Mechanism and Primitive Description
Round-trip efficiency (RTE) of an electrochemical storage cell is the ratio of energy delivered through the external load on discharge to energy supplied through the external source on charge, integrated over a complete cycle and at matched starting and ending states of charge. For a redox-active cell the maximum RTE is bounded above by the thermodynamic equality of charge and discharge free energies and bounded below by the sum of all loss mechanisms: activation overpotential at each electrode, ohmic IR drop across the cell stack, mass-transport polarization at high current, and any parasitic side reactions (self-discharge, shuttle currents, electrolyte decomposition) that consume coulombs without delivering useful work.
The cooperative-cleavage cell architecture targets an RTE of 80 to 88 percent, competitive with the 85 to 95 percent typical of high-quality lithium-ion architectures and substantially above the 40 to 60 percent typical of conventional hydrogen-based fuel-cell-with-electrolyzer round trips. The target is not set by catalyst selection alone; it is set by the architectural composition of cooperative cleavage with carbon-bound hydrogen substrates, in which the energy released on discharge is dominated by re-aromatization of the substrate carbon network rather than by an isolated H₂/O₂ recombination, and in which the activation overpotential for the rate-limiting C-H cleavage step is reduced by cooperative interaction with adjacent cleavages along the substrate.
The disclosed primitive is the engineered RTE envelope as a design target: a cell architecture and operating envelope in which the charge and discharge overpotentials sum to a fraction of the cell voltage that places integrated RTE within the 80 to 88 percent band, with the realization of that band verified through cycle-resolved energy-in versus energy-out measurement and recorded as a credentialed attestation. The primitive is not the numerical target alone; it is the engineered combination of substrate, mechanism, and verification record.
Operating Parameters and Engineering Envelope
The RTE envelope is parameterized by state of charge, current density, and temperature. At a fixed reference current of 10 mA/cm² and 25 °C, the architecture targets RTE within 84 to 88 percent across the 20 to 80 percent state-of-charge window. At higher currents (100 mA/cm² and above) RTE drops into the 78 to 84 percent band as ohmic IR drop and activation overpotential scale with current. Below 5 mA/cm² RTE approaches 88 to 90 percent as overpotential terms become small relative to thermodynamic voltage, but absolute power is constrained.
Charging overpotential is set by the catalyst that mediates protonation of the substrate carbon during charge. Exchange-current densities j₀ above 10⁻³ A/cm² admit charging overpotentials below 100 mV at the reference current, contributing 4 to 5 percent loss to RTE. Discharge overpotential is set by the cascade: the local potential shift required to initiate cleavage, the propagation kinetics of the cascade through the substrate, and the kinetics of water formation at the second electrode. The cascade's cooperative character, adjacent cleavages reducing the activation barrier for the next, caps discharge overpotential at approximately 150 to 250 mV at the reference current, contributing 6 to 10 percent loss to RTE.
Ohmic loss across electrolyte and contacts contributes a further 2 to 4 percent at the reference current, scaling linearly. Self-discharge over a 24-hour rest is below 0.5 percent of capacity in the disclosed envelope, contributing negligibly to single-cycle RTE but bounding multi-cycle behavior. The full operating-point efficiency curve, RTE as a joint function of current, state of charge, and temperature, is recorded continuously through commissioning and operation as the credentialed admissibility profile of the cell, providing the auditable evidence that the architecture meets its disclosed target.
Alternative Embodiments
Alternative embodiments shift the RTE envelope by trading absolute efficiency against power or cycle life. A high-power embodiment sacrifices 4 to 6 percentage points of RTE (operating in the 76 to 82 percent band) for a fivefold increase in continuous current capability, by increasing catalyst loading and reducing catalyst utilization to flatten the activation-overpotential curve. A long-cycle-life embodiment operates within a narrower state-of-charge window (35 to 65 percent) at the reference current, raising RTE to 86 to 90 percent and extending calendar life by limiting exposure to the high-overpotential regions that drive parasitic loss.
