Glass transition and molecular mobility in polymer thin films

Interplay between dynamic heterogeneity and interfacial gradients in a model polymer film

Glass-forming liquids exhibit long-lived, spatially correlated dynamical heterogeneity, in which some nm-scale regions in the fluid relax more slowly than others. In the nanoscale vicinity of an interface, glass-formers also exhibit the emergence of massive interfacial gradients in glass transition temperature Tg and relaxation time τ. Both of these forms of heterogeneity have a major impact on material properties. Nevertheless, their interplay has remained poorly understood. Here, we employ molecular dynamics simulations of polymer thin films in the isoconfigurational ensemble in order to probe how bulk dynamic heterogeneity alters and is altered by the large gradient in dynamics at the surface of a glass-forming liquid. Results indicate that the τ spectrum at the surface is broader than in the bulk despite being shifted to shorter times, and yet it is less spatially correlated. This is distinct from the bulk, where the τ distribution becomes broader and more spatially organized as the mean τ increases. We also find that surface gradients in slow dynamics extend further into the film than those in fast dynamics-a result with implications for how distinct properties are perturbed near an interface. None of these features track locally with changes in the heterogeneity of caging scale, emphasizing the local disconnect between these quantities near interfaces. These results are at odds with conceptions of the surface as reflecting simply a higher "rheological temperature" than the bulk, instead pointing to a complex interplay between bulk dynamic heterogeneity and spatially organized dynamical gradients at interfaces in glass-forming liquids.

The microscopic origins of stretched exponential relaxation in two model glass-forming liquids as probed by simulations in the isoconfigurational ensemble

The origin of stretched exponential relaxation in supercooled glass-forming liquids is one of the central questions regarding the anomalous dynamics of these fluids. The dominant explanation for this phenomenon has long been the proposition that spatial averaging over a heterogeneous distribution of locally exponential relaxation processes leads to stretching. Here, we perform simulations of model polymeric and small-molecule glass-formers in the isoconfigurational ensemble to show that stretching instead emerges from a combination of spatial averaging and locally nonexponential relaxation. The results indicate that localities in the fluid exhibiting faster-than-average relaxation tend to exhibit locally stretched relaxation, whereas slower-than-average relaxing domains exhibit more compressed relaxation. We show that local stretching is predicted by loose local caging, as measured by the Debye-Waller factor, and vice versa. This phenomenology in the local relaxation of in-equilibrium glasses parallels the dynamics of out of equilibrium under-dense and over-dense glasses, which likewise exhibit an asymmetry in their degree of stretching vs compression. On the basis of these results, we hypothesize that local stretching and compression in equilibrium glass-forming liquids results from evolution of particle mobilities over a single local relaxation time, with slower particles tending toward acceleration and vice versa. In addition to providing new insight into the origins of stretched relaxation, these results have implications for the interpretation of stretching exponents as measured via metrologies such as dielectric spectroscopy: measured stretching exponents cannot universally be interpreted as a direct measure of the breadth of an underlying distribution of relaxation times.

Crystallization of Poly(ethylene)s with Regular Phosphoester Defects Studied at the Air-Water Interface

Poly(ethylene) (PE) is a commonly used semi-crystalline polymer which, due to the lack of polar groups in the repeating unit, is not able to form Langmuir or Langmuir-Blodgett (LB) films. This problem can be solved using PEs with hydrophilic groups arranged at regular distances within the polymer backbone. With acyclic diene metathesis (ADMET) polymerization, a tool for precise addition of polar groups after a certain interval of methylene sequence is available. In this study, we demonstrate the formation of Langmuir/LB films from two different PEs with regular phosphoester groups, acting as crystallization defects in the main chain. After spreading the polymers from chloroform solution on the water surface of a Langmuir trough and solvent evaporation, the surface pressure is recorded during compression under isothermal condition. These π-A isotherms, surface pressure π vs. mean area per repeat unit A, show a plateau zone at surface pressures of ~ (6 to 8) mN/m, attributed to the formation of crystalline domains of the PEs as confirmed by Brewster angle and epifluorescence microscopy. PE with ethoxy phosphoester defects (Ethoxy-PPE) forms circular shape domains, whereas Methyl-PPE-co-decadiene with methyl phosphoester defects and two different methylene sequences between the defects exhibits a film-like morphology. The domains/films are examined by atomic force microscopy after transferring them to a solid support. The thickness of the domains/films is found in the range from ~ (2.4 to 3.2) nm depending on the transfer pressure. A necessity of chain tilt in the crystalline domains is also confirmed. Grazing incidence X-ray scattering measurements in LB films show a single Bragg reflection at a scattering vector qxy position of ~ 15.1 nm-1 known from crystalline PE samples.

