Thermally-powered self-charging capacitors

Abstract

Thermally-powered self-charging capacitors convert ambient thermal energy (heat) into electricity. Such capacitors can include a first electrode, a second electrode, a region between the first electrode and the second electrode that is at least partially filled with an electrolyte. and an asymmetric element that that spontaneously generates a charge imbalance between the first electrode and the second electrode by separating electrolyte ions. Examples of asymmetric elements include oppositely-charged electrets disposed on distal surfaces of the electrodes, electrodes made of two dissimilar metals or semiconductors, or one or more chemically asymmetric membranes.

Description

PATENT Attorney Docket No.116669-000210PC-1483007 THERMALLY-POWERED SELF-CHARGING CAPACITORS CROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims priority to U.S. Application No.63 / 623,067, filed January 19, 2024, the disclosure of which is incorporated by reference herein. TECHNICAL FIELD

[0002] This disclosure relates to energy storage devices and in particular to thermally- powered self-charging capacitors. BACKGROUND

[0003] The capacitor is the archetypal electrical energy storage system: easy to understand, relatively inexpensive and simple to construct, and usually free of complex electrochemical reactions. For applications requiring high power density, capacitors are generally superior to traditional electrochemical cells (batteries). The energy densities of capacitors, however, tend to be inferior to those of most batteries.

[0004] A happy compromise between the high energy density of batteries and the high power density of capacitors is the supercapacitor. Intermediate in energy and power densities, the supercapacitor bridges an important gap in power and energy densities for an increasing number of applications. Supercapacitors may come to rival rechargeable batteries in some use-cases, such as electric vehicles, portable electronics, and energy storage for renewable energy systems.

[0005] A supercapacitor is a capacitor that provides a very large electrode surface area in combination with a very small capacitor plate separation distance (e.g., a few angstroms). Large electrode surface areas are typically achieved using materials such as activated carbon, carbon nanotubes, or carbon aerogel. Using such materials, a multi-farad supercapacitor can fit within a few cubic centimeters of volume. Several types of supercapacitors have been developed, among which are the electrostatic double-layer (EDL) capacitor, pseudocapacitor, and hybrid capacitor-battery. Supercapacitors typically exhibit significantly lower energy densities and substantially higher instantaneous power densities than most batteries.SUMMARY

[0006] Described herein are embodiments of thermally-powered self-charging capacitors (“SCC”) that can convert ambient thermal energy (heat) into electricity. Such capacitors can include a first electrode, a second electrode, a region between the first electrode and the second electrode that is at least partially filled with an electrolyte, and an asymmetric element that that spontaneously generates a charge imbalance between the first electrode and the second electrode via thermal diffusion by separating electrolyte ions. Examples of asymmetric elements include oppositely-charged electrets disposed on distal surfaces of the electrodes, electrodes made of two dissimilar metals or semiconductors, or one or more chemically asymmetric membranes. Power densities for SCCs may reach 106or 107W / m3.

[0007] According to some embodiments, a capacitor can comprise: a first electrode; a second electrode; an electrically insulating separator disposed between the first electrode and the second electrode; an electrolyte at least partially filling a region between the first electrode and the second electrode, wherein the electrically insulating separator is made of a material that is permeable to the electrolyte; and an asymmetric element comprising one or more structures that spontaneously generate a charge imbalance between the first electrode and the second electrode.

[0008] In various embodiments, the asymmetric element can comprise any of: a split electret having a positively charged material on the first electrode and a negatively charged material on the second electrode; dissimilar materials in the first electrode and the second electrode; a bipolar membrane with the electrically insulating separator disposed on both sides of the bipolar membrane; an anion exchange membrane disposed on a surface of the first electrode and a cation exchange membrane disposed on a surface of the second electrode; an anionic chemical receptor disposed on a surface of the first electrode and a cationic chemical receptor disposed on a surface of the second electrode.

[0009] In these and other embodiments, the first electrode and the second electrode can include carbonaceous materials that increase a surface area of the first electrode and the second electrode.

[0010] According to some embodiments, a capacitor can comprise: a first electrode at a first side; a second electrode at a second side; a polarizable material disposed in a region between the first electrode and the second electrode; and an electret that spontaneously generates a charge imbalance between the first electrode and the second electrode. Forexample, the electret can establish a permanent electrostatic potential difference between the first side and the second side of the capacitor.

[0011] In these and other embodiments, the electret can include a first electret layer disposed on at least a portion of a distal surface of the first electrode and a second electret layer disposed on at least a portion of a distal surface of the second electrode, where the first electret layer and the second electret layer have opposite electric charges.

[0012] In these and other embodiments, the electret can be made at least in part of charged paraffin wax, stacked layers of charged Teflon, or charged Kapton tape.

[0013] In these and other embodiments, the polarizable material can include one or more of: an electrolyte solution; a semiconductor; or a dielectric.

[0014] According to some embodiments, a capacitor can comprise: a first electrode at a first side, at least a portion of the first electrode being made of a first material; a second electrode at a second side, at least a portion of the second electrode being made of a second material; and an electrolyte in a region between the first electrode and the second electrode; and an electrically insulating separator disposed between the first electrode and the second electrode, the electrically insulating separator being permeable to the electrolyte. The first material and the second material are different materials having different contact potentials, thereby creating a potential difference between the first electrode and the second electrode. For example, the first material and the second material can be different metals, or the first material and the second material can be different semiconductors.

[0015] According to some embodiments, a capacitor can comprise: a first electrode at a first side; a second electrode at a second side; a chemically asymmetric membrane disposed between the first electrode and the second electrode; and an electrolyte in solution in a region between the first electrode and the second electrode, wherein the chemically asymmetric membrane spontaneously generates a concentration gradient in the electrolyte.

[0016] In these and other embodiments, the chemically asymmetric membrane can comprise a bipolar membrane disposed within the region between the first electrode and the second electrode, the bipolar membrane defining a first separator region between the bipolar membrane and the first electrode and a second separator region between the bipolar membrane and the second electrode. The first and second separator regions can each be filledwith a non-conductive material (e.g., a separator material) that is permeable by the electrolyte.

[0017] In these and other embodiments, the chemically asymmetric membrane can comprise: an anion exchange membrane disposed adjacent to the first electrode; and a cation exchange membrane disposed adjacent to the second electrode, and a region between the anion exchange membrane and the cation exchange membrane can be filled with a non- conductive material (e.g., a separator material) that is permeable by the electrolyte.

[0018] In these and other embodiments, the anion exchange membrane can comprise anionic chemical receptors disposed on a surface of the first electrode and the cation exchange membrane ca comprise cationic chemical receptors disposed on a surface of the second electrode.

[0019] According to some embodiments, a capacitor can comprise: a first electrode at a first side; a second electrode at a second side; a first chemically-functionalized material disposed on a distal side of the first electrode; a second chemically-functionalized material disposed on a distal side of the second electrode, wherein the first chemically-functionalized material and the second chemically-functionalized material attract oppositely-charged ions; and an electrolyte solution in a region between and around the first electrode and the second electrode, wherein the first chemically-functionalized material and the second chemically- functionalized material spontaneously generate a charge imbalance between the first electrode and the second electrode. For example, the first chemically-functionalized material can comprise an anion exchange membrane, and the second chemically-functionalized material can comprise a cation exchange membrane.

