Patent Publication Number: US-2022219987-A1

Title: Monolithic and fractal carbon foams and methods of preparing and using same

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present patent application hereby claims the benefit of priority based on U.S. Provisional Application No. 62/851,793, filed May 23, 2019. Furthermore, the entire content and disclosure of the U.S. provisional patent application is incorporated herein by reference in its entirety. 
    
    
     BACKGROUND 
     Field of the Invention 
     The present invention relates generally to highly porous carbon foams and the preparation thereof. 
     BACKGROUND OF THE INVENTION 
     Energy storage, such as in supercapacitors, is important for improving energy efficiency. Previous studies have shown that nano-carbon foams are suitable materials for constructing electrodes in supercapacitors. However, existing methods of preparing nano-carbon foams are not scalable for industrial production. 
     For example, chemical solution-based methods require a significant number of pre-and post- processing steps. As a result, these methods are not only both time-consuming and costly, they also generate chemical waste. Moreover, these methods produce nano-carbon foams containing impurities due to use of chemical reagents and surfactants. 
     As another example, U.S. Patent Application Publication No. U.S. 2017/0297923 A 1  reports a hot-pressing method for preparing a nano-carbon foam from hollow onion-like carbon nanoparticles. This hot-pressing method eliminates the need for chemical reagents and surfactants. Yet, the nano-carbon foam produced thereby has low mechanical stability and inconsistent foam density. 
     Thus, there is a need for novel methods suitable for industrial scale production of nano-carbon foams having improved structural and mechanical properties.  
     SUMMARY 
     In one aspect, the present invention relates to a monolithic carbon foam that contains fused onion-like carbon (“OLC”) nanoparticles having interconnected pores, has a volumetric micropore surface area of 200 m 2 /cc-600 m 2 /cc (preferably, 200 m 2 /cc-500 m 2 /cc), and has an electrical conductivity of 20 s/cm-140 s/cm (preferably, 40 s/cm-75 s/cm). In one embodiment, the foam has a Young&#39;s modulus of 1 Gpa-4 GPa (preferably 1 Gpa-3 GPa). In another embodiment, the foam further contains a material that is a non-OLC-based material (preferably including activated carbon), a semiconductor material, an oxide material, or a metal; specific examples of the material include silicon, molybdenum oxide, and molybdenum disulfide. The material can be in the form of a fiber, a tube, a hollow sphere, a wire, a sheet, or a powder. Also covered by the present invention is a foam powder prepared by crushing the above-described monolithic carbon foam. 
     The above-described monolithic carbon foam can be prepared by (i) compacting OLC nanoparticles, (ii) placing the compacted OLC nanoparticles in a vacuum or in a space filled with an inert gas (e.g., N 2  and Ar), and (iii) spark plasma sintering the OLC nanoparticles at a pressure of 30 MPa-1000 MPa (preferably, 40 MPa-300 MPa) and a temperature of 300 ° C.-800 ° C. (preferably, 400 ° C.-600 ° C.) for a duration of 2 seconds-30 minutes. In one embodiment, the OLC nanoparticles is compacted with a material in the form of a fiber, a tube, a hollow sphere, a wire, a sheet, or a powder, the material being a non-OLC-based material, an oxide material, a metal, and a semiconductor material. In addition to this method, a monolithic carbon foam prepared thereby is within the scope of the instant invention as well. 
     In another aspect, the present invention relates to a fractal carbon foam. The fractal carbon foam is prepared by (i) crushing the monolithic carbon foam described above to form a monolithic carbon foam powder, (ii) compacting the monolithic carbon foam powder, (iii) placing the compacted monolithic carbon foam powder in a vacuum, and (iv) spark plasma sintering the monolithic carbon foam powder at a pressure of 30 MPa-1000 MPa (preferably, 40 MPa-200 MPa) and a temperature of 300 ° C.-800 ° C. (preferably, 600 ° C.-800 ° C.) for 2 seconds-30 minutes (preferably, 2 seconds-10 minutes) to form the fractal carbon foam. This method is also within the scope of this invention. 
     Also disclosed herein are an electrode for use in a supercapacitor containing an active material made of the above-described monolithic or fractal carbon foam and a supercapacitor including such an electrode. More specifically, a supercapacitor of this invention including (i) a negative electrode and a positive electrode both formed of the monolithic or fractal carbon foam depicted above, (ii) a separator disposed between the negative and positive electrodes to prevent a short circuit by direct contact thereof, and (iii) an electrolyte ionically connecting the electrodes, in which the inner surface of each electrode contacts with the electrolyte and the outer surface of each electrode is covered by a current collector. 
     The details of the invention are set forth in the drawings, the definitions, and the detailed description below. Other features, objects, and advantages of the invention will be apparent from the following actual examples and claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The description below refers to the accompanying drawings, of which: 
