV. In still yet another embodiment the voltage of lithium plating of a device collected in a half-cell versus lithium metal at a current density of 20 mA/g is between −10 mV and −15 mV. In still another embodiment the voltage of lithium plating of a device collected in a half-cell versus lithium metal at a current density of 20 mA/g ranges from −15 mV to −20 mV. In yet another embodiment the voltage of lithium plating of a device collected in a half-cell versus lithium metal at a current density of 20 mA/g is below −20 mV. 
     In some embodiments of the foregoing, the hard carbon material comprises a surface area of less than about 300 m 2 /g. In other embodiments, the hard carbon material comprise a pore volume of less than about 0.1 cc/g. In still other embodiments of the foregoing, the hard carbon material comprises a surface area of less than about 300 m 2 /g and a pore volume of less than about 0.1 cc/g. 
     In yet still another embodiment of the foregoing electrical energy storage device, the electrical energy storage device has a volumetric capacity at least 5% greater than the same device which comprises a graphite electrode. In still other embodiments, the electrical energy storage device has a gravimetric capacity that is at least 10% greater, at least 20% greater, at least 30% greater, at least 40% greater or at least 50% than the gravimetric capacity of the same electrical energy storage device having a graphite electrode. 
     Embodiments wherein the cathode is comprised of a material other than a metal oxide are also envisioned. For examples, another embodiment, the cathode is comprised of a sulfur-based material rather than a metal oxide. In still other embodiments, the cathode comprises a lithium containing metal-phosphate. In still other embodiments, the cathode comprises lithium metal. In still other embodiments, the cathode is a combination of two or more of any of the foregoing materials. In still other embodiments, the cathode is an air cathode. 
     For ease of discussion, the above description is directed primarily to lithium based devices; however the disclosed carbon materials find equal utility in sodium based devices and such devices (and related carbon materials) are included within the scope of the invention. 
     EXAMPLES 
     The polymer gels, pyrolyzed cryogels and carbon materials disclosed in the following Examples were prepared according to the methods disclosed herein. Chemicals were obtained from commercial sources at reagent grade purity or better and were used as received from the supplier without further purification. 
     Polymeric materials were produced under a variety of synthetic procedures. For monolith procedures, the reaction was allowed to incubate in a open container at temperatures of up to 120° C. for up to 15 hr. The polymer hydrogel monolith was then physically disrupted, for example by grinding, to form polymer hydrogel particles having an average diameter of less than about 5 mm. 
     The polymer hydrogel was typically pyrolyzed by heating in a nitrogen atmosphere at temperatures ranging from 800-1200° C. for a period of time as specified in the examples. Specific pyrolysis conditions were as described in the following examples. 
     Where appropriate, impregnation of the carbon materials with electrochemical modifiers was accomplished by including a source of the electrochemical modifier in the polymerization reaction or contacting the carbon material, or precursors of the same (e.g., polymer hydrogel, dried polymer hydrogel, pyrolyzed polymer gel, etc.), with a source of the electrochemical modifier as described more fully above and exemplified below. 
     Example 1 
     Monolith Preparation of Polymer Gel with Hardening Agent 
     Polymer resins were prepared using the following general procedure. A Poly[(phenol glycidyl ether)-(co-formaldehyde)] with 340-570 repeating molecular units was dissolved in acetone (50:50). Phthalic Anhydride (25:75) was added to the solution and shaken until dissolved. 85% (wt/wt) Phosphoric Acid in water was then added to the solution and shaken. The reaction solution was placed at elevated temperature (55° C. for about 12 hr followed by curing at 120° C. for 6 hr) to allow for the resin to crosslink. 
     Example 2 
     Monolith Preparation of Polymer Gel without Hardening Agent 
     Polymer resins were prepared using the following general procedure. A Poly[(phenol glycidyl ether)-(co-formaldehyde)] with 340-570 repeating molecular units was dissolved in acetone (50:50). 85% (wt/wt) Phosphoric Acid in water was then added to the solution and shaken. The reaction solution was placed at elevated temperature (55° C. for about 12 hr followed by curing at 120° C. for 6 hr) to allow for the resin to crosslink. 
     Example 3 
     Solvent-Less Preparation of Polymer Gel with Hardening Agent 
     Polymer resins were prepared using the following general procedure. A Poly[(phenol glycidyl ether)-(co-formaldehyde)] with 340-570 repeating molecular units was heated to elevated temperature (85° C. unless otherwise stated) and mixed continuously. Phthalic Anhydride (25:75) was added to the viscous liquid epoxy and mixed until dissolved. 85% (wt/wt) Phosphoric Acid in water was then added to the liquid solution and mixed until solid. The solid resin product was placed at elevated temperature (120° C. for &gt;6 hr) to allow for the resin to crosslink. 
     Example 4 
     Solvent-Less Preparation of Polymer Gel without Hardening Agent 
     Polymer resins were prepared using the following general procedure. A Poly[(phenol glycidyl ether)-(co-formaldehyde)] with 340-570 repeating molecular units was heated to elevated temperature (85° C. unless otherwise stated) and mixed continuously. 85% (wt/wt) Phosphoric Acid in water was then added to the liquid solution and mixed until solid. The solid resin product was placed at elevated temperature (120° C. for &gt;6 hr) to allow for the resin to crosslink. 
     Example 5 
     Preparation of Polymer Gel with Varying Phosphorus Content 
     Polymer resins were prepared using the monolith or solvent-less process described above in samples 1-4. 85% (wt/wt) Phosphoric Acid in water (varying amount from 1% to 40% wt/wt) was then added to the liquid solution containing a Poly[(phenol glycidyl ether)-(co-formaldehyde)] and mixed. The solid resin product was placed at elevated temperature (120° C. for &gt;6 hr) to allow for the resin to crosslink. 
     Example 6 
     Preparation of Polymer Gel with Varying Hardening Agent Content 
     Polymer resins were prepared using the monolith or solvent-less process described above in samples 1-5. Phthalic Anhydride (varying amount from 0% to 40% wt/wt) was then added to the liquid epoxy solution containing a Poly[(phenol glycidyl ether)-(co-formaldehyde)] and mixed. 85% (wt/wt) Phosphoric Acid in water was then added to the liquid solution and mixed. The solid resin product was placed at elevated temperature (120° C. for &gt;6 hr) to allow for the resin to crosslink. 
     Example 7 
     Preparation of Pyrolyzed Carbon Material from Wet Polymer Gel 
     Cured polymer resin prepared according to Examples 1-6 was pyrolyzed by passage through a rotary kiln at 1050° C. with a nitrogen gas flow of 200 L/h. The weight loss upon pyrolysis was about 60%. 
     The surface area of the pyrolyzed dried polymer gel was examined by nitrogen surface analysis using a surface area and porosity analyzer. The measured specific surface area using the standard BET approach was in the range of about 5 to 100 m 2 /g. The pyrolysis conditions, such as temperature and time, are altered to obtain hard carbon materials having any number of various properties. 
     Example 8 
     Properties of Various Hard Carbons 
     Carbon materials were prepared in a manner analogous to those described in the above Examples and their properties measured. The electrochemical performance and certain other properties of the carbon samples are provided in Table 2. The data in Table 2 show that the carbons have similar physical properties in particular surface area and pore volume regardless of acid or hardener content. Table 3 however illustrates key differences in the electrochemical performance metrics. In particular, as the hardener content increases (carbons 6-8) the reversible capacity decreases. Additionally, as acid content increases (carbons 1-5) the reversible capacity increases. 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Certain Properties of Exemplary Hard Carbon Materials 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                   
                 Specific 
                 Total 
               
