Depth-dependent inhomogeneous characteristics in supported glassy polystyrene films revealed by ultra-low x-ray reflectivity measurements

ABSTRACT This study reports X-ray reflectivity measurements of the glass transition of polystyrene thin films supported on Si substrates and heated at low heating rates that ranged from 0.14

to 0.01 °C min−1. At a heating rate of 0.14 °C min−1, the glass transition temperature _T_g was independent of the film thickness down to a thickness of 6 nm. However, at a heating rate of

0.04 °C min−1, the value of _T_g decreased with decreased thickness. The reduction in _T_g was most significant at the ultra-low heating rate of 0.01 °C min−1. Furthermore, with decreased

film thickness, the linear thermal expansivity in the glassy state _α_glass slightly decreased at a heating rate of 0.14 °C min−1, whereas _α_glass exhibited a significant increase at the

ultra-low heating rate of 0.01 °C min−1. Reconstructed depth profiles of thermal expansivity, which were obtained by fitting the _α_glass values using an integral model, indicated a decrease

in the thickness of the interfacial dead layer with a decrease in the heating rate, whereas the volume fraction of the free surface region increased under this condition. The observed

reduction in _T_g can be attributed to surface and interface effects perturbing the glass transition dynamics of the thin films under slower probing conditions. SIMILAR CONTENT BEING VIEWED

BY OTHERS KINETICS AND MORPHOLOGIES OF SYNDIOTACTIC POLYSTYRENE CRYSTALLIZED ISOTHERMALLY OVER A WIDE TEMPERATURE RANGE Article 28 March 2023 SURFACE AND INTERFACIAL AGGREGATION STATES IN

THIN FILMS OF A POLYSTYRENE/POLYROTAXANE BLEND Article 19 March 2025 THE EFFECT OF ULTRASMALL GRAIN SIZES ON THE THERMAL CONDUCTIVITY OF NANOCRYSTALLINE SILICON THIN FILMS Article Open

access 23 July 2021 INTRODUCTION In polymer thin films, the properties in regions near interfaces differ from the bulk properties. To date, several studies have reported the presence of a

distinct region near the free surface that is characterized by reduced _T_g and enhanced mobility.1, 2, 3, 4, 5 These differences are often attributed to the special circumstances of polymer

thin films that result in lowered activation barriers for molecular rearrangements. However, the region near the substrate interface is expected to have an increased _T_g with lowered

mobility because the molecular chains are pinned onto the substrate via interactions between the molecules and the substrate.6, 7, 8, 9, 10 Although the glass transition behavior of polymer

thin films appears to be understood, there is no indication that the study of this issue has ceased over the past two decades. As mentioned earlier, several studies have reported reductions

in _T_g and enhancements in the surface mobility of ultrathin supported films,11, 12 whereas few studies claim thickness independence of _T_g in glassy polymer thin films.13, 14, 15, 16, 17,

18 In addition, few studies have reported that the _T_g of polystyrene (PS) films decreases with decreasing thickness, whereas the linear thermal expansivity in the glassy state _α_glass

has been reported to increase under such conditions.1, 19, 20 This phenomena can be explained by assuming that the increase in _α_glass is related to the enhanced mobility in the region near

the free surface. However, a few other experimental studies21, 22, 23, 24 have indicated that _α_glass is either independent of the film thickness or exhibits a decreasing trend with

decreasing thickness, which is accompanied by a reduction in _T_g. A significant decrease in _T_g has been observed in thin, freestanding PS films, in which _α_glass is reportedly

independent of the film thickness4 or tends to decrease with decreasing thickness.25 Furthermore, atomic force microscopy analysis26 of the region near the free surface with gold nanospheres

embedded in the PS surface has indicated that the temperature-dependent relaxation time of the free surface region ranges from a few thousand seconds at room temperature to being on the

order of seconds at temperatures near the bulk _T_g. Optical photobleaching studies27 have indicated that the thickness of the mobile layer at the region near the free surface increases with

temperature. Moreover, the properties at the region near the free surface depend not only on the temperature but also on the heating and cooling rates. For the region near the substrate

interface, dewetting experiments28 have suggested that film rupture strongly depends on its thermal history, especially the aging time, thus indicating that the relaxation time of supported

films is significantly long and has an unusual temperature dependence, even for the relatively weak interactions between the film and the substrate. The _T_gs of thin PS films at various

cooling rates have been effectively measured via ellipsometric and calorimetric methods.29, 30 According to these studies, _T_g decreases with decreasing thickness, with the reduction in

