Patent Publication Number: US-2023163303-A1

Title: Power storage device and electrode for power storage device

Description:
CROSS REFERENCES TO RELATED APPLICATIONS 
     The present application is a U.S. National Phase Application under 35 U.S.C. § 371 of International Patent Application No. PCT/JP2021/014103, filed Apr. 1, 2021, which claims priority of Japanese Patent Application Nos. 2021-005803, filed Jan. 18, 2021, and 2020-066211, filed Apr. 1, 2020. The entire contents of which are hereby incorporated by reference. 
    
    
     TECHNICAL FIELD 
     The technical field of the present specification relates to a power storage device and an electrode for power storage device, using a carbon material(s). 
     BACKGROUND 
     Secondary batteries, electric double layered capacitors, and the like can be listed as chargeable and dischargeable power storage devices. Moreover, lithium-ion secondary batteries, lithium-ion primary batteries, and lithium-ion capacitors can be listed as power storage devices using lithium ions, for example. 
     For example, JP 2668678 discloses a lithium-ion secondary battery including a positive electrode, a negative electrode, a separator, and a nonaqueous electrolytic solution. A technology using lithium cobaltate or lithium nickelate as the positive-electrode active material and using carbon as the negative-electrode active material is a disclosed (in the scope of claims and working examples in Patent Literature 1). Graphite is used as the carbon material in many cases. Graphite can occlude or release one lithium ion per six carbon atoms in a six-membered ring. 
     SUMMARY Currently, the maximum weight energy density of lithium-ion secondary batteries is approximately 250 Wh/kg. If the weight energy density of the secondary battery is improved, for example, an output power and a cruising range of an electric vehicle will be improved. Moreover, long duration operation of electronic devices can also be realized. For that purpose, it is preferable that the positive-electrode active material or negative-electrode active material can occlude or release more lithium ions. Alternatively, it is preferable to be able to involve more lithium ions or lithium atoms in chemical reactions even by methods except for occlusion or release. 
     The problem to be solved by the technology disclosed herein is to provide an electrode for power storage device and a power storage device that make it possible to involve more lithium ions in a charge-discharge reaction. 
     An electrode for power storage device in a first aspect includes a current collector and an active material layer on the current collector. The active material layer includes a carbon nanowall. The carbon nanowall is capable of involving, in a charge-discharge reaction, two or more lithium ions per carbon atom in a single charge or discharge. 
     The present electrode for power storage device includes a carbon nanowall. The carbon nanowall is capable of involving, in a charge-discharge reaction, two or more lithium ions per carbon atom in a single charge or discharge. 
     In contrast, graphite used for conventional electrodes can occlude or release one lithium ion per six carbon atoms in a six-membered ring. More specifically, graphite can occlude or release one lithium ion per six carbon atoms. 
     The electrode for power storage device using the carbon nanowall can involve 12 times or more lithium ions in the charge-discharge reaction as compared with the electrode using graphite. Therefore, the power storage device including the electrode using the carbon nanowall has excellent volume energy density and weight energy density. Accordingly, the present power storage device can operate electronic devices, home electronics, vehicles, and the like over a long duration with a single charge. 
     Provided herein are the electrode for power storage device and the power storage device that make it possible to involve more lithium ions in the charge-discharge reaction. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG.  1    is a schematic structure diagram illustrating a lithium-ion secondary battery LiB 1  according to a first embodiment. 
         FIG.  2    is a diagram conceptually illustrating a structure of a carbon nanowall CNW 1  in the lithium-ion secondary battery LiB 1  according to the first embodiment. 
         FIG.  3    is a diagram schematically illustrating a cross section of the carbon nanowall CNW 1  in the lithium-ion secondary battery LiB 1  according to the first embodiment. 
         FIG.  4    is a diagram schematically illustrating an inclination of the carbon nanowall in the lithium-ion secondary battery LiB 1  according to the first embodiment. 
         FIG.  5    is a diagram illustrating the carbon nanowall in the lithium-ion secondary battery LiB 1  according to the first embodiment viewed in a perpendicular orientation from a surface of a negative electrode current collector N 1 . 
         FIG.  6    is a diagram for describing a case where an average angle θ between the first surface N 1   a  of the negative electrode current collector N 1  and the carbon nanowall is small. 
         FIG.  7    is a diagram hypothetically illustrating an aspect of an occlusion of lithium ions and a deposition of lithium or lithium compounds by the carbon nanowall CNW 1  in the lithium-ion secondary battery LiB 1  according to the first embodiment. 
         FIG.  8    is a schematic structure diagram illustrating a configuration of a manufacturing apparatus for growing the carbon nanowall CNW 1  in the lithium-ion secondary battery LiB 1  according to the first embodiment. 
         FIG.  9    is a schematic structure diagram illustrating a lithium-ion capacitor LiC 1  according to a second embodiment. 
         FIG.  10    is a schematic structure diagram illustrating a lithium-ion capacitor LiC 2  of a modified example according to the second embodiment. 
         FIG.  11    shows a microphotograph of carbon nanowalls viewed from a direction perpendicular to a plate surface of a metal plate. 
         FIG.  12    shows a microphotograph of the carbon nanowalls illustrating a cross section thereof perpendicular to the plate surface of the metal plate. 
         FIG.  13    is a graphic chart illustrating a relationship between capacity and voltage of a lithium-ion secondary battery using a carbon nanowall with a height of 1 μm for the negative electrode. 
         FIG.  14    is a graphic chart illustrating a relationship between capacity and voltage of a lithium-ion secondary battery using a carbon nanowall with a height of 4 μm for the negative electrode. 
         FIG.  15    is a graphic chart illustrating a relationship between capacity and voltage of a lithium-ion secondary battery using a carbon nanowall with a height of 10 μm for the negative electrode. 
         FIG.  16    is a graphic chart illustrating a relationship between capacity and voltage of a lithium-ion secondary battery using graphite for the negative electrode. 
         FIG.  17    is a diagram for comparing charging voltages of lithium-ion secondary batteries in a case of using the carbon nanowall for the negative electrode and using graphite for the negative electrode. 
         FIG.  18    is a graphic chart illustrating discharging characteristics of a lithium-ion secondary battery using a negative electrode including a carbon nanowall with a height of 0 nm. 
         FIG.  19    is a graphic chart illustrating discharging characteristics of a lithium-ion secondary battery using a negative electrode including a carbon nanowall with a height of 20 nm. 
         FIG.  20    is a graphic chart illustrating discharging characteristics of a lithium-ion secondary battery using a negative electrode including a carbon nanowall with a height of 50 nm. 
         FIG.  21    is a graphic chart illustrating discharging characteristics of a lithium-ion secondary battery using a negative electrode including a carbon nanowall with a height of 100 nm. 
         FIG.  22    is a graphic chart illustrating discharging characteristics of a lithium-ion secondary battery using a negative electrode including a carbon nanowall with a height of 200 nm. 
         FIG.  23    is a graphic chart illustrating discharging characteristics of a lithium-ion secondary battery using a negative electrode including a carbon nanowall with a height of 500 nm. 
         FIG.  24    is a scanning electron micrograph illustrating a surface of the carbon nanowall with a height of 500 nm. 
         FIG.  25    is a scanning electron micrograph illustrating a cross section of the carbon nanowall with the height of 500 nm. 
         FIG.  26    is a scanning electron micrograph illustrating a surface of the carbon nanowall with a height of 50 nm. 
         FIG.  27    is a scanning electron micrograph illustrating a cross section of the carbon nanowall with the height of 50 nm. 
         FIG.  28    is a scanning electron micrograph (Part 1) illustrating a carbon nanowall after repeating charging and discharging. 
         FIG.  29    is a scanning electron micrograph (Part 2) illustrating the carbon nanowall after repeating charging and discharging. 
         FIG.  30    is a scanning electron micrograph (Part 3) illustrating the carbon nanowall after repeating charging and discharging. 
         FIG.  31    is a scanning electron micrograph illustrating a cross section of a negative electrode in the lithium-ion secondary battery after charging. 
         FIG.  32    is a graphic chart illustrating an X-ray diffraction result of the negative electrode in the lithium-ion secondary battery after charging. 
     