A thermal-management embodiment captures the irreversible heat from overpotential losses for combined-heat-and-power use, preserving the electrical RTE within the disclosed band while adding a thermal-energy delivery channel that lifts the system-level energetic recovery above 90 percent. A regenerative-pulse embodiment uses brief high-current pulses with intervening relaxation intervals to characterize the operating-point efficiency curve in situ, refreshing the credentialed attestation across the cell's life.
Composition with Adjacent Primitives
The RTE primitive composes with the local-potential-shift primitive, which sets the relationship between current density and electrode-level overpotential and supplies the per-electrode loss terms. It composes with the cooperative-cascade primitive, which caps the discharge-side overpotential at a level below that of any non-cooperative C-H cleavage chemistry and is the architectural source of the disclosed RTE band's discharge-half advantage.
It composes with the full carbon-bound cell architectural class, turbostratic graphene substrate, hierarchical porosity preservation through fabrication, three-phase boundary engineering, providing the substrate context within which the RTE target is realized. It composes with the credentialed admissibility profile primitive that records the operating-point efficiency curve as the auditable verification artifact, and with the discharge-management primitive that holds the operating point within the band where the credentialed RTE applies.
Prior-Art Distinctions
Prior art on lithium-ion cell efficiency reports RTE in the 85 to 95 percent band but operates by intercalation chemistry whose loss mechanisms (SEI formation, intercalation overpotential, ohmic loss) and architectural constraints (flammable organic electrolyte, dendrite risk, cobalt and lithium supply) are distinct from the cooperative-cleavage architecture. Prior art on hydrogen fuel-cell-with-electrolyzer systems reports round-trip electric-to-electric efficiencies in the 40 to 60 percent band, dominated by the round-trip cost of two separate Pt-catalyzed gas-phase reactions and the compression and storage of free H₂; the disclosed cooperative-cleavage architecture replaces free-H₂ storage with carbon-bound hydrogen, eliminating the compression and storage loss term entirely.
Prior art on flow batteries (vanadium redox, zinc-bromine) reports 65 to 80 percent RTE limited by pumping parasitic loss, membrane crossover, and aqueous overpotential; the disclosed architecture is solid-substrate and not subject to pumping loss or crossover. Prior art on metal-air batteries (zinc-air, lithium-air) reports discharge RTE at the cell level but suffers severe charging overpotential at the oxygen-evolution electrode, capping round-trip RTE at 50 to 70 percent.
Cooperative-cleavage chemistry is distinct from each of these prior-art classes: it is not intercalation, not gas-phase fuel-cell-with-electrolyzer, not flow, and not metal-air, and its loss-budget profile differs accordingly. The disclosed RTE target band is a property of this architectural class, not a numeric reproduction of prior-art numbers.
Disclosure Scope
The disclosure covers the RTE primitive as an engineered envelope: any cooperative-cleavage cell architecture whose charge and discharge overpotentials, summed and integrated over a complete cycle at a disclosed reference operating point, place RTE within the 80 to 88 percent band, with that placement verified by cycle-resolved energy-in versus energy-out measurement and recorded as a credentialed attestation in the cell's admissibility profile.
Claim scope extends across catalyst classes, electrolyte classes, and substrate-loading fractions provided the cooperative-cascade discharge mechanism and the carbon-bound hydrogen substrate are preserved. It extends across reference operating points (10 mA/cm² is exemplary; embodiments at other reference points are admitted provided the operating-point efficiency curve is recorded). It extends to the verification record itself: the operating-point efficiency curve as a credentialed attestation is part of the disclosed scope and is the operational meaning of "the architecture meets its target."
Claim scope does not extend to RTE numerical bands realized by prior-art chemistries (intercalation, fuel-cell-with-electrolyzer, flow, metal-air) absent the cooperative-cleavage mechanism, nor to architectures that report RTE as a single point estimate without the operating-point efficiency curve. The boundary is operational: the disclosed primitive is the engineered RTE envelope verified by recorded curve, and the claim runs to architectures that realize and record the envelope as such.
