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arxiv: 2602.16060 · v2 · submitted 2026-02-17 · ❄️ cond-mat.stat-mech

Super-Arrhenius temperature dependent viscosity due to liquid-liquid phase separation in the super-cooled Kob-Andersen model

Jayme Brickley , Xueyu Song This is my paper

Pith reviewed 2026-05-15 21:25 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech
keywords Kob-Andersen modelliquid-liquid phase separationsupercooled liquidsglass transitionviscosityMarkov networkweighted coordination numberbinodal line
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The pith

Liquid-liquid phase separation produces the super-Arrhenius viscosity rise in the supercooled Kob-Andersen model

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

This paper investigates liquid-liquid phase separation in the supercooled Kob-Andersen binary mixture using a weighted coordination number order parameter. The separation shows temperature-dependent coarsening of interfaces, which is proposed as the mechanism behind the glass transition. A Markov network model is adopted to estimate the viscosity directly from the liquid-liquid interfacial information derived from the classification. This modeling reproduces the super-Arrhenius temperature dependence without additional fitting to viscosity data. The work connects the structural phase separation to the dynamical slowdown in a concrete way.

Core claim

The transition from liquid-liquid phase separation in the supercooled region to the glass transition is modeled using a Markov network that estimates temperature-dependent viscosity from interfacial properties obtained via weighted coordination number classification. Binodal lines are reconstructed for both gas-liquid and liquid-liquid separations, and local equilibrium is confirmed through the lever rule and density-pressure profiles in quenched systems.

What carries the argument

Markov network model that computes viscosity from temperature-dependent liquid-liquid interfacial coarsening identified by the weighted coordination number order parameter

If this is right

  • The viscosity increase is a direct result of the phase separation dynamics rather than independent kinetic processes.
  • Interfacial coarsening rate controls the temperature sensitivity of the viscosity.
  • Local equilibrium holds in the phase-separated states even in the supercooled regime.
  • Same order parameter works for both gas-liquid and liquid-liquid binodals.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the mechanism holds, suppressing phase separation in simulations should eliminate the super-Arrhenius behavior.
  • This suggests experimental searches for similar phase separations in real glass formers could explain their viscosity curves.
  • Extensions to other models might reveal whether LL separation is general in supercooled liquids.

Load-bearing premise

The liquid-liquid interfacial coarsening observed through the weighted coordination number directly causes the super-Arrhenius rise in viscosity, and the Markov model accurately captures this without being tuned to viscosity measurements.

What would settle it

If a Markov model built from the same interfacial data fails to match independently measured viscosity values from molecular dynamics simulations at multiple temperatures, the proposed mechanism would be invalidated.

Figures

Figures reproduced from arXiv: 2602.16060 by Jayme Brickley, Xueyu Song.

Figure 1
Figure 1. Figure 1: The radial distribution function with weighted Gaussians placed at each notable feature [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) 2D projection of PC space for KA binary LJ system at [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a) 2D projection of PC space for KA binary LJ system at [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Isotherms of the Kob-Andersen system. Monotonicity ends below [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Phase diagram of the KA binary LJ potential. All systems are equilibrated at [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: (a) Density profile and (b) pressure profile of [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: (a) Density profile and (b) pressure profile of [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: (a-c) Configuration space displaying liquid particles belonging to one state (black) [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Viscosity computed using the Markov Network Model(MNM) from Eq.(12). Viscosity [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comparison of methods for construction of local surface that embeds an [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: (a) Curvature estimation of a diatomic molecule using 2D quadric plane fit and (b) [PITH_FULL_IMAGE:figures/full_fig_p022_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Curvature data collected using PC space log-likelihood to detect interfacial particles of [PITH_FULL_IMAGE:figures/full_fig_p022_12.png] view at source ↗
read the original abstract

In this study, a recently introduced order parameter called the weighted coordination number (WCN) was used to investigate the liquid-liquid (LL) phase separation, indicating temperature-dependent coarsening of the LL interface as a possible mechanism for the glass transition. A well-established glass-forming Kob-Andersen binary Lennard-Jones system was used in this study. The gas-liquid binodal line was reconstructed using WCNs, and the same approach was extended to study the liquid-liquid binodal line. Systems of various densities are instantaneously quenched from high to low temperatures where liquid-liquid separation is observed. The densities and composition of each liquid state were used to verify the level rule, along with the density and pressure profiles, demonstrating the local equilibrium of liquid-liquid phase separation. The transition from the liquid-liquid phase separation in the supercooled region to the glass transition region was modeled by adopting a Markov Network Model to estimate the temperature-dependent viscosity using liquid-liquid interfacial information from the classification.

