Glasses denser than the supercooled liquid

When aged below the glass transition temperature, Tg, the density of a glass cannot exceed that of the metastable supercooled liquid (SCL) state, unless crystals are nucleated. The only exception is when another polyamorphic SCL state exists, with a density higher than that of the ordinary SCL. Experimentally, such polyamorphic states and their corresponding liquid–liquid phase transitions have only been observed in network-forming systems or those with polymorphic crystalline states. In otherwise simple liquids, such phase transitions have not been observed, either in aged or vapor-deposited stable glasses, even near the Kauzmann temperature. Here, we report that the density of thin vapor-deposited films of N,N′-bis(3-methylphenyl)-N,N′-diphenylbenzidine (TPD) can exceed their corresponding SCL density by as much as 3.5% and can even exceed the crystal density under certain deposition conditions. We identify a previously unidentified high-density supercooled liquid (HD-SCL) phase with a liquid–liquid phase transition temperature (TLL) ∼35 K below the nominal glass transition temperature of the ordinary SCL. The HD-SCL state is observed in glasses deposited in the thickness range of 25 to 55 nm, where thin films of the ordinary SCL have exceptionally enhanced surface mobility with large mobility gradients. The enhanced mobility enables vapor-deposited thin films to overcome kinetic barriers for relaxation and access the HD-SCL state. The HD-SCL state is only thermodynamically favored in thin films and transforms rapidly to the ordinary SCL when the vapor deposition is continued to form films with thicknesses more than 60 nm.

Glasses are formed when the structural relaxations in supercooled liquids (SCLs) become too slow, causing the system to fall out of equilibrium at the glass transition temperature (Tg). The resulting out-of-equilibrium glass state has a thermodynamic driving force to evolve toward the SCL state through physical aging (1). At temperatures just below Tg, the extent of equilibration is limited by the corresponding SCL state, while at much lower temperatures, equilibration is limited by the kinetic barriers for relaxation. As such, the degree of thermodynamic stability achieved through physical aging is limited (2).Physical vapor deposition (PVD) is an effective technique to overcome kinetic barriers for relaxation to produce thermodynamically stable glasses (3–10). The accelerated equilibration in these systems is due to their enhanced surface mobility (11–14). During PVD, when the substrate temperature is held below Tg, molecules or atoms can undergo rearrangements and adopt more stable configurations at the free surface and proximate layers underneath (13). After the molecules are buried deeper into the film, their relaxation dynamics significantly slow down, which prevents further equilibration. Through this surface-mediated equilibration process, stable glasses can achieve low-energy states on the potential energy landscape that would otherwise require thousands or millions of years of physical aging (2, 3, 15, 16).As such, the degree of enhanced surface mobility and mobility gradients are critical factors in the formation of stable glasses (3, 11, 17, 18). While the effect of film thickness on the surface mobility and gradients of liquid-quenched (LQ) glasses has been studied in the past (19, 20), there are limited data on the role of film thickness in the stability of vapor-deposited glasses. In vapor-deposited toluene, it has been shown that decreasing the film thickness from 70 to 5 nm can increase the thermodynamic stability but decrease the apparent kinetic stability (5, 6). In contrast, thin films covered with a top layer of another material do not show a significant evidence of reduced kinetic stability (21), indicating the nontrivial role of mobility gradients in thermal and kinetic stability.Stable glasses of most organic molecules, with short-range intramolecular interactions, have properties that are indicative of the same corresponding metastable SCL state as LQ and aged glasses, without any evidence of the existence of generic liquid–liquid phase transitions that can potentially provide a resolution for the Kauzmann entropy crisis (22). The Kauzmann crisis occurs at the Kauzmann temperature (TK), where the extrapolated SCL has the same structural entropy as the crystal, producing thermodynamically impossible states just below this temperature. Recently, Beasley et al. (16) showed that near-equilibrium states of ethylbenzene can be produced using PVD down to 2 K above TK and hypothesized that any phase transition to an “ideal glass” state to avoid the Kauzmann crisis must occur at TK.In some glasses of elemental substances (23, 24) and hydrogen-bonding compounds (25, 26), liquid–liquid phase transitions can occur between polyamorphic states with distinct local packing structures that correspond to polymorphic crystalline phases. For example, at high pressures, high- and low-density supercooled water phases are interconvertible through a first-order phase transition (27, 28). Recent studies have demonstrated that such polyamorphic states can also be accessed through PVD in hydrogen-bonding systems with polymorphic crystal states at depositions above the nominal Tg (29, 30). However, these structure-specific transitions do not provide a general resolution for the Kauzmann crisis.Here, we report the observation of a liquid–liquid phase transition in vapor-deposited thin films of N,N′-bis(3-methylphenyl)-N,N′-diphenylbenzidine (TPD). TPD is a molecular glass former with only short-range intermolecular interactions. When thin films of TPD are vapor deposited onto substrates held at deposition temperatures (Tdep) below the nominal glass transition temperature of bulk TPD, Tg (bulk), films in the thickness range of 25 nm<h<55 nm achieve a high-density supercooled liquid (HD-SCL) state, which has not been previously observed. The liquid–liquid phase transition temperature (TLL) between the ordinary SCL and HD-SCL states is measured to be TLL≃Tg(bulk)−35 K. The density of thin films deposited below TLL tangentially follows the HD-SCL line, which has a stronger temperature dependence than the ordinary SCL. When vapor deposition is continued to produce thicker films (h>60 nm), the HD-SCL state transforms into the ordinary SCL state, indicating that the HD-SCL is only thermodynamically favored in the thin-film geometry. This transition is qualitatively different from the previously reported liquid–liquid phase transitions, as it is not related to a specific structural motif in TPD crystals, and it can only be observed in thin films, indicating that the energy landscape of thin films is favoring this high-density state.We observe an apparent correlation between enhanced mobility gradients in LQ thin films of TPD and the thickness range where HD-SCL states are produced during PVD. We hypothesize that enhanced mobility gradients are essential in providing access to regions of the energy landscape corresponding to the HD-SCL state, which are otherwise kinetically inaccessible. This hypothesis should be further investigated to better understand the origin of this phenomenon.