    
    
     DETAILED DESCRIPTION 
     Hereinafter, specific embodiments will now be described with reference to the drawings, listing an electrode for power storage device and a power storage device as examples. In this specification, a power storage device is a device that can be charged and discharged. The power storage devices include lithium-ion primary batteries, lithium-ion secondary batteries, lithium-ion capacitors, and other devices that are charged and discharged using lithium ions. 
     First Embodiment 
     1. Lithium-Ion Secondary Battery 
       FIG.  1    is a schematic structure diagram illustrating a lithium-ion secondary battery LiB 1  according to the first embodiment. The lithium-ion secondary battery LiB 1  includes a positive electrode PE, a negative electrode NE, a separator Sp 1 , an electrolytic solution ES 1 , and a vessel V 1 . 
     The positive electrode PE is a positive electrode of the lithium-ion secondary battery LiB 1 . The positive electrode PE includes a positive electrode current collector P 1  and a positive electrode active material layer P 2 . A positive electrode active material layer P 2  is formed on each of a first surface P 1   a  and a second surface P 1   b  of the positive electrode current collector P 1 . 
     The positive electrode current collector P 1  is, for example, a metallic foil. The shape of the positive electrode current collector P 1  may be any other shape. A material of the positive electrode current collector P 1  is, for example, Al or Ti. The material of the positive electrode current collector P 1  may be an electric conductor, such as any other metal. 
     The positive electrode active material layer P 2  contains a positive-electrode active material, a conductive auxiliary agent, and a binder. The positive electrode active material layer P 2  may contain a thickening agent or the like. For example, lithium cobaltate, lithium manganate, lithium nickelate, and a ternary system are listed as the positive-electrode active material. For example, carbon black is listed as the conductive auxiliary agent. For example, SBR is listed as the binder. For example, carboxymethylcellulose is listed as the thickening agent. Thus, the positive electrode active material layer P 2  includes lithium atoms. 
     The negative electrode NE is a negative electrode of the lithium-ion secondary battery LiB 1 . The negative electrode NE includes a negative electrode current collector N 1  and a negative electrode active material layer N 2 . A negative electrode active material layer N 2  is formed on each of a first surface Nla and a second surface Nib of the negative electrode current collector N 1 . 
     The negative electrode current collector N 1  is, for example, a metallic foil. The shape of the negative electrode current collector N 1  may be any other shape. A material of the negative electrode current collector N 1  is, for example, Cu. The material of the negative electrode current collector N 1  may be an electric conductor, such as any other metal. 
     The negative electrode active material layer N 2  contains a negative-electrode active material. The negative electrode active material layer N 2  includes a carbon nanowall CNW 1  as the negative-electrode active material. The carbon nanowall CNW 1  will be described below. 
     The separator Sp 1  is used for electrically insulating between the positive electrode PE and the negative electrode NE. The separator Sp 1  allows the lithium ions in the electrolytic solution ES 1  to permeate therethrough. 
     The electrolytic solution ES 1  has a property of transferring the lithium ions between the positive electrode PE and the negative electrode NE. The Electrolytic solution ES 1  fills the vessel V 1 . Electrolytic solution ES 1  is a liquid obtained by dissolving, for example, a lithium salt, such as lithium hexafluorophosphate (LiPF 6 ), in dimethyl carbonate (DMC), diethyl carbonate (DEC), ethyl methyl carbonate (EMC), or the like. 
     The vessel V 1  accommodates the positive electrode PE, the negative electrode NE, the separator Sp 1 , and the electrolytic solution ES 1  therein. The vessel V 1  includes a material that cannot easily react with the electrolytic solution ES 1 . 
     2. Carbon Nanowall 
     In this specification, the carbon nanowall is a conductive nanostructure mainly composed of carbon atoms arranged in a wall-like configuration on a base material, such as the negative electrode current collector N 1 . 
       FIG.  2    is a diagram conceptually illustrating a structure of a carbon nanowall CNW 1  in the lithium-ion secondary battery LiB 1  according to the first embodiment. In  FIG.  2   , one graphene sheet GS 10  is conceptually illustrated. The carbon nanowall CNW 1  has electrical conductivity. The carbon nanowall CNW 1  may be composed a plurality of graphene sheets GS 1 . The graphene sheet GS 1  may be a thin film mainly composed of carbon having a six-membered ring structure, instead of a complete graphene structure. The graphene sheet GS 1  may have a mosaic structure mainly composed of carbon having a six-membered ring structure. The mosaic structure is a structure where a plurality of regions having a six-membered ring structure are discretely arranged. That is, the carbon nanowall CNW 1  does not have to be an all-single crystal in a six-membered ring. 
     The negative electrode NE includes a negative electrode current collector N 1  and a negative electrode active material layer N 2 . The negative electrode active material layer N 2  includes an amorphous carbon layer AC 10  and the carbon nanowall CNW 1 . 
     The carbon nanowall CNW 1  is a graphite-like substance in which around ten layers of the graphene sheets GS 1  are stacked in a thickness direction of the carbon nanowall CNW 1 . The stacked number thereof may be other than the above-described number. Since the carbon nanowall CNW 1  is a graphite-like substance, the carbon nanowall CNW 1  has higher electric conductivity than that of carbon materials, such as activated carbon. 
     The amorphous carbon layer AC 1  is located between the negative electrode current collector N 1  which is electric conductor, such as a metal and the carbon nanowall CNW 1 . The amorphous carbon layer AC 1  is a layer that can be a starting point of growth of the graphene sheet GS 1  composing the carbon nanowall CNW 1 . The film thickness of the amorphous carbon layer AC 1  is, for example, equal to or grater than 10 nm and equal to or less than 300 nm. Preferably, the film thickness thereof is equal to or grater than 10 nm and equal to or less than 100 nm. More preferably, the film thickness thereof is equal to or grater than 12 nm and equal to or less than 30 nm. It is to be noted that the amorphous carbon layer AC 1  may not be necessary depending on a growing method of the carbon nanowall. The amorphous carbon layer AC 1  is electrically conductive. 
     The carbon nanowall CNW 1  has a root portion R 1  at a side of t the negative electrode current collector N 1  and an end portion El at a side opposite to the negative electrode current collector N 1 . The root portion R 1  is a fixed portion that is being fixed to the negative electrode current collector N 1  through the amorphous carbon layer AC 1  in many cases. The root portion R 1  is also a connection portion that is being electrically connected to the negative electrode current collector N 1  or the amorphous carbon layer AC 1 . 
     In the carbon nanowall CNW 1 , the graphene sheet GS 1  is formed in an orientation that intersects the surfaces (the first surface N 1   a  and the second surface Nib) of the negative electrode current collector N 1 . In  FIG.  2   , the graphene sheet GS 1  and the negative electrode current collector N 1  are substantially perpendicular to each other. Therefore, the end of the graphene sheet GS 1  has the end portion El. The end portion El is a portion located at the end of the graphene sheet GS 1 . 
     As described above, the carbon nanowall CNW 1  is a graphite obtained by stacking many graphene sheets GS 1 . In fact, the graphene sheets GS 1  are not always completely extended in parallel to each other. Since the graphene sheets GS 1  grow in different directions in each initial growth nucleus, the graphene sheets GS 1  actually have a randomly merged and superimposed shape (refer to  FIG.  11   ). As illustrated in  FIG.  2   , a distance between the graphite having the wall-like configuration adjacent to each other is referred to as a wall spacing. 
     The average wall spacing D 1  which is the average value of the wall spacing is related to a density of the carbon nanowall CNW 1 . That is, the wider the average wall spacing D 1 , the lower the density of the carbon nanowall CNW 1 . Conversely, the narrower the average wall spacing D 1 , the denser the carbon nanowall CNW 1 . 
     2-1. Wall Size 
       FIG.  3    is a diagram schematically illustrating a cross section of the carbon nanowall CNW 1  in the lithium-ion secondary battery LiB 1  according to the first embodiment. The average height H 1  of the carbon nanowall CNW 1  is preferably equal to or grater than 100 nm. Alternatively, the average height H 1  of the carbon nanowall CNW 1  may be equal to or grater than 200 nm. When the average height H 1  of the carbon nanowall CNW 1  is equal to or grater than 100 nm, lithium easily deposits starting from the carbon nanowall CNW 1 . 
     There is no problem even if the average height H 1  of the carbon nanowall CNW 1  is high. However, it requires a long time in order to form such a high carbon nanowall CNW 1 . From the viewpoint of productivity enhancement, the average height H 1  of the carbon nanowall CNW 1  is preferably equal to or less than 200 μm. Preferably, the average height thereof is equal to or less than 100 μm. More preferably, the average height thereof is equal to or less than 50 μm. Still more preferably, the average height thereof is equal to or less than 10 μm. 
     Accordingly, the average height H 1  of the carbon nanowall CNW 1  is, for example, equal to or grater than 100 nm and equal to or less than 200 μm. Preferably, the average height thereof is equal to or grater than 100 nm and equal to or less than 50 μm. More preferably, the average height thereof is equal to or grater than 100 nm and equal to or less than 10 μm. Alternatively, the average height H 1  of the carbon nanowall CNW 1  may be equal to or grater than 200 nm and equal to or less than 200 μm. Alternatively, the average height thereof may be equal to or grater than 200 nm and equal to or less than 100 μm. Alternatively, the average height thereof may be equal to or grater than 200 nm and equal to or less than 10 μm. 
     The average thickness W 1  of the carbon nanowall CNW 1  is equal to or grater than 0.5 nm and equal to or less than 100 nm. Preferably, the average thickness thereof is equal to or grater than 1 nm and equal to or less than 50 nm. More preferably, the average thickness thereof is equal to or grater than 1.5 nm and equal to or less than 30 nm. 
     A layer spacing of the graphite is approximately 0.35 nm. Therefore, the thickness of the carbon nanowall CNW 1  composed of ten layers of the graphene sheets GS 1  is approximately 3.5 nm. Dependent on manufacturing conditions, it is considered that the average thickness of the carbon nanowall CNW 1  is approximately 3.5 nm. Typically, it is considered that the carbon nanowall CNW 1  may be composed of 5 to 20 layers of the graphene sheets GS 1 . The thickness of the carbon nanowall CNW 1  is equal to or grater than 1.5 nm and equal to or less than 7 nm. 
     2-2. Wall Spacing 
     The average wall spacing D 1  between the carbon nanowall CNW 1  and the carbon nanowall CNW 1  adjacent to each other is, for example, equal to or grater than 10 nm and equal to or less than 500 nm. Preferably, the average wall spacing thereof is equal to or grater than 15 nm and equal to or less than 100 nm. More preferably, the average wall spacing thereof is equal to or grater than 20 nm and equal to or less than 50 nm. These numerical value ranges may merely be exemplifications and may be numerical values other than above values. It is noted that long walls of the carbon nanowalls do not necessarily grow in parallel to each other, and the walls may merge with each other (refer to  FIG.  11   ). Therefore, the spacing between the carbon nanowalls CNW 1  near this merging portion is narrower than the spacing between the carbon nanowalls CNW 1  at other portions. 
     2-3. Wall Angle 
       FIG.  4    is a diagram schematically illustrating an inclination of the carbon nanowall in the lithium-ion secondary battery LiB 1  according to the first embodiment.  FIG.  4    illustrates a case where the carbon nanowalls CNW 1  are projected onto the first surface N 1   a  of the negative electrode current collector N 1 . 
     A projection region PR 1  where a carbon nanowall CNW 1 ( a ) is projected onto the first surface N 1   a  of the negative electrode current collector N 1  does not include a carbon nanowalls CNW 1 ( b ) except for the carbon nanowall CNW 1 ( a ). However, this is not the case at the merging portion between the carbon nanowalls CNW 1 . The electrolytic solution and the lithium ions need only be able to enter a minute region partitioned by the merging the carbon nanowalls CNW 1 . If the electrolytic solution and a lithium ions can enter the minute region partitioned by the carbon nanowalls CNW 1 , reactions required for an operation of battery will occur in the minute region. 
     As illustrated in  FIG.  4   , an intermediate region PR 2  exists between the projection region PR 1  and the projection region PR 1 . The intermediate region PR 2  is a visible region that can be observed by an observer with a scanning electron microscope (SEM) or the like, when the negative electrode current collector N 1  is viewed from an orientation of the arrow J 1  illustrated in  FIG.  4   . Herein, the orientation of the arrow J 1  in illustrated  FIG.  4    is an orientation perpendicular to the first surface N 1   a  of the negative electrode current collector N 1 . 
     The average angle θ between the first surface Nla of the negative electrode current collector N 1  and the carbon nanowall CNW 1  is equal to or grater than 80° and equal to or less than 90°. The average angle θ disclosed herein is the average value of angles of equal to or less than 90°. If one angle θ1 formed between the carbon nanowall and the negative electrode current collector N 1  is an acute angle, the other angle θ2 is an obtuse angle. Among these angles, the average angle θ is obtained by averaging the smaller angles θ1. 
     By arranging each carbon nanowall so as to substantially perpendicularly grow, since the carbon nanowalls do not in contact with each other at the end portions El of the carbon nanowalls, and thereby the electrolytic solution and the lithium ions can enter between the carbon nanowalls. Therefore, the entire carbon nanowall can effectively function as an electrode. 
     However, this is not the case in the vicinity of where the carbon nanowalls merge with each other. When the carbon nanowalls are formed on a substrate having a large area, there may be some portions where the carbon nanowalls in contact with each other at the end portions El of the carbon nanowalls, but this does not degrade the overall functionality. 
     The average angle θ is determined by growth conditions of the carbon nanowalls, and therefore the average height H 1  and the average wall spacing D 1  of the carbon nanowalls should be set so that the carbon nanowalls do not in contact with each other at the upper edge of the carbon nanowall due to the average angle θ. Depending on the values of the average height H 1  and the average wall spacing D 1 , the electrolytic solution and the lithium ions cannot enter gaps between the carbon nanowalls, and therefore some of the carbon nanowalls cannot function as the electrode. 
     For example, when the average height H 1  is 5 μm and the average wall spacing D 1  is 100 nm of the carbon nanowalls, an angle of equal to or grater than 88.9° is required to avoid in contact with adjacent perpendicular walls. Alternatively, when the average height H 1  is 0.6 μm and the average wall spacing D 1  is 100 nm of the carbon nanowalls, an angle of equal to or greater than 80.4° is required to avoid in contact with adjacent perpendicular walls. 
     Table 1 illustrates numerical values indicating a structure of the carbon nanowalls CNW 1 . However, these numerical value ranges may merely be exemplifications and are not limited to these numerical value ranges. 
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
             
