Glasses denser than the supercooled liquid

Significance

Enhanced surface mobility enables rapid equilibration of vapor-deposited glasses toward the supercooled liquid (SCL). We demonstrate that thin films of N,N′-bis(3-methylphenyl)-N,N′-diphenylbenzidine molecular glass, when vapor deposited below a certain temperature, can access a high-density supercooled liquid (HD-SCL) state through a liquid–liquid phase transition $\sim$35 K below the nominal glass transition temperature of ordinary SCL. The HD-SCL phase transforms into the ordinary SCL when the thickness is increased above 60 nm, demonstrating that HD-SCL is only thermodynamically favored in thin films. These results provide a recipe for accessing kinetically inaccessible regions in the energy landscape, which are critical for understanding the glass transition phenomenon. High-density stable glass states that can resist crystallization and dewetting is also important in various applications.

Abstract

When aged below the glass transition temperature, ${\mathit{T}}_{\mathit{g}}$, 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 (${\mathit{T}}_{\mathit{L}\mathit{L}}$) $\sim$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 ($T_g$). 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 $T_g$, 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 $T_g$, 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 ($T_{\mathrm{K}}$), 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 $T_{\mathrm{K}}$ and hypothesized that any phase transition to an “ideal glass” state to avoid the Kauzmann crisis must occur at $T_{\mathrm{K}}$.

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 $T_g$ (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 ($T_{\mathrm{d}\mathrm{e}\mathrm{p}}$) below the nominal glass transition temperature of bulk TPD, $T_g$ (bulk), films in the thickness range of $25\hspace{0.17em}\mathrm{n}\mathrm{m}<h<55\hspace{0.17em}\mathrm{n}\mathrm{m}$ achieve a high-density supercooled liquid (HD-SCL) state, which has not been previously observed. The liquid–liquid phase transition temperature ($T_{LL}$) between the ordinary SCL and HD-SCL states is measured to be $T_{LL}\simeq T_g\left(\mathrm{b}\mathrm{u}\mathrm{l}\mathrm{k}\right)-35\hspace{0.17em}\mathrm{K}$. The density of thin films deposited below $T_{LL}$ 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 ($h>60\hspace{0.17em}\mathrm{n}\mathrm{m}$), 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.

Results

Structural Characterization of Vapor-Deposited Films.

PVD was used to produce smooth and uniform TPD thin films as detailed in Materials and Methods and SI Appendix. Fig. 1 shows the in-plane ($q_{xy}$) and out-of-plane ($q_z$) grazing incidence wide-angle X-ray scattering (GIWAXS) data for films deposited at a substrate deposition temperature of $T_{\mathrm{d}\mathrm{e}\mathrm{p}}=264\pm 3\hspace{0.17em}\mathrm{K}$, as well as a 200-nm LQ glass film. The two-dimensional data used to extract these spectra are shown in SI Appendix, Fig. S10. X-ray diffraction measurements of TPD crystal are shown in SI Appendix, Fig. S11 as a reference. The GIWAXS data for the 203-nm vapor-deposited film (Fig. 1A) show a noticeable difference between the scattering intensity along the in-plane $q_{xy}$ and out-of-plane $q_z$ directions, indicating a significant anisotropy in this film. In contrast, the 200-nm LQ film (Fig. 1D) has a broad isotropic scattering signal, which is typically observed in LQ glasses. The anisotropy of the thick PVD film is consistent with previous observations in TPD (31, 32) and other stable glass systems (31–36). In the data shown in Fig. 1A, the anisotropy observed in the intramolecular scattering region ($q\sim$ 1.4 Å⁻¹, $\sim$0.5-nm length scale) is attributed to the orientational order of TPD molecules (31), while the peak observed in the out-of-plane direction at $q_z\sim 0.8$ Å⁻¹ ($\sim 0.8-\mathrm{n}\mathrm{m}$ length scale) is due to molecular layering normal to the film surface (35, 37). This feature has been observed in a broad range of stable glasses (31, 37, 38). As the film thickness is reduced at this deposition temperature, the differences between $q_{xy}$ and $q_z$ are diminished (Fig. 1 B and C), and the films become more isotropic. Films of all thicknesses remain amorphous, with no sign of crystallization.

Fig. 1.

In-plane ($q_{xy}$) and out-of-plane ($q_z$) GIWAXS scattering intensity for film vapor deposited at $T_{\mathrm{d}\mathrm{e}\mathrm{p}}=264\pm 3\hspace{0.17em}\mathrm{K}$ with thicknesses of (A) 203 nm, (B) 53 nm, and (C) 32 nm and (D) a 200-nm LQ glass film. The anisotropic features observed in A can be attributed to molecular orientation ($q\sim 1.4$ Å⁻¹) and layering ($q\sim 0.8$ Å⁻¹), respectively.