         FIG. 1( a )  is a schematic representation of spark plasma sintering (“SPS”) of OLC particles. 
         FIG. 1( b )  are schematic illustrations showing that SPS transforms OLC particles into a monolithic carbon foam having enhanced density and surface and strong and conductive interparticle bonding. 
         FIG. 1( c )  is a graph showing the gravimetric and volumetric surface areas of monolithic carbon foams prepared at a pressure 80 MPa and at various temperatures, i.e., 300-700 ° C. 
         FIG. 2( a )  is a graph showing the Young&#39;s moduli of a monolithic carbon foam prepared by the SPS process and a carbon foam prepared by a conventional hot-pressing process. 
         FIG. 2( b )  is a graph showing the conductivity and material density of SPS-processed monolithic carbon foams and conventional hot-pressed monolithic carbon foams. 
         FIG. 3  is a schematic illustration of an exemplary pouch-cell type supercapacitor, which contains a monolithic carbon foam or a fractal carbon foam. 
         FIG. 4( a )  is a schematic illustration of a monolithic carbon foam according to an embodiment of the present invention. The monolithic carbon foam, formed from OLC nanoparticles, has a pore structure characterized by a series of mesopores and micropores. 
         FIG. 4( b )  is a schematic illustration of a fractal carbon foam according to an embodiment of the present invention. This fractal carbon foam, formed from monolithic  carbon foam powder, has a hierarchical pore structure characterized by macropores connected to a series of mesopores and micropores in the monolithic carbon foam powder. 
         FIG. 5  is a Ragone plot showing a comparison of device performance of supercapacitors containing different electrode materials, i.e., monolithic graphene foam (“MGF”), fractal graphene foam (“FGF”), activated carbon, edge free graphene, and reduced graphite oxide (“rGO”); the inset is an overlay of Nyquist plots of the MGF electrode and FGF electrode showing the diffusion speed of ions within these electrodes, wherein a steeper slope corresponds to a higher diffusion rate. 
         FIG. 6  is a Raman spectrum of a MoS 2 / carbon hybrid monolithic carbon foam. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Described in detail below are the monolithic carbon foam, the fractal carbon foam, the methods of preparing them, and the supercapacitors constructed from them as set forth in the SUMMARY section above. 
     For purposes of the present disclosure, the term “onion-like carbon nanoparticles” or “OLC nanoparticles” refers to quasi-spherical nanoparticles consisting of fullerene-like carbon layers enclosed by concentric graphitic shells. They exhibit unique zero-dimensional spherical or concentric shell structures with small (e.g., &lt;50 nm) diameters. They are also commonly referred to as nano-onions. These nanoparticles have properties different from other carbon nanostructures such as graphite, nanodiamonds, and nanotubes due to their highly symmetric structure. 
     Furthermore, the term “spark plasma sintering” or “SPS” refers to a pressure-assisted pulsed-current or direct current process in which powder samples are loaded in an electrically conducting die and sintered under a uniaxial pressure. Spark plasma sintering is a technique that uses pressure-driven powder consolidation in which a pulsed direct electric current passes through a sample compressed in a graphite matrix. It is also known as field-assisted sintering or pulse electric current sintering. The term “hot-press” refers to a process that supplies thermal energy from an external heating source to a sample with applied pressure. 
     Finally, the term “monolithic carbon foam” refers to a material prepared by SPS onion-like carbon nanoparticles, the term “monolithic carbon foam powder” refers to the powder formed by crushing monolithic carbon foam by any known means, and the term “fractal carbon foam” refers to a carbon foam formed from monolithic carbon foam powder.  
     To reiterate, a monolithic carbon foam of this invention (i) contains fused OLC nanoparticles having interconnected pores, (ii) has a volumetric micropore surface area of 200 m 2 /cc-600 m 2 /cc, and (iii) has an electrical conductivity of 20 s/cm-140 s/cm. The foam can be prepared by first compacting OLC nanoparticles and then subjecting the compacted OLC nanoparticles in a vacuum or inert gas environment or in a space filled with an inert gas to a SPS process at a pressure of 30 MPa-1000 MPa and a temperature of 300 ° C.-800 ° C. for 2 seconds-30 minutes. 
     In one embodiment, the monolithic carbon foam thus prepared contains micropores, mesopores, and, optionally, macropores, which, respectively, have diameters of 0.723 nm-2 nm, 2 nm-50 nm, and &gt;50 nm. 
     In another embodiment, the monolithic carbon foam has a volumetric micropore surface area higher (e.g., 500%-1435%) than that of the OLC nanoparticles and its material density increases (e.g., 0.1 g/cc to 1 g/cc) with respect to the OLC nanoparticles, whereas its gravimetric total surface area decreases minimally (e.g., from 1200 m 2 /g to 857 m 2 /g) also with respect to the OLC nanoparticles. 
