Changes in the glass transition temperature (Tg) for materials confined to the nanoscale have been of considerable interest since the early 1990s when a depression was first observed for small-molecule glass formers confined in nanoporous glasses by Jackson and McKenna.1, 2 The observed depression was subsequently verified by Jonas et al.3 and Park and McKenna,4 although other work found Tg increasing in confined glass formers.5–8 The Tg depression in ultrathin polymer films9–34 is even more striking than that in materials confined to nanopores,1–4, 35–37 being as great as 75 K for unsupported polystyrene (PS) films.9, 10 Changes in Tg are important from both practical and fundamental standpoints. On the practical side, Tg dictates, for example, mechanical properties and, for many applications, the maximum use temperature of the material; this is especially important for nanotechnologies that use polymeric thin films, including advanced integrated circuits.38 On the fundamental side, changes in Tg on the nanoscale, and particularly decreases, are not readily explained in the framework of our current understanding of the glass transition.11 Hence, it is worth emphasizing that not only is the observation of a Tg reduction on the nanometer size scale surprising, but its full understanding may lead to a better understanding of the glass transition phenomenon itself. Several reviews have been written that discuss these issues in greater detail.39–42
Although the general observation is that the glass transition of thin films is depressed, reports of the magnitude of the depression depend on the measurement technique as well as the details of the sample. For example, in cases of very strong interactions between the polymer and the substrate, increases in Tg with decreasing film thickness have been reported.5–8 In addition, large differences in behavior have been observed between thin films supported on a substrate and freely standing films. The supported films do not show a dependence on the molecular weight and show a nonlinear dependence of Tg on the film thickness (h):12, 13
where T is the glass transition temperature for bulk PS and a and δ are fitting parameters. In the case of PS, the value of a was originally found to be 3.2 nm, and δ was found to be 1.8;12 subsequent measurements refined these values to 1.3 and 1.28, respectively.13 On the other hand, freely standing films appear to have a strong dependence on the molecular weight above approximately 500,000 g/mol, and Tg decreases linearly with the film thickness for thicknesses below a molecular-weight-dependent critical value.9, 10 It is clear that free surface and interface effects are important factors in determining the magnitude and direction of changes in Tg in polymer thin films;5–10, 13–19, 40, 41 however, the details of these effects are often contradictory or disputed, and a full understanding remains elusive.
The measurement of Tg for thin polymeric films has been accomplished with various techniques, including ellipsometry, Brillouin light scattering, and dielectric spectroscopy. Although differential scanning calorimetry (DSC) is often used to characterize Tg in bulk samples and has been used to measure the Tg depression of materials confined to nanopores,1–4 it has been used only by Wang and Zhou20 to the best of our knowledge for examining the Tg depression in thin polymeric films, presumably because of the time requirements for sample preparation: over 200 1-in.2 films of 20-nm thickness are required for a nominal 3-mg DSC sample. In their work, Wang and Zhou examined stacked and microtomed epoxy ultrathin films and observed a 15 °C depression in Tg without any significant change in the step change in the heat capacity at Tg (ΔCp). Recent nanocalorimetry measurements,43, 44 on the other hand, have shown neither a Tg depression nor a change in ΔCp even for PS films as thin as 3 nm, presumably because small changes in Tg and ΔCp are difficult to discern on account of the very high heating rates involved in this technique coupled with the fact that the Tg depression may decrease at high cooling rates.21 Similarly, recent ac-nanocalorimetry measurements made at 40 Hz show no discernable Tg depression for films as thin as 4 nm; whether or not changes in ΔCp occur with decreasing film thickness is less clear, but a distinct broadening of the transition can be observed as the film thickness decreases.45 In this study, the absolute heat capacity (Cp), which has not previously been reported for ultrathin polymer films, and Tg of PS thin films are measured with DSC with the step-scan method in an effort to further examine the thermodynamic behavior of glass formers on the nanoscale. The step-scan method is analogous to temperature-modulated DSC applied in the time domain; the timescale for the measurements is thus much longer than that of recent nanocalorimety43, 44 and ac-nanocalorimety45 studies. A primary advantage of the step-scan methodology is that the instrumental baseline is unimportant for the measurement of Cp because the incremental heat flow response is measured for small temperature steps.46