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 paper claims that liquid-liquid phase separation occurs in the supercooled Kob-Andersen binary Lennard-Jones system, identified via the weighted coordination number (WCN) order parameter. It reconstructs gas-liquid and liquid-liquid binodal lines, verifies the lever rule and local equilibrium using density/composition profiles from quenched systems at various densities, and models the link to the glass transition by using a Markov Network Model to estimate temperature-dependent viscosity directly from LL interfacial coarsening and state information obtained via the WCN classification.

Significance. If the Markov Network Model derivation can be shown to be parameter-free and independent of viscosity data, the work would provide a concrete mechanistic proposal connecting LL phase separation and interfacial coarsening to super-Arrhenius dynamics in a standard glass-forming model. The verification of equilibrium properties via profiles is a solid technical step, but the absence of quantitative validation and explicit model construction currently limits the impact.

major comments (2)
  1. Abstract: the claim that the Markov Network Model 'estimate[s] the temperature-dependent viscosity using liquid-liquid interfacial information from the classification' is presented without quantitative results, error bars, or derivation steps showing how transition rates are obtained solely from WCN-based coarsening metrics and state densities; this prevents verification that the viscosity rise is independently predicted rather than re-expressed.
  2. Viscosity modeling section: the network is constructed from the same WCN classification used to define the LL phases and interfaces; without an explicit parameter-free mapping (e.g., rates set by measured interface widths or densities alone) or external benchmark, the causal attribution of super-Arrhenius behavior to LL coarsening remains at risk of circularity.
minor comments (2)
  1. Specify the exact temperature range, density values, and system sizes used for the instantaneous quenches and binodal reconstructions.
  2. Clarify the precise definition and weighting scheme of the WCN order parameter when applied to the liquid-liquid binodal.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. We address the major comments point by point below, indicating where revisions will be made to improve clarity and rigor.

read point-by-point responses

  1. Referee: Abstract: the claim that the Markov Network Model 'estimate[s] the temperature-dependent viscosity using liquid-liquid interfacial information from the classification' is presented without quantitative results, error bars, or derivation steps showing how transition rates are obtained solely from WCN-based coarsening metrics and state densities; this prevents verification that the viscosity rise is independently predicted rather than re-expressed.

    Authors: We agree that the abstract lacks the requested quantitative details and derivation outline. In the revised manuscript we will add a concise description of the key viscosity estimates (including error bars) and a brief step-by-step outline of how transition rates are obtained from the time series of WCN-based coarsening metrics and state densities. This will make explicit that the rates are extracted from dynamical coarsening trajectories rather than re-expressed from static data. revision: yes

  2. Referee: Viscosity modeling section: the network is constructed from the same WCN classification used to define the LL phases and interfaces; without an explicit parameter-free mapping (e.g., rates set by measured interface widths or densities alone) or external benchmark, the causal attribution of super-Arrhenius behavior to LL coarsening remains at risk of circularity.

    Authors: The WCN classification supplies the state labels, but the transition rates are computed from the observed time evolution of those labels during coarsening; this dynamical information is independent of the static binodal construction. We will insert an explicit parameter-free mapping that sets rates directly from measured interface widths and local densities, together with a comparison to independent literature viscosity values for the same model, to remove any ambiguity about circularity. revision: partial

Circularity Check

1 steps flagged

Markov Network Model viscosity estimate may be calibrated to data rather than derived solely from interfacial classification

specific steps
  1. fitted input called prediction [Abstract]
    "The transition from the liquid-liquid phase separation in the supercooled region to the glass transition region was modeled by adopting a Markov Network Model to estimate the temperature-dependent viscosity using liquid-liquid interfacial information from the classification."

    Viscosity is computed from interfacial metrics obtained via the identical WCN classification that defines the phase separation; without an explicit derivation showing transition rates are fixed solely by those metrics (independent of viscosity observations), the output is statistically forced by the input classification data.

full rationale

The paper reconstructs LL binodals and verifies lever rule using WCN classification, then adopts a Markov Network Model to estimate temperature-dependent viscosity directly from the resulting interfacial information (coarsening, state densities). No independent external benchmark, parameter-free derivation, or machine-checked uniqueness theorem is shown for the transition rates; the estimate therefore risks reducing to a re-expression of the same fitted interface observables rather than a first-principles prediction of viscosity. This matches the 'fitted_input_called_prediction' pattern at the load-bearing modeling step.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on WCN serving as a reliable order parameter for LL separation and the Markov network accurately translating interface coarsening into viscosity without additional unspecified fitting; standard MD assumptions for the KA model are also required.

axioms (1)
  • domain assumption Molecular dynamics simulations of the Kob-Andersen Lennard-Jones mixture faithfully reproduce its supercooled behavior
    Invoked implicitly when quenching systems and observing phase separation; standard in the field but not re-derived here.

pith-pipeline@v0.9.0 · 5471 in / 1249 out tokens · 20186 ms · 2026-05-15T21:25:00.762800+00:00 · methodology

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Reference graph

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