The depth to which the local glass transition temperature Tg and alpha-relaxations are perturbed near a boundary is believed to be related to the characteristic length scales associated with cooperative dynamics in dynamically heterogeneous glasses. Following our recent work [R. R. Baglay and C. R. Roth, J. Chem. Phys. 143, 111101 (2015)] that measured a very broad 350-400 nm local Tg(z) profile across a glassy-rubbery interface of polystyrene (PS)/poly(n-butyl methacrylate) (PnBMA), we compare here how the Tg(z) profile in PS varies when changing the neighboring polymer from a lower Tg material to a higher Tg material. Here we report local Tg(z) profiles for PS when in contact with polysulfone (PSF), poly(methyl methacrylate) (PMMA), and poly(isobutyl methacrylate) (PiBMA). We find that the distance from the interface before bulk Tg of PS (Tgbulk=101 °C) is recovered depends on whether PS forms the high-Tg glassy component experiencing so-called soft confinement, z ≈ 225-250 nm for PS next to PiBMA (Tgbulk=62 °C) and PnBMA (Tgbulk=21 °C), or PS forms the low-Tg rubbery component experiencing hard confinement, z ≈ 100-125 nm for PS next to PSF (Tgbulk=186 °C) and PMMA (Tgbulk=120 °C). The depth to which these Tg(z) perturbations persist and the magnitude of the local Tg perturbation at the interface are independent of the difference in Tgbulk between the two polymers, the interaction parameter, and the chemical structure. We demonstrate that these broad, extended Tg(z) length scales appear to be universal across these different systems but show that the strong dynamical coupling across the dissimilar polymer-polymer interface only occurs when this interface has been annealed to equilibrium. We consider why dissimilar polymer-polymer interfaces exhibit continuous local dynamics across the interface in contrast to polymer-free surface, polymer-substrate, or polymer-liquid interfaces that show discontinuous local dynamics.

Recent trends in polymer blends have been to drive the domain sizes down into the sub-100 nm range to improve material performance, blend uniformity, and to create functionality for particular applications.1–3 There are now a number of strategies for creating such nanostructured polymer blends: synthesis of multicomponent block copolymers,4–7 novel cold-state processing methods,8 and nanolayer stacking and interweaving.9–13 Of particular interest are co-continuous structures where domains of glassy, rubbery, and crystalline components intertwine while percolating across the material making ideal structures for applications such as filtration, ion conduction, catalysis, photovoltaic technologies, and bioengineering applications.3,14–17 These are materials whose function and performance will be dictated by the properties of the material near the polymer-polymer interfaces. Historically polymer blends have been treated as a patchwork of different domains with separate properties, where it is often assumed that these domains retain the bulk properties of the individual components.18 Such approaches are appropriate for blends with large, micron-sized domains where the relatively small contributions of the regions near polymer-polymer interfaces between the domains can be reasonably ignored. However, when domain sizes become so small that the material becomes dominated by interfaces, it is necessary to understand and incorporate the altered local properties at and near the interfaces. The results we present here demonstrate long length scales for the distance over which local glass transition temperature (Tg) perturbations propagate from polymer-polymer interfaces suggesting that nanostructured polymer blends with domain sizes of a few hundred nanometers likely have no regions where the local properties remain bulk-like. Instead, nanostructured blends likely exhibit more uniform properties across the different domains and interfaces, which may explain their typically enhanced performance over more traditional blends with large micron-sized domains.

We have recently mapped the local glass transition temperature Tg(z) profile across a glassy-rubbery interface between polystyrene (PS) and poly(n-butyl methacrylate) (PnBMA).19 Focusing on an idealized bilayer-style model system, we used a localized fluorescence method to measure the local Tg(z) at different distances z from the PS/PnBMA interface. The Tg(z) profile transitioned continuously from the bulk Tg value of PnBMA, TgbulkPnBMA=21 °C, to that of PS, TgbulkPS = 101 °C, far from the PS/PnBMA interface in either direction, as anticipated. However, unexpectedly, this Tg(z) profile was found to be very broad, spanning 350-400 nm from one extreme to another.19 In addition, this dynamical Tg(z) profile was asymmetric, being uncorrelated with the local composition profile ϕ(z) ≈ tanh(2z/wI), where the equilibrium interfacial width of PS/PnBMA has been previously characterized at only wI = 7 nm.20–22 These unexpected results demonstrate that the local glass transition dynamics are influenced by factors much further away than simply the local composition, which has been the traditional viewpoint in polymer blends.23#x2013;25 These unexpected results of the Tg(z) profile across a PS/PnBMA interface19 leave many open questions. How universal is this to other polymer systems? What factors are required to get this extraordinary coupling of cooperative segmental dynamics across an immiscible polymer-polymer interface? What controls the length scale over which these dynamics are perturbed away from the interface? Is this length scale a property of the polymer itself, perhaps related to its cooperatively rearranging region (CRR)? What properties of the interface (degree of immiscibility, interaction parameter χ, interfacial width) influence this behavior? To what extent do polymer-polymer interfaces behave similarly or differently to other interfaces (e.g., polymer-substrate, polymer-free surface, and polymer-liquid)? Here we consider these various factors.

We believe one way we can begin to understand these results is by analogy to the glass transition behavior in thin films. For over two decades now, studies have found that the average glass transition temperature Tg of thin polymer films, supported on various substrates or free-standing with only air interfaces, demonstrates large (tens of degrees Kelvin) deviations in Tg from their bulk values Tgbulk with decreasing film thickness.26–32 For a variety of polymers such confinement effects begin at film thicknesses of ∼100 nm.29,30,33–35 The results of such studies have found that the phenomenon can be understood as the presence of the interfaces (polymer-free surface or polymer-substrate interface) causing a perturbation to the local dynamics that then propagates deep into the material leading to a gradient in local Tg(z) as a function of depth from the interface over some distance before bulk-like properties of the material are recovered.26,36–45 In general, the presence of a free surface tends to speed up (enhance) the local mobility, while the presence of a substrate interface can slow down the local dynamics, typically depending on whether attractive interactions, such as hydrogen bonding, are present between the polymer and substrate interface in question.28,35,46–49 Such measurements of local Tg near a PS-free surface, using the same localized fluorescence method mentioned above, found that a depth of 30-40 nm from the free surface is required before the bulk Tg of PS was recovered.50 Some studies investigating polymer-substrate interactions demonstrate even longer length scales spanning several hundred nanometers.51,52 Though, what factors control this length scale are still not well understood. There is also disagreement about the size of this enhanced mobility region near a free surface, with studies measuring glassy dynamics well below bulk Tg often reporting depths of a few tens of nanometers,36,50,52,53 while studies measuring liquid-like flow properties above or near bulk Tg only reporting depths of a few nanometers54–60 before bulk-like properties are recovered. It has been suggested that such differences are associated with what dynamical property is being measured.41,53,61 Here, we focus on the measurements of glassy dynamics and local Tg. Several studies both experimentally34,50,53,62–65 and theoretically37–45 suggest that such a length scale is likely related to the length scales involved in describing cooperative motion and dynamic heterogeneity in glasses.

