Cell Voltage Thermodynamic Basis

Mechanism

The carbon-bound cell stores energy by reversible interconversion between two carbon-centered phases: a charged state dominated by graphane (a hydrogenated graphene derivative) and a discharged state dominated by graphene oxide (an oxygenated graphene derivative). The overall cell reaction couples hydrogen insertion and oxygen functionalization to the production of water and electrical work. During charging, electrical energy drives the formation of metastable graphane while graphene-oxide functional groups are reduced and water is consumed; during discharging, the metastable graphane releases hydrogen, oxygen functionalities are re-formed, water is produced, and electrical work is delivered to the load.

The cell voltage is the per-electron Gibbs free-energy difference between the charged and discharged states, computed as V = -ΔG / (nF), where n is the number of electrons transferred per overall reaction and F is the Faraday constant. The Gibbs free-energy difference is dominated by the enthalpy difference between graphane and graphene oxide together with the formation enthalpy of the water produced or consumed. Because the carbon scaffold itself is not consumed, it functions as a topologically stable host that alternately binds hydrogen and oxygen, the relevant enthalpies are those of the bound functional groups, not those of bulk carbon allotropes.

The voltage observed at the cell terminals under negligible current, the open-circuit voltage, coincides with the thermodynamic voltage to within millivolts. Under finite current the terminal voltage is shifted by overpotential contributions from charge-transfer kinetics, mass-transport limitations, and ohmic drop across electrolyte and contacts; these kinetic contributions are treated separately and do not alter the thermodynamic basis of the open-circuit voltage discussed here.

Operating Parameters

Three component enthalpies aggregate to produce the cell voltage, each thermodynamically established from independent measurement and computational chemistry. Graphane-formation enthalpy is +30 to +60 kJ/mol C, positive, reflecting the metastability of the hydrogenated phase relative to graphene plus molecular hydrogen. The positive sign is essential to the cell's operation as a storage device: it is precisely this metastability that allows charging to deposit free energy into the carbon-hydrogen bond network and subsequent discharging to recover that energy.

Graphene-oxide-formation enthalpy is -100 to -250 kJ/mol C, strongly negative, reflecting the stability of oxygenated graphene relative to graphene plus molecular oxygen. The wide range captures the diversity of functional-group populations present in graphene oxide: epoxide, hydroxyl, carbonyl, and carboxyl groups each contribute differently to the aggregate, and the equilibrium population depends on synthesis history and operating conditions. Water-formation enthalpy is the well-established -237 kJ/mol H₂O (Gibbs free energy of formation at standard conditions); the value is fixed and contributes uniformly to every cycle.

Aggregating across the three components yields an open-circuit voltage in the 1.0 to 1.3 V range. The variation within this range is set by the specific charged-state composition: cells charged to a hydrogen-rich graphane phase with minimal residual oxygen functionality lie near the upper bound, while cells charged to a partially hydrogenated state with residual oxygen functionality lie near the lower bound. Cell-to-cell variation within manufacturing tolerance typically spans 50 to 100 mV; cycle-to-cycle variation within a single cell typically spans 20 to 50 mV.

The voltage shifts monotonically with state of charge. At full charge the open-circuit voltage approaches 1.3 V, reflecting the maximally hydrogenated graphane phase; near the discharge limit the open-circuit voltage falls toward 1.0 V, reflecting the partially restored graphene-oxide phase. The shift is approximately linear over the central portion of the discharge curve and steepens at both endpoints, where compositional changes per unit charge are largest.

Alternative Embodiments

A high-energy-density embodiment maximizes the graphane-formation contribution by charging deeply into the metastable phase; the open-circuit voltage at full charge approaches the upper bound and the cell delivers correspondingly higher specific energy at the cost of slower charging kinetics and reduced cycle life. A high-power embodiment retains a partially hydrogenated charged state to preserve fast surface kinetics, accepting an open-circuit voltage near the middle of the range in exchange for higher peak current density.