[0020] The following detailed description, together with the accompanying drawings, will provide a better understanding of the nature and advantages of the claimed invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] FIG.1 shows a simplified side cross-section view of an SCC according to some embodiments.

[0022] FIG.2 shows a schematic diagram of an electrical equivalent circuit for an SCC coupled to a load resistor according to some embodiments.

[0023] FIG.3 shows a simplified schematic cross-section view of an electret SCC (E-SCC) according to some embodiments.

[0024] FIG.4 shows a schematic view of an E-SCC with a closed path drawn through its main components according to some embodiments.

[0025] FIG.5 is a graph of energy density versus EDL volume, illustrating a charge- discharge work cycle for the SCC shown in FIG.2 according to some embodiments.

[0026] FIG.6 shows a graph of a representative voltage-time curve for an E-SCC charging and discharging according to some embodiments.

[0027] FIG.7 shows a simplified schematic cross-section view of a bimetal SCC (B-SCC) according to some embodiments.

[0028] FIG.8 shows a simplified schematic cross-section view of a membrane SCC (M- SCC) according to some embodiments.

[0029] FIG.9 shows a simplified schematic cross-section view of another M-SCC according to some embodiments.

[0030] FIG.10 shows a simplified schematic cross-section view of another M-SCC according to some embodiments.

[0031] FIG.11 shows a simplified schematic cross-section view of another M-SCC according to some embodiments. DETAILED DESCRIPTION

[0032] The following description of exemplary embodiments of the invention is presented for the purpose of illustration and description. It is not intended to be exhaustive or to limit the claimed invention to the precise form described, and persons skilled in the art will appreciate that many modifications and variations are possible. The embodiments have been chosen and described in order to best explain the principles of the invention and its practical applications to thereby enable others skilled in the art to best make and use the invention in various embodiments and with various modifications as are suited to the particular use contemplated.

[0033] Disclosed herein are embodiments of a type of capacitor referred to as a “self- charging capacitor” (or “SCC”). SCCs are distinguished by their ability to harvest thermalenergy (heat) from their environments to charge themselves. One type of SCC uses electrets to induce charges in its electrodes, which then attract counter ions from an electrolyte to form an electric double layer (EDL) capacitor at each electrode. Another type uses a chemically asymmetric membrane between its electrodes to generate charge concentration gradients. Any type of SCC can be implemented as a standard capacitor or a supercapacitor (“super- SCC”). A super-SCC combines self-charging with the simplicity, achemicality, longevity, and intermediate power and energy densities of supercapacitors. SCCs can provide various improvements in energy production, storage, and use.

[0034] In some embodiments, individual SCCs may provide relatively low voltages; however, when arranged in series-parallel configurations, they can perform comparably to standard capacitors (or supercapacitors) in an array of technological applications and offer the advantage of self-charging behavior. Examples of applications for SCCs include power sources for trickle chargers, field sensors, portable phones, computers, smart devices (e.g., Internet of Things devices), and potentially any device that consumes electricity.

[0035] The fundamental physical principles undergirding the SCCs have been developed in related technologies. The electret SCC (E-SCC) and bimetal SCC (B-SCC) can be shown to be electrostatic cognates of a solid state thermal capacitor, while the membrane SCC (M- SCC) is related to a thermal battery. (Thermal capacitors and thermal batteries have been described in D.P. Sheehan, “A self-charging concentration cell: Theory,” Batteries 9372 (2023) and in D.P. Sheehan et al., “Concentration cell powered by a chemically asymmetric membrane: Experiment,” Sust. Ener. Assess. Technol.52102194 (2022).)

[0036] Example embodiments of SCCs, including the E-, B-, and M-SCC types are described herein. Those skilled in the art with access to this disclosure will appreciate that additional embodiments can be constructed without departing from the scope of this disclosure. Overview of SCCs

[0037] FIG.1 shows a simplified side cross-section view of an SCC 100 according to some embodiments. SCC 100 is bounded at either side by two identical, chemically-inert, electrically-conductive electrodes 102, 104, which can have generally planar proximal surfaces in a plane transverse to the plane of the cross section. Electrodes 102, 104 can be made of materials such as tantalum, aluminum, copper, niobium, and / or titanium. For asupercapacitor implementation, each of electrodes 102, 104 can be coupled to a respective supercapacitor electrode matrix 103, 105, which can be made of a material that provides a high ratio of surface area to volume, such as activated carbon, carbon nanotubes, carbon aerogel, or other carbonaceous materials. Such materials may be chemically inert or chemically functionalized, as described below. Depending on the particular implementations, electrodes 102 and 104 and / or supercapacitor electrode matrices 103, 105 can be physically and / or chemically symmetric or asymmetric. In some embodiments, supercapacitor electrode matrices 103, 105 can be omitted, and SCC 100 can be implemented as a standard capacitor or supercapacitor as desired.

[0038] SCC 100 also includes an asymmetric element 110, at least a portion of which is located between electrodes 102 and 104. Asymmetric element 110 represents one or more chemical and / or physical structures that can spontaneously generate a charge imbalance between electrodes 102, 104 and whose electrostatic capacitive energy is ultimately derived from environmental heat (thermal energy) via classical diffusion of particles, without requiring application of an external emf, thereby providing self-charging behavior. In various embodiments, asymmetric element 110 can incorporate any of an electret, a bimetal, a bipolar membrane, an anionic or cation exchange membrane, chemically-functionalized electrodes, or the like, in combination with a polarizable medium such as an electrolyte, a polarizable material, a semiconductor, or other material or medium to support the development of a charge imbalance between electrodes 102, 104 (e.g., via thermal diffusion of ions). The charge imbalance gives rise to an atomically-thick (on the order of angstroms) Helmholtz electrostatic double-layer (EDL) capacitor at each electrode. In addition to structures that generate a charge imbalance, asymmetric element 110 can incorporate a structure that maintains physical separation between electrodes 102, 104 to prevent shorting of the electrodes (e.g., an electrolyte-permeable separator material of the kind used in conventional capacitors or batteries). Specific example implementations of asymmetric element 110 according to various embodiments are described below.

[0039] The operational behavior of SCC 100 can be understood in terms of basic circuit elements. FIG.2 shows a schematic diagram of an electrical equivalent circuit 200 for SCC 100 switchably coupled to a load resistor 202 having resistance ^^^. As shown, load resistor 202 is coupled between electrodes 102, 104. Internal asymmetric element 110 is equivalent to an emf (^) with high internal resistance (^^^), represented by voltage source 204 and resistor 206. The two series capacitors 208, 210, with respective capacitances and ^^ଶcorrespondto the EDLs that form on electrodes 102, 104, and resistor 212, with resistance ^^ாௌோ, represents the effective series resistance (ESR) of capacitors 208, 210. Parameters ^, ^^^, ^^ଶ, ^^^, and ^^ாௌோare largely determined by chemical-thermodynamic parameters, i.e., chemical boundary conditions, ion mobility and concentration, diffusion coefficients for the electrolytic ions, as well as operating temperature. The particular values vary depending onthe implementation of SCC 100. In general, ^^^ ≫ ^^ாௌோ. A switch 214 controls the applicationof the system emfs and the flow of currents.