_T_g being significantly higher with decreases in the cooling rate. In our recent study,31 we demonstrated a significant reduction in _T_g at a relatively slower cooling rate of 0.01 °C 

min−1, and the width of the glass transition _w_ was found to decrease with decreases in the cooling rate. These results clearly indicated that unique confinement effects can be notably

observed at very low heating and cooling rates or at low frequencies. In the present study, we have investigated the thickness and temperature dependence of _T_g and _α_glass in supported PS

films via X-ray reflectivity (XR) at low heating rates ranging from 0.14 to 0.01 °C min−1. We have reanalyzed our previously published data32 to obtain deeper insights on the thickness and

rate dependence of the glass transition temperature of supported PS films and to show a reconstructed novel depth profile of linear expansivity. Our results indicate a slight decrease in

_α_glass at a heating rate of 0.14 °C min−1, whereas we observed a significant increase in _α_glass at an ultra-low heating rate of 0.01 °C min−1. The reconstructed depth profiles of the

thermal expansivity obtained by fitting the obtained _α_glass values with an integral model indicate a change in the relaxation process over the entire film from the free surface to the

substrate interface. EXPERIMENTAL PROCEDURE In this study, atactic PS (Polymer Source Inc., Montreal, QC, Canada) with a molecular weight of _M_w=5.4 × 104 g mol−1 (_M_w/_M_n=1.04, _R_g∼6 

nm) was used to prepare PS films. In a typical process, a predetermined quantity of PS was dissolved in toluene to form the precursor solution, which was subsequently spin coated onto a Si

(100) wafer that was covered with a native silicon dioxide layer. The spin-coating process was performed at a speed of 4000 r.p.m. for 50 s. The thickness of the PS film was controlled by

varying the concentration of PS dissolved in toluene (0.11 × 10−2, 0.16 × 10−2, 0.35 × 10−2, 1.0 × 10−2 and 2.0 × 10−2 g mol−1 for 4, 6, 12, 25 and 60 nm films, respectively). The

spin-coated films were annealed in a low vacuum at 127 °C (_T_g(bulk)+27 °C) for 12 h and subsequently cooled to room temperature over a time period of 4 h. Before XR data acquisition, the

surface topography of the films was observed using atomic force microscopy. Later, specular XR measurements were performed using a high-resolution four-circle X-ray diffractometer equipped

with a Ge (200) crystal monochromator (0.15406 nm (CuK_α_1 radiation); SLX2000+Ultra-X, Rigaku Co., Akishima, Japan). Data were acquired for 25 min at each isothermal step, and the XR curve

was collected under a dry nitrogen atmosphere. The sample temperature was controlled using a homemade heater coupled with a thyristor regulator (SU12AM241-MSNNNN, CHINO, Tokyo, Japan) that

was capable of controlling the temperature with an accuracy of ±0.2 °C. Following the XR measurements at a certain temperature, the sample was heated in 5 °C increments with a constant

heating rate (0.5, 0.05 and 0.01 °C min−1) from room temperature to 130 °C. Taking into account the XR data acquisition time and the cooling time, the average (actual) heating rates during

the heating process were estimated to be 0.14, 0.04 and 0.01 °C min−1, respectively. The XR data were fitted using Parratt formalism by assuming a three-layer model comprising air, a PS

layer and a Si substrate. From the XR data, the thickness of the PS film was determined with an accuracy of 0.01 nm. The details of the analysis have been previously described.32, 33 RESULTS

