Article pubs.acs.org/Macromolecules
Glassy Dynamics of Polymers with Star-Shaped Topologies: Roles of Molecular Functionality, Arm Length, and Film Thickness Bradley R. Frieberg,†,‡ Emmanouil Glynos,⊥ Malvina Stathouraki,# Georgios Sakellariou,# and Peter F. Green*,†,‡,§,∥ †
Department of Macromolecular Science and Engineering, ‡Biointerfaces Institute, §Department of Materials Science and Engineering, and ∥Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States ⊥ Institute of Electronic Structure and Laser, Foundation for Research and Technology − Hellas, P.O. Box 1385, Heraklion, Crete GR 71110, Greece # Department of Chemistry, National and Kapodistrian University of Athens, Panepistimiopolis, Zografou, 15771 Athens, Greece ABSTRACT: Structural relaxations of a substance quenched to a temperature Tage below its glass transition temperature Tg enable the structure of the substance to approach equilibrium. This phenomenon, also known as physical aging, has been studied for many decades in bulk linear-chain polymer systems, where the aging rates are generally, to first order, independent of chain length. More recently, the phenomenon has been of keen interest in thin films, where the aging rate is shown to be film thickness H dependent, for films in the thickness range of nanometers to a few hundred nanometers. We show here, based on a study of polystyrene star-shaped polymers of a wide range of functionalities 2 ≤ f ≤ 64 and arm molecular weights Marm, that in the limit of sufficiently large values of Marm the aging behavior is similar to that of linear chainsindependent of Marm and f. More importantly, in the limit of sufficiently small Marm and large f, the aging rate is independent of film thickness. Otherwise, the rate is a nonmonotonic function of f, for constant Marm and H. We present a general physical picture that rationalizes the H, f, and Marm dependencies of the aging rates of these star-shaped macromoleculesthis behavior may be entirely understood in terms of Tage − Tg(x), where Tg(x) is the Tg at distance x from an interface and is a function of H, Marm, and f.
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mechanism.14−18 Different mechanisms associated with the internal annihilation of vacancies,2,7,15,19,20 and the escape of free volume from the external interfaces,11 have been proposed. The latter mechanism is important for films in the micrometer thickness, which are shown to age faster than their bulk analogues.3,12,15,18,21 Models that account for a contraction of the “lattice” have also been proposed to describe timedependent changes in free volume associated with aging in the bulk.22,23 To date, there still exists no universally accepted mechanisms by which aging in bulk polymers occur. More recently, there has been an interest in thin films, where the aging of linear chain thin films is dependent on film thickness (in the range of tens to hundreds of nanometers), due to the effect of external interfacesfree surface and substrate on the segmental packing and associated local free volume. Physical aging rates are therefore not uniform in thin films and depend locally on the differences between Tage and the local depth-dependent Tg’s, Tg(x), within the film. Recall that in the bulk the rate depends on Tg − Tage, with Tg defined at the average glass transition temperature of the material. Gas permeability studies of films with thicknesses ranging from tens
INTRODUCTION Structural relaxations and physical aging, occurring at temperatures T < Tg, where Tg is the glass transition temperature of the substance, are responsible for time-dependent changes of physical properties, including the specific volume, thermal conductivity, gas permeability, and optical properties, in glassforming materials.1−5 At a temperature T = Tage < Tg, the material possesses excess free volume and attempts to reach equilibrium via a structural relaxation process.1−5 As such a substance approaches equilibrium, its specific volume, v(t), is known to exhibit a sigmoidal dependence on aging time, tage.5 Specifically, v(t) exhibits an initial plateau, followed by an intermediate regime where v(t) ∼ log(tage),5−7 and subsequently the third and final (plateau) regime, the terminal response. The onset of the terminal response increases with decreasing Tage and may range from hours to weeks, or considerably longer. Physical aging is believed to be accommodated by local segmental relaxations−structural relaxations.8 The excess free volume is spatially distributed throughout the sample, with regions of high and low fractional free volume.3,9 The aging rate is known to depend on macromolecular topology (stars, chain, rings), stiffness of the backbone, the side groups, and the cohesive energy densities.9−13 During aging it has been suggested that free volume migrates via a vacancy diffusion © XXXX American Chemical Society
Received: January 16, 2017 Revised: April 11, 2017
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DOI: 10.1021/acs.macromol.7b00091 Macromolecules XXXX, XXX, XXX−XXX