            
               
                   
                 Wall Height 
                 100 nm or more 
                 200 μm or less 
               
               
                   
                 Wall Thickness 
                 0.5 nm or more 
                 100 nm or less 
               
               
                   
                 Wall Spacing 
                 10 nm or more 
                 500 nm or less 
               
               
                   
                 Wall Angle 
                 80° or more 
                 90° or less 
               
               
                   
                   
               
            
           
         
       
     
     2-4. Surface Area of Carbon Nanowall 
     A surface area of the carbon nanowall CNW 1  will now be described. For simplicity of understanding, a shape of the carbon nanowall is assumed to be a grid shape. Since the wall rarely extends linearly, the shape of the carbon nanowall actually deviates from the grid shape. 
       FIG.  5    is a diagram illustrating the carbon nanowall in the lithium-ion secondary battery LiB 1  according to the first embodiment viewed in a perpendicular orientation from a surface of a negative electrode current collector N 1 . In  FIG.  5   , the shape of the carbon nanowall is assumed to be a grid shape as described above. 
     Assuming that the spacing I 1  of a pitch of the carbon nanowalls, the area SS1 of a square with the spacing I 1  on one side is I 1   2 . The area SS1 is a surface area of a carbon material when the surface of a negative electrode current collector N 1  is solidly coated with the carbon material, instead of the carbon nanowall. In  FIG.  5   , the area SS2 of the side surface of the carbon nanowall occupying a square of which one side is the spacing I 1 , which is a repeat unit, is expressed by the following equation. 
     
       
         
           
             
               
                 
                   
                     SS 
                     ⁢ 
                     2 
                   
                   = 
                   
                     8 
                     × 
                     
                       ( 
                       
                         D 
                         ⁢ 
                         1 
                         / 
                         2 
                       
                       ) 
                     
                     × 
                     H 
                     ⁢ 
                     1 
                   
                 
               
             
             
               
                 
                   = 
                   
                     4 
                     × 
                     D 
                     ⁢ 
                     1 
                     × 
                     H 
                     ⁢ 
                     1 
                   
                 
               
             
           
         
       
     
     where H 1  is the average height of the carbon nanowall and 
     D 1  is the average wall spacing. 
     The surface area SS3 of the carbon nanowall in the square region of which one side is the spacing I 1  in the case of existing the carbon nanowall is expressed by the following equation. 
         SS 3= SS 1+ SS 2 
     Accordingly, the ratio SS3/SS1 indicates an increasing rate of the surface area depending on the presence or absence of the carbon nanowall. 
     
       
         
           
             
               
                 
                   
                     
                       SS 
                       ⁢ 
                       3 
                       / 
                       SS 
                       ⁢ 
                       1 
                     
                       
                     = 
                     
                       
                         ( 
                         
                           4 
                           × 
                           D 
                           ⁢ 
                           1 
                           × 
                           H 
                           ⁢ 
                           1 
                           × 
                           I 
                           ⁢ 
                           
                             1 
                             2 
                           
                         
                         ) 
                       
                       / 
                       I 
                       ⁢ 
                       
                         1 
                         2 
                       
                     
                   
                 
               
               
                 
                   
                       
                     
                       ≠ 
                       
                         4 
                         × 
                         D 
                         ⁢ 
                         1 
                         × 
                         H 
                         ⁢ 
                         1 
                         / 
                         I 
                         ⁢ 
                         
                           1 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   
                       
                     
                       ≠ 
                       
                         4 
                         × 
                         H 
                         ⁢ 
                         1 
                         / 
                         D 
                         ⁢ 
                         1 
                       
                     
                   
                 
               
             
             ⁢ 
             
 
             
               
                 where 
                 ⁢ 
                     
                 H 
                 ⁢ 
                 1 
                     
                 &gt;&gt; 
                     
                 I 
                 ⁢ 
                 1 
                 ⁢ 
                     
                 and 
                 ⁢ 
                     
                 D 
                 ⁢ 
                 1 
               
               ≠ 
               
                 I 
                   
                 1. 
               