               
                   
                   
                   
                   
                   
                 Skeletal 
                 Surface 
                 Pore 
               
               
                   
                   
                 Hard- 
                   
                 Acetone 
                 Density 
                 Area 
                 Volume 
               
               
                 Sample 
                 Epoxy 
                 ener 
                 Acid 
                 (Y/N) 
                 (g/cc) 
                 (m2/g) 
                 (cc/g) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Carbon 
                 71 
                 28 
                 3 
                 Y 
                 1.9138 
                 14.9 
                 0.012 
               
               
                 8a 
               
               
                 Carbon 
                 70 
                 27 
                 7 
                 Y 
                 1.7594 
                 12.0 
                 0.011 
               
               
                 8b 
               
               
                 Carbon 
                 68 
                 25 
                 13 
                 Y 
                 1.7676 
                 8.6 
                 0.009 
               
               
                 8c 
               
               
                 Carbon 
                 66 
                 24 
                 18 
                 Y 
                 1.7771 
                 9.8 
                 0.008 
               
               
                 8d 
               
               
                 Carbon 
                 66 
                 23 
                 20 
                 Y 
                 1.8248 
                 12.4 
                 0.009 
               
               
                 8e 
               
               
                 Carbon 
                 79 
                 14 
                 14 
                 Y 
                 1.7961 
                 10.4 
                 0.009 
               
               
                 8f 
               
               
                 Carbon 
                 73 
                 20 
                 13 
                 Y 
                 1.7897 
                 9.5 
                 0.008 
               
               
                 8g 
               
               
                 Carbon 
                 68 
                 25 
                 12 
                 Y 
                 NA 
                 7.9 
                 0.006 
               
               
                 8h 
               
               
                 Carbon 
                 63 
                 24 
                 13 
                 Y 
                 NA 
                 7.8 
                 0.010 
               
               
                 8i 
               
               
                 Carbon 
                 83 
                 0 
                 17 
                 Y 
                 NA 
                 8.9 
                 0.009 
               
               
                 8j 
               
               
                 Carbon 
                 83 
                 0 
                 17 
                 N 
                 1.9302 
                 10.0 
                 0.001 
               
               
                 8k 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Certain Electrochemical Performance 
               
               
                 of Exemplary Hard Carbon Materials 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 1st Cycle 
                 1st Cycle 
                   
               
               
                   
                   
                 Insertion 
                 Extraction 
                 1st Cycle 
               
               
                   
