1. Problem And Architectural Premise

The dominant cycle-life behavior in commercial battery architectures is monotonic capacity-fade. Lithium-ion cells, the dominant chemistry of the past three decades, exhibit fade rates of 0.02 to 0.10 percent per cycle under typical usage, with end-of-life conventionally defined at 80 percent of nameplate capacity. The fade is driven by parasitic chemistry: solid-electrolyte-interphase (SEI) growth consumes cyclable lithium and increases ohmic resistance, lithium plating at the graphite anode under high-rate or low-temperature conditions further consumes inventory, electrolyte decomposition produces gas and increases impedance, and mechanical degradation, particle cracking, binder failure, current-collector delamination, reduces the active electrode surface area available for charge transfer. Every one of these mechanisms is irreversible under normal operation; capacity lost is capacity gone.

The architectural premise of cycling-induced compaction is that none of those parasitic mechanisms operate in the disclosed sealed carbon-bound cell, and that the dominant cycling-driven structural change in the cell is, instead, a beneficial mechanical densification of the carbon electrode. The cell uses no liquid alkyl-carbonate electrolyte (so no SEI grows), no metal anode (so no plating occurs), no organic binder susceptible to oxidative decomposition, and no current-collector–electrode interface susceptible to delamination. What it does have is a polymer-bound carbon electrode in mechanical contact with a polymer-electrolyte membrane, all enclosed in an envelope that is engineered to be rigid and to have a low thermal conductance to the external environment. Cycling drives heat generation and concentration gradients inside this envelope; the envelope's mechanical constraint and thermal accumulation convert what would otherwise be transient operational byproducts into a slow, cumulative, beneficial structural change. The use-dependent capacity-rise property is the architectural inversion of capacity-fade and is the subject of this disclosure under U.S. provisional application 64/052,368, filed April 29, 2026.

2. Core Architectural Primitive

The core architectural primitive is a sealed cell in which three engineered envelopes, thermal, mechanical, and ionic, are jointly tuned so that ordinary cycling drives a self-densification process in the carbon electrode. The thermal envelope is bounded by an enclosure with overall heat-transfer coefficient to the external environment in the range of 1 to 20 W/m²·K, sufficient to retain a fraction of the heat generated by cycling and to raise interior temperature by an engineered increment ΔT above ambient. The mechanical envelope is bounded by a rigid structural enclosure (typically a metal or fiber-composite case, or, in the cavity-bath integration, the surrounding cement-bound cavity wall) whose stiffness exceeds 1 GPa effective and whose interior dimensions do not grow under cycling-induced expansion stresses below 50 MPa. The ionic envelope is bounded by the polymer-electrolyte membrane and the carbon electrode geometry, which together set the diffusion coefficients, the gradient relaxation timescales, and the osmotic-pressure response to gradient magnitude.

Inside this triple-envelope, the active electrode is a polymer-bound carbon aggregate at initial bulk density 0.6 to 1.1 g/cm³, with inter-particle void fraction 35 to 60 percent at first cycle. The void fraction is not parasitic: it is a designed reservoir for compaction. The first-cycle capacity is set by the as-fabricated electrode's accessible surface area, but the asymptotic capacity is set by the post-compaction electrode's accessible surface area, which is larger in the disclosed architecture because compaction increases inter-particle electrical contact, reduces dead-zone volume, and brings active surface into the percolation network that was previously isolated. The primitive is, therefore, an as-fabricated electrode that is mechanically and electrically sub-optimal at first cycle by design, with a known reserve of structural compactability that cycling will draw down across the break-in period.

3. Thermal Generation And Accumulation

Cycling generates thermal energy through three primary channels. Joule heating dissipates I²R across the cell's total electrical resistance, which is the sum of electrode bulk resistance, electrode-membrane interfacial resistance, membrane ionic resistance, and current-collector resistance; for cells operating at C-rates of C/2 to 2C with total internal resistance of 5 to 100 mΩ, Joule heating produces 0.5 to 50 W per cell during charge or discharge. Reaction enthalpies of the C-H and C-O bond formation and cleavage events that drive the cell's redox chemistry contribute an additional thermal flux of 0.1 to 5 W per cell, with sign depending on charge or discharge direction. Entropy of mixing during ion redistribution, the ΔS·T term, contributes a smaller but non-negligible thermal flux of 0.01 to 0.5 W per cell.