A simple mean-field model of glassy dynamics and glass transition

We propose a phenomenological model to describe the equilibrium dynamic behavior of amorphous glassy materials. It is assumed that a material can be represented by a lattice of cooperatively re-arranging regions (CRRs), with each CRR having two states, the low-temperature "solid" and the high-temperature "liquid". At low temperatures, the material exhibits two characteristic relaxation times, corresponding to the slow large-scale motion between the "solid" CRRs (α-relaxation) and the faster local motion within individual CRRs (β-relaxation). At high temperatures, the α- and β-relaxation times merge, as observed experimentally and suggested by the "Coupling Model" framework. Our new approach is labeled "Two-state, two (time)scale model" or TS2. It is shown that the TS2 treatment can successfully describe the "two-Arrhenius" relaxation time behavior described in several recent experiments. We also apply TS2 to describe the pressure- and molecular-weight dependence of the glass transition temperature in bulk polymers, as well as its dependence on film thickness in thin films.

Glassy state molecular mobility and its relationship to the physico-mechanical properties of plasticized hydroxypropyl methylcellulose (HPMC) films

Changes in tensile properties and the glass transition temperature (T_g) of plasticized polymer films are typically attributed to molecular mobility, often with no empirical data to support such an assertion. Herein solvent cast HPMC films containing varying amounts of PEG, as the plasticizer, were used to assess the dependence of tensile properties and the T_g on glassy state molecular mobility. Molecular mobility (molecular relaxation time and temperature) parameters were determined by Thermally Stimulated Current Spectroscopy (TSC). The tensile properties and T_g of the HPMC films were determined by texture analysis and DSC, respectively. Molecular mobilities detected by TSC were cooperative and occurred at temperatures (T_g′) well below (113 to 127 °C) the bulk T_g. The relaxation times (τ) were 71 ± 1, 46 ± 1, 42 ± 1, 36 ± 1 and 29 ± 1 s for HPMC films containing 0, 6, 8, 11 and 17% (w/w) PEG, respectively. The T_g and glassy state molecular mobility were found to be intimately linked and demonstrated a linear dependence. While tensile strength was found to be linearly related to molecular relaxation time, tensile elongation and elastic modulus exhibited a non-linear dependence on molecular mobility. The data presented in this work demonstrates the complex nature of the relationship between plasticizer content, molecular mobility, T_g and tensile properties for plasticized polymeric films. It highlights the fact that the dependence of the bulk physico-mechanical properties on glassy state molecular mobility, differ greatly. Therefore, empirical characterization of molecular mobility is important to fully understand and predict the thermo-mechanical behavior of plasticized polymer films. This work demonstrates the unique capability of TSC to provide key information relating to molecular mobility and its influence on the bulk properties of materials. Data generated using TSC could prove useful for stability and performance ranking, in addition to the ability to predict materials behavior using data generated at or below typical storage conditions in the pharmaceutical, food, and polymer industries.

Why we need to look beyond the glass transition temperature to characterize the dynamics of thin supported polymer films

There is significant variation in the reported magnitude and even the sign of [Formula: see text] shifts in thin polymer films with nominally the same chemistry, film thickness, and supporting substrate. The implicit assumption is that methods used to estimate [Formula: see text] in bulk materials are relevant for inferring dynamic changes in thin films. To test the validity of this assumption, we perform molecular simulations of a coarse-grained polymer melt supported on an attractive substrate. As observed in many experiments, we find that [Formula: see text] based on thermodynamic criteria (temperature dependence of film height or enthalpy) decreases with decreasing film thickness, regardless of the polymer-substrate interaction strength ε. In contrast, we find that [Formula: see text] based on a dynamic criterion (relaxation of the dynamic structure factor) also decreases with decreasing thickness when ε is relatively weak, but [Formula: see text] increases when ε exceeds the polymer-polymer interaction strength. We show that these qualitatively different trends in [Formula: see text] reflect differing sensitivities to the mobility gradient across the film. Apparently, the slowly relaxing polymer segments in the substrate region make the largest contribution to the shift of [Formula: see text] in the dynamic measurement, but this part of the film contributes less to the thermodynamic estimate of [Formula: see text] Our results emphasize the limitations of using [Formula: see text] to infer changes in the dynamics of polymer thin films. However, we show that the thermodynamic and dynamic estimates of [Formula: see text] can be combined to predict local changes in [Formula: see text] near the substrate, providing a simple method to infer information about the mobility gradient.

