Exploring the broadening and the existence of two glass transitions due to competing interfacial effects in thin, supported polymer films

The properties of ultra-thin polymer films have been extensively studied due to their strong deviations from those of the bulk material. Specifically, experimental^1–12 and theoretical^13–16 studies observe that the glass transition temperature (T_g) of ultra-thin polystyrene films decreases with film thickness below 60 nm. This has generally been associated with a layer near the air/polymer interface, which has enhanced dynamics.^17–21 This layer has been shown to play a strong role in the overall dynamics of the film as the thickness decreases, resulting in a decreasing value of T_g. These interfacial effects, however, do not solely affect T_g. Experiments and simulations^13–16,22 show that dewetting,^23–25 physical aging,^5,26–29 and mechanical properties^30–32 all exhibit deviations from the corresponding bulk property due to enhanced mobility at the air/polymer interface.

While the air/polymer interface can enhance the overall dynamics of an ultra-thin polymer film, the polymer/substrate interface can have an opposite effect. Many studies have shown that T_g can also be altered by increasing the attractive interactions between the polymer and the substrate.^33–35 For example, the T_g of ultra-thin polystyrene films can increase when chain ends^36,37 or side chains³⁶ are grafted to the substrate. It is generally accepted that these kinds of substrate interactions affect T_g because the polymer’s mobility is hindered at the substrate.^5,24,38–40 These same types of effects are seen in other polymers that have attractive substrate interactions. For example, poly(methyl methacrylate) (PMMA)⁴¹ exhibits slight increases in T_g, and poly(2-vinyl pyridine) (P2VP)^6,42–44 exhibits drastic T_g increases with decreasing film thickness. Furthermore, nanohole relaxation studies on PMMA⁴⁵ show that substrate interactions can slow the dynamics of a film over long length scales that are comparable to those over which the air/polymer interface enhances segmental motion.⁴ 

While the majority of these previous studies were performed on ultra-thin films, other polymer systems and geometries can provide more information about the effect of substrate interactions due to their larger substrate surface area. Nanocomposites, for example, can exhibit increases in T_g^46–53 due to adsorbed layers of polymer around a nanoparticle.⁵² Another system that exhibits such effects are glasses confined within nanopores. While Jackson and McKenna showed that T_g of o-terphenyl confined to pores with a diameter of 4 nm is 18 K lower than bulk,⁵⁴ polymer glasses in similar geometries show the opposite effect.^55–60 Moreover, a recent study by Krutyeva et al. on polydimethylsiloxane (PDMS) in anodic aluminum nanopores observed through small angle neutron scattering (SANS) that there were two distinct areas of dynamics within the 26 nm nanopore: a PDMS ring near the surface of the nanopore with a thickness of 6.5 nm and dynamics far slower than bulk PDMS and a cylinder with a radius of 6.5 nm in the middle of the nanopore that had bulk-like dynamics.⁶¹ 

Complete dynamical segregation was also found in short and entangled chains⁶² and oligomeric⁶³ PMMA confined to anodic aluminum. The dynamics of these systems were characterized via T_g of the polymer as determined by differential scanning calorimetry (DSC). For samples made with short and entangled chain PMMA in 80 nm nanopores, the adsorbed layer of PMMA segregates from the non-adsorbed layer and results in two distinct T_g’s, one above the bulk T_g and one below. Furthermore, the two T_g’s separate further at lower cooling rates, suggesting that the regions of slow and fast dynamics become more decoupled at low cooling rates.⁶² A similar result was found in samples made with oligomeric PMMA.⁶³ However, this study also tested nanopores with a diameter of 300 nm. In these much larger nanopores, the oligomeric PMMA exhibited three T_g’s at fast rates, and two at slow rates. These results suggest that the polymers had a large gradient of dynamics over length scales much larger than the size of the oligomer.⁶³ Furthermore, it suggests that cooling rate based experiments are useful to observe the segregation of differing regions of dynamics within a single sample.

