Non-exponential relaxation without dynamic heterogeneity in van der Waals liquids above the melting point

Niklas Pfeiffer; Rolf Zei{\ss}ler; Thomas Blochowicz

REVIEW 3 major objections 6 minor 42 references

Non-exponential relaxation without dynamic heterogeneity in van der Waals liquids above the melting point

T0 review · 3 major / 6 minor · reviewed 2026-08-02 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Above the melting point, the stretched relaxation shape of three van der Waals liquids is unchanged even at 99% dilution, indicating the stretching is intrinsic to the molecules rather than a symptom of dynamic heterogeneity.

desk verdict A smart dilution experiment with excellent controls that makes a provocative high-temperature claim; the moderate-dilution evidence is solid, but the full invariance claim is not yet quantified. read the letter →

arxiv 2602.13858 v1 pith:2IHYROD3 submitted 2026-02-14 cond-mat.soft

Rolf Zei{ss}ler , Niklas Pfeiffer , Thomas Blochowicz This is my paper · ORCID

classification cond-mat.soft

keywords dynamicheterogeneitynon-exponentialrelaxationdepolarizedlightscatteringvanderWaalsliquidsCole-Davidsondilutionrotationaldynamicsglasstransition

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks why the rotational relaxation of simple van der Waals liquids remains stretched (non-exponential) well above their melting point, a regime where dynamic heterogeneity is usually expected to have vanished. Using depolarized dynamic light scattering, the authors measure the relaxation shape of three anisotropic probe liquids (diethyl phthalate, tributyl phosphate, n-tridecane) both in bulk and diluted in optically isotropic carbon tetrachloride, up to 99% solvent for one system. The spectral shape is indistinguishable from the bulk at all concentrations, with Cole-Davidson width parameters unchanged (0.74, 0.53, and 0.83). In control systems with deliberately introduced heterogeneity—molecules with internal rotating groups or mixtures of alkanes of different sizes—dilution clearly changes the shape. The authors conclude that the stretched relaxation of these single-component liquids above the melting point is an intrinsic molecular property, not a fingerprint of dynamic heterogeneity, and that relaxation mechanisms must change between the glass-transition temperature and the melting point.

What carries the argument

The experimental scheme is depolarized dynamic light scattering (DDLS), which yields the imaginary part of the susceptibility via the fluctuation-dissipation theorem, combined with a dilution test: anisotropic probe molecules are dispersed in CCl4, an optically isotropic solvent that scatters weakly, so the relaxation spectrum is dominated by the probes. The shape comparator is the Cole-Davidson width parameter β_CD, which quantifies asymmetric stretching of the relaxation peak; spectra are normalized and shifted to overlay low-frequency flanks, and the solvent contribution is subtracted assuming an ideal mixing law. The control experiments—P13 with internal rotation, and C14/C7 size-mismatc

What would settle it

A high-precision DDLS measurement of DEP or TBP in CCl4 at a solvent molar fraction above 0.99 that resolves the relaxation peak and yields a Cole-Davidson width parameter measurably different from the bulk value (beyond experimental error) would directly contradict the central claim.

Watch

Extended reading notes

Core claim

The central discovery is that diluting optically anisotropic probe molecules (DEP, TBP, n-tridecane) in the optically isotropic solvent CCl4, down to solvent molar fractions as high as 0.99, does not alter the shape of the relaxation peak in the depolarized light-scattering susceptibility once the solvent contribution is subtracted under an ideal mixing law. In contrast, for a molecule with internal degrees of freedom (1-phenyltridecane) and for binary mixtures of n-tetradecane and n-heptane—both carrying an explicit source of dynamic heterogeneity—dilution changes the relaxation shape. The authors take the shape invariance as evidence that dynamic heterogeneity has negligible influence on t

Load-bearing premise

The argument rests on the premise that diluting a probe molecule in CCl4 is a neutral manipulation: if dynamic heterogeneity were present in the pure liquid, the solvent would necessarily perturb it and show up as a shape change, and the subtraction procedure does not hide such a change.