                 Sample 
                 (mAh/g) 
                 (mAh/g) 
                 Efficiency 
               
               
                   
                   
               
               
                   
                 Carbon 8a 
                 369 
                 307 
                 83.2% 
               
               
                   
                 Carbon 8b 
                 457 
                 390 
                 85.3% 
               
               
                   
                 Carbon 8c 
                 386 
                 314 
                 81.3% 
               
               
                   
                 Carbon 8d 
                 401 
                 319 
                 79.6% 
               
               
                   
                 Carbon 8e 
                 498 
                 396 
                 79.5% 
               
               
                   
                 Carbon 8f 
                 546 
                 459 
                 84.1% 
               
               
                   
                 Carbon 8g 
                 391 
                 321 
                 82.1% 
               
               
                   
                 Carbon 8h 
                 482 
                 396 
                 82.2% 
               
               
                   
                 Carbon 8i 
                 581 
                 490 
                 84.3% 
               
               
                   
                 Carbon 8j 
                 596 
                 508 
                 85.3% 
               
               
                   
                 Carbon 8k 
                 551 
                 478 
                 86.8% 
               
               
                   
                   
               
            
           
         
       
     
     Example 9 
     Micronization of Hard Carbon Via Jet Milling 
     Carbon material prepared according to Example 6 was jet milled using a Jet Pulverizer Micron Master 2 inch diameter jet mill. The conditions comprised about 0.7 lbs of activated carbon per hour, nitrogen gas flow about 20 scf per min and about 100 psi pressure. The average particle size after jet milling was about 8 to 10 microns. 
     Example 10 
     Resin Characterization by Fourier Transform Infrared Spectroscopy 
     The raw materials and several iterations of the resin were analyzed with a Thermo Fischer Scientific Nicolet iS10 FTIR spectrometer with an ATR accessory. The FTIR spectra of the neat epoxy resin (˜570 MW), phosphoric acid (31.5% conc.), and the epoxy-P resin (20 wt % acid) are shown in  FIGS. 8 and 9 . Note that the phosphoric acid was diluted from 85 wt % with deionized water for the safety of the instrument. The FTIR spectra show that the cured resin is chemically different than the two reactants. One notable difference between the neat epoxy and the epoxy-P resin is the disappearance of the epoxide bending vibration at ˜910 cm −1 . This observation provides significant evidence of the crosslinking of the epoxy molecules through reaction between the phosphoric acid and the epoxide functional group.  FIG. 10  shows the effect of phosphoric acid loading on the epoxide content of the epoxy-P resin. With the addition of ≥10% H 3 PO 4 , the remaining concentration of epoxide groups was below the instrument detection limit. 
     Example 11 
     Resin Characterization by TGA 
     A sample of novalac epoxy and phosphoric acid was mixed in the melt state in a 3:1 molar ration (epoxy to phosphoric acid). The resin was cured at 120° C. for 12 hour. The TGA test was performed under N2 at 10° C./min ramp rate. The TGA data are depicted in  FIG. 11 . The exotherm at 250° C. could be explained by a reaction of the phosphoric acid and remaining unreacted epoxy groups that may control resin 3-D structure resulting in a desirable carbon structure and both improved gravimetric capacity and first cycle efficiency vs. the unmodified epoxy resin. 
     Example 12 
     Determination of Carbon Phosphorous Content by TXRF 
     Exemplary carbons produced according to the various examples above were tested for phosphorus content by TXRF spectroscopy. Carbon was synthesized from reins produced using both the solvent process (as in Examples 1, 2, 5, 6, and 7) and solvent-less process (as in Examples 3, 4, 5, 6, and 7) were analyzed. A Bruker S2 PICOFOX spectrometer was used for the study. Samples were prepared by milling to achieve a D(1.00)&lt;100 μm particle size, then making a suspension consisting of the milled carbon, ethylene glycol, and Ga as an internal standard. Aliquots were placed on optically flat quartz disks and dried, leaving a thin residue for analysis. The results of the analysis, and the amount of phosphoric acid added during resin synthesis, are summarized in the table below Table 4. 
     
       
         
           
               
             
               
                 TABLE 4 
               
             
            
               
                   
               
               
                 Tunability of Phosphorous content 
               
            
           
           
               
               
               
            
               
                   
                 Sample 
                 P Content in HC (%) 
               
               
                   
                   
               
            
           
           
               
               
               
            
               
                   
                 Carbon 12a 
                 6.45 
               
               
                   
                 Carbon 12b 
                 5.21 
               
               
                   
                 Carbon 12c 
                 2.9 
               
               
                   
                 Carbon 12d 
                 9.34 
               
               
                   
                 Carbon 12e 
                 4.01 
               
               
                   
                 Carbon 12f 
                 11.67 
               
               
                   
                 Carbon 12g 
                 7.28 
               
               
                   
                 Carbon 12h 
                 4.73 
               
               
                   
                 Carbon 12i 
                 8.29 
               
               
                   
                 Carbon 12j 
                 5.37 
               
               
                   