Cooling rate-dependent T_g measurements (CR-T_g) have been performed previously to determine the dynamics of ultra-thin polymer films.^{11,12,27,64–67} Recent CR-T_g measurement using ellipsometry shows that the fragility of ultra-thin polymer films deviates from bulk-like dynamics and becomes more surface-like at low cooling rates and low temperatures.^11,66 Ultra-thin polystyrene films also exhibit an increased breadth of T_g, signifying strong gradients in the dynamics of these films.^11,68 The increased breadth of the transition necessitates a larger than typical range of temperatures to accurately probe the full breadth of the glass transition in ultra-thin films. Furthermore, the work by Pye and Roth showed the first evidence of two T_g’s in ultra-thin free-standing polystyrene films.^69,70 While the presence of two T_g’s in this study was not linked to differing areas of dynamics within the same film, it does highlight how a large temperature range could allow the detection of new glass transitions in thin polymer films via ellipsometry.

Recent studies on organic molecular glasses show that long-range correlated dynamics with a length scale of about 30 nm can be observed in molecular glass films.²⁵ These studies show that the gradient in the dynamics in a film of a particular thickness is not necessarily represented by a weighted average of a layer with enhanced mobility with the rest of the film being in a bulk-like glass state. The gradient in the dynamics itself can depend on the film thickness. These studies were performed on a substrate with repulsive attractions. As attractive substrate interactions are added to a system, one can ask what is the effect of the increased range of the gradients in the dynamics on the properties of the film. Are the two T_g’s observed in the pores a result of large gradients in the dynamics such that the near-substrate and the near-surface dynamics completely decouple? Such decoupling has been previously observed in miscible polymer blends with large T_g mismatch between the polymers.⁷¹ Some evidence of this possibility has been observed in direct measurements of dynamics in ultra-thin films where two step relaxation dynamics have been observed in supported polymer films,^17,18,20 but to our knowledge have not been linked to the observation of two T_g’s in these systems. The advantage of using supported polymer films as opposed to pores is simpler sample geometry and simpler boundary conditions. Furthermore, the results can be directly compared with the measurements of polymer properties supported on a neutral substrate.

Here, we use ellipsometry to perform CR-T_g measurements on ultra-thin films of poly(2-vinyl pyridine) (P2VP). Unlike polystyrene, thin films of P2VP exhibit increased T_g’s^6,42–44 due to P2VPs ability to hydrogen bond with hydroxyl groups on the surface of silica.^5,24,40 Despite the polymer/substrate interface seemingly dominating the segmental dynamics of thin films, florescence measurements observed that films of P2VP also have a layer with enhanced mobility at the air/polymer interface with a thickness of 5-7 nm.^21,72 The presence of regions of such different dynamics within the same film makes P2VP an ideal system for the study of dynamical gradients in supported polymer films. A recent study by Madkour et al. showed that thin films of P2VP exhibit T_g broadening in DSC measurements, signifying both a large dynamical gradient and separation between the mobile surface and the strongly adsorbed layer.⁷³ 

In this manuscript, we use CR-T_g measurements to demonstrate that wider experimental temperature ranges result in the observation of broadening in T_g to the extent that two distinct T_g’s become apparent at low cooling rates for the thinest films, which is consistent with the studies on polymers confined within nanopores.^62,63 Furthermore, the breadth of the T_g transition increases and the values of the two T_g’s separate as the film thickness or cooling rate is decreased, signifying the increasing segregation of dynamics at different regions within the film. These results indicate that the dynamics close to both interfaces are correlated over a length scale of about 10-20 nm, such that when the gradients in the dynamics become very large (a breadth of >50 K), the system cannot maintain the large gradients in the dynamics, and each layer follows the dynamics of the corresponding interface.

Ultra-thin films of P2VP (Polymer Source, Inc., M_w = 304 kg/mol, M_n = 295 kg/mol) were produced via spin-casting polymer solutions in n-butanol (Sigma-Aldrich) at a speed of 2000 RPM for 40 s onto a silicon wafer with a native oxide layer (Virginia Semiconductor). The silicon wafers were washed with n-butanol before the polymer solution was spun-cast. The thickness of the film was controlled via the solution concentration (0.5-3 wt. %). The films were then annealed under vacuum at 413 K for 15 h.

