1. Problem And Architectural Premise

Conventional rechargeable battery architectures, lithium-ion, lithium-iron-phosphate, nickel-metal-hydride, lead-acid, share a common structural assumption: the cell's external volume should remain constant across the operational state-of-charge envelope. Volume change during charge and discharge is treated as an unwanted side effect to be suppressed through binder formulation, electrode microstructure engineering, particle-size optimization, electrolyte additives, mechanical compression layers, and pack-level rigid envelopes. The engineering target is a cell whose external dimensions, internal pressure, and bulk density are as nearly invariant as the chemistry permits. Energy is stored along a single axis: the chemical-bond enthalpy associated with intercalation, alloying, or conversion reactions at the electrode interfaces.

This premise is structurally costly. The strain-management subsystems required to suppress volume change consume mass and volume budget that would otherwise carry active material. Binder content typically occupies 2 to 10 percent of electrode mass; mechanical-accommodation layers, expansion gaps, and rigid pack envelopes occupy a further 10 to 25 percent of cell volume. Each percent of strain-management overhead is a percent of capacity foregone. Worse, the constant-volume target leaves the density axis unused as an energy-storage modality: cells in which volume change is suppressed cannot store energy in inter-particle compaction, in framework hybridization transitions, in electrostatic strain, or in mass-addition density change, because each of these mechanisms manifests as the very volume change the architecture is engineered to prevent.

The architectural premise of the disclosed sealed carbon-bound cell is the inverse: the cell's density change with state of charge is not an engineering nuisance to suppress; it IS the operative storage axis. Charging proceeds by mass addition (bound hydrogen at the first electrode, bound oxygen at the second), by sp²-to-sp³ phase transformation at hydrogen-saturated carbon sites, by inter-particle aggregation under reduced electrostatic repulsion, and by electrostatic-strain energy accumulation across the cell's polarized configuration. Each mechanism contributes to the cell's measurable density. The aggregate density change IS the cell's state of charge. Engineering targets are flipped: maximize density swing rather than minimize it; instrument density as the SOC observable rather than reconstruct SOC from coulombic integration; eliminate the strain-management subsystems whose only purpose was to suppress the very signal the disclosed architecture treats as primary.

2. Core Architectural Primitive: Density-As-Storage

The core primitive is joint chemical-bond and electrode-density encoding of state of charge. State of charge is represented not as a scalar derived from coulomb counting but as a joint state along two coupled state variables: a chemical-bond state variable (the fraction of carbon sites occupied by C-H bonds on the first electrode and the fraction occupied by C-O bonds on the second electrode) and an electrode-density state variable (the bulk density of the bond-saturated electrodes and the inter-particle compressive strain field across the electrode microstructure). Both state variables evolve together during charging and discharging, both are physically observable, and both contribute substantively and additively to the cell's stored energy.

The architectural primitive recites the density axis as a co-equal contributor with the chemical-bond axis in the cell's energy budget. Conventional architectures store energy exclusively in chemical bonds; the disclosed architecture stores energy in chemical bonds plus the energy associated with framework hybridization change (sp²-to-sp³ reorganization stores 2 to 4 eV per converted C-H pair beyond the bond enthalpy alone), plus the energy associated with inter-particle compaction against electrostatic repulsion (typically 0.5 to 5 J/g of active material at full charge), plus the electrostatic-strain energy held in the cell's polarized configuration (0.05 to 5 J/g per the U = ½CV² governing relation). Total energy capacity per unit cell volume in disclosed embodiments exceeds the chemical-bond-only single-axis baseline by 15 to 40 percent depending on architecture.

Density-as-storage admits a measurement architecture qualitatively distinct from conventional SOC inference. Density is directly observable through mass measurement, dimensional measurement, internal-pressure measurement, or combined density measurement, with each modality producing an independent SOC reading from a different physical pathway. Multi-modality cross-validation reduces SOC uncertainty below any single-modality estimate and admits decision-grade SOC determination at full-charge and full-discharge limits where conventional electrochemical methods accumulate the largest error. The primitive is recited under U.S. provisional 64/052,368 as the architectural orientation of the class, with the four constituent density-change mechanisms (mass-addition, sp²-to-sp³ phase transformation, inter-particle aggregation, electrostatic strain) as required component primitives.