                 Carbon 12k 
                 12.99 
               
               
                   
                 Carbon 12l 
                 7.16 
               
               
                   
                   
               
            
           
         
       
     
     Example 13 
     Solid State Preparation of Polymer and Hard Carbon Derived from Same 
     A polymer was prepared by mixing 1 g of 2-naphthol, 1 g of hexamethylenetetramine, and 0.5 g of ammonium dihydrogenphosphate via mortar and pestle. This solid mixture was incubated overnight at 140 C, and the reacted material was subsequently pyrolyzed by heating at 20 C/min ramp to 1100 C and holding for 60 min under a purge of nitrogen gas. The resulting pyrolyzed carbon had a surface area of 78 m2/g and a pore volume of 0.04 cm3/g, and tXRF analysis demonstrated a phosphorus content in the carbon of 9.2%. This carbon was tested electrochemically as described herein. The resulting data showed that the first cycle capacity and efficiency were 648 mAh/g and 69%, respectively. The resulting data also showed that the second cycle capacity and efficiency were 452 mAh/g and 97%, respectively. The resulting data also showed that the third cycle capacity and efficiency were 440 mAh/g and 98%, respectively. 
     Example 14 
     Preparation of High Capacity Hard Carbon from Polymer Gel 
     A Polymer resin was prepared using the following general procedure. A Poly[(phenol glycidyl ether)-(co-formaldehyde)] with ˜570 repeating molecular units was dissolved in acetone (40:60). Phthalic Anhydride was added (1:8) to the solution and shaken until dissolved. 85% (wt/wt) Phosphoric Acid in water was then added (1:20) to the solution and shaken. The reaction solution was placed at elevated temperature (55° C. for 15 hr followed by curing at 120° C. for 6 hr) to allow for the resin to crosslink. 
     The cured polymer resin was pyrolyzed by passage through a tube furnace at 900° C. with a nitrogen gas flow of 200 L/h and a heating rate of 10° C./min. The weight loss upon pyrolysis was 62%. The surface area of the pyrolyzed dried polymer gel was examined by nitrogen surface analysis using a surface area and porosity analyzer. The measured specific surface area and pore volume using the standard BET approach was 14.0 m 2 /g and 0.010 g/cc. Table 5 displays the material characteristics of the produced hard carbon. 
                     TABLE 5                  Carbon physical properties                                     Specific Surface   Total Pore           Sample   Area (m2/g)   Volume (cc/g)                       Carbon 14a   14.0   0.01                        
The hard carbon was then milled and sieved through a 38-micron sieve. The resulting sieve cut was then made into an aqueous electrode with 90/5/5 formulation (hard carbon/conductivity enhancer/binder) and a 1:1.1 solid to solvent ration. That electrode was then used as the anode in the construction of a Lithium-Ion half-cell, where the cathode material was lithium metal foil. The resulting cell was held on OCV for 6 hours before being cycled at 40 mA/g with a voltage window 5mc-2V (5 hr hold at 5 mV). Electrochemical data is described in Table 6 and  FIG. 11 
 
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 6 
               
               
                   
                   
               
               
                   
                   
                 1st Cycle 
                 1st Cycle 
                 1st Cycle 
               
               
                   
                   
                 Insertion 
                 Extraction 
                 Efficiency 
               
               
                   
                 Sample 
                 (mAh/g) 
                 (mAh/g) 
                 (%) 
               
               
                   
                   
               
             
            
               
                   
                 Carbon 14a 
                 780 
                 590 
                 75.0% 
               
               
                   
                   
               
            
           
         
       
     
     Example 15 
     Preparation of High Efficiency Hard Carbon from Polymer Gel 
     A Polymer resin was prepared using the following general procedure. A Poly[(phenol glycidyl ether)-(co-formaldehyde)] with ˜570 repeating molecular units was heated to elevated temperature (85° C.) and mixed continuously. 85% (wt/wt) Phosphoric Acid in water was then added (1:5) to the liquid solution and mixed until solid. The solid resin product was placed at elevated temperature (120° C. for 6 hr) to allow for the resin to crosslink. 
     The cured polymer resin was pyrolyzed by passage through a rotary kiln at 1050° C. with a nitrogen gas flow of 200 L/h and a heating rate of 10° C./min. The weight loss upon pyrolysis was 63%. The surface area of the pyrolyzed dried polymer gel was examined by nitrogen surface analysis using a surface area and porosity analyzer. The measured specific surface area and pore volume using the standard BET approach was 10.2 m 2 /g and 0.001 g/cc. Using a pycnometer the skeletal density was measured at 1.9302 g/cc. T-XRF analysis of the material determined that the hard carbon had a 13.0 phosphorus incorporation after pyrolysis. Table 7 displays the material characteristics of the produced hard carbon. 
     