[0040] The primary operations of circuit 200 include: (i) SCC 100 self-charging while not under external load (when switch 214 is open); and (ii) SCC 100 discharging through external load (when switch 214 is closed). Basic circuit theory can be applied to each case. For convenience, the two capacitors can be combined into a single equivalent capacitor (^^^^ൌ ^భ^మ^భା^మ, which reduces to ^^^^ ൌ ^^^⁄ 2 ൌ ^^ଶ / 2 when ^^^ ൌ ^^ଶ).

[0041] When switch 214 is open, SCC 100 charges with characteristic RC-timeand when switch 214 is closed, SCC 100 discharges withcharacteristic RC-timeProvided that ^^^ ≫ ^^ாௌோ, ^^^ has negligibleeffect on ^^^୧^ୡ. Miniaturization of certain distances in SCC 100 may reduce these time constants considerably, as described below.

[0042] It should be understood that FIG.1 has been simplified to illustrate certain operating principles that guide the implementation of an SCC. Additional components may also be present. For example, the entire structure shown in FIG.1 can be enclosed in a housing through which electrical contacts to electrodes 102, 104 protrude. In some embodiments, the housing, or a portion thereof can be filled with electrolyte or other liquid polarizable medium. The liquid can be confined to the region between electrodes 102, 104. For instance, an electrically insulating sealing material can be used to create a seal at the edges of the electrode plates. In some embodiments, liquid can also be allowed to fill areas around the sides and distal surface of the electrodes.

[0043] Example embodiments implementing SCC 100 will now be described. The embodiments differ in the implementation of asymmetric element 110, with all embodiments producing behaviors corresponding to equivalent circuit 200.Electret SCC

[0044] FIG.3 shows a simplified schematic cross-section view of an electret SCC (E-SCC) 300 according to some embodiments. E-SCC 300 represents an implementation of SCC 100 in which the asymmetric element incorporates an electret. Specifically, in E-SCC 300 the asymmetric element includes an electret 312, 314 disposed on the distal surface (an outer surface oriented away from the other electrode) of each electrode 102, 104, as well as a polarizable medium 316. In some embodiments, polarizable medium 316 can include an electrolyte-permeable screen made of a non-conductive separator material such as a poly(ether ether ketone), or PEEK; cellulose cloth; or the like, which can be bathed in an electrolyte solution. In other embodiments, other polarizable materials can be used, including semiconductors, dielectrics, or other materials (e.g., any material usable to separate anode and cathode in a battery cell). As described above, supercapacitor electrode matrices 103, 105 can be included or omitted as desired.

[0045] Electrets 312, 314 can be made of one or more layers of dielectric materials with a quasi-permanent electric charge, with the two electrets 312, 314 having opposite charge. In the example shown in FIG.3, electret 312 has positive charge while electret 314 has negative charge. In some embodiments, electrets 312, 314 can be formed using charged paraffin wax, stacked layers of charged polytetrafluoroethylene (PTFE, sold as Teflon), or charged polyimide tape (e.g., Kapton tape). Additionally or instead, anionic and cation exchange membranes (AEM and CEM) as described below can be used.

[0046] In operation, the placement of oppositely-charged electrets 312, 314 on electrodes 102, 104 establishes a permanent electrostatic potential difference between the two sides of E-SCC 300. Electrets 312, 314 induce charges in electrodes 102, 104. The local electric field at each electrode attracts counter-ions from the electrolyte in polarizable medium 316 to electrode plates 102, 104, establishing a Helmholtz EDL capacitor at each plate. This is somewhat analogous to the behavior of conventional supercapacitors. However, in E-SCC 300, electrets 312, 314 enhance charge accumulation, enabling significant spontaneous charge accumulation through thermal diffusion.

[0047] The electrostatic configuration of E-SCC 300 can be analyzed using the time-independent form of Faraday's Law: ∮ ^^ ∙ ^^^^ ൌ 0. FIG. 4 shows a schematic view of E-SCC300 with a closed path 400 (dashed line) drawn through its main components forming a loop(through Points 1 → 2 → 3 → 4 → 1^. As shown, negative ions 418 in region 416 (which canbe filled, e.g., with an electrolyte solution or other material containing mobile ions) are attracted toward electrode 102 while positive ions 420 in region 416 are attracted toward electrode 104.

[0048] Starting in positively-charged electret 312 (Point 1) the Faraday line integral proceeds clockwise around path 400. The upper half of the line integral (from Point 1 to Point 2) passes through electrets 312, 314, metal electrodes 102, 104, the Helmholtz EDLs formed on each plate, and the electrolyte solution in region 416, while the lower half passes through electrets 312, 314 but not through other components. The potential drops across the twoEDLs (∆^^^ , ∆^^ଶ ) and between the two electrets 312, 314 (∆^^ ୪^ୡ^୰^^^) sum to zero; that is:corresponds to Point 1. (Itshould be understood that, at equilibrium, the electric fields inside the metal electrodes 102, 104 and inside the bulk electrolyte in region 416 would be zero because otherwise electric currents would be driven in them.)

[0049] In the infinite-plane approximation (parallel plate approximation for capacitors), thepotential drop ∆^^ ୪^ୡ^୰^^^ between the two electrets (across the distance L shown in FIG. 4)can be written in terms of areal charge density ^^ [C / m2] as ∆^^ఙ ୪^ୡ^୰^^^ ൌఢ ^^, where ^^ is the electrical permittivity of the intervening material and ^^ is the thickness of the material. Forsymmetric EDLs, the potential drop across each will be roughly half of ∆^^ ୪^ୡ^୰^^^; that is,∆^^ ^ ^,ଶ≃ ଶ^^ ୪^ୡ^୰^^^.

[0050] Electric fields, on the other hand, scale as ^^ ~ ∆^^ / ^^, where ^^ is the thickness of thefield. For the EDLs in supercapacitors, ^^ can be quite small, e.g., ^^ ≡ ∆^^~5 ൈ 10ି^^ m, inwhich case the electric field of an EDL can be substantial, perhaps in excess of 10ଽV / m. For thermally maintained potentials, as for E-SCC 300, electric fields are expected to beconsiderably less, but still substantial, e.g., ^^~10^ െ 10଼ V / m.

[0051] The capacitive (electrostatic) volumetric energy density stored in electric fields scales quadratically with field strength; that is, ^^^^J / mଷ^ ~ ^^^^ଶ / 2. If the electrets’ potentialdifference, ∆^^ ୪^ୡ^୰^^^, is divided equally between the two equivalent EDL capacitors ofthickness ∆^^, then their total areal potential energy density ^^^[J / m2] can be expressed as:where ^^^^ ൌ ^ఢ^ ଶ∆௫) is the equivalent capacitance of the capacitor pair.

[0052] Referring to FIG.2, the energy density of Eq. (1) corresponds to the high-energy equilibrium (or meta-equilibrium) state of SCC 100 when electric switch 214 is open. When switch 214 is closed, the potential difference between electrodes 102, 104 relaxes as the electrostatic energy in capacitors 208, 210 is released, and current flows through load resistor 202. The EDLs collapse as the ions disperse to a lower energy (mixed) state configuration within the electrolyte. The timescale for collapse is set by the RC-time constant ^^^୧^ୡ, as described above. Thereafter, when switch 214 is opened, SCC 100 returns to the high-energy equilibrium state at a timescale set by the RC-time constant ^^ୡ୦, as described above.