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increases, with constant arm length, the arms necessarily experience increasing entropic losses because the arms are forced stretch due to steric effects associated with the large number of arms. In fact, molecules of low Marm and high f are packed in a manner similar to that of soft colloidal particles, which has the effect of reducing the number of segments in contact with the external “walls”.45,46,49−53 Under these spherelike packing conditions, the deformation cost for interacting with an external substrate offsets the entropic gain from adsorption onto the substrate. This behavior is manifested in physical properties, including mechanical properties,48 wetting and dewetting,45,46 and the glass transition,43,44,54 with varying the parameters f and Marm.10,37,47 Of specific interest in this paper is the fact that the glass transition of thin films of molecules with star-like molecular topologies are functions of f and Mnarm.43,44 An obvious challenge would be to understand how the entropic packing effects in thin films would influence the physical aging. What general rules would be uncovered that would codify the behavior of star-shaped macromolecules of varying f and Marm. The aging behaviors of thin films (50 nm < H < 1 μm) of starshaped polymers of 2 < f ≤ 64 and 1 kg/mol < Marm ≤ 140 kg/ mol were investigated. The picture that emerges is that for large arm lengths and moderate functionalities the aging behavior was similar to linear chain PS. However, in the regime where the molecules are packed like soft colloids, the aging rates exhibited no thickness dependence. In the regime where the molecules experience increasing losses in entropy to accommodate the interactions with the “walls” the aging rate decreased with increasing f, for constant Marm. However, when f continues to increase the trade-off between the energy gains from interacting with the walls are offset by the deformation cost of the molecule, the aging rates no longer increase with increasing f; instead, they exhibit a decreasing trend. Eventually in the colloidal limit, the aging rate is independent of film thickness. We show that the aging rates of these molecules in thin films are reconciled in terms of differences between Tg(x) and Tage.
of nanometers to several hundred micrometers reveal the role of thickness-dependent aging phenomena on gas transport.22,23 For films with thicknesses on the order of hundreds of nanometers, it was demonstrated that as the film thickness decreased the permeability decreased, suggesting an increased aging rate with decreasing film thickness.24,25 These data were rationalized in terms of a free volume diffusion mechanism, where the free surface acts as “sinks”. Differential scanning calorimetery (DSC) studies of thin freely standing polystyrene films yield similar conclusions about the thickness-dependent aging behavior.26 Recent advances in DSC techniques have led to the ability to probe single free-standing polymer films27,28 and also probing the long-term aging behavior at even lower temperatures.29,30 It has also been demonstrated in a series of recent works the importance of internal stresses and quench conditions and how they relate to comparison between freestanding and supported films.31−33 The foregoing results, however, cannot be entirely reconciled with other aging studies. Specifically, fluorescence spectroscopy34,35 and spectroscopic ellipsometry36−38 studies indicate that linear chain poly(methyl methacrylate) (PMMA) and polystyrene (PS) thin films of similar thicknesses both exhibit aging rates that decrease with decreasing film thickness. This observation is compounded by the fact that PS and PMMA films, supported by oxidized silicon (SiOx/Si) substrates, exhibit substantially different overall trends of their thickness (and depth) dependent Tg’sthe Tg for PS/SiOxSi systems decreases with decreasing H whereas for PMMA/SiOx/Si systems the Tg increases with increasing film thickness.34,39−43 This aging behavior has been rationalized in terms of a driving force determined by the differences between the local Tg (i.e., Tg(x)) and Tage. Because the local Tg varies with depth away from an external interface, the driving force varies locally within the sample. Consequently, the aging rates would be film thickness dependent.36,37 The natural question that follows is whether the local Tglocal − Tage is the most appropriate parameter that dictates aging rates of polymer films, particularly when the films possess different molecular topologies. A critical assessment of this proposal could be accomplished by investigating the aging behavior of polymers with different molecular topologies. Star-shaped polymers would represent an excellent test case because the local thickness-dependent glass transition temperatures of these materials also depend on their molecular functionalities f and their arm lengths−molecular weights Marm.43,44 Recall that relative intermolecular interactions between the chain segments and an external interface are known to influence the average glass transition Tg(H) of a film of thickness H and the local glass transition Tg(x) at a depth x below an external interface. When the segment/ interface interactions are strong (e.g., hydrogen bonding), the local Tg at the interface is