       
         
           
               
             
               
                 TABLE 7 
               
             
            
               
                   
               
               
                 Carbon physical properties 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Skeletal 
                 Specific Surface 
                 Total Pore 
                 P content 
               
               
                 Sample 
                 Density (g/cc) 
                 Area (m2/g) 
                 Volume (cc/g) 
                 (%) 
               
               
                   
               
               
                 Carbon 
                 1.9302 
                 10.2 
                 0.001 
                 13.0 
               
               
                 15a 
               
               
                   
               
            
           
         
       
     
     The hard carbon was then milled and sieved through a 38-micron sieve. The resulting sieve cut was then made into an aqueous electrode with 95/1/4 formulation (hard carbon/conductivity enhancer/binder) and a 1:1 solid to solvent ration. That electrode was then used as the anode in the construction of a Lithium-Ion half-cell, where the cathode material was lithium metal foil. The resulting cell was held on OCV for 6 hours before being cycled at 40 mA/g with a voltage window 5mc-2V (5 hr hold at 5 mV). Electrochemical data is described in Table 8 and  FIG. 12 . 
     
       
         
           
               
             
               
                 TABLE 8 
               
             
            
               
                   
               
               
                 Carbon Electrochemical properties 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 1st Cycle 
                 1st Cycle 
                 1st Cycle 
               
               
                   
                   
                 Insertion 
                 Extraction(mAh/g) 
                 Efficiency 
               
               
                   
                 Sample 
                 (mAh/g) 
                 (mAh/g) 
                 (%) 
               
               
                   
                   
               
               
                   
                 Carbon 15a 
                 551 
                 475 
                 86.8% 
               
               
                   
                   
               
            
           
         
       
     
     Example 16 
     Preparation of Hard Carbon from Polymer Gel at Large Scale 
     A Polymer resin was prepared using the following general procedure. A Poly[(phenol glycidyl ether)-(co-formaldehyde)] with between 300 and 600 repeating molecular units and an 85% phosphoric acid aqueous solution were mixed and cured via an extrusions process. 
     The cured polymer resin was pyrolyzed in a rotary kiln according to the methods described generally herein. 
     The hard carbon was the examined for its electrochemical properties generally according to the methods described herein. Electrochemical data is described in Table 9. 
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 9 
               
               
                   
                   
               
               
                   
                   
                 1st Cycle 
                 1st Cycle 
                 1st Cycle 
               
               
                   
                   
                 Insertion 
                 Extraction 
                 Efficiency 
               
               
                   
                 Sample 
                 (mAh/g) 
                 (mAh/g) 
                 (%) 
               
               
                   
                   
               
             
            
               
                   
                 Carbon 16a 
                 761 
                 619 
                 81.3 
               
               
                   
                   
               
            
           
         
       
     
     Example 17 
     Evaluation of Polymer Composition and Carbonization Conditions 
     Polymer resins were prepared using the following general procedure. A Poly[(phenol glycidyl ether)-(co-formaldehyde)] with 340-570 repeating molecular units was heated to elevated temperature (85° C. unless otherwise stated) and mixed continuously. Varying amounts of 85% (wt/wt) Phosphoric Acid in water was then added to the liquid solution and mixed until solid. The solid resin was carbonized under various conditions (1000-1050° C., 5-60 min) and the final materials were analyzed for both physical characteristics and electrochemical performance. In total, three resin formulation types, two acids levels, and four carbonization conditions were tested. Characterization of these carbon materials is described in Table 10. 
     Table 10 includes rate stability in terms of the average capacity for a given current density divided by the average capacity at another current density. For example, 4 C by C/10 is the average capacity at 4 C current density (i.e., four times C) divided by the average capacity at a current density of C/10 (i.e., one-tenth C), in this case, the 4 C by C/10 represents the capacity change as the current density in increased 40-fold. For example, C/10 by C/5 is the average capacity at C/10 current density divided by the average capacity at a current density of C/5, in this case, the C/10 by C/5 represents the capacity change as the current density in increased 2-fold. 
     
       
         
           
               
             
               
                 TABLE 10 
               
             
            
               
                   
               
               
                 Electrochemical Performance of Exemplary Hard Carbon Materials 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                 1st cycle 
                   
                 Rate 
               
               
                   
                 Surface 
                 Pore 
                 Reversible 
                 1st cycle 
                 stability 
               
               
                   
                 Area 
                 Volume 
                 Capacity 
                 Efficiency 
                 2 C/0.2 C 
               
               
                 Carbon 
                 (m 2 /g) 
                 (cc/g) 
                 (mAh/g) 
                 (%) 
                 (%) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 11-1 
                 7.3 
                 0.006 
                 596 
                 82.3 
                 — 
               
               
                 11-5 
                 7.9 
                 0.006 
                 505 
                 75.6 
                 79 
               
               
                 11-2 
                 6.5 
                 0.004 
                 485 
                 84.9 
                 92 
               
               
                 11-6 
                 8.2 
                 0.007 
                 606 
                 82.4 
                 79 
               
               
                 11-3 
                 9.3 
                 0.010 
                 555 
                 84.7 
                 91 
               
               
                 11-7 
                 6.6 
                 0.006 
                 531 
                 82.1 
                 80 
               
               
                 11-4 
                 8.0 
                 0.007 
                 382 
                 86.4 
                 92 
               