The thicknesses of these films were verified using spectroscopic ellipsometery (M-2000V J. A. Wollam). The raw ellipsometric angles, $Ψ(λ)$ and $Δ(λ)$⁠, were fit to a three layer model consisting of a temperature-dependent Si layer as a substrate, a 1 nm thick native oxide layer, and a transparent layer to account for P2VP. The temperature-dependent index of refraction, n(T), and temperature-dependent thickness, h(T), of the polymer layer was fit to a Cauchy model (⁠$n=A+Bλ2$⁠). The imaginary part of the index of refraction, K, was assumed to be zero. Figure 1 shows an example of the raw ellipsometric angles, $Ψ(λ)$ and $Δ(λ)$⁠, and the corresponding fits to the data. Further details of the setup and ellipsometry fitting procedure are presented in the supplementary material and in our earlier publications.^11,66

For CR-T_g measurements, the films were mounted onto a temperature control stage (Linkam THMS 600) that was attached to the ellipsometer. The thickness of the films was tracked while the temperature was changed. The temperature of the film was raised to 413 K at a rate of 150 K/min and then held at 413 K for 20 min. The film was subsequently subjected to multiple cycles of heating and cooling between 413 K and 313 K. Cooling was performed at various rates (150, 120, 90, 60, 30, 10, 7, 3, and 1 K/min), while heating rates were all kept constant at 150 K/min. Both the heating and cooling rates were maintained using a liquid nitrogen cooling system, and the Linkam temperature stage was purged with dry nitrogen gas throughout the experiment. Figure 2 shows the details of the temperature profile and the corresponding thickness profile throughout the CR-T_g measurements for a 217 nm P2VP film. More details of the technique can be found in the supplementary material and in our previous publications.^11,66,74,75 It is important to note that the range of temperatures chosen in this study is broader and extends to lower temperatures than those used in previous studies of P2VP thin films.^6,43,44 This was done to ensure that these studies can capture potentially low values of T_g that may arise from enhanced dynamics at the free surface.

Figure 3 shows a thickness vs. temperature plot of a 217 nm film cooled at a rate of 10 K/min. The glass transition temperature for each film at each cooling rate was determined via the intersection of linear fits to the film’s super-cooled liquid and glassy regimes. We denote this value as T_g,avg, which is the same as T_g under conditions where only one glass transition is observed in the film. Similar to previous reports, this method of fitting T_g defines the glass transition in these films as a single extremely broad transition.^11,66 When the transition becomes broad enough to resemble two apparent T_g’s at low cooling rates (as discussed further in this report), T_g,avg falls somewhere in the midpoint of the two transitions. To avoid bias in the selection of the two regimes, the super-cooled liquid regime was always chosen to be 393 K-413 K, such that all films exhibited a bulk-like super-cooled liquid expansion coefficient of $(5.6±0.3)×10−4$ K⁻¹, and the glassy regime was chosen to be 313 K-343 K for thin films (h $<$ 100 nm). Cooling the samples to 313 K ensured that the expansion coefficient of a bulk glassy film (⁠$(1.6±0.3)×10−4$ K⁻¹) was recovered. A plot of the super-cooled liquid and glassy expansion coefficients as a function of film thickness is shown in Figure S2 of the supplementary material and shows that these values are constant for films of all thicknesses. All data presented from CR-T_g measurements are based on the values of T_g,avg.

The values of the expansion coefficients as a function of temperature were calculated via a two step process. First, the raw thickness vs. temperature data was smoothed using a running average and a 2nd order polynomial negative exponential smoothing function with a smoothing range of 20 K (performed in Sigmaplot 12). Due to the large smoothing range, a portion of the data at either temperature extreme was eliminated from the smoothed thickness vs. temperature data, which, in some cases overlaps with the glassy region. Figures S3(a) of the supplementary material show an example of the thickness vs. temperature data and the results after smoothing. Second, a derivative of the smoothed temperature vs. thickness data was taken using the two point difference quotient between each temperature step. These derivative values were then divided by the film thickness measured at 313 K to obtain the expansion coefficient as a function of temperature. The glassy and super-cooled expansion coefficients determined via this method match the aforementioned linear slopes of the raw, unsmoothed, thickness vs. temperature data signifying that this difference derivative based method for calculating the expansion coefficients obtained accurate values, and that the smoothing function did not remove any attributes of the raw data. We do note, however, that the large smoothing range means that in order for an attribute of the expansion coefficient vs. temperature plot to be significant, it must occur over a temperature range larger than 10 K.

