Session D32: Polymer Glasses

Invited: Glass transition of polymers under ultrafine nanoconfinement: interfacial dynamics and the spatial gradients

Polymers under nanoconfinement can exhibit large alterations in dynamics or mechanical properties from their bulk values. These large changes in properties impact strongly the macroscopic properties of multicomponent or multiphase polymeric materials that have been widely used for engineering applications. The large influence of the nanoconfinement has often been attributed to an interface effect. However, the origin of the interface effect and its connection with the bulk glass transition remains a topic of active debate. In particular, a spatial gradient in polymer dynamics near an interface has been widely acknowledged. On the other hand, experimental characterizations of the interfacial dynamics gradient remain rare, hindering an in-depth understanding of the interface effect and its relationship to the nanoconfinement effect. In this contribution, we prepare ultrathin polymer films of ~10 nm in thickness and perform systematic dynamics measurements through broadband dielectric spectroscopy. The structural relaxation over a wide temperature range will be presented. The glass transition of these ultrathin films will also be discussed in detail, with a special focus on the spatial gradient of interfacial dynamics and its relationship to the glass transition.   

Acoustic Wave Propagation as a Long-Range Mechanism for Interactions in Glasses: Experimental Evidence from Studies on Glassy-Rubbery Polymer Bilayers

Over the years several different experiments in nanoconfined systems have demonstrated unexplained long-ranged interactions of interfacial effects. For example, our group has observed profiles in local glass transition temperature Tg(z) across glassy-rubbery polymer-polymer interfaces that can span ~200+ nm. We have found that the range and magnitude of this effect correlate with the interfacial width between the two polymer domains and the modulus of the neighboring domain. More recently, we have investigated shear wave propagation in glassy polystyrene (PS) and rubbery poly(butadiene) (PB) bilayers using a quartz crystal microbalance (QCM), finding that a broad gradient in modulus G(z) emerges upon formation of the ~5 nm PS/PB compositional interface, consistent with the broad Tg(z) profile in this system. We propose that how interfaces impact the propagation of acoustic waves across the system, reflecting or transmitting at interfaces, may be key to understanding this behavior and other long-range effects in glasses. In particular, the propagation of acoustic waves ~5 nm that can hybridize with quasilocalized excitations (QLEs) associated with collective oscillations, which have been computationally linked to cooperative alpha-relaxation events. These ideas are supported by existing literature demonstrating changes to the vibrational density of states (VDoS) near the boson peak in thin films. This talk will summarize what evidence exists in support of such a long-range mechanism.   

How Does the Length of End-grafted Polystyrene Chains Alter the Spatial Gradient in Local Glass Transition Temperature Tg(z) Near Silica Interfaces?

A first-principles understanding of how grafted chains alter material properties in polymer nanocomposites is not yet solidified due to the experimental difficulty of spatially resolving changes to material properties, especially within composite materials. We address this by assembling multilayer samples that enable using a localized fluorescence method to spatially resolve the local glass transition temperature Tg(z) at different positions z from the substrate interface. Focusing on polystyrene (PS) matrix chains intermixed with grafted PS chains at the silica interface allows us to isolate the topological changes to the local dynamics caused by grafting, as bare PS/silica interfaces do not perturb local Tg. Our recent work showed large +45 K increases in local Tg(z=0) next to the grafted silica interface, independent of grafted chain length between Mn = 9 kg/mol and 200 kg/mol and grafting density across the mushroom-to-brush transition regime. Here, we expand on that work by measuring the spatial gradient in local Tg(z) as a function of distance from the interface, constructing Tg(z) profiles for varying grafted chain lengths. We observe long gradients in Tg(z), significantly longer than the extent of the grafted chains themselves, with a saturating molecular weight dependence reminiscent of Tg(Mn) in bulk.   

Correlation between Fragility and Surface Tg of Polymers

The fragility of glass describes how rapidly its molecules slow down as it cools near its glass transition temperature. In nanoscale films, polymer glasses with higher fragility experience larger reductions in their T_g compared to those with lower fragility. We investigated whether this is due to the free surface of the polymers, which can cause the surface T_g (T_g^surf) to decrease relative to the bulk T_g. By measuring the T_g^surf of various polymers, we found that the shift in T_g^surf relative to the bulk T_g increased with fragility. This suggests that more fragile polymers are more susceptible to the free surface effect. We explain this using the concept of energy landscape, as it is used to explain the different slowdown rates between strong and fragile glass-formers at T_g.   