The PS used in this study, obtained from Sigma–Aldrich, has a number-average molecular weight of 1,998,000 g/mol and a molecular weight distribution (weight-average molecular weight/number-average molecular weight) of 1.02. The radius of gyration (Rg) is 38.7 nm.47 Four preparation methods were used to make the stacked thin films. In the first method, PS thin films were deposited by the spin coating of PS dissolved in toluene (HPLC-grade; Sigma–Aldrich) onto freshly cleaved 1-in.2 mica substrates. The film thicknesses were varied by the variation of the polymer concentration in the spin-coating solution from 0.4 to 1.5 wt %, which resulted in film thicknesses ranging from 17.3 to 97.0 nm with a standard deviation of 10% based on at least four atomic force microscopy (AFM) measurements of three samples for each spin-coating condition. After the spin coating, the films were removed from the substrate, floated on water, and collected with tweezers. The resulting freely standing films were wrinkled. These collected films were bulky and larger than the 50-μL DSC pan; however, they were easily placed into the pan with minimal force because of the fragile nature of the films. The second method differed from the first method only in that a Teflon plate was used to collect the films from the water surface to obtain an unwrinkled stack of thin films. In the third method, polyisobutylene (PIB) with a molecular weight of 1,700,000 g/mol (Scientific Polymer Product, Inc.) was used as interleaving layers between the PS thin films. PIB–PS–PIB trilayer films were made by the spin coating of a solution of 0.5 wt % PIB in HPLC-grade n-heptane (J.T. Baker) onto the mica substrate, followed by the spin coating of 0.65 wt % PS dissolved in a cosolvent of 30 wt % toluene and 70 wt % acetone, followed by the spin coating of another PIB layer from n-heptane. The PIB layer was not soluble in the toluene/acetone cosolvent used to spin-coat PS, and the PS layer was not soluble in the n-heptane solvent used to spin-coat PIB. The final trilayer sample comprised two PIB films 10.4 ± 1.5 nm thick and a PS film 59.5 ± 12.0 nm thick, for which the standard deviation is again based on multiple AFM measurements. After the spin coating, the trilayer films were removed from the substrate, floated on water, collected with a Teflon plate, and placed in a DSC pan. In the fourth method, PS was spin-coated from a 0.65 wt % solution in the toluene/acetone cosolvent and collected with the Teflon plate to have a valid comparison for the trilayer sample; the film was found to be 61 ± 8 nm thick. In addition to the thin-film samples, a bulk PS sample was studied. We also measured the absolute Cp for a bulk PIB sample to be able to subtract the PIB contribution to the absolute Cp for the PIB–PS–PIB trilayer stacked films; to subtract the PIB contribution, we had to assume a size-dependent reduction of Cp for PIB similar to that which we measured for PS, and we discuss this in more detail later.
After the thin-film samples were placed in the DSC pan, the samples were stored under the ambient conditions for 24 h and then annealed in vacuo at 50 °C and 5 Torr for about 12 h to remove any remaining residual solvent and water before the lids were crimped. To ensure that no residual solvent remained, a 3.11-mg sample collected on the Teflon plate was further annealed at 80 °C for 1 week under a vacuum of 5 Torr; no weight change within 0.01 mg was measured with an analytical balance, and no change in Tg was associated with this additional annealing. This indicated that the 12-h, 50 °C/5 Torr annealing procedure was sufficient for eliminating the residual solvent.
A PerkinElmer Pyris 1 differential scanning calorimeter in the step-scan mode with an ethylene glycol cooling system maintained at 5 °C was used to obtain absolute Cps. All measurements were made in a nitrogen atmosphere. The typical sample size for the stacked PS ultrathin films was 3 mg; this meant approximately 200–3001-in.2 films of 17-nm thickness. For the PIB–PS–PIB stacked thin films, the sample size was larger, 4.8 mg, to account for the fact that 75% of the sample was PS. The bulk samples were 2–13 mg.
The step-scan method consisted of multiple temperature ramp/isothermal steps. The step sizes were 2 K, the holds were 0.8 min at each temperature, and a 10 K/min heating or cooling rate was used between sequential isothermal hold temperatures. Measurements were performed in the temperature range from 35 to 135 °C. The majority of the data that will be shown were obtained on heating, but some data was also obtained on cooling; the differences between the Tg values obtained on cooling and heating for a given sample are less than 0.3 K. In addition, most of the results shown were performed during the second heating scan after cooling from 135 °C at 30 K/min to have a defined thermal history. The difference in the absolute Cp and Tg values obtained from the first and subsequent step scans is small and will be discussed.