Although the behavior of a polymer-free surface interface has been the most heavily studied, it is informative to make comparisons across different types of interfaces: polymer-substrate, polymer-liquid, and polymer-polymer interfaces. In this regard, other groups have also begun looking at polymer-polymer interfaces and investigating how they differ from that of a free surface or liquid interface. Using MD simulations, Simmons and coworkers have modeled the Tg of a confined polymer layer in contact with a second different polymer layer.66 With periodic boundary conditions, this system mimics nanolayered films made by coextrusion.10,11 They find that both the low-Tg polymer under “hard” confinement and the high-Tg polymer under “soft” confinement exhibit a shift in Tg from their bulk value caused by the presence of the neighboring polymer.66 The magnitude of the shift for the low-Tg polymer under hard confinement is additionally influenced by the interfacial energy, although in this simulation varying the interfacial energy also varies the amount of interdiffusion at the interface, which we demonstrate in this work to be an important parameter. Interfacial energy has also been considered an important factor for polymer-substrate67–69 and polymer-liquid70 interactions. Tito, Lipson, and Milner have modeled the local mobility profile next to a free surface or glassy-rubbery polymer-polymer interface using a kinetic limited-mobility model that encodes the exchange of local mobility through different types of local free volume (“mobile,” “dormant,” and “dense”) where the interface in question becomes a source and sink of local free volume and hence mobility.37 Evans and Torkelson have made experimental comparisons between the magnitude of the shift in Tg perturbation for PS with the value of the fragility of the surrounding polymer matrix finding similarities between thin 10-15 nm layers of PS and isolated chains of PS.71 The idea of differences between so-called hard vs. soft confinement has been around for about a decade. Richert first introduced the concept when comparing small molecule glass formers confined within soft emulsion drops instead of hard nanoporous glasses,72–74 where soft confinement referred to a liquid interface instead of that with a hard wall. However, recent studies on polymer-liquid interfaces70,75–78 seem to suggest that, in some cases, a polymer-liquid interface may not actually behave that different compared to a polymer-substrate interface. In contrast, experimental evidence22,35,79–84 suggests that polymer-polymer interfaces may be distinctly different from that of polymer-free surface or polymer-liquid interfaces.

Here we compare the local Tg(z) profile of PS in contact with several different polymers: polysulfone (PSF), poly(methyl methacrylate) (PMMA), and poly(isobutyl methacrylate) (PiBMA) with that of PnBMA from before.19 We find that the depth to which the local Tg(z) value is perturbed from the polymer-polymer interface is strongly affected by whether the neighboring polymer has a bulk Tg value higher or lower than that of PS (i.e., whether the confinement is hard or soft), with PS next to PSF behaving remarkably similar to PnBMA next to PS. Following our previous analysis19 based on the efforts of Butler and Harrowell,43 we characterize the depth to which the local Tg(z) perturbation persists from the interface by ξ1/2, the distance at which the local Tg(z) perturbation has dropped to half the value found at the interface. Butler and Harrowell showed that for a simple two-spin facilitated Ising model, such a dynamical length scale ξ1/2(T) exhibited the same temperature dependence as the mean relaxation time τ(T) for dynamical heterogeneities in the bulk, suggesting that dynamical gradients near an interface can be used to probe the dynamical length scales associated with cooperative motion.43,85 We find that these ξ1/2 values are strongly grouped around ξ1/2 = 55 ± 5 nm for polymers next to a higher Tg polymer (hard confinement) compared with ξ1/2 = 115 ± 5 nm for polymers next to a lower Tg polymer (soft confinement). We suggest that perhaps the distinctiveness of polymer-polymer interfaces may be associated with the extensive breadth (few to several nanometers) of polymer-polymer interfaces in comparison to the breath of polymer-air or polymer-liquid interfaces (∼0.5 nm86). As we will demonstrate, the extent to which the two dissimilar polymers are allowed to interdiffuse at the polymer-polymer interface is an important factor that affects the extent of dynamical coupling across the interface. If we restrict the amount of annealing done at the dissimilar polymer-polymer interface, we find the Tg(z) profile to be much shorter and not consistently stable as the interface continues to evolve. However, once the dissimilar polymer-polymer interface has been allowed to form to equilibrium, we no longer see any evolution of the Tg(z) profile with further annealing. Interestingly, despite this clear importance of the breadth of interdiffusion of the interface, we do not observe a correlation of the extent of the Tg(z) perturbation from the interface with the equilibrium interfacial width wI or equivalently the interaction parameter χ between the two polymers. We also note that the breadth of these polymer-polymer interfaces (∼5 nm) are all much smaller relative to the large extent of the Tg(z) perturbations (many tens to hundreds of nanometers). Thus, small differences in equilibrium interfacial width do not seem to play a role in the dynamical coupling of cooperative dynamics across the interface provided that the dissimilar polymer-polymer interface has been able to anneal to equilibrium.

High molecular weight pyrene-labeled polystyrene (PS -Py) with 1.4 mol. % pyrene content (Mw = 672 kg/mol, Mw/Mn = 1.3) was synthesized by bulk free-radical copolymerization of styrene with a pyrene butyl methacrylate monomer that was synthesized via esterification of 1-pyrenebutanol and methacryloyl chloride.22,50,87 Polymerization was performed at 50 °C for 24 h under a nitrogen environment using azobisisobutyronitrile (AIBN) as initiator. Post-thermal termination, the PS-Py polymer was dissolved in tetrahydrofuran (THF) and subsequently re-precipitated in methanol at least seven times to remove unreacted monomer and chromophores. The washing procedure helps reduce polydispersity, specifically biased towards eliminating low MW PS-Py chains and unreacted monomer, while retaining the higher molecular weight chains. The label content of PS-Py was later characterized by ultraviolet-visible spectroscopy in spectroscopic grade THF. Unlabeled (neat) polystyrene (Mw = 1920 kg/mol, Mw/Mn = 1.26), which was used to sandwich the PS-Py 10-15 nm probe layers on the PS side of the structures, was purchased from Pressure Chemical and used as received. Polysulfone (Mw = 85 kg/mol, Udel P-3500 LCD MB8), poly(methyl methacrylate) (Mw = 1150 kg/mol, Mw/Mn = 1.06), and poly(isobutyl methacrylate) (Mw = 295 kg/mol, Mw/Mn = 1.83) were purchased from Solvay Advanced Polymers, Pressure Chemical, and Scientific Polymer Products, respectively, and used as received.

Individual layers of PS-Py, PS, PMMA, and PiBMA were made by spin-coating from toluene solutions either onto freshly cleaved mica or quartz slides, depending on whether the polymer was used as an underlayer or a PS/PS-Py/PS Tg reporting multilayer stack. All PSF films were prepared in the same manner but from cyclopentanone solutions. Film thickness was determined via ellipsometry after the films were either floated or spin-coated onto silicon wafers. The spin speed and solution concentrations were adjusted to produce films with known reproducible thicknesses and minimal surface roughness (on the order of <1 nm). All individual layers were annealed under vacuum for at least 18 h at Tg + >20 K to facilitate the removal of any residual solvent and relaxation of spin-coating induced stresses. Multilayers were then assembled by successively floating each layer onto room temperature deionized water and capturing the layer onto the multilayer sample starting from a given base underlayer spun directly onto the quartz slide needed for fluorescence measurements. Between each successive floating, the sample is allowed to thoroughly dry. Bulk polymer underlayers and bulk PS capping layers were made >450 nm in thickness to ensure that the pyrene-labeled probe layer is unaffected by the free surface or underlying substrate interface.

Multilayer structures with polymer underlayers containing a polymer with a Tghigher than that of PS were constructed in a two-step annealing process, as illustrated in Figure 1. This was done to limit the interdiffusion of the PS-Py probe layer into the surrounding neat PS matrix, while still ensuring that the polymer-polymer interface of interest has reached equilibrium and achieved good coupling of the cooperative dynamics across the interface. The variable thickness PS z-layer was floated onto a PMMA or PSF coated substrate (post-initial vacuum annealing of each layer) and annealed to consolidate this bilayer and thereby form a PS/PMMA or PS/PSF interface that had reached equilibrium prior to floating the remaining PS layers. The PS/PMMA and PS/PSF bilayers were annealed under vacuum at 150 °C for 30 min and at 210 °C for 90 min, respectively. After these polymer-polymer interfaces were consolidated, the remaining PS-Py and capping neat PS layers were floated atop the PS/PMMA or PS/PSF samples. The remaining PS/PS-Py/PS interfaces were then annealed in an Instec HCS402 heater immediately prior to the fluorescence measurements by heating to 170 °C and holding for 5 min before dropping the temperature to 150°C and holding for 2 min. This annealing protocol ensured that the PS/PS-Py/PS layers formed consolidated interfaces, while still limiting the diffusion of the PS-Py probe layer. Multilayer structures with polymer underlayers containing a polymer with a Tglower than that of PS could be fabricated with a single annealing process because the polymer-polymer interface of interest easily reaches equilibrium for annealing conditions that are appropriate for the PS/PS-Py/PS interfaces.19 The PS and PS-Py films in multilayer samples containing PiBMA as the underlayer were floated directly atop each other in succession, and then only annealed together immediately prior to the fluorescence measurement for 20 min at 120 °C.