higher than the bulk (e.g., PMMA on SiOx). Because the Tg at the free surface is lower than the bulk, the average Tg of a sufficiently thin film of thickness H, Tg(H), is higher than the bulk. Weaker van der Waals interactions between the chain segments and the substrate, as is the case for PS/SiOx, have the opposite effect; Tg(H) is less than the bulk Tg. With regard to star-shaped molecules, entropically driven interactions change significantly with f and Marm. Stars suffer lower entropic losses upon adsorption onto a “wall” than linear chains of the same degree of polymerization and of identical chemical structure.10,37,43−48 An entropically driven attraction between the molecule and a “wall” increases with increasing f, for a constant Marm. As the number of arms per molecule
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EXPERIMENTAL SECTION
Using procedures described in ref 37,44 a series of high functionality star-shaped polystyrenes were synthesized via anionic polymerization under high vacuum. Several other star-shaped and linear polymers were purchased from Polymer Source and Pressure Chemical, respectively. The polymers used in this study are described in Table 1. Thin PS films were spin-coated from toluene solutions onto precleaned silicon wafers (Wafer World Inc.) with a native oxide layer of 1.5 nm, as was determined by variable angle spectroscopic ellipsometry, VASE (M-2000, J.A. Woollam Co.). The concentrations of the solutions were varied from 0.5 to 15 wt % in order to control the resulting polymer film thickness. The silicon wafers, prior to spincasting, were cleaned with ethanol and acetone followed by UV-ozone treatment for 3 min. The wafers were finally rinsed with toluene immediately prior to spin-coating. Each sample was annealed at 50 °C above its corresponding bulk Tg for 24−48 h. The final polymer film thickness was measured using VASE. The supported films were confirmed to be uniform by performing atomic force microscopy analyses both before and after annealing. The glass transition temperatures, Tg’s, and thermal expansion coefficients of all films were measured by monitoring the change in film thickness upon cooling from 150 °C down to room temperature at a rate of 1 K/min using VASE equipped with an Instec heating stage. The VASE measurements were performed at a fixed incident angle of 70° while the samples were in an inert atmosphere of nitrogen during. Liquid nitrogen was used in order to maintain the temperature B
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Macromolecules Table 1. Polymers Used in This Study polymer e
PS-3arm-19K (SPS-3-19K) PS-4arm-4K (SPS-4-4K)e PS-8arm-10K (SPS-8-10K)e PS-8arm-25K (SPS-8-25K)e PS-8arm-35K (SPS-8-35K)e PS-8arm-42K (SPS-8-42K)e PS-8arm-47K (SPS-8-47K)e PS-16arm-13K (SPS-16-13K) PS-16arm-28K (SPS-16-28K) PS-32arm-9K (SPS-32-9K) PS-64arm-9K (SPS-64-9K) PS-64arm-36K (SPS-64-36K) PS-64arm-52K (SPS-64-52K) PS-64arm-80K (SPS-64-80K) PS-64arm-140 K (SPS-64-140K)
functionality ( f)a
Marmb
Narm
PDId
3 4 8 8 8 8 8 16 16 32 64 64 64 64 64
19 4 10 25 35 42 47 13 28 9 9 36 52 80 140
183 38 96 240 337 404 452 125 269 87 87 346 500 769 1346
1.03 1.03 1.03 1.03 1.02 1.03 1.03 1.02 1.02 1.03 1.02 1.01 1.01 1.01 1.01
a
Functionality, f, determined by the ratio (Mw)star/(Mn)arm. bFrom low angle laser light scattering in THF at 25 °C. cFrom membrane osmometry in toluene at 35 °C. dFrom SEC in THF at 40 °C calibrated with linear PS standards. ePurchased from Polymer Source Inc. Figure 1. Normalized film thicknesses are plotted as a function of the aging time tage = t − t0,10 at Tage = Tg − 50 °C for (A) the 8-arm and for (B) 64 arm star-shaped molecules. These data, plotted on a semilog scale, are normalized by the initial thickness of the film at T = Tage. Only the data in the intermediate power law regime are required for the analysis and are plotted here.
and cooling rate. The thickness, h(T), and refractive index, n(T), of each sample were determined by fitting the ellipsometric angles Δ and Ψ to a Cauchy/SiO2/Si model over the wavelengths of 400−1700 nm. Each Tg was determined by the intersection of extrapolated linear fits through the glassy and rubbery regions of the data. The physical aging experiments were conducted on films with thicknesses ranging from 50 to 1000 nm films using VASE. Each sample was heated to a temperature of T = Tg + 50 °C for 30 min in order to remove any thermal history. The samples were subsequently quenched at a rate of 85 °C/min to room temperature and then ramped back to the aging temperature, Tage, where the sample thickness was monitored as a function of time. An acquisition time of 30 s was used to measure the thickness every 60 s. The experimental time of 360 min was used in this study, which has been reported to be sufficient to determine the average aging rate of the material within the experimental error.38 The experiment was repeated a total of 3−5 times for each aging temperature in order to ensure that that the results were reproducible. Each aging rate is reported as the average of all of the aging tests, where the error is taken as half the difference between the maximum and minimum aging rates at a given temperature.