     The monolithic carbon foam can be a hybrid monolithic carbon foam, namely, a doped monolithic carbon foam that includes a carbon-based material (e.g., activated carbon), an oxide material (e.g., molybdenum oxide), a metal, and a semiconductor material (e.g., silicon and molybdenum disulfide). The material can be in the form of fibers, tubes, hollow spheres, 2D materials, or powders. In a preferred embodiment, the material is 2D molybdenum disulfide (MoS2). In another preferred embodiment, the material is silicon nanoparticles. 
     Further covered by this invention is a fractal carbon foam prepared from the above-described monolithic carbon foam by crushing the monolithic carbon foam to form a monolithic carbon foam powder; compacting the monolithic carbon foam powder, placing the compacted monolithic carbon foam powder in a vacuum or inert gas environment or in a space filled with an inert gas, and subjecting the monolithic carbon foam powder to a SPS process at a pressure of 30-1000 MPa and a temperature of 300-800 ° C. for 2 seconds-30 minutes. 
     Typically, the fractal carbon foam of this invention has a hierarchical pore structure, i.e., including interconnected micropores, mesopores, and macropores. The micropores, the mesopores, and the macropores, respectively, have diameters of 0.723 nm-2 nm, 2 nm-50 nm, and &gt;50 nm.  
     A hybrid fractal carbon foam, another contemplated invention, can be formed from the hybrid monolithic carbon foam described above. 
     Also within the scope of this invention is an electrode for use in a supercapacitor, the electrode containing an active material made of the monolithic or fractal carbon foam described above. The supercapacitor includes such a negative electrode and such a positive electrode, a separator disposed between the negative and positive electrodes to prevent a short circuit by direct contact thereof, and an electrolyte ionically connecting the electrodes, in which the inner surface of each electrode contacts with the electrolyte and the outer surface of each electrode is covered by a current collector. A suitable material, such as an Al laminated file, can be used to package the supercapacitor. 
     Without further elaboration, it is believed that one skilled in the art can, based on the above description, utilize the present invention to its fullest extent. The following specific examples are, therefore, to be construed as merely illustrative, and not limitative of the remainder of the disclosure in any way whatsoever. 
     All publications, including patent documents, cited herein are incorporated by reference in their entirety. 
     EXAMPLE 1: Preparation and Characterization of Non-doped Monolithic Carbon Foams 
     Non-doped monolithic carbon foams were prepared according to the process shown in  FIG. 1( a )  ( 100 ) and described below. 
     Briefly, OLC nanoparticles (Ketjenblack® EC-600JD, LION Specialty Chemicals Co., Ltd.) of a desired weight (102) were compacted in a mold (104). Subsequently, the compacted OLC nanoparticles were loaded into a SPS chamber, which was then evacuated to subject these nanoparticles to a vacuum (106). Thereafter, the OLC nanoparticles were spark plasma sintered under desired conditions (e.g., a pressure of 110 MPa and a temperature of 600 ° C. for 30 minutes) (108 and 110) to generate a monolithic carbon foam. A conventional paste-based coating process was optionally used to form a thin film (&lt;100 μm) before the SPS process. The pressure in the SPS chamber was then reestablished at atmospheric pressure, after which the monolithic carbon foam was removed from the SPS chamber (112). 
     As illustrated in  FIG. 1( b ) , during the SPS process, the OLC nanoparticles were crushed and restructured through fusing neighboring nanoparticles, thereby resulting in a monolithic carbon foam. More specifically, the uniaxial pressure applied to the OLC nanoparticles during this process induced particle sliding and frictional force between the  nanoparticles, which in turn, led to the crushing and exfoliating of these nanoparticles, thus generating the microporous surface of the monolithic carbon foam. It was unexpected that the localized energy generated by the SPS process induced strong and conductive interparticle bonding in the resulting carbon foam. 
     In general, conventional sintering processes lower the surface area of a sample while increasing its material density. By contrast, as shown in Table 1 below, while the above-described process resulted in monolithic carbon foams having increased densities as compared to OLC nanoparticles, the gravimetric micropore surface and volumetric micropore surface areas of micropore of these foams were unexpectedly higher than those of the nanoparticles. 
     For example, the OLC nanoparticles had a density of 0.1 g/cc and volumetric micropore surface area of 34.6 m 2 /g, whereas a monolithic carbon foam, having a density of 1 g/cc, had a volumetric micropore surface area of 497.47 m 2 /g. In other words, the process of this invention increased the volumetric micropore surface area of the OLC nanoparticles from 34.6 m 2 /cc to 497.47 m 2 /cc, i.e., a 1435% enhancement. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Gravimetric and volumetric surface areas of  
               