Editorial extensions

If this is right

The non-exponential relaxation shapes of these liquids above Tm are intrinsic properties of the individual molecules, not collective effects of the local environment.
Orientational cross-correlations contribute negligibly to the DDLS spectra above Tm in these systems, because dilution would otherwise suppress them and change the observed shape.
Persistent relaxation stretching at high temperatures cannot be taken as evidence of dynamic heterogeneity in this regime; a shape change upon dilution is a more sensitive indicator that heterogeneity is present.
Assuming the heterogeneous picture near Tg is correct, a qualitative change in the mechanism of structural relaxation must occur somewhere between Tg and Tm, which constrains models of glass-forming liquids.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The same dilution protocol could be applied to dielectric spectroscopy of polar probes to separate intrinsic single-molecule stretching from collective dipole cross-correlations, which are known to contaminate dielectric spectra.
A testable extension is to repeat the dilution with a different isotropic solvent of different molecular size or viscosity (e.g., CS2); if the probe's spectral shape changes with solvent identity, the intrinsic-molecule interpretation would need revision.
If the claim generalizes, simulations should find that four-point dynamic susceptibility remains small above Tm for single-component systems while still growing near Tg, consistent with the proposed mechanism switch.
The control results suggest that dilution can be used as a practical diagnostic to expose hidden dynamic heterogeneity in complex liquid mixtures.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Quick take: this is a genuinely new test of an old assumption. Rössler and others showed that stretching persists above Tm, but nobody had directly asked whether the stretching is heterogeneous in origin by diluting an anisotropic probe in an isotropic solvent. The control experiments are the best part: P13, with its internal rotation, changes shape on dilution, and the C14/C7 mixture broadens further. That shows the experiment would have caught a shape change if one were present. Credit where due: the idea is simple, the systems are well chosen, and the manuscript is clearly written.

The moderate-dilution data are visually convincing. Up to Φ=0.907 for DEP and 0.75 for TBP and C13, the raw spectra collapse onto the bulk relaxation peak without any processing. That alone supports the core claim that dilution does not change the shape. The high-dilution results are weaker. For Φ>0.9, the spectra only become interpretable after subtracting the CCl4 contribution via Eq. 2, and the assumption that CCl4's spectrum is unaltered in the mixture is explicitly called 'not obvious' and then justified by the collapse it produces. That is a consistency check, not independent validation. It does not sink the paper, because the moderate-dilution data already carry the argument, but the abstract's 'negligible influence' wording goes beyond what is demonstrated at the highest dilutions.

The missing error bars are a real weakness, as the stress-test note says. The text claims β_CD is unchanged 'in the bulk and in mixtures of any concentration' but gives only bulk values. A null result needs a bound on detectable change. Without uncertainties on the fitted widths, a 5–10% systematic change could hide in the noise. This is fixable in revision: report fitted β_CD with uncertainties for each mixture, and ideally a formal test for shape equality. The C13 dilution is only handled visually, with no β_CD quoted for the diluted alkane—minor, but consistent with the quantitative analysis lagging the qualitative claims.

Who this is for: anyone working on glass-forming liquids, especially the Rössler/Lunkenheimer discussion about stretching at high temperature. It deserves a serious referee. The core observation is likely real; the interpretation—a mechanistic crossover between Tg and Tm—is speculative but clearly labeled. The circularity is acknowledged, not buried.

My recommendation: send it to peer review, with the request that the authors add error bars, report the diluted β_CD values, and either strengthen or soften the high-dilution claim. As it stands, a conditional accept is the right call.