[0053] FIG.5 is a graph 500 of energy density versus EDL volume, illustrating a charge- discharge work cycle for EDL capacitors 208, 210 shown in FIG.2. FIG.5 can be understood as an electrostatic analogue of a classic pressure-volume (P-V) gas work cycle. Here, the ordinate (y-axis) is the EDL's energy density (^^^, which has units of electrostaticpressure (Pa)), and the abscissa (x-axis) has units of volume (Δ^^ ⋅ ^^). Analogously toconventional P-V diagrams, the area circumscribed by the cycle corresponds to the electrostatic pressure-volume work performed by the SCC cycle.

[0054] For convenience of description, a cycle is treated as starting at point 501, which corresponds to a discharged state. When switch 214 is opened, the cycle proceeds counter- clockwise, along path 502, toward point 503 as positive and negative ions in the electrolyte are drawn to their respective (oppositely-charged) electrode plates, thereby decreasing Δ^^ and increasing the system's capacitive energy. At point 503, the EDLs are fully formed and the system reaches its high-energy, meta-equilibrium state when Δ^^ reaches its minimum value(e.g., Δ^^ ≃ 5 ൈ 10ି^^ m for supercapacitors). Next, when switch 214 is closed, capacitors208, 210 discharge through load resistor 202, performing work, and the cycle continues counterclockwise, along path 504. The system arrives back at point 501 and is ready to repeat the cycle. The enclosed area of the cycle corresponds to the net work performed on the load.

[0055] Various prototype E-SCCs (constructed using the principles described above) have been experimentally tested in standard capacitor mode (without high surface area carbonaceous electrodes) with three kinds of electrets: (i) paraffin wax; (ii) multiple stackedlayers of 5 ൈ 10ିହ m thick PTFE (Teflon) charged via high-voltage corona discharges in air;and (iii) charged Kapton tape (polyimide with silicone adhesive). The electrolyte for the prototype E-SCCs was aqueous 10ିଷM NaCl solution.

[0056] Capacitor disc electrodes (diameter = 3.2 cm) were constructed from either1.25 ൈ 10ିସm or 7.5 ൈ 10ିହm thick tantalum foil. The separators were 1-5 layers ofchemically inert PEEK polymer screen (polyether ether ketone, 1.25 ൈ 10ିସm thick; openvolume 75%). Electrets were in direct physical contact with the tantalum electrodes. Electretelectric fields were estimate to be roughly 10ସ െ 10ହ V / m. Various load resistors ^^^ wereengaged (10ସΩ ^ ^^ ^^ ^ 10 Ω).

[0057] When cycled off and allowed to equilibrate, the prototype wax E-SCC exhibited stable, long-lived relatively large voltages (70 mV between electrodes) for days on end. Because it was a standard capacitor, its capacitance was minute (e.g., 10ିହF). Capacitance can be increased, e.g., by increasing the surface area of the electrodes (e.g., using etched surfaces or activated carbon).

[0058] FIG.6 shows a graph 600 of a representative voltage-time curve 602 for a prototype wax E-SCC during an experiment, near the end of a 22-hour run. The ordinate (y-axis) is the voltage drop across the 10ହΩ load resistor (in units of mV) and the abscissa (x-axis) is time (in seconds). Switch 214 (FIG.2) was closed and ^^^engaged on a 10% duty cycle; that is, 6 seconds discharging, 54 seconds recharging.

[0059] The cycling of curve 602 is indicative of capacitive charging and discharging. The slope of the discharge is steep, indicating short ^^^୧^ୡ, followed by a longer, slower recharge. Based on circuit parameters (FIG.2), the discharge RC-time constant is estimated atapproximately ^^ ହ ିହ^୧^ୡ ≃ ^^^^^^^ ≃ 10 Ω ⋅ 10 F≃ 1 second, which is roughly what is indicatedin FIG.6. The recharge RC-time constant is roughly 30 times longer, indicating that the ^^^isroughly 3 ൈ 10^Ω. This satisfies the criterion stated above that ^^^ ≫ ^^ாௌோ , ^^^. (This analysisalso presumes ^^^ ≫ ^^ாௌோ.)

[0060] The voltage excursion for the capacitors was between roughly 1-7.5 mV. The inferred average current was roughly 50 nA. The overall behavior is consistent with theoretical expectations for the E-SCC.

[0061] The steady cycling of the prototype E-SCC is compatible with repetitive electrostatic charging of capacitors, not with electrochemical processes. Once the capacitor settles down, a steady-state on-off cycle is established, as shown in FIG.5. Voltage declinescharacteristic of chemical reactions were not observed. It is also noted that the materials used to construct the E-SCC prototype were chosen to be chemically inert with respect to each other and known chemical reactions at the system operating temperature (290 K). For instance, the capacitor housing was machined acrylic, the electrodes tantalum, the electrets wax or Teflon, and the electrolyte 10ିଷM NaCl.

[0062] In some embodiments, an E-SCC may be modified into traditional capacitor jellyroll geometry and should be scalable into large series-parallel arrays. Most of the critical dimensions of an E-SCC can be substantially miniaturized so as to increase power densities significantly, as described below. Bimetal SCCs

[0063] FIG.7 shows a simplified schematic cross-section view of a bimetal SCC (B-SCC) 700 according to some embodiments. B-SCC 700 represents an implementation of SCC 100 in which the asymmetric element is provided by making electrodes 702, 704 of two dissimilar metals (or semiconductors). A polarizable medium 716 (which can be similar or identical to polarizable medium 316 described above and can include an electrolyte solution and an electrolyte-permeable separator material) separates electrodes 702, 704. As described above, supercapacitor electrode matrices 103, 105 can be included or omitted as desired. A potential difference (and electric field) is spontaneously generated using the contact (built-in) potentials between the two dissimilar metals (or semiconductors). In most respects, the principles of operation of B-SCC 700 are the same as for E-SCC 300 described above.

[0064] The manner in which current (or power) can be produced from the contact potential between two dissimilar metals (or semiconductors) will now be described. It is generally observed that the Fermi level between conjoined metals (or semiconductors) will quickly flatten out so that there is no net current flow inside the material; that is, there is no net chemical potential gradient across the material. For metals this leveling is nearlyinstantaneous (^^~10ି^ହ െ 10ି^^ sec), while for semiconductors it can take substantiallylonger (^^~10ି^ െ 10ି଼ sec, depending on doping. Heavily doped semiconductors actelectrically much like metals. Their respective plasma frequencies largely determine their leveling times. The price paid for flattening the Fermi level is the redistribution of charge, as well as the production of electric fields and potentials in, on, and around the materials.

[0065] The Fermi level flattening between dissimilar metals creates the contact potential between the metals, whereas for dissimilar semiconductors a built-in potential is established, as exemplified at the junction of a pn diode. The potentials are usually modest, typically 0-3 volts for contact potentials and less than 1 volt for built-in potentials; however, these are always expressed over very short distances (typically less than a micron), in which case very strong electric fields can be generated (> 106V / m) in and around the materials. Electric fields store electrostatic potential energy that can be released by a reconfiguration (switching) of the system’s boundary conditions. When properly marshalled, these intrinsic fields can create electricity. The discharge of a capacitor is an example of this.

[0066] Although there is expected to be no charge flow inside B-SCC 700 at equilibrium, there are expected to be equilibrium electrostatic fields that can be harnessed to carry out work, i.e., produce electricity, under appropriate circumstances. It is expected that a charging-discharging signature similar to that of the prototype wax E-SCC (as shown in FIG. 6) would be observed when under similar loads, reflecting repetitive electrostatic charging of a capacitor rather than electrochemical processes.