Figure 1 illustrates the temperature dependence of the normalized thicknesses that were obtained at heating rates of 0.14 °C min−1 (open circles), 0.04 °C min−1 (open squares) and 0.01 °C 

min−1 (open triangles). The initial thickness values measured at room temperature were ∼60 nm (Figure 1a), 24 nm (Figure 1b), 12 nm (Figure 1c) and 6 nm (Figure 1d). The solid curves shown

in Figure 1 are the fitted curves obtained by assuming the ‘tanh’ profile approximation:4 where _w_ and _c_ represent the width of the glass transition and the thickness at _T_=_T_g,

respectively. _M_ and _G_ correspond to the curve’s slope, extrapolated to the lowest and highest temperatures, respectively, which could be estimated separately by applying a linear fit to

the data in both the rubbery and glassy regimes. The values of _M_ and _G_ are regarded as constants in the fitting procedure for obtaining _w_, _c_ and _T_g using Equation (1). The dashed

lines in Figure 1 correspond to the linear fits of the slope equal to _M_ or _G_. The intersection of the dashed lines corresponds to _T_g. As observed in Figure 1a, the _T_g value of the

60-nm-thick PS films was apparently shifted to lower temperatures with decreases in the heating rate (the arrows denote the _T_g values). The heating rate dependence of _T_g was also

confirmed in Figures 1b and c. A significant reduction in the _T_g value was observed in the 6-nm-thick PS films (Figure 1d), where _T_g decreased from 92±2 to 60±2 °C when the heating rate

was decreased from 0.14 to 0.01 °C min−1. The values obtained are summarized in Table 1, and these results clearly indicate that the magnitude of the _T_g reduction was notably larger for

thinner films compared with thicker films. In addition, the thermal linear expansivity in the rubbery state _α_rubber and that in the glassy state _α_glass, which correspond to the values of

_G_ and _M_ in Equation (1), respectively, are also listed in Table 1. At temperatures above _T_g, the value of _α_rubber appears to be independent of the heating rate for all of the films,

with the exception of the film with the lowest thickness of 6 nm. With decreases in film thickness, the value of _α_rubber increased, which was consistent with the trend reported in

previous studies.20, 34 At temperatures below _T_g, the value of _α_glass for the 60-nm-thick film at a heating (an unexpectedly small _α_glass is observed at a heating rate of 0.04 °C min−1

(Figure 1c), which can be considered as an effect of insufficient thermal treatment of this sample) rate of 0.14 °C min−1 was determined to be 1.6 × 10−4 °C−1, which is in good agreement

with previously reported values.21, 23 In the case of thicker films (∼60 and 24 nm), no remarkable increase in the value of _α_glass was observed with decreases in the heating rate. This

result is again consistent with the _α_glass value reported for 70-nm-thick films of molecular weight 2.34 × 105 g mol−1 measured at heating rates of 0.5 and 0.01 °C min−1.32 However, in the

case of the thinner films (∼12 and 6 nm), the _α_glass value was found to increase with decreases in the heating rate. DISCUSSION Figure 2 illustrates the temperature dependence of the _T_g

of PS films obtained at various heating rates. The solid curves correspond to the fitted values obtained using the following equation: which can be referred to as a ‘three-layer model’

developed from the widely accepted empirical expression _T_g(_h_)=_T_g(∞)[1−(_A/h_)γ] that is conventionally used to describe the _T_g reduction in thin polymer films. Here, _T_g(∞) and

_T_g(_h_) represent the glass transition temperatures of a bulk and thin film, respectively; _h_ is the film thickness; _A_ and _B_ are the characteristic length scales corresponding to the

reduction in _T_g depression and the increase in _T_g, respectively; and _γ_1 and _γ_2 are dimensionless exponents. The _T_g obtained at a heating rate of 0.14 °C min−1 appeared to be

independent of the film thickness, and the _T_g obtained at a heating rate of 0.04 °C min−1 tended to decrease with decreasing thickness. A significant reduction in _T_g was observed at an

ultra-low heating rate of 0.01 °C min−1. From the data measured at a heating rate of 0.14 °C min−1, the best-fit parameters were obtained as _T_g(∞)=94.0±0.5 °C, _A_=0.2±0.1 nm,