               
                 SPS-processed monolithic carbon foams 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 Monolithic 
                 Monolithic 
                 Monolithic 
               
               
                   
                 OLC 
                 carbon 
                 carbon 
                 carbon 
               
               
                   
                 nanoparticles 
                 foam 
                 foam 
                 foam 
               
               
                   
                 (0.1 g/cc) 
                 (0.55 g/cc) 
                 (0.75 g/cc) 
                 (1 g/cc) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 Gravimetric 
                 346.57 
                 453.72 
                 479.25 
                 497.47 
               
               
                 micropore 
                   
                   
                   
                   
               
               
                 surface area 
                   
                   
                   
                   
               
               
                 &lt;2 nm (m 2 /g) 
                   
                   
                   
                   
               
               
                 Gravimetric total 
                 1174 
                 1083 
                 945 
                 857 
               
               
                 surface area 
                   
                   
                   
                   
               
               
                 (m 2 /g) 
                   
                   
                   
                   
               
               
                 Volumetric 
                 34.6 
                 249.546 
                 359.4375 
                 497.47 
               
               
                 micropore 
                   
                   
                   
                   
               
               
                 surface area 
                   
                   
                   
                   
               
               
                 &lt;2 nm (m 2 /cc) 
                   
                   
                   
                   
               
               
                 Volumetric total 
                 117.4 
                 595.65 
                 708.75 
                 857.00 
               
               
                 surface area 
                   
                   
                   
                   
               
               
                 (m 2 /cc) 
               
               
                   
               
            
           
         
       
     
