Mechanism & Primitive Description

Cell density, defined as instantaneous mass divided by instantaneous occupied volume, functions as the most fundamental state-of-charge indicator under the joint-encoding architecture disclosed in Provisional 64/052,368. Whereas conventional state-of-charge surrogates such as terminal voltage, coulomb integration, or impedance spectra each respond to only a subset of the physical processes that govern stored energy, density responds to all of them simultaneously. The disclosed primitive accordingly treats density itself, not voltage, not accumulated charge, not impedance, as the primary observable from which state-of-charge is inferred.

Four density-change mechanisms are jointly captured by a single density measurement. First, mass-addition mechanisms: ingress or egress of working species (lithium, water, gas) across the cell envelope changes mass while volume responds elastically. Second, sp²/sp³ transformation mechanisms: bond-hybridization changes within carbon-bearing electrode phases alter local mass density without net mass exchange. Third, inter-particle aggregation mechanisms: progressive reduction of inter-particle voids during cycling-driven compaction increases effective density without altering mass. Fourth, electrostatic strain mechanisms: charge-state-dependent lattice strain modifies occupied volume at fixed mass. Each mechanism produces a characteristic signature in the joint mass-volume trajectory, and the combined density reading admits decomposition into mechanism-specific contributions when the trajectory is observed over time.

The primitive is realized through co-located high-precision sensing: a scale or load-cell measures mass, while either dimensional sensors (capacitive, optical, or strain-gauge) or an internal pressure transducer measures volume. The two readings are timestamp-aligned and divided to yield instantaneous density. The resulting density estimate, paired with its derived uncertainty, is signed into the cell's credentialed admissibility profile as a composite state-of-charge attestation.

Operating Parameters & Engineering Envelope

The mass channel operates across a dynamic range determined by the cell mass itself (typically 50 grams to 50 kilograms for laboratory through grid-scale formats) with target precision of one part in 10^4 or better. Sub-milligram resolution is feasible for laboratory cells using force-restoration balances; for grid-scale modules, strain-gauge load cells with integrated temperature compensation deliver one-part-in-10^3 resolution sufficient for the architecture's signal-to-noise budget.

The volume channel operates across the cell's free deformation envelope, typically 0.1% to 5% of nominal volume. Dimensional sensing employs three or more orthogonal displacement transducers placed on the cell envelope; their readings are combined through a calibrated geometric model to recover total enclosed volume. Internal pressure sensing offers an alternative: at fixed temperature and known compliance of the cell envelope, internal pressure is monotonically related to internal volume occupied by the active stack, and a pressure measurement substitutes for direct dimensional measurement when the envelope geometry is impractical to instrument.

Temperature compensation is mandatory on both channels. Mass measurement is influenced by buoyancy variation with ambient air density; volume measurement is influenced by thermal expansion of both the cell and the sensing fixture. The disclosed primitive incorporates a co-located ambient-temperature probe and applies a calibrated correction to each channel before division. Sampling cadence ranges from 1 Hz (continuous monitoring) to one sample per cycle (commissioning verification); higher cadences resolve transient density excursions during charge-discharge events while lower cadences suffice for asymptotic capacity verification. The sensor fixture is mechanically isolated from the cell's compressive constraint envelope so that compaction force does not bias the mass reading.

Alternative Embodiments

Several alternative embodiments fall within the disclosed primitive. In a first embodiment, mass is measured by a force-restoration balance directly beneath the cell while volume is measured by laser interferometry against a reference flat affixed to the cell's upper face. In a second embodiment, the cell is suspended in a sealed pressure-controlled chamber and volume is inferred from the chamber's pressure response to a calibrated volumetric perturbation, while mass is measured by the suspension load.

In a third embodiment, particularly suited to flooded or aqueous cells, the cell is partially or wholly submerged in a fluid of known density and the apparent-weight differential between submerged and dry states yields mass and volume simultaneously through Archimedes' principle. In a fourth embodiment, internal pressure of a sealed cell substitutes for external dimensional sensing; the cell envelope's known compliance translates pressure to volume. In a fifth embodiment, the mass-volume pair is sampled at multiple operating temperatures within a cycle, and the temperature-resolved density trajectory enables decomposition of strain-driven and aggregation-driven density components.

Composition with Adjacent Primitives

The combined-density-SOC primitive composes naturally with the multi-modality cross-validated SOC primitive disclosed in a sibling article. Where the present primitive cross-validates two physically independent axes (mass and volume) within the density modality, the multi-modality primitive cross-validates the resulting density-derived SOC against electrochemical-impedance and coulomb-counting estimates. Composition produces a four-axis attestation: mass, volume, impedance, and integrated charge.

The primitive further composes with the credentialed admissibility profile primitive. Each density measurement is signed at the moment of acquisition and bound to the cell's persistent identity record, producing a tamper-evident lifetime density log. Composition with the asymptotic-equilibrium-saturation primitive is also disclosed: density readings during break-in cycling reveal the approach to the asymptotic compaction state and provide an objective trigger for the transition to the plateau-capacity operating regime.

Prior-Art Distinctions

Conventional lithium-ion state-of-charge methods rely on terminal-voltage lookup, coulomb counting, or electrochemical impedance spectroscopy. Each measures a process-specific surrogate rather than the underlying density state. Voltage methods require a calibrated open-circuit-voltage curve and degrade as the curve drifts with age. Coulomb counting accumulates integration error and requires periodic recalibration at known endpoints. Impedance methods are sensitive to temperature, frequency choice, and contact resistance, and respond to a subset of internal processes.

Prior-art density measurement of batteries, where it appears at all, is performed ex-situ at end-of-life or at manufacturing acceptance. No prior-art system is known to the inventor that performs continuous, in-situ, joint mass-and-volume sensing on an operating cell, divides the two channels in real time to produce a density observable, and binds the resulting estimate to a credentialed admissibility profile. The combined-density primitive is therefore distinct in measurand (density rather than charge surrogate), in topology (joint two-axis sensing rather than single-axis), and in epistemic role (decision-grade attestation rather than diagnostic indication).

Disclosure Scope

The disclosure encompasses any state-of-charge determination apparatus or method in which density of a working cell is computed from temporally co-acquired mass and volume measurements, and in which the resulting density estimate is reported, logged, or used as input to a control or admissibility system. Scope extends to all sensing modalities that yield mass (gravimetric, inertial, hydrostatic) and all sensing modalities that yield volume (dimensional, pressure-derived, displacement-derived, optical-interferometric).

Scope further encompasses density-derived state-of-charge as applied to any electrochemical, electromechanical, or hybrid storage device whose stored-energy state correlates with bulk density: including but not limited to lithium-ion, sodium-ion, flow, metal-air, and carbon-based architectures. Scope encompasses both stand-alone density-SOC determinations and density-SOC determinations composed with other modalities through Bayesian or equivalent statistical combination. Scope encompasses the credentialed-attestation aspect: any system in which a density-derived SOC is cryptographically bound to a cell-identity record and presented to downstream consumers as a verifiable measurement event falls within the disclosed primitive.