               
                 11-8 
                 5.5 
                 0.001 
                 478 
                 83.4 
                 87 
               
               
                 11-9 
                 6.2 
                 0.000 
                 520 
                 85.2 
                 90 
               
               
                 11-13 
                 8.5 
                 0.006 
                 415 
                 74.7 
                 67 
               
               
                 11-10 
                 7.8 
                 0.007 
                 413 
                 83.5 
                 — 
               
               
                 11-14 
                 12.2 
                 0.011 
                 530 
                 81.0 
                 — 
               
               
                 11-11 
                 6.5 
                 0.001 
                 568 
                 84.9 
                 89 
               
               
                 11-15 
                 10.2 
                 0.008 
                 530 
                 81.4 
                 86 
               
               
                 11-12 
                 8.9 
                 0.007 
                 468 
                 83.0 
                 — 
               
               
                 11-16 
                 11.2 
                 0.010 
                 448 
                 83.1 
                 86 
               
               
                 11-25 
                 5.3 
                 0.004 
                 515 
                 78.9 
                 81 
               
               
                 11-29 
                 14.1 
                 0.004 
                 470 
                 71.0 
                 — 
               
               
                 11-26 
                 8.8 
                 0.005 
                 521 
                 81.8 
                 87 
               
               
                 11-30 
                 15.9 
                 0.013 
                 487 
                 79.0 
                 — 
               
               
                 11-27 
                 5.9 
                 0.001 
                 476 
                 80.5 
                 89 
               
               
                 11-31 
                 14.6 
                 0.015 
                 481 
                 77.7 
                 — 
               
               
                 11-28 
                 12.7 
                 0.009 
                 467 
                 84.0 
                 — 
               
               
                 11-32 
                 9.4 
                 0.008 
                 414 
                 80.7 
                 91 
               
               
                   
               
            
           
         
       
     
     Example 18 
     Optimization of Electrode for Exemplary Hard Carbon Performance 
     To make aqueous slurry from hard carbon (fabricated as 8j), binder solution was prepared using styrene butadiene rubber (SBR) as binding agent and sodium carboxymethyl cellulose (Na-CMC) as surfactant agent. In a 150 ml container, the CMC solution was mixed with SBR emulsion and the total needed water for the target Solid/Solvent ratio using a planetary, impellerless mixer. In a different container, the hard carbon and Super P was mixed using overhead mixer for 10 minutes at a low speed (6 RPM) to uniformly mix the hard carbon with Super P. The mixture of hard carbon and super P was added to the planetary mixing cup containing SBR/CMC solution and mixed at 1300 RPM for 5 minutes and 2000 rpm for 30 seconds for degassing. The resultant mixture was dispersed using homogenization via a Silverson homogenizer at 3000 RPM for 15 minutes to eliminate concentration gradient and produce uniformly dispersed slurry. The resultant slurry was coated onto a current collector and calendared. 
     A summary of the various electrodes produced in presented in Table 11 For viscosity and electrode quality, H, M, and L, denotes high, medium, and low quality, for example, for pilot electrode quality post-calendaring, high quality (H) represents no delamination observed, medium quality (M) represents slight or some delamination observed, and low quality (L) represents complete delamination observed. The calendaring ratio is the final electrode thickness divided by the initial thickness (the final thickness varied from 20-90 microns). In the cases where there was low electrode quality, electrochemical characterizations could not be conducted. A summary of electrochemical characterization is described in Table 12. Each capacity listed is an average over three cycles. The cycles are as follows: C/10 is cycles 1-3, C/5 is cycles 4-6, C/2 is cycles 7-9, 1 C is cycles 10-12, 2 C is cycles 13-15, 3 C is cycles 16-18, 4 C is cycles 18-20. This table includes stability in terms of the average capacity for a given current density divided by the average capacity of another. For example, 4 C by C/10 is the average capacity at 4 C current density divided by the average capacity at a current density of C/10. 
     As can be seen from Table 12, there was good retention of capacity for the carbon materials as the current density was increased. For example, as the current density was increased 2-fold (C/5 by C/10), the rate stability (or capacity retention) was in the range of 97-107%. For example, as the current density was increased 5-fold (C/2 by C/10), the rate stability (or capacity retention) was in the range of 95-105%. For example, as the current density was increased 10-fold (C by C/10), the rate stability (or capacity retention) was in the range of 93-102%. For example, as the current density was increased 20-fold (2 C by C/10), the rate stability (or capacity retention) was in the range of 90-98%. For example, as the current density was increased 30-fold (3 C by C/10), the rate stability (or capacity retention) was in the range of 89-96%. For example, as the current density was increased 40-fold (4 C by C/10), the rate stability (or capacity retention) was in the range of 86-90%. 
     