3. Two Coupled Storage Axes

State of charge is encoded jointly along two coupled state variables. The chemical-bond state variable comprises the fraction of carbon sites occupied by C-H bonds on the first electrode (typically 0 to 8 weight percent hydrogen content corresponding to 0 to 100 percent of carbon sites converted toward graphane stoichiometry) and the fraction of sites occupied by C-O bonds on the second electrode (typically 0 to 15 weight percent oxygen content corresponding to 0 to 100 percent toward graphene-oxide stoichiometry). The electrode-density state variable comprises the bulk density of the bond-saturated electrodes (typically varying by 1 to 5 percent across the SOC envelope at the electrode level) and the inter-particle compressive strain field (typically varying by 0.01 to 0.5 percent across the SOC envelope at the cell level).

The two axes are physically coupled, not independent. Higher chemical-bond population produces higher mass-addition density: each bound hydrogen adds 1.008 amu to the carbon framework at the binding site, and each bound oxygen adds 16.00 amu plus the geometric reorganization that accompanies C-O species formation. Higher inter-particle compaction admits higher chemical-bond population by improving accessibility of binding sites at particle-particle contact regions. The coupling is bidirectional and operates through the cell's physical state, not through external coordination. Each axis informs the other through the carbon framework's coupled response to bond formation and mechanical loading.

Both axes are substantively additive in total stored energy. The cell's energy capacity per unit cell volume exceeds what a single-axis (chemical-bond-only) architecture would deliver because the density axis stores energy a constant-density architecture would discard. The discarded fractions in conventional architectures are the framework hybridization energy (lost as suppressed mechanical work against the rigid pack envelope), the inter-particle compaction energy (lost as suppressed mechanical work against binder stiffness), and the electrostatic-strain energy (lost as suppressed dielectric polarization in low-permittivity electrolyte films). The disclosed architecture recovers each of these as productive storage capacity by admitting the density change rather than suppressing it.

4. Four Density Change Mechanisms

Density change during charging in the disclosed cell arises through four physically distinct, independent mechanisms whose contributions sum at the cell level. (1) Mass-addition: bound hydrogen at the first electrode (up to 7.7 weight percent at full graphane conversion) and bound oxygen at the second electrode (up to 15 weight percent at full graphene-oxide conversion) add real mass to the cell's electrodes. The added atoms come from sorbed water that was previously distributed in the polymer-electrolyte membrane; the bonded form adds to electrode mass and produces direct density increase at the electrode microstructure level. Mass-addition typically contributes 1 to 5 percent of the cell's total density change.

(2) sp²-to-sp³ phase transformation: as hydrogen atoms bond to carbon sites at the first electrode, those sites convert from sp² (planar, three-coordinate, π-bonded) hybridization to sp³ (puckered, tetrahedral, four-coordinate) hybridization. C-C distance at converted sites increases from approximately 0.142 nm to approximately 0.154 nm; out-of-plane displacement increases from approximately 0 nm (planar) to approximately 0.05 nm (chair-puckered). Net volumetric density change attributable to phase transformation alone is approximately 5 to 10 percent decrease at full saturation, partially offsetting the mass-addition density-increase, but the combined effect remains monotonic increase because mass-addition dominates. Phase transformation contributes approximately 20 to 30 percent of total density change.

