Provided is an internal hybrid electrochemical cell comprising: (a) a pseudocapacitance-like cathode comprising a cathode active material that contains both graphene sheets and a porphyrin compound, including porphyrin or a porphyrin complex, wherein the porphyrin compound is bonded to or supported by primary surfaces of graphene sheets to form a redox pair for pseudocapacitance; (b) a battery-like anode comprising an anode active material selected from sodium metal, a sodium metal alloy, a sodium intercalation compound, a sodium-containing compound, or a combination thereof, and (c) a sodium-containing electrolyte in physical contact with the anode and the cathode; wherein the cathode active material has a specific surface area no less than 100 m.sup.2/g which is in direct physical contact with the electrolyte.

Provided is an internal hybrid electrochemical cell comprising: (a) a pseudocapacitance-like cathode comprising a cathode active material that contains both graphene sheets and a porphyrin compound, including porphyrin or a porphyrin complex, wherein the porphyrin compound is bonded to or supported by primary surfaces of graphene sheets to form a redox pair for pseudocapacitance; (b) a battery-like anode comprising an anode active material selected from sodium metal, a sodium metal alloy, a sodium intercalation compound, a sodium-containing compound, or a combination thereof, and (c) a sodium-containing electrolyte in physical contact with the anode and the cathode; wherein the cathode active material has a specific surface area no less than 100 m.sup.2/g which is in direct physical contact with the electrolyte.

Provided is an internal hybrid electrochemical cell comprising: (A) a pseudocapacitance cathode comprising a cathode active material that contains a conductive carbon material and a porphyrin compound, wherein the porphyrin compound is bonded to or supported by the carbon material to form a redox pair for pseudocapacitance, wherein the carbon material is selected from activated carbon, activated carbon black, expanded graphite flakes, exfoliated graphite worms, carbon nanotube, carbon nanofiber, carbon fiber, a combination thereof; (B) a battery-like anode comprising lithium metal, lithium metal alloy, or a prelithiated anode active material (e.g. prelithiated Si, SiO, Sn, SnO.sub.2, etc.), and (C) a lithium-containing electrolyte in physical contact with the anode and the cathode; wherein the cathode active material has a specific surface area no less than 100 m.sup.2/g which is in direct physical contact with the electrolyte.

In an aspect, an electrode for an electrochemical cell comprises: a structure having a nano- or micro-architected three-dimensional geometry; said structure comprising one or more active carbon allotrope materials; wherein said structure is characterized by an average density less than or equal to 2.3 g cm.sup.3 and an average specific strength (strength-to-density ratio) greater than or equal to 0.004 GPa g.sup.1 cm.sup.3. Also disclosed herein are methods for making an electrode for an electrochemical cell, and methods for making an electrochemical cell.

Provided is an internal hybrid electrochemical cell comprising: (A) a pseudocapacitance cathode comprising both graphene sheets and a 2D inorganic material, in a form of nanodiscs, nanoplatelets, or nanosheets that are bonded to or supported by primary surfaces (not the edges) of the graphene sheets and the 2D inorganic material and graphene sheets form a redox pair for pseudocapacitance; (B) a battery-like anode comprising a prelithiated anode active material (e.g. prelithiated Si, SiO, Sn, SnO.sub.2, etc.), and (C) a lithium-containing electrolyte in physical contact with the anode and the cathode; wherein the cathode active material has a specific surface area no less than 100 m.sup.2/g which is in direct physical contact with the electrolyte.

Provided is an internal hybrid electrochemical cell comprising: (A) a pseudocapacitance cathode comprising a cathode active material that contains both graphene sheets and a porphyrin complex, wherein said porphyrin complex is bonded to or supported by primary surfaces of said graphene sheets to form a redox pair for pseudocapacitance; (B) a battery-like anode comprising lithium metal, lithium metal alloy, or a prelithiated anode active material (e.g. prelithiated Si, SiO, Sn, SnO.sub.2, etc.), and (C) a lithium-containing electrolyte in physical contact with the anode and the cathode; wherein the cathode active material has a specific surface area no less than 100 m.sup.2/g which is in direct physical contact with the electrolyte.

A hybrid energy storage device includes a positive pole formed by stacking a supercapacitor first electrode and a battery positive electrode, a negative pole formed by stacking a supercapacitor second electrode and a battery negative electrode, and a separator located between the positive pole and the negative pole. The supercapacitor second electrode, the battery negative electrode, the supercapacitor first electrode, the battery positive electrode, and the separator are planar structures. The supercapacitor first electrode, the supercapacitor second electrode, the battery positive electrode, the battery negative electrode, the separator and electrolyte are packaged in a shell.

A hybrid energy storage device includes a positive pole formed by stacking a supercapacitor first electrode and a battery positive electrode, a negative pole formed by stacking a supercapacitor second electrode and a battery negative electrode, and a separator located between the positive pole and the negative pole. The supercapacitor second electrode, the battery negative electrode, the supercapacitor first electrode, the battery positive electrode, and the separator are planar structures. The supercapacitor first electrode, the supercapacitor second electrode, the battery positive electrode, the battery negative electrode, the separator and electrolyte are packaged in a shell.

Disclosed is a hybrid electrochemical cell with a first conductor having at least one portion that is both a first capacitor electrode and a first battery electrode. The hybrid electrochemical cell further includes a second conductor having at least one portion that is a second capacitor electrode and at least one other portion that is a second battery electrode. An electrolyte is in contact with both the first conductor and the second conductor. In some embodiments, the hybrid electrochemical cell further includes a separator between the first conductor and the second conductor to prevent physical contact between the first conductor and the second conductor, while facilitating ion transport between the first conductor and the second conductor.

A battery module includes a first liquid battery and a first solid battery. The first liquid battery is a unit cell. The first solid battery is a unit cell that has a larger volume than a volume of the first liquid battery.