In a cell with engineered thermal envelope, this thermal generation accumulates rather than dissipating instantaneously. The steady-state interior temperature rise ΔT above ambient follows ΔT ≈ Q̇ / (h·A), where Q̇ is the time-averaged thermal generation, h is the envelope's overall heat-transfer coefficient, and A is the envelope's external surface area. For cells in the disclosed envelope envelope, ΔT typically lies in the range of 5 to 30 °C, with thermal time constants of 10 minutes to several hours. The thermal accumulation is bounded above by safety considerations, 60 °C is a conservative upper bound for most polymer-electrolyte chemistries, and bounded below by the requirement that ΔT be large enough to drive the Arrhenius-mobility increase that the compaction mechanism depends on. Cell architecture and cycling protocol are jointly engineered to land ΔT in the productive 10 to 25 °C window for the majority of operational time. Insulation is achieved through a combination of intrinsic enclosure conductance (selecting case materials with thermal conductivity below 5 W/m·K), engineered thermal-break gaskets at electrical-terminal penetrations, and, where applicable, vacuum or low-conductance gas gaps in multi-wall enclosure geometries. The thermal envelope's behavior is also engineered for transient response: thermal time constants are tuned so that ΔT rises to its productive range within the first few cycles of any operational session and returns to ambient during multi-day idle periods, which avoids over-compaction during continuous operation while preserving the compaction trajectory across the cell's intended duty cycle.

4. Ion-Mobility Increase And Gradient Relaxation

Counter-ion mobility in polymer-electrolyte membranes follows an Arrhenius temperature dependence μ(T) = μ₀ · exp(−Eₐ/RT), with activation energies Eₐ typically in the range of 15 to 35 kJ/mol for Nafion-class and analogous proton-conducting polymers and 25 to 50 kJ/mol for lithium- and sodium-conducting polymer electrolytes. At Eₐ ≈ 25 kJ/mol, mobility approximately doubles per 20 °C increase in operating temperature. The mobility increase has two consequences relevant to compaction. First, the membrane's ionic resistance falls, partially offsetting the Joule-heating mechanism that produced the temperature rise (a self-limiting feedback that contributes to the asymptotic equilibrium). Second, the rate at which concentration gradients relax through the electrode and membrane volume increases proportionally.

Concentration gradients of bound and sorbed counter-ion species accumulate during the active half of each cycle, with peak magnitudes set by the cycling current density and the local diffusion coefficient. In a typical disclosed cell at C/2 cycling, peak gradients across the electrode thickness are 50 to 500 mol/m⁴ (concentration per unit length), corresponding to local concentration differences of 5 to 50 mM across electrode thicknesses of 100 to 500 μm. During the inactive half of each cycle (and during the rest period between cycles), these gradients relax through diffusion at characteristic timescales τ ≈ L²/D, where L is the diffusion path length and D is the local diffusion coefficient. With elevated temperature increasing D by approximately 2× per 20 °C, relaxation that would take hours at ambient temperature completes within tens of minutes at the cell's operating ΔT, allowing the gradient-relaxation engine to run on every cycle rather than only on long rest periods.

5. Osmotic Pressure In Constrained Geometry

In an unconstrained electrochemical cell, gradient relaxation proceeds through a combination of diffusive ion flux and electrode volume change, the electrode swells locally in regions of high counter-ion concentration. In the disclosed cell, the rigid mechanical envelope does not permit volume change. The electrodes are confined laterally by the cell case, axially by the polymer-electrolyte membrane on one side and by the current collector on the other, and through-thickness by the integrated stiffness of the surrounding mechanical structure. With volume expansion blocked, the thermodynamic driving force for relaxation manifests as osmotic pressure on the carbon electrode structure, calculable from the van't Hoff relation Π = i·c·R·T, where i is the van't Hoff factor (1 to 2 for the disclosed counter-ion species), c is the gradient-induced concentration difference, R is the gas constant, and T is the absolute temperature.

For typical disclosed-cell gradient magnitudes of 5 to 50 mM and operating temperatures of 25 to 55 °C, the resulting osmotic pressure is in the range of 12 to 300 kPa per cycle event, with peak transient pressures up to 1 MPa during high-current excursions. The pressure transmits as compressive stress on the inter-particle aggregation network of the carbon electrode, acting to reduce inter-particle separation and to increase the electrode's effective bulk density. Because the gradient is, on average, oriented through the electrode thickness, the compressive stress acts predominantly normal to the electrode-membrane interface, which is precisely the direction in which inter-particle compaction increases percolation-path connectivity and reduces electrode tortuosity. The geometry of the cell, the orientation of the membrane, the orientation of the gradient, and the orientation of the mechanical constraint, is engineered so that the osmotic pressure does productive work on the electrode rather than producing parasitic interfacial stress.

