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arxiv: 2601.21591 · v2 · submitted 2026-01-29 · ❄️ cond-mat.stat-mech · cond-mat.soft· physics.chem-ph

Recognition: 2 theorem links

· Lean Theorem

The roles of bulk and surface thermodynamics in the selective adsorption of a confined azeotropic mixture

Katie L. Y. Zhou , Anna T. Bui , Stephen J. Cox
Authors on Pith no claims yet

Pith reviewed 2026-05-16 09:45 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cond-mat.softphysics.chem-ph
keywords azeotropic mixtureconfined adsorptionselectivitydensity functional theoryLennard-Jones mixturesupercritical regimepartial molar volumeinterfacial free energy
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The pith

When wall-fluid interactions are identical for both species, a confined pore becomes completely unselective at the bulk azeotropic composition, even in supercritical conditions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper applies an efficient neural-enhanced classical density functional theory to a binary Lennard-Jones mixture that forms an azeotrope. It demonstrates that equal wall affinities for the two components cause adsorption selectivity to vanish exactly at the bulk azeotropic composition. This unselective point holds across wide ranges of pressure, temperature, and composition, including well into the supercritical regime. The finding is tied to bulk thermodynamic features at the azeotrope, such as equal partial molar volumes and an extremum in isothermal compressibility. Unselective adsorption is further shown to correspond to an aneotrope of zero relative adsorption together with an extremum in interfacial free energy, while the two pore walls remain effectively independent even in narrow slits.

Core claim

In a binary Lennard-Jones mixture that exhibits azeotropic phase behavior, when the wall-fluid interaction strength is the same for both species, the slit pore exhibits zero adsorption selectivity precisely at the bulk azeotropic composition. This unselective point persists far from liquid-vapor coexistence, including throughout the supercritical regime. The azeotropic composition coincides with equal partial molar volumes and an extremum in the isothermal compressibility of the bulk equation of state. Thermodynamic analysis shows that the unselective adsorption corresponds to an aneotrope (zero relative adsorption) and an extremum in the interfacial free energy.

What carries the argument

Neural LMFT: a classical density functional theory that combines a neural functional trained on single-component repulsive reference systems with a mean-field treatment of attractions, allowing efficient computation of confined binary mixture thermodynamics.

Load-bearing premise

The neural functional trained only on a single-component repulsive reference system plus mean-field attractions remains accurate for the full attractive binary mixture across the wide range of state points examined.

What would settle it

Grand canonical Monte Carlo simulations performed at the bulk azeotropic composition with equal wall-fluid affinities that show nonzero selectivity in the supercritical regime would falsify the central claim.

read the original abstract

Fluid mixtures that exhibit an azeotrope cannot be purified by simple bulk distillation. Consequently, there is strong motivation to understand the behavior of azeotropic mixtures under confinement. We address this problem using an ML-enhanced classical density functional theory (cDFT) applied to a binary Lennard-Jones mixture that exhibits azeotropic phase behavior. As proof-of-principle of a "train once, learn many" strategy, our approach combines a neural functional trained on a single-component repulsive reference system with a mean-field treatment of attractive interactions, inspired by the connection between cDFT and local molecular field theory. The theory faithfully describes capillary condensation and results from grand canonical Monte Carlo simulations. Moreover, by taking advantage of a known accurate equation of state, the "neural LMFT" we present well-describes bulk thermodynamics by construction. Exploiting the computational efficiency of neural LMFT, we systematically evaluate adsorption selectivity across a wide range of compositions, pressures, temperatures, and wall-fluid affinities. In cases where the wall-fluid interaction is the same for both species, we find that the pore becomes completely unselective at the bulk azeotropic composition. Strikingly, this unselective point persists far from liquid-vapor coexistence, including in the supercritical regime. Analysis of the bulk equation of state across a wide range of thermodynamic state points shows that the azeotropic composition coincides with equal partial molar volumes and an extremum in the isothermal compressibility. A thermodynamic analysis demonstrates that unselective adsorption corresponds to an aneotrope (a point of zero relative adsorption) and an extremum in the interfacial free energy. We also find that the two interfaces of the slit pore behave independently down to remarkably small slits.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript develops a neural local molecular field theory (neural LMFT) that combines a neural density functional trained solely on single-component repulsive reference data with a mean-field treatment of attractions, while incorporating an accurate external bulk equation of state by construction. Applied to a binary Lennard-Jones mixture exhibiting azeotropy, the approach is used to map adsorption selectivity in slit pores over wide ranges of composition, pressure, temperature, and wall affinity. The central claim is that identical wall-fluid interactions for both species produce exactly zero selectivity at the bulk azeotropic composition, with this unselective point (an aneotrope) persisting into the supercritical regime; this is tied to equal partial molar volumes and an extremum in isothermal compressibility, and the two pore interfaces are shown to behave independently even at small widths.