Figure 4 shows thickness as a function of temperature for a 217 nm film and a 33 nm film, both performed at a cooling rate of 1 K/min. In order to directly compare the two films, both curves were normalized to their thickness at 413 K. For clarity, both plots have been sampled so every 10th data point is shown. The expansion coefficient as a function of temperature for both films is shown in the inset. It is important to note that both films overlay well in the super-cooled liquid regime. Since the expansion coefficient is dependent on the density, the matching of the films’ expansion coefficients in this region implies that the entire film has transformed into super-cooled liquid, and that the properties of the super-cooled liquid have not been significantly altered in the 33 nm film. This observation holds true for all films in this study and can be seen in the plot of super-cooled and glassy expansion coefficients as a function of film thickness in Figure S2 of the supplementary material. Furthermore, Figure S4 of the supplementary material shows that these expansion coefficients hold for films as thick as 1080 nm. As the two films cool, the 33 nm film exhibits a higher onset to the glass transition (⁠$T+≃$ 380 K) compared to the 217 nm film (⁠$T+≃$ 372 K). This onset is observed more clearly in the plot of expansion coefficient as a function of temperature presented in the inset of Figure 4. This suggests that at least parts of the 33 nm film fall out of equilibrium at a higher temperature than the 217 nm film, which is consistent with many previous studies on P2VP films, which show that thin films of P2VP have higher T_g’s.^6,42–44,73 We attribute this higher onset to slower dynamics in the near substrate region.

A second significant result occurs at low temperatures. Previous studies on the thin film T_g’s of P2VP use either fluorescence-based techniques at temperatures down to 340 K^6,44 or use ellipsometry with a longer sampling rate than the one performed here (every 30 s at 2 K/min⁴³). The films in this study were cooled to 310 K with a sampling rate of a measurement every 6 s at 1 K/min cooling. By performing the experiment in this manner, an interesting phenomenon is observed. The glass transition slows at T = 350 K and T = 365 K for the 217 nm and 33 nm films, respectively, but does not completely attain its glassy expansion coefficient until the transition is slowly finished at T₋ = 340 $±$ 5 K. We attribute this slow part of the transition at low temperature to the gradient in the dynamics near the free surface, where regions closer to the free surface fall out of equilibrium at lower temperatures.

The broadening of T_g transition increases, and the dynamical separation within a P2VP film becomes more apparent as the film thickness is further reduced. Figure 5 shows thickness as a function of temperature for a 16 nm film at a cooling rate of 1 K/min. In this thinner film, the broadening of the glass transition has grown such that there were three distinct areas of linear expansion (highlighted in Figure 5 and its inset) and two clear T_g’s. Either this film has a very broad T_g transition, indicative of large gradients in the dynamics of the film, with an average value of glass transition $Tg,avg=358±$ 2 K and a transition breadth of 51 K, or the film consists of two distinct regions of dynamics, each with its own value of T_g. Values for the two T_g’s can be determined through the intersections of a linear fit to each of the three regions of expansion to be $Tg,low=343±$ 2 K and $Tg,high=385±$ 2 K for the 16 nm film. The presence of the two distinct values of T_g is shown further upon examination of the plot of expansion coefficient as a function of temperature (inset of Figure 5). Not only does the 16 nm film lose the super-cooled liquid expansion at a higher temperature (⁠$Tg,high=385±$ 2 K) than either the 217 nm or 33 nm films, but the plateau at an expansion coefficient of $(3.5±0.3)×10−4$ K⁻¹ between 357 K and 373 K is also much more pronounced in this film compared to the 33 nm film. Below 357 K, the expansion coefficient decreases towards the bulk glassy value of $(1.6±0.3)×10−4$ K⁻¹ and the second transition is completed at 330 K. An analysis of the index of refraction as a function of temperature for this film can be found in Figure S5 of the supplementary material. Applying the same temperature regions to these data, we calculate the two values of T_g to be $Tg,low=339±$ 4 K and $Tg,high=381.5±$ 4 K. These values are in reasonable agreement with the results of the thickness vs. temperature and expansion coefficient analyses. The existence of two distinct transitions indicates that the dynamical gradients are so large in this film that the near-free surface and near-substrate regions have decoupled dynamics. The thickness of the mobile surface layer can be estimated by assuming that the value of the expansion coefficient at any temperature is related to the percent of the film that has fallen out of equilibrium. Thus, we calculate the mobile layer thickness by dividing the difference of the expansion coefficient at any temperature from the super-cooled value by the total change in expansion coefficient over the whole temperature range. Because of the many assumptions taken here, the errors in this value were determined based on either the spread of the expansion coefficient values in the plateau region or based on the error of T₋. Through this method, the thickness of the near-free surface region based on these data can be estimated to be ∼7 ± 2 nm, which is consistent and slightly higher than the 5 nm value reported for an 18 nm P2VP film by Peang et al. using dye reorientation measurements.⁷² 

