Real-time microscopy of the relaxation of a glass

The study addresses how ultrastable molecular glasses relax into the supercooled liquid upon heating above the glass transition temperature. While it is widely accepted that dynamic heterogeneities underlie the dramatic slowing down near the glass transition, direct experimental identification of their spatial extent and role during devitrification has been challenging. Conventional views often assume a gradual, spatially homogeneous softening with nanometre-scale correlations. The authors instead probe a temperature/time regime above the onset of devitrification where relaxation proceeds via localized liquid regions within a glassy matrix. Using a trilayer architecture that converts local liquid formation into measurable surface instabilities, they aim to directly visualize the spatio-temporal evolution of relaxation, quantify the spacing between fast-mobility regions, and relate dynamic length and time scales during the transformation of a stable glass.

Prior work identified dynamic heterogeneities as central to glassy dynamics, inferred from experiments but rarely visualized directly due to small structural signatures and broad time-scale distributions. Bulk melting of vapor-deposited ultrastable glasses has been suggested to proceed via nucleation-and-growth with large length scales separating liquid patches, supported by calorimetry and crossover-length analyses in thin films. Simulations also point to heterogeneous dynamics and localized liquid regions above Ton. Wrinkling and surface instability literature shows that thin stiff films on soft substrates can exhibit thermally induced or locally triggered undulations, providing a route to transduce subsurface mechanical/phase changes into measurable topography. The present study integrates these strands by using wrinkling instabilities as a mechanical reporter of localized liquid formation, enabling direct mapping of dynamic heterogeneity and facilitation in ultrastable glasses.

- Materials and sample architecture: A trilayer thin-film stack was prepared on native oxide Si: 13 nm TCTA / 63 nm TPD / 13 nm TCTA. TPD (N,N'-bis(3-methylphenyl)-N,N'-diphenylbenzidine) has Tg = 333 K (10 K min−1), and TCTA (tris(4-carbazoyl-9-ylphenyl)amine) has Tg = 428 K. TPD was vapor-deposited at 0.85 Tg (285 K) to form an ultrastable glass with fictive temperature Tf = 292 ± 2 K (about 40 K below Tg). Growth rate was 0.08 nm s−1 for both materials. Capping with TCTA on both sides suppresses surface-induced front melting and enforces bulk-like transformation upon heating. - AFM imaging protocol: Samples were mounted on a heating stage within a vibration- and acoustically isolated chamber (RH < 10%). Temperature was increased in steps: first to Tg + 10 K at 5 K min−1 to stabilize, then to Tg + 16 K (349 ± 1 K). AFM intermittent-contact mode (PPP-NCHR tips, ~42 N m−1, 250–350 kHz) was used to repeatedly scan the same location in situ during isothermal anneals. Typical imaging: 512 points/line, 2 lines/s, ~256 s per frame (~4+ min). Spatial calibration applied; lateral dimensions at high T may be underestimated by up to ~10%. Apparent heights were not corrected for temperature-dependent interactions. Complementary optical microscopy imaging was also performed. - Data extraction: AFM images provided topography evolution and wrinkle emergence. Line profiles and FFT-based power spectral density (PSD) analyses quantified wrinkle amplitudes and dominant wavelengths. The number and spatial distribution of newly formed wrinkle sites (interpreted as liquid seeds) were counted vs time to estimate nucleation rates and length scales. Radial growth of individual wrinkles provided propagation velocities. Transformed liquid fraction was estimated from wrinkled area; errors estimated from perimeters (≈10%). Spatio-temporal maps were built marking the time-of-appearance of each liquid region. - Controls: Bilayers (TPD capped only on top by TCTA) showed immediate widespread wrinkling due to surface/interface front propagation, confirming that double-sided capping is necessary to observe localized, time-evolving patterns and bulk-like transformation. - Finite element modelling (FEM): Axisymmetric ANSYS simulations modeled the trilayer on a semi-infinite Si substrate under linear thermoelastic loading to 349 K. Cylindrical SCL regions within TPD were introduced as weakened inclusions. The SCL region was modeled as (i) linear elastic with low modulus, or (ii) neo-Hookean hyperelastic: U = C(I1 − 3) + δ(detF − 1)^2, capturing reduced modulus and compressibility. Parameter ranges explored included C ~ 3.84×10^6–1.43×10^7 Pa and δ ~ 1.12×10^−7–2.79×10^−7 Pa^−1; representative fits used C = 3.71×10^9 Pa and δ = 5.58×10^−10 Pa^−1 for comparison to AFM shapes. Simulations reproduced the onset of a single ridge evolving to periodic wrinkles as the SCL cylinder radius increased (250–1,000 nm), and matched experimental undulation shapes and wavelengths. Grazing-incidence XRD and TEM verified the amorphous nature post-treatment.