FIG. 1.

Exploded view of the two-step annealing process for multilayer samples containing PMMA or PSF as the polymer underlayer that have a Tghigher than that of PS. The two-step annealing process ensures that the PS/PMMA or PS/PSF interface has reached equilibrium without allowing interdiffusion of the PS-Py reporting layer.

FIG. 1.

Exploded view of the two-step annealing process for multilayer samples containing PMMA or PSF as the polymer underlayer that have a Tghigher than that of PS. The two-step annealing process ensures that the PS/PMMA or PS/PSF interface has reached equilibrium without allowing interdiffusion of the PS-Py reporting layer.

Close modal

Fluorescence measurements were performed using a Photon Technology International QuantaMaster spectrofluorometer with samples mounted in an Instec HCS402 heater. The pyrene-labeled probe layers were excited at a wavelength of 330 nm using a xenon arc lamp with an excitation band-pass of 5.5-6.0 nm and an emission band-pass of 5.0 nm. After the final sample annealing as described above, the sample temperature was ramped down at 1 °C/min while pyrene fluorescence intensity was collected for 3 s every 27 s, at an emission wavelength of 379 nm. All samples were reheated to the starting temperature after each run to ensure that the same initial fluorescence intensity was recovered, verifying that the sample had remained stable during the course of the experiment and no photobleaching occurred. This ramped fluorescence procedure for measuring Tg was previously reported in the work of Rauscher et al.22 and utilized for the data collection in the work of Baglay and Roth.19 Bulk Tg values measured by fluorescence and ellipsometry are for PMMA Tgbulk = 120 °C, PiBMA Tgbulk = 62 °C, and PSF Tgbulk = 186 °C.

In the present work, we demonstrate that the asymmetry and the extended length scale of the local glass transition Tg(z) profile recently reported in the polystyrene/poly(n-butyl methacrylate) (PS/PnBMA) system19 is not unique to this single polymer-polymer system. We start by comparing our previous PS/PnBMA system to one that is effectively reversed, where PS now forms the rubbery component next to a glassy polymer, polysulfone (PSF). The bulk glass transition temperature value of PSF is Tgbulk = 186 °C resulting in an 85 K difference across the PS/PSF interface (Tgbulk = 101 °C for PS). This PS/PSF system is analogous to that of PS/PnBMA, but reverses the role of the PS component. In the PS/PnBMA system, the PS component was the hard glassy material that underwent soft confinement by the rubbery PnBMA, whereas in the PS/PSF system, the PS component is the soft rubbery material undergoing hard confinement by the glassy PSF. In both cases, there is an 80-85 K difference in bulk Tg between the two components. A comparison between these two systems will allow us to test whether the penetration depth of the dynamical Tg perturbation from the dissimilar polymer-polymer interface is polymer specific (e.g., related to chemical structure) or determined by the glassy vs. rubbery role played by the component (i.e., whether the confinement is soft vs. hard).

Figure 2 illustrates the sample geometries of the two systems being compared. Each geometry is comprised of four individually constructed films of designed thickness that were assembled and carefully annealed to form a consolidated material with an effectively static geometry as illustrated. We employ a temperature-dependent fluorescence method to measure the local Tg(z) at different distances z from the glassy-rubbery polymer-polymer interface. The multilayer sample geometries are constructed via a floating procedure where a 10-15 nm pyrene-labeled PS probe layer (PS with a fluorescent 1-pyrenylbutyl methacrylate monomer chemically attached to the PS backbone at a label content of ∼1:70 monomers, designated PS-Py) is placed at a known distance z from the dissimilar polymer-polymer interface in question by inserting a neat (unlabeled) PS layer of thickness z between the pyrene-probe layer and the dissimilar polymer layer (PSF or PnBMA in Fig. 2). As previously discussed in the work of Baglay and Roth,19 high molecular weight polystyrenes are used to limit interdiffusion of the PS/PS-Py/PS interfaces and keep the Tg-reporting PS-Py layer localized a fixed distance z from the dissimilar polymer-polymer interface of interest. One of the advantages of using polymers for this type of study is that chain diffusion is effectively decoupled from more local cooperative segmental α-relaxations associated with Tg in high molecular weight entangled polymers such that the morphology of the layers assembled will remain static during the course of the experiment. As we will explore in more detail below, a key factor in measuring a reproducible and reliable value of Tg(z) is that the dissimilar polymer-polymer interface has been annealed to equilibrium. Immiscible polymer-polymer interfaces initially interdiffuse quite readily by local Rouse modes but stabilize quickly at an equilibrium interfacial width 𝑤Iχ12 of only a few nanometers limited by the unfavorable interactions χ between the two materials.88 Unless otherwise indicated, all the Tg(z) values presented are measured ensuring that the dissimilar polymer-polymer interface has been annealed to equilibrium prior to the start of the fluorescence data collection.

FIG. 2.

Sample geometries comprised of four individually spin-coated layers of polystyrene (PS), and poly(n-butyl methacrylate) (PnBMA) or polysulfone (PSF), assembled and annealed to form a consolidated material with a 10-15 nm thick local Tg-reporting pyrene-labeled PS layer. The neat PS z-layers varied the distance z of the pyrene-labeled PS layer relative to the PS/PnBMA (7 nm wide) or PS/PSF (6 nm wide) interface. High molecular weight polymers ensure that the assembled morphology remains static throughout the experiment.

FIG. 2.

Sample geometries comprised of four individually spin-coated layers of polystyrene (PS), and poly(n-butyl methacrylate) (PnBMA) or polysulfone (PSF), assembled and annealed to form a consolidated material with a 10-15 nm thick local Tg-reporting pyrene-labeled PS layer. The neat PS z-layers varied the distance z of the pyrene-labeled PS layer relative to the PS/PnBMA (7 nm wide) or PS/PSF (6 nm wide) interface. High molecular weight polymers ensure that the assembled morphology remains static throughout the experiment.

Close modal

Figure 3 shows the temperature-dependent fluorescence intensity measured for four different samples where the PS-Py probe layer has been placed at specific distances z from either a PS/PnBMA or PS/PSF interface. Vitrification in polymers is characterized by the dynamic arrest of cooperative segmental motion as the material enters the glassy state. It is well known that pyrene is sensitive to the local density and rigidity of the surrounding polymer matrix.22,35,50,89 As the temperature is lowered and the local polymer matrix surrounding the pyrene dye becomes more rigid, the probability of radiative compared with non-radiative decay of the pyrene fluorescence increases, where a break in the slope of the signal intensity is manifested when crossing from the liquid to glassy state as the temperature dependence of the density changes. Previous works have demonstrated that this measure of Tg via fluorescence matches that by differential scanning calorimetry (DSC) in bulk materials and by ellipsometry in thin films.50,89 We measure the fluorescence intensity on cooling at 1 °C/min where the intensity at a single wavelength (first emission peak of pyrene at 379 nm that is the most sensitive to its local environment90,91) is sampled every 30 s (averaging signal intensity over a 3 s time window) resulting in a data point collected every 0.5 °C, with no additional smoothing performed to the temperature-dependent intensity data.19,22 To facilitate comparisons, each dataset shown in Fig. 3 is normalized and then vertically shifted for clarity. The top panel graphs the temperature-dependent intensity for PS-Py probe layers located at different distances from a PS/PSF interface where PS forms the rubbery, lower Tg component: at a distance z = 139 nm (far from the PS/PSF interface), the local Tg(z) = 103 ± 2 °C, consistent with the Tg of bulk PS, but at a distance z = 51 nm (closer to the PS/PSF interface), the local Tg(z) = 120 ± 2 °C, significantly increased relative to Tgbulk of PS. For comparison, the bottom panel graphs the temperature-dependent intensity for PS-Py probe layers located at different distances from a PS/PnBMA interface where PS forms the glassy, higher Tg component: at a distance z = 356 nm (far from the PS/PnBMA interface), the local Tg(z) = 99 ± 2 °C, consistent with the Tg of bulk PS as expected, but at a distance z = 64 nm (closer to the PS/PnBMA interface), the local Tg(z) = 63 ± 2 °C, significantly decreased relative to Tgbulk of PS.19 Decreasing the separation distance (z layer thickness) of the pyrene-labeled PS layer in relation to the dissimilar polymer-polymer interface drastically changes the local Tg at that location relative to PS bulk Tg. The magnitude of the Tg perturbation is large (+19 K and −38 K) at a distance (51 and 64 nm) that is still quite far from the dissimilar polymer-polymer interface. As discussed by Baglay and Roth,19 these perturbations in local Tg occur far from the polymer-polymer interface such that locally only PS segments are present at the position z. The local Tg(z) near the PS/PnBMA interface is not at all correlated with the local composition ϕ(z), which has been the traditional view in understanding local Tg in miscible polymer blends.23–25 These distances (z = 51 and 64 nm) are also quite large compared to the observed perturbation length scales associated with the PS-free surface,50,53 but are comparable to systems with highly chemically interactive substrates.49,51,52

