Mechanism and Primitive Description
Capacity-rise inversion is the observable, integrated consequence of cycling-induced compaction acting on a confined porous carbon electrode that hosts the hydrogen-oxygen redox couple. During each charge-discharge cycle, the electrode experiences gradient pressures driven by ionic and gaseous species redistributing between the bulk pore network and the active interface. In a mechanically constrained geometry, those gradient pressures cannot be relieved by bulk expansion; instead, they relax internally through diffusion, leaving residual compressive stress on the carbon skeleton. The skeleton responds by progressive plastic deformation: particles slide and rotate into denser packing, inter-particle adhesion strengthens, and previously empty pore volume collapses. Each of these microstructural changes increases the volumetric density of accessible redox sites per unit electrode volume, raising the cell's effective capacity.
Because plastic deformation is cumulative across cycles while elastic deformation reverses on each unloading, the net densification grows monotonically with cycle count until the elastic resistance of the densified skeleton balances the per-cycle compressive stress. At that point the electrode reaches an asymptotic state in which further cycling produces no net microstructural change, and capacity ceases to rise. The integrated capacity trajectory therefore follows a saturating curve: rapid rise during the early break-in cycles, decelerating gain across mid break-in, and a flat plateau thereafter. The qualitative inversion of fade is the first-order behavioral signature of this trajectory and is the primitive claimed in this article.
The primitive is defined behaviorally rather than mechanistically: any cell architecture exhibiting monotonic capacity rise across an initial cycling interval, followed by an asymptotic plateau, in the absence of factory pre-conditioning, falls within scope. The disclosed sealed carbon-bound hydrogen-oxygen architecture is one embodiment; the primitive itself is the qualitative class property.
Operating Parameters and Engineering Envelope
The capacity-rise envelope is bounded by three engineering parameters: break-in cycle count, rise magnitude, and asymptotic stability. Break-in cycle count is the number of full charge-discharge cycles required to traverse from first-cycle capacity to within five percent of the asymptotic value. The disclosed embodiments span fifty to five hundred cycles, with shorter break-in associated with higher per-cycle compressive stress and tighter mechanical confinement. Rise magnitude, the ratio of asymptotic capacity to first-cycle capacity, less unity, ranges from zero (a cell already at compaction equilibrium at first cycle) to approximately fifty percent. The upper bound is set by the initial void fraction of the carbon electrode and the practical limit of inter-particle adhesion strengthening before mechanical failure of the binder phase.
Asymptotic stability characterizes the flatness of the post-break-in plateau. Once the elastic resistance of the densified skeleton matches the per-cycle compressive stress envelope, residual capacity drift is below measurement noise across multi-thousand-cycle horizons in the disclosed embodiments. This stability is critical for the multi-decade structural-storage applications motivating the primitive: a cell that completes break-in during a building's commissioning phase is expected to operate at near-asymptotic capacity for the remaining operational lifetime.
Operating temperature, depth of discharge, and charge rate each modulate the per-cycle compressive stress and therefore the break-in trajectory, but not the qualitative inversion. Higher temperature accelerates diffusion-limited gradient relaxation, shortening break-in. Deeper discharge increases per-cycle stress amplitude, raising the asymptotic density. Charge rate influences the spatial uniformity of compaction. Across the disclosed parameter envelope, capacity rise is robust to operating-condition variation; the inversion does not require a narrow tuning window.
Alternative Embodiments
The primitive admits embodiments differing in carbon morphology, confinement geometry, electrolyte composition, and break-in scheduling. Carbon morphology may range from high-surface-area activated carbon through structured graphitic phases to engineered hierarchical pore networks; each yields a different rise magnitude and break-in duration but preserves the qualitative inversion. Confinement geometry may be cylindrical, prismatic, or planar, with the constraining structure provided by the cell housing, by adjacent structural elements in a structural-storage installation, or by an internal mandrel.
Break-in may be performed at constant current, constant power, or under field-representative load profiles. Field break-in during the commissioning phase of a structural-storage installation is a preferred embodiment because it eliminates the cost and logistical burden of factory pre-conditioning. Alternative embodiments include staged break-in, in which the cell is cycled at progressively increasing depth of discharge, and accelerated break-in, in which elevated temperature is applied to shorten the asymptote-approach interval. The primitive scope encompasses any break-in protocol that traverses the rise envelope without exceeding the mechanical or chemical stability limits of the cell.