      The above-described process provides monolithic carbon foams having micropores and mesopores at various ratios, which are preferred for different applications. For example, a higher percentage of micropores is preferred for energy storage applications, e.g., supercapacitors, as it maximizes energy density. On the other hand, a greater percentage of mesopores is preferred for applications requiring higher power density, as it permits faster charging and discharging. A suitable combination of micropores and mesopores is crucial for optimizing both the energy density and the power density of a supercapacitor. Through the SPS process, the ratio of micropores and mesopores can be controlled by adjusting the temperature and pressure at which the process is performed. For example, as shown in  FIG. 1( c ) , both the gravimetric and volumetric surface areas of a monolithic carbon foam were enhanced by increasing the temperature, e.g., from 300 ° C. to 700 ° C., at which the SPS process was performed, while keeping the pressure at 80 MPa. 
     A study was performed to compare the mechanical stability of the monolithic carbon foam prepared by the SPS method described above and the carbon foams prepared by three conventional methods, i.e., (1) hot-pressing at 800 ° C. and 40 MPa, (2) cold-pressing at 1 GPa followed by annealing at 800 ° C., and (3) cold-pressing at 1 GPa. More specifically, the SPS-processed monolithic carbon foam and the hot-pressed/cold-pressed monolithic carbon foams were sonicated in isopropyl alcohol (IPA) for 5 minutes (sonication power of 600 W). All three samples containing carbon foams prepared by the conventional methods disintegrated and dispersed, as evidenced by tinting of IPA. By contrast, the sample containing SPS-processed monolithic carbon foam remained clear, indicating that this monolithic carbon foam, mechanically stable, was intact after sonication. 
     To quantify the differences in mechanical stability between monolithic carbon foams prepared by the above-described SPS process and carbon foams prepared by the conventional hot-pressing process, a second study was conducted to measure the Young&#39;s moduli of carbon foams prepared by the six processes: (1) SPS-processed at 600 ° C. and 40 MPa, (2) SPS-processed at 600 ° C. and 120 MPa, (3) SPS-processed at 800 ° C. and 40 MPa, (4) SPS-processed at 800 ° C. and 120 MPa, (5) hot-pressed at 600 ° C. and 40 MPa, and (6) hot-pressed at 800 ° C. and 40 MPa. The results of this study, shown in  FIG. 2( a ) , demonstrate that the SPS-processed monolithic carbon foams unexpectedly had Young&#39;s moduli greater than the hot-pressed carbon foams.  
     The results of these two studies demonstrate the unexpected mechanical stability of SPS-processed monolithic carbon foam of this invention, as compared to carbon foams prepared by prior art methods. 
     A different study was conducted to compare the conductivities and densities of the SPS-processed monolithic carbon foams prepared under three conditions, i.e., 800 ° C. and 20 MPa, 500 ° C. and 40 MPa, and 600 ° C. and 40 MPa, with two conventional hot-pressed carbon foams, i.e., hot-pressed at 800 ° C. and 20 MPa and at 800 ° C. and 40 MPa. The results of this study, shown in Table 2 below and in  FIG. 2( b ) , indicate that the SPS-processed monolithic carbon foams, regardless of preparation conditions, unexpectedly had higher conductivities than the hot-pressed carbon foams. Under the same condition, i.e., 800 ° C. and 20 MPa, the SPS-processed monolithic carbon foams unexpectedly had higher density than the hot-pressed carbon foams. 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Conductivities and densities of SPS-processed monolithic 
               
               
                 carbon foams and hot-pressed monolithic carbon foams 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Hot- 
                 Hot- 
                 SPS- 
                 SPS- 
                 SPS-  
               
               
                   
                 pressed 
                 pressed 
                 processed 
                 processed 
                 processed 
               
               
                   
                 (800° C., 
                 (800° C., 
                 (800° C., 20 
                 (500° C., 
                 (600° C., 
               
               
                   
                 20 MPa) 
                 40 MPa) 
                 20 MPa) 
                 40 MPa) 
                 40 MPa) 
               
               
                   
               
               
                 Density 
                  0.429 
                  0.58 
                 0.5 
                  0.55 
                  0.58 
               
               
                 (g/cc) 
                   
                   
                   
                   
                   
               
               
                 Conductivity 
                 23.94 
                 32.12 
                 39.31 
                 40   
                 42   
               
               
                 (S/cm) 
               
               
                   
               
            
           
         
       
     
     The monolithic carbon foam can be used as an electrode for supercapacitors that do not contain conductive additives and binders. OLC nanoparticles were compacted in a mold. Subsequently, the compacted OLC nanoparticles were loaded into a SPS chamber, which was then evacuated to subject these nanoparticles to a vacuum. Thereafter, the OLC nanoparticles were spark plasma sintered under a pressure of 30 MPa and a temperature of 600 ° C. for 10 minutes Eliminating conductive additives and binders from an electrode is desirable, as they reduce energy density and hinder performance severely.  FIG. 3  shows an exemplary pouch-cell type supercapacitor containing a monolithic carbon foam electrode (or a fractal carbon foam, preparation of which is described in EXAMPLE 2 below). The supercapacitor was constructed based on a commercial laboratory test setup for supercapacitor analysis. 
     The capacitance retention of an exemplary supercapacitor, indicative of its lifetime, was compared to a commercial supercapacitor having a binder-based paste coated activated  carbon electrode (3.0 V, 70 ° C., SBPBF4/PC electrolyte). The results are shown in Table 3 below. Of note, capacitance retention was calculated by: 
     