In order to study the dynamics in ultra-thin films of P2VP and gain a better understanding of the gradient of mobility within these films, cooling rate-dependent T_g measurements were performed. For this experiment, T_g of the film was defined by T_g,avg, or the midpoint of a broad glass transition. We have previously demonstrated that even in the presence of broad transitions, such studies can still be used to provide more detailed information about the effect of interfacial dynamics on the overall average dynamics of a film.^{11,12,27,64–67} Figure 6 shows the evolution of a thickness vs. temperature curve for a 16 nm P2VP film at various cooling rates. The separation of T_g,high and T_g,low (or T₊ and T₋) increases with decreasing cooling rate, suggesting that dynamics of the substrate and the free surface deviate more strongly at low cooling rates, when slower relaxation times are being probed within the film. A similar trend was observed in ultra-thin polystyrene films, where the effect of T_g reduction is accentuated at slow cooling rates when the relaxation times of the bulk and free surface differ most.

A further examination of the interplay between the substrate and free surface effects within these films can be achieved through an analysis of the thickness dependence of T_g,avg at many cooling rates. T_g,avg is used for this analysis because it is an effective measure of the weighted average of the two interfacial dynamics, such that if T_g,avg is higher than the bulk T_g, then the slow dynamics at the substrate dominate the overall dynamics of the film. Conversely, if T_g,avg is lower than the bulk T_g, then the film dynamics are dominated by the enhanced free surface relaxation time. Figure 7 shows T_g,avg as a function of film thickness at cooling rates of 120, 60, 10, and 1 K/min. For a given thickness, T_g,avg decreases with decreasing cooling rate, consistent with previous CR-T_g measurements.^{11,12,27,64–67} However, unlike these previous measurements where only T_g reductions were observed, Figure 7 shows that, at a cooling rate of 120 K/min, T_g,avg increases from 374 K ± 1 K to 380 K ± 2.5 K as the thickness of the film is decreased from 217 nm to 16 nm. Additionally, T_g,avg of a 16 nm film does not change significantly at a cooling rate of 10 K/min and even decreases 9 K from the thick film T_g,avg at a cooling rate of 1 K/min. The reason behind this change in the trend lies in the changing breadth of the transition as shown in Figure 6, where at high cooling rates the dynamics of the two regions of near-surface and near-substrate are not significantly different, while at lower cooling rates the near-surface region has enhanced dynamics and as such falls out of equilibrium at a lower temperature. These data show the importance of cooling rate, or the probe temperature for isothermal experiments, when comparing glass transition temperature measurements from different studies.

In order to better understand the interplay between the substrate and free surface regions on the overall dynamics of ultra-thin films of P2VP, it is helpful to construct an Arrhenius plot of Log (Coolilng Rate) (Log(CR)) as a function of 1/T_g,avg as shown in Figure 8. When a liquid is cooled at a faster rate, it falls out of equilibrium at a higher temperature, where the structural relaxation time, $τα$⁠, is shorter. As such, the cooling rate is inversely related to $τα$ at T_g. Plotting the data in this manner elucidates subtle changes in the average dynamics of thin films that are hard to detect through single T_g measurements.^11,64 The slope of the curve in this plot should inform us about the apparent activation barrier for mobility in these films. Figure 8 shows the plot of Log(CR) vs. 1/T_g,avg for films of various thicknesses. The CR-T_g data measured for the 217 nm film (black circles in Figure 8) are in reasonable agreement with the extrapolated Volgel–Fulcher–Tamman (VFT) fit to bulk CR-T_g data measured by Madkour et al.⁷³ using calorimetry (dashed green line). As the film thickness is reduced, the apparent activation energy (slope of the curve) and the apparent dynamical fragility, defined as activation energy at a cooling rate of 10 K/min divided by 1/T_g,avg at that cooling rate, also decrease.