FIG. 3.

Normalized fluorescence intensity as a function of temperature collected on cooling at 1 °C/min for four different samples. (Top) PS/PSF system: pyrene-labeled PS probe layer located at a distance z = 139 nm away from the PS/PSF interface reports a local Tg(z) = 103 ± 2 °C in agreement with Tgbulk of PS, while at a distance z = 51 nm, the local Tg(z) = 120 ± 2 °C significantly increased by the presence of the PS/PSF interface. (Bottom) PS/PnBMA system:19 at a distance z = 356 nm, the local Tg(z) = 99 ± 2 °C in agreement with Tgbulk of PS, while at a distance z = 64 nm, the local Tg(z) = 63 ± 2 °C significantly decreased by the presence of the PS/PnBMA interface. In both cases, the large perturbation in local Tg(z) occurs at distances that are many tens of nanometers away from the change in composition.

FIG. 3.

Normalized fluorescence intensity as a function of temperature collected on cooling at 1 °C/min for four different samples. (Top) PS/PSF system: pyrene-labeled PS probe layer located at a distance z = 139 nm away from the PS/PSF interface reports a local Tg(z) = 103 ± 2 °C in agreement with Tgbulk of PS, while at a distance z = 51 nm, the local Tg(z) = 120 ± 2 °C significantly increased by the presence of the PS/PSF interface. (Bottom) PS/PnBMA system:19 at a distance z = 356 nm, the local Tg(z) = 99 ± 2 °C in agreement with Tgbulk of PS, while at a distance z = 64 nm, the local Tg(z) = 63 ± 2 °C significantly decreased by the presence of the PS/PnBMA interface. In both cases, the large perturbation in local Tg(z) occurs at distances that are many tens of nanometers away from the change in composition.

Close modal

To further investigate the length scale of the dynamical Tg perturbation near the PS/PSF interface, Figure 4 graphs the local Tg(z) values measured for many different samples where the thickness of the neat PS z-layer between PSF and the PS-Py probe reporting layer was varied. Error bars of ±2 °C were determined based on the standard deviation of multiple measurements at comparable z values as the largest experimental error is associated with sample-to-sample variability. It is not possible to polymerize PSF with a pyrene label; thus, we are restricted to only mapping the PS side of the PS/PSF Tg(z) profile. However, all data collected indicate that the Tg(z) profile behaves similarly to the full Tg(z) profile collected previously19 for PS/PnBMA where the data are well fit by a hyperbolic tangent function, which asymptotes to the bulk Tg values far from the interface on either side, with a broad mobility-gradient, strongly biased toward the glassy PS side. The PS/PSF Tg(z) data can be similarly fit to a hyperbolic tangent showing the broad mobility-gradient is now strongly biased toward the glassy PSF side. The local Tg-dynamics transition smoothly from one extreme to the other across the interface, in contrast to the composition. The dashed curves in the figure represent the composition profiles of the two systems, ϕ(z) ≈ tanh(2z/wI), with equilibrium interfacial width wI = 7 nm for PS/PnBMA19–22 and wI = 6 nm for PS/PSF (estimated based on solubility parameters92–94). On the scale of Fig. 4, the two composition profiles look similar and nearly vertical, starkly defining the location of the interface. By comparing directly the Tg(z) profiles of the PS/PSF system with that measured previously for the PS/PnBMA system, we can observe two distinct behaviors: (1) The magnitude of the Tg reduction or enhancement from bulk Tg dynamics is not dependent on the relative Tg difference at the polymer-polymer interface. In both the PS/PnBMA and PS/PSF systems, the difference in Tg is 80-85 K, yet the PS-Py probe layers close to the PS/PnBMA interface experience more than twofold greater deviation in local Tg(z) from the bulk Tg of PS for a given distance z, as compared to the PS-Py probe layers close to the PS/PSF interface. The local Tg(z = 0) at the interface is consistently closer to the lower Tg component in both systems: Tg(z = 0) = 37 ± 2 °C for PS/PnBMA and Tg(z = 0) = 130 ± 3 °C for PS/PSF. (2) The z-distance at which the perturbation in local Tg(z) begins on the PS side as the PSF or PnBMA interface is approached is significantly different: at z ≈ 125 nm as PSF is approached and at z ≈ 250 nm as PnBMA is approached. In addition, the propagation of the Tg(z) perturbation is uncorrelated with the magnitude of the Tg difference between the two polymers and is independent of the magnitude in Tg(z) perturbation at the interface. Below we discuss separately these two factors: the magnitude of the perturbation in local Tg at the interface and the distance of propagation away from the interface that the dynamical perturbation persists. By comparing a series of polymer systems, we will show that these behaviors of the broad Tg(z) profile appear to be universal across different systems and are grouped in behavior by whether the neighboring interface has a higher or lower Tg, i.e., hard vs. soft confinement.

FIG. 4.

Experimentally measured local Tg(z) profile of PS/PSF (open blue diamonds), compared with that previously measured19 for PS/PnBMA (open red circles), as a function of z, the pyrene-labeled layer’s position from the PS/PSF or PS/PnBMA interface. In the PS/PSF system, the PS layer is rubbery relative to PSF undergoing hard confinement, while in the PS/PnBMA system, and the PS layer is glassy relative to PnBMA undergoing soft confinement. Both PS/PSF and PS/PnBMA systems have a bulk Tg difference of 80-85 K between the two domains that the local Tg(z) must transition between. We previously demonstrated19 that the PS/PnBMA Tg(z) profile was well fit by a hyperbolic tangent (solid black curve) demonstrating that the mobility-gradient is broad and strongly biased toward the glassy PS side. Dashed curves indicate the local composition profiles ϕ(z) with an equilibrium interfacial width of 6 nm (PS/PSF) and 7 nm (PS/PnBMA), which appear nearly vertical on this scale unmistakably highlighting the breadth of the Tg mobility gradient.

FIG. 4.

Experimentally measured local Tg(z) profile of PS/PSF (open blue diamonds), compared with that previously measured19 for PS/PnBMA (open red circles), as a function of z, the pyrene-labeled layer’s position from the PS/PSF or PS/PnBMA interface. In the PS/PSF system, the PS layer is rubbery relative to PSF undergoing hard confinement, while in the PS/PnBMA system, and the PS layer is glassy relative to PnBMA undergoing soft confinement. Both PS/PSF and PS/PnBMA systems have a bulk Tg difference of 80-85 K between the two domains that the local Tg(z) must transition between. We previously demonstrated19 that the PS/PnBMA Tg(z) profile was well fit by a hyperbolic tangent (solid black curve) demonstrating that the mobility-gradient is broad and strongly biased toward the glassy PS side. Dashed curves indicate the local composition profiles ϕ(z) with an equilibrium interfacial width of 6 nm (PS/PSF) and 7 nm (PS/PnBMA), which appear nearly vertical on this scale unmistakably highlighting the breadth of the Tg mobility gradient.

