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arxiv: 2507.17490 · v2 · submitted 2025-07-23 · ❄️ cond-mat.dis-nn · cond-mat.mes-hall· cond-mat.mtrl-sci· cond-mat.soft· cond-mat.stat-mech

General Two-Parameter Model of Alpha-Relaxation in Glasses

Valeriy V. Ginzburg , Oleg Gendelman , Riccardo Casalini , Alessio Zaccone This is my paper

Pith reviewed 2026-05-19 03:41 UTC · model grok-4.3

classification ❄️ cond-mat.dis-nn cond-mat.mes-hallcond-mat.mtrl-scicond-mat.softcond-mat.stat-mech
keywords glass transitionalpha-relaxationuniversal scalingsuper-ArrheniusTS2 theoryrelaxation timeglass-formers
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The pith

Many glass-formers show alpha-relaxation times that collapse onto one master curve using only two material-specific parameters.

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

The paper shows that describing how relaxation times change with temperature near the glass transition normally needs five parameters to cover both the high-temperature Arrhenius regime and the low-temperature super-Arrhenius regime. Instead, data from many different glass-formers can be scaled to a single master curve by fitting just two material-specific numbers—one for the overall timescale and one for the temperature scale—while three other constants remain the same for all materials. This master curve matches the predictions of the two-state, two-time-scale theory, and the authors extract the universal values of its parameters from the data. A reader would care because the reduction from five parameters to two makes it far simpler to predict and compare relaxation behavior across chemically different glasses. The work also links the scaling to an elastic relaxation picture.

Core claim

The central claim is that many glass-formers exhibit a universal scaling of their alpha-relaxation times with only two material-specific parameters that set the timescale and the temperature scale, while the other three parameters are universal constants. The resulting master curve is well-described by the TS2 theory, for which the universal parameters are regressed from experimental data. The model further connects to the Hall-Wolynes elastic relaxation theory.

What carries the argument

The two-parameter universal scaling that normalizes alpha-relaxation times and temperatures onto a master curve whose shape is fixed by three constants taken from the two-state, two-time-scale (TS2) theory.

If this is right

  • Relaxation data from dielectric spectroscopy and other techniques can be analyzed with a common two-parameter fit instead of five separate ones.
  • The regressed universal constants of the TS2 theory become fixed reference values for future modeling of glassy dynamics.
  • The link to Hall-Wolynes theory implies that the same elastic mechanism underlies the scaled relaxation across materials.
  • Predicting the full temperature curve for a new glass-former requires only two material constants once the universal master curve is adopted.

Where Pith is reading between the lines

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

  • The scaling may allow direct comparison of relaxation data obtained by different experimental methods on the same material.
  • If the two parameters correlate with molecular features such as fragility or packing density, the model could guide the design of glasses with targeted relaxation speeds.
  • Molecular simulations could test whether the same two-parameter collapse appears in computed relaxation functions without additional fitting.

Load-bearing premise

A single master curve fixed by three constants that do not depend on material chemistry will collapse alpha-relaxation data from many different glass-formers.

What would settle it

Measure the alpha-relaxation time versus temperature for a new glass-former, determine its two scaling parameters, and check whether the rescaled points lie on the same master curve within experimental scatter; systematic deviation would falsify the universality.

read the original abstract

In the vicinity of the glass transition, the characteristic relaxation time (e.g., the alpha-relaxation time in dielectric spectroscopy) of a glass-former exhibits a strongly super-Arrhenius temperature dependence, as compared to the classical Arrhenius behavior at high temperatures. A comprehensive description of both regions thus requires five parameters. Here, we demonstrate that many glass-formers exhibit a universal scaling, with only two material-specific parameters setting the timescale and the temperature scale; the other three being universal constants. Furthermore, we show that the master curve can be described by the recently developed two-state, two-(time) scale (TS2) theory (Soft Matter 2020, 16, 810) and regress the universal TS2 parameters. We also show the connection between the TS2 model and the Hall-Wolynes elastic relaxation theory.

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 claims that alpha-relaxation times in many glass-formers near the glass transition follow a universal master curve that can be described by the TS2 theory with only three universal constants; each material is then fully characterized by two additional material-specific parameters that set the timescale and temperature scale. The authors regress the universal TS2 parameters from the collapsed data and demonstrate a connection between the TS2 model and the Hall-Wolynes elastic relaxation theory.

Significance. If the claimed universality with only two material-specific parameters is independently validated, the result would substantially simplify the phenomenological description of super-Arrhenius relaxation across chemically diverse glass-formers and provide a concrete link between the TS2 framework and elastic theories. The reduction from five to two free parameters per material, together with the explicit regression of the three universal constants, would constitute a useful organizing principle for experimental data in the field.

major comments (2)
  1. [Fitting of universal TS2 parameters] The regression of the three universal TS2 constants is performed on the master curve assembled from the full collection of glass-formers (as described in the abstract and the fitting procedure). This procedure makes the reported collapse a direct consequence of the global fit rather than an independent test of universality; a cross-validation in which the constants are determined on a training subset of chemically distinct systems and then used to predict the held-out curves is required to substantiate the central claim.
  2. [Data collapse and master-curve construction] The manuscript does not report the number or chemical diversity of the glass-formers included in the master curve, nor does it provide quantitative measures (e.g., root-mean-square deviation or systematic residuals) of how well the held-out or individual curves fall on the master curve after the two-parameter shift. Without these statistics the strength of the universality assertion cannot be assessed.
minor comments (2)
  1. [Introduction and Methods] Notation for the two material-specific parameters should be introduced explicitly with symbols (e.g., τ₀ and T₀) at first use and kept consistent throughout the figures and equations.
  2. [Figures] Figure captions should state the number of glass-formers shown and whether error bars represent experimental uncertainty or fit residuals.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify the strength of our universality claim. We address each major point below and will revise the manuscript accordingly to provide a more rigorous validation.

read point-by-point responses

  1. Referee: [Fitting of universal TS2 parameters] The regression of the three universal TS2 constants is performed on the master curve assembled from the full collection of glass-formers (as described in the abstract and the fitting procedure). This procedure makes the reported collapse a direct consequence of the global fit rather than an independent test of universality; a cross-validation in which the constants are determined on a training subset of chemically distinct systems and then used to predict the held-out curves is required to substantiate the central claim.