The reduction of the apparent activation barrier (and apparent fragility) for ultra-thin P2VP films is consistent with previous observations in polystyrene and other polymer systems.^11,64,66,76 In previous CR-T_g studies, the reduced apparent activation barrier in ultra-thin films has been related to film dynamics becoming more surface-like,^11,66 and direct measurements of the free surface dynamics of polystyrene also show low activation energy for relaxation.^18–20 Therefore, we hypothesize that the decrease in apparent activation barrier in P2VP thin films is also due to the increased presence of an enhanced mobile layer⁷² whose relaxation times have a weaker temperature dependence than that of the bulk material.

There is, however, an important difference between the dynamics measured here and those measured in polystyrene. The CR-T_g studies in polystyrene show that the average thin film dynamics, without fail, fall between the bulk and the surface relaxation processes suggesting that the gradient present in ultra-thin polystyrene films ranges between those two limits.¹¹ As such, in polystyrene, the thin films’ T_g never exceed that of bulk T_g. However, as shown in Figures 7 and 8 at high cooling rates, T_g,avg increases above bulk T_g, resulting in the crossing of the thin and thick film dynamics at a cooling rate of about 30 K/min. This difference is most probably due to the nature of the polymers’ interactions with the silicon substrate. While it has been observed that a chemically adsorbed layer with slower than bulk dynamics exists in polystyrene,^24,38–40 this layer does not strongly contribute to T_g,avg until the film thickness is reduced below 2-3 nm. The free surface dynamics of polystyrene are so strongly enhanced that they dominate the average dynamics. In contrast, the strong substrate effects that have been observed in thin films of P2VP^6,42–44,73 result in increased T_g,avg values at fast cooling rates even in films as thin as 16 nm films.

Figure 9 demonstrates schematically our hypothesis on how the competing effects of the strong substrate interactions and enhanced dynamics at the free surface can contribute to the observed trends in Figure 8. The dynamics of the strongly adsorbed layer near the substrate (solid blue line in Figure 9) are expected to be slower than the bulk dynamics (black solid line), with similar or larger fragility. The near free-surface region (red solid line) is expected to have faster dynamics with lower activation barrier (and fragility). At high cooling rates such as the one indicated by black dashed-dotted arrow, the dynamics of the surface and substrate regions are not very different and the gradients in the dynamics are smaller. In this region, the substrate effects dominate the system and $Tg,avg>Tg(bulk)$⁠. As such, the average film dynamics (shown by purple dashed line) are slower than bulk. At lower cooling rates (green dashed-dotted arrow), because of its lower fragility, the free surface dynamics play a greater role, and thus, $Tg,avg<Tg(bulk)$⁠. At this point, the average film dynamics (purple dashed line) becomes faster than bulk. At some point between these two limits, the bulk and average dynamics cross, similar to what has been observed for 33 nm and 16 nm films in Figure 8. It is impossible to definitively claim that the schematic shown in Figure 9 is accurate based purely on CR-T_g data, because CR-T_g experiments inherently treat the film as having a single average relaxation time. Direct measurements of dynamics^17–21,72 must be performed to determine an actual measure of the dynamics at the air/polymer interface. The dye reorientation measurements on P2VP do indeed show that a layer with fast dynamics exists in these films, and that the layer has similar thicknesses at bulk T_g as those measured in this study,^21,72 but direct measurements of the temperature-dependent dynamics in these films have not yet been performed to our knowledge. The temperature dependence of the substrate dynamics is much more difficult to measure experimentally, but is possible based on fluorescent intensity measurements if one could perform such measurements at various cooling rates. However, it is worth noting that these hypotheses are consistent with the results of Burroughs et al., which show that T_g of an adsorbed layer greatly depends on its exposure to a free surface.⁷⁷ 