             
           
         
       
     
     Thus, the higher the height of the carbon nanowalls and the narrower the spacing between the carbon nanowalls, the larger the surface area of the carbon material of the lithium-ion secondary battery LiB 1 . 
     Table 2 is a table illustrating a relationship between the size and angle of the carbon nanowall and the increasing rate of the surface area. It is considered that the larger the surface area of the carbon nanowalls, the larger the number of lithium ions that react on the surface of the active material layer. Therefore, it is considered that the larger the surface area of the carbon nanowalls, the faster the charge and discharge rate of the lithium-ion secondary battery LiB 1 . 
     As illustrated in Table 2, when the average angle θ between the first surface N 1   a  of the negative electrode current collector N 1  and the carbon nanowall is equal to or greater than 80° and equal to or less than 90°, the surface area of the carbon material in the lithium-ion secondary battery LiB 1  can be increased equal to or greater than 20 times. Preferably, the average angle θ is equal to or greater than 83°. More preferably, the average angle θ is equal to or greater than 85°. Still more preferably, the average angle θ is equal to or greater than 88°. Moreover, in the case of equal to or greater than 89°, the increasing rate of the surface area is equal to or greater than approximately 400 times. 
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 Wall Height 
                 Wall 
                 Wall 
                 Increasing 
               
               
                   
                 Rate of 
                 Spacing 
                 Angle 
                 Surface Area 
               
               
                   
                 (μm) 
                 (nm) 
                 (°) 
                 (times) 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 1.0 
                 200 
                 78.5 
                 20 
               
               
                   
                 1.0 
                 50 
                 87.1 
                 80 
               
               
                   
                 2.0 
                 400 
                 78.5 
                 20 
               
               
                   
                 2.0 
                 50 
                 88.6 
                 160 
               
               
                   
                 5.0 
                 500 
                 84.3 
                 40 
               
               
                   
                 5.0 
                 50 
                 89.4 
                 400 
               
               
                   
                 10.0 
                 50 
                 89.7 
                 800 
               
               
                   
                 10.0 
                 20 
                 89.9 
                 2000 
               
               
                   
                 20.0 
                 50 
                 89.9 
                 1600 
               
               
                   
                 20.0 
                 20 
                 89.9 
                 4000 
               
               
                   
                 30.0 
                 50 
                 89.9 
                 2400 
               
               
                   
                 30.0 
                 20 
                 89.9 
                 6000 
               
               
                   
                 50.0 
                 50 
                 89.9 
                 4000 
               
               
                   
                 50.0 
                 20 
                 89.9 
                 10000 
               
               
                   
                   
               
            
           
         
       
     
     2-5. When Average Angle is Small 
     There will now be described a case where an average angle θ between the first surface N 1   a  of the negative electrode current collector N 1  and the carbon nanowall is small. 
       FIG.  6    is a diagram for describing a case where an average angle θ between the first surface N 1   a  of the negative electrode current collector N 1  and the carbon nanowall is small. As illustrated in  FIG.  6   , a projection region PR 3  where a carbon nanowall CNW 1 ( c ) is projected onto the first surface N 1   a  of the negative electrode current collector N 1  includes a carbon nanowalls CNW 1 ( d ) except for the carbon nanowall CNW 1 ( c ). 
     When the end portion El of the carbon nanowall CNW 1 ( c ) is projected onto the first surface N 1   a  of the negative electrode current collector N 1 , the end portion El of the carbon nanowall CNW 1 ( c ) crosses a side surface of the adjacent carbon nanowall CNW 1 ( d ). 
     Thus, when the average angle θ is small, it is difficult for the electrolytic solution to enter the vicinity of the root portion R 1  of the carbon nanowalls CNW 1 . If the electrolytic solution does not cover the entire carbon nanowall, the battery capacity is reduced by the corresponding amount. 
     3. Charge-Discharge Reaction Involving Lithium Ions 
     3-1. Charge-Discharge Reaction 
     The negative electrode NE includes the carbon nanowall CNW 1 . The carbon nanowall CNW 1  is capable of involving, in the charge-discharge reaction, two or more lithium ions per carbon atom in a single charge or discharge. 
     The charge-discharge reaction is, for example, a chemical reaction expressed by the following chemical equation. 
       Li +   +e   − ↔Li  (1)
 
       6C+ x Li +   +xe   − ↔C 6 Li x   (2)
 
       Li 1−x CoO 2   +x Li +   +xe   − ↔LiCoO 2   (3)
 
     The equation (1) or equation (2) is, for example, a reaction that can occur inside the negative electrode active material layer N 2 . The equation (3) is, for example, a reaction that can occur inside the positive electrode active material layer P 2 . Both reactions involve the lithium ions and the electrons. The charge-discharge reaction is a chemical reaction in which the lithium ions are involved as well as the electronic transmission/reception occurs in the positive electrode PE or the negative electrode NE. This charge-discharge reaction can cause phenomena, such as occlusion or release of the lithium ions, and deposition, accumulation, adsorption, and dissolution of lithium or lithium compounds. When the lithium or the lithium compound deposited, the charge-discharge reaction can occur outside the positive electrode active material layer P 2  or negative electrode active material layer N 2 . The type of charge-discharge reaction is changed depending on the materials of the positive electrode active material layer P 2  and the negative electrode active material layer N 2 . 
     3-2. Deposition of Lithium in Carbon Nanowall 
     The carbon nanowall CNW 1  includes a surface on which lithium can be deposited. Therefore, during the charging or discharging, lithium may be deposited on the surface of the carbon nanowall CNW 1 . 
     The carbon nanowall CNW 1  is capable of involving, in the charge-discharge reaction, two or more lithium ions per carbon atom in a single charge or discharge. The carbon nanowall CNW 1  is capable of involving, in the charge-discharge reaction, ten or more lithium ions per carbon atom in a single charge or discharge. The carbon nanowall CNW 1  is capable of involving, in the charge-discharge reaction, twenty or more lithium ions per carbon atom in a single charge or discharge. 
     Carbon nanowall CNW 1  can deposit lithium. Therefore, in principle, there is no upper limit to the number of lithium ions that can be involved in the charge-discharge reaction per carbon atom. However, the larger the number of lithium ions involved in the charge-discharge reaction per carbon atom in a single charge or discharge, the larger the volume of lithium to be deposited. Accordingly, the number of lithium ions to be involved in the charge-discharge reaction per carbon atom may be, for example, equal to or less than 100,000. Preferably, the number of lithium ions is equal to or less than 10,000. More preferably, the number of lithium ions is equal to or less than 1,000. Still more preferably, the number of lithium ions is equal to or less than 150. 
     The height of lithium to be deposited may be, for example, equal to or less than 200 μm. Preferably, the height of lithium is equal to or less than 100 μm. More preferably, the height of lithium is equal to or less than 50 μm. 
     For example, when 30 lithium per carbon atom is deposited on the surface of the carbon nanowall CNW 1 , a state thereof can be virtually expressed by the following chemical formula (composition formula). 
       Li 30 C 
     Thus, when the lithium is deposited on the surface of the carbon nanowall CNW 1 , it is virtually expressed by the following chemical formula (composition formula). 
       Li x C 
     where X is a real number equal to or greater than zero and varies with charge and discharge. Since lithium is deposited, a theoretical maximum value of X is infinite.
 