Referee Report

3 major / 6 minor

Summary. The paper reports depolarized dynamic light scattering (DDLS) measurements at 300 K on three van der Waals liquids (DEP, TBP, C13) in bulk and diluted in CCl4, and compares them with two systems in which dynamic heterogeneity is explicitly present: P13, which has a phenyl ring that undergoes internal rotation, and C14/C7 mixtures, which contain a distribution of molecular sizes. The central claim is that the relaxation shape, as quantified by the Cole-Davidson width parameter, is unchanged on dilution up to CCl4 molar fractions as high as 0.99, and therefore that dynamic heterogeneity has a negligible influence on the rotational dynamics of these single-component liquids above their melting points. The authors interpret the result as evidence for a crossover from heterogeneous dynamics near Tg to homogeneous but intrinsically stretched dynamics above Tm. The high-dilution data rely on subtracting a mole-fraction-scaled CCl4 spectrum via Eq. (2). The positive controls show shape changes on dilution, which the authors take as evidence that the dilution test is sensitive.

Significance. If the quantitative claim can be established, the paper is significant: it directly challenges the default assumption that non-exponential structural relaxation above Tm is a signature of dynamic heterogeneity, and it sharpens the temperature range in which a change of relaxation mechanism would have to occur. The strongest parts of the paper are the two control experiments: P13, where internal rotation produces a bimodal spectrum whose components respond to dilution, and C14/C7, where a size distribution causes dilution-dependent broadening. These controls make the null result for DEP, TBP, and C13 more credible than a single dilution series alone. The scenario-based Discussion is also clear. However, the central null result is presently supported mainly by visual superposition, with no fitted width parameters or error bars for the diluted systems, and the high-dilution result depends on a subtraction procedure that is justified by its own outcome. The paper is likely to be influential if these gaps are closed.

major comments (3)

[Section III.A, Figs. 1(b), 2(d), 3; Section IV] Quantitative support for shape invariance is missing. The text states that the Cole-Davidson parameters of DEP and TBP are unchanged in mixtures 'of any concentration', but only bulk beta_CD values (0.74 and 0.53) are reported, and C13 is not quantified at all. The figures show normalized, frequency-shifted spectra that visually collapse, but no statistical test and no uncertainties on beta_CD are supplied. For a null result, a bound on the detectable change is needed; without it, a 5-10% systematic variation in beta_CD could be hidden by noise and by the normalization/shifting procedure. Please report fitted beta_CD values (or an equivalent shape metric) with confidence intervals for every concentration studied, including C13, and state the smallest shape change the experiment could have detected.
[Eq. (2), Fig. 3, Section III.A] The high-dilution conclusion depends on a subtraction of the CCl4 contribution under an ideal-mixing assumption. The authors write that this assumption is 'not obvious, however, is justified by the results of this subtraction procedure'; this is a circular validation. The issue is load-bearing because the clearest part of the claim (Phi_CCl4 = 0.99 for DEP, and the TBP/C13 data above 0.75) exists only after subtraction. In addition, Eq. (2) scales the pure CCl4 spectrum by mole fraction without justifying why the DID scattering intensity should be linear in mole fraction. An independent validation is needed: for example, a test with a different anisotropic probe, a check against volume-fraction scaling, or residual analysis with propagated uncertainties.
[Section IV, scenarios (i)-(iii)] The inference from 'shape unchanged on dilution' to 'dynamic heterogeneity has negligible influence' rests on the premise that dilution would necessarily perturb any heterogeneity contribution. This is a reasonable working hypothesis, but the paper does not make its falsifiable content quantitative and does not examine solvent specificity: only CCl4 is used, and the data do not rule out a solvent-induced change in single-molecule relaxation shape that could mask a heterogeneity contribution. Please state explicitly what size of heterogeneity effect would be detectable under the dilution protocol, or provide a model illustrating the expected shape change under heterogeneity; at minimum, discuss the single-solvent limitation.

minor comments (6)

