The Volumetric Measurement Primitive
Volumetric state-of-charge measurement is one of three primary SOC measurement modalities admitted by the disclosed sealed cell architecture (per Provisional 64/052,368, Section 13). Where mass-based measurement (gravimetric) operates on the cell's total mass and combined-density measurement (joint mass-volume) operates on cell density, volumetric measurement operates on the cell's geometric and pressure state. The primitive admits two physically distinct sensing pathways: dimensional sensing (measuring external enclosure dimensions or internal volume directly) and pressure sensing (measuring internal pressure of any gas-phase free volume within the enclosure).
The dimensional-sensing pathway exploits the four density-change mechanisms recited in the density-as-storage primitive, mass-addition, sp²-to-sp³ phase transformation, inter-particle aggregation, and electrostatic strain, to produce measurable external dimension change as charging proceeds. With the cell's mass conserved through internal cycling, the volumetric change directly reflects density change, and density change directly reflects state of charge. Strain-gauge sensing on the enclosure surface, capacitive proximity sensing, laser-interferometric measurement, or LVDT (linear variable differential transformer) displacement sensing each admit dimensional measurement at the appropriate sensitivity scale.
The pressure-sensing pathway exploits any gas-phase free volume within the cell enclosure. While the disclosed cell holds water exclusively in covalently-bound and sorbed forms (per the no-bulk-liquid-water primitive of Section 4), engineered cells may incorporate a small headspace of inert gas (argon, nitrogen) for mechanical accommodation of the electrode density swing. The headspace pressure varies inversely with electrode-occupied volume per Boyle's law (P_1·V_1 = P_2·V_2 at constant temperature and constant gas mole count). Pressure sensors integrated into the headspace volume admit direct SOC determination through the headspace pressure reading.
Operating Parameters And Engineering Envelope
Dimensional change across the full SOC range is in the 0.5 to 5 percent linear-dimension range depending on cell architecture and density-swing magnitude. For a typical prismatic cell with linear dimensions of 100 mm, dimensional change is 0.5 to 5 mm across SOC, well within strain-gauge measurement range (typical sensitivity 0.001 mm or better) and laser-interferometric range (sub-nanometer sensitivity at relevant standoff distances). Sensitivity admits SOC resolution in the 0.1 to 1 percent range from dimensional measurement alone.
Internal pressure variation in a 1 to 10 cm³ headspace at typical density swings is in the 0.1 to 2 atm range. Engineered cells operate at headspace internal pressure 0.5 to 2 atm per Provisional 64/052,368, Section 12, the disclosed envelope; the volumetric SOC range maps cleanly onto the operational pressure envelope. Commercial pressure transducers in the 0 to 5 atm range deliver 0.001 atm sensitivity, admitting SOC resolution in the 0.05 to 0.5 percent range from pressure measurement alone.
Operating temperature affects both modalities. Dimensional sensing requires temperature compensation (carbon-electrode thermal expansion coefficient ≈ 1×10⁻⁶ /K, polymer-membrane coefficient ≈ 80×10⁻⁶ /K, enclosure-material coefficient ≈ 10 to 25×10⁻⁶ /K), practical implementations co-locate temperature sensing with dimensional sensing for compensation. Pressure sensing similarly requires temperature compensation through PV/T = constant for the gas-phase headspace.
Alternative Embodiments
The volumetric primitive admits alternative embodiments along several axes. Dimensional-sensing modality embodiments: surface-mounted strain gauges (low cost, distributed measurement, susceptible to thermal noise); LVDT or capacitive proximity sensors (medium cost, point measurement, robust to thermal noise); laser interferometry (high cost, high sensitivity, requires line-of-sight); fiber-optic Bragg-grating sensors (medium cost, distributed and embedded sensing, high temperature stability). Each admits the same SOC determination through different cost-sensitivity-environment trade-offs.