(3) Inter-particle aggregation: bond-saturated electrodes occupy configurations of reduced inter-particle separation under reduced mutual electrostatic repulsion in the charged state. Particles in discharged state carry residual surface charge from unsaturated bonds, holding them at greater separation than the equilibrium minimum; in charged state, surface charge is reduced and particles relax toward closer packing. (4) Electrostatic-strain energy accumulation: the bound C-H species (partial positive character) and bound C-O species (partial negative character) establish macroscopic polarization across the cell, producing electrostatic force fields that drive inter-particle repositioning beyond mechanical equilibrium and accumulate strain energy in the carbon framework. Each mechanism is independent of the others; aggregate cell density at any operating point is calculable from the four component contributions under the cell's specific architecture and history.

5. Density-Based State-Of-Charge Measurement

The density-based encoding admits state-of-charge measurement modalities qualitatively distinct from the electrochemical-impedance and coulomb-counting methods used in conventional rechargeable cells. Mass-based measurement determines SOC through gravimetric measurement of the sealed cell on a precision scale; the cell's total mass is constant in the absolute sense (no mass crosses the cell boundary) but the spatially-distributed mass within the cell shifts measurably during charging as sorbed water in the membrane converts to bound H and O at the electrodes. The electrode mass change relative to membrane mass change is detectable through differential gravimetric techniques and admits SOC resolution in the 0.1 to 1 percent range.

Volumetric measurement determines SOC through dimensional sensing of the cell enclosure or through internal-pressure sensing in any engineered gas-phase free volume. Dimensional sensing exploits the cumulative density change across the four mechanisms to produce measurable external dimension change of 0.5 to 5 percent across the SOC envelope, well within strain-gauge, capacitive, LVDT, laser-interferometric, or fiber-optic Bragg-grating sensitivity ranges. Pressure sensing exploits Boyle's-law variation of inert-gas headspace pressure (argon, nitrogen) at typical headspace volumes of 1 to 10 cm³, producing 0.1 to 2 atm pressure variation across SOC at sensitivity admitting 0.05 to 0.5 percent SOC resolution.

Combined density measurement (joint mass and volume) admits the most accurate single SOC determination through redundant axes; cross-validation between mass and volume reduces uncertainty below either single-modality estimate because measurement errors in mass and volume sensors are uncorrelated. Multi-modality composition adds conventional electrochemical impedance spectroscopy and coulomb counting through Bayesian-class fusion, with three-modality composition typically reducing aggregate uncertainty by approximately the square root of the modality count. The disclosed primitive recites the multi-modality composition as a property of the architectural class, supporting decision-grade SOC for safe operation near full-charge and full-discharge limits, accurate dispatch in grid-services applications, and end-of-life-phase transitions where single-modality methods accumulate unacceptable error.

6. Operating Parameters And Engineering Envelope

The disclosed architecture admits engineered scope across multiple operating-parameter axes. Hydrogen content envelope at the first electrode is 1 to 8 weight percent, with 8 wt% corresponding to fully-saturated graphane (CH stoichiometry) and engineered cells typically operating in the 2 to 6 wt% envelope corresponding to 25 to 75 percent sp³ saturation fraction. Oxygen content envelope at the second electrode is 2 to 15 weight percent, with 15 wt% corresponding to fully-saturated graphene-oxide (CO and COH dominant species) and engineered cells typically operating in the 4 to 12 wt% envelope. Open-circuit voltage envelope is 1.0 to 1.3 V per cell, with effective polarization voltage attributable to bound-species charge separation in the 0.3 to 0.8 V range.

Effective cell capacitance falls in the 1 to 100 F per gram of active material range depending on electrode microstructure (BET surface area 100 to 2,500 m²/g), inter-electrode spacing (membrane thickness 25 to 250 μm), and dielectric properties of the polymer-electrolyte membrane (relative permittivity 5 to 25 depending on hydration state and chemistry). Total cell-level density change across full SOC envelope is 1 to 8 percent depending on architecture and saturation envelope, with corresponding linear-dimension change of 0.5 to 5 percent for typical prismatic geometries. Headspace internal pressure variation is 0.1 to 2 atm at engineered headspace volumes of 1 to 10 cm³ per the headspace primitive recited under provisional Section 12.