6. Operating Parameters And Engineering Envelope

Compressive stress at the inter-particle level drives a combination of plastic and elastic deformation. Plastic deformation includes particle re-arrangement (small rotations and translations of individual carbon particles into more closely packed configurations), inter-particle adhesion strengthening (formation of new contact points with mechanical and electrical continuity), and progressive closure of inter-particle voids through local plastic flow of the polymer binder. Elastic deformation includes reversible compression of the carbon particles and the polymer binder, which contributes to stress equilibration but does not drive permanent densification.

Cumulative deformation across cycles increases bulk electrode density progressively. A typical disclosed cell starts at first-cycle bulk density 0.7 g/cm³ and progresses asymptotically to 0.95 to 1.15 g/cm³ at break-in saturation. Inter-particle void fraction falls from 50 percent to 25 to 35 percent. Effective electronic conductivity through the electrode rises from 5 to 50 S/m to 50 to 500 S/m as percolation paths multiply. Accessible capacity rises in approximate proportion to the increase in active percolation network, with first-cycle to asymptotic gains of 0 to 50 percent depending on starting density, mechanical constraint stiffness, polymer binder modulus, and cycling protocol intensity. The break-in cycling period, the number of cycles required to reach asymptotic equilibrium, ranges from 50 cycles for soft, high-void electrodes under aggressive cycling to 500 cycles for dense, low-void electrodes under gentle cycling, and is engineered through cell architecture and protocol selection. Operational parameters across the engineering envelope: cycling C-rate C/10 to 2C; depth of discharge 60 to 100 percent; rest period between cycles 0 to 8 hours; ambient temperature −10 to +45 °C; mechanical constraint stiffness 1 to 50 GPa effective; polymer binder modulus 0.1 to 5 GPa.

7. Alternative Embodiments

Several alternative embodiments fall within the disclosure. A passive break-in embodiment allows compaction to proceed under the cell's normal operational duty cycle, with no special protocol; the cell reaches asymptotic capacity over its first 100 to 500 service cycles, and the early-life capacity-rise behavior is exposed to the end user as a feature. An accelerated factory break-in embodiment subjects the cell to a controlled high-rate cycling protocol (C/2 to 2C cycling at elevated ambient temperature, 35 to 45 °C, with reduced rest periods) at the manufacturing facility prior to shipment, compressing the break-in to 50 to 100 cycles and shipping a cell that is already at or near asymptotic capacity.

A staged break-in embodiment combines a brief factory protocol that takes the cell partway through compaction (perhaps to 70 percent of the asymptotic gain) with a passive in-service completion of the remaining gain, balancing factory throughput against in-service capacity-rise behavior. A constraint-tunable embodiment adjusts the mechanical envelope stiffness through operational set points, for example, by varying the pressure of an inert-gas chamber surrounding the cell, or by varying the torque applied to a clamping mechanism, admitting in-service tuning of the compaction trajectory. An external-pressure-assisted embodiment applies an external mechanical pressure (via cavity-bath wall deformation, or via an integral hydraulic actuator) during the first 10 to 50 cycles to accelerate compaction; once asymptotic equilibrium is reached, the external pressure is removed and the now-compacted electrode retains its densified state.

8. Composition With Broader Architecture

Cycling-induced compaction composes naturally with the cavity-bath architecture (Provisional 64/050,895) because the cavity wall and integrated hollow rebar provide exactly the rigid mechanical envelope that the compaction mechanism requires. A cement-bound cavity wall of 25 to 75 mm thickness has effective stiffness in the 5 to 30 GPa range, well above the threshold required for effective osmotic-pressure transmission to the electrode. The cavity-bath cell, therefore, exhibits the capacity-rise property natively: across its first 50 to 500 cycles in service, accessible capacity rises by 0 to 50 percent of first-cycle, locking in at an asymptotic value that the cell maintains for the remainder of its multi-decade structural service life. The composition is what makes building-integrated structural storage a use-improving asset rather than a use-degrading one.