β=−
1 dH H∞ d log(tage)
(1)
where H∞ is the thickness at equilibrium. The value of H∞ was estimated from the temperature dependence of the film thickness during the Tg test.38 With regard to the data for the 8-arm star in Figure 1a, the slower aging rate exhibited by the thinner film. In contrast, the aging rates for the f = 64-arm films, H = 50 nm and H = 1000 nm, are virtually identical. In Figure 2 the physical aging rates for the 8- and 64-arm polystyrenes, with thicknesses H = 50 and 1000 nm, are reported as a function of aging temperature; a maximum is clearly observed for all cases, as expected. Additionally, the aging rates of the 64-arm star are identical for both the 50 and 1000 nm films. The aging rates of polymers exhibit maxima with decreasing temperature due to two competing effects.3,4,10,11,36 Close to the Tg, the rate is comparatively slow because the driving force determined by Tage − Tg, the departure from equilibrium, is small. With decreasing T, the driving force further increases and the rate increases. However, the aging rate eventually decreases upon a further decrease in T due to the reduction in thermal energythe thermally activated structural relaxation processes are slower with decreasing T. These two competing effects are responsible for the maximum. The foregoing observations may be understood from the following. Previously we showed that the thickness dependence of the aging of thin polymer films may be rationalized in terms of a driving force determined by the difference between the aging temperature and the local Tg.37 This was specifically illustrated for linear chain PS and for 8-arm star PS. The local Tg behavior of the 8- and 64-arm star have previously been
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RESULTS AND DISCUSSION Time-dependent changes in the thicknesses of films with initial thicknesses H = 50 and 1000 nm are plotted as a function of aging time tage = t − t0 (t0 is the time that denotes the onset of the intermediate regime; see ref 10) for the 8-arm and 64-arm star-shaped molecules in Figure 1. The molecular weights per arm of both polymers are comparable, Marm ≈ 10 kg/mol. These molecules were chosen because their vitrification properties placed them in different regimes of the “diagram of states”.43,44 Specifically, the Tg of the 64-arm molecule is independent of film thickness, whereas that of the 8-arm molecule increases with decreasing film thickness. Moreover, the glass transition at a free surface Tg(x = 0) and at the substrate Tg(x = H) is higher than the bulk glass transition temperature Tg. The aging rates β of the films are defined as38 C
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Figure 2. Average aging rate vs scaled temperature ΔTage. The data are comparing a 50 nm film to a 1 μm thick film for (A) a 16-arm star with Marm = 13 kg/mol. and (B) a 64-arm star with Marm = 9 kg/mol. The solid lines represent quadratic fits to the data as described in a previous publication. The dashed line is a prediction from the model described in the main text.
Figure 3. (A) Normalized aging rates β(H)/βbulk are plotted as a function of film thickness for several different star-shaped molecules. All aging rates are measured at 50 °C below the average Tg of the film. The solid lines are guides to the eye. (B) β(H = 50)/βbulk is plotted as a function of f.
