Irreversible Gradient-Ratcheting Composites (IGRC)

A governing materials architecture in which operational energy gradients irreversibly increase internal structural order rather than dissipating it

I. Doctrine Statement

In composite systems exposed to sustained mechanical, thermal, or vibrational gradients below melting or catastrophic failure thresholds, durability claims are valid only if internal structural evolution is explicitly tracked as a function of exposure trajectory. Where internal interfaces undergo irreversible, gradient-driven reconfiguration, endpoint-equivalent treatments cannot reproduce the resulting material state.

Irreversible Gradient-Ratcheting Composites (IGRC) define a class of architectures in which environmental gradients act not merely as degradation drivers, but as directional selectors that permanently bias interfacial topology, alignment order, and load transfer pathways. Structural improvement, if present, is conditional on history and is not inferable from endpoint properties alone.

II. Architectural Scope (What IGRC Is)

IGRC describes composite architectures that satisfy all of the following conditions:

  • A semi-crystalline or partially ordered polymer matrix capable of localized microstructural rearrangement without melting
  • A mechanically anisotropic secondary phase that concentrates stress and thermal gradients at the interface
  • Covalently tethered, mechanochemically active interfacial linkages that undergo irreversible bond rupture and re-formation under super-threshold gradients
  • No reversible, supramolecular, self-healing, electronic, or externally actuated mechanisms

The defining feature is not material composition, but the existence of an irreversible, gradient-activated interfacial ratchet that accumulates directional order over service exposure.

III. Governing Mechanism (Physics, Not Outcome)

IGRC exploits localized interfacial instability rather than bulk phase transformation. Differential thermal expansion, cyclic strain, or sustained pressure gradients amplify stress at the polymer–secondary phase boundary. When a critical threshold is exceeded:

  • Mechanophoric interfacial bonds rupture at localized sites
  • Latent reactive groups are exposed and irreversibly re-bond in a new topology
  • Polymer chains adjacent to the interface re-align and become topologically trapped
  • Reverse reactions are thermodynamically and kinetically forbidden under service conditions

Each activation event reduces local configurational entropy while global entropy increases through heat dissipation and chemical bond formation, satisfying the second law for the system plus environment.

IV. MTI-1 State Vector (Required)

Any claim of IGRC behavior requires explicit tracking of a minimum internal state vector:

  • ψif — density of irreversibly transitioned interfacial bonds (direction-resolved)
  • Φal — alignment order parameter of the secondary phase
  • Λcr — fraction of low-defect, high-alignment crystalline or ordered matrix domains

These variables must evolve monotonically and path-dependently under gradient exposure. Endpoint measurements of modulus, strength, or crystallinity alone are insufficient and invalid for trajectory-based claims.

V. Non-Commutativity as the Integrity Test

IGRC architectures are intrinsically non-commutative. Identical endpoint conditions reached via different exposure sequences do not yield equivalent internal states.

If endpoint treatments reproduce the same internal state, the system does not qualify as IGRC.

VI. Earliest Failure Mode (Architectural Truth)

If the IGRC architecture is invalid, failure manifests first at the polymer–secondary phase interface.

VII. Single Decisive Falsification Test

A standardized composite coupon is subjected to directional gradients and mechanical cycling. The system fails if ratcheted internal state variables do not evolve irreversibly or are reproducible by endpoint treatments.

VIII. Regime Boundaries

Applies only where persistent gradients dominate lifetime behavior.

IX. Edge of Knowledge Judgment

IGRC asserts that when irreversible, gradient-driven interfacial evolution is physically present, durability claims must be trajectory-accounted or considered structurally invalid.

Invariant Closure (Canonical)

Symmetry group (𝑮): Gradient-preserving exposure transformations (thermal, mechanical, vibrational) under which internal structure evolves.

Conserved quantity (𝑸): Total material mass and chemical inventory. No energy gain, healing, or reversible ordering is conserved across transformations.

Invariant spectrum (𝑺): The set of irreversible internal state variables {ψif, Φal, Λcr}encoding gradient history.

Failure signature on 𝑺: Either (a) absence of monotonic, path-dependent evolution, or (b) reproducibility of the same spectrum through endpoint-only treatments.

Legitimacy boundary: Any durability, improvement, or safety claim not explicitly grounded in the invariant spectrum is not legitimate within this regime and must be rejected.

Edge of Knowledge papers define governing constraints, not products, predictions, or prescriptions. This document establishes a binary legitimacy boundary for claims in gradient-exposed composite systems.