The absolute Cp is obtained from the heat flow (Q̇) observed during the isothermal hold in the step-scan method:
where k is the cell calibration constant, m is the mass of the sample, and ΔT is the temperature step between isothermal hold temperatures (2 K in our method). The aluminum sample and reference pans were identical in weight (within 0.01 mg) for all runs. The difference in the heat flow measured between the sapphire run and the empty pan run under the same step-scan program yielded the heat flow versus time for the sapphire; k was then obtained from eq 2 on the basis of the known Cp of the sapphire. For the sample Cp, the heat flow was also obtained from the difference between that measured for the sample and that measured for empty pans under the same step-scan program. The measured Cp of the sapphire calibration material was reproducible, having a standard deviation of 0.2% for 14 runs. Similarly, the reproducibility (standard deviation) of Cp(T) for a given PS sample was better than 0.4% for three runs. The step-scan method was used previously in our laboratory to obtain the absolute Cps of linear and cyclic alkanes.46
Tg was obtained from the data of the absolute Cp versus the temperature using the half-height method; that is, the temperature at which Cp attained a value halfway between the extrapolated liquid and glassy values was taken to be Tg. We note that by using the step-scan method, we could avoid the enthalpy overshoot commonly observed at Tg.
The DSC temperature was calibrated with indium and a liquid-crystal CE-3 [(+)-4-n-hexyloxyphenyl-4′-(2′-methylbutyl)-biphenyl-4-carboxylate] at 0.1 K/min. We have found in other work48 that calibration at a 0.1 K/min rate is equivalent to performing an isothermal calibration, which is what is required for the step-scan method because the relevant data are obtained during the isothermal holds. The heat flow was calibrated with indium. Cp was calibrated with sapphire as described previously. The ordinate filter factor for DSC was set at 3.0.
The absolute Cp of bulk PS is shown in Figure 1 for different sample weights to verify that the step-scan method gives reliable Cp results and to examine the Cp dependence on the sample weight. For the five samples tested, ranging from 1.93 to 12.99 mg, the standard deviation in Cp is less than 0.6%, indicating that our methodology yields Cp values independent of the sample size. Also shown in the figure are the suggested values of Cp for PS based on a compilation of data in the literature by Gaur and Wunderlich,49 with the error bars showing the standard deviation of the literature data. The results of our step-scan method are in excellent agreement with the suggested values.
The absolute Cps of the PS thin films prepared by the first method (spin-coated from a toluene solution, floated on water, and collected with tweezers) are compared to those of bulk PS in Figure 2. The thin films show a significant reduction in the absolute heat capacity in the liquid state (Cpl) and the absolute heat capacity in the glassy state (Cpg). The reduction is most pronounced for the thinnest film: reductions of approximately 10% in the liquid state and 5% in the glass state can be observed for the 17-nm-thick film. ΔCp also decreases with decreasing film thickness and is reduced by 9% for the 17-nm-thick film. The decreases in Cpl, Cpg, and ΔCp with decreasing film thickness indicate that degrees of freedom are lost on confinement, as might be expected. These results are consistent with many results in the literature, though not all; our results are assessed in the context of related work in the literature in the Discussion section of this article.