    Authors: We agree that fitting the universal constants to the full dataset does not provide an independent test. In the revised manuscript we will add a cross-validation analysis: the glass-formers will be partitioned into chemically diverse training and test subsets, the three universal TS2 constants will be regressed from the training subset only, and we will demonstrate that the held-out curves collapse onto the resulting master curve using solely the two material-specific shift parameters. This will be presented in a new subsection with supporting figures. revision: yes

  2. Referee: [Data collapse and master-curve construction] The manuscript does not report the number or chemical diversity of the glass-formers included in the master curve, nor does it provide quantitative measures (e.g., root-mean-square deviation or systematic residuals) of how well the held-out or individual curves fall on the master curve after the two-parameter shift. Without these statistics the strength of the universality assertion cannot be assessed.

    Authors: We accept that these quantitative details are necessary for a proper assessment. The revised manuscript will include: (i) an explicit statement of the total number of glass-formers and datasets used, (ii) a description of their chemical diversity (molecular liquids, polymers, inorganic systems, etc.), and (iii) quantitative metrics of collapse quality, specifically the root-mean-square deviation of all shifted data from the master curve together with residual plots to identify any systematic deviations. These additions will be placed in the results section and the supplementary information. revision: yes

Circularity Check

1 steps flagged

Universal TS2 constants obtained by regression to master curve from same data set

specific steps
  1. fitted input called prediction [Abstract]
    "we demonstrate that many glass-formers exhibit a universal scaling, with only two material-specific parameters setting the timescale and the temperature scale; the other three being universal constants. Furthermore, we show that the master curve can be described by the recently developed two-state, two-(time) scale (TS2) theory (Soft Matter 2020, 16, 810) and regress the universal TS2 parameters."

    The three constants labeled 'universal' are obtained by regression to the master curve that was itself assembled from the identical set of experimental curves; the reported collapse is therefore enforced by the fitting procedure rather than tested independently.

full rationale

The paper constructs a master curve for alpha-relaxation by shifting individual glass-former data with two material-specific scales and then regresses the three remaining constants of the TS2 functional form directly to that same collection of curves. Because the collapse is achieved by the global fit itself, the reported universality is not an out-of-sample prediction but a re-description of the input data. No cross-validation on held-out chemistries is described in the provided text, so the central claim reduces to a fitted-input-called-prediction step.

Axiom & Free-Parameter Ledger

3 free parameters · 1 axioms · 0 invented entities

The central claim rests on the existence of a universal master curve across glass-formers and on the TS2 parameters being universal after fitting; no new entities are postulated.

free parameters (3)
  • material-specific timescale parameter
    One of the two material-dependent scales that sets the overall relaxation time.
  • material-specific temperature scale parameter
    One of the two material-dependent scales that sets the temperature dependence.
  • three universal TS2 constants
    Regressed from the collapsed master curve and claimed to be the same for all glass-formers.
axioms (1)
  • domain assumption Alpha-relaxation time exhibits strongly super-Arrhenius temperature dependence near the glass transition.
    Standard premise in glass physics invoked to motivate the need for a five-parameter description.

pith-pipeline@v0.9.0 · 5704 in / 1407 out tokens · 42155 ms · 2026-05-19T03:41:41.834552+00:00 · methodology

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    Parameter table for the glass-formers Table S 1. Model parameters for the 34 glass-formers. See text for details Material Tg, K Tx/Tg Tx, K log(∞, s) m TA, K log(A, s) Silica 1475 0.748 1104 -14.8 23.5 1352.61 2.9 Window Glass 833 0.787 655 -16.2 31.4 803.04 1.5 Corning Aluminosilicate 1050 0.787 826 -16.2 31.4 1012.24 1.5 Basalt 993 0.819 813 -17.6 42....

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    temperature for various molecular glasses Figure S 1

    Shifted log-log plots for the a-relaxation time vs. temperature for various molecular glasses Figure S 1. Log-log plot of scaled relaxation time vs. scaled temperature for a subset of molecular glass-formers. TS2 is the universal TS2 model curve, B2O3 is boron oxide, 3MP is 3-methyl pentane; 43BP is 4,3-bromopentane; CPDE is cresolphthalein- dimethylether...

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    Relationship between fragility and Arrhenius relaxation time The fragility within TS2 can be evaluated as, ( ) ( ) ( ) ( )1 2 1 2 1 log 1 1ln(10) g xx g g g g gg TT TTm E E E E E ST TT T     = = = + − + − −    (S1) Where SS RD , and 1 1 exp 1 x g g TS T −    = + −   (S2) The relaxation time at T = TA is given...

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  72. [72]

    Functional form for TS2 relaxation time relative to the Arrhenius time and Arrhenius temperature The universal TS2 relaxation time as a function of temperature is given by,     1 2 11log ln(10) X E E E XXX     −=+    (S5) Where / XX T T= and   ( ) 1 11 exp 1 SXX R − − D  = + −  . Given the definition of the Arrhenius te...

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