Experimental investigation of the glass transition of polystyrene thin films in a broad frequency range

In this study, we investigate the α process of a polystyrene thin film using inelastic neutron scattering (INS), dielectric relaxation spectroscopy (DRS), and thermal expansion spectroscopy (TES). The DRS and TES measurements exhibited a decrease in glass transition temperature (T_{g}) with film thickness. On the other hand, an increase in T_{g} was observed in INS studies. In order to interpret this contradiction, we investigated the temperature dependence of the peak frequency (f_{m}) of the α process probed by DRS and TES. The experiments revealed an increase in the peak frequency (f_{m}) with decreasing film thickness in the frequency region. This observation is consistent with the observed decrease in T_{g} with thickness. Interestingly, the increase in T_{g} with film thickness was confirmed by fitting the temperature dependence measurements of the peak frequency with the Vogel-Fulcher-Tammann equation, within the frequency region probed by INS. The discrepancy between INS and DRS or TES descriptions of the α process is likely to be attributed to a decrease in the apparent activation energy with film thickness and reduced mobility, due to the impenetrable wall effect.

Structure and Mechanical Properties of Polybutadiene Thin Films Bound to Surface-Modified Carbon Interface

The structure and mechanical properties of polybutadiene (PB) films on bare and surface-modified carbon films were examined. There was an interfacial layer of PB near the carbon layer whose density was higher (lower) than that of the bulk material on the hydrophobic (hydrophilic) carbon surface. To glean information about the structure and mechanical properties of PB at the carbon interface, a residual layer (RL) adhering to the carbon surface, which was considered to be a model of "bound rubber layer", was obtained by rinsing the PB film with toluene. The density and thickness of the RLs were identical to those of the interfacial layer of the PB film. In accordance with the change in the density, normal stress of the RLs evaluated by atomic force microscopy was also dependent on the surface free energy: the RLs on the hydrophobic carbon were hard like glass, whereas those on the hydrophilic carbon were soft like rubber. Similarly, the wear test revealed that the RLs on the hydrophilic carbon could be peeled off by scratching under a certain stress, whereas the RLs on the hydrophobic carbons were resistant to scratching.

Distribution of glass transition temperatures Tg in polystyrene thin films as revealed by low-energy muon spin relaxation: A comparison with neutron reflectivity results

In a previous paper [Phys. Rev. E 83, 021801 (2011)] we performed neutron reflectivity (NR) measurements on a five-layer polystyrene (PS) thin film consisting of alternatively stacked deuterated polystyrene (dPS) and hydrogenated polystyrene (hPS) layers (dPS/hPS/dPS/hPS/dPS, ∼100 nm thick) on a Si substrate to reveal the distribution of Tg along the depth direction. Information on the Tg distribution is very useful to understand the interesting but unusual properties of polymer thin films. However, one problem that we have to clarify is if there are effects of deuterium labeling on Tg or not. To tackle the problem we performed low-energy muon spin relaxation (μSR) measurements on the above-mentioned deuterium-labeled five-layer PS thin film as well as dPS and hPS single-layer thin films ∼100 nm thick as a function of muon implantation energy. It was found that the deuterium labeling had no significant effects on the Tg distribution, guaranteeing that we can safely discuss the unusual thin film properties based on the Tg distribution revealed by NR on the deuterium-labeled thin films. In addition, the μSR result suggested that the higher Tg near the Si substrate is due to the strong orientation of phenyl rings.

Polymer dynamics near the surface and in the bulk of poly(tetrafluoroethylene) probed by zero-field muon-spin-relaxation spectroscopy

The results of many experiments on polymers such as polystyrene indicate that the polymer chains near a free surface exhibit enhanced dynamics when compared with the bulk. We have investigated whether this is the case for poly(tetrafluoroethylene) (PTFE) by using zero-field muon-spin-relaxation spectroscopy to characterize a local probe, the F-Mu(+)-F state, which forms when spin-polarized positive muons are implanted in PTFE. Low-energy muons (implantation energies from 2.0 to 23.0 keV) were used to study the F-Mu(+)-F state between ∼ 23 and 191 nm from the free surface of PTFE. Measurements were also made with surface muons (4.1 MeV) where the mean implantation depth is on the order of ∼ 0.6 mm. The relaxation rate of the F-Mu(+)-F state up to ∼ 150 K was found to be significantly higher for muons implanted at 2.0 keV than for higher implantation energies, which suggests that the polymer chains in a region on the order of a few tens of nanometers from the free surface are more mobile than those in the bulk.