Pressure-sensing modality embodiments: integral diaphragm pressure transducers (welded into headspace), MEMS pressure sensors (low cost, small footprint), capacitive pressure sensors (low power), and acoustic resonance pressure sensors (no electrical connection through the cell wall). Headspace gas embodiments admit argon (chemically inert, low solubility), nitrogen (lower cost, slight solubility), or vacuum (zero-pressure baseline; pressure increase from any outgassing or swelling). The disclosed primitive admits all three.
Free-volume engineering embodiments: rigid-enclosure cells with engineered headspace (welcomes pressure-sensing modality), flexible-pouch cells with engineered swell pattern (welcomes dimensional-sensing modality), hybrid cells with both rigid frame and flexible regions (admits both modalities simultaneously).
Composition With Adjacent Primitives
The volumetric measurement primitive composes with the four density-change mechanisms upstream, mass-addition, sp²-to-sp³ phase transformation, inter-particle aggregation, and electrostatic strain, which jointly produce the cell's measurable volumetric change. The primitive composes with the joint-bond-density-encoding primitive (Provisional 64/052,368, Section 13) by providing measurement access to the electrode-density state variable along the volumetric axis.
Downstream compositions: with the combined-density-SOC primitive, where simultaneous mass and volume measurements yield density directly with cross-validated uncertainty; with the multi-modality cross-validated SOC primitive (Section 13), where volumetric measurement composes with electrochemical impedance spectroscopy and coulomb counting through Bayesian-class fusion. The credentialed admissibility profile records the multi-modality measurement contributions and produces decision-grade SOC estimates that support safe operation near full-charge and full-discharge limits, accurate dispatch in grid-services applications, and end-of-life-phase transitions.
Prior-Art Positioning And Distinctions
Pressure sensing in sealed electrochemical cells is established prior art in nickel-hydrogen aerospace cells (Pickett, 1975; Lim & Verzwyvelt, 1988), where headspace H₂ pressure varies with SOC through Sieverts' law, and pressure measurement is the primary SOC modality. Dimensional sensing in pouch-cell lithium-ion architectures has been studied for swelling-detection during overcharge or thermal runaway events. The disclosed primitive draws on this established sensor technology applied to a fundamentally distinct cell architecture.
Distinctions from Ni-H₂ aerospace cells: prior art measures gaseous H₂ partial pressure as the storage species. The disclosed cell stores hydrogen and oxygen as covalent C-H and C-O bonds rather than as gas-phase species; the volumetric modality measures density change in the electrode framework, not gas-phase species concentration. The measurement physics are distinct.
Distinctions from Li-ion swelling sensors: prior-art swelling detection is binary, operating versus failure mode. The disclosed primitive operates as a continuously-variable SOC indicator across the full operating envelope. Distinctions from coulomb counting: coulomb counting is integrative and accumulates measurement error over time. The disclosed volumetric primitive is direct and accumulates no time-dependent error, a fundamental sensor-architecture advantage for long-life applications.
Disclosure Scope
The volumetric state-of-charge measurement primitive is disclosed under U.S. provisional 64/052,368, filed April 29, 2026, as one of three primary SOC measurement modalities admitted by the density-as-storage architecture. The disclosure recites the dimensional-sensing pathway (strain-gauge, LVDT, capacitive, laser-interferometric, fiber-optic Bragg sensors), the pressure-sensing pathway (Boyle's-law application to engineered headspace gas-phase free volume), the operating ranges (0.5 to 5 percent linear dimension change, 0.1 to 2 atm headspace pressure variation), the SOC resolution envelope (0.05 to 1 percent depending on modality), the temperature-compensation requirement, the rigid-enclosure and flexible-pouch architectural embodiments, and the multi-modality composition with mass-based and electrochemical SOC modalities.
The disclosure admits implementations developed subsequent to filing, alternative dimensional-sensing technologies, novel pressure-sensor architectures, engineered headspace gas compositions, hybrid rigid-flexible enclosure designs, and improved Bayesian fusion algorithms across modalities, provided the underlying volumetric SOC mechanism is operative. Class membership at the architectural level admits broad freedom-to-operate blocking against variants that arrive at sealed-cell SOC measurement through volumetric pathways.