that the thickness of the liquid-like layer increased with decreasing temperature for T < Tg. However, previous work from our group (ref 37) demonstrated that such a two-layer model fails to capture the behavior of star-shaped macromolecules, which exhibit similar thickness dependent aging rates, yet opposite trends for their Tg versus depth, x, dependencies. The Tg at the free surface of short (arms less that the molecular weight between entanglements) 8-arm polystyrenes is larger than the bulk, and the Tg at the substrate is also larger than the bulk.37 In an effort to address this problem, we could not use a two-layer model and instead used the experimentally determined depthdependent Tgs of our samples. This more versatile Tg gradient model enabled prediction of the thickness dependence and the temperature dependence of the aging rate of thin linear chain and 8-arm star polystyrenes.37 Our clear finding was that the aging rate of a polymer thin film was determined by the difference between the aging temperature Tage and the local Tg, which we denote as Lg(x), at depth x. It should be noted that our model in ref 37 predicts that the thickness of the liquid-like layer decreases with decreasing temperature for T < Tg, which is consistent with experiment of linear chain polymers.42 Specifically in our model, the average Tg(H) of a film of thickness H was expressed in terms of Lg(x):
reported; the local Tg near the free interface for the 8-arm star with Marm ≈ 10 kg/mol is higher than in the bulk,43 whereas for the 64-arm star, the local Tg was independent of the depth throughout the film.44 Since the aging rate is dependent on Tage − Tglocal, and Tglocal is independent of film thickness, then the aging rate of the 64-arm molecule would be independent of film thickness. The observations in Figure 2B are consistent with this expectationno thickness dependence in the aging rate. Normalized aging rates β(H)/βbulk of stars of varying functionalities, and comparable arm lengths, are plotted as a function of film thickness H in Figure 3. These data reveal that the thickness dependence of the aging rates depends on functionality in a nonmonotonic manner. The aging rates are most rapid for the 8-arm star, yet slower for the linear chain molecules. The trends in Figure 3A are better illustrated by plotting the ratio A = β(H = 50 nm)/β(bulk) as a function of functionality f in Figure 3B. It is apparent that the aging rate decreases from f = 2 and exhibits a minimum at f = 8, beyond which it increases with increasing f. Several models have been introduced in the literature to explain the thickness-dependent aging rate of polymer thin films. It is recognized that a gradient in aging rates would likely exist throughout the depth of film and, moreover, that the glass transition temperature would also change throughout the depth of the filmit is lowest at the free surface, for linear chain polymers, and increases toward the substrate where it is bulklike.36 In describing the data a two-layer modela surface layer that does not age because its Tg is below the aging temperature and a second layer that is bulk-likewas used. This model adequately described the aging rate versus film thickness results for linear chain polymer films. A further implication, however, is
Tg(H ) =
∫0
H
Lg (x) dx /
∫0
H
dx
(2)
The Lg(x) profiles were determined by fitting the model to the average Tg vs H data shown in Figure 4A. These data in Figure 4 were obtained from a recent publication on the vitrification of star-shaped molecules.44 The resultant profiles for Lg(x) for the D
DOI: 10.1021/acs.macromol.7b00091 Macromolecules XXXX, XXX, XXX−XXX
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commensurate with the minimum exhibited by the aging rate in Figure 3Bthe aging rate must undergo a minimum, if the local ΔTg (in this case the surface Tg) undergoes a maximum with functionality. This is addressed more quantitatively in the next section. We turn our attention to how local changes in the Tg will influence the local aging rate. We do this by employing a model that was previously used to describe aging in thin polymer films.37 According to the model, the thickness-dependent aging rate can be attained from the bulk aging rate and the local Tg profiles, Lg(x). The bulk aging behavior is determined by empirically fitting the temperature-dependent aging rate of the micrometer thick films to a quadratic equation, β(ΔTage) = a(ΔTage)2 + b(ΔTage) + c, where ΔTage = Tage − Tg(H). The fits to the quadratic equation are shown as solid lines in Figure 2. The local aging rate may be attained by combining β(ΔTage) and Lg(x). This is accomplished by replacing the average Tg of the film with the local Tg, Lg(x). In doing so, a relation is derived to estimate the local aging rate as a function of depth from the free surface, β(Tage − Lg(x)). The average aging rate of a thin film may then be described by averaging the local aging rate throughout the depth of a polymer film: β(h , Tage) = Figure 4. (A) Change in Tg as a function of film thickness for several different star polystyrenes. The data in this plot are reproduced from a recent publication.43,44 The solid lines represent fits to the thickness dependence as described by a recently published model. (B) Depthdependent local Tg for several different star polystyrenes with Marm ≈ 10 kg/mol measured by variable energy PALS. The data are reproduced from a recent publication.44 The solid lines represent fits to the model described in the main text.
∫0
h
β(Tage − Lg (x)) dx /
∫0
h
dx
(3)
Using the model fits from Figures 2 and 5, the average aging rate for a given film thickness and temperature may be estimated. They are shown as the dashed lines in Figure 2 and the open symbols in Figure 3B. It is evident that the model captures and estimates the effect of confinement quite well for the full range of star-shaped molecules without incorporating any thickness-dependent aging data. Thus far, we have only discussed a single Marm and varied the functionality of the arm. These effects could similarly be investigated for a constant f and varying Marm. Decreasing Marm yields a similar effect to increasing f; the polymers gradually approach a soft colloid-like behavior. This is due to the fact that as the length of each arm decreases the monomer density and crowding effect experienced by the chain segments are enhanced. This effect has previously been mapped out in the form of a “diagram of states” for the changes in the glass transition.44 The effect on the aging rate is shown in Figure 6, where the ratio A = β(H = 50)/βbulk is plotted as a function of 1/Marm; this enables a more direct comparison to the data in Figure 3B. For linear chain PS, there is no effect of the
different star PS molecules used in this study are shown in Figure 5. For linear chains, the local Tg near the free surface is
Figure 5. Local Tg as a function of depth from the free surface of a 50 nm film for several different star-shaped polystyrenes. The local Tg is a result of the model described in the main text.