[0067] Like the E-SCC, the B-SCC may be modified into traditional capacitor geometries, may be scaled into large series-parallel arrays; and most of the critical dimensions can be substantially miniaturized so as to increase power densities significantly. Membrane SCCs

[0068] Membrane SCCs (M-SCCs) are SCCs constructed using chemically asymmetric membranes, including various combinations of anion and cation exchange membranes or fused versions of the two (referred to as bipolar membranes). As used herein, an “anion exchange membrane” (AEM) refers to a semipermeable membrane that selectively allows anions to pass through while blocking cations (and neutral atoms or molecules), and a “cation exchange membrane” (CEM) refers to a semipermeable membrane that selectively allows cations to pass through while blocking anions. A “bipolar membrane” (BPM) combines an AEM and a CEM, allowing anions to pass through in one direction and cations to pass through in the other direction. Numerous examples of such membranes are known in the art and are commercially available. Examples of M-SCCs will now be described.

[0069] FIG.8 shows a simplified schematic cross-section view of an M-SCC 800 according to some embodiments. M-SCC 800 represents an implementation of SCC 100 inwhich the asymmetric element incorporates a BPM 812 disposed between two regions 814, 816 of polarizable medium can be similar or identical to polarizable medium 316 described above. For instance, each region 814, 816 can be filled with an electrolyte solution and an electrolyte-permeable separator material. BPM 812 can be formed as an AEM fused to a CEM. (Some BPMs may have additional catalytic inner layers.) Any type of BPM can be used; examples are known in the art. As described above, supercapacitor electrode matrices 103, 105 can be included or omitted as desired. BPM 812 can have a strong built-in chemical potential gradient in which each side preferentially attracts its counter-ion. Via asymmetric diffusion through BPM 812, cations may be preferentially directed into region 814 while anions are preferentially directed into region 816 (or vice versa). This spontaneously generated difference in ion concentration gives rise to a potential difference (and electric field) between the electrodes.

[0070] Prototypes of an M-SCC implementing M-SCC 800 were constructed using commercially-available Fumasep bipolar membrane in 10ିଷM sodium chloride solution.Electrodes were low-surface area tantalum foil. Long-term voltages (2 ൈ 10ିଶV) anddischarge currents (^^ ∼ 10ି^ A) were measured across moderate load resistors (^^ ସ^ ൌ 10 െ10ହΩ in FIG.2), and the results indicated that the capacitor can produce steady, reliable output with charging and discharging cycles analogous to FIG.6 described above. When membrane orientation was reversed, the output voltage also reversed, as expected. Althoughthe capacitive charging times were relatively long (10ଷ െ 10ସ sec), this was unsurprisinggiven the thickness of the membrane stack (250 microns). If the stack is thinned to 1 micron or less, diffusion theory predicts that recharge times should shorten considerably and could be far less than a second.

[0071] The physical chemistry of M-SCC 800 can be further understood by reference to a thermal battery (e.g., as described in WO 2022 / 169773, “Thermal Diffusion Membranes, Devices, Systems, and Methods,” published November 8, 2022). In particular, it has been shown via theory, experiment, and numerical simulation that chemically asymmetric membranes can spontaneously generate concentration gradients of ions via directed diffusion, and that these gradients in turn can be used to power electrochemical concentration cells and, by extension, electronic and electromechanical devices. In effect, thermal batteries transduce environmental heat into electricity. M-SCC 800 can leverage the same effect while operating as a capacitor rather than as a battery. For instance, in M-SCC 800, the layer directly attached to the inner-facing side of each electrode 102, 104 can be a chemically-inert, high-surface-area supercapacitor electrode matrix 103, 105 (e.g., activated carbon). At the center of M-SCC 800 is BPM 812, which is a chemically asymmetric membrane. To either side are solution reservoirs (regions 814, 816) whose relative concentrations can be quantitatively shifted due to thermal diffusion through BPM 812, thereby creating a potential difference (and electric field) between electrodes 102, 104. Similar to the thermal battery, the emf (Φ^^^^) of M-SCC 800 is given by the Nernst relation:Here ^^^^ is thermal energy (J), ^^ is an electronic charge (C), and ^^^^୦ / ୪are the high / low concentrations of solute ^^ (in particles / m3or molarity) generated in regions 814, 816.

[0072] Power density ^^ [W / m3] for M-SCC 800 is predicted to scale as:Here ^^ is the diffusion coefficient of the active species ^^ (m2 / s); ^^ is the species mobility (C⋅s / kg); and ^^ is the thickness of the membrane and reservoir across which diffusion occurs. This is similar to the predicted scaling for thermal batteries described in WO 2022 / 169773.

[0073] Note that thermal energy (^^^^) and membrane thickness (^^) in Eq. (3) both appear quadratically. The ^^ଶdependence underscores the thermal nature of the effect. Eq. (3) suggests that higher power densities can be achieved through various combinations of elevated temperatures, high species mobility ^^, high concentrations ^^^^, and small diffusionlength ^^. Theoretical power densities of 10^ െ 10^ W / m3 are predicted for M-SCC 800,which again is similar to predictions for thermal batteries described in WO 2022 / 169773.

[0074] Other constructions and arrangements can exploit chemically asymmetric membranes to create concentration gradients.

[0075] FIG.9 shows a simplified schematic cross-section view of another M-SCC 900 according to some embodiments. M-SCC 900 represents an implementation of SCC 100 in which the asymmetric element incorporates an AEM 914 and a CEM 916, each of which is disposed between a respective one of electrodes 102, 104 and a region 912 containing a polarizable medium, which can be similar or identical to polarizable medium 316 described above and can include an electrolyte solution and an electrolyte-permeable separator material.Any type of AEM and CEM can be used; examples are known in the art. The AEM and CEM should be matched to the polarizable medium (e.g., electrolyte fluid or other mobile ions) in region 912. As described above, supercapacitor electrode matrices 103, 105 can be included or omitted as desired. A potential difference (and electric field) is spontaneously generated as a result of a concentration gradient that is spontaneously generated via directed diffusion through AEM 914 and CEM 916. Operation is similar to M-SCC 800 described above; the difference is that, rather than having the AEM and CEM seamlessly connected as a BPM, they are individuated, with a chemically inert separator between them. Spatially separating the AEM and CEM may prevent chemical interactions or interference between them and can also eliminate the need for an interface layer (present in many commercially available BPMs) that may have undesirable chemical effects.