3-3. Comparison with Conventional Examples
 
     Conventionally, one lithium ion would enter per six-membered ring of carbon atoms. A state thereof is expressed by the following formula. 
       LiC 6    
     Accordingly, the carbon nanowall CNW 1  according to the first embodiment can involve extremely many lithium ions in the charge-discharge reaction compared with conventional examples. That is, the performance of the lithium-ion secondary battery LiB 1  according to the first embodiment is high. 
     3-4. Occlusion State and Deposition State 
       FIG.  7    is a diagram hypothetically illustrating an aspect of an occlusion of lithium ions and a deposition of lithium or lithium compounds by the carbon nanowall CNW 1  in the lithium-ion secondary battery LiB 1  according to the first embodiment. 
     A virtual example is illustrated in  FIG.  7   . As illustrated in the region LA 1  in  FIG.  7   , it is considered that lithium ions will enter inside the carbon nanowall CNW 1 . Theoretically, the maximum lithium ion intercalation is LiC 6 . Therefore, the number of lithium atoms per carbon atom cannot exceed ⅙. 
     As illustrated in the region LA 2  in  FIG.  7   , it is considered that lithium atoms or lithium ions are adsorbed or deposited on the surface of the carbon nanowall CNW 1 , and lithium or lithium compound in a metallic state are deposited thereon. 
     As described above, the carbon nanowall CNW 1  can occlude or deposit lithium. It is considered that if the occlusion of lithium is thermodynamically more advantageous than the deposition of lithium, the occlusion of lithium would occur first, the occlusion of lithium would be saturated, and then deposition of lithium would occur. It is considered that if the deposition of lithium is thermodynamically more advantageous than the occlusion of lithium, the lithium would be deposited without occlusion of the lithium occurring. 
     As the lithium-ion secondary battery LiB 1  continues to be charged, lithium is deposited on the surface of the carbon nanowall CNW 1 . As the lithium-ion secondary battery LiB 1  further continues to be charged, the lithium will fill gaps in the carbon nanowalls CNW 1 . As the lithium-ion secondary battery LiB 1  still further continues to be charged, it is considered that the lithium will be deposited thereon so as to exceed the height of the carbon nanowall CNW 1 . 
     3-5. Other States 
     Phenomena, such as dissolution of lithium, and deposition, accumulation, adsorption, and dissolution of lithium compounds, can occur in addition to the occlusion or release of lithium ions, and the deposition, accumulation, and adsorption of lithium. 
     4. Manufacturing Apparatus 
     There will now be described a manufacturing apparatus for forming the carbon nanowall CNW 1  on the surface of the negative electrode current collector N 1 . 
       FIG.  8    is a schematic structure diagram illustrating a configuration of a manufacturing apparatus  1  for growing the carbon nanowall CNW 1  in the lithium-ion secondary battery LiB 1  according to the first embodiment. The manufacturing apparatus  1  includes a plasma generation chamber  46  and a reaction chamber  10 . A plasma generation chamber  46  is used for generating plasma inside the plasma generation chamber and also for generating radicals to be supplied to the reaction chamber  10 . The reaction chamber  10  is used for forming the carbon nanowall CNW 1  using the radicals generated in the plasma generation chamber  46 . 
     The manufacturing apparatus  1  includes a waveguide  47 , a quartz window  48 , and a slot antenna  49 . The waveguide  47  is used for introducing microwave  39 . The slot antenna  49  is used for introducing the microwave  39  from the quartz window  48  into the plasma generation chamber  46 . 
     The plasma generation chamber  46  is used for generating surface wave plasma (SWP) with the microwave  39 . A radical source inlet  42  is provided in the plasma generation chamber  46 . The radical source inlet  42  is used for supplying a gas serving as a radical source to the inside of plasma  61  generated in the plasma generation chamber  46 . 
     A partition wall  44  is provided between the plasma generation chamber  46  and the reaction chamber  10 . The partition wall  44  is used for partitioning between the plasma generation chamber  46  and the reaction chamber  10 . The partition wall  44  also serves as a first electrode  22  for applying voltage. Moreover, through holes  14  are formed in the partition wall  44 . It is used for supplying the radicals generated in the plasma generation chamber  46  to the reaction chamber  10 . 
     The reaction chamber  10  is used for generating capacitively coupled plasma (CCP). Moreover, the reaction chamber  10  is also used for forming the carbon nanowall CNW 1  on the negative electrode current collector N 1 . The reaction chamber  10  includes a second electrode  24 , a heater  25 , a raw material inlet  12 , and an exhaust port  16 . The second electrode  24  is used for applying voltage between the first electrode  22  and the second electrode. A heater  25  is used for heating the negative electrode current collector N 1  to control a temperature of the negative electrode current collector N 1 . The raw material inlet  12  is used for supplying carbon based gas  32  serving as a raw material of the carbon nanowall. The exhaust port  16  is connected to a vacuum pump and the like. The vacuum pump is used for adjusting a pressure inside the reaction chamber  10 . 
     As described above, the partition wall  44  serves as the first electrode  22  for applying the voltage between the second electrode  24  and the first electrode. An electronic power supply and a circuit are connected to the first electrode  22 . They are used for temporally controlling a potential of the first electrode  22 . The second electrode  24  is used for applying the voltage between the first electrode  22  and the second electrode. Moreover, the second electrode  24  is also used for a mounting base for mounting the negative electrode current collector N 1 . The second electrode  24  is grounded. A distance between the first electrode  22  and the second electrode  24  is approximately 5 cm. Of course, it is not limited to this value. 
     5. Manufacturing Method of Negative Electrode 
     5-1. Amorphous Carbon Layer Formation Process 
     First, the negative electrode current collector N 1  before forming the carbon nanowall CNW 1  is mounted inside the manufacturing apparatus  1 . At this time, the first surface Nia of the negative electrode current collector N 1  is up and the second surface Nib is in contact with the second electrode  24 . Next, the microwaves  39  are introduced into the waveguide  47 . The microwaves  39  are introduced into the plasma generation chamber  46  from the quartz window  48  by the slot antenna  49 . Consequently, high density plasma  60  is generated. 
     Then, this high density plasma  60  diffuses inside the plasma generation chamber  46  to become the plasma  61 . This plasma  61  contains radical source ions supplied from the radical source inlet  42 . Hydrogen is used as the radical source. Alternatively, oxygen, nitrogen, or other gases may be used thereas. Most of the ions in the plasma  61  collide with the partition wall  44  and are neutralized to become radicals. The radicals  38  pass through the through hole  14  of the partition wall  44  and enter the reaction chamber  10 . 
     In addition to the radicals  38 , the carbon based gas  32  is supplied from the raw material inlet  12  to inside the reaction chamber  10 . The carbon based gas  32  is, for example, CH 4  or C 2 F 6 . Of course, it may be anything else. Then, the voltage is applied between the first electrode  22  and the second electrode  24 . Consequently, the plasma  34  is generated inside the reaction chamber  10 . 
     In the atmosphere of the plasma  34 , particles and the like derived from the carbon based gas  32 , which is the raw material, and radicals  38  are mixed. Then, the amorphous carbon layer AC 1  grows on the surface of the negative electrode current collector N 1  in the atmosphere of this plasma  34 . 
     Thus, the carbon based gas plasmaized inside the manufacturing apparatus  1  is supplied to the negative electrode current collector N 1 , and thereby the amorphous carbon layer AC 1  is formed on the negative electrode current collector N 1 . 
     A pressure inside the reaction chamber  10  is within a range of equal to or greater than 5 mTorr and equal to or less than 2000 mTorr (equal to or greater than 0.65 Pa and equal to or less than 267 Pa). A temperature of the negative electrode current collector N 1  is within a range equal to or greater than 100° C. and equal to or less than 800° C. Of course, these numerical value ranges may merely be exemplifications and are not limited to these numerical value ranges. 
     5-2. Carbon Nanowall Growth Process 
     Subsequently, inside the manufacturing apparatus  1 , the carbon nanowall CNW 1  is grown on the amorphous carbon layer AC 1 . The plasma  61  is generated in the same manner as the case of growing the amorphous carbon layer AC 1 . Hydrogen gas is used as the radical source of the radicals  38 , and CH 4  or C 2 F 6 , for example, is used as the carbon based gas  32 . 
     Thus, the carbon based gas plasmaized inside the manufacturing apparatus  1  is supplied to the negative electrode current collector N 1 , and thereby the carbon nanowall is grown on the amorphous carbon layer AC 1 . 
     The pressure inside the reaction chamber  10  is within a range of equal to or greater than 5 mTorr and equal to or less than 2000 mTorr (equal to or greater than 0.65 Pa and equal to or less than 267 Pa). The temperature of the negative electrode current collector N 1  is within a range equal to or greater than 100° C. and equal to or less than 800° C. Of course, these numerical value ranges may merely be exemplifications and are not limited to these numerical value ranges. 
     5-3. Cleaning Process 
     After the growth of the carbon nanowall CNW 1  has progressed to some extent, the negative electrode current collector N 1  is removed from the manufacturing apparatus  1 . The height H 1  of the carbon nanowall CNW 1  at this case is, for example, 1000 nm. 