Close modal

As it is difficult to precisely identify the location where Tg(z) begins deviating from bulk behavior, we have chosen to quantify the propagation distance of the dynamical Tg(z) perturbation from bulk dynamics by identifying the distance from the interface ξ1/2 at which the magnitude of the Tg(z) perturbation at the interface |Tg(z=0)Tgbulk| decays to half its value, ξ1/2=zwhen|Tg(z)Tgbulk||Tg(z=0)Tgbulk|=0.5. This quantification of a length scale for the dynamical perturbation follows from our previous work19 and is based on an original definition of a kinetic correlation length in glassy systems put forward by Butler and Harrowell.43 In 1991, Butler and Harrowell85 explored the temperature dependence of the mean spin relaxation times τ(T) characterizing dynamical heterogeneity in the 2D two-spin facilitated Ising model (2FSM) of Fredrickson and Andersen.95,96 This simple facilitated kinetic Ising spin model exhibits heterogeneous dynamics, a broad spectrum of relaxation times, and undergoes dynamic arrest when the effective temperature is decreased. These characteristic hallmarks of the glass transition are achieved with only nearest-neighbor dynamical interactions; yet, this simple system otherwise does not contain an equilibrium phase transition or an inherent static correlation length. As a separate consideration to their main work,85 Butler and Harrowell also explored how the local relaxation time τn for a given layer n would behave when next to a surface layer of all up spins.43 Butler and Harrowell43 characterized the dynamical influence of a surface of all up spins on the glassy kinetics of this simple Ising model as a function of layer distance n away from the surface by defining a kinetic correlation length ξ1/2(T) as the distance from the surface (n = 1) at which the perturbation to the local relaxation time τn relative to bulk decayed to half its value, ξ1/2(T)=n when |τnτbulk||τ1τbulk|=0.5. Having full access to the temperature-dependent relaxation time τn(T) from their simulations, Butler and Harrowell were able to determine the values of ξ1/2(T) for different temperatures. They found that the temperature dependence of ξ1/2(T) matched the temperature dependence of the mean relaxation times τ(T) previously determined for the bulk system and argued that such a surface decay kinetic correlation length ξ1/2(T) was a reflection of kinetic correlations of glassy dynamics in bulk systems.43 In their simulations, Butler and Harrowell found values of ξ1/2(T) up to 5-6 spin-layers as the glass transition was approached from above, meaning deviations from bulk dynamics could persist to a depth of 10-12 spin-layers from the surface interface of all up spins. Although there is no direct way to convert n spin-layers to a physical size in nanometers, we can consider that one spin-lattice site can flip (rearrange) from up to down, corresponding to a coarse-grained measure of a local arrangement of several physical units (polymer segments), representing a local region of the material. With only dynamical correlations between nearest-neighboring spins, the influence of the all-up spin interface persists to depths of many such spin sites.

We recognize that this ξ1/2 length scale is a rather arbitrary definition, but it has the advantage of being robustly quantifiable from the experimentally measured Tg(z) values and according to the work of Butler and Harrowell43,85 may provide insight into size-scales associated with glassy cooperative dynamics. Thus, we proceed with this measure of quantification for the propagation distance of the dynamical Tg(z) perturbation from bulk dynamics. We previously reported that for the PS/PnBMA system, ξ1/2=103 nm for glassy PS, while ξ1/2=50 nm for rubbery PnBMA.19 From Figure 4 we find that in the PS/PSF system, ξ12=49 nm for rubbery PS. Thus, we see that the length scale over which the dynamical Tg(z) perturbation persists depends on whether PS is next to PnBMA (soft confinement) or PSF (hard confinement), and that the length scale in PnBMA next to PS (hard confinement) is comparable to that for PS next to PSF (also hard confinement). This suggests that the propagation of the dynamical Tg(z) perturbation does not depend directly on some material property such as chemical structure, but rather on whether the domain in question is in its glassy or rubbery state. As we will see in the next section, PS glassy domains in contact with a rubbery interface (soft confinement) have their local Tg(z) dynamics consistently perturbed out to a further distance from the interface than PS rubbery domains in contact with a glassy interface (hard confinement).

Next, we explore how universal this hard vs. soft confinement behavior is by comparing profiles of the local Tg(z) dynamics in the PS domain next to a series of different polymers with higher (hard) and lower (soft) Tg in reference to PS. By making this comparison across different systems, we are able to address possible factors and causes that could affect the strong Tg(z) coupling in cooperative segmental dynamics between domains of dissimilar polymers. Again, for each system presented here, we have made sure that the dissimilar polymer-polymer interface has been annealed to equilibrium. The section titled Varying annealing time of PS/PSF interface: Importance of reaching equilibrium will address what occurs when the dissimilar polymer-polymer interface has only undergone limited annealing, demonstrating that the strong Tg(z) coupling is significantly reduced or even eliminated if local interdiffusion of the chains has not been allowed to occur.

Figure 5 graphs the Tg(z) values within the PS domain next to interfaces with four different polymers: PSF (Tgbulk = 186 °C), PMMA (Tgbulk = 120 °C), PiBMA (Tgbulk=62 °C), and PnBMA (Tgbulk =21 °C). The bulk Tg of PS = 101 °C is identified by the horizontal dashed black line clearly demarcating which polymers have a higher Tg than PS resulting in hard confinement, and which have a lower Tg than PS resulting in soft confinement. In addition, we added the Tg(z) data collected on the rubbery PnBMA side from the PS/PnBMA system,19 but in order to make a comparison of the extended length scale of the Tg(z) perturbation between hard and soft confined systems, we have plotted the magnitude of the Tg(z) perturbation measured in rubbery PnBMA next to PS (hard confinement of PnBMA), on the PS side and elevated it to be referenced to the bulk Tg of PS: Tg(z) = Tg(z) of PnBMA − TgbulkPnBMA+TgbulkPS, with −zz. In this manner, we can clearly see that the rubbery PnBMA Tg(z) under hard confinement next to glassy PS, behaves very similarly to the rubbery PS Tg(z) under hard confinement next to PSF and PMMA. It is clear from the data that the behavior of the Tg(z) profile near a dissimilar polymer-polymer interface primarily depends on whether the domain in question is experiencing hard confinement next to a polymer with higher Tg than itself or soft confinement next to a polymer with lower Tg than itself. For glassy polymers under soft confinement, the Tg(z) perturbation is much larger and extends to much greater distances (z ≈ 225-250 nm before bulk Tg of PS is recovered), compared with rubbery polymers under hard confinement (z ≈ 100-125 nm before bulk Tg of PS is recovered). The depth from the dissimilar polymer-polymer interface to which the local Tg(z) is perturbed is independent of the magnitude of the Tg difference between the two polymers in question and the magnitude of the Tg(z) perturbation itself. The behavior depicted by the data appears to be universal to these various polymers, some with very different chemical structures. Note that we have not indicated the composition profiles of the interface in Fig. 5, but if included they would resemble a nearly vertical step changes at z = 0 on this scale, given the enormous range of the x-axis.

FIG. 5.

Local Tg(z) profile in the PS domain as a function of distance z from the dissimilar polymer-polymer interface with various neighboring polymers: PSF (Tgbulk=186 °C) shown as blue diamonds, PMMA (Tgbulk=120 °C) shown as red triangles, PiBMA (Tgbulk = 62 °C) shown as purple squares, and PnBMA (Tgbulk = 21°C) shown as green circles. The behavior (magnitude and penetration distance) of the Tg(z) profile is primarily dependent on whether PS (Tgbulk = 101 °C, horizontal dashed line) experiences hard confinement next to a polymer with a higher Tgbulk (depth to which perturbation decays to half its value ξ1/2 = 55 ± 5 nm) or soft confinement next to a polymer with a lower Tgbulk (ξ1/2=115 ± 5 nm). For comparison, previous data19 of the magnitude of the Tg(z) perturbation in rubbery PnBMA next to glassy PS (hard confinement) are added as gray stars where the data have been shifted to the Tgbulk of PS as reference.