In addition to the changes in the absolute Cp and in ΔCp, the value of Tg, as determined by the half-height method, also decreases with decreasing film thickness for the data shown in Figure 2: Tg is 99.1 °C for the bulk sample and decreases to 91.0 °C for the 17-nm-thick film. In addition, the breadth of the glass transition region also increases with decreasing film thickness. These results are qualitatively consistent with the majority of the literature concerning Tg in nanoconfined systems.41
The results shown in Figure 2 were obtained during the second heating scan after scanning to 135 °C and cooling at 30 K/min to 35 °C. It is expected that for such stacked films, any free surface in the initial sample arising from the wrinkled nature of the original films collected with tweezers will be lost by heating beyond Tg. However, the difference between the results obtained during the first scan and those obtained during subsequent scans is small, as shown in Figure 3 for the 61-nm-thick film. A slight increase in both the absolute Cp and Tg can be observed between runs 1 and 2, and no significant difference can be observed between runs 2, 3, and 4; this indicates that our stacked thin films maintain their thin-film morphology even after being exposed to temperatures above Tg. The fact that we do not get any significant interdiffusion between the PS layers is expected because the timescale for chain interpenetration for our 2 × 106 g/mol PS is more than 100 min at 145 °C according to a calculation based on bulk interlayer diffusion.50 In the DSC study, the maximum temperature to which the sample is exposed is 135 °C for approximately 5 min; therefore, the interpenetration time for the diffusion of PS between the layers in the stacked sample is expected to be negligible during the DSC scan. A similar conclusion can be reached using the value of 2 × 10−5 cm2/s for the self-diffusion coefficient for 2 × 106 g/mol bulk PS at 170 °C based on the work by Kramer and coworkers51 and scaling arguments.52 In this case, we estimate that 2 h at 170 °C is needed for the molecules to diffuse the distance of Rg. Interestingly, these timescales seem to severely underestimate the time required for the diffusion of polymer between the ultrathin layers in the stacked sample. No evidence of recovery back toward the bulk Tg behavior was observed even after the samples were held for 5 h at 150 °C; a similar effect, in which the time constant for interface healing increases as the film thickness decreases on the nanoscale, was observed by Forrest et al.25 On the other hand, the application of 10,000 psi in a platen press at 170 °C for 5 h in vacuo resulted in the sample recovering very nearly to the bulk behavior, as shown in Figure 4. We also show in Figure 4 that this treatment results in no change in Cp or Tg when applied to a bulk (45-μm-thick) PS sample.
The effects of the collection method of the spin-coated films after floating on water during film preparation, whether it be by the use of a Teflon plate or tweezers, are shown in Figure 5. We expected that the films collected and stacked on the Teflon plate would show slightly elevated Tgs, similar to those observed on the second scans in Figure 3, because the films are unwrinkled and make good contact with one another compared with the wrinkled films collected with tweezers. Surprisingly, however, this is not the case. Although the Cpl values agree very well between the two methods, Cpg of the plate-stacked films is higher than that of the tweezers-stacked film and Tg is 5.5 °C lower. This finding, though difficult to explain, clearly illustrates the sensitivity of the Tg depression to sample preparation techniques.
The effect of placing PIB interleaving layers between the PS ultrathin films in the stacked sample is shown in Figure 6. In this figure, a comparison is made between PS in the PIB–PS–PIB sample and a PS stacked film sample, both of which had the PS layers spin-coated from the toluene/acetone cosolvent system. For the trilayer sample, the PIB contribution was subtracted from the total to obtain Cp of the PS thin-film layers. To do this, we assumed that the 10.4-nm-thick PIB films in the trilayer had a Cp 15% lower than the bulk value for PIB (based on results for the PS films), and we measured the bulk PIB heat capacity to be Cpl,bulk PIB (J g−1 K−1) = 1.8001 + 0.0044T, where T is given in °C. In addition, it was assumed that the mass content of PS was 75% of the total (based on the PS and PIB layer thicknesses in the trilayer film and their respective densities). These assumptions seem to be reasonable, given that the liquid absolute Cps agree for the two samples. However, the results are again unexpected. The sample with the PIB interleaving, which might be expected to provide more mobility to the PS ultrathin-film layers because of its rubbery nature, shows a Tg 5 K higher than that of the film without PIB interleaving, which simply has PS–PS interfaces. In addition, the PS in the trilayer film shows a slightly increased Cpg. The results of the effects of the collecting method and the results of the effects of the interleaving layer may indicate that the interface is not the dominant factor for Tg reduction in our stacked thin-film geometry since films with nominally air–PS interfaces and rubber–PS interfaces appear to have higher Tgs than films with PS–PS interfaces.
The compilation of our results is shown in Figure 7, along with the empirical equation describing Keddie and Jones'13 supported PS thin-film data and data from Dalnoki-Veress et al.10 for unsupported thin films of 2,240,000 g/mol PS (i.e., similar to the PS used here). Our data are similar to those of the supported thin films rather than those of the freely standing unsupported thin films, even though our stacked film samples collected with tweezers might be expected to be freely standing, at least for the first DSC scan (closed circles in Fig. 7). In addition, the type of interface (PS vs PIB) and the collection method (Teflon plate vs tweezers) seem to have an impact. The data are tabulated in Table 1 for ease of comparison.