[0076] FIG.10 shows a simplified schematic cross-section view of another M-SCC 1000 according to some embodiments. M-SCC 1000 represents an implementation of SCC 100 in which the asymmetric element incorporates a first chemically-functionalized electrode matrix 1014 disposed on electrode 102 and a second chemically-functionalized electrode matrix 1016 disposed on electrode 104. M-SCC 1000 is similar to M-SCC 900, except that instead of using discrete AEM and CEM structures to direct charge, the electrode matrix material itself is chemically functionalized with anionic or cationic chemical receptors that attract and bind their counter ions to form an EDL. The functionalization is asymmetric; for instance, if first chemically-functionalized electrode matrix 1014 is functionalized with anionic chemical receptors, then second chemically-functionalized electrode matrix 1016 is functionalized with cationic chemical receptors. Such configurations are referred to herein as “asymmetrically functionalized electrode” (AFE) configurations. Various combinations of matrix materials and chemical receptors can be used. For example, in embodiments where the electrode matrix material is activated carbon, examples of suitable chemical receptors include COOH, NH2, and NO2.A region 1012 containing a polarizable medium is disposed between first chemically-functionalized electrode matrix 1014 and second chemically-functionalized electrode matrix 1016. The polarizable medium in region 1012 can be similar or identical to polarizable medium 316 described above and can include an electrolyte solution and an electrolyte-permeable separator material. A potential difference (and electric field) is spontaneously generated as a result of a concentration gradient that is spontaneously generated via asymmetric behavior of first chemically-functionalized electrode matrix 1014 and second chemically-functionalized electrode matrix 1016. Operation is similarly to M-SCC 900 described above. In an AFE configuration, the charging and charge storage processes are integrated into a single layer.

[0077] FIG.11 shows a simplified schematic cross-section view of another M-SCC 1100 according to some embodiments. M-SCC 1100 represents an implementation of SCC 100 in which the asymmetric element incorporates an AEM or other first chemically-functionalized material 1114 disposed on a distal surface of electrode 102 and a CEM or other second chemically-functionalized material 1116 disposed on a distal surface of electrode 104. Region 1112 placed between electrodes 102 and 104 can contain a separator material 1113 that is permeable to the electrolyte solution, and the entire structure can be immersed in a bath 1118 of electrolyte solution. In some embodiments, separator material 1113 can also extend around the peripheral and distal surfaces of electrodes 102, 104 and chemically- functionalized materials 1114, 1116. M-SCC 1100 is similar to M-SCC 1000, except that the chemically-functionalized materials are placed on the distal surface of the electrodes rather than the proximal side as in M-SCC 1000. As in other configurations shown herein, a charge imbalance is created in the electrodes with respect to the electrolyte, giving rise to an EDL at each electrode. A variety of materials can be applied to the distal sides of the electrodes, including AEM and CEM materials, dried ion-exchange solution, or the like. Although not shown in FIG.11, it should be understood that the surface area of the proximal surfaces of electrodes 102, 104 can be increased, e.g., by application of a carbonaceous matrix material as described above.

[0078] Each of M-SCCs 800, 900, 1000, 1100 includes an asymmetric element that is able to separate positive electric charges from negative ones (e.g., BPM 812 in M-SCC 800; AEM 914 and CEM 916 in M-SCC 900; first chemically-functionalized electrode matrix 1014 and second chemically-functionalized electrode matrix 1016 in M-SCC 1000; first chemically- functionalized material 1114 and second chemically-functionalized material 1116 in M-SCC 1100) such that each charge species preferentially takes up residence in a distinct high- surface-area, electrically-conducting material attached to each capacitor electrode (e.g., matrix 103 and matrix 105 in M-SCCs 800 and 910; first chemically-functionalized electrode matrix 1014 and second chemically-functionalized electrode matrix 1016 in M-SCC 1000). Electrodes 102 and 104 (and matrices 103, 105; chemically-functionalized matrices 1014, 1016; or chemically-functionalized materials 1114, 1116) are separated and electrically isolated from one another, e.g., by a non-conducting separator membrane (e.g., PEEK membrane, cellulose cloth), which is permeable to the electrolyte ions; the separatormembrane can occupy regions 814, 816 in M-SCC 800; region 912 in M-SCC 900; region 1012 in M-SCC 1000; or region 1112 in M-SCC 1100. In M-SCCs, the charged electrodes attract counter-ions from the surrounding electrolyte (which can be, e.g., sulfuric acid, sodium chloride, hydrochloric acid, or the like) to form an atomically-thin, capacitive Helmholtz layer, the EDL. The combination of large surface area and thin capacitive layer satisfies the condition for large capacitance. Power Density Estimation for SCCs

[0079] Because of their unconventional designs, SCCs (like thermal batteries) invite a reevaluation of traditional energy metrics. Energy density (^^^(J / m3)) and power density (^^ (W / m3)) are two of the most prominent. Power density determines whether a power source is sufficient to drive a given application (e.g., an electrical load) from moment to moment, while energy density indicates how long the power source can continue to operate without recharging.

[0080] Energy density is often a focus of battery design because the energy reserves are assumed to be finite and in need of regular replenishment from a external, secondary energy source over which one might have only limited control (e.g., oil wells, wind, sun, electrical grid). For SCCs, however, energy density is largely irrelevant because their external, secondary energy source is the ambient heat bath, which by definition, permeates the system's environment and is, in most scenarios, effectively limitless in size. Given this, we now focus on power density.

[0081] As described above, power density for SCCs is expected to scale similarly to the estimate for thermal batteries (Eq. (3)). A rudimentary estimate of the maximum power density for fully miniaturized SCCs can be made as follows. Consider a cubic meter of E- SCCs (e.g., E-SCC 300) consisting of a stack of N thin, planar, 1-m2, parallel-plate capacitors. The thickness of a single SCC (^^୮) in meters is, therefore, equal to 1 / N. An individual E-SCC is composed of the following layers: two electrets 312, 314; two electrodes 102, 104; two electrode matrices 103, 105 (e.g., activated carbon layers); one separator 3116;plus electrolyte. Let each layer have a thickness of 2 ൈ 10ି^m, for a total E-SCC thickness of^^ ି^ ହ୮ ൌ 1.4 ൈ 10 m; thus, ^^ ൌ 1 / ^^୮ ≃ 7 ൈ 10 layers. The equivalent capacitance for asingle E-SCC is ^^^Letting the dielectric constant of the medium be ^^ ൌ 3, Δ^^ ൌ6 ൈ 10ି^^m, and A = 100 m ଶ, one obtains the capacitance: ^^^ ൌ 2.5 F. If arranged inelectrical parallel, the total capacitance of the entire stack of N E-SCCs is: ^^^^௧^^ ൌ ^^ ⋅ ^^^ ൌ1.8 ൈ 10^F. (The value of A = 100 m2 is estimated by assuming the activated carbon particlesare 10nm in size and packed comfortably into the 200nm layer on the electrode.)

[0082] The total capacitive energy (^^) stored in the N layers, assuming that the maximumcapacitor voltage is thermal in magnitude (i.e., Δ^^ ൌ 2^^^^ / ^^ ≃ 5 ൈ 10ିଶ V), is given by thetextbook definition of capacitive energy: ^^ ൌ ^ ଶ ଷଶ^^^^௧^^Δ^^ ൌ 2.3 ൈ 10 J. This is a ratherunimpressive value, but as noted above, energy density may be of less interest than power density.

[0083] Power density scales as ^^ ∼ ^^ / ^^, where ^^ is the characteristic time for charging ordischarging. Experimental evidence (as described above) indicates that charging is the rate- limiting process for SCCs. Because SCC charging is diffusion limited, ^^ is taken to be thediffusion time of ions across the thickness of the capacitor's interior, which is roughly ^^ ≃5 ൈ 10ି^m in the posited construction. Appealing to Fick’s law of diffusion, the averagesquared diffusion distance (^^) scales with time as: ^ ^^ଶ ^ൌ 2^^^^^^. For the SCC, we assumethat: ^^ ≡ ^^; ^^ ≡ ^^; ^ ^^ଶ ^∼ ^^ଶ; the diffusion coefficient (^^) is that of typical aqueous ionsat room temperature (^^ ≃ 10ିଽ m2 / s); and that the dimensionality of the system is taken tobe ^^ ൌ 1. This gives ^^ ൌିହଶ^^≃ 10 s. From this, the SCC's power density is estimated to be:^^ ∼ ^^ / ^^ ൌ 2 ൈ 10^ W / m3 (which compares favorably with power density estimates forthermal batteries).