[Section II.A] The manuscript repeatedly refers to the SI for temperature independence and fitting details, but no SI is included with the arXiv manuscript. Please include the fit model, fit ranges, and temperature-independence data, or summarize the relevant results in the main text.
[Section III.C] 'Tertiary mixtures' should be 'ternary mixtures' for three-component systems. Also define Phi_CCl4 at first use, since it is introduced without a formal definition.
[Fig. 3] The black curves are said to 'represent' Debye and Cole-Davidson susceptibilities. State explicitly whether they are fits to the diluted data, and if so give the fitted parameters and ranges; if they are fixed model functions, say so.
[Table I and Fig. 1(a)] The text uses 'Tbl. I' and 'Table I' inconsistently. In the Fig. 1(a) inset, specify the exact form of the red ideal-mixing line, since it is related to the scaling used in Eq. (2).
[Section III.B] For the P13 positive control, the change in relative amplitude and dynamic separation is described as 'possible' and a quantitative fit is declared out of scope. Since P13 is a control for the sensitivity of the dilution test, a quantitative peak-position/width table would strengthen the argument.
[References] Reference [18] lists 'A. Loid'; this appears to be a typo for 'A. Loidl'.

Circularity Check

1 steps flagged · score 2.0 of 10

Main claim is experimental and not derived from a fit; only mild self-validation in the CCl4-subtraction procedure.

other [Section III.A, Eq. (2) and following paragraph]
"under assumption of an ideal mixing law: χ″probe(ν) = χ″total(ν) − ΦCCl4·χ″CCl4(ν). ... For this subtraction method to work, the contribution of CCl4 in the mixtures has to be largely unaltered with respect to its bulk spectrum, apart from being scaled by concentration. This assumption is not obvious, however, is justified by the results of this subtraction procedure presented in Fig. 3."

The high-dilution shape-invariance claim is established from spectra processed with Eq. (2), whose key assumption is that the CCl4 contribution in each mixture is the bulk CCl4 spectrum scaled by mole fraction. The paper explicitly validates that assumption by the very collapse of the subtracted spectra (Fig. 3) that is then used as evidence for shape invariance. Thus the conclusion at the highest CCl4 concentrations is not a fully independent test of the assumption; it is a self-consistent output of the subtraction scheme. This is not a mathematical tautology — the subtraction could in principle fail to collapse — but it is a mild self-validating loop in the data-processing chain.

full rationale

The central derivation is experimental and self-contained: bulk and diluted DDLS spectra are measured, normalized, and compared; the conclusion that the relaxation shape is unchanged upon dilution is not obtained from a fitted parameter or from an equation that contains the conclusion. No self-definitional relation, no fitted-input-called-prediction, and no author-imported uniqueness theorem is present. The only circular flavor is in Section III.A: Eq. (2) assumes an ideal-mixing, unaltered CCl4 contribution, and the paper justifies that assumption by the collapse of the subtracted spectra, i.e., by the same shape-invariance the procedure is used to demonstrate. This affects only the highest-dilution data points and does not force the main claim, since the subtraction could have produced non-collapsing artifacts. Self-citations (refs. 22–24, 42) support control-system interpretation and a secondary cross-correlation remark, not the load-bearing null result. Therefore the paper is largely non-circular; score 2 reflects the one self-validating processing step.

Assumptions & free parameters 7 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new physical entities. The fitted β_CD values are outputs of the analysis, not free parameters used to force a derivation; the claim rests on their invariance. The main unstated premises are the passivity of the diluent, ideal mixing for the CCl4 contribution, and negligible orientational cross-correlations.

free parameters (7)

β_CD (DEP) = 0.74
Cole-Davidson width parameter fitted to the DDLS relaxation peak of DEP in bulk and in CCl4 mixtures; used to quantify shape invariance. The claim depends on its constancy, not its absolute value.
β_CD (TBP) = 0.53
Fitted to bulk and diluted TBP relaxation peaks.
β_CD (C13) = 0.83
Fitted to bulk and diluted n-tridecane relaxation peaks.
β_CD (C14) = 0.85
Fitted to pure n-tetradecane peak; baseline for the alkane-mixture control.
β_CD (C14/C7 1:1) = 0.68
Binary alkane mixture with explicit size-distribution heterogeneity.
β_CD (C14/C7/CCl4 Φ_CCl4=0.5) = 0.62
Tertiary mixture after CCl4 subtraction.
β_CD (C14/C7/CCl4 Φ_CCl4=0.9) = 0.52
Tertiary mixture after CCl4 subtraction; increasing broadening with dilution.