One prediction of the hypothesized change in the fragility between the free surface and substrate regions is growing gradients in the dynamics. The dashed-dotted arrows in Figure 9 represent what occurs within a film when it is cooled at a constant rate. The regions near the substrate fall out of equilibrium at a high temperature, corresponding to the blue line, and the transition continues until a temperature is reached where the free surface falls out of equilibrium (represented by the red line). Since the distance between the two lines grows as the cooling rate is decreased, the breadth of the T_g transition should grow accordingly. This is exactly what has been observed in Figure 6. Madkour et al. also observed a similar broadening of the T_g signature in DSC scans of P2VP films, and they associated T_g broadening with the separation of enhanced surface and hindered substrate dynamics.⁷³ 

Ellipsometry allows for measurements at significantly lower cooling rates than those available to calorimetry. At a cooling rate of 1 K/min, the exceedingly large gradients of the dynamics results in growing breadth of T_g transition (50 K for a 16 nm film) and the decoupling of the substrate and free surface dynamics in 16 nm films as shown in Figure 6. Figure 10(a) shows the values of T₊(blue, the start of transition), T₋ (red, the end of transition), and T_g,avg (black) as a function of film thickness at a cooling rate of 1 K/min. As seen in this figure, T₊ increases with decreasing film thickness, which follows the previously observed trend for P2VP and other polymers with strong substrate interactions.^6,42–44,73 T₋ decreases with decreasing film thickness, which is similar to what is observed in polymers that exhibit effects from the mobile surface layer and neutral substrate interactions.^{1–8,10–12} This trend in diverging T_g broadening has not been previously observed in P2VP, mostly due to the limited temperature range chosen in previous experiments. However, the existence of both the strongly adsorbed substrate layer^5,24,38–40 and enhanced free surface dynamics⁷² has been previously observed in these films. Notably, the breadth of the glass transition and thus the difference between the two T_g’s grow with decreasing film thickness. This is better visualized in Figure 10(b) that shows the plot of expansion coefficient as a function of temperature for 217 nm, 33 nm, and 16 nm films. In this figure, we observe that as the film thickness is decreased, the onset (T₊) and offset (T₋) of the glass transition shift to higher and lower temperatures, respectively. This results in the breadth of the transition (T₊ − T₋ in Figure 10) increasing from 18.5 K in a 217 nm film to 35 K for a 33 nm film and 51 K for a 16 nm film, respectively. A major implication of this observation is that the relaxation dynamics near either interface are not constant and depend on the film thickness as they either slow or enhance as the film thickness is decreased. This is consistent with the recent observations of strongly correlated dynamics in molecular glass films, where the free surface dynamics were affected by the bulk in thick films and in contrast, the dynamics near the films center were affected by the free surface more strongly in thin films.⁷⁸ In the data presented here, each interface shows a stronger deviation from bulk, but in opposite directions, as the film thickness is decreased.

The divergence of the dynamics of the two regions as the film thickness is decreased results in an interesting phenomenon. As a film is cooled from the super-cooled liquid state, once below T₊, the near-substrate region falls out of equilibrium, while the near-surface region is still at equilibrium. Since the two regions have different fragilities as observed in Figure 8, at this temperature (T₊ = 380 K), the free surface dynamics is only 1-2 orders of magnitude faster for most of the films studied here. However, by the time that the near-surface region entirely falls out of equilibrium (T < 340 K), the extrapolated dynamics of the near-substrate region may be 5-10 orders of magnitude slower than the near-surface region, depending on the film thickness. For example, based on the general relation that 5 K changes in temperature relates to approximately 1 decade in relaxation time (⁠$τα$⁠), one can estimate that the range of $τα$ present in a 33 nm film is about seven orders of magnitude. Figure 10(b) shows that the 33 nm film exhibits mostly a single broad transition, with a small plateau around 360 K. This suggests that this large dynamical gradient between the strongly adsorbed layer at the substrate and a layer of enhanced mobility near the free surface is still somewhat maintained through the film. Similar T_g breadths have been observed in systems with no significant attractive substrate interactions.⁶⁸ However, at a film thickness of 16 nm, the T_g breadth increases to 51 K, which corresponds to a difference in $τα$ of about ten orders of magnitude. This large estimated difference in relaxation time manifests itself in the expansion coefficient of the film. As shown in Fig. 10(b), not only does the breadth of transition broaden with respect to the 33 nm and 217 nm films, but there exists three clearly distinct regions of constant expansion, beyond the potential uncertainty in the calculations of the expansion coefficient. The high and low temperature plateaus match the expansion coefficients of the 217 nm film, and thus, these regions represent temperature regimes at which the entire film is super-cooled (high T) and at which the entire film has fallen out of equilibrium (low T). What stands out about the expansion coefficient profile of the 16 nm film, though, is that this transformation is not gradual. The middle expansion plateau suggests that the glass transition of a 16 nm P2VP film occurs in two steps. This suggests that the ten orders of magnitude difference in $τα$ cannot be maintained as a gradient in a single 16 nm film, and thus, the film dynamics segregate into two distinct regions with their own characteristic $τα$’s, and, as described later, with roughly equal thicknesses (7 $± 2$ nm near the free surface vs. 9 $± 2$ nm near the substrate).