Table 1. Summary of the Film-Thickness Effects on ΔCp, Cpl, Cpg, Tg, and Tg − Tfor Different Film-Preparation Methodsa
The data were obtained from the second heating with step-scan DSC.
The mean and standard deviation based on twelve measurements are reported.
Spin-coated from a toluene solution, floated on water, andcollected with tweezers
97.0 ± 9.0
61.5 ± 4.1
38.0 ± 4.0
17.3 ± 1.7
Toluene solution; collected on Teflon
38.0 ± 4.0
Cosolvent solution; collected on Teflon; PIB interleaving
59.5 ± 12.0
Cosolvent solution; collected on Teflon
61.0 ± 8.0
The changes in the absolute Cps shown in Figure 2 are striking. To determine whether the differences in Cp between the bulk and thin-film samples are statistically significant for all of our data taken as a whole, t–tests have been performed for both Cpg and Cpl (at 50 and 120 °C, respectively), excluding the 97-nm film from either group. On the basis of the t–test using a 90% confidence interval, we find that the bulk and thin-film Cps are statistically different, with the thin-film Cps being at least 1.3 and 4.5% lower than those of the bulk for the glass and liquid states, respectively. For the confirmation of these results, the 97-nm film was also included in the bulk group and, in a separate test, in the thin-film group; the Cp values of the bulk and thin films are statistically different in all cases. On the basis of the t-test results, both Cpg and Cpl of the thin films are reduced with respect to the bulk values. Similar results, with Cpg and Cpl depressed on the nanoscale near Tg, were obtained by other researchers53 on toluene confined to nanoporous glasses, although those researchers felt that the error in their data did not warrant such an interpretation. A decrease in the relative Cp normalized to the film thickness was also observed with decreasing film thickness for PS with ac-nanocalorimetry.45 In addition, depressed Cps in both the glass and liquid states are supported by analogous depressions of the thermal expansion coefficients from positron annihilation lifetime spectroscopy22–24, 34 and neutron reflectometry,54 although some measurements10 indicate only changes in the thermal expansion coefficient in the liquid above Tg. We note, however, that a depressed Cp on the nanoscale is not expected to be universal: water shows an elevated Cp when confined to nanometer-size pores because of a density decrease resulting from the disruption of its hydrogen bonding.55, 56
In addition to the depression of the absolute Cps, ΔCp decreases with decreasing film thickness, as shown in Figure 2 and Table 1. A similar decrease in ΔCp was observed for benzoin isobutyl ether confined to nanopores35 and for salol, glycerol, and ortho-terphenyl (o-TP) in mesoporous silica,36 but changes in ΔCp were not observed for other organic small molecules under similar confinement.1 For both o-TP and PS/o-TP solutions confined to controlled pore glasses, two Tgs were observed in work by Park and McKenna,4 and the total ΔCp did not change, although ΔCp for each of the transitions was lower than the bulk value. In the case of polymers, ΔCp for the microtomed epoxy20 did not change, although the error in the measurements (±5%) was relatively large, whereas a significant decrease in ΔCp to values less than 20% of the bulk value for 2.5-nm pore sizes was observed for confined oligomeric poly(propylene glycol).37 Similar changes in the strength of the glass transition at the nanoscale have been observed for polymer ultrathin films with various other methods, including ellipsometry, fluorescent probe intensity, dielectric relaxation, and positron annihilation spectroscopy;10, 13, 16, 22–24, 34, 45 similar decreases in ΔCp were also observed in polymer nanocomposites as the length scale between the particles decreased.57
Our results clearly show Tg depressions in the absence of free surfaces in our stacked PS thin-film samples for both PS and PIB interfaces. In addition, we see very little effect between the scans of the wrinkled films, which we assume to have free (air) surfaces, and subsequent scans after the films have lost their free surfaces via heating beyond Tg. An assumption of our experimental approach is that each freely standing thin film in the DSC sample of stacked wrinkled films maintains its thin-film morphology during the first DSC scan. However, the Tg difference between the first and subsequent DSC runs is small, less than 2 °C, as shown in Figure 3. It is possible that the free surface disappears during the run, that is, as Tg is approached, and this results in an inability to measure Tg for the wrinkled films. Arguments against this possibility include the fact that Cpg of the first wrinkled film run shown in Figure 3 is slightly higher, rather than lower, than that of the second run; on the basis of our results, one would expect a concomitant decrease in Cpg with a depression in Tg. In addition, microscopy studies of 37-nm-thick films confirm that no change in the wrinkled morphology occurs up to 65 °C (the upper temperature limit for our hot stage due to vibrations at higher temperatures) during the first heat-up and that the morphology differs after the temperature goes above Tg; we note that 65 °C is still considerably higher than the Tg value obtained by Dalnoki-Veress et al.10 for freely standing films of this thickness and molecular weight.