     Next, the inside of the manufacturing apparatus  1  is cleaned. The carbon material is scraped off from the internal wall surface thereof. Alternatively, the carbon material is removed from the internal wall surface by means of hydrogen plasma or the like. Thus, in this process, while stopping the growth process, the inside of the manufacturing apparatus  1  is cleaned. 
     5-4. Repetition of Processes, Etc. 
     Then, the carbon nanowall growth process and the cleaning process described above are repeated. Consequently, the carbon nanowall CNW 1  having a sufficient height H 1  can be obtained. Furthermore, the negative electrode current collector N 1  is turned over in order to form the carbon nanowall CNW 1  on the second surface Nib of the negative electrode current collector N 1 . It is noted that even if the negative electrode current collector N 1  is disposed so that the carbon nanowall CNW 1  is facing down, there is no problem with the carbon nanowall CNW 1 . 
     6. Manufacturing Method of Lithium-Ion Secondary Battery 
     6-1. Negative Electrode Manufacturing Process 
     As described above, the negative electrode NE is manufactured. The negative electrode active material layer N 2  is formed on the negative electrode current collector N 1 . 
     6-2. Positive Electrode Manufacturing Process 
     Next, the positive electrode PE is manufactured. A coating liquid is coated on the positive electrode current collector P 1  to be made to dry. The coating liquid contains a positive-electrode active material, a conductive auxiliary agent, and a binder. Moreover, a press process may be implemented to the positive electrode PE. 
     6-3. Electrolytic Solution Injection Process 
     Next, the positive electrode PE and the negative electrode NE are alternately arranged through separator Sp 1 , inside the vessel V 1 . Then, the electrolytic solution ES 1  is injected into the inside of the vessel V 1 . Subsequently, an opening of the vessel V 1  may be sealed. 
     6-4. Other Processes 
     Other processes, such as the aging process, may be implemented. 
     7. Effect of First Embodiment 
     The negative electrode NE in the lithium-ion secondary battery LiB 1  according to the first embodiment includes the carbon nanowall CNW 1 . The surface area of the carbon nanowall CNW 1  is sufficiently large. The carbon nanowall CNW 1  is capable of involving extremely many lithium ions per carbon atom in the charge-discharge reaction. Therefore, the capacity of the lithium-ion secondary battery LiB 1  is extremely large. 
     As described above, the carbon nanowall CNW 1  is capable of involving extremely many lithium ions in the charge-discharge reaction. Therefore, the amount of the carbon nanowall CNW 1  can be small. That is, the size of the negative electrode is smaller than that of the conventional example, and the weight of the negative electrode is lighter than that of the conventional example. Accordingly, the volume energy density and the weight energy density of the lithium-ion secondary battery LiB 1  are improved compared with the conventional example. 
     8. Modified Examples 
     8-1. Formed Surface of Positive Electrode Active Material Layer or Negative Electrode Active Material Layer 
     The positive electrode active material layer P 2  may be formed only on one surface of the positive electrode current collector P 1 . The negative electrode active material layer N 2  may be formed only on one surface of the negative electrode current collector N 1 . 
     8-2. Carbon Nanowall of Positive Electrode 
     Depending on the type of the power storage device, the carbon nanowall may be formed on the positive electrode current collector P 1 . Even in this case, the electrode for power storage device includes the current collector and the active material layer on the current collector. The active material layer includes the carbon nanowall. 
     8-3. Amorphous Carbon Layer 
     The negative electrode NE does not need to have the amorphous carbon layer AC 1 . In that case, the carbon nanowall CNW 1  is formed directly on the negative electrode current collector N 1 . The amorphous carbon layer AC 1  may or may not function as the negative-electrode active material. 
     8-4. Amorphous Carbon on Carbon Nanowall CNW 1   
     Moreover, the surface of the carbon nanowall CNW 1  may be covered with amorphous carbon immediately after the growth of the carbon nanowall CNW 1 . This amorphous carbon can be removed by H 2 O 2 . 
     8-5. Stacked Structure 
     The electrode may be a stacked structure obtained by stacking the positive electrode PE and the negative electrode NE. In the stacked structure, the positive electrode PE and the negative electrode NE are alternately stacked, and the separator Sp 1  is inserted between the positive electrode PE and the negative electrode NE. 
     8-6. Cleaning Process 
     The cleaning process may be omitted depending on the height of the carbon nanowall CNW 1 . It may be omitted depending on the manufacturing apparatus  1 . 
     8-7. Combination 
     The above-described modified examples may be freely combined with one another. 
     Second Embodiment 
     There will now be described a second embodiment. 
     1. Lithium-Ion Capacitor 
       FIG.  9    is a schematic structure diagram illustrating a lithium-ion capacitor LiC 1  according to a second embodiment. The lithium-ion capacitor LiC 1  includes a positive electrode PE 2 , a negative electrode NE, a separator Sp 1 , an electrolytic solution ES 1 , and a vessel V 1 . 
     The positive electrode PE 2  includes a positive electrode current collector P 1  and a positive electrode active material layer P 3 . The positive electrode active material layer P 3  is, for example, activated carbon. 
     2. Modified Examples 
       FIG.  10    is a schematic structure diagram illustrating a lithium-ion capacitor LiC 2  of a modified example according to the second embodiment. The lithium-ion capacitor LiC 2  includes a positive electrode PE 3 , a negative electrode NE, a separator Sp 1 , na electrolytic solution ES 1 , and a vessel V 1 . 
     The positive electrode PE 3  includes a positive electrode current collector P 1  and a positive electrode active material layer P 4 . The positive electrode active material layer P 4  includes a carbon nanowall CNW 2 . The carbon nanowall CNW 2  of the positive electrode PE 3  is the same as the carbon nanowall CNW 1  of the negative electrode NE. Of course, conditions, etc. of the walls may be changed. 
     Third Embodiment 
     There will now be described a third embodiment. 
     A basic structure of a lithium-ion secondary battery according to the third embodiment is the same as the basic structure of the lithium-ion secondary battery LiB 1  according to the first embodiment. 
     1. Amount of Active Material Layer 
     As described in the first embodiment, the carbon nanowall CNW 1  is capable of involving extremely many lithium ions in the charge-discharge reaction. Therefore, the negative electrode active material layer N 2  is extremely lighter and has smaller volume than those of the positive electrode active material layer P 2 . 
     The number of lithium atoms that the positive electrode active material layer P 2  can contain per unit area is equal to or greater than twice the number of carbon atoms that the negative electrode active material layer N 2  can contain per unit area. The number of lithium atoms that the positive electrode active material layer P 2  can contain per unit area is preferably equal to or greater than 100 times of the number of carbon atoms that the negative electrode active material layer N 2  can contain per unit area. The number of lithium atoms that the positive electrode active material layer P 2  can contain per unit area is preferably equal to or less than 100,000 times of the number of carbon atoms that the negative electrode active material layer N 2  can contain per unit area. The upper limit herein is limited by the volume of lithium to be deposited. 
     2. Effect of Third Embodiment 
     The number of the carbon atoms in the lithium-ion secondary battery according to the third embodiment is small. Therefore, the volume energy density and the weight energy density of this lithium-ion secondary battery are high. Accordingly, this lithium-ion secondary battery can contribute to a low-carbon society. 
     3. Modified Examples 
     3-1. Lithium-Ion Capacitor 
     The technology of the third embodiment can be similarly applied to lithium-ion capacitors. 
     Practical Examples 
     (Experiments) 
     1. Carbon Nanowall on Current Collector 
     1-1. Manufacturing Method 
     A carbon nanowall is grown on a metal plate made by Ti, using the manufacturing apparatus  1 . 
     1-2. Carbon Nanowall 
       FIG.  11    shows a microphotograph of carbon nanowalls viewed from a direction perpendicular to a plate surface of a metal plate. As illustrated in  FIG.  11   , the carbon nanowalls grow randomly. Moreover, the wall-like walls are growing and then merging with each other. However, the spacing therebetween is uniform to some extent. 
       FIG.  12    shows a microphotograph of the carbon nanowalls illustrating a cross section thereof perpendicular to the plate surface of the metal plate. As illustrated in  FIG.  12   , the carbon nanowalls are formed substantially perpendicularly to the substrate. 
     2. Lithium-Ion Secondary Battery 
     2-1. Manufacturing of Lithium-Ion Secondary Battery 
     As a practical example, the lithium-ion secondary battery LiB 1  according to the first embodiment is manufactured. The positive electrode current collector P 1  is aluminum, and the positive-electrode active material is lithium cobaltate. The negative electrode current collector N 1  is copper, and the negative-electrode active material is a carbon nanowall. The electrolytic solution is 1M LiPF 6 . The positive electrode active material layer is a region 1.6 cm in diameter. The negative electrode active material layer is a region 1.3 cm in diameter. The carbon nanowalls are of three heights: 1 μm, 4 μm, and 10 μm. 
     The weight of the lithium cobaltate is summarized in Table 3. The weight of the carbon nanowall is obtained by subtracting the weight of the substrate before growing the carbon nanowall from the weight of the substrate after growing the carbon nanowall. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 3 
               