Spectroscopic ellipsometry was also used to evaluate the structural anisotropy of as-deposited films through measurements of optical birefringence (35, 39) (more details are in Materials and Methods and SI Appendix). In thick TPD films ($h>60\hspace{0.17em}\mathrm{n}\mathrm{m}$), birefringence strongly varies with the deposition temperature, becoming more negative at lower $T_{\mathrm{dep}}$, which indicates a preferred in-plane molecular orientation, consistent with the GIWAXS data (Fig. 1 and SI Appendix, Fig. S10) and previous studies (31, 36). In contrast, films with $h<60\hspace{0.17em}\mathrm{n}\mathrm{m}$ show zero or small positive birefringence values when the ellipsometry data are fit to a birefringent optical model. However, the error in defining birefringence in ellipsometry measurements increases with decreasing film thickness (detailed in SI Appendix, SI Text and Fig. S15). As such, given the reduced anisotropy observed in GIWAXS experiments (Fig. 1), isotropic fitting was used to fit the data for films with $h<60\hspace{0.17em}\mathrm{n}\mathrm{m}$. We note that the choice of the model (birefringent vs. isotropic) does not affect the measured film thicknesses and the calculated density (SI Appendix, Fig. S16B).

Dilatometry Experiments.

Fig. 2A shows ellipsometry-based dilatometry measurements for films vapor deposited at $T_{\mathrm{d}\mathrm{e}\mathrm{p}}=264\pm 3\hspace{0.17em}\mathrm{K}$. Films of all thicknesses have higher initial density (lower initial film thickness) compared with their transformed LQ states as shown in Fig. 2B. As the film thickness is decreased, the relative density ($\mathrm{\Delta }\rho$) is increased dramatically, reaching a maximum at $h\sim 40\hspace{0.17em}\mathrm{n}\mathrm{m}$. $\mathrm{\Delta }\rho$ decreases slowly as the film thickness is further decreased. It is notable that for $h<60\hspace{0.17em}\mathrm{n}\mathrm{m}$, $\mathrm{\Delta }\rho$ exceeds the extrapolated density of the SCL at $T_{\mathrm{d}\mathrm{e}\mathrm{p}}=264\pm 3\hspace{0.17em}\mathrm{K}$ (the dashed line in Fig. 2B). The initial film density can also be independently evaluated through measurements of the index of refraction, $n$, which is related to the density through the Lorentz–Lorenz relationship (40). SI Appendix, Fig. S19 shows that films of all thicknesses also have higher initial average indices of refraction compared to their transformed states, in agreement with the dilatometry results in Fig. 2A.

Fig. 2.

(A) Normalized thickness vs. temperature during dilatometry cycles for films deposited at $T_{\mathrm{d}\mathrm{e}\mathrm{p}}=264\pm 3\hspace{0.17em}\mathrm{K}$. Dashed black lines are linear fits to the SCL and LQ glass regions of the 206-nm film to determine $T_g\left(\mathrm{b}\mathrm{u}\mathrm{l}\mathrm{k}\right)=330\pm 2\hspace{0.17em}\mathrm{K}$. The long black arrow shows the determination of relative density ($\mathrm{\Delta }\rho$) for the 25-nm film with respect to its LQ glass state. Short arrows show the direction of the thermal cycle. (B) $\mathrm{\Delta }\rho$ (evaluated at 298 K) vs. film thickness. The horizontal dashed line shows $\mathrm{\Delta }\rho$ of the extrapolated ordinary SCL at 264 K ($\mathrm{\Delta }{\rho }_{\mathrm{S}\mathrm{C}\mathrm{L}}=3.3\pm 0.2\%$). (Inset) The molecular structure of TPD. Some error bars in B are smaller than the symbol size.

To further investigate the effect of deposition temperature and film thickness on the relative density change ($\mathrm{\Delta }\rho$) and index of refraction ($n$), TPD films were vapor deposited on substrates with a temperature gradient ($T$-grad) along their long axis (details are in Materials and Methods as well as in SI Appendix). This high-throughput method allows simultaneous depositions at a broad range of $T_{\mathrm{d}\mathrm{e}\mathrm{p}}$ values (33, 41). Fig. 3 shows $\mathrm{\Delta }\rho$ and $n$ vs. $T_{\mathrm{d}\mathrm{e}\mathrm{p}}$ for $T$-grad films of various thicknesses. In Fig. 3B, for films where a birefringent model was used to fit the ellipsometry data (h $>$ 50 nm), the average index of refraction is shown. The corresponding birefringence data for these films are shown in SI Appendix, Fig. S20 (details of measurements and calculations are in SI Appendix, SI Text). Fig. 3A shows that in thick films ($h>60\hspace{0.17em}\mathrm{n}\mathrm{m}$), $\mathrm{\Delta }\rho$ is limited by the extrapolated density of the SCL [$\mathrm{\Delta }\rho \hspace{0.17em}\left(\mathrm{S}\mathrm{C}\mathrm{L}\right)$; dashed line] and does not exceed this value. Close to the nominal $T_g$ (bulk), the density of the as-deposited films can reach this limiting value, while at lower $T_{\mathrm{d}\mathrm{e}\mathrm{p}}$, the system is kinetically trapped with $\mathrm{\Delta }\rho <\mathrm{\Delta }\rho \hspace{0.17em}\left(\mathrm{S}\mathrm{C}\mathrm{L}\right)$. This observation is similar to the previous reports in stable glasses of TPD and other molecules (7, 16, 33, 39).

Fig. 3.

(A) Relative density change, $\mathrm{\Delta }\rho$, vs. deposition temperature, $T_{\mathrm{d}\mathrm{e}\mathrm{p}}$, for $T$-grad films with various thicknesses. The dashed line shows the extrapolated density of bulk SCL. (B) Index of refraction ($n$) of as-deposited films vs. $T_{\mathrm{d}\mathrm{e}\mathrm{p}}$, measured at the wavelength $\lambda =632.8\hspace{0.17em}\mathrm{n}\mathrm{m}$. For the 72-nm and 206-nm films, which are birefringent, the average value of $n$ is plotted.

In thin films ($h<60\hspace{0.17em}\mathrm{n}\mathrm{m}$), remarkably high values of density are observed (Fig. 3A) and $\mathrm{\Delta }\rho$ well exceeds the extrapolated SCL density. For example, at $T_{\mathrm{d}\mathrm{e}\mathrm{p}}=264\hspace{0.17em}\mathrm{K}$, $\mathrm{\Delta }\rho \hspace{0.17em}\left(\mathrm{S}\mathrm{C}\mathrm{L}\right)=3.3\pm 0.2\%$, while for 45-nm vapor-deposited film, $\mathrm{\Delta }\rho =6.3\%$. These trends continue as $T_{\mathrm{d}\mathrm{e}\mathrm{p}}$ is further decreased, with a maximum $\mathrm{\Delta }\rho$ of 8.4% achieved in 37-nm and 45-nm films deposited at $T_{\mathrm{d}\mathrm{e}\mathrm{p}}\sim 230\hspace{0.17em}\mathrm{K}$. High-density states are also seen in 30-nm and 25-nm films but to a smaller extent. The index of refraction ($n$) of as-deposited films also increases dramatically as the film thickness is decreased (Fig. 3B), providing additional independent evidence for the dramatic density increase in vapor-deposited thin films. Using $n$, the estimated densities of the 30-nm and 25-nm films appear to exceed those of 45-nm and 55-nm films for $240\hspace{0.17em}\mathrm{K}<T_{\mathrm{d}\mathrm{e}\mathrm{p}}<300\hspace{0.17em}\mathrm{K}$. This difference in the observed trends can be explained by the fact that $\mathrm{\Delta }\rho$ is calculated relative to the transformed LQ state, while $n$ is directly measured in as-deposited films. We observe that the indices of refraction of the SCL and LQ glass states are also increased in thin films compared with their bulk values (SI Appendix, Fig. S22), resulting in smaller relative $\mathrm{\Delta }\rho$ when values are compared. If relative $\mathrm{\Delta }n$ values were used instead of $n$, trends would be very similar to those observed with $\mathrm{\Delta }\rho$, as $\mathrm{\Delta }n$ is strongly correlated with $\mathrm{\Delta }\rho$ (SI Appendix, Fig. S21; more details in SI Appendix, SI Text).

The observation that the index of refraction of the supercooled liquid is increased in thin films (SI Appendix, Fig. S22) indicates that the density of the supercooled liquid state is also higher in thin films than that of the bulk. A similar effect was previously observed in polymer thin films (42, 43), but its origins are not well understood and should be further investigated. However, we note that the error in evaluating $n$ also increases with decreasing film thickness. As such, we opt to frame the discussions in this manuscript around $\mathrm{\Delta }\rho$ obtained based on film thickness, providing a more conservative estimation of the magnitude of the observed phenomenon.

Another factor that affects the calculated $\mathrm{\Delta }\rho$ is the fact that the glass transition temperature of thin TPD films is lower than $T_g$ (bulk) (19). As such, each sample is compared with a slightly different reference state. To eliminate this effect, we present the data using the estimated specific volume ($V_{\mathrm{s}\mathrm{p}}$) of each film at the deposition temperature, $T_{\mathrm{d}\mathrm{e}\mathrm{p}}$ (Fig. 4).

Fig. 4.

(A) Normalized specific volume ($V_{\mathrm{s}\mathrm{p}}$) vs. $T_{\mathrm{d}\mathrm{e}\mathrm{p}}$ for $T$-grad films of various thicknesses. The cooling curve of a 200-nm LQ glass is shown as reference (10 K/min cooling, extrapolated by the gray dotted line). The black dashed line is the extrapolated SCL line for this film. The thick red dashed line shows the apparent marginal specific volume for thin films, assigned as the HD-SCL state. $T_{LL}$ (small black arrow) indicates the location of the phase transition between SCL and HD-SCL states. The purple dashed–dotted line shows the estimated $V_{\mathrm{s}\mathrm{p}}$ of the monoclinic TPD crystal vs. temperature based on the crystal density measured at 298 K (star symbol) (44) and 90 K (45) (point not shown). (B) Normalized $V_{\mathrm{s}\mathrm{p}}$ vs. $T_{\mathrm{d}\mathrm{e}\mathrm{p}}$ for 45- and 55-nm $T$-grad films for an extended $T_{\mathrm{d}\mathrm{e}\mathrm{p}}$ range. In both graphs, $T_g$ (bulk) for LQ TPD is indicated for reference.

Discussion

Polyamorphism in Thin Films.

Fig. 4A shows a plot of normalized specific volume ($V_{\mathrm{s}\mathrm{p}}$) vs. $T_{\mathrm{d}\mathrm{e}\mathrm{p}}$ for films of various thicknesses (detailed calculations are in SI Appendix). The $V_{\mathrm{s}\mathrm{p}}$ values for all samples were normalized to their corresponding SCL state at 348 K. As seen in Fig. 4A, in thick films ($h>60\hspace{0.17em}\mathrm{n}\mathrm{m}$) deposited at $T_{\mathrm{d}\mathrm{e}\mathrm{p}}>310\hspace{0.17em}\mathrm{K}$, the as-deposited glass reaches the same specific volume as the corresponding SCL state, implying that these films have enough surface mobility during vapor deposition to reach the metastable equilibrium state and do not further evolve. At $T_{\mathrm{d}\mathrm{e}\mathrm{p}}<300\hspace{0.17em}\mathrm{K}$, thick films do not have enough mobility, and their $V_{\mathrm{s}\mathrm{p}}$ increases toward that of the LQ glass state. These data are consistent with previous studies that identify the SCL state as the limiting state achieved during PVD (33, 37, 39).

The temperature dependence of $V_{\mathrm{s}\mathrm{p}}$ is remarkably different in films with $h<60\hspace{0.17em}\mathrm{n}\mathrm{m}$. In these films, the limiting value of $V_{\mathrm{s}\mathrm{p}}$ appears along a line with a higher slope than that of the extrapolated bulk SCL line. This apparent HD-SCL was previously unidentified in TPD. The trends of $V_{\mathrm{s}\mathrm{p}}$ vs. $T_{\mathrm{d}\mathrm{e}\mathrm{p}}$ with respect to this limiting HD-SCL state are qualitatively similar to what is observed in thick films with respect to the ordinary SCL state; as $T_{\mathrm{d}\mathrm{e}\mathrm{p}}$ is decreased, $V_{\mathrm{s}\mathrm{p}}$ reaches a minimum at some low deposition temperature, where the system is no longer able to kinetically reach this metastable HD-SCL state, and deposition below this point produces glasses with higher specific volume and lower density than the extrapolated HD-SCL line.

The liquid–liquid phase transition between the two polyamorphic SCL and HD-SCL states is observed at $T_{LL}\simeq 295\pm 5\hspace{0.17em}\mathrm{K}$ [$\sim 35^{○}$K below the nominal $T_g$ (bulk) of the SCL] and is relatively abrupt. As shown in Fig. 4B, when $T_{\mathrm{d}\mathrm{e}\mathrm{p}}$ is well above $T_{LL}$ (i.e., $T_{\mathrm{d}\mathrm{e}\mathrm{p}}>320\hspace{0.17em}\mathrm{K}$), $V_{\mathrm{s}\mathrm{p}}$ reaches the $V_{\mathrm{s}\mathrm{p}}$ of the ordinary SCL and does not further evolve, indicating that the ordinary SCL is the energetically favored state in this deposition range. As $T_{\mathrm{d}\mathrm{e}\mathrm{p}}$ is decreased, after a transition region with nonmonotonic density change ($295\hspace{0.17em}\mathrm{K}<T_{\mathrm{d}\mathrm{e}\mathrm{p}}<320\hspace{0.17em}\mathrm{K}$), the $V_{\mathrm{s}\mathrm{p}}$ of vapor-deposited thin films follows the HD-SCL line. For $270\hspace{0.17em}\mathrm{K}<T_{\mathrm{d}\mathrm{e}\mathrm{p}}<T_{LL}$, these films appear to reach their corresponding equilibrium state, which is the HD-SCL state. The specific volume reaches a minimum value around $T_{\mathrm{d}\mathrm{e}\mathrm{p}}\sim 230\hspace{0.17em}\mathrm{K}\hspace{0.17em}\left(0.78\hspace{0.17em}{T}_{LL}\right)$ in 37-nm to 45-nm films, below which the samples appear to be kinetically trapped, relative to the extrapolated HD-SCL.

As shown in Fig. 1, despite their exceptionally high density, thin films produced in the HD-SCL state are amorphous and do not show any sign of crystallization. Without the existence of a liquid–liquid phase transition, it is impossible to produce amorphous states with densities larger than SCL. The evidence for a phase transition is strengthened when we focus on the films deposited in the region close to $T_{LL}$ (Fig. 4B). We observe a transition region in the deposition range of $T_{LL}<T_{\mathrm{d}\mathrm{e}\mathrm{p}}<320\hspace{0.17em}\mathrm{K}$, where the specific volume in thin films changes nonmonotonically. The specific volume follows the $V_{\mathrm{s}\mathrm{p}}$ of the ordinary SCL above this deposition range and the $V_{\mathrm{s}\mathrm{p}}$ of the HD-SCL below this range. The nonmonotonic change in $V_{\mathrm{s}\mathrm{p}}$ can be a sign of phase transition, where in this region, a coexisting mixture of the two phases is deposited, resulting in this nontrivial behavior. In this region, we also observe high surface roughness in as-deposited thin films (atomic force microscopy images are shown in SI Appendix, Figs. S7–S9). The increased roughness may be interpreted as a sign of enhanced surface mobility and mobility gradients in vapor-deposited films, similar to what has been previously observed in liquid quenched TPD films (19). However, enhanced mobility is expected to make more stable glasses with lower $V_{\mathrm{s}\mathrm{p}}$ values, which is not the case here. Alternatively, the roughness can be an indirect sign of proximity to a phase transition, which can cause large volume fluctuations and thus, larger surface roughness. Regardless, above and below this transition region the specific volume clearly follows two distinct slopes, which intersect at $T_{LL}$, providing strong evidence for polyamorphism in thin films. It is therefore also possible that the actual phase transition point is in the region with maximum density ($\sim$310 K, the middle of the coexistence region). More detailed experiments in this transition region, as well as direct calorimetry experiments, should be employed in the future to provide further insight into details of this liquid–liquid transition.

Without polyamorphism, the values of enthalpy and specific volume cannot decrease below their corresponding SCL values either through physical aging or through vapor deposition (7, 34, 39). Beasley et al. (16) recently showed that in $\sim 400-\mathrm{n}\mathrm{m}$ films of ethylbenzene, the density of vapor-deposited glasses follows the extrapolated SCL density down to 2 K above the Kauzmann temperature. As such, it has been hypothesized that any resolution of the Kauzmann crisis will occur at $T_{\mathrm{K}}$ for bulk systems. Our data shown in Fig. 4A paints a remarkably different picture in thin films, where geometrical constraints appear to produce a modified energy landscape where an amorphous packing with exceptionally high density can be equilibrated during vapor deposition. In thin films, molecules are packed in significantly closer proximity than both known crystal forms of TPD, the monoclinic and the orthorhombic crystals (44, 45) (values are listed in SI Appendix). In thick films, the crystal state is the equilibrium phase that minimizes the free energy. In thin films deposited below $T_{LL}$, the HD-SCL is expected to have a lower free energy than the SCL state. While this phase has a higher density than the bulk crystal, it is not immediately clear whether a corresponding crystal state also exists in thin films with higher density than the bulk crystal. However, we have not observed any evidence of crystallization in our experiments, which indicates that the HD-SCL may indeed be the equilibrium phase that minimizes the free energy as opposed to a metastable phase. Regardless, the observation of the phase transition is strong evidence that the thin-film geometry can equilibrate amorphous structures that are not otherwise thermodynamically favored in bulk films.

It is important to note that our data do not necessarily offer a resolution for the Kauzmann crisis. Given the large slope of the HD-SCL compared with the ordinary SCL, the apparent Kauzmann temperature is even higher for the HD-SCL state and is estimated to be at $T_{\mathrm{K}}\left(\mathrm{H}\mathrm{D}-\mathrm{S}\mathrm{C}\mathrm{L}\right)\simeq 265\hspace{0.17em}\mathrm{K}$ as opposed to $T_{\mathrm{K}}\left(\mathrm{S}\mathrm{C}\mathrm{L}\right)\simeq 190\hspace{0.17em}\mathrm{K}$ for bulk films. SI Appendix, Fig. S18 shows the corresponding fictive temperatures of vapor-deposited films with respect to each state. Furthermore, in the temperature range of $220\hspace{0.17em}\mathrm{K}<T_{\mathrm{d}\mathrm{e}\mathrm{p}}<250\hspace{0.17em}\mathrm{K}$, the density actually exceeds that of the crystal. However, density is not the correct metric for the Kauzmann crisis, and one needs to evaluate the corresponding entropy of each state with respect to the crystal entropy. While in the ordinary SCL, the density typically follows the trends in entropy, there is no thermodynamical reason why this should also be the case for HD-SCL. To our knowledge, these are some of the highest-density states ever seen in molecular glasses in ambient pressures. As such, understanding the details of this packing, its corresponding structural entropy, and how the thin-film geometry enables its equilibration merits further studies.

The Role of Surface Mobility in Accessing HD-SCL.

A major contrast between the polyamorphism observed here and those previously seen in bulk stable glasses is that the $T_{LL}$ in TPD thin films is well below its nominal $T_g\left(\mathrm{b}\mathrm{u}\mathrm{l}\mathrm{k}\right)$. In bulk TPD, the estimated relaxation time at 295 K (where $T_{LL}$ is measured here) is $\sim 10^{22}\hspace{0.17em}\text{s}$. ($\sim 10^{14}\hspace{0.17em}\mathrm{y}$) (12). As such, even if the HD-SCL could exist in the bulk, it would not be an accessible state through physical aging. Even during vapor deposition, at $T_{\mathrm{d}\mathrm{e}\mathrm{p}}=295\hspace{0.17em}\mathrm{K}$ thick films are in kinetically trapped states, making the HD-SCL also inaccessible through physical vapor deposition.

During PVD, stable glasses are formed because of the enhanced mobility at the free surface (3, 11, 36, 46) and layers directly underneath (13, 17). Surface mobility gradients allow molecules in the surface region to adopt more efficient packing structures, before falling out of equilibrium at locations deeper into the film. The ability to access the otherwise inaccessible HD-SCL by thin films provides a strong evidence that the dynamics near the surface region of thin films are significantly enhanced compared with those of thick films. This relatively enhanced mobility would allow thin films to equilibrate into the HD-SCL state at low deposition temperatures. There is indirect evidence for this hypothesis in measurements of liquid-quenched TPD films. Measurements of mobility in thin liquid-quenched TPD films (19) as well as measurements of the breadth of the $T_g$ transition in these films (20) show that they have faster mobility at the free surface and enhanced mobility across their entire thickness. When comparing $\mathrm{\Delta }\rho$ in vapor-deposited films with the breadth of the $T_g$ transition in LQ counterparts (SI Appendix, Fig. S25), it appears that the highest-density films produced during PVD are in the thickness range where LQ films still have some portions with slow, bulk-like mobility (presumably in regions close to the substrate), producing broad mobility gradients in these films. In thinner films ($h<35\hspace{0.17em}\mathrm{n}\mathrm{m}$), mobility of LQ films is enhanced throughout their thickness, and PVD films show a smaller extent of density increase (more details are in SI Appendix). We interpret these observations to mean that in order to produce a stable glass, sufficient enhanced mobility needs to be coupled with the ability to fall out of equilibrium deep inside the film. The details of this correlation and the specific pathways toward different regions in the energy landscape merit further future studies.

Another strong indication for the role of enhanced mobility gradients in accessing the HD-SCL state is the observation that thin PVD films are more isotropic than thick films, based on both the limited GIWAXS data for films deposited at $T_{\mathrm{d}\mathrm{e}\mathrm{p}}=264\hspace{0.17em}\mathrm{K}$ (Fig. 1) and the birefringence values when the ellipsometry data in thin films are fit to a birefringent model (SI Appendix, Fig. S16). It has been previously demonstrated that slower deposition rates can produce more isotropic stable glasses (47) because the molecules have a chance to equilibrate at layers well below the free surface. As such, the templated orientation at the free surface region can be erased. Recent computer simulations have also provided evidence for reorientation below the free surface during vapor (13) deposition. In TPD thin films, the longer range of mobility gradients compared with the bulk films can have a similar effect in reducing their orientational anisotropy, analogous to a change in the deposition rate.

While it is not clear whether the HD-SCL state is ubiquitous in vapor-deposited thin films, enhanced surface and thin-film mobility has been broadly observed in organic and polymeric thin films (5, 48–51). As such, it is likely that the strong variations in mobility gradients due to the free surface and its interplay with substrate interactions would significantly affect stable glass formation in films with intermediate thicknesses. For example, one can hypothesize that using a substrate with more favorable interactions, which affects the mobility gradients (20), would also produce highly stable glasses or HD-SCL states in even thinner films. This can provide an exciting opportunity to produce ultrathin stable glass films with varying degrees of orientational order and stability, through an interplay between the surface and substrate dynamics. While liquid quenched thin films can rapidly dewet or crystallize (19, 51), hindering their applications, vapor-deposited films with similar thicknesses can be produced with lower roughness and better thermal stability, with exceptionally high density.

The Importance of Thin-Film Geometry in the Stabilization of HD-SCL.

A unique and unexpected feature of the data presented in this study is the rapid transformation of thin films from the HD-SCL state to a much lower-density state upon continued deposition. For example, as seen in Fig. 3A, at $T_{\mathrm{d}\mathrm{e}\mathrm{p}}=230\hspace{0.17em}\mathrm{K}$, 37-nm and 45-nm films have nearly the same density ($\mathrm{\Delta }\rho =8.4\%$). However, upon the deposition of another 10 nm, the 55-nm film has an average density of $\mathrm{\Delta }\rho =4.5\%$. Increasing the film thickness further to 206 nm results in a film that is marginally stable, with a density even lower than that of the ordinary SCL. If the bottom 45 nm of the film remained at the same initial HD-SCL density while the deposition continued, one would expect the 206-nm film to have at least a density of $\mathrm{\Delta }\rho =1.8\%$, which is not the case. This means that as the deposition is continued, the entire film actually dilates and transforms into a different corresponding state, presumably to that of the ordinary SCL. Future in situ measurements and computer simulations are needed to elucidate the details of this phenomenon.

It is difficult to rationalize this phenomenon without assuming that thin films have distinctly different equilibrium states than thick films. This observation provides strong evidence that the geometry and boundary conditions in thin films produce a unique energy landscape, which allows an otherwise thermodynamically disfavored phase (HD-SCL) to become the equilibrium phase in thin films. This is analogous to a tilting of the energy landscape due to an external driving force. After the thickness exceeds the point where the free energy of this state is higher than that of the ordinary SCL, the system returns to the ordinary SCL state, resulting in the rapid observed transformation. This hypothesis can explain the nontrivial behavior of the 55-nm film with respect to $T_{\mathrm{d}\mathrm{e}\mathrm{p}}$, which appears to fall somewhere between the SCL and HD-SCL lines depending on the deposition temperature (Fig. 4A). This hypothesis would also imply that the 55-nm film still has enough enhanced mobility, even at $T_{\mathrm{d}\mathrm{e}\mathrm{p}}=230\hspace{0.17em}\mathrm{K}$, to entirely transform from HD-SCL to SCL upon PVD. Interestingly, by the time a 200-nm film is deposited, the film mobility even at its free surface is so low that it cannot even form a typical stable glass. This collective behavior suggests that surface mobility and mobility gradients strongly depend on both the film thickness and temperature, which is also supported by limited existing data in liquid-quenched thin films (19, 20, 50).

However, it is still surprising that the 55-nm film continues to evolve into a less-dense state to produce a marginally stable state when the thickness reaches 200 nm. Based on measurements of mobility in LQ TPD films (19, 20), we do not expect these films to have equilibrium relaxation times that are fast enough to evolve into the ordinary SCL state. Indeed, if that was the case, we would expect the system to stop evolving after ordinary SCL state was achieved, which is significantly higher density than the density observed in 200-nm PVD films at low deposition temperatures. The only possible justification is that after the energy landscape is tilted to make the ordinary SCL the equilibrium state for the thick films, a driving force is generated for the system to rapidly dilate. This phenomenon appears analogous to volume recovery of pressurized glasses (52) after the pressure is removed or memory effects in physical aging after a temperature up-jump event (53, 54), both of which result in volume evolution that is faster than the nominal relaxation times of the system. Here, the change in the energy landscape from the thin-film geometry to the bulk state appears to trigger a similar effect, resulting in an apparent dilation that is faster than the equilibrium relaxation times of the system. However, this connection is not immediately trivial or clear. In situ experiments to measure volume recovery upon rapid vapor deposition or flash differential scanning calorimetry (DSC) experiments to measure whether strong changes in activation entropy occur due to the changing boundary conditions can be employed to further study this rather surprising phenomenon (54).

The origins of widely changing dynamical gradients and their corresponding thickness effects in liquid-quenched thin films remain poorly understood (20). The data here indicates that depending on the method of preparation (quenching the liquid vs. PVD), either liquid-like (dewetting, low-$T_g$) or stable and dense states (corresponding to HD-SCL) can be achieved that belong to distinctly different regions in the energy landscape. However, regardless of their nature, most of these effects, including the observation of higher-density values in LQ and ordinary SCL films (SI Appendix, Fig. S22), rapidly disappear when the film thickness is increased above 60 nm. As such, thin films can be strong candidates to experimentally explore various theories of glass transition and their validity in deeply supercooled states as well as at small length scales. The existence of similar effects in other glassy systems should be explored to evaluate the generality of this phenomenon.

Conclusions

We have demonstrated that vapor-deposited thin films of molecular glass TPD produce amorphous states with densities much higher than the ordinary SCL state. Screening across a wide range of deposition temperatures, we identify a previously unidentified high-density supercooled liquid (HD-SCL) state with a liquid–liquid phase transition temperature $T_{LL}\approx T_g\left(\mathrm{b}\mathrm{u}\mathrm{l}\mathrm{k}\right)-35\hspace{0.17em}\mathrm{K}$. The densest glasses have densities that are comparable with or higher than the TPD crystal density. The HD-SCL state is produced at a thickness range where large mobility gradients are also observed in LQ TPD films ($37\hspace{0.17em}\mathrm{n}\mathrm{m}<h<45\hspace{0.17em}\mathrm{n}\mathrm{m}$), providing a strong correlation between enhanced mobility gradients and ability to kinetically access the polyamorphic HD-SCL state. Upon further deposition, films with thicknesses of 50 nm and higher rapidly dilate and lose their high-density conformations, demonstrating that the HD-SCL state is only thermodynamically favored in the thin-film geometry, enabled by its unique energy landscape.

Materials and Methods

TPD (the structure is shown in SI Appendix, Fig. S1) was used as purchased (MilliporeSigma). The bulk glass transition temperature was determined by DSC (TA Instruments; Q2000) to be $T_g\left(\mathrm{b}\mathrm{u}\mathrm{l}\mathrm{k}\right)=330\pm 2\hspace{0.17em}\mathrm{K}$ (SI Appendix, Fig. S2). TPD powder was premelted in a vacuum oven (Fisherbrand Isotemp Model 281A) before use. TPD was thermally evaporated on silicon substrates (Virginia Semiconductor), bridged between two independently temperature-controlled (Omega controllers) stages in a custom ultrahigh-vacuum chamber (base pressure $\sim 2\hspace{0.17em}\times 10^{-7}\hspace{0.17em}\mathrm{T}\mathrm{o}\mathrm{r}\mathrm{r}$) (17, 55). A temperature gradient ($T$-grad) was established across the two stages for high-throughput sample preparation. More details of sample preparation and temperature control can be found in SI Appendix, SI Text and Figs. S3–S5. The variation of film thickness along the $T$-grad samples was below 3% of the average film thickness (SI Appendix, Fig. S6). All depositions were performed at a deposition rate of $r_{\mathrm{d}\mathrm{e}\mathrm{p}}=0.030\pm 0.005\hspace{0.17em}\mathrm{n}\mathrm{m}/\mathrm{s}$. AFM (Agilent 5420) was used to characterize surface morphology. Except for the data shown in Fig. 4B, the data reported here were limited to samples with as-deposited rms roughness less than 2 nm to reduce uncertainties of thickness measurements (details are in SI Appendix, SI Text and Figs. S7 and S8). AFM was also performed on samples after dilatometry to rule out dewetting or crystallization (SI Appendix, Fig. S9). GIWAXS measurements were conducted at the National Synchrotron Light Source II, Brookhaven National Laboratory, with a beam energy of 18.2 keV (details are in SI Appendix). Variable-angle spectroscopic ellipsometry (J. A. Woollam M-2000) was performed to determine the thickness $h$, indices of refraction $n_{xy}$ and $n_z$, and optical birefringence $\delta n=n_z-n_{xy}$ of as-deposited films (details are in SI Appendix, Figs. S14–S16). Dilatometry experiments were performed by heating as-deposited films at 10 K/min either to 348 K and holding for 20 min for thin films or to 353 K and holding for 30 min for thick films to complete the transformation. The films were subsequently cooled at 10 K/min to 298 K to form liquid-quenched glasses. The film thickness and indices of refraction were measured in situ during dilatometry, at a frequency of 2.5 s with zone averaging, at an angle of incidence of 70° (Fig. 2A and SI Appendix, Fig. S19). Using these data, the fictive temperature ($T_f$), thick and thin film $T_g$, and the onset of transformation ($T_{\mathrm{onset}}$) values were determined (SI Appendix, Figs. S17 and S18). $\mathrm{\Delta }\rho$ was evaluated based on the initial and final thickness of the films, measured at 298 K, at an array of locations across the $T$-grad sample using variable-angle spectroscopic ellipsometry, from where their specific volumes ($V_{\mathrm{s}\mathrm{p}}$) were deduced (more details are in SI Appendix).

Data Availability

All study data are included in the article and/or SI Appendix.