Real-time microscopy of the relaxation of a glass

The dynamics of glasses above their devitrification temperature (*T_g*) remain incompletely understood. A key aspect is the presence of dynamic heterogeneities – clusters of atoms or molecules with correlated mobility that influence the slowing down of dynamics and the glass transition. While previous studies have inferred the existence of these clusters, directly identifying them and their length scales has been experimentally challenging. The common view is that glass relaxation into a supercooled liquid (SCL) at *T_on* (devitrification temperature on heating) involves gradual softening across the entire volume. However, recent research suggests an alternative scenario involving the formation of localized liquid regions within a glassy matrix above *T_on*, a hypothesis supported by simulations but lacking direct experimental confirmation of the associated length scale. This study uses vapor-deposited stable glasses as model systems to explore this alternative scenario. The authors utilize a novel approach based on the mechanical instabilities generated by liquid regions on a rigid ultrathin layer atop the glass, leading to surface undulations observable by AFM and optical microscopy, enabling direct visualization of the spatiotemporal dynamics during the transformation from a glassy to a liquid state.

The authors review existing literature on dynamic heterogeneities in glasses and the glass transition. They highlight the challenges in experimentally characterizing the length scales of dynamic heterogeneities. They discuss previous work suggesting that the bulk transformation of stable glasses might proceed through a nucleation-and-growth process with giant length scales between liquid patches. The paper cites various studies supporting the use of vapor-deposited stable glasses for exploring this area and simulations indicating localized liquid formation during glass relaxation.

The study uses a trilayer structure: a 63 nm layer of N,N'-bis(3-methylphenyl)-N,N'-diphenylbenzidinem (TPD) sandwiched between two 13 nm layers of tris(4-carbazoyl-9-ylphenyl)amine (TCTA) on a silicon substrate. TPD's *T_g* is 333 K, while TCTA's is 428 K. The TPD layer acts as the glass undergoing transformation. The TCTA layers provide a rigid cap to induce localized mechanical instabilities. The sample is annealed above TPD's *T_g* (at 349 K, *T_g* + 16 K). Real-time AFM and optical microscopy are used to observe the formation and growth of surface wrinkles caused by localized liquid regions within the TPD layer. Finite element modeling (FEM) is employed to correlate the formation of surface undulations with the appearance of SCL regions. The FEM simulations use linear thermoelasticity and the neo-Hookean hyperelastic model to simulate the behavior of the trilayer system under thermal stress. The analysis involves measuring the cumulative number of liquid regions, their growth rate, and the overall transformed fraction of the liquid over time. The dominant wavelength of the wrinkled pattern was obtained through power spectral density (PSD) analysis of the fast Fourier transform (FFT) of the AFM images. Calorimetric measurements were also performed to study the glass's transition.

The real-time AFM imaging reveals the heterogeneous nature of the glass relaxation. Localized liquid regions form and grow radially, separated by giant length scales (micrometers) within the TPD glass. The radial propagation speed of these wrinkles (0.3 ± 0.1 nm/s) is consistent with the growth front velocity of the SCL TPD at the annealing temperature (0.4 ± 0.1 nm/s), confirming the correlation between wrinkle formation and liquid expansion. The dominant wavelength of the surface wrinkles in the fully transformed sample is approximately 912 nm, calculated via PSD analysis. The formation of new liquid regions exhibits an accelerating trend over time, possibly due to either matrix softening or the intrinsic distribution of relaxation times in the glass. A significant induction period of approximately 2 hours is observed before the appearance of any surface features, reflecting the high stability of the glass. The average 'formation frequency' of liquid nuclei is estimated at 2 × 10⁷ nuclei m⁻² s⁻¹, leading to a mean separation distance between liquid droplets of about 130 µm after 1 second, and about 2 µm after 3000 seconds. This aligns with previous estimates of the crossover length in thin films. Spatiotemporal maps of the liquid evolution highlight the influence of dynamic facilitation, where regions of high mobility trigger adjacent regions to transform into liquid. Roughly 10-15% of the glass remains untransformed even after significant annealing time.

The findings strongly support the hypothesis of localized liquid formation and growth during the glass relaxation above *T_g*. The direct visualization of this process clarifies previous indirect experimental observations and theoretical predictions. The observation of giant length scales between liquid regions provides direct experimental evidence of dynamic heterogeneities in ultrastable glasses. The consistency between the radial propagation velocity of the wrinkles and the growth velocity of the liquid front further validates the interpretation of the surface undulations as a direct consequence of liquid formation. The accelerating formation of liquid regions could potentially be explained by either the gradual softening of the glass matrix or the shape of the relaxation time distribution within the glass. The study bridges the gap between experiments and computer simulations by providing direct microscopic information on glass transformation dynamics.

This study presents a novel approach to visualize and quantify the relaxation dynamics of a stable glass. The combination of real-time AFM imaging, optical microscopy, and FEM simulations provides a detailed spatiotemporal map of the transformation, highlighting the heterogeneous nature of the process. The discovery of giant length scales separating regions of fast mobility underscores the importance of dynamic heterogeneities in glass behavior. Future work could explore the impact of different glass compositions, layer thicknesses, and annealing conditions on the relaxation dynamics, potentially leading to a more comprehensive understanding of glass transitions.

The spatial resolution of the AFM is limited by the thickness of the middle TPD layer, preventing the observation of the very initial stages of liquid droplet formation. The interpretation of the accelerating trend in the formation of liquid regions is not definitively concluded; further investigation is needed to distinguish between the effects of matrix softening and the intrinsic distribution of relaxation times. Additionally, the uncorrected height measurements in AFM analysis require further calibration for greater accuracy.