assumptions (4)

domain assumption Dilution with CCl4 is a passive, non-perturbing manipulation that would expose any dynamic heterogeneity by changing the spectral shape.
This is the interpretive core of the dilution experiment; stated in the Introduction (last paragraph) and Discussion scenarios (i)-(iii). If dilution instead creates or destroys heterogeneity in a compensating way, the central conclusion fails.
domain assumption The CCl4 contribution to the mixture DDLS spectrum is identical to its bulk spectrum multiplied by molar fraction (ideal mixing).
Used in Eq. 2 to subtract the solvent contribution at high dilution; the authors state this is 'not obvious' but is 'justified by the results,' which is a mild circular justification.
domain assumption Orientational cross-correlations contribute negligibly to the DDLS susceptibility of the studied liquids above Tm.
Invoked in the Discussion to argue that shape invariance cannot be explained by cross-correlation screening; supported by prior work (Refs. 41, 42) but not directly measured here.
domain assumption The relaxation peak in the DDLS susceptibility of the probe molecules reflects rotational relaxation, with the vibrational part well separated.
Required for the spectral-shape analysis; based on prior assignments for these systems (Refs. 21, 25, 26).

how reviews work

0 comments

Cite this review

Pith. "Pith review of Non-exponential relaxation without dynamic heterogeneity in van der Waals liquids above the melting point." pith.science (2026). https://pith.science/paper/2IHYROD3

@misc{pith2026260213858,
  author       = {Pith},
  title        = {Pith review of: Non-exponential relaxation without dynamic heterogeneity in van der Waals liquids above the melting point},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2IHYROD3}},
  note         = {Machine review of arXiv:2602.13858}
}

read the original abstract

We investigate the influence of dynamic heterogeneity on the spectral shape of structural relaxation in van der Waals liquids above the melting point by means of depolarized dynamic light scattering. To this end, we study optically anisotropic probe molecules both in the bulk and when diluted in an optically isotropic solvent. Strikingly, the relaxation shape of the probe molecules in dilution is indistinguishable from that of the pure liquid composed of the probe molecules. By contrast, when explicit dynamic heterogeneity is introduced, e.g., through internal degrees of freedom or a distribution of probe molecule sizes, the relaxation shape becomes sensitive to the solvent concentration. These findings indicate that dynamic heterogeneity has a negligible influence on the rotational dynamics of single component van der Waals liquids above the melting point, despite the pronounced non-exponential character of their relaxation shape.

Figures

Figures reproduced from arXiv: 2602.13858 by the authors.

**Figure 2.** FIG. 2. Analogous analysis to Fig. 1 for probe molecules TBP (a-b) and C13 (c-d). [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 4.** FIG. 4. DDLS spectra of P13 and mixtures of P13 and CCl [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

Figures from the paper (2 more)

**Figure 3.** Figure 3: FIG. 3. DDLS spectra after subtraction of the CCl [PITH_FULL_IMAGE:figures/full_fig_p005_3.png]

**Figure 5.** Figure 5: FIG. 5. a) DDLS spectra of C14, binary mixture of C14 [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

42 extracted references · 4 canonical work pages

[1]

B¨ ohmer, Curr

R. B¨ ohmer, Curr. Opin. Solid State Mater. Sci.3, 378 (1998)

1998
[2]

Sillescu, J

H. Sillescu, J. Non-Cryst. Solids243, 81 (1999)

1999
[3]