FIG. 5.

Local Tg(z) profile in the PS domain as a function of distance z from the dissimilar polymer-polymer interface with various neighboring polymers: PSF (Tgbulk=186 °C) shown as blue diamonds, PMMA (Tgbulk=120 °C) shown as red triangles, PiBMA (Tgbulk = 62 °C) shown as purple squares, and PnBMA (Tgbulk = 21°C) shown as green circles. The behavior (magnitude and penetration distance) of the Tg(z) profile is primarily dependent on whether PS (Tgbulk = 101 °C, horizontal dashed line) experiences hard confinement next to a polymer with a higher Tgbulk (depth to which perturbation decays to half its value ξ1/2 = 55 ± 5 nm) or soft confinement next to a polymer with a lower Tgbulk (ξ1/2=115 ± 5 nm). For comparison, previous data19 of the magnitude of the Tg(z) perturbation in rubbery PnBMA next to glassy PS (hard confinement) are added as gray stars where the data have been shifted to the Tgbulk of PS as reference.

Close modal

To make quantitative comparisons between the various Tg(z) datasets shown in Figure 5, we calculate the Tg(z = 0) value at the interface between the two dissimilar polymers and determine the distance ξ1/2 from the interface at which the Tg(z) perturbation decays to half its value. These values are tabulated in Table I for the various systems, along with the bulk Tg of the polymer in contact with PS, and the difference ΔTg between the two bulk Tg values. We clearly observe a pattern where polymer domains under soft confinement (next to a polymer interface with a lower Tg than itself) exhibit a large decrease in Tg(z) near the interface over an extremely large length scale ξ1/2 = 115 ± 5 nm, while polymer domains under hard confinement (next to a polymer interface with a higher Tg than itself) exhibit a more modest increase in Tg(z) near the interface over a comparatively smaller length scale ξ1/2 = 55 ± 5 nm. For reference we also include values for the equilibrium interfacial width wI between the two immiscible polymers and the fragility m of the neighboring polymer next to PS. Although the equilibrium interfacial widths of the composition profile ϕ(z) vary between 5 and 7 nm, these are very small differences that appear to have little if any influence on the Tg(z) behavior. (Although there are no reports in the literature of PS/PiBMA equilibrium interfacial widths or even χ values, we suspect it is likely comparable to that between PS/PnBMA as the magnitude and temperature dependence of the surface tension of PiBMA is very similar to that of PnBMA.97) Perhaps this is unsurprising given the small size of the composition profile in comparison to the large range of the dynamical Tg(z) profile. However, as we discuss further in the section titled Varying annealing time of PS/PSF interface: Importance of reaching equilibrium, we do believe that the broad nature of polymer-polymer interfaces, in comparison to the sharp (≤0.5 nm) polymer-air, polymer-liquid, or polymer-substrate interfaces plays some unique role in leading to the enormous dynamical Tg(z) profiles we observe.

TABLE I.

Tabulated values of the experimentally determined Tg(z = 0) at the interface between the two dissimilar polymers, the distance ξ12 from the interface at which the Tg(z) perturbation decays to half its value, and for reference the Tg bulk of the polymer in contact with the PS domain, along with the difference ΔTg between the two bulk Tg values of the system, the equilibrium interfacial width wI of the composition profile, and the fragility98m of the neighboring polymer next to PS. In the last row of the table are the corresponding values for PnBMA in contact with PS.

PolymerTgbulk (°C)ΔTg (K)Tg (z = 0) (°C)Penetration distance ξ12 (nm)Interfacial width wI (nm)Fragility m
PS/ PSF 186 85 130 49 6 (Ref. 92141 (Ref. 101
 PMMA 120 19 112 59 5 (Ref. 122145 (Ref. 102
 PiBMA 62 39 75 127 … 67 (Ref. 123
 PnBMA 21 80 37 103 7 (Ref. 2056 (Ref. 101
PnBMA/ PS 101 80 37 50 7 (Ref. 20139 (Ref. 103
PolymerTgbulk (°C)ΔTg (K)Tg (z = 0) (°C)Penetration distance ξ12 (nm)Interfacial width wI (nm)Fragility m
PS/ PSF 186 85 130 49 6 (Ref. 92141 (Ref. 101
 PMMA 120 19 112 59 5 (Ref. 122145 (Ref. 102
 PiBMA 62 39 75 127 … 67 (Ref. 123
 PnBMA 21 80 37 103 7 (Ref. 2056 (Ref. 101
PnBMA/ PS 101 80 37 50 7 (Ref. 20139 (Ref. 103

Evans et al. have recently measured the experimental Tg value of thin PS layers surrounded by large (500-nm thick) bulk layers of different polymers.71 They found that as the PS layer thickness decreased, the Tg of the PS layer increased or decreased relative to TgbulkPS and approached the bulk Tg value of the surrounding polymer in their trilayer systems. For the thinnest films of 14-nm PS, the maximum shift in Tg of the PS domain was equivalent to previous measurements99,100 of the component Tg of isolated PS chains (0.1 wt. % blends at near-infinite dilution) in a matrix of different polymer that was the same as the surrounding polymer in the trilayer system. Evans et al. argued that the magnitude of the perturbation to the PS Tg in these trilayer and near-infinite dilution systems was correlated with the fragility value of the neighboring (surrounding) polymer.71,100 We consider now if our experimentally measured magnitude of the perturbation in local Tg is correlated with the fragility of the neighboring domain. Our maximum perturbation in local Tg occurs at the dissimilar polymer-polymer interface (z = 0). Following the work of Evans et al.,71 we calculate the relative shift in the magnitude of the Tg perturbation at the interface as |Tg(z=0)Tgbulk|/ΔTg from the data presented in Table I. For the perturbation to the PS component in our systems, we find at best only a loose correlation between fragility of the neighboring domain with the magnitude of the Tg perturbation. However, it is not consistent with PSF and PMMA, which have comparable fragilities101,102 (141 and 145), but significantly different magnitudes in perturbation (35% and 60% of maximum, respectively). We can also estimate how universal this correlation with neighboring fragility might be by determining the magnitude of the Tg perturbation for the other polymers at the dissimilar polymer-polymer interface caused by the presence of the PS domain. The magnitude of the Tg perturbation at the interface (z = 0) varies from 20% to 65% for the different polymers presented in Table I, while the fragility of the neighboring domain (PS) is a fixed value (m = 139).103 Thus, for our systems, it does not appear that fragility is a key parameter in controlling the magnitude of the Tg perturbation. However, we do have a qualitatively different geometry of two semi-infinite domains in contact, instead of isolated chains or small domains of PS surrounded by a dissimilar polymer.

Recently a number of theoretical and computational efforts have explored the dynamics of glassy systems in proximity to high mobility interfaces. Of particular interest to the present study is a limited mobility model by Tito et al.37,104 where they have modeled exchanges in local mobility within a heterogeneous glassy material and investigated local mobility profiles near various interfaces. Their 2013 work37 modeled a slab of a glassy or rubbery domain that was sandwiched by material that had either a lower or higher mobility. Within this kinetic lattice model, probabilities for mobility exchange between neighboring lattice sites transitioned a given site between three different states (“awake,” “sleep,” or “dense”), where a series of exchange parameters collectively governed the dynamics of the system. Profiles of the local mobility as a function of position across the system showed different penetration depths to which the local dynamics were perturbed by the interface between the glassy-rubbery domains at different temperatures. The Tito et al. work37 predicted an asymmetric mobility profile at the glassy-rubbery interface that extends further into the glassy (lower mobility side) than into the rubbery (higher mobility side). This prediction of an asymmetric mobility profile is consistent with our experimental results shown in Fig. 5 for the various glassy-rubbery polymer-polymer interfaces. This suggests that the observed asymmetry in the Tg(z) profiles (i.e., the difference in penetration depth of perturbed dynamics between the glassy and rubbery sides) may reflect a property of how glassy dynamics behave near interfaces.