lower than the bulk, consistent with literature.39,41,42 For the 8and 16-arm star-shaped molecules the local Tg near both interfaces, i.e., free surface and substrate, is higher than that of the bulk. As discussed earlier, the enhanced local Tg is associated with the enhanced interfacial attraction of stars to both external interfaces.45,46,49−53 Recall that the local enhancement of Tg is not monotonic with f due to the so-called “soft colloidal-like regime”for values of f = 64 the local Tg is independent of depth. The maximum exhibited by ΔTg in Figure 4B is
Figure 6. Confinement effect metric A as a function of 1/Marm. The parameter A is the aging rate of a 50 nm film normalized by the aging rate of the 1 μm thick film. The solid lines represent guides to the eye. E
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P.F.G.: National Renewable Energy Laboratory (NREL), Golden, CO 80401.
molecular weight on the thickness dependence of the aging rate within the range that was examined. The 64-arm star captures all of the regimes from a soft colloid to a polymer-like behavior; for long arms (i.e., low values of 1/Marm), the aging rate has values similar to that of linear chain PS (black square in Figure 6). As the molecular weight per arm decreases (i.e., 1/Marm increases), β(H = 50)/βbulk decreases to approximately 0.6, indicating that thin films age progressively slower with decreasing arm length. This is the result of the enhancements of the local Tg at both interfaces due to the gradually increasing attraction of such molecules to interfaces. As Marm further decreases, the β(H = 50)/βbulk goes through a minimum and returns to a value close to 1 in the low Marm limit. In this limit the star-shaped polymer exhibits soft colloid-like behavior. Moreover, they form uniform structures across the film with no gradients in both the Tgs and the aging rates.44 For the 8-arm star, only a monotonic decrease in β(H = 50)/βbulk with Marm is observed, at least within the molecular weight range investigated in this work. Therefore, the transition from linear chain behavior to soft colloid-like behavior is not captured.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS Support for this research, performed at the University of Michigan, was provided by the National Science Foundation (NSF), Division of Material Research (DMR-1305749), and is gratefully acknowledged. G.S. and M.S. performed the synthesis in Athens; E.G was at the University of Michigan at the time these measurements were performed.
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CONCLUSION The phenomenon of physical aging of bulk polymers is characterized by an aging rate β that exhibits a maximum with decreasing Tage, for Tg > Tage, due to two competing mechanisms: an increasing driving force with increases with Tg − Tage and the fact that the thermal energy for the segmental relaxations decreases with decreasing Tage. The aging rates of linear chain polymers are moreover independent of molecular weight. It is well established that the aging rate is film thickness dependent for sufficiently thin films. However, the notion of whether the aging rate increases or decreases with decreasing H is not so much a function of mechanism of the glassy dynamics process, but more a function of the difference between the local glass transition of the material and Tage. Because the local Tg(x) at an interface differs from the bulk, the aging rate near an interface differs from the bulk. Fundamentally, those competing entropic interactions− entropically driven adsorption of molecules to an interface for an energetic gain with increasing f, which are offset by the cost deformation energy of the molecule which also increases with increasing f (for constant Marm)have been shown to be responsible for changes in the local glass transition temperatures Tg(x). For molecules that pack like soft colloids and for which the local Tg is independent of film thickness, the aging rate is independent of film thickness. Indeed, the interactions that are responsible for changes in the wetting behavior are also fundamentally responsible for changes in the local glass transition temperatures. These factors are also responsible for the changes in the aging behavior of molecules with star-like topologies.
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REFERENCES
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected] (P.F.G.). ORCID
Bradley R. Frieberg: 0000-0002-0125-4278 Peter F. Green: 0000-0002-2024-0832 Present Addresses
B.F.: Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, MD 20899. F
DOI: 10.1021/acs.macromol.7b00091 Macromolecules XXXX, XXX, XXX−XXX
Article
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DOI: 10.1021/acs.macromol.7b00091 Macromolecules XXXX, XXX, XXX−XXX