Operating temperature envelope is approximately -20 °C to +80 °C for polymer-electrolyte membrane embodiments, with extension to higher temperatures admitted by ceramic proton-conductor membrane embodiments (yttrium-doped barium zirconate operating at 200 to 600 °C). Cycle life targets are 5,000 to 50,000 deep-cycle operations for engineered cells, supported by the absence of dissolution and dendrite mechanisms that limit conventional lithium chemistries. Self-discharge rate is set by the metastability of bound C-H and C-O species in the absence of catalytic discharge pathways and is typically below 1 percent per month at room temperature operating points.

7. Alternative Embodiments

The density-as-storage architecture admits alternative embodiments along the carbon-source, dopant, membrane, enclosure, and operating-envelope axes. Carbon-source embodiments include single-layer chemical-vapor-deposited graphene (cleanest planar-to-chair phase transition with minimal lateral framework stress), multi-layer turbostratic graphene (admits inter-layer slipping accommodation during framework reorganization), single-walled and multi-walled carbon nanotubes (curvature-modulated saturation kinetics), graphitic activated carbon (high BET surface area at the cost of disordered local sp² stabilization), graphene oxide (pre-functionalized starting state for the second electrode), and amorphous or diamond-like carbon (limit configurations admitting local sp²-to-sp³ transition without long-range chair ordering).

Dopant embodiments admit substitutional N, B, P, S, and Mg dopants that modify the relative stability of sp² and sp³ configurations and the partial-charge character of bound species. N-doping stabilizes sp³ configurations and accentuates electrostatic-strain contribution; B-doping stabilizes sp² configurations and reduces phase-transformation contribution; engineered dopant patterns admit selective control of saturation fraction at engineered cell potentials. Membrane embodiments include perfluorinated sulfonic acid (Nafion-class, ε_r ≈ 5 to 15), sulfonated polysulfone with engineered hydrophilic domains (ε_r up to 25), bilayer composites (low-permittivity inner conductive layer plus high-permittivity outer storage layers), and ceramic proton-conductor compositions for elevated-temperature operation.

Enclosure embodiments admit rigid-frame architectures (welcome pressure-sensing modality through engineered headspace volumes), flexible-pouch architectures (welcome dimensional-sensing modality through engineered swell pattern), and hybrid rigid-frame-with-flexible-region architectures (admit both pressure and dimensional sensing simultaneously). Operating-envelope embodiments admit shallow-cycling (10 to 30 percent saturation swing, lowest mechanical stress, longest cycle life), moderate-cycling (30 to 70 percent swing, balanced energy-density and cycle-life), and deep-cycling (70 to 100 percent swing, maximum capacity per active mass). Each embodiment combination produces distinct cell-level performance characteristics under the same architectural class.

8. Composition With Broader Architecture

The density-as-storage primitive composes upstream with the reversible C-H bond formation primitive and the reversible C-O bond formation primitive (which establish the chemical-bond axis), with the cooperative-cleavage primitive (which mediates discharge through cascade re-aromatization at the first electrode), with the polymer-electrolyte membrane primitive (which sets the dielectric and inter-electrode geometry governing electrostatic strain), and with the carbon-source-class primitive (which determines phase-transformation density-contribution magnitude). The four density-change mechanisms are constituent primitives of the eight-element class membership recited under provisional Section 12.

Lateral compositions: the primitive interacts with the cycling-induced compaction primitive (recited under provisional Section 10), in which long-term mechanical loading from repeated charge-discharge produces irreversible inter-particle consolidation that composes with the SOC-dependent reversible aggregation as a co-acting density-change contribution. It composes with the optional-dopant primitive (Section 9), in which substitutional dopants modify each of the four density-change mechanism magnitudes. It composes with the cell-voltage primitive (Section 11), which sets the polarization-voltage envelope governing electrostatic-strain contribution.

