Transient Nano-Dense Molecular States as a Persistence–Stabilization Closure for Combustion Nanoparticle Inception

Saylam, Ahmad

doi:10.5281/zenodo.20258147

Transient Nano-Dense Molecular States as a Persistence–Stabilization Closure for Combustion Nanoparticle Inception

Author: Dr. Ahmad Saylam

Document type: Open scientific preprint

Version: v1

Publication date: 17 May 2026

Scientific status: Falsifiable hypothesis and reduced modelling framework. The proposed transient nano-dense molecular state is not presented as an experimentally established universal physical state or as a universally validated nanoparticle-inception mechanism.

DOI and Zenodo record: 10.5281/zenodo.20258147

Abstract

Nanoparticle inception remains one of the least constrained stages in predictive combustion-particle modelling. Detailed gas-phase mechanisms may describe fuel decomposition, aromatic growth, polycyclic aromatic hydrocarbon chemistry, radical pathways, oxidation and surface growth, while the transition from molecular precursors to the first persistent particles is often represented by empirical nucleation expressions, selected dimerization steps or source terms into an initial particle bin.

This paper formulates the transient nano-dense molecular state hypothesis as a persistence–stabilization closure for that transition. An NDMS is defined as a transient, non-equilibrium, locally dense ensemble of associated molecular or sub-molecular precursor units. The associated ensemble remains reversible on the dissociation timescale and contributes to persistent particle inception only when chemical or structural stabilization competes successfully with dissociation and other losses.

The framework separates precursor association, cluster dissociation, competing non-stabilizing loss and stabilization into distinct model components. It introduces an operational density-enhancement criterion, association- and stabilization-weighted precursor descriptors, bounded stabilization probabilities and a minimal zero-dimensional demonstration.

Implementation routes are outlined for detailed chemical mechanisms, sectional population balances, moment methods and reduced CFD closures. For soot, the architecture offers a structured way to connect PAH association with radical-driven stabilization and chemical ageing. For inorganic flame aerosols, illustrated using titanium dioxide formation, the same mathematical architecture is considered only as a system-specific modelling possibility—not as evidence that carbonaceous and inorganic particles share one microscopic pathway.

The hypothesis is explicitly falsifiable. It should be retained only where a constrained NDMS closure improves inception-specific observables such as onset location, pressure dependence, early particle-number density, precursor sensitivity and cluster-sensitive diagnostics relative to simpler alternatives.

Persistence–stabilization concept

The central proposition is that reversible molecular association is not by itself equivalent to particle inception. A transient associated reservoir contributes to persistent particle formation only when a stabilization pathway competes successfully with dissociation and non-stabilizing removal.

The reduced model distinguishes:

formation and availability of molecular precursors;
reversible precursor association;
formation of a transient NDMS reservoir;
dissociation of the associated reservoir;
competing non-stabilizing losses;
chemical or structural stabilization;
formation of persistent incipient-particle matter.

Minimal closure equations

In the reduced formulation, the transient-reservoir formation rate is represented as:

R_form = k_on × C_assoc^m

A minimal balance for the transient NDMS reservoir Z is:

dZ/dt = R_form − (k_off + k_loss + k_stab) × Z

The bounded probability that a transient associated state becomes stabilized is:

P_stab = k_stab / (k_off + k_loss + k_stab)

The corresponding source term for persistent incipient-particle matter is:

S_NDMS = k_stab × Z

Under the quasi-steady approximation used in the illustrative zero-dimensional demonstration:

S_NDMS =
(k_stab × k_on × C_assoc^m) /
(k_off + k_loss + k_stab)

For non-negative rate coefficients, 0 ≤ P_stab ≤ 1. This mathematical bound prevents the stabilization probability from exceeding its physical probability range.

These expressions are a reduced closure for model development and sensitivity analysis. They are not validated rate laws for a specified fuel, flame, pressure, temperature or particle system.

Potential implementation routes

coupling detailed precursor chemistry to cluster master equations;
introducing stabilized inception sources into sectional population-balance models;
embedding the closure within moment methods;
constructing reduced source terms for CFD calculations;
using sensitivity analysis to identify influential association, dissociation, loss and stabilization parameters;
comparing the closure against simpler empirical or dimerization- based inception descriptions.

Evidence and maturity

NDMS physical proposition: Scientific hypothesis: a testable description of a possible transient molecular-to-particle regime, not an experimentally established universal state.
Persistence–stabilization equations: Research prototype: a reduced mathematical closure suitable for transparent analysis and future model development.
Python script and notebook: Reproducible zero-dimensional demonstrations using illustrative parameter values. They demonstrate mathematical behaviour but do not provide system-specific prediction.
Industrial or regulatory application: Not established. Any such use would require system-specific chemistry, calibrated parameters, uncertainty analysis and independent validation.

Validation and falsification targets

Development of the framework should focus on observations capable of distinguishing reversible association from stabilized particle formation. Useful targets may include:

molecular-cluster distributions and lifetimes;
precursor production and depletion rates;
onset of persistent particle signals;
early particle-number density and size distributions;
pressure and temperature dependence;
fuel, precursor-class and radical-pool sensitivity;
isotope or chemical-marker evidence;
comparison with molecular simulation and alternative inception closures.

Failure to improve inception-specific observables, or evidence that the required stabilization pathway is physically implausible, should lead to modification or rejection of the proposed closure for that system.

Scope and evidence boundary

NDMS is a scale-local, non-equilibrium modelling descriptor. It is not asserted to be a new equilibrium thermodynamic phase or a directly confirmed universal microscopic state.

The framework does not replace detailed gas-phase chemistry, molecular association models, particle dynamics or population balances. It addresses only the conditional transition from a reversible associated reservoir to persistent incipient-particle matter.

Carbonaceous soot formation and inorganic flame-aerosol formation may share a useful mathematical architecture while retaining different precursor chemistry, interaction energies, stabilization pathways and characteristic timescales. Transfer between systems must therefore be tested rather than assumed.

The illustrative zero-dimensional parameters are not fitted to a specific experiment. The executable model does not yet predict particle-number density, particle-size distribution, soot-volume fraction, emissions compliance or industrial process performance.

Full text

Licence and reuse

The preprint is distributed under the Creative Commons Attribution 4.0 International licence .

The companion repository separates publication and software rights: the software components are licensed under the MIT License, while the scientific papers remain subject to their respective publication licences. Documentation, figures and third-party material should be reused only according to their explicit rights notices.

Recommended citation

Saylam, A. (2026). Transient Nano-Dense Molecular States as a Persistence–Stabilization Closure for Combustion Nanoparticle Inception. Version v1. Zenodo. https://doi.org/10.5281/zenodo.20258147

Companion repository

The public repository contains the reduced equations, explanatory documentation, a Python demonstration, a Jupyter notebook, figures, tests and both NDMS companion papers: