Effect of substrate interactions on the glass transition and length-scale of correlated dynamics in ultra-thin molecular glass films

Thin glassy films have drawn great research interest due to their striking property differences compared to their bulk counterparts,^1–18 which can negatively affect their application. As the thickness is reduced, the interfacial dynamics, in particular, at the free surface, become dominant factors in controlling the overall properties of ultra-thin glass films. In a recent study,⁹ we demonstrated that for ultra-thin molecular glass films of N, N′-Bis(3-methylphenyl)-N, N′-diphenylbenzidine (TPD) supported on weakly interacting silicon substrates, the glass transition temperature is substantially decreased when the film thickness is decreased below ∼60 nm. We also used isothermal dewetting (as a measure of viscosity) and cooling-rate (CR)-dependent T_g measurements to evaluate the film-averaged activation barrier for relaxation around the bulk T_g for films of various thicknesses. The results showed a rapid turnover from bulk-like glassy dynamics to liquid-like dynamics with a mid-point at the thickness of ∼30 nm. We demonstrated that this rapid turnover cannot be simply described by a typically used two-layer model^1,2,19,20 and is an indication of correlated dynamics over a long-range (h ∼ 30 nm) resulting in a saturation in the range of relaxation times across the film at sufficiently low film thicknesses (h < 20 nm). Similar effects were also observed in pure polystyrene (PS) thin films and PS/poly (phenylene oxide) (PPO) miscible blend thin films, with the turnover in the bulk dynamics happening at a similar length-scale.^8,21 These observations are also consistent with earlier studies on bilayer films that showed that T_g changes can couple across two layers with different T_g values.^5,22–25 In particular, Ellison and Torkelson showed that changes in T_g of the near-surface film is influenced by the thickness of the layer below of the same type of polymer, with the strongest effect observed at a thickness of ∼25 nm,⁵ indicating coupling of the dynamics of the two films over this length scale.

The origin of this effect is not well-understood and cannot be well described by current theoretical models, but it can be relevant for answering fundamental questions in glass physics, and as such it is important to decipher the origins of this effect. Given the challenges associated with modifying the free surface interactions, one strategy to explore correlated dynamics is to modify the interfacial interactions and study their effects on the properties of thin films.^{10,22,23,26–30} In supported films, there are two interfaces that can simultaneously play a role in the overall film dynamics, the free surface, and the film/substrate interface. The characteristics of the substrate interface such as the surface energy,^31–35 roughness,²⁹ and rigidity^22,29 can all affect the local near-substrate dynamics and by extension the overall film dynamics, making it an interface with more possible variations compared to the air/film interface. It has been previously shown that depending on the nature of the film-substrate interactions, the substrate interface can either suppress or enhance the overall thin film dynamics in polymeric films.^32,36 In a recent study, Glor et al. demonstrated that for strong substrate interactions, the dynamics of the polymer film close to the two interfaces can decouple and present two distinct glass transitions at film thicknesses below ∼20 nm,¹⁰ indicating the long-range influence of the interfacial effects on the film dynamics. However, in polymeric systems, it is often challenging to separate chain effects from effects due to glassy dynamics and it is unclear which effect dominates here.

In this study, we investigate the effect of the substrate interactions on the T_g, the gradients of the dynamics, and their length scale in ultra-thin films of molecular glass-former, TPD. To modify the substrate interactions, a thin layer of strongly adsorbed polystyrene (PS) layer (dead-layer)^37–42 was used as the substrate. It is found that the PS dead-layer substrate significantly improves the wettability of TPD films compared to the silicon substrates, thus preventing dewetting even for ultra-thin TPD films. T_g reductions are still observed on this substrate when the film thickness is reduced below ∼60 nm, but to a lesser extent than what is observed on the silicon substrates. The measurements of the high- and low-onsets of the glass transition on both substrates show that while the extent of the overall enhancement is the dynamics is smaller in the films supported on the PS dead-layer substrate compared to the silicon substrate, the length scale of the effects remain the same within our experimental accuracy. Cooling-rate dependent T_g (CR-T_g)^8,9,21,43 measurements show a turnover in the value of the apparent activation energies for relaxation from the bulk value towards a lower value at the same length scale of ∼30 nm compared to films supported on silicon. However, the activation energies measured for the thinnest films remain higher for the PS dead-layer substrate compared to the silicon substrate.

To understand these results, coarse-grained molecular dynamics (MD) simulations were performed on model un-entangled polymer chains with either weak or neutral substrate interactions. It is found that the dynamics near the substrate for both types of substrates enhance as the film thickness is reduced below a certain thickness due to the effect of surface dynamics, which itself remains enhanced at all film thicknesses, consistent with previous studies.^28,29,44,45 While these simulations are performed at significantly shorter relaxation times than the experiments, the results are qualitatively similar to the experimental measurements where it is observed that as the film thickness is reduced below a certain value, the dynamics at the substrate interface enhance due to the influence of the free surface, resulting in narrowing of the range of the gradients in the dynamics due to the correlation between the surface and substrate dynamics.

The results suggest that by increasing the substrate-film interface attraction, the extent of T_g reduction can be modified due to the competition between the substrate/film interface and the air/film interface. However, the length-scale over which the fast and slow dynamics correlate appears to remain unchanged, signifying the universal feature of this observation.

Following the procedure detailed by Burroughs et al.³⁸ to produce an irreversibly adsorbed layer, PS films were spin-coated onto silicon substrates from a 3 wt. % PS solution in toluene. The as-spun polystyrene films were annealed under vacuum at the temperature of 423 K for 24 h to promote the growth of the irreversibly adsorbed layer (PS dead-layer) near the substrate interface. The annealed PS films were then soaked in a good solvent (toluene) for 30 min to dissolve the loosely adsorbed polystyrene chains and then rinsed several times with fresh toluene. The PS dead-layers were then thoroughly dried by annealing at room temperature in the vacuum oven for 12 h. The thicknesses of the PS layers were measured to be in the range of 4 nm–7 nm. More details of the preparation and measurement of this layer can be found in Figs. S1 and S2 of the supplementary material. For each sample, the PS dead-layer thickness was measured before the spin-coating of the TPD layer and was held constant during the measurements to prevent overfitting as detailed in supplementary material.

Contact angle measurements show that the addition of the PS dead-layer changes the contact angle of water on the substrate from 25.5 ± 0.5° for silicon substrates to 82.5 ± 0.8° for PS substrates. The contact angle of water on the TPD film was measured to be 88.1 ± 2.3°, indicating near-neutral interactions between TPD and the PS substrate. The contact angle of TPD on silicon was also directly measured after fully dewetting a 60 nm film of TPD on silicon for 6 days at 360 K and was determined to be 70 ± 1° (Fig. S3 of the supplementary material). However, similar measurements were not possible of TPD on the PS dead-layer. This is because at these low temperatures, TPD does not tend to dewet PS and at high temperatures the two compounds mix instead of dewetting of one component on the other (Fig. S4). These measurements further confirm that the interactions of TPD and PS are near-neutral as the two compounds are fully miscible.

It is important to note that due to this strong miscibility, it is possible that some TPD molecules diffuse into the PS film during the spin-coating process. However, due to its strong absorption to the substrate, PS is unlikely to migrate away from the substrate, particularly at the temperature range of our measurements where the PS layer is always kept below its T_g. The TPD molecules are also small and are expected to preferentially migrate to the free surface even if the interactions are completely neutral.^46,47 Furthermore, if mixing was dominant in ultra-thin films, one would expect the T_g of thin films to increase towards the PS T_g and thus be higher than the bulk T_g of TPD. We do not observe such increases in T_g. As shown in Fig. S4, we only observe any evidence of mixing of PS and TPD after prolonged annealing at the PS T_g and only in films thin enough (h < 2 nm) that they can dewet. To avoid any potential effect of miscibility, all measurements of TPD T_g values were performed below the T_g of the PS dead-layer (Fig. S1) where the PS dead-layer behaves as a rigid substrate with very long relaxation times, preventing either mixing or TPD diffusion into the PS substrate. The thickness of the films reported in our study was also limited to 9 nm. More details of the substrate modification and sample preparations can be found in the supplementary material. Spectroscopic ellipsometry (M-2000 V J. A. Wollam) equipped with a heating stage was used for T_g and CR-T_g measurements as detailed in Figs. S5–S7 of the supplementary material and in our previous publications.^8–10,43

The molecular dynamics simulations were performed using a slightly modified version of the standard Kremer-Grest bead-spring polymer model with N = 20 monomers per chain, which is below the entanglement chain length for this model. The system was equilibrated at the reduced temperature T^* = 0.45, just above the simulated $Tg*=0.44$⁠. The relaxation time was measured by calculating the intermediate scattering function, $Fs(q,τ)=cosq⋅[ri(t)−ri(t+τ)]$⁠, where the average is taken over orientations of the wave vector q in the xy plane, particles i, and time origins t. The value of τ_α was taken as the time where F_s(q, t = τ_α) = 0.2, and the magnitude of the wave vectors employed was constant at |q| = 7.14. To measure local relaxation times, τ_α(z), monomers were sorted by their z position, and τ_α was calculated for distinct groups of 500 monomers; the z-position assigned to this τ_α is the average z position of group of 500 monomers. More details can be found in the supplementary material.

In our previous studies,⁹ we observed spontaneous dewetting of ultrathin TPD films on silicon substrates, indicating weak film/substrate interactions. When supported on PS dead-layer, TPD ultrathin films show increased morphological stability and are less prone to dewetting, as shown in Fig. S2 of the supplementary material and discussed above. We attribute this observation to the near-neutral interactions between TPD and the PS dead-layer, due to the similar surface energies between TPD and PS as measured by contact angle measurements as well as the observation of the miscibility of PS and TPD, as detailed in Figs. S3 and S4 of the supplementary material.

T_g of ultrathin TPD films of various thicknesses on the two types of substrates were measured upon cooling from the super-cooled liquid state to the glassy state (348 K to 303 K at a rate of 10 K/min). The thickness change during the cooling of each film was monitored by in situ ellipsometry (details in the supplementary material). Figure 1 shows typical normalized thickness vs. temperature curves during cooling for thick (115 nm) and ultrathin (18 nm) films supported on silicon (solid symbols) and PS (open symbols), respectively. The excellent overlap of the super-cooled liquid region for all film thicknesses, supported on both substrates, indicates that in this region the properties of the films are similar to the extent that can be resolved by ellipsometry. The thickness curves for the 115 nm thick films on the two types of substrates overlap with each other, indicating that the change of the substrate does not affect the overall properties of the super-cooled liquid and glassy states of bulk-like films. Both films have a T_g value of T_g = 330 ± 1 K. However, the cooling curves for 18 nm TPD films show different behaviors beyond the instrumental noise on the two different substrates. The dynamics of the 18 nm TPD film supported on the neutral substrate fall out of equilibrium at a higher temperature than the film with the same thickness supported on the weakly interacting substrate, indicative of slower overall dynamics in the ultrathin films supported on the neutral substrate, likely due to slower dynamics near the PS interface compared to the silicon interface. As a result, the overall dynamics in the film are also slower. As detailed below, $Tg$s are measured to be T_g = 324 ± 1 K and T_g = 315 ± 1 K for the neutral and weakly interacting substrates, respectively. The average glass transition temperature and the transition width of each TPD film were obtained by fitting the normalized thickness versus temperature profiles using the following equation⁴⁸ and the results are reported in Fig. S9 of the supplementary material

Here h(T) is the thickness at temperature T normalized to thickness at 348 K, M and G are thermal expansion coefficients of the super-cooled and glassy regimes, $w$ is the width of the glass transition, and c is the normalized thickness of the film at T_g. The thermal expansion coefficients of the super-cooled liquid and glass regimes were kept constant and equal to the corresponding values for the thick films (bulk values) measured to be M = (6.6 ± 0.3) × 10⁻⁴ K⁻¹ and G = (2.1 ± 0.2) × 10⁻⁴ K⁻¹. We have not observed any significant difference in the values of the apparent thermal expansion coefficients as the film thickness was decreased for either substrate (Fig. S8). $w$⁠, T_g, and c were free fit parameters. This method is used because, for ultra-thin films the range of glassy state in the window available to our experiments are too small to fit a straight line to obtain T_g values. It has been previously demonstrated that this method results in the same value of T_g within the error as direct measurements using linear fits to the glassy and super-cooled liquid regimes.^8,48 However, this method is more accurate in defining the onset temperatures for the glass transition temperature, as the derivatives of T_g can become extremely noisy at low film thickness values.

Figure 2(a) plots the average T_g for various film thicknesses supported on the two types of substrates. The general trend is the same and consistent with various previous studies^1,2,8,13 in thin glassy and polymer films, where the T_g decreases with decreasing film thickness. However, the extent of the T_g reduction is clearly different at lower film thicknesses on the two substrates. At thicknesses below ∼30 nm, the T_g decreases more sharply on the weakly interacting substrate compared to the neutral substrate. For example, for a 18 nm film ΔT_g = 15 ± 2 K vs. ΔT_g = 6 ± 1 K for the weakly interacting and neutral substrates, respectively. We note that for ultrathin films below ∼16 nm supported on the weakly interacting silicon substrates, the onset of dewetting is observed during the temperature ramps and thus the data were not included.

To investigate the origin of the differences in the values of ΔT_g for the two substrates, the high and low onset temperatures for the glass transition, T₊ and T₋, were obtained assuming $T±=Tg±w2$⁠. T₊ signifies the onset of the start of the transition from the super-cooled liquid to glassy state where the slowest portion within the film starts to fall out of equilibrium upon cooling. T₋ signifies the completion of the glass transition which is representative of when the fastest portion of the film falls out of equilibrium. Figure 2 shows the change of T_g, T₊, and T₋ as a function of film thickness on the neutral and weakly interacting substrates. For films with thicknesses h > 60 nm on both substrates, there are no significant changes in T_g, T₊, or T₋, and the width of the transition, ΔT_g = 10 ± 1 K, is mostly due to the dynamical heterogeneity inherent to glassy systems. When the film thickness is decreased below 60 nm, there are immediate drops in the value of T₋ on both substrates. We attribute this to the contribution from the enhanced free surface dynamics, which results in the reduction of T_g in the near-surface region and thus the low onset of transition as well as the overall average T_g of the film. In this regime (30 nm < h < 60 nm), T₊ on both substrates remains more or less constant, indicating that some portions of these films, presumably the region near the substrate, still have bulk-like glassy dynamics. Thus the average T_g reduction in this thickness range originates from the increasing ratio of the free surface region with enhanced dynamics to the overall film thickness. We speculate that in this region, the near-substrate portion of the film has bulk-like, or slightly slower dynamics, depending on the type of the substrate. However, within our ability to resolve, T₊ does not seem to increase, meaning that the substrate effects are not as pronounced as the free surface effects. This is consistent with previous studies in polymers such as polystyrene, where the substrate does not appear to have a large effect on the overall film properties.⁴⁹ In this thickness range, the magnitude of the T_g reduction as well as the range of the gradients in the dynamics induced by the free surface are nearly identical on the two substrates suggesting that the substrate and the free surface are dynamically decoupled and do not influence each other.

Interfacial effects dominate the dynamics as the film thickness is further decreased below h < 30 nm. The first observation is that in this regime, on two types of substrates, both T₊ and T₋ values decrease sharply, resulting in a sharper decrease in the average T_g. The decrease in T₊ suggests that there is no longer any part within the film that behaves bulk-like and thus the enhanced dynamics at the free surface has affected and enhanced the dynamics everywhere in the film, including the substrate dynamics. On both types of substrates, the enhancement from the free surface still dominates below 30 nm resulting in overall enhanced dynamics with slightly less enhancement on the neutral substrate.

More surprisingly, while at all film thicknesses, the T₊ remains larger on the neutral substrate compared to the weakly attracting substrate, and due to stronger interaction energies, the T₋ is also larger for the neutral substrate compared to the weakly interacting substrate. This means that on the neutral substrate, even the dynamics at the free surface are slower than the free surface dynamics of the weakly interacting substrate. Thus the width of the transition, an indirect measure of the range of the gradients in the film’s dynamics, remains similar for these two substrates in this regime (Fig. S7). This is a strong indication of strong correlation between the dynamics at the two interfaces in this regime. One may expect that a further increase in the film/substrate interaction would alter the average T_g behavior from the reduction trend to constant as the example of PMMA on silicon or increase the trend as seen in P2VP on silicon.^10,36 Surprisingly, the differences in the substrate interactions do not affect the thickness at which the onset of these interfacial effects are observed. While the degree of enhancement seems to be determined by the interplay between the effects of the two interfaces, the thickness at which the two interfacial regions show a correlation in their dynamics resulting in the saturation in the range of their dynamical gradients seems to be independent of the type of the substrate and stays constant at h ∼ 30 nm.

To further investigate how this effect manifests, we performed MD simulations on Lennard-Jones (LJ) polymer films supported on either neutral (ε_PS = 1) or weakly attractive (ε_PS = 0.6) substrates at a temperature just above the simulated T_g. Here ε_PS is the LJ potential interaction between the polymer chain and the substrate. Figure 3 shows the mobility profiles for the simulated polymer for two interactions with the supporting substrate and four film thicknesses. Near the free surface, the relaxation time sharply decreases for all systems and is largely independent of the interactions with the substrate, except for the thinnest film with neutral substrate interactions (dashed blue line) where τ_α near the free surface increases slightly. Close to the substrate, τ_α increases, and the magnitude of the increase depends on both the interaction with the substrate and the film thickness. For films of both h = 4 and 10σ, the relaxation time near the substrate is reduced compared to the thicker films. Furthermore, the reduction is more pronounced in the system with a weaker substrate interaction than in the neutral system; near z ≈ 1, the relaxation time is reduced by approximately a factor of 5 in the neutral film, while the reduction is closer to a factor of 20 in the weakly adsorbing film, similar to previous simulations.⁴⁵ This observation is qualitatively consistent with the trends observed in T₊ and T₋ values. However, in simulations, the effect of interfaces on the overall dynamics of the film appears to be limited; when τ_α is averaged over the film thickness, the average dynamics are not strongly affected by the interfaces down to a thickness of 4σ (Fig. S11), though we note that this is consistent with experiments performed at much higher cooling rates.⁵⁰ 

Measurements of T_g as a function of film thickness were performed for a range of cooling rates (1 K/min < CR < 90 K/min) for TPD films supported on PS and were compared with the previously reported measurements on silicon substrates.⁹ Cooling rate-dependent T_g (CR-T_g) is an effective method to indirectly probe the average relaxation times in glasses at temperatures near their T_gs.^8,9,43,51 For most bulk organic glasses, when the system is cooled at 10 K/min, the super-cooled liquid falls out of equilibrium when the average structural relaxation time of the system is equal to τ_α ≃ 100 s. If the system is cooled more slowly, it falls out of equilibrium at a larger value of viscosity. As such, the cooling rate (CR) is inversely proportional to both η and τ_α with measurements at 10 K/min as a point of reference. The relaxation time can be estimated based on the empirical relationship that τ × CR = 1000. The details of CR-T_g measurements were described in the supplementary material and in earlier studies.^8,9,43 For TPD, we have previously shown that in thick films, this technique agrees well with measurements of dielectric relaxation times⁵² and direct and indirect viscosity measurements.⁹ 

Figure 4, shows a plot of log CR versus 1000/T_g for TPD films of various thicknesses on the neutral substrate. In the limited temperature window near T_g, we can use Arrhenius fits to each data set. The slope for each film thickness represents the apparent activation energy for relaxation near T_g, which is proportional to the dynamical fragility (Fig. S10).^8,10,51 Consistent with what has been observed in polymers^8,21 and TPD on silicon substrates,⁹ it is apparent that with a decrease in film thickness the activation barrier or the fragility decreases, indicating overall enhanced dynamics in ultrathin films.

In Fig. 5(a), the apparent activation barrier for rearrangement, E_a, for TPD films, evaluated from the slopes in Fig. 4, is plotted versus film thickness for films supported on the neutral substrate along with our previous results from dewetting and CR-T_g measurements for films supported on the weakly interacting silicon substrates.⁹ While both E_a and T_g start to decrease around h ∼ 60 nm, the E_a values do not show any significant differences on the two types of substrates until the film thickness is decreased below h ∼30 nm. The similar values of T_g and E_a in the thickness range of 30 nm < h < 60 nm on different substrates suggest that in this thickness range, while the near interface dynamics are affected by enhanced surface dynamics, a significant portion of the film still maintains bulk-like dynamics and thus the films on the two types of substrates have similar overall dynamics. This is further confirmed with the data shown in Fig. 2 where the T₊ values in this region remain bulk-like, suggesting that even if there is a slow region near the substrate it comprises a volume small enough to not be reflected in the measurement. Furthermore, the decrease in the values of E_a and T₋ and thus the enhancement in the dynamics near the free surface appears to be similar in films supported on the two types of substrates, meaning that the near surface dynamics are not affected by the substrate dynamics. The simulation data shown in Fig. 3 also confirm similar behavior for films with h > 25σ thickness.

On both substrates, we observe a sharp enhancement in the dynamics around h ∼ 30 nm, compared to the bulk glassy dynamics, and much lower E_a values are measured compared to the predictions of two- or three-layer models where a layer with constant thickness and enhanced dynamic are considered [Fig. 5(b) with details of the calculations in the supplementary material]. This thickness at which a turnover from the bulk to another value of E_a is observed is consistent with the thickness range where we start to see strong changes in T₊ and T₋ values as well as strong substrate dependence on the E_a and T₋ values depending on the substrate type (Fig. 2). The sharp drop in the values of T₊ indicates that the dynamics of the entire film, including the near substrate region are enhanced due to the influence of the free surface. Interestingly, the degree of change in T₊ and T₋ are similar as the film thickness is decreased such that the width of the transition on both types of substrates does not exceed 15-20 K. This is an indication that the range in dynamics of the entire film has narrowed compared to films with thicknesses h > 30 nm, due to the correlation in the dynamics of the two interfaces. Interestingly, assuming that T₋ can be interpreted as indicative of the mobility of the free surface, this data suggest that the dynamics in the free surface region (as well as the entire film) are slower on the neutral substrate compared to the weakly interacting substrate for films with h < 30 nm, while the free surface dynamics appear to be nearly identical on the two substrates for h > 30 nm due to the lack of influence from the substrate. To our knowledge, this narrowing of the range of dynamics due to the correlation in the dynamics of the two interfaces has not been reported previously in either polymeric or molecular glass thin films. The simulated data shown in Fig. 3 further demonstrate that the dynamics of the free surface themselves are also influenced by the substrate and are slower on the neutral substrate compared to the weakly interacting substrate, explaining the smaller degree of enhancement in T₋ values for the films supported on the neutral substrate as well as the larger overall E_a values in these films.

Below ∼15 nm, the average dynamics become weakly thickness dependent and appear to have a limiting low value of activation energy depending on the type of substrate. The dynamics of the substrate as well as the free surface influence the limiting value of E_a and no bulk-like dynamics are observed in this regime as measured by T₊. This rapid turnover in the thickness-dependence of the dynamics suggests that the interfacial effects can propagate and facilitate the overall dynamics in a non-linear fashion over a very large length-scale, which is beyond the range of local short-range interaction potentials. This nontrivial correlation between the dynamics of the free surface and the near-substrate dynamics cannot be explained by a simple two- or three-layer model^20,53 where the average film dynamics is a weighted average of a near surface layer with enhanced dynamics, a bulk-like layer with varying thicknesses, and a near-substrate region with a constant thickness, regardless of whether this layer is assumed to have uniform dynamics or gradients in the dynamics that are constant and independents of the film thickness itself. As shown in Fig. 5(b), if one assumes constant interfacial layers with enhanced mobility, the turnover is smooth and E_a decreases gradually, while in experiments on both substrates below ∼50 nm E_a strongly decreases below the predicted values. Furthermore, in two- or three-layer models one would also expect the values of T₋ to remain independent of the type of the substrate for all film thicknesses. The range of the gradient and the degree of enhancement of the dynamics of each region is instead correlated over a length scale of ∼30 nm, which is much larger than the short-range interaction potentials in both experimental and simulated systems. The strong deviation from a two-layer model is significant as it suggest that models and theories based on local interactions, where the free surface effects the enthalpy⁵⁴ or entropy⁵⁵ at the interface over a constant length scale cannot explain the observations presented in Figs. 2 and 5, while they appear to work in simulated coarse grain systems²⁸ where the range of these effects is smaller.

The turnover from glassy to enhanced liquid-like dynamics occurs at a constant film thickness of ∼30 nm independent of the interaction energies provided by the interfaces. While the interfacial interactions can perturb the low limit value of E_a, they seem to have little effect on the mid-point of the transition. The bulk activation barrier (or fragility) can also be tuned by changing chemistry, as demonstrated in our previous studies on PS and PPO miscible blends with varying compositions.²¹ That study similarly showed that changes in the value of the glassy limit of this transition is also ineffective in changing the mid-point of this transition for polymers, which also have a transition mid-point of about ∼30 nm. This is a surprising observation which indicates that this length scale is set by something other than the perturbations used to observe it. A similar transition was also observed for polymers on soft substrates except that the length scale may be different than on rigid substrates.^22,23

The interfaces may only act as perturbations to the system, while the length-scale of the correlated dynamics is set by the bulk glass and is a universal feature in organic systems. The correlation length-scale we observed here is also very different from the typical thickness range of the surface induced mobile layer which is usually reported to be only a few mono-layers thick,⁶ again suggesting that this apparently universal long-range non-local length-scale is possibly more than the interfacial effect. Such bulk property determined transition in the dynamics and the large correlated length-scale may be important in understanding the bulk glass transition near this length-scale. Despite the seemingly universal behavior we observed in different organic systems, the physical nature of such large non-local length-scale is not clear. We note that the observation of this length scale is not limited to CR-T_g measurements as previous studies have also shown a strong tendency to dewetting as the film thickness changed below 30 nm at temperatures well below bulk T_g.⁹ These observations are also consistent with earlier studies on bilayer films that showed non-monotonic changes in T_g of the near-surface film by changing the thickness of the layer below, indicating coupling of the dynamics of the two films.^5,22,23

Based on the current and previous studies, we find that the lower thickness limit of $Ea$ or the interfacial limit can be tuned by the strength of the interactions at the interfaces. Similarly, the upper thickness limit of $Ea$ or the bulk limit can be tuned by changing the chemistry of the studied system and thus the glass fragility.²¹ However, in the systems that have been studied thus far, neither perturbation of the bulk or interfacial dynamics seems to significantly affect the film thickness of the mid-point of the transition. The ability to tune this midpoint could be important for understanding the nature of such transitions in the dynamics and the physical origin of the non-local interactions that are causing this phenomenon. Interestingly, recent studies by Baglay and Roth²³ have indicated that the elasticity of the substrate may provide a strong way to tune the value of the mid-point, which suggests an important role of elasticity in the existence of this non-local transition. To our knowledge, theories based on changes in the local enthalpy and entropy at the free surface do not predict such a large length scale, a sharp drop in the activation energies, or the strong correlations between the substrate and free surface dynamics. More recent theories based on non-local elastic barriers^56,57 predict a larger length scale for the T_g transition,¹⁵ but appear to be consistent with a smooth transition such as the one shown in Fig. 5(b). In their current form, these models also do not predict the apparent strong correlation of the dynamics between the interfaces. A recent study of local soft-spots in simulated glass thin films show that the enhanced surface dynamics is due to structure-independent processes that are already present in bulk systems but are strongly influenced and enhanced by the free surface.⁵⁸ This observation is consistent with the data presented here that shows the non-local effects may have originated in the bulk glass dynamics. The data presented here may provide a guide for future models that predict interfacial phenomenon in glassy systems.

In summary, in this study, we have changed interactions at the substrate/film interface in ultrathin molecular glass TPD films from weakly interacting to neutral by a simple approach of coating the silicon substrates with a very thin polystyrene dead-layer. Stronger film/substrate interaction for TPD on the PS dead-layer substrate results in a smaller extent of T_g reduction in films with thicknesses below around 30 nm. This simple approach of substrate modification has also improved the stability of ultrathin molecular glass films towards dewetting that can be important in relevant applications. By investigating the start and end temperatures of T_g transition (T₊ and T₋) as well as apparent activation energies for rearrangement obtained by CR-T_g measurements, we observed long-range correlation in the dynamics of the free surface and substrate in films thinner than ∼30 nm such that the free surface dynamics were slower in films supported on the neutral substrates compared to those supported on the weakly interacting substrates. Compared with TPD thin film glasses supported on bare silicon substrates, the length-scale of the transition remains the same but with increased activation barrier at the limit of zero film thickness. The drop in the apparent activation energy as well as the T₊ values (indicating enhanced dynamics at the slow portion of the film) occurred at the same film thickness independent of the substrate type, indicating the bulk origin of the long-range, non-local correlation length in this system. Coarse-grained MD simulations qualitatively confirmed these observations in short polymer chains.

See supplementary material for the characterization of the dead layer (Fig. S1), the wetting properties of the dead layer and TPD (Figs. S2–S4), details of the molecular dynamics simulations, discussion of the two and three layer models, additional details about the ellipsometry characterization (Figs. S5–S7), the thermal expansion coefficients (Fig. S8), the T_g width (Fig. S9), and the fragility (Fig. S10).

This work was funded by NSF-DMREF-1628407 and the University of Pennsylvania Materials Research Science and Engineering Center (MRSEC) (Grant No. DMR-1720530), and partially funded by NSF-PIRE (Grant No. OISE 154884, funding M.A. and C.N.W). Computational resources were provided by the San Diego Supercomputer Center through XSEDE allocation No. TG-DMR150034. The authors thank Laura Bradley and Gang Duan from Daeyeon Lee group for help with contact angle measurements.