_γ_1=1.4±0.3, _B_=0.4±0.3 nm and _γ_2=1.8±0.2. Upon decreasing the heating rate, the parameter _A_ increased, whereas the parameter _B_ decreased, as indicated in the inset presented in

Figure 2. This behavior corresponds to the change in _T_g observed under the slow heating processes. The _T_g reduction of free-standing films with decreasing thicknesses was much steeper

than that of the supported films obtained at rates of 0.14 and 0.04 °C min−1, suggesting that the molecular chains confined in the substrate region greatly influence the _T_g reduction.

However, at an ultra-low heating rate, the _T_g reduction of the supported films became noticeable, and the _T_gs of supported films with several nm thicknesses observed at 0.01 °C min−1

were comparable to the _T_gs of free-standing films with a thickness of ∼30 nm. Figure 3 shows the variations in _α_glass obtained at the various heating rates. At a heating rate of 0.04 °C 

min−1, a slightly larger value of _α_glass was estimated for the film with the lowest thickness of 6 nm. However, at a heating rate of 0.14 °C min−1, the value of _α_glass slightly decreased

with thickness, which is similar to the XR results reported in the literature,23 although _α_glass exhibited less significant changes in the present results. Furthermore, at an ultra-low

heating rate of 0.01 °C min−1, a significant increase in _α_glass was observed, and this trend qualitatively agrees with the ellipsometric measurements previously reported.1, 20 The

dash-dotted curve in Figure 3 corresponds to the data obtained by fitting a two-layer model 1 to the data obtained at a heating rate of 0.01 °C min−1. The corresponding best-fit parameters

were , and _ξ_=(7.2±0.4) nm, which are consistent with the values reported in Keddie _et al._1 These results suggest that enhanced mobility in the region near the free surface can be

achieved, especially at ultra-low heating rates. The solid curves in Figure 3 correspond to the fitted results obtained using an integral multilayer model:35 where 〈_α_(_h_)〉 is the average

thermal expansivity value of the film; _L__α_(_X_) is a profile function of expansivity, which depends on the distance from the solid substrate _X_; and _w_(_X_) is the weight function,

which was assumed to be unity in this study. For the supported films, _L__α_(_X_) in the glassy state can be defined as35 where and are the fixed expansivities of the glassy and rubbery

states of bulk PS, respectively. Both of these values are consistent with the values reported in the literature.19, 21 In the equation above, the parameter _δ_I represents a characteristic

length scale in the immobilization region near the solid substrate, where the polymer segments are pinned onto the substrate to form a dead layer that is characterized by severely reduced

thermal expansivity. With an increase in _X_, the pinning effect decreases, and the polymer chains consequently exhibit properties similar to those observed in bulk polymers. In addition,

the parameter _λ_I represents a characteristic length scale that indicates the region devoid of the pinning effect.35 The parameter _δ_S represents the thickness of the region with enhanced

mobility near the free surface that has a thermal expansivity of . The parameter _λ_S reflects a perturbation length scale, within which the enhanced mobility can propagate into the interior

of the PS film. In this model, the buried interfacial region of thickness _δ_I is responsible for the decrease in expansivity. The average value of thermal expansivity in the glassy state

of thin films with a thickness of _h_>(_δ_I+_δ_S), (<_α_(_h_)>glass) is readily obtained from Equations (3) and (4) as follows: The insets in Figure 3 show the fitted values of _δ_s

and _λ_s. As shown in the upper inset, a decrease in the heating rate resulted in a decrease in _δ_I (full circles) and an increase in _δ_S (full triangles). In contrast, as shown in the