       
         
           
             
               
                 Capacitance 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 after 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 reliability 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   test 
                   ⁡ 
                   
                     ( 
                     
                       F 
                       g 
                     
                     ) 
                   
                 
               
               
                 Capacitance 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 of 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 As 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 prepared 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   device 
                   ⁡ 
                   
                     ( 
                     
                       F 
                       g 
                     
                     ) 
                   
                 
               
             
             × 
             1 
             ⁢ 
             0 
             ⁢ 
             0 
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Capacitance retention for  
               
               
                 supercapacitors containing SPS-processed  
               
               
                 monolithic carbon foam or activated carbon 
               
            
           
           
               
               
            
               
                   
                 Load time (hrs.) 
               
            
           
           
               
               
               
               
               
            
               
                 Supercapacitor 
                 0 
                 150 
                 300 
                 500 
               
               
                   
               
               
                 SPS-processed 
                 100 
                 102 
                 100 
                 100 
               
               
                 monolithic carbon 
                   
                   
                   
                   
               
               
                 foam (%) 
                   
                   
                   
                   
               
               
                 Activated carbon (%) 
                 100 
                  85 
                  82 
                  80 
               
               
                   
               
            
           
         
       
     
     As shown in Table 3 above, after a 500-hour reliability test conducted at 3.0 V and 70° C., the supercapacitor containing the monolithic carbon foam unexpectedly had a capacity retention of 100%, whereas the activated carbon device had a capacity retention of only 80%. These results indicate that, unlike the commercial supercapacitor, the monolithic carbon foam-containing supercapacitor is suitable for use at a rated voltage of 3.0 V. 
     EXAMPLE 2: Preparation and Characterization of a Fractal Carbon Foam 
     A fractal carbon foam was prepared by a procedure adapted from that used to prepare monolithic carbon foams set forth in EXAMPLE 1 above. 
     More specifically, a monolithic carbon foam was crushed into a powder having a grain size of a few hundred nanometers to a few microns. The monolithic carbon foam powder was then subjected to the SPS process described in EXAMPLE 1. 
     The fractal carbon foam thus prepared had an interconnected hierarchical pore structure, in which macropores were connected to the mesopores and micropores contained in the monolithic carbon foam powder. Compared to the pore structure of the monolithic carbon foam shown in  FIG. 4( a ) , which did not contain a macropore-network, the pore structure of the fractal carbon foam shown in  FIG. 4( b )  included macropore-network that provided a greater pore accessibility. The greater pore accessibility of the fractal carbon  foam facilitated diffusion of ions and molecules. Indeed, Nyquist plots of a 100 μm monolithic graphene foam (“MGF”) electrode and a 100 μm fractal graphene foam (“FGF”) electrode (see  FIG. 5 , inset) show that the diffusion speed of ions was faster in the FGF electrode, as evidenced by the steeper slope of its Nyquist plot. 
     A study was conducted to compare the device performance of supercapacitors containing different electrode materials, i.e., monolithic graphene foam, fractal graphene foam, activated carbon, edge free carbon, and reduced carbon oxide (“rGO”). The results are shown in  FIG. 5 , a Ragone plot. It was found that the fractal graphene foam, while having lower energy as compared to the monolithic graphene foam, had a higher power density due to its greater pore accessibility. Importantly, both the fractal graphene foam and the monolithic graphene foam had higher energy and power densities as compared to activated carbon, edge free carbon, and rGO. In other words, the carbon foams of this invention, both monolithic and fractal, are unexpectedly superior to the other carbon materials in supercapacitor applications. 
