The Self-Trapping Selectivity Principle: Zeolite Shape-Selectivity and Pt–Sn Ensemble Effects.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-21
DOI
https://doi.org/10.5281/zenodo.22851704
Primary Topic
Zeolite Catalysis and Synthesis
Type
preprint
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preprint

The Self-Trapping Selectivity Principle: Zeolite Shape-Selectivity and Pt–Sn Ensemble Effects.

Pablo Nogueira Grossi
Zenodo (CERN European Organization for Nuclear Research)
Zeolite Catalysis and Synthesis
preprint

The Self-Trapping Selectivity Principle: Zeolite Shape-Selectivity and Pt–Sn Ensemble Effects.

Pablo Nogueira Grossi
preprint en

Abstract

webpage: The Self-Trapping Selectivity Principle: Zeolite Shape-Selectivity and Pt–Sn Ensemble Effects. Formerly: Operator Firing Order as a Mechanism for Ethanol-to-Hydrocarbon Selectivity: A Contact-Geometric Analysis of ZSM-5 and MCM-22 Zeolites Note on this version: V5 is a new version of the same Zenodo record series as V1–V4 ("Operator Firing Order as the Missing Mechanism..."), but it replaces that framing rather than extending it. The pathway is no longer analyzed as an ordered pipeline of four operators (compression/constraint/fold/unfold); it is bounded instead by a single self-trapping radius derived from the DNLS equation. Readers arriving from V4 should treat this as a different theorem about the same two zeolites, not a revision of Theorem 4/5. Sousa et al. (2014) posed a specific mechanistic question that remains unanswered: HZSM-5 and HMCM-22 have nominally identical acid chemistry and both possess 10-ring apertures, yet ethanol conversion over them gives markedly different product distributions, coke locations and deactivation profiles. This paper proposes a mechanism and states it as a theorem: a reaction pathway's spatial extent is bounded by a DNLS self-trapping radius r*(λ) = a√(J/λ) (a a lattice length scale, J inter-site coupling, λ on-site binding energy), giving a transition-state selectivity σ = 1 − (J/λ)(a/r_pore)². The contact manifold used for coordinates has a Reeb flow that is volume-preserving and does not itself confine anything; confinement comes from the DNLS self-trapping transition, not from the Reeb dynamics, and is tagged as a model, not a derivation from first principles. Pt–Sn ensemble effects (Corollary 1) are treated as a second instance of the same bound. Every claim carries a status tag (VERIFIED / DERIVED / SIMULATION / MODEL / OPEN). The algebraic core is formalized in Lean 4 (13 theorems, no sorry; compiled by the author under Lean 4.32.0 / Mathlib v4.32.0, not yet run under the source repository's pinned v4.14.0). Three supporting files are included and were checked the same way: an elementary model of the Reeb flow (8 of 11 written theorems kernel-audited), a check that its exterior derivative equals Mathlib's (11 of 13), and the volume-preservation / no-attracting-set argument (9 of 9), each in a simplified coordinate model; the general contact-manifold statement is derived by hand, not machine-checked. Open items are stated as open, not implied solved: the quantitative fit to Sousa et al.'s selectivity data (their measured numbers are not in the publicly accessible text); the normalization of r*; Prediction 1, whose earlier formula is withdrawn in this version with no replacement yet; and the definition of the operator pipeline C/K/F/U as actual operators on L²(X_cat). What was cut from earlier drafts stays cut, not silently reintroduced: the seven-domain "Coherence Bridge," the macroscopic extrudate-pellet corollary, the "helical phase" prediction, and the unified-theory / clean-energy framing. Ps. The paper's abstract still says the Lean files haven't been run on Lean v4.14.0. That understates things: io's CI builds CatGT_Main.lean and ContactMorphism.lean on v4.14.0. Will fix that for V6

Zenodo (CERN European Organization for Nuclear Research)
GfK (United States) (US)
Zeolite Catalysis and Synthesis
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