Using Rheological and Dielectric Spectroscopy Measurements of Time-Temperature Superposition Breakdown to Validate Heterogeneous Rouse Model

Time-Temperature Superposition (TTS) is a technique used widely to analyze materials dynamic and mechanical data. However, beginning with Plazek in the 1960’s, the breakdown of TTS was reported in diverse polymers near the glass transition. For example, rheological data on polystyrene show clear evidence of TTS breakdown between 105 ℃ and 130 ℃. This breakdown takes the form of a decoupling of the polymer chain and segmental dynamics, with viscosity generally exhibiting a weaker temperature dependence than the segmental dynamics. No settled consensus on the mechanistic origins of this breakdown has emerged over the last half century, despite its extensive utilization to predict and characterize polymer linear rheological response near the glass transition temperature (T_g).

Recently, our group introduced the Heterogeneous Rouse Model (HRM) to explain TTS breakdown. HRM is based on the existence of a distribution of relaxation times near T_g. Here, we report on extensions of this model to predict multiple linear-regime rheological behaviors, and we compare these predictions to new experimental data for TTS breakdown in multiple polymers, combining dielectric spectroscopy and rheological measurements. Results suggest that TTS breakdown near T_g can be understood and quantitatively described via the HRM, providing a new basis for analysis of near-T_g linear rheological response.   

A random walk description of mobility in glasses

Molecular motion is believed to be the key to the glass transition and the glassy behavior in general. Yet in the theoretical models the time dependent quantities are continuous e.g., density modes. Particles in condensed matter interact strongly and there does not seem to be a method of describing their movement short of the MD simulation. Here we investigate if a single particle model of molecular motion can capture at least some characteristic features of the glass forming systems. The target properties are the mean squared displacement (MSD) and the orientational autocorrelators as simulated via MD or extracted from the spectroscopic data. These properties exhibit rich behaviors in liquid and glassy state; e.g., the MSD exhibits a sub-diffusive plateau followed at longer times by asymptotic diffusive regime, where the length of the plateau increases dramatically with cooling toward the glass transition.

The translational diffusive behavior as well as the Debye rotational relaxation can be modeled as a discrete random walk. But what about the other features, including the MSD plateau? We analyze a sequence of random walk models of increasing complexity to establish what is required to reproduce the experimentally observed features of translational and rotational relaxation. The models include biased random walk and random walk on a cage structure of different topology in one, two, and three dimensions. The random walk models are able to account for: the sub-diffusive regime, dynamic heterogeneity, emergence of the α- and β- relaxation processes, wedge-like shape of the α- relaxation spectrum, and the relative rate of decay of the first and second Legendre polynomials of the cosine of the rotation angle.  Unlike the traditional models, the random walk models do not involve overcoming potential energy barriers. The characteristic slowing down of the mobility in the random walk-based models results from increasing tortuosity of the path a molecule follows.      

Evidence for Two Mechanisms Driving Molecular Weight Dependence of the Glass Transition Temperature in Linear Polymers

Recently, the canonical understanding for the relationship between molecular weight, M, and the glass transition temperature, Tg, has become the focus of renewed attention. Several studies in the past decade have shown that the 70-year-old functional forms used to describe this trend are at best first-order approximations and do not apply to all polymers across the full domain of M (spanning from the monomer to the infinite linear chain). This work analyzes monomer-resolution dynamics of a diverse trio of polymers from molecular dynamics which adds to this growing body of evidence that Fox-Flory-like arguments of chain end effects are not the leading cause of the decrease of Tg with smaller M. To the contrary, we see that chain end effects are negligible in a fully-flexible polymer, and chain end effects present in stiff polymers surprisingly become weaker on cooling towards Tg. Our data suggests M effects on Tg can be separated into two components, wherein enhanced chain end mobility is chemistry-dependent and a separate whole-chain effect is present in all models. Continued work on this fundamental relationship may further guide the long-standing effort for a comprehensive theory describing the glass transition.   