A low-temperature embodiment exploits the relative temperature insensitivity of the graphane-formation enthalpy: because the entropy term in the Gibbs free energy is small for solid-phase functionalization reactions, the open-circuit voltage shifts only weakly with temperature, admitting predictable behavior across the polymer-membrane operating range. A high-temperature ceramic-membrane embodiment shows a slightly larger temperature sensitivity owing to thermal population of vibrational modes in the graphane phase, with open-circuit voltage at full charge falling by approximately 50 mV per 200 °C of temperature rise above 200 °C.

Composition

The voltage-versus-state-of-charge relationship is exposed to the cell controller and to upstream composers as a credentialed predicate: a callable mapping from measured open-circuit voltage to estimated state of charge. The predicate is signed under the cell's credentialed admissibility profile and is refined over service life as accumulated cycle history shifts the voltage curve. State-of-charge estimation by voltage measurement complements density-based estimation (which exploits the small mass change associated with hydrogen insertion) and impedance-based estimation (which exploits the change in interfacial impedance with composition); a fused estimate from all three modalities is itself a credentialed surface available to the cell's composers.

Composition with the operating envelope is direct: the open-circuit voltage at the lower envelope bound (0.5 V discharge cutoff) corresponds to a specific state-of-charge depletion below which further discharge produces irreversible damage to the graphene-oxide phase. The thermodynamic basis disclosed here provides the principled grounding for that envelope bound rather than a purely empirical cutoff.

Prior-Art Distinction

Conventional carbon-electrode storage cells, including supercapacitors, lithium-ion cells with graphite anodes, and lithium-air cells, derive their operating voltages from intercalation enthalpies, double-layer capacitance, or oxygen-reduction half-cell potentials, none of which involve the simultaneous hydrogen-insertion-and-oxygen-functionalization couple disclosed here. The carbon-bound cell's voltage is set by the enthalpy difference between two carbon-centered functionalized phases, not by ion intercalation into a host or by gas-phase reduction at an electrode surface.

The exposed credentialed voltage-state-of-charge predicate distinguishes the cell from conventional batteries that publish voltage curves only as static datasheet curves. The combination, coupled-functionalization thermodynamic basis, three-mode state-of-charge estimation, and credentialed predicate composition, is not present in prior carbon-electrode storage architectures.

Disclosure Scope

The cell voltage thermodynamic basis disclosed in Provisional 64/052,368 covers cells whose open-circuit voltage derives from the aggregate of graphane-formation enthalpy (+30 to +60 kJ/mol C), graphene-oxide-formation enthalpy (-100 to -250 kJ/mol C), and water-formation enthalpy (-237 kJ/mol H₂O), aggregating to 1.0 to 1.3 V depending on charged-state composition. The disclosure spans the voltage-versus-state-of-charge relationship, its exposure as a credentialed predicate, and its composition with the cell's operating envelope and with density-based and impedance-based state-of-charge modalities.

The disclosure does not constrain the specific functional-group population within the graphene-oxide phase, the specific hydrogenation pattern within the graphane phase, or the specific carbon scaffold morphology beyond the requirement that the aggregate enthalpies fall within the disclosed ranges and the aggregate voltage fall within the disclosed bounds.

The disclosure further covers methods of voltage-curve calibration over service life. As the cell accumulates cycles, the equilibrium populations of functional groups within the graphene-oxide phase shift modestly, producing a slow drift in the open-circuit voltage curve that, if uncompensated, would degrade the accuracy of voltage-based state-of-charge estimation. The disclosed calibration method recovers the current voltage curve by combining periodic full-cycle reference measurements with continuous fusion against the density-based and impedance-based modalities, producing an updated credentialed predicate that is signed under the cell's admissibility profile and made available to upstream composers without requiring controller replacement.

The disclosure additionally covers methods of cell-to-cell voltage-curve harmonization within a multi-cell pack. Because cell-to-cell variation within manufacturing tolerance produces voltage offsets of 50 to 100 mV at equal state of charge, naive parallel or series operation would produce circulating currents or charge imbalances. The disclosed harmonization method registers each cell's individual voltage curve as a credentialed predicate and combines the predicates at the pack-controller boundary, admitting balanced operation without requiring physical voltage matching across cells. The pack-level predicate is itself a credentialed surface inheriting the audit semantics of its constituent cell predicates.