- Direct, real-time visualization: AFM revealed the emergence of localized Gaussian-like protuberances that evolved into concentric, radially growing wrinkle patterns upon isothermal annealing at 349 K (Tg + 16 K). Corrugation is irreversible and persists at room temperature; the trilayer remains amorphous (no crystallization). - Dominant wrinkle length scale: PSD analysis of fully transformed surfaces showed a prominent wavelength d = 912 ± 70 nm. - Temporal evolution and induction: A long induction period (~2 h) with no discernible surface features precedes the appearance of the first liquid regions, consistent with the high kinetic/thermodynamic stability of the ultrastable glass and possibly slower initial growth of sub-cap seeds under pressure. - Nucleation kinetics and giant length scales: Between ~0.9–1.25×10^5 s, the cumulative number of liquid seeds per area increased approximately linearly, yielding an average formation frequency ν ≈ 2×10^7 nuclei m^−2 s^−1. This corresponds to a mean separation between droplets appearing in 1 s of ~130 µm (3D estimate). Over ~3,000 s, the average inter-seed distance (~2 µm) matches the order of the front-propagation distance (~1.2 µm at Tg + 16 K) inferred from independent measurements, corroborating prior crossover-length estimates (≈1–4 µm). - Radial propagation velocity: The lateral growth of individual wrinkle regions proceeded at 0.3 ± 0.1 nm s^−1, consistent with the independently determined supercooled-liquid front velocity νfront = 0.4 ± 0.1 nm s^−1 at this temperature. This links the mechanical instability propagation to the advance of the liquid front. - Transformed fraction and facilitation: The liquid fraction vs time followed a sharp sigmoidal profile, reflecting continuous nucleation with acceleration. Spatio-temporal maps show that most of the glass transforms via dynamic facilitation: initially formed liquid regions ignite adjacent zones, leading to lateral progression of mobility across giant length scales. After 1.5×10^4 s at Tg + 16 K, ~10–15% of the glass remained untransformed. - Modelling corroboration: FEM reproduced the onset and evolution of undulations from a single ridge to periodic wrinkles as SCL regions grow, matching AFM undulation shapes and supporting the interpretation that localized SCL formation under compressive thermal loads drives the observed patterns. The approach establishes a correlation between dynamic time scales (nucleation/growth rates) and emergent length scales (seed spacing, wrinkle wavelength).

The results directly address the long-standing challenge of visualizing and quantifying dynamic heterogeneity during the devitrification of ultrastable glasses. By converting local liquid formation into measurable surface wrinkling, the study demonstrates that relaxation does not proceed homogeneously but via localized liquid regions separated by micrometre-scale distances, which subsequently grow and facilitate neighboring regions to equilibrate. The measured nucleation rate and radial growth velocity quantify the time scales of these processes and align with independent front-propagation measurements, thereby linking microscopic dynamics to emergent length scales. The observation of an extended induction period, followed by accelerated nucleation and sigmoidal transformation, supports a nucleation-and-growth picture, with dynamic facilitation dominating the later stages. FEM confirms that the mechanical instabilities are consistent with localized SCL regions within the TPD interlayer under thermal stress transfer to the stiffer TCTA caps. Together, these findings provide a spatio-temporal map of relaxation, validate previous indirect inferences of giant dynamic length scales in ultrastable glasses, and bridge experimental observations with simulation-based predictions of heterogeneous melting and facilitation.

This work introduces a real-time, microscopy-based methodology to map the relaxation of ultrastable molecular glasses into the supercooled liquid by leveraging mechanically transduced surface wrinkling in a designed trilayer stack. It provides direct evidence for heterogeneous devitrification with giant micrometre-scale separations between fast-mobility regions, quantifies nucleation and growth kinetics, and establishes a correlation between dynamic time scales and emergent length scales. Finite element simulations substantiate the mechanistic link between localized SCL formation and observed undulation patterns. The approach offers a pathway to interrogate the microscopic dynamics of other glass formers, including liquid-cooled glasses with shorter intrinsic length and time scales. Future work could tune layer thicknesses and material combinations to adjust spatial resolution, extend to different chemistries, integrate faster scanning modalities for earlier-stage detection, and couple with calorimetry or spectroscopy to correlate mechanical signatures with thermodynamic and molecular mobility measures.

- Spatial resolution limit: AFM cannot detect the very earliest formation of liquid nuclei; surface instabilities become visible only when the liquid region exceeds the middle-layer thickness, effectively limiting resolution to ~TPD thickness (~63 nm). - Temporal resolution: Each AFM frame requires ~256 s, potentially missing rapid early-stage events and exact nucleation times. - Metrology uncertainties: High-temperature scans underestimate lateral dimensions by up to ~10% due to piezoscanner coefficient changes; apparent heights are uncorrected and may be underestimated. Re-positioning the exact same area after thermal cycles is difficult due to piezo hysteresis. - Anisotropy of mobility: While radial, average growth is observed, the local morphology of mobility propagation (e.g., string-like or fractal) cannot be resolved. - Model assumptions: FEM treats SCL regions with simplified elastic or neo-Hookean behavior and axisymmetric geometry; actual viscoelastic/plastic effects and 3D heterogeneity may differ. Processing stresses are assumed negligible (stress-free at deposition temperature). - Generalizability: Observations are demonstrated for a specific TCTA/TPD/TCTA architecture and temperature (Tg + 16 K); behavior may vary with different materials, thicknesses, or thermal histories.