Composition with Adjacent Primitives
Capacity-rise inversion composes directly with the cycling-compaction primitive that supplies its mechanism, with the progressive-deformation primitive that describes the microstructural response, and with the Terzaghi-consolidation analogy that grounds the relaxation physics in established prior art. In the parent provisional, these primitives are arranged hierarchically: cycling-compaction is the operational primitive, progressive-deformation is the microstructural primitive, capacity-rise inversion is the system-level behavioral primitive, and the Terzaghi analogy is the physical-admissibility primitive.
The behavioral primitive also composes with the structural-storage primitive family, because the multi-decade installation context is what makes field break-in operationally feasible. A cell installed in a load-bearing structural element is cycled by ordinary building-operation loads across its commissioning phase, producing the asymptotic capacity at no additional cost. Composition with the osmotic-pressure-constrained-geometry primitive is required: without mechanical confinement, gradient relaxation drives bulk expansion rather than skeleton compaction, and the rise inversion is not realized.
Prior-Art Distinctions
Prior-art lithium-ion cells exhibit monotonic capacity fade across cycling, driven by solid-electrolyte-interphase growth, lithium plating, active-material loss, and electrolyte decomposition. Capacity-fade trajectories are well documented across the lithium-ion literature and are the dominant degradation signature of the entire architectural class. The disclosed architecture inverts this signature qualitatively: capacity rises rather than falls across the analogous early-life interval.
Prior-art batteries do exhibit limited break-in phenomena, including formation cycling that stabilizes the solid-electrolyte interphase and modest reversible capacity recovery after rest. None of these phenomena produce the magnitude (up to fifty percent of first-cycle capacity), the duration (fifty to five hundred cycles), or the qualitative inversion of fade that characterizes the disclosed primitive. Formation cycling is a factory operation; the disclosed break-in is a field operation. Rest-induced recovery is small and transient; the disclosed rise is large and asymptotic.
Capacity rise has been reported in narrow contexts, certain conversion-type electrodes during early cycles, but always as an artifact of incomplete first-cycle utilization rather than as a structural densification of the host electrode. The disclosed primitive is mechanistically distinct: it arises from cycling-induced compaction of the porous carbon skeleton hosting the redox chemistry, not from progressive activation of unutilized active material.
Disclosure Scope
The disclosure scope of capacity-rise inversion encompasses any cell, of any chemistry, exhibiting monotonic capacity rise across an initial cycling interval followed by an asymptotic plateau, in which the rise is produced by cycling-induced compaction of a porous host electrode under mechanical confinement. Scope is not limited to the sealed carbon-bound hydrogen-oxygen embodiment of the parent provisional; the qualitative inversion is the claimed primitive, and any chemistry-host pair satisfying the mechanism description falls within scope.
The scope explicitly excludes capacity recovery that is reversible on rest, capacity gain that arises from progressive activation of initially inaccessible active material, and capacity stabilization following formation cycling at the factory. The distinguishing criterion is the structural origin of the rise: cumulative plastic deformation of a confined porous skeleton driven by cycling-induced compressive stress.
Within this scope, the primitive may be claimed independently of the cell chemistry, the carbon morphology, the confinement geometry, and the break-in protocol. It may also be claimed in combination with any of the adjacent primitives in the cycling-compaction family disclosed in U.S. Provisional Application 64/052,368, supporting both narrow embodiment claims and broad behavioral claims at the architectural class level.
Detection and verification of the primitive require monitoring cell capacity across the cycling interval and confirming three diagnostic features: monotonic rise across the break-in cycle count, asymptotic stability following the rise, and irreversibility of the gain across rest periods. Cells exhibiting all three features are within the disclosure regardless of the specific mechanism inferred to produce the rise; cells exhibiting only one or two features lie outside the primitive's claimed scope. This diagnostic framework supports examination by patent practitioners and characterization by cell developers seeking to establish whether a given cell architecture practices the disclosed primitive. The framework also supports the construction of method claims directed at field break-in protocols that traverse the rise envelope efficiently, including protocols specifying minimum cycle counts, depth-of-discharge schedules, and temperature profiles tailored to particular structural-storage installation contexts.