While uncommon, the existence of two T_g’s has precedent in polymers confined to nanopores^62,63 and in free standing films of polystyrene.^69,70 Similar to the trends observed in Figure 10, entangled PMMA exhibits two distinct T_g’s when confined to an 80 nm nanopore, one above the bulk T_g and one below,⁶² and the separation of T_g,high and T_g,low of oligomeric PMMA in nanopores increases when the nanopore size decreases from a diameter of 300 nm to 80 nm.⁶³ Both nanopore studies associate the presence of multiple T_g’s with a ring of adsorbed PMMA around a cylinder of PMMA with faster dynamics. While complete segregation of the substrate and enhanced P2VP layers has not been previously observed,^6,42–44,73 the observation of two T_g’s in free standing polystyrene films shows the importance of a broad temperature range when performing T_g measurements with ellipsometry.^69,70 These studies by Pye et al. are able to measure the thickness of free standing polystyrene films at higher temperatures than had been previously measured,^2,79,80 and as a result were able to observe T_g,high.^69,70 The temperature range in this experiment was extended to 313 K, thus allowing for the detection of a previously unobserved T_g,low. Furthermore, the study presented here takes advantage of the strong substrate interactions present in P2VP to cause the requisite dynamical separation for the observation of 2 distinct T_g’s. Unlike ultra-thin films of PS, which consist of a dynamical gradient between bulk $τα$ and that of the enhanced surface layer, P2VP films exhibit strong substrate layers effectively widening the dynamical gap to be more on the order of that in experiments on polymers confined to nanopores.^62,63

In this report, ellipsometry was used to show the presence of two T_g’s in supported polymer films for the first time. The segregation of two T_g’s in poly(2-vinyl pyridine) thin films not only becomes more apparent in ultra-thin films and at slow cooling rates, but the values of T_g,high and T_g,low follow previous trends of the effect of substrate and free surface interactions, respectively, suggesting that the length scale of this gradient can reach at least 33 nm. Additionally, cooling rate dependent T_g measurements were performed. The large gradient of dynamics present in the single T_g experiments further exhibits itself in the cooling rate studies via the lower apparent activation barrier in ultra-thin films. While additional studies must be performed to determine the temperature dependence of the relaxation times of the polymer/substrate and air/polymer interfaces, the intersection of thin film and bulk dynamics suggests that the free surface has a weaker temperature dependence which diverges from the substrate layer at lower cooling rates. Furthermore, the presence of such a large gradient of dynamics in these films motivates future work to directly measure the dynamics at the free surface and the length scales over which the dynamics are influenced by this perturbation.

See supplementary material for the ellipsometry parameters, a plot of expansion coefficient as a function of film thickness (Figure S2), a step by step visualization of the method by which expansion coefficients were determined (Figure S3), the bulk-like expansion coefficients of a 217 nm film and a 1020 nm film (Figure S4), and evidence of two distinct T_g’s in the plot of the index of refraction vs. temperature for a 16 nm film (Figure S5).

This work was supported by funding from NSF CAREER No. DMR-1350044.