lower inset, a decrease in the heating rate resulted in a slight increase in _λ_I (full circles) and a significant increase in _λ_S (full triangles). All of the fitted parameters are listed

in Table 2. The heating rates can be correlated with relaxation times by assuming from posteriori knowledge that a rate of temperature variation of 10 °C min−1 corresponds to a relaxation

time of ∼100 s for polymers in the glassy state.29, 36 In Figure 4, the heating rates have been directly converted to the relaxation time using this relationship, and the _δ_Ss values (solid

squares) represent the thickness of the mobile surface layer. The triangles and circles in Figure 4 correspond to the thickness of the surface layer at a temperature near the bulk _T_g

(triangles: 94 °C) and at room temperature (circles: 26 °C), which was estimated by embedding gold nanoparticles into the free surface of PS.26 When the temperature lies between _T_RT and

_T_g(bulk), any data for the mobile surface layer thickness that is labeled according to the relaxation time should lie in the region between the solid curves (the hatched region indicates

_T_RT<_T_<_T_g(bulk)). Because the temperature is between _T_RT and _T_g(bulk), the heating rate-dependent _δ_S values obtained in this study (solid squares in Figure 4) are quite

reasonable. Moreover, the _δ_Ss values are also consistent with previously reported values,27 in which the thicknesses of the surface layer were calculated to range from 0 to 4 nm when the

temperature increased from 47 to 94 °C. Figure 5 illustrates the reconstructed profiles of _L__α_(_X_)glass that were calculated from the fitted parameters. These data provide deeper insight

into the thermal expansivities in PS films with thicknesses comparable to the end-to-end average distance of the molecular chains. At a heating rate of 0.14 °C min−1 (Figure 5a), we

observed a 5-nm-thick dead layer with zero expansion near the substrate (0<_X_<5 nm) and an ultrathin region near the free surface with the most enhanced expansivity (11.5 

nm<_X_<12 nm). Between them, there exists a 6-nm-thick region that has the same expansivity as the bulk PS. When the heating rate was decreased (Figure 5b), the thickness of the

interfacial dead layer (0 nm<_X_<3 nm) decreased, whereas that of the free surface region (10.5 nm<_X_<12 nm) increased. At an ultra-low heating rate of 0.01 °C min−1 (Figure

5c), the reconstructed thermal expansivity profile continuously decreased with decreases in _X_, in contrast to the step-like profile shown in Figure 5a. The trend observed in the

reconstructed thermal expansivity profiles, which were obtained using the multilayer model, strongly suggests that the polymer segments in the region near the substrate can relax under the

ultra-low temperature variations. Furthermore, it suggests that the effects of enhanced mobility in the region adjacent to the free surface are only observable on very long time scales,

which leads to an increase in the average thermal expansivity as well as a reduction in the _T_g value of the film. The negligible thickness dependence of _T_g at a heating rate of 0.14 °C 

min−1 is consistent with previously reported results,15 as there was no reduction in the _T_g value of PS at a conventional temperature variation rate (2 °C min−1) with decreases in the

thickness to 10 nm. To analyze this result, the following two modes of relaxation were considered: (1) a segmental mode resulting from the configurational translations of a few monomer

segments and (2) a normal mode associated with fluctuations in the end-to-end distance of the molecular chains.15 The negligible thickness dependence of _T_g can be attributed to the weak,

short length-scale free surface effect on cooperative motion,15, 37 which can be verified from the step-like profile with small _δ_S seen in Figure 5a. Nonetheless, several studies,

including those associated with free-standing films showing reductions in _T_g around a heating rate of 0.5 °C min−1,4, 25, 38 contradict the result at 0.14 °C min−1 that was obtained in the

present study. One reason for this discrepancy may be the stepwise variation in temperature when the samples were held isothermally for some time for the XR data acquisition (∼20 min) and

then subjected to continuous temperature variation at a constant rate to reach the target temperature. However, the trend of a large reduction in _T_g at slower rates qualitatively agrees