Distribution of glass transition temperature in multilayered poly(methyl methacrylate) thin film supported on a Si substrate as studied by neutron reflectivity

We studied the distribution of glass transition temperature (Tg) through neutron reflectivity in a poly(methyl methacrylate) (PMMA) thin film supported on a silicon substrate with a five-layered PMMA thin film consisting of deuterated-PMMA and hydrogenated-PMMA. The depth distribution of Tg was successfully observed in the PMMA thin film. Compared to the previously reported distribution of Tg in a polystyrene thin film, the presence of a long-range interfacial effect, supposedly caused by an interaction between PMMA and the substrate, is considered to be responsible for the differences in both the distribution of Tg and the thickness dependence of Tg in both polymers. Therefore, it is expected that the thickness dependence of Tg reported for single-layered polymer thin films can, in principle, be understood from the viewpoint of the difference in the depth distribution of Tg.

Density profile in thin films of polybutadiene on silicon oxide substrates: a TOF-NR study

We have investigated thin films from fully deuterated polybutadiene (PB-d6) on silicon substrates with the aim of detecting and characterizing a possible interphase in the polymer film near the substrate using time-of-flight neutron reflectometry (TOF-NR). As substrates, thermally oxidized silicon wafers were either used as such or they were coated with triethylethoxysilyl modified 1,2-PB prior to deposition of the PB-d6 film. TOF-NR reveals that, for both substrates, the scattering length density (SLD) of the PB films decreases near the solid interface. The reduction of SLD is converted to an excess fraction of free volume. To further verify the existence of the interphase in PB-d6, we attempt to model the TOF-NR curves with density profiles which do not feature an interphase. These density profiles do not describe the TOF-NR curves adequately. We conclude that, near the solid interface, an interphase having an SLD lower than the bulk of the film is present.

Glass transition in thin supported polystyrene films probed by temperature-modulated ellipsometry in vacuum

Glass transition in thin (1-200 nm thick) spin-cast polystyrene films on silicon surfaces is probed by ellipsometry in a controlled vacuum environment. A temperature-modulated modification of the method is used alongside a traditional linear temperature scan. A clear glass transition is detected in films with thicknesses as low as 1-2 nm. The glass transition temperature (T(g)) shows no substantial dependence on thickness for coatings greater than 20 nm. Thinner films demonstrate moderate T(g) depression achieving 18 K for thicknesses 4-7 nm. Less than 4 nm thick samples are excluded from the T(g) comparison due to significant thickness nonuniformity (surface roughness). The transition in 10-20 nm thick films demonstrates excessive broadening. For some samples, the broadened transition is clearly resolved into two separate transitions. The thickness dependence of the glass transition can be well described by a simple 2-layer model. It is also shown that T(g) depression in 5 nm thick films is not sensitive to a wide range of experimental factors including molecular weight characteristics of the polymer, specifications of solvent used for spin casting, substrate composition, and pretreatment of the substrate surface.

Slow dynamics, dynamic heterogeneities, and fragility of supercooled liquids confined in random media

Using molecular dynamics simulations, we study the slow dynamics of supercooled liquids confined in a random matrix of immobile obstacles. We study the dynamical crossover from glass-like to Lorentz-gas-like behavior in terms of the density correlation function, the mean square displacement, the nonlinear dynamic susceptibility, the non-gaussian parameter, and the fragility. We find the cooperative and spatially heterogeneous dynamics to be suppressed as the obstacle density increases, leading to a more Arrhenius-like behavior in the temperature dependence of the relaxation time. Our findings are qualitatively consistent with the results of recent experimental and numerical studies for various classes of spatially heterogeneous systems. We also investigate the dependence of the dynamics of mobile particles on the protocol used to generate the random matrix. A re-entrant transition from the arrested phase to the liquid phase as the mobile particle density increases is observed for a class of protocols. This re-entrance is explained in terms of the distribution of the volume of the voids that are available to the mobile particles.

Distributions of glass-transition temperature and thermal expansivity in multilayered polystyrene thin films studied by neutron reflectivity

We performed neutron reflectivity measurements on multilayered polymer thin films consisting of alternatively stacked deuterated polystyrene (d-PS) and hydrogenated polystyrene (h-PS) layers ∼200 Å thick as a function of temperature covering the glass-transition temperature T(g), and we found a wide distribution of T(g) as well as a distribution of the thermal expansivity α within the thin films, implying the dynamic heterogeneity of the thin films along the depth direction. The reported anomalous film thickness dependences of T(g) and α were reasonably understood in terms of the distributions, showing that the surface mobile layer and the bottom hard interfacial layer are, respectively, responsible for the depressions of T(g) and α with decreasing film thickness. The molecular mobility in each layer is also discussed in relation to the distribution of T(g), based on the results on mutual diffusion at the layer interface.