[0084] Pulling together the strands of this analysis, one can infer the following general scaling relation for the SCC's thermally-driven power density ^^:Note the similarities between this and the scaling relation for the thermal battery (Eq. (3)), in particular, the linear dependence on diffusion (^^), and the quadratic dependence on temperature and system size, ^் ଶ^ ^ .Design Parameters and Construction

[0085] SCCs should operate over a wide range of physical parameters and material constructions. The following is a summary of some design considerations relevant to selecting materials and parameters for a given implementation.

[0086] Charge-Separation Elements: As described above, SCCs rely on charge separation, e.g., via electrets, membranes, or ion-binding chemicals.

[0087] (a) Electrets: As noted above, an electret generally refers to a dielectric material that holds a quasi-permanent electric charge. Examples of suitable materials include: paraffin, a relatively chemically-inert, hydrophobic hydrocarbon; Teflon (PTFE – polytetrafluoroethylene), a chemically-inert and highly triboelectronegative polymer; and Kapton tape (polyimide) with silicone adhesive.

[0088] Electrets can be charged by various techniques, including triboelectric rubbing with triboelectropositive materials (e.g., wool), corona discharge surface charging, liquid charging (corona discharge into melted wax), charge layering (multiple layers of surface-charged Teflon), or simply by contact and separation (such as unspooling tape from a roll).

[0089] E-SCCs rely on the electrets maintaining their charge. If charge is buried in the electret bulk and if the electret material is electrically insulating (e.g., Teflon, glass, non- conductive organic polymers), then electrets can retain their charge for years or decades. Surface charge, in contrast, is more easily lost. Electrets based on buried charge should be sufficiently thick — e.g., at least a micron or more — and electrically resistive enough that charge can be maintained for a usefully long time. In contrast to this, for electrets with bound charges, e.g., charged ionic solids and molecules, or electrically aligned dipolar molecules, the thickness of the electrets can, in principle, be made molecularly thin.

[0090] Optimum materials, electret thicknesses, and morphologies that produce the largest magnitude and most long-lasting voltages can be determined for a given application. Various modes of electret charging — including corona discharge, physical tribocharging, charged particle beams (electrons ions, charged radicals) — can be applied. Layering of charged thin Teflon sheets has been experimentally validated as a way to increase electret electric field by discrete jumps.

[0091] (b) Membranes and Ionic Materials: Ion exchange membranes are known to isolate and concentrate ions. For experiments described herein, commercial BPMs were used(Fumasep), but individual AEM and CEM films may also be used, as described above. For SCCs, desirable membrane and ion binding chemicals should preferentially and spatially bind and segregate cations from anions in order to create a persistent net voltage difference between the SCC electrode plates and in the EDLs.

[0092] Electrodes: As noted above, chemically inert electrode materials may increase the lifespan of SCCs. Examples of suitable materials include tantalum foil or gold foil, both of which are well known for chemical inertness. (In the case of tantalum, chemical inertness is derived from a thin surface layer of tantalum pentoxide.) Other possible electrode materials include aluminum and niobium. To boost capacitance, it is well known that roughening or etching surfaces of an electrode can increase effective surface area by a factor of 200 or more. Electrodes composed of or coated with a film of small particles, e.g., activated carbon or carbon nanotubes (CNTs), can increase plate surface area by a factor of 10ହor more. Film coating should be carried out judiciously because thick films can increase diffusion times, thus possibly degrading power density, as discussed above.

[0093] Electrolytes: Numerous liquid and solid electrolytes (organic and inorganic) have proven successful for supercapacitors and may be suitable for SCCs. Specific electrolytes that have been tested in prototypes include aqueous NaCl and HCl. Many electrolytic and supercapacitors use electrolyte solutions at concentrations in excess of 1M, and it is expected that electrolyte concentrations from roughly 10ିହM to multi-molar valuesshould be effective in an SCC. (In prototypes, concentrations in the range of 10ିଷ െ 10ିଶ Mhave been used.) In principle, any ion type, inorganic or organic, should support the SCC effect. In the interest of fast diffusion (and faster charging), high-mobility ions are preferable (e.g., alkali metal, alkali earth metal, halides). Hydrogen-based acids, like HCl and H2SO4, may be preferred, given the high mobility of the hydronium ion.

[0094] Separators: Separators (spacers) between plates should be chemically inert and thin so as to reduce the capacitor's equivalent series resistance (represented by resistor 212 in FIG.2), as well as to augment ion transport. Experiments described herein use PEEK screen and cellulose cloth of the kind used commercial supercapacitors. Other porous, electrically insulating materials can also be used. Thin separators should improve ion diffusion rates and boost power density.

[0095] Temperature and Pressure: Pressure should not play a decisive role in the performance of the SCC, however, as indicated in Eq. (4), power density is expected to scalequadratically with temperature. In some embodiments, high-temperature SCCs may act as secondary energy harvesters from high-temperature chemical processes or energy generation systems.

[0096] Miniaturization: As indicated by Eq. (4), energy and power densities for SCCs can increase significantly as key distances are reduced, especially ^^ and Δ^^. Accordingly, miniaturization may be advantageous. The miniaturization of an SCCs’ dimensions could employ many of the well-developed techniques that have supported the semiconductor revolution for the last half-century (e.g., micron- and sub- micron material deposition and patterning). Example Applications of SCCs

[0097] As described above, asymmetric charge distribution through an SCC is driven and supported by a built-in asymmetry in chemical potential. Since it is diffusive in nature, the potentials attainable by the SCC are likely to be not much more than a few times thermal energy. Because of this, the energy densities (not power densities) of individual SCCs are expected to be 2-4 orders of magnitude less than comparably constructed commercial supercapacitors (typical voltage 2-9 V). Nevertheless, such energy densities should be adequate for many applications, such as low-power sensors, trickle-chargers for batteries, or the Internet of Things. Other applications may include scenarios where modest sustained power is required but not conveniently available. The charging rate for an SCC may also be slower than that of conventional supercapacitors because the latter can employ considerable charging overpotential (much greater than thermal energy) so as to enforce rapid charging.

[0098] Despite these seeming disadvantages, the power densities of SCCs could becomparable to that of standard supercapacitors (on the order of 10^ െ 10^ W / m ଷ). Forinstance, the discharge rates of both SCCs and conventional supercapacitors are set by charge diffusion and internal resistance of the carbonaceous electrode material.