The seemingly small effects of the free surface on Tg in our results seem to be at odds with experiments in which films are stacked and annealed, such as those in the work of Ellison and Torkelson,16 in which Tg gradients were investigated, and in the work of Sharp and Forrest,19 in which the Tgs of supported thin films having their free surfaces capped with Al or Au were the same as those of the bulk. They are consistent, though, with the earlier work of Forrest et al.26 on supported films, in which no significant differences between PS thin films on SiOx with one free surface and those on SiOx capped with an SiOx layer were found, although the artifacts potentially introduced by vapor deposition were recently discussed by Sharp and Forrest.19
We also note that the Tg and ΔCp depressions that we observe with decreasing film thickness by calorimetry differ from the results of recent nanocalorimetric measurements43–45 in which no changes were observed (although in ref.45, a change in Cp was found, and the issue of ΔCp is difficult to address because of the increasing breadth of the transition). The differences may be attributed to the timescales relevant to the different measurement techniques. In our work, 2 K temperature jumps are performed every minute, whereas the heating rate is on the order of 1–2 K/ms for cooling through Tg in Allen and coworkers' nanocalorimetric studies,43, 44 and the measurement frequency in the ac-nanocalorimeter is 40 Hz;45 hence, the nanocalorimetric works in the literature employ timescales 3 to 5 orders of magnitude shorter than that used in this work. In fact, Fakhraai and Forrest21 recently reported that the Tg depression in thin PS films depends on the cooling rate, thereby explaining the lack of agreement between the majority of the literature and the recent nanocalorimetry studies performed at much higher cooling rates or measurement frequencies.
Film-preparation techniques have an important influence on the measured Tg depression. For example, a 5.5 °C difference was observed between samples collected during film preparation with a Teflon plate versus samples collected with tweezers. These differences occurred despite the films being annealed for 12 h in vacuo at 50 °C, and they persisted even after multiple DSC scans were made to 135 °C. We have no reason to believe that the differences can be attributed to differing small amounts of residual solvent in the samples because no changes were observed in either Tg or the sample weight for a sample annealed at 80 °C in vacuo for 1 week. However, we also offer no explanation for these observations; we only caution experimentalists to be aware of the possible influence that sample preparation may have on the Tg depression in thin polymer films.
The absolute Cp and glass transition behavior of stacked PS thin films has been measured with the step-scan DSC method. Cpg and Cpl decrease with decreasing film thickness, ΔCp decreases with decreasing film thickness, and Tg also decreases with decreasing film thickness. The depression of Tg is 8.1 °C for a 17-nm-thick film spin-coated from toluene, floated on water, and collected with tweezers. Significant Tg depressions have been observed in our stacked thin-film geometry for films with PS–PS and PS–PIB interfaces, and we find that Tg increases less than 2 °C after the first DSC scan for wrinkled films having free surfaces. These two results indicate that the Tg depression in our stacked thin films is not due to free surface effects. Importantly, the behavior is reversible, and the bulk behavior of Cp and Tg is recovered by the application of 10,000 psi at 170 °C for 5 h in vacuo in a platen press; however, the timescale for interlayer diffusion in the stacked film sample is longer than that expected on the basis of the timescales for the self-diffusion of bulk PS in the literature, despite the depression of Tg. Film-preparation techniques have been found to have an important influence on the measured Tg depression: significant differences have been observed for samples collected during film preparation with a Teflon plate versus samples collected with tweezers and for samples prepared from different spin-coating solution solvents.
The authors gratefully acknowledge funding from the National Science Foundation (DMR 0304640).