Compaction composes with the credentialed admissibility profile because the cycling history that drove the compaction is recorded in the cell's lineage chain, with the asymptotic capacity value entered as a state transition in the per-cell record. Warranty terms can be written against the asymptotic capacity rather than the first-cycle capacity, and capacity guarantees can be expressed as a guaranteed minimum break-in performance and a guaranteed minimum post-asymptotic flatness. Compaction composes with grid services and energy-management scheduling because the asymptotic capacity is stable for thousands of subsequent cycles, providing a known, flat, dispatchable resource that does not require derating across its service life. Compaction composes with thermal-management primitives because the heat generated by cycling is the same heat that drives the Arrhenius mobility increase that drives the relaxation that drives the osmotic pressure that drives the compaction; the cell's thermal envelope is an active engineering variable jointly tuned for safety, for round-trip efficiency, and for compaction trajectory.

9. Prior-Art Distinctions

The mechanism is structurally analogous to three established prior-art lines in mechanics and materials science. Terzaghi soil-mechanics consolidation describes the progressive densification of saturated soils under repeated loading, with pore-pressure dissipation and effective-stress transfer driving the densification; the cell's compaction is analogous, with osmotic pressure playing the role of pore pressure and inter-particle contact playing the role of effective-stress transfer. Reynolds dilatancy and consolidation describes the densification of granular materials under cyclic stress, with grain re-arrangement converging to a dense-random-packed asymptotic state; the cell's electrode is analogous, with the carbon particles converging to an asymptotic packing density. Cyclic thermal-stress densification describes the progressive compaction of porous ceramics, metals, and composites under repeated thermal-mechanical cycling, with creep and ratcheting accumulating across cycles; the cell's compaction is analogous, with the cycling-induced thermal and osmotic stresses driving the ratcheting.

What distinguishes this disclosure from each prior-art line is the integration of the mechanism into a sealed electrochemical cell architecture in which the cycling that drives the compaction is also the cycling that produces the cell's primary economic output. No prior-art line teaches the use of the cell's own cycling to densify its own electrode through coupled thermal-osmotic mechanism, nor the engineered envelope (thermal, mechanical, ionic) that makes the densification productive rather than parasitic, nor the use-dependent capacity-rise as the architectural inversion of capacity-fade. Conventional battery break-in (formation cycling at low rate to grow a stable SEI, used in lithium-ion manufacturing) is also distinct: formation cycling is a one-time interfacial-chemistry event executed at the factory and immediately followed by capacity-fade through service life; the disclosed compaction is a bulk-mechanical process that proceeds across the cell's first 50 to 500 service cycles and is followed by thousands of cycles at the asymptotic plateau.

10. Disclosure Scope

This primitive is disclosed under U.S. provisional 64/052,368, filed April 29, 2026. The disclosure recites thermal generation from cycling across the three identified channels (Joule heating, reaction enthalpies, entropy of mixing); thermal accumulation in engineered envelope with overall heat-transfer coefficients in the 1 to 20 W/m²·K range; Arrhenius ion-mobility increase with characteristic doubling per 20 °C; concentration-gradient accumulation and relaxation across the cycling waveform; osmotic-pressure generation in constrained geometry calculable from the van't Hoff equation, with engineering envelope of 12 to 300 kPa typical; compressive stress transmission to inter-particle aggregation network; progressive plastic and elastic deformation through particle re-arrangement, adhesion strengthening, and void closure; asymptotic equilibrium at break-in saturation across 50 to 500 cycles; capacity gain magnitude across 0 to 50 percent of first-cycle; the three prior-art analogies (Terzaghi consolidation, Reynolds dilatancy, cyclic thermal-stress densification); and the use-dependent capacity-rise property as architectural inversion of capacity-fade. Sub-primitives include the passive, accelerated, staged, constraint-tunable, and external-pressure-assisted break-in embodiments. Sub-primitives further include the engineered initial-density and initial-void-fraction targets that define the compactability reserve, the engineered thermal time constant that defines the duty-cycle interaction with compaction, the asymptotic-capacity warranty primitive in which guarantees are written against post-break-in capacity rather than first-cycle capacity, and the lineage-chain primitive in which the entire cycling history that produced compaction is retained as credentialed per-cell record. Continuation and divisional applications are anticipated against each sub-primitive as the operational data set from deployed cells matures, with particular attention to the empirical relationships between the initial mechanical-envelope stiffness, the operating thermal envelope, and the realized capacity gain across diverse chemistries and form factors.