     EXAMPLE 3: Preparation and Characterization of Hybrid Monolithic Carbon Foams 
     Two hybrid monolithic carbon foams, i.e., a MoS 2 /carbon hybrid monolithic carbon foam and a Si/carbon hybrid monolithic carbon foam were prepared via procedures described below. 
     For the MoS2/carbon hybrid monolithic carbon foam, a MoS2/carbon precursor material containing Ketjenblack (AkzoNobel; EC600 grade) and MoS2 was first prepared. Briefly, 10 mg of Ketjenblack and 20 mg of ammonium tetrathiomolybdate (Sigma-Aldrich) were respectively dispersed in 10 mL and 2 mL of N,N-dimethylformamide (“DMF”). Both dispersions were sonicated for 30 minutes, mixed together, and then sonicated for 2 hours to allow for the Ketjenblack to be thoroughly impregnated with ammonium tetrathiomolybdate. The resulting solution was transferred into a 25 mL Teflon-lined stainless steel autoclave and tightly sealed. The autoclave was heated at 200 ° C. for 15 hours and allowed to cool to room temperature. The resulting MoS2/carbon precursor material was collected by centrifugation and washed with several aliquots of ethanol and deionized water. The washed precursor material was dried overnight in an oven at 60° C. 
     To obtain the MoS 2 /carbon hybrid monolithic carbon foam, a spray-gun was connected with a nitrogen gas supply and mounted at 10 cm from the tip of the nozzle above a hotplate, where Mo circular foils (Alfa Aesar; 14 mm diameter, effective area 1.4 cm 2 )  were secured with heat resistance tape. The Mo foils were used as current collectors. The MoS2/carbon precursor material was dispersed in DMF and used as the feedstock for spraying. The hotplate was heated at 190 ° C. to dry the Mo foils. Mass loading of up to 1 mg/cm 2  was obtained by varying the duration of spraying. To perform the SPS process, the electrodes were sandwiched between graphite foils then loaded into a tungsten carbide mold. SPS was conducted at 500 ° C. and 600 ° C. with a uniaxial pressure of 2-30 MPa for 30 minutes under vacuum. The mold was cooled rapidly afterwards with the cooling water system in the furnace, after which the hybrid monolithic carbon foam thus formed was removed from it. The resulting MoS2/carbon hybrid monolithic carbon foam was characterized by Raman spectroscopy, which confirmed the presence of both MoS2 and carbon in the foam. See  FIG. 6 . 
     For the Si/carbon monolithic carbon foam, a precursor solution containing Si nanoparticles (“SiNP”), trimethoxymethylsilane (“TMMS”), and Ketjenblack was first prepared prior to the SPS process. More specifically, 20 mg Si nanopowder (US Research Nanomaterials, Inc.; diameter =30-50 nm) was dispersed in 40 ml ethanol by batch sonication for 2 hours, after which 1 mL of TMMS (Sigma Aldrich; 98%) was added to the solution and sonicated for 1 hour. Subsequently, 6.6 mg of Ketjenblack (AkzoNobel; EC600 grade) was dispersed in 40 ml of isopropyl alcohol (“IPA”) for 2 hours to obtain a homogeneous solution. The two solutions were then mixed together and sonicated for 1 hour to obtain a well-dispersed SiNP/TMMS/Ketjenblack precursor solution. 
     To obtain the Si/carbon hybrid monolithic carbon foam, Mo circular foils (Alfa Aesar; 14 mm diameter, effective area 1.4 cm 2 ) were placed on a hotplate heated set to 50 ° C. A spray-gun was then connected with a nitrogen gas supply and mounted at 10 cm (from the tip of the nozzle) above the hotplate. The SiNP/TMMS/Ketjenblack precursor solution was slowly sprayed on the Mo foil to drive out ethanol and IPA, thereby obtaining a Si/Ketjenblack films on the foil. The Si/Ketjenblack films were then subjected to the SPS process, which was performed at 800 ° C. and a uniaxial pressure of 2-30 MPa for 30 minutes under vacuum. 
     The cycling performance of the two hybrid monolithic carbon foams as electrodes in Li-ion batteries were tested. It was found that these two hybrid foams unexpectedly retained high capacity after as many as 800 cycles, indicating that these materials are excellent electrode materials for Li-ion battery applications.  
     OTHER EMBODIMENTS 
     All of the features disclosed in this specification may be combined in any combination. Each feature disclosed in this specification may be replaced by an alternative feature serving the same, equivalent, or similar purpose. Thus, unless expressly stated otherwise, each feature disclosed is only an example of a generic series of equivalent or similar features. 
     Further, from the above description, one skilled in the art can easily ascertain the essential characteristics of the present invention, and without departing from the spirit and scope thereof, can make various changes and modifications of the invention to adapt it to various usages and conditions. Thus, other embodiments are also within the claims.