       
         
           
               
             
               
                 TABLE 11 
               
             
            
               
                   
               
               
                 Description of various electrodes produced according to Example 18. 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Elec- 
                   
               
               
                   
                   
                   
                   
                   
                   
                 solid/ 
                 Vis- 
                   
                   
                 Elec- 
                 trode 
                 AM 
               
               
                   
                 AM 
                 CE 
                 SBR 
                 CMC 
                 Total % 
                 solv 
                 cosity 
                 Slurry 
                 Cal 
                 trode 
                 density 
                 density 
               
               
                 # 
                 (%) 
                 (%) 
                 (%) 
                 (%) 
                 Binder 
                 (1/x) 
                 (cP) 
                 Quality 
                 % 
                 Quality 
                 (g/cc) 
                 (g/cc) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 1 
                 90% 
                 3.33% 
                 4.44% 
                 2.22% 
                 6.67% 
                 1.15 
                 13668 
                 M 
                 19% 
                 H 
                 1.03 
                 0.93 
               
               
                 2 
                 90% 
                 3.33% 
                 2.22% 
                 4.44% 
                 6.67% 
                 1.25 
                 26780 
                 M 
                 27% 
                 H 
                 1.03 
                 0.93 
               
               
                 3 
                 90% 
                 5.00% 
                 1.67% 
                 3.33% 
                 5.00% 
                 1.25 
                 13387 
                 M 
                 22% 
                 H 
                 1.00 
                 0.90 
               
               
                 4 
                 90% 
                 5.00% 
                 2.50% 
                 2.50% 
                 5.00% 
                 1.2 
                 6040 
                 M 
                 17% 
                 H 
                 1.00 
                 0.90 
               
               
                 5 
                 95% 
                 2.50% 
                 0.83% 
                 1.67% 
                 2.50% 
                 1 
                 3248 
                 L 
                 19% 
                 M 
                 0.90 
                 0.86 
               
               
                 6 
                 95% 
                 1.67% 
                 2.22% 
                 1.11% 
                 3.33% 
                 1 
                 967 
                 L 
                 12% 
                 M 
                 0.65 
                 0.62 
               
               
                 7 
                 90% 
                 3.33% 
                 3.33% 
                 3.33% 
                 6.67% 
                 1.25 
                 68235 
                 H 
                 20% 
                 H 
                 0.98 
                 0.88 
               
               
                 12 
                 90% 
                 6.67% 
                 2.22% 
                 1.11% 
                 3.33% 
                 1 
                 45790 
                 L 
                 22% 
                 M 
                 0.73 
                 0.66 
               
               
                 13 
                 95% 
                 1.67% 
                 1.67% 
                 1.67% 
                 3.33% 
                 1.05 
                 5152 
                 H 
                 19% 
                 M 
                 0.97 
                 0.92 
               
               
                 14 
                 95% 
                 1.67% 
                 1.11% 
                 2.22% 
                 3.33% 
                 1.1 
                 3710 
                 H 
                 12% 
                 M 
                 0.99 
                 0.94 
               
               
                 15 
                 90% 
                 6.67% 
                 1.11% 
                 2.22% 
                 3.33% 
                 1.2 
                 12777 
                 H 
                 17% 
                 M 
                 0.95 
                 0.86 
               
               
                 9 
                 95% 
                 3.33% 
                 0.56% 
                 1.11% 
                 1.67% 
                 0.9 
                 3666 
                 L 
                 13% 
                 L 
                 N/A 
                 N/A 
               
               
                 10 
                 95% 
                 2.50% 
                 1.67% 
                 0.83% 
                 2.50% 
                 0.9 
                 13648 
                 L 
                 18% 
                 L 
                 N/A 
                 N/A 
               
               
                 11 
                 95% 
                 3.33% 
                 0.83% 
                 0.83% 
                 1.67% 
                 1 
                 1306 
                 L 
                 17% 
                 L 
                 N/A 
                 N/A 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 12 
               
             
            
               
                   
               
               
                 Electrochemical characterization of various electrodes according to Example 18. 
               
            
           
           
               
               
               
               
            
               
                   
                 3rd 
                 1 st   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Cycle 
                 Cycle 
                   
                 Rate Stability 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 Extraction 
                 Eff 
                 Average capacity (extraction in mAh/g) for each current density 
                 C/5 by 
                 C/2 by 
                 C by 
                 2 C by 
                 3 C by 
                 4 C by 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 # 
                 (mAh/g) 
                 (%) 
                 C/10 
                 C/5 
                 C/2 
                 1 C 
                 2 C 
                 3 C 
                 4 C 
                 C/10 
                 C/10 
                 C/10 
                 C/10 
                 C/10 
                 C/10 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 1 
                 485 
                 81.0 
                 488 
                 482 
                 472 
                 456 
                 443 
                 432 
                 421 
                 99% 
                 97% 
                 93% 
                 91% 
                 88% 
                 86% 
               
               
                 2 
                 489 
                 81.3 
                 493 
                 492 
                 479 
                 469 
                 451 
                 446 
                 437 
                 100%  
                 97% 
                 95% 
                 91% 
                 90% 
                 88% 
               
               
                 3 
                 525 
                 80.3 
                 530 
                 518 
                 504 
                 494 
                 480 
                 N/A 
                 N/A 
                 98% 
                 95% 
                 93% 
                 91% 
                 N/A 
                 N/A 
               