Downstream compositions admit the multi-modality cross-validated SOC primitive (Section 13), in which density-based measurement composes with electrochemical impedance and coulomb counting through Bayesian-class fusion. The credentialed admissibility profile records the multi-modality measurement contributions and produces decision-grade SOC estimates supporting safe operation near full-charge and full-discharge limits, accurate dispatch in grid-services applications, and end-of-life-phase transitions. The architectural orientation also admits engineering-simplification compositions in which strain-management subsystems required by constant-volume architectures are eliminated, with mass and volume budget previously dedicated to strain management redirected to active material, admitting cell-level energy density gains both from the additional storage axis and from the strain-management overhead reduction.

9. Prior-Art Distinctions

The density-as-storage architecture's prior-art context spans rechargeable battery chemistries (lithium-ion, lithium-iron-phosphate, nickel-metal-hydride, lead-acid, lithium-sulfur, lithium-air, sodium-ion), supercapacitor architectures, hydrogen-storage materials (metal hydrides LaNi5, MgH2, NaAlH4; chemisorbed-hydrogen activated carbons), and aerospace nickel-hydrogen cells with pressure-based SOC measurement. The disclosed architecture is structurally distinct from each prior-art class through the integrated density-as-storage primitive operative across the four constituent density-change mechanisms.

Distinctions from lithium-ion intercalation chemistries: lithium intercalation in graphite (Li_xC_6) does not change carbon hybridization, graphite remains sp² throughout the SOC envelope. The disclosed primitive transitions hybridization at hydrogen-bound sites; the energy-storage axis is structurally distinct. Distinctions from lithium-air and metal-air chemistries: prior-art metal-air consumes external oxygen mass during discharge and releases it during charge, so cell mass varies with SOC. The disclosed cell is sealed; mass is conserved in the absolute sense and density change arises from internal mass redistribution rather than external mass exchange.

Distinctions from supercapacitors: prior-art supercapacitors store energy primarily through electrochemical double-layer formation at electrode-electrolyte interfaces, with energy density bounded by surface area available for double-layer formation (typically 5 to 10 Wh/kg). The disclosed cell stores energy primarily through covalent C-H and C-O bond formation (200+ Wh/kg target), with electrostatic-strain a small additive component on top of chemical-bond storage. Distinctions from Ni-H₂ aerospace cells: prior art measures gaseous H₂ partial pressure directly as the storage species; the disclosed cell stores hydrogen and oxygen as covalent bonds rather than gas-phase species, and pressure-sensing modality measures density change in the carbon framework rather than gas-species concentration. The mass conservation despite SOC-dependent density change is non-obvious from any prior architecture in which mass change accompanies energy change.

10. Disclosure Scope

The density-as-storage primitive is disclosed under U.S. provisional 64/052,368, filed April 29, 2026. The disclosure recites joint chemical-bond and electrode-density encoding of state of charge, the mass-addition density mechanism, the sp²-to-sp³ phase-transformation density mechanism, the inter-particle aggregation density mechanism, the electrostatic-strain density mechanism, the mass-based gravimetric SOC measurement modality, the volumetric SOC measurement modality (dimensional sensing and pressure sensing), the combined density-based SOC measurement, the multi-modality cross-validated SOC composition, the density-as-storage architectural inversion (engineering targets flipped from minimization to maximization of density swing), the engineering simplification through strain-management subsystem elimination, and the mass conservation despite SOC-dependent density change.

The disclosure admits implementations developed subsequent to filing, alternative carbon-source classes, novel dopant patterns, engineered shallow-versus-deep cycling envelopes, alternative membrane chemistries, hybrid sp²-sp³ ordered phases, novel pressure-sensor and dimensional-sensor architectures, engineered headspace gas compositions, hybrid rigid-flexible enclosure designs, and improved Bayesian fusion algorithms across SOC modalities, provided the underlying density-as-storage primitive is operative within the eight-element architectural class. Class membership at the architectural level admits broad freedom-to-operate blocking against variants that arrive at density-as-storage outcomes through alternative implementation paths.