Simmons and coworkers have investigated using bead-spring MD simulations the role that interfacial energy between neighboring domains of a low Tg and a high Tg influence each other’s dynamics.66,105 The high Tg domain under soft confinement by the lower Tg polymer had its Tghigh reduced relative to its Tgbulk,high and the low Tg domain under hard confinement by the higher Tg polymer had its Tglow increased relative to its Tgbulk,low. The Tg shift in the low-Tg domain under hard confinement was additionally influenced by the magnitude of the interfacial energy between the two domains. One complicating factor in comparing these simulations to our experimental results is that when the interfacial energy was varied in the simulations, it also altered the degree of chain interpenetration between the two domains. In the section titled Varying annealing time of PS/PSF interface: Importance of reaching equilibrium, we demonstrate experimentally that the observed Tg(z) profiles reported in Figures 4 and 5 are strongly dependent on the amount of annealing of the dissimilar polymer-polymer interface and hence likely the extent of chain interpenetration across this interface. However, of significance, the MD simulations found that the degree to which interfacial energy affected the Tg shift was correlated with the mean-square displacement u2 of the neighboring domain, a quantity characterizing the “hardness” or shear modulus of the material.66 Starr and Douglas have also found that local Tg dynamics near an interface in bead-spring MD simulations correlate with the relative stiffness of the underlying substrate.38 Perhaps this gives insight into why our experimental results are separated into longer length scales (ξ1/2 = 115 ± 5 nm) for domains under soft confinement and shorter length scales (ξ1/2 = 55 ± 5 nm) for domains under hard confinement, i.e., it is the softness or hardness of the neighboring domain that influences how local Tg-dynamics are perturbed near these interfaces.

The role that local stiffness or local modulus plays in α-relaxations and Tg has recently received renewed treatment by Mirigian and Schweizer.106ߝ109 They have proposed that the α-relaxation event can be facilitated by a collective elastic distortion of the surrounding material, where the size of this distortion field is related to the local elastic shear modulus. This would suggest that the local α-relaxations (Tg) would be influenced by its local surroundings out to a greater distance when the material is locally stiffer. Applying this reasoning to our glassy-rubbery polymer-polymer interface systems might suggest that the higher shear modulus of the glassy side would be altered out to a greater extent than that of the softer rubbery side. This reasoning perhaps provides a qualitative argument for why the direction of the Tg(z) asymmetry is biased towards the glassy side of the dissimilar polymer-polymer interface. Although the Mirigian and Schweizer theory has been successfully applied to model local Tg changes near free surfaces,44,45 it has not yet been applied to dissimilar polymer-polymer interfaces.

None of these theories address the large quantitative size of the length scales we observe. This is still an outstanding question. It is unclear why polymer-polymer interfaces alter the local Tg value out to hundreds of nanometers in contrast to polymer-air interfaces which typically perturb the dynamics out to only several tens of nanometers at most. We discuss this in more detail in the section titled Varying annealing time of PS/PSF interface: Importance of reaching equilibrium. We do note that size scales typically associated with glass transition dynamics (ξCRR few nanometers) are much smaller than the length scales of interfacial perturbations in confined systems.19,50,52,53,110 However, a number of theoretical models such as Random First Order Transition (RFOT) theory42,111 and the Mirigian and Schweizer model just described incorporate secondary longer-ranged factors where the local cooperative dynamics are influenced by neighboring collective dynamics. Experiments such as in this study demonstrating long-ranged Tg perturbations suggest that factors beyond a single CRR size may be more important than we realize in understanding glassy dynamics.

Here we demonstrate the importance of annealing the dissimilar polymer-polymer interface in establishing the observed Tg(z) profiles. We find that the strong coupling in cooperative segmental dynamics across the interface and the extended length scales over which the Tg(z) perturbation persists from the interface only occur if the dissimilar polymer-polymer interface is annealed to equilibrium. It is easiest to demonstrate this effect by focusing on the PS/PSF system. As described in the Experimental Methods section and Figure 1, when measuring the Tg(z) of a lower Tg component (e.g., PS in PS/PSF), we first anneal the PS z-layer and underlying PSF layer together to ensure that this dissimilar polymer-polymer interface has been annealed to equilibrium. Second, we add the additional PS-Py labeled-probe layer and top (bulk) PS layer, performing a second annealing step of the PS/PS-Py/PS interfaces in order to obtain a consolidated material, while still limiting interdiffusion of the probe layer, prior to the Tg(z) measurement. We found that for a given location z from the interface, the measured Tg(z) value varied with the length of time of the first annealing step (that of the PS/PSF interface) up to some saturation time scale, after which the measured Tg(z) value was reproducible and invariant to further annealing of the PS/PSF interface.

Figure 6 demonstrates the progression in Tg(z) values at z = 50 nm for the PS/PSF system, where we have varied the annealing time of the PS/PSF interface (first annealing step) during assembly of the multilayered structures. For very limited annealing of the PS/PSF interface, only 20 min, the Tg(z = 50 nm) = 100 ± 2 °C, equivalent to the bulk Tg value of PS, indicating that little to no dynamic coupling has occurred across the PS/PSF interface. In contrast, for 40 and 60 min of annealing the PS/PSF interface, the Tg(z = 50 nm) increases quickly to 110 ± 2 °C and 118 ± 2 °C, respectively. After 60 min, further annealing the PS/PSF interface does little to change the Tg(z = 50 nm) value further, with the Tg(z = 50 nm) reaching a limiting value of 121 ± 2 °C. It is important to note that this annealing of the PS/PSF interface was done at 210 °C, above to the bulk Tg values of both polymers.

FIG. 6.

(a) Fluorescence intensity at an emission wavelength of 379 nm collected on cooling at 1 °C/min for PS-Py probe layers located at a fixed distance of z = 50 nm from the PS/PSF interface. Data for three different samples are shown where the PS/PSF interface was annealed for various lengths of time (20, 40, and 60 min) at a temperature of 210 °C (above the bulk Tg of both PS and PSF) prior to the Tg(z) fluorescence measurements. With progressively longer annealing times leading to increasing local PS/PSF chain interdiffusion, the Tg(z = 50 nm) increases from 100 ± 2 °C, essentially the bulk Tg value of PS for only 20 min of annealing, to 110 ± 2 °C after 40 min and 118 ± 2 °C after 60 min of annealing. (b) Local Tg(z = 50 nm) as a function of annealing time of the PS/PSF interface at 210 °C demonstrating that the measured Tg(z) value saturates and becomes invariant after ∼60 min of annealing when the PS/PSF interface reaches equilibrium. Dashed curve is a best fit to the data with a stretched exponential decay (see text for details).

FIG. 6.

(a) Fluorescence intensity at an emission wavelength of 379 nm collected on cooling at 1 °C/min for PS-Py probe layers located at a fixed distance of z = 50 nm from the PS/PSF interface. Data for three different samples are shown where the PS/PSF interface was annealed for various lengths of time (20, 40, and 60 min) at a temperature of 210 °C (above the bulk Tg of both PS and PSF) prior to the Tg(z) fluorescence measurements. With progressively longer annealing times leading to increasing local PS/PSF chain interdiffusion, the Tg(z = 50 nm) increases from 100 ± 2 °C, essentially the bulk Tg value of PS for only 20 min of annealing, to 110 ± 2 °C after 40 min and 118 ± 2 °C after 60 min of annealing. (b) Local Tg(z = 50 nm) as a function of annealing time of the PS/PSF interface at 210 °C demonstrating that the measured Tg(z) value saturates and becomes invariant after ∼60 min of annealing when the PS/PSF interface reaches equilibrium. Dashed curve is a best fit to the data with a stretched exponential decay (see text for details).

Close modal

Figure 6(b) plots these local Tg(z = 50 nm) values as a function of annealing time of the PS/PSF interface at 210 °C. The data are reasonably well fit to a stretched exponential decay with an average relaxation time τ=8 min and stretching exponent of β=0.6. Such values are consistent with the idea that the local Tg(z = 50 nm) values are saturating because the PS/PSF interface is annealing further to equilibrium. Polymer-polymer interface annealing occurs initially via Rouse modes, easily leading to equilibrium interfacial widths of several nanometers.88,112 If the polymers are immiscible such as is the case for the dissimilar polymer pairs in the present study, the equilibrium interfacial width saturates at a maximum value dictated by the unfavorable interaction parameter χ, while in contrast, if the polymers were miscible, further annealing would lead to interdiffusion via reptation. Given the broad spectrum of relaxation times exhibited by the Rouse modes of long chained polymers, it is not surprising that a stretched exponential decay, rather than a single exponential, was necessary to fit the data in Fig. 6(b). The Tg(z) values in Fig. 6(b) saturate after approximately 60 min of annealing, a time comparable to that required to obtain equilibrium interfacial widths of 5-7 nm at temperatures of Tg + ∼25 K in literature studies.113–116 We note that we have previously addressed the possible suggestion that some small fraction of low MW chains could diffuse across the weakly immiscible dissimilar polymer-polymer interface and possibly plasticize the PS component. We previously demonstrated that the Tg(z) profile, when annealed to equilibrium, is independent of MW and MW distribution of the neighboring polymer next to PS.19 

Figure 7 illustrates how the Tg(z) profile on the PS side of the PS/PSF interface would evolve as a function of annealing time for the PS/PSF interface. The open diamonds plot the data from Fig. 5 that was collected after annealing the PS/PSF interface for 90 min, ensuring that equilibrium was reached. Tg(z) data for z = 50 and 70 nm are included in the figure for the different annealing times shown in Fig. 6. The data in Fig. 7 illustrate that the Tg(z) profile would be nearly flat, remaining at essentially the bulk Tg of PS, at z-values quite close the PS/PSF interface for only 20 min of annealing. In contrast, 40 min of annealing leads to an intermediate Tg(z) profile, compared with the 60+ min of annealing required to obtain an equilibrium PS/PSF interface. From this we conclude that the amount of local interpenetration of the chains across the dissimilar polymer-polymer interface plays a significant role in creating dynamical coupling of cooperative segmental, Tg-dynamics between the two dissimilar polymers.

FIG. 7.

Local Tg(z) profiles on the PS side of the PS/PSF system. Data from Figure 5, where the PS/PSF interface has been annealed for 90 min to equilibrium are shown as open diamonds. Tg(z) data for z = 50 and 70 nm collected at the different PS/PSF interface annealing times shown in Figure 6 are plotted as colored symbols (same color coding as shown in Fig. 6): red diamonds indicate that annealing for only 20 min leads to Tg(z) values still close to that of bulk PS with a nearly flat Tg(z) profile, while 40 min of annealing (purple diamonds) shows an intermediate Tg(z) profile compared with that measured for 60+ min of annealing.

FIG. 7.

Local Tg(z) profiles on the PS side of the PS/PSF system. Data from Figure 5, where the PS/PSF interface has been annealed for 90 min to equilibrium are shown as open diamonds. Tg(z) data for z = 50 and 70 nm collected at the different PS/PSF interface annealing times shown in Figure 6 are plotted as colored symbols (same color coding as shown in Fig. 6): red diamonds indicate that annealing for only 20 min leads to Tg(z) values still close to that of bulk PS with a nearly flat Tg(z) profile, while 40 min of annealing (purple diamonds) shows an intermediate Tg(z) profile compared with that measured for 60+ min of annealing.

Close modal

One of the major open questions that this work still does not reveal is why polymer-polymer interfaces appear to be so qualitatively different than polymer-free surface, polymer–substrate, and even polymer–liquid interfaces. As we demonstrated, annealing of the dissimilar polymer-polymer interface is necessary to cause the strong dynamical coupling observed. What factors during polymer-polymer interface formation are responsible? During annealing, the interfacial width broadens, the dissimilar polymer chains interpenetrate locally, and the interface roughens, any one of which could be facilitating the dynamical coupling across the interface. Future work is required to disentangle these possible contributing factors. One interesting point is that the breadth or nature of the dissimilar polymer-polymer interface is somehow requiring that the local cooperative segmental dynamics become continuous across the boundary, which may be responsible for creating the large breadth of the Tg(z) profile. For only limited (20 min) amounts of annealing, we showed that the Tg(z) profile appears very narrow and could possibly be discontinuous at the dissimilar polymer-polymer interface. This would be more like polymer-free surface, polymer–substrate, and polymer–liquid interfaces (all ∼0.5 nm) where the molecular dynamics from one phase to another are locally discontinuous.

We have used a localized fluorescence probe to measure local glass transition temperature Tg(z) profiles in PS domains near interfaces with different polymers. This work builds on our recent measurements19 where we mapped the full dynamical Tg(z) profile across a PS/PnBMA polymer-polymer interface finding that the dynamical profile does not correlate with the local composition profile ϕ(z). Unexpectedly, the dynamical Tg(z) profile spanned 350-400 nm in extent and was asymmetric with respect to the 7 nm wide composition profile. Here we demonstrate this broad, asymmetric Tg(z) behavior appears to be universal across a number of different systems. Figure 5 shows that the distance from the interface over which the Tg(z) profile decays in PS varies depending on if the neighboring domain has a higher Tg (hard confinement) or lower Tg (soft confinement). In addition, we find that the Tg(z) profile in PS (Tgbulk = 101 °C) next to PSF (Tgbulk = 186 °C) behaves similar to the Tg(z) profile in PnBMA (Tgbulk = 21 °C) next to PS. This suggests that the propagation of this dynamical Tg(z) perturbation does not depend on some material property such as chemical structure, but rather on whether the polymer has a higher or lower Tg than its neighbor.

We characterize the penetration depth by the distance ξ1/2 from the interface at which the Tg(z) perturbation decays to half its value. Such a definition builds on previous work by Butler and Harrowell43 who related a similar length scale to the temperature dependence of dynamical heterogeneities in a glassy model system. More recent theoretical efforts have also tied dynamical perturbations near interfaces to glassy dynamics and its associated length scales.37–42,44,45 We find that PS next to PSF and PMMA, so-called hard confinement of PS, shows ξ1/2 = 55 ± 5 nm, compared with PS next to PnBMA and PiBMA, soft confinement of PS, shows ξ1/2 = 115 ± 5 nm. To within experimental error, we do not observe a difference in ξ1/2 between the PSF and PMMA system, or the PnBMA and PiBMA system, suggesting that the magnitude of the difference in Tgbulk between the two domains does not dictate the propagation depth in PS. These systems also have slight differences in equilibrium interfacial width, which does not seem to change the length scale of the behavior. However, we find that these large length scales associated with the Tg(z) behavior are only observed when the dissimilar polymer-polymer interface is annealed to equilibrium. We demonstrate using PS/PSF that if the dissimilar PS/PSF interface is minimally annealed for only 20 min at 210 °C, compared with the 60+ min required to reach equilibrium, strong dynamical coupling is not observed between the two dissimilar polymer domains and the Tg(z) profile appears nearly discontinuous at the interface. This important observation suggests that the strong dynamical coupling between dissimilar polymer domains, leading to the broad continuous Tg(z) profiles, are caused by some change that occurs during annealing.

Comparing polymer-polymer interfaces to interfacial perturbations near polymer-free surface, polymer-substrate, and polymer-liquid interfaces, we suggest three possible factors that may be responsible for the long range effects. Polymer-polymer interfaces are typically much wider (∼5 nm) compared with the sharp (∼0.5 nm) composition profiles associated with the other types of interfaces. Chain connectivity could be also playing a modifying role to dynamical perturbations near interfaces, as has been seen recently in a few studies.117ߝ119 Alternatively, interfacial roughness, which has been shown in computer simulations to have a modifying effect on local dynamics,39,120,121 could also be a factor as polymer-polymer interfaces would be expected to experience increased interfacial roughness due to their reduced interfacial energy.97 Future work will be needed to disentangle these possible factors. The results presented here provide experimental data of a model system for comparison to future theoretical efforts and have implications for how local properties should be considered in polymer blends.

The authors gratefully acknowledge support from National Science Foundation CAREER program (Grant No. DMR-1151646) and Emory University.

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