Significance. If the neural LMFT accuracy holds for the binary attractive case, the work supplies an efficient route to explore confined mixture thermodynamics far from coexistence and links bulk azeotropic features directly to interfacial selectivity via thermodynamic identities. The 'train once, learn many' strategy, exact reproduction of bulk thermodynamics, and GCMC validation for capillary condensation are clear strengths that could enable systematic studies of separation under confinement.

major comments (2)
  1. The central claim of exact unselectivity at the bulk azeotropic composition (including supercritically) rests on the neural LMFT producing accurate density profiles and excess free energies for the attractive binary mixture. However, the neural functional is trained exclusively on single-component repulsive data; binary repulsive cross-correlations are therefore handled only by network transferability, and mean-field attractions cannot correct reference-functional errors in local packing. No quantitative error metrics (e.g., integrated density deviations or free-energy errors versus GCMC) are supplied for binary supercritical state points, which directly affects the reliability of the reported coincidence with equal partial molar volumes.
  2. The thermodynamic demonstration that unselective adsorption corresponds to an aneotrope and an extremum in interfacial free energy relies on the neural LMFT output satisfying the necessary identities. Because bulk thermodynamics are taken from an external EOS while the selectivity scan uses the neural functional, an explicit check that the confined excess quantities remain consistent with the bulk-derived partial molar volumes (without introducing spurious shifts) is needed to confirm the reported persistence of the unselective point.
minor comments (2)
  1. The abstract states that the theory 'faithfully describes' GCMC results but provides no numerical error measures or training-set details; adding these (even briefly) would improve clarity.
  2. Notation for the neural functional and the mixing rules applied to binary repulsive terms should be defined explicitly in the methods section to allow readers to assess transferability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive evaluation of our work and for the detailed and constructive comments. We address each major comment below.

read point-by-point responses

  1. Referee: The central claim of exact unselectivity at the bulk azeotropic composition (including supercritically) rests on the neural LMFT producing accurate density profiles and excess free energies for the attractive binary mixture. However, the neural functional is trained exclusively on single-component repulsive data; binary repulsive cross-correlations are therefore handled only by network transferability, and mean-field attractions cannot correct reference-functional errors in local packing. No quantitative error metrics (e.g., integrated density deviations or free-energy errors versus GCMC) are supplied for binary supercritical state points, which directly affects the reliability of the reported coincidence with equal partial molar volumes.

    Authors: The exact location of zero selectivity at the bulk azeotropic composition is a general thermodynamic consequence of the equality of partial molar volumes and the extremum in isothermal compressibility at the azeotrope; these features produce an aneotrope (zero relative adsorption) and an extremum in interfacial free energy. This identity holds independently of the details of the density functional, provided the bulk equation of state is reproduced accurately—which is enforced by construction in our neural LMFT. The neural functional is used only to compute the adsorption isotherms efficiently over wide parameter ranges, and we have already validated the overall approach against GCMC for capillary condensation. We agree that quantitative error metrics for binary supercritical state points would strengthen the presentation of the density profiles and will add such metrics (e.g., integrated density deviations versus GCMC) in the revised manuscript. revision: yes

  2. Referee: The thermodynamic demonstration that unselective adsorption corresponds to an aneotrope and an extremum in interfacial free energy relies on the neural LMFT output satisfying the necessary identities. Because bulk thermodynamics are taken from an external EOS while the selectivity scan uses the neural functional, an explicit check that the confined excess quantities remain consistent with the bulk-derived partial molar volumes (without introducing spurious shifts) is needed to confirm the reported persistence of the unselective point.

    Authors: We will add an explicit numerical verification in the revised manuscript. Specifically, we will compare the composition at which the computed selectivity vanishes against the azeotropic composition obtained directly from the external bulk EOS for multiple state points (including supercritical conditions). This check will confirm that no spurious shifts arise from the neural functional and that the confined excess quantities remain consistent with the bulk partial molar volumes. revision: yes

Circularity Check

0 steps flagged

No significant circularity; bulk EOS external and confinement results computed independently

full rationale

The paper explicitly states that bulk thermodynamics are matched 'by construction' via an external accurate equation of state, while the neural functional (trained solely on single-component repulsive data) plus mean-field attractions is used to compute confined density profiles and excess free energies. The central claims—that the pore is unselective exactly at the bulk azeotropic composition even in the supercritical regime—are obtained by direct numerical evaluation of the neural-LMFT theory across state points, followed by post-hoc thermodynamic analysis linking unselectivity to equal partial molar volumes and aneotropy. No step reduces a prediction to a fitted parameter by definition, no load-bearing self-citation chain is invoked to force uniqueness, and the coincidence with the azeotrope is an emergent numerical result rather than an input. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The method rests on a neural functional trained solely on a repulsive reference system and a mean-field treatment of attractions; bulk thermodynamics are supplied by an external accurate equation of state.

axioms (1)
  • domain assumption Mean-field treatment of attractive interactions is sufficient when combined with the neural repulsive functional
    Explicitly stated as inspired by the connection between cDFT and local molecular field theory.

pith-pipeline@v0.9.0 · 5630 in / 1220 out tokens · 32521 ms · 2026-05-16T09:45:27.269659+00:00 · methodology

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