               
                   
                   
               
             
            
               
                   
                 Lithium cobaltate 
                 0.046 g 
               
               
                   
                 Carbon nanowall 
                 0.00004 g (1 μm in height) 
               
               
                   
                 Carbon nanowall 
                 0.00016 g (4 μm in height) 
               
               
                   
                 Carbon nanowall 
                 0.00040 g (10 μm in height) 
               
               
                   
                   
               
            
           
         
       
     
     The positive electrode active material layer contains a lithium cobaltate, a conductive auxiliary agent, and a binder. The conductive auxiliary agent is acetylene black. The binder is PVDF. The weight ratio of the lithium cobaltate, the acetylene black, and the PVDF is 100:5:3. 
     Moreover, as a comparative example, a lithium-ion secondary battery including a negative electrode made of graphite instead of the carbon nanowall is manufactured. The other conditions are the same as those of the practical example. The weight of the graphite is summarized in Table 4. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 4 
               
               
                   
                   
               
             
            
               
                   
                 Lithium cobaltate 
                 0.046 g 
               
               
                   
                 Graphite 
                 0.010 g 
               
               
                   
                   
               
            
           
         
       
     
     2-2. Capacity of Lithium-Ion Secondary Battery 
       FIG.  13    is a graphic chart illustrating a relationship between capacity and voltage of a lithium-ion secondary battery using a carbon nanowall with a height of 1 μm for the negative electrode. The horizontal axis of  FIG.  13    indicates charge/discharge capacity. The vertical axis of  FIG.  13    indicates voltage. The charge current or discharge current is 0.5 mA. As illustrated in  FIG.  13   , the discharge capacity of the lithium-ion secondary battery is 9.0 mAh. 
       FIG.  14    is a graphic chart illustrating a relationship between capacity and voltage of a lithium-ion secondary battery using a carbon nanowall with a height of 4 μm for the negative electrode. The horizontal axis of  FIG.  14    indicates charge/discharge capacity. The vertical axis of  FIG.  14    indicates voltage. The charge current or discharge current is 0.5 mA. As illustrated in  FIG.  14   , the discharge capacity of the lithium-ion secondary battery is 9.0 mAh. 
       FIG.  15    is a graphic chart illustrating a relationship between capacity and voltage of a lithium-ion secondary battery using a carbon nanowall with a height of 10 μm for the negative electrode. The horizontal axis of  FIG.  15    indicates charge/discharge capacity. The vertical axis of  FIG.  15    indicates voltage. The charge current or discharge current is 0.5 mA. As illustrated in  FIG.  15   , the discharge capacity of the lithium-ion secondary battery is 9.0 mAh. 
     As illustrated in  FIGS.  13  to  15   , although the heights of the carbon nanowalls are different from one another, the discharge capacities of the lithium-ion secondary batteries are 9.0 mAh. This suggests that the charge/discharge capacity of the active material on the negative electrode side has a surplus, but it is limited by the charge/discharge capacity of the active material on the positive electrode side. 
     In addition, as indicated in the following equation, the measured discharge capacity reaches approximately 72% of a theoretical capacity value of lithium cobaltate, 274 mAh/g. 
       9.0 mAh/ 0.046 g= 196 mAh/g    
     This supports inference that it is limited due to the charge/discharge capacity of the active material at the positive electrode side. 
       FIG.  16    is a graphic chart illustrating a relationship between capacity and voltage of a lithium-ion secondary battery using graphite for the negative electrode. The horizontal axis of  FIG.  16    indicates charge/discharge capacity. The vertical axis of  FIG.  16    indicates voltage. The charge current or discharge current is 0.5 mA. As illustrated in  FIG.  16   , the discharge capacity of the lithium-ion secondary battery is 3 mAh. 
       FIG.  17    is a diagram for comparing charging voltages of lithium-ion secondary batteries in a case of using the carbon nanowall for the negative electrode and using graphite for the negative electrode. The horizontal axis of  FIG.  17    indicates charging capacity. The vertical axis of  FIG.  17    indicates voltage. 
     As illustrated in  FIG.  17   , the charging voltage in the case of using the graphite for the negative electrode rises gently. The lithium ions is intercalated between the graphene sheet layers of graphite. Stages of this intercalation change step by step from stage 4 (LiC 24 ) to stage 1 (LiC 6 ). Corresponding to the temporal changes of this stage, the charging voltage also changes gently. 
     In contrast, the charging voltage in the case of using the carbon nanowall for the negative electrode rises sharply. This suggests two possibilities. In the first possibility, the intercalation stage change is ended for a short time, and the lithium is deposited. In the second possibility, the lithium is deposited without intercalation occurring. 
     2-3. Lithium-Ion Secondary Battery 
     As illustrated in  FIG.  17   , the charging voltage in the charging voltage in the case of using the carbon nanowall for the negative electrode is approximately 0.1 V higher than the charging voltage in the case of using the graphite for the negative electrode. 
       Li +   +e   − ↔Li  (1)
 
       −3.04 V  
 
       6C+ x Li +   +xe   − ↔C 6 Li x   (2)
 
       −2.90 V  
 
       Li 1−x CoO 2   +x Li +   +xe   − ↔LiCoO 2   (3)
 
       +0.90 V    
     Formula (1) indicates a case where lithium is deposited or a case where lithium is ionized. Formula (2) indicates a case where lithium ions intercalate or deintercalate between the layers of the graphene structure. Formula (3) indicates a case where lithium cobaltate releases or occludes lithium ions. 
     When the reaction in formula (1) occurs, the charging voltage is as follows. 
       0.90 V −(−3.04 V )=3.94 V  
 
     When the reaction in formula (2) occurs, the charging voltage is as follows. 
       0.90 V −(−2.90 V )=3.80 V  
 
     It is considered that a difference between the charging voltage in the case of using the carbon nanowall for the negative electrode and the charging voltage in the case of using the graphite for the negative electrode is caused by the difference between the formula (1) and formula (2). That is, it is considered that when the carbon nanowall is used for the negative electrode, the reaction of formula (1) mainly occurs during charging and discharging, and when the graphite is used for the negative electrode, the reaction of formula (2) mainly occurs during charging and discharging. 
     2-4. Capacity of Carbon Nanowall 
     A theoretical capacity of graphite is 372 mAh/g. The chemical formula at this case is expressed by LiC 6 . 
     The capacity of a carbon nanowall with a height of 1 μm is 2250000 mAh/g. 
       9.0 mAh/ 0.000040 g= 2250000 mAh/g    
     The capacity of the carbon nanowall with the height of 1 μm is approximately 600 times the theoretical capacity of graphite. 
       2250000 mAh/g/ 372 mAh/g= 600 
     Accordingly, the chemical formula (composition formula) for the Li deposition state in the carbon nanowall is expressed as follows. 
       Li 600 C 6 (Li 100 C) 
     3. Height Dependence of Carbon Nanowall 
     3-1. Lithium-Ion Secondary Battery 
     A lithium-ion secondary battery is fabricated in which Li metal is used as the positive electrode used and a carbon nanowall formed on Cu is used as the negative electrode. The electrolytic solution is an electrolytic solution used in the lithium-ion secondary batteries. 
     3-2. Charging and Discharging Characteristics 
       FIG.  18    is a graphic chart illustrating discharging characteristics of a lithium-ion secondary battery using a negative electrode including a carbon nanowall with a height of 0 nm. The horizontal axis of  FIG.  18    indicates capacity. The vertical axis of  FIG.  18    indicates voltage. In this case, there is no carbon nanowall but there is only copper foil, in the negative electrode. As illustrated in  FIG.  18   , the voltage drops immediately after the start of discharge. 
       FIG.  19    is a graphic chart illustrating discharging characteristics of a lithium-ion secondary battery using a negative electrode including a carbon nanowall with a height of 20 nm. The horizontal axis of  FIG.  19    indicates capacity. The vertical axis of  FIG.  19    indicates voltage. The capacity is 1.6 mAh as illustrated in  FIG.  19   . 
       FIG.  20    is a graphic chart illustrating discharging characteristics of a lithium-ion secondary battery using a negative electrode including a carbon nanowall with a height of 50 nm. The horizontal axis of  FIG.  20    indicates capacity. The vertical axis of  FIG.  20    indicates voltage. The capacity is 7.1 mAh as illustrated in  FIG.  20   . 
       FIG.  21    is a graphic chart illustrating discharging characteristics of a lithium-ion secondary battery using a negative electrode including a carbon nanowall with a height of 100 nm. The horizontal axis of  FIG.  21    indicates capacity. The vertical axis of  FIG.  21    indicates voltage. The capacity is 13.2 mAh as illustrated in  FIG.  21   . 
       FIG.  22    is a graphic chart illustrating discharging characteristics of a lithium-ion secondary battery using a negative electrode including a carbon nanowall with a height of 200 nm. The horizontal axis of  FIG.  22    indicates capacity. The vertical axis of  FIG.  22    indicates voltage. The capacity is 13.3 mAh as illustrated in  FIG.  22   . 
       FIG.  23    is a graphic chart illustrating discharging characteristics of a lithium-ion secondary battery using a negative electrode including a carbon nanowall with a height of 500 nm. The horizontal axis of  FIG.  23    indicates capacity. The vertical axis of  FIG.  23    indicates voltage. The capacity is 13.2 mAh as illustrated in  FIG.  23   . 
     Experimental data is summarized in Table 5. As illustrated in Table 5, when the height of the carbon nanowall is equal to or greater than 100 nm, the capacity of the lithium-ion secondary battery is saturated. It is also considered that when the height of the carbon nanowall is equal to or greater than 100 nm, all lithium of the positive electrode is consumed. Therefore, the height of the carbon nanowall is preferably equal to or greater than 100 nm. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 5 
               
               
                   
                   
               
               
                   
                 Height of CNW 
                 Capacity 
               
               
                   
                 (nm) 
                 (mAh) 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 0 
                 0.5 
               
               
                   
                 20 
                 1.6 
               
               
                   
                 50 
                 7.1 
               
               
                   
                 100 
                 13.2 
               
               
                   
                 200 
                 13.3 
               
               
                   
                 500 
                 13.2 
               
               
                   
                 1000 
                 12.5 
               
               
                   
                   
               
            
           
         
       
     
     3-3. SEM Images 
       FIG.  24    is a scanning electron micrograph illustrating a surface of the carbon nanowall with a height of 500 nm.  FIG.  25    is a scanning electron micrograph illustrating a cross section of the carbon nanowall with the height of 500 nm. The carbon nanowalls are growing greatly. 
       FIG.  26    is a scanning electron micrograph illustrating a surface of the carbon nanowall with a height of 50 nm.  FIG.  27    is a scanning electron micrograph illustrating a cross section of the carbon nanowall with the height of 50 nm. The carbon nanowalls are not growing so much. 
     4. Deposition of Lithium (Part 1) 
     4-1. Lithium-Ion Secondary Battery 
     A lithium-ion secondary battery is fabricated in which Li metal is used as the positive electrode used and a carbon nanowall formed on Cu is used as the negative electrode. The electrolytic solution is an electrolytic solution used in the lithium-ion secondary batteries. The height of the carbon nanowall is 200 nm. 
     4-2. SEM Images 
       FIG.  28    is a scanning electron micrograph (Part 1) illustrating a surface of a carbon nanowall when repeating charging and discharging.  FIG.  28    clearly shows the wall of carbon nanowalls. 
       FIG.  29    is a scanning electron micrograph (Part 2) illustrating a surface of a carbon nanowall when repeating charging and discharging.  FIG.  29    illustrates an aspect that metal lithium is deposited in a gap between the carbon nanowalls, and the metal lithium fills most of the gap. 
       FIG.  30    is a scanning electron micrograph (Part 3) illustrating a surface of a carbon nanowall when repeating charging and discharging.  FIG.  30    illustrates an aspect that the deposited metal lithium has also filled the upper layer of the carbon nanowall. 
     As illustrated in  FIGS.  29  and  30   , the metal lithium is deposited is fills the gaps between carbon nanowalls. Therefore, more lithium ions are involved in the charge-discharge reaction than that of the conventionally examples. It is possible to involve equal to or greater than two lithium ions per carbon atom in the charge-discharge reaction. 
     The fabricated lithium-ion secondary battery is charged and discharged for 30 cycles. Even after that, no dendrites are observed. It is assumed that this is because the metal lithium is deposited from the surface of the carbon nanowalls as a starting point, and since the crystallinity of the metal lithium is proper, thereby preventing dendrites from being generated. 
     5. Deposition of Lithium (Part 2) 
     5-1. Manufacturing of Lithium-Ion Secondary Battery 
     A coin-type lithium-ion secondary battery is manufactured. The positive electrode current collector P 1  is aluminum, and the positive-electrode active material is lithium cobaltate. The negative electrode current collector N 1  is copper, and the negative-electrode active material is a carbon nanowall. The electrolytic solution is 1M LiPF 6 . The positive electrode active material layer is a region 1.6 cm in diameter. The negative electrode active material layer is a region 1.3 cm in diameter. The height of the carbon nanowall is 1 μm. 
     5-2. Charging 
     The above-described coin type lithium-ion secondary battery is charged at 0.5 mA for 18 hours. 
     5-3. Deposition of Lithium 
     The charge Q is expressed by the following equation. 
         Q= 0.5 mA· 18 h= 32.4 C    
     The number N of lithium ions that receive the charge is expressed by the following equation. 
       N=32.4/(1.6×10 −19 )=2.0×10 20 (pieces)
 
     Assume that the lithium ions received electrons at the negative electrode and become lithium crystals. Lithium has a body-centered cubic lattice structure. Two lithium atoms are included into one lattice. The lattice constant of the lithium crystal is 0.35 nm. 
     The number density n of lithium ions is expressed by the following equation. 
     
       
         
           
             
               
                 
                   n 
                   = 
                   
                     2. 
                     × 
                     
                       10 
                       20 
                     
                     / 
                     
                       { 
                       
                         2 
                         · 
                         
                           
                             ( 
                             
                               0.35 
                               × 
                               
                                 10 
                                 
                                   - 
                                   9 
                                 
                               
                             
                             ) 
                           
                           3 
                         
                       
                       } 
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     4.29 
                     × 
                     
                       10 
                       
                         - 
                         9 
                       
                     
                     ⁢ 
                         
                     
                       m 
                       
                         - 
                         3 
                       
                     
                   
                 
               
             
           
         
       
     
     The height HL of lithium to be deposited is expressed by the following equation. 
     
       
         
           
             
               
                 
                   HL 
                   = 
                   
                     4.29 
                     × 
                     
                       10 
                       
                         - 
                         9 
                       
                     
                     / 
                     
                       ( 
                       
                         0.0065 
                         × 
                         0.0065 
                         × 
                         3.14 
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     32 
                     × 
                     
                       10 
                       
                         - 
                         6 
                       
                     
                     ⁢ 
                         
                     m 
                   
                 
               
             
             
               
                 
                   = 
                   
                     32 
                     ⁢ 
                         
                     μ 
                     ⁢ 
                     m 
                   
                 
               
             
           
         
       
     
     5-4. Cross Section of Lithium Crystal 
       FIG.  31    is a scanning electron micrograph illustrating a cross section of a negative electrode in the lithium-ion secondary battery after charging. As illustrated in  FIG.  31   , the height of lithium crystal after the charging was 32 μm. Therefore, the height of the lithium crystal illustrated in  FIG.  31    matches with the above-described calculated result. 
     5-5. X-Ray Diffraction 
       FIG.  32    is a graphic chart illustrating an X-ray diffraction result of the negative electrode in the lithium-ion secondary battery after charging.  FIG.  32    illustrates X-ray peaks detected by the 0-20 method. The horizontal axis of  FIG.  32    indicates d/A. The vertical axis of  FIG.  32    indicates X-ray intensity. 
     As illustrated in  FIG.  32   , the peaks of Li (110), Li (200), Li (211), Li (220), and Li (310) are observed. The peak value of Li (110) is the largest. 
     5-6. Lithium 
     From the above, it can be found that the lithium is deposited on the carbon nanowall. 
     (Appendix) 
     An electrode for power storage device in a first aspect includes a current collector and an active material layer on the current collector. The active material layer includes a carbon nanowall. The carbon nanowall is capable of involving, in a charge-discharge reaction, two or more lithium ions per carbon atom in a single charge or discharge. 
     An electrode for power storage device in a second aspect includes a current collector and an active material layer on the current collector. The active material layer includes a carbon nanowall. The carbon nanowall includes a surface on which lithium can be deposited. 
     In the electrode for power storage device in a third aspect, the carbon nanowall is capable of involving, in a charge-discharge reaction, two or more lithium ions per carbon atom in a single charge or discharge. 
     In the electrode for power storage device in a fourth aspect, the active material layer includes an amorphous carbon layer between the current collector and the carbon nanowall. 
     In the electrode for power storage device in a fifth aspect, a film thickness of the amorphous carbon layer is equal to or more than 10 nm and equal to or less than 300 nm. 
     In the electrode for power storage device in a sixth aspect, a projection region where the carbon nanowall is projected onto the surface of the current collector does not include other carbon nanowalls except for the projected carbon nanowall. 
     In the electrode for power storage device in a seventh aspect, an average angle between the current collector and the carbon nanowall are equal to or greater than 80° and equal to or less than 90°. 
     In the electrode for power storage device in an eighth aspect, a height of the carbon nanowall from the current collector is equal to or greater than 100 nm and equal to or less than 10 μm. 
     A power storage device in a ninth aspect includes a positive electrode current collector, a positive electrode active material layer on the positive electrode current collector, a negative electrode current collector, and a negative electrode active material layer on the negative electrode current collector. The negative electrode active material layer includes a carbon nanowall. The carbon nanowall is capable of involving, in a charge-discharge reaction, two or more lithium ions per carbon atom in a single charge or discharge. 
     A power storage device in a tenth aspect includes a positive electrode current collector, a positive electrode active material layer on the positive electrode current collector, a negative electrode current collector, and a negative electrode active material layer on the negative electrode current collector. The negative electrode active material layer includes a carbon nanowall. The carbon nanowall includes a surface on which lithium can be deposited. 
     A power storage device in an eleventh aspect includes a positive electrode current collector, a positive electrode active material layer on the positive electrode current collector, a negative electrode current collector, and a negative electrode active material layer on the negative electrode current collector. The positive electrode active material layer contains lithium atoms. The negative electrode active material layer includes a carbon nanowall. The number of lithium atoms that the positive electrode active material layer can contain per unit area is equal to or greater than twice the number of carbon atoms that the negative electrode active material layer can contain per unit area. 
     In the power storage device in a twelfth aspect, a height of the carbon nanowall from the negative electrode current collector is equal to or greater than 100 nm and equal to or less than 10 μm.