C. A. Angell, K. L. Ngai, G. B. McKenna, P. F. McMil- lan, and S. W. Martin, J. Appl. Phys.88, 3113 (2000)

2000
[4]

M. D. Ediger, Annu. Rev. Phys. Chem.51, 99 (2000)

2000
[5]

Richert, J

R. Richert, J. Phys. Condens. Matter14, R703 (2002)

2002
[6]

Cavagna, Phys

A. Cavagna, Phys. Rep.476, 51 (2009)

2009
[7]

Richert, N

R. Richert, N. Israeloff, C. Alba-Simionesco, F. Ladieu, and D. L’Hˆ ote, Dynamical Heterogeneities in Glasses, Colloids, and Granular Media , 152 (2011)

2011
[8]

B¨ ohmer, R

R. B¨ ohmer, R. Chamberlin, G. Diezemann, B. Geil, A. Heuer, G. Hinze, S. Kuebler, R. Richert, B. Schiener, H. Sillescu,et al., J. Non-Cryst. solids235, 1 (1998)

1998

Show all 42 references

[9]

M. T. Cicerone, F. Blackburn, and M. Ediger, J. Chem. Phys.102, 471 (1995)

1995
[10]

Schiener, R

B. Schiener, R. B¨ ohmer, A. Loidl, and R. Chamberlin, Science274, 752 (1996)

1996
[11]

Paeng, H

K. Paeng, H. Park, D. T. Hoang, and L. J. Kaufman, Proc. Natl. Acad. Sci. U.S.A.112, 4952 (2015)

2015
[12]

K. Kim, S. Lee, T. Kim, Y. K. Chung, J. Huh, J. Yang, A. Lee, and K. Paeng, J. Chem. Phys.157(2022), 10.1063/5.0127024

2022 doi
[13]

G. P. Johari and J. Khouri, J. Chem. Phys.137(2012), 10.1063/1.4748355

2012 doi
[14]

Petzold, B

N. Petzold, B. Schmidtke, R. Kahlau, D. Bock, R. Meier, B. Micko, D. Kruk, and E. R¨ ossler, J. Chem. Phys.138 (2013)

2013
[15]

Schmidtke, N

B. Schmidtke, N. Petzold, B. Potzschner, H. Weingart- ner, and E. Rossler, J. Phys. Chem. B118, 7108 (2014)

2014
[16]

E. A. R¨ ossler and M. Becher, J. Chem. Phys.163(2025)

2025
[17]

L. C. Pardo, P. Lunkenheimer, and A. Loidl, Phys. Rev. E76, 030502 (2007)

2007
[18]

Lunkenheimer, U

P. Lunkenheimer, U. Schneider, R. Brand, and A. Loid, Contemp. Phys.41, 15 (2000)

2000
[19]

M. P. Eastwood, T. Chitra, J. M. Jumper, K. Palmo, A. C. Pan, and D. E. Shaw, J. Phys. Chem. B117, 12898 (2013)

2013
[20]

Pabst and S

F. Pabst and S. Baroni, Phys. Rev. E111, L023401 (2025)

2025
[21]

Cummins, G

H. Cummins, G. Li, W. Du, R. M. Pick, and C. Dreyfus, Phys. Rev. E53, 896 (1996)

1996
[22]

Zeißler, F

R. Zeißler, F. Pabst, T. B¨ ohmer, and T. Blochowicz, Phys. Chem. Chem. Phys.25, 16380 (2023)

2023
[23]

Zeißler, J

R. Zeißler, J. P. Gabriel, D. Posselt, and T. Blochowicz, Phys. Chem. Chem. Phys.27, 7258 (2025)

2025
[24]

Zeißler, S

R. Zeißler, S. Kr¨ uger, R. Horstmann, T. B¨ ohmer, M. Vo- gel, and T. Blochowicz, arXiv preprint arXiv:2512.19863 (2025)

2025 arXiv
[25]