[0099] SCCs share some features with thermal batteries, in particular, a physical-chemical asymmetric structure by which heat is converted into electrical energy; however, SCCs have several distinctive advantages. For instance, unlike thermal batteries, SCCs do not rely entirely on a solute concentration difference between sides of a cell, but instead on separation of electric charge. Additionally, SCCs do not use chemical reactions or reservoirs of chemical species, which are prone to degradation; instead, an SCC operates as a capacitor, a device thatsimply stores charge and releases it electrically. These design and operational differences confer advantages to SCCs over various types of electrochemical cells. Examples of such advantages include: (1) Design and construction can be simplified and less expensive because SCCs lack chemical anodes and cathodes. (2) SCCs can be largely immune to chemical degradation of the electrodes since chemically inert materials can be used. Electrode degradation is the primary limitation on the operational life of most rechargeable batteries, as measured in effective discharge-recharge cycles. Modern lithium ion batteries, for example, have an operational life of about 500 cycles, at which point their charging capacity is reduced by roughly 20% and the battery is often replaced. In contrast, when operated within their specified temperature and voltage limits, the operational life of capacitors can be much longer. Traditional capacitors can cyclevirtually without limit, and conventional supercapacitors can cycle roughly 10ହ െ 10^ timeswithout appreciable degradation. SCCs are expected to exhibit similarly long operational life. (3) SCCs capture and convert heat from the environment into electricity. Environmental heat is effectively limitless in magnitude. The SCCs’ physical and chemical changes operate at much lower energy than chemical reactions in conventional batteries, reducing or minimizing degradation and chemical damage to SCC electrodes and electrolytes. (4) A self-charging supercapacitor can charge and discharge simultaneously. For continuous, low-power applications, this could be highly desirable. Additional Embodiments

[0100] Embodiments described herein provide self-charging capacitors that are powered by environmental heat and rely on asymmetric physical-chemical diffusion to generate an electric potential difference between the electrodes. SCCs as described herein include a pair of spaced-apart electrodes and an asymmetric element (e.g., an arrangement of materials relative to electrodes) that spontaneously creates a charge imbalance between the electrodes via thermal diffusion of an electrolyte, thereby giving rise to a thin (e.g., atomic-scale, on the order of angstroms) Helmholtz EDL at each electrode. SCCs advantageously do not rely on chemical reactions or on semiconductor processes, which may make them simpler and less expensive to construct, as well as less susceptible to chemical degradation. As describedabove, SCCs can be expected to operate through large numbers of charge-discharge cycles and to provide high power densities are substantial. Inexpensive and scalable SCC capacitor banks may be constructed.

[0101] While the invention has been described with reference to specific embodiments, those skilled in the art will appreciate that variations and modifications are possible. All numerical values and ranges provided herein are illustrative and may be modified. Unless otherwise indicated, drawings should be understood as schematic and not to scale. While various specific materials and dimensions are identified, those skilled in the art with the benefit of this disclosure will recognize that other materials can be substituted and that all dimensions can be modified as desired.

[0102] Accordingly, although the invention has been described with respect to specific embodiments, it will be appreciated that the invention is intended to cover all modifications and equivalents within the scope of the following claims.

Claims

WHAT IS CLAIMED IS:

1. A capacitor comprising: a first electrode; a second electrode; an electrically insulating separator disposed between the first electrode and the second electrode; an electrolyte at least partially filling a region between the first electrode and the second electrode, wherein the electrically insulating separator is made of a material that is permeable to the electrolyte; and an asymmetric element comprising one or more structures that spontaneously generate a charge imbalance between the first electrode and the second electrode.

2. The capacitor of claim 1 wherein the asymmetric element comprises a split electret having a positively charged material on the first electrode and a negatively charged material on the second electrode.

3. The capacitor of claim 1 wherein the asymmetric element comprises dissimilar materials in the first electrode and the second electrode.

4. The capacitor of claim 1 wherein the asymmetric element comprises a bipolar membrane and the electrically insulating separator is disposed on both sides of the bipolar membrane.

5. The capacitor of claim 1 wherein the asymmetric element comprises an anion exchange membrane disposed on a surface of the first electrode and a cation exchange membrane disposed on a surface of the second electrode.

6. The capacitor of claim 1 wherein the asymmetric element comprises an anionic chemical receptor disposed on a surface of the first electrode and a cationic chemical receptor disposed on a surface of the second electrode.

7. The capacitor of claim 1 wherein the first electrode and the second electrode include carbonaceous materials that increase a surface area of the first electrode and the second electrode.

8. A capacitor comprising:a first electrode at a first side; a second electrode at a second side; a polarizable material disposed in a region between the first electrode and the second electrode; and an electret that spontaneously generates a charge imbalance between the first electrode and the second electrode.

9. The capacitor of claim 8 wherein the electret establishes a permanent electrostatic potential difference between the first side and the second side of the capacitor.

10. The capacitor of claim 8 wherein the electret includes a first electret layer disposed on at least a portion of a distal surface of the first electrode and a second electret layer disposed on at least a portion of a distal surface of the second electrode, wherein the first electret layer and the second electret layer have opposite electric charges.

11. The capacitor of claim 8 wherein the electret is made at least in part of charged paraffin wax, stacked layers of charged Teflon, or charged Kapton tape.

12. The capacitor of claim 8 wherein the polarizable material includes one or more of: an electrolyte solution; a semiconductor; or a dielectric.

13. A capacitor comprising: a first electrode at a first side, at least a portion of the first electrode being made of a first material; a second electrode at a second side, at least a portion of the second electrode being made of a second material; and an electrolyte in a region between the first electrode and the second electrode; and an electrically insulating separator disposed between the first electrode and the second electrode, the electrically insulating separator being permeable to the electrolyte, wherein the first material and the second material are different materials having different contact potentials, thereby creating a potential difference between the first electrode and the second electrode.

14. The capacitor of claim 13 wherein the first material and the second material are different metals.

15. The capacitor of claim 13 wherein the first material and the second material are different semiconductors.

16. A capacitor comprising: a first electrode at a first side; a second electrode at a second side; a chemically asymmetric membrane disposed between the first electrode and the second electrode; and an electrolyte in solution in a region between the first electrode and the second electrode, wherein the chemically asymmetric membrane spontaneously generates a concentration gradient in the electrolyte.

17. The capacitor of claim 16 wherein the chemically asymmetric membrane comprises a bipolar membrane disposed within the region between the first electrode and the second electrode, the bipolar membrane defining a first separator region between the bipolar membrane and the first electrode and a second separator region between the bipolar membrane and the second electrode.

18. The capacitor of claim 17 wherein the first and second separator regions each are filled with a non-conductive material that is permeable by the electrolyte.

19. The capacitor of claim 16 wherein the chemically asymmetric membrane comprises: an anion exchange membrane disposed adjacent to the first electrode; and a cation exchange membrane disposed adjacent to the second electrode, wherein a region between the anion exchange membrane and the cation exchange membrane is filled with a non-conductive material that is permeable by the electrolyte.

20. The capacitor of claim 19 wherein the anion exchange membrane comprises anionic chemical receptors disposed on a surface of the first electrode and the cation exchange membrane comprises cationic chemical receptors disposed on a surface of the second electrode.

21. A capacitor comprising: a first electrode at a first side; a second electrode at a second side; a first chemically-functionalized material disposed on a distal side of the first electrode; a second chemically-functionalized material disposed on a distal side of the second electrode, wherein the first chemically-functionalized material and the second chemically-functionalized material attract oppositely-charged ions; and an electrolyte solution in a region between and around the first electrode and the second electrode, wherein the first chemically-functionalized material and the second chemically-functionalized material spontaneously generate a charge imbalance between the first electrode and the second electrode.

22. The capacitor of claim 21 wherein the first chemically-functionalized material comprises an anion exchange membrane and the second chemically-functionalized material comprises a cation exchange membrane.

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