[Paper Review] Surface tension fluctuations and a new spinodal point in glass-forming liquids

Chiara Cammarota, Andrea Cavagna+3 more|arXiv (Cornell University)|Apr 9, 2009

Material Dynamics and Properties32 references17 citations

TL;DR

This study presents the first direct measurement of surface tension in a model glass-forming liquid, demonstrating its vanishing at the energy threshold separating minima from saddles—evidencing a new spinodal point for amorphous metastable order. The results confirm the random first-order theory (RFOT) prediction that surface tension suppression triggers the dynamic slowdown in glass formers, with reduced fluctuations at low temperatures aligning with nonexponential relaxation dynamics.

ABSTRACT

The dramatic slowdown of glass-forming liquids has been variously linked to increasing dynamic and static correlation lengths. Yet, empirical evidence is insufficient to decide among competing theories. The random first order theory (RFOT) links the dynamic slowdown to the growth of amorphous static order, whose range depends on a balance between configurational entropy and surface tension. This last quantity is expected to vanish when the temperature surpasses a spinodal point beyond which there are no metastable states. Here we measure for the first time the surface tension in a model glass-former, and find that it vanishes at the energy separating minima from saddles, demonstrating the existence of a spinodal point for amorphous metastable order. Moreover, the fluctuations of surface tension become smaller for lower temperatures, in quantitative agreement with recent theoretical speculation that spatial correlations in glassy systems relax nonexponentially because of the narrowing of the surface tension distribution.

Motivation & Objective

• To empirically test the random first-order theory (RFOT) by measuring surface tension in a model glass-former, a key but previously unmeasured parameter.
• To determine whether surface tension vanishes at a critical energy threshold, signaling a spinodal point beyond which metastable states cease to exist.
• To investigate the role of surface tension fluctuations in governing the static correlation length and nonexponential relaxation in glassy systems.
• To validate the theoretical link between surface tension distribution narrowing and the emergence of static correlations in supercooled liquids.

Proposed method

• The surface energy is computed via energy differences between hybrid inherent structures formed by exchanging particles within a sphere of radius R between two inherent states (ISs).
• The surface tension Y(R) is extracted from the energy difference using a finite-size scaling approach, with corrections for finite-size effects modeled via a power-law correction term.
• The exponent ω in the correction term is determined self-consistently by analyzing the R-dependence of the variance of the surface energy, ensuring independence of the variance from R at the correct ω.
• The distribution P(Y; R) of surface tensions is computed across many IS pairs, and its evolution with R is used to infer the point-to-set correlation function q_c(R).
• The minimal surface energy E^s_β₀,α is computed by minimizing E_αβ over β for fixed α, yielding P₀(Y), which is used to refine the overlap calculation and estimate the anomaly ζ.
• Theoretical expressions from RFOT are used to relate the surface tension distribution P(Y; R) to the point-to-set correlation function q_c(R), with the inflection point ξ identified as the correlation length.

Experimental results

Research questions

• RQ1 Does surface tension vanish at a critical energy threshold, indicating a spinodal point for amorphous metastable order in glass-formers?
• RQ2 How do fluctuations in surface tension relate to the emergence of static correlation lengths and nonexponential relaxation in supercooled liquids?
• RQ3 To what extent does the distribution of surface tensions P(Y; R) govern the decay of the point-to-set correlation function q_c(R)?
• RQ4 Is the surface tension distribution consistent with the theoretical prediction that its narrowing at low temperatures drives nonexponential relaxation?

Key findings

• The surface tension Y(R) is found to vanish at the energy separating inherent state minima from saddles, providing direct evidence for a new spinodal point in glass-forming liquids.
• The exponent ω in the surface energy correction is determined to be 1.5(2), consistent across temperatures and validating the finite-size scaling approach.
• The distribution P(Y; R) of surface tensions narrows significantly at lower temperatures, supporting the theoretical link between fluctuation suppression and nonexponential relaxation.
• The point-to-set correlation function q_c(R) decays rapidly near R ≈ ξ, with the correlation length ξ extracted from the inflection point of the decay, consistent with RFOT predictions.
• The anomaly ζ, derived from the minimal surface energy distribution P₀(Y), is found to be ≈4.4, comparable to the value ≈4.2 obtained from the full P(Y), confirming robustness of the result.
• The measured surface tension vanishing at the spinodal point supports the RFOT framework, where metastable states lose stability when surface tension vanishes, leading to ergodicity and dynamic slowdown.