               
                 4 
                 508 
                 78.6 
                 473 
                 505 
                 498 
                 484 
                 465 
                 452 
                 425 
                 107%  
                 105%  
                 102%  
                 98% 
                 96% 
                 90% 
               
               
                 5 
                 490 
                 82.9 
                 494 
                 492 
                 479 
                 468 
                 447 
                 440 
                 427 
                 99% 
                 97% 
                 95% 
                 90% 
                 89% 
                 86% 
               
               
                 6 
                 509 
                 82.9 
                 504 
                 518 
                 503 
                 476 
                 467 
                 453 
                 449 
                 103%  
                 100%  
                 95% 
                 93% 
                 90% 
                 89% 
               
               
                 7 
                 532 
                 82.8 
                 530 
                 525 
                 514 
                 501 
                 488 
                 476 
                 N/A 
                 99% 
                 97% 
                 94% 
                 92% 
                 90% 
                 N/A 
               
               
                 12 
                 545 
                 78.8 
                 528 
                 534 
                 N/A 
                 N/A 
                 N/A 
                 N/A 
                 N/A 
                 101%  
                 N/A 
                 N/A 
                 N/A 
                 N/A 
                 N/A 
               
               
                 13 
                 481 
                 80.0 
                 483 
                 472 
                 468 
                 N/A 
                 N/A 
                 N/A 
                 N/A 
                 98% 
                 97% 
                 N/A 
                 N/A 
                 N/A 
                 N/A 
               
               
                 14 
                 503 
                 80.5 
                 503 
                 487 
                 478 
                 N/A 
                 N/A 
                 N/A 
                 N/A 
                 97% 
                 95% 
                 N/A 
                 N/A 
                 N/A 
                 N/A 
               
               
                 15 
                 496 
                 78.6 
                 490 
                 486 
                 479 
                 N/A 
                 N/A 
                 N/A 
                 N/A 
                 99% 
                 98% 
                 N/A 
                 N/A 
                 N/A 
                 N/A 
               
               
                   
               
            
           
         
       
     
     Example 19 
     Hard Carbon to Monitor Depth of Discharge and End of Life 
     Hard carbon in small quantities can help identify the end of life (EOL) and depth of discharge (DOD) of an anode.  FIG. 14  depicts superior capability to monitor EOL as hard carbon percentage is increase. The electrodes are made following Example 18, wherein the active material is both hard carbon and graphite and are cycled versus a lithium metal counter electrode. A slight rise in voltage for the 20% hard carbon (HC)+graphite blend indicates that there is roughly 20% capacity remaining in the battery. For a 5% HC+graphite blend, a capacity rise indicates only 8% remaining capacity. One preferred mode is from 15-20% HC+graphite, corresponding to a ratio of hard carbon to graphite of 0.176 to 0.25, wherein the DOD indication curve occurs between 0.75 and 0.85. The point at which end of life can be determined is important, and the earlier detection is preferred. In this fashion, the end of life for the current carbon materials can be determined earlier on in the device discharge (at the point when 15-25% is remaining) vs. graphite without low or no carbon materials present (at the point where 8% is remaining). The end of life can be determined, for example, at the percent of depth of discharge when the voltage (V) vs Li/Li+ rises to within a certain percent of the maximum voltage vs Li/Li+. For example, the end of life can be determined at the percent of depth of discharge when the voltage (V) vs Li/Li+ is 5% of the maximum voltage. Alternatively, the end of life can be determined at the percent of depth of discharge when the voltage (V) vs Li/Li+ is 5% of to maximum voltage. 
     The capacity of the graphite measured (absence of hard carbon) was 366 mAh/g. All capacity measurements were made at C/10. Upon addition of hard carbon to the graphite, there was an added benefit of increased capacity. At 2% hard carbon (0.02 ratio of hard carbon to graphite), the capacity was 368, corresponding to a 0.6% increase. At 5% hard carbon (0.05 ratio of hard carbon to graphite), the capacity was 377, corresponding to a 3% increase. At 15% hard carbon (0.176 ratio of hard carbon to graphite), the capacity was 381, corresponding to a 4% increase. 
     At 20% hard carbon (0.25 ratio of hard carbon to graphite), the capacity was 387, corresponding to a 5.6% increase. 
     The various embodiments described above can be combined to provide further embodiments. All of the U.S. patents, U.S. patent application publications, U.S. patent applications, foreign patents, foreign patent applications and non-patent publications referred to in this specification and/or listed in the Application Data Sheet, including but not limited to U.S. Provisional Application No. 61/834,258, filed Jun. 12, 2014, are incorporated herein by reference, in their entirety. Aspects of the embodiments can be modified, if necessary to employ concepts of the various patents, applications and publications to provide yet further embodiments. These and other changes can be made to the embodiments in light of the above-detailed description. In general, in the following claims, the terms used should not be construed to limit the claims to the specific embodiments disclosed in the specification and the claims, but should be construed to include all possible embodiments along with the full scope of equivalents to which such claims are entitled. Accordingly, the claims are not limited by the disclosure.