Pabst and T

F. Pabst and T. Blochowicz, J. Chem. Phys.157(2022)

2022
[26]

Pabst, H

F. Pabst, H. Forbert, and D. Marx, arXiv preprint arXiv:2511.14940 (2025)

2025
[27]

Williams and P

G. Williams and P. J. Hains, Chem. Phys. Lett.10, 585 (1971)

1971
[28]

G. P. Johari and C. P. Smyth, J. Chem. Phys.56, 4411 (1972)

1972
[29]

Paeng and L

K. Paeng and L. J. Kaufman, J. Chem. Phys.149(2018), 10.1063/1.5047215

2018 doi
[30]

S. A. Mackowiak, L. M. Leone, and L. J. Kaufman, Phys. Chem. Chem. Phys.13, 1786 (2011)

2011
[31]

L. M. Leone and L. J. Kaufman, J. Chem. Phys.138 (2013), 10.1063/1.4773889

2013 doi
[32]

Wang and R

L.-M. Wang and R. Richert, J. Chem. Phys.120, 11082 (2004)

2004
[33]

Yang and R

M. Yang and R. Richert, Chem. Phys.284, 103 (2002)

2002
[34]

Goldstein, J

M. Goldstein, J. Chem. Phys.51, 3728 (1969)

1969
[35]

G¨ otze and L

W. G¨ otze and L. Sj¨ ogren, Rep. Prog. Phys.55, 241 (1992)

1992
[36]

Novikov and A

V. Novikov and A. Sokolov, Phys. Rev. E67, 031507 (2003)

2003
[37]

R¨ ossler, Phys

E. R¨ ossler, Phys. Rev. Lett.65, 1595 (1990)

1990
[38]

Chang and H

I. Chang and H. Sillescu, J. Phys. Chem. B101, 8794 (1997)

1997
[39]

S. F. Swallen, P. A. Bonvallet, R. J. McMahon, and M. Ediger, Phys. Rev. Lett.90, 015901 (2003)

2003
[40]

B¨ ohmer, F

T. B¨ ohmer, F. Pabst, J. P. Gabriel, R. Zeißler, and T. Blochowicz, J. Chem. Phys.162(2025)

2025
[41]

H´ enot, P.-M

M. H´ enot, P.-M. D´ ejardin, and F. Ladieu, Phys. Chem. Chem. Phys.25, 29233 (2023)

2023
[42]

Pabst, A

F. Pabst, A. Helbling, J. Gabriel, P. Weigl, and T. Blo- chowicz, Phys. Rev. E102, 010606 (2020)

2020

Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.

[1] [1]

B¨ ohmer, Curr

R. B¨ ohmer, Curr. Opin. Solid State Mater. Sci.3, 378 (1998)

1998

[2] [2]

Sillescu, J

H. Sillescu, J. Non-Cryst. Solids243, 81 (1999)

1999

[3] [3]

C. A. Angell, K. L. Ngai, G. B. McKenna, P. F. McMil- lan, and S. W. Martin, J. Appl. Phys.88, 3113 (2000)

2000

[4] [4]

M. D. Ediger, Annu. Rev. Phys. Chem.51, 99 (2000)

2000

[5] [5]

Richert, J

R. Richert, J. Phys. Condens. Matter14, R703 (2002)

2002

[6] [6]

Cavagna, Phys

A. Cavagna, Phys. Rep.476, 51 (2009)

2009

[7] [7]

Richert, N

R. Richert, N. Israeloff, C. Alba-Simionesco, F. Ladieu, and D. L’Hˆ ote, Dynamical Heterogeneities in Glasses, Colloids, and Granular Media , 152 (2011)

2011

[8] [8]

B¨ ohmer, R

R. B¨ ohmer, R. Chamberlin, G. Diezemann, B. Geil, A. Heuer, G. Hinze, S. Kuebler, R. Richert, B. Schiener, H. Sillescu,et al., J. Non-Cryst. solids235, 1 (1998)

1998