with several ellipsometric measurements.1, 20 The characteristics of polymer chains at interfaces strongly depend on their thermal history. During the spin coating process, polymer segments

might have established intimate contact with the substrate, and consequently they may have tended to deviate from the natural configuration of the molecular chains. Furthermore, the

postannealing treatment under vacuum eliminates residual solvent, thereby leading to a more relaxed configuration in the sample. However, realizing a fully relaxed configuration is almost

practically impossible, especially at the deeply buried interface. Furthermore, the dewetting experiments performed by Reiter _et al._28 indicated the presence of persistent residual stress

in the region near the substrate interface, where the relaxation time was significantly longer. Remarkably lower heating or cooling rates might encourage the molecular chains in the

interfacial region to form more relaxed configurations that typically require longer time. The reconstructed thermal expansivity profiles presented in Figure 5 support this perspective. At

lower heating rates, a slow relaxation peculiar to the bulk glass-like region gradually proceeds toward the solid substrate. This process causes a decrease in the dead-layer region, which is

characterized by zero-_α_glass, while also increasing the thickness of the mobile layer at the free surface. The explanation for the observed reduction in _T_g at the lower heating rates of

0.04 and 0.01 °C min−1, shown in Figure 3, can thus be twofold—namely, the decrease in _δ_I and the increase in _δ_S. As evident from Figure 5a, the aforementioned effects would not cause a

reduction in _T_g at the rate of 0.14 °C min−1. CONCLUSIONS We have performed long-time measurements to evaluate the glass transition of PS thin films supported on Si substrates at various

heating rates using XR. At a heating rate of 0.14 °C min−1, the glass transition temperature _T_g was found to be independent of the film thickness down to a thickness of 6 nm. However, at a

lower heating rate of 0.04 °C min−1 and an ultra-low heating rate of 0.01 °C min−1, _T_g was found to decrease with decreasing thickness. Furthermore, with decreasing thickness, the linear

thermal expansivity of the glassy state _α_glass decreased slightly at a heating rate of 0.14 °C min−1, whereas it increased at the lower heating rates of 0.04 and 0.01 °C min−1. Moreover,

reconstructed depth profiles of thermal expansivity were obtained by fitting the obtained _α_glass values to an integral model. The reconstructed depth profiles indicated that the length

scale of the interfacial dead region decreases with decreases in the heating rate, whereas the thickness of the mobile surface layer increases. These results directly explain the confinement

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(2011). Article  CAS  Google Scholar  Download references ACKNOWLEDGEMENTS This study was financially supported by the Japan Society for the Promotion of Science (Grant-in-Aid for

Scientific Research(C) 24560033). AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai, China Chunming Yang * Department

of Physics, School of Science and Technology, Kwansei Gakuin University, Sanda, Japan Kohei Ishimoto, Syunsui Matsuura, Naoki Koyasu & Isao Takahashi Authors * Chunming Yang View author

publications You can also search for this author inPubMed Google Scholar * Kohei Ishimoto View author publications You can also search for this author inPubMed Google Scholar * Syunsui

Matsuura View author publications You can also search for this author inPubMed Google Scholar * Naoki Koyasu View author publications You can also search for this author inPubMed Google

Scholar * Isao Takahashi View author publications You can also search for this author inPubMed Google Scholar CORRESPONDING AUTHORS Correspondence to Chunming Yang or Isao Takahashi. RIGHTS

AND PERMISSIONS Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Yang, C., Ishimoto, K., Matsuura, S. _et al._ Depth-dependent inhomogeneous characteristics in supported glassy

polystyrene films revealed by ultra-low X-ray reflectivity measurements. _Polym J_ 46, 873–879 (2014). https://doi.org/10.1038/pj.2014.80 Download citation * Received: 29 April 2014 *

Revised: 17 July 2014 * Accepted: 17 July 2014 * Published: 10 September 2014 * Issue Date: December 2014 * DOI: https://doi.org/10.1038/pj.2014.80 SHARE THIS ARTICLE Anyone you share the

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