Combined Modeling of the Volume, Dielectric, and Stress Relaxation and Fatigue Behavior in Glassy Polymers

We combine our recently developed two-state amorphous material model, “SL-TS2”¹ with simple linear elasticity describing the affine bulk and shear deformations. Due to the hierarchy of timescales, the slowest (“α”) relaxation process is described by the nonlinear Trachenko-Zaccone² equation. We show that for the mechanical stress relaxation (shear or tensile/compressive), this equation can be re-written as the Eyring plasticity equation,³ resulting in the asymptotic Guiu-Pratt⁴ logarithmic solution. Interestingly, the same solution can be also approximated by the Kohlrausch-Williams-Watts (KWW) function, at least in the intermediate time range. Finally, we describe the potential application of the model to the prediction of a material fatigue lifetime based on a simplified approach of Janssen et al.,⁵ and discuss other applications and modifications of the proposed theory. References: 1. Ginzburg, V. V; Zaccone, A.; Casalini, R. Soft Matter 2022, 18, 8456–8466. 2. Trachenko, K.; Zaccone, A. Journal of Physics: Condensed Matter 2021, 33 (31), 315101. 3. Eyring, H. J Chem Phys 1936, 4 (4), 283–291. 4. Guiu, F.; Pratt, P. L. Physica status solidi (b) 1964, 6 (1), 111–120. 5. Janssen, R. P. M.; Govaert, L. E.; Meijer, H. E. H. Macromolecules 2008, 41 (7), 2531–2540.   

Local structural effects on thermodynamic properties and dynamic response

In this talk I will outline our recent progress in linking dynamic response of glassy materials to their thermodynamic properties which, in turn, link to local molecular structure. For example, the response of a bulk sample to an isothermal increase in pressure is slower segmental relaxation. We have shown this can be predicted using our independent equation-of-state analysis of thermodynamic data, which reveals both how the total volume and the free volume of the material change with pressure. Further, it turns out that an increase in total volume does not necessarily track with an increase in free volume. [1] Being able to deconvolute the two using a first principles theory is key to understanding the impact of local packing changes on dynamic response. The latter is tracked using our simple theory that exploits a rate model to capture both the volume and temperature dependence of segmental relaxation . I will focus on two kinds of systems that illustrate this thermodynamic-dynamic linkage: One comprises two sets of nanocomposites, the other a family of increasingly crosslinked polyvinylethylenes. This work has been supported through NSF-DMR-2006504.   

Segmental (α-) and Slow (SAP) Relaxation Processes: Connections with Thermodynamic Properties and Physical Aging

In this talk we will discuss recent work in modeling and comparing two molecular level processes that are important in the relaxation of glass-forming materials: the "segmental" α- relaxation process (well-known for its association with glassy behavior) and another, slower, Arrhenius-like process, the "SAP". Both can be tracked using dielectric spectroscopy. Recent evidence indicates that the SAP drives certain stages of the physical aging process and other equilibration processes, e.g. adsorption. The SAP also appears to be connected with rheological properties, and its kinetics exhibit a compensation effect between activation energy and activation entropy. These observations motivate our interest in understanding how the SAP mechanism works and how its dynamics are connected to a material's corresponding thermodynamic properties. Using equation of state analysis and kinetic models we have recently shown strong correlations between the α- process and thermodynamic properties, e.g. free volume, thermal expansivity and close-packing. In this talk we will present results revealing thermodynamic connections to the SAP.   

Spatial variations in dynamic heterogeneity in polymer thin films

Polymers in the nanoscale vicinity of interfaces can exhibit immense alterations in relaxation dynamics and glass formation behavior. These alterations take the form of large spatially-organized gradients in relaxation dynamics near an interface. At the same time, bulk glass-forming liquids such as polymers exhibit a substantial degree of spatial dynamic heterogeneity in the form of a distribution of local relaxation times, albeit without the degree of static spatial organization inherent to interfacial gradients in dynamics. Here, we describe results of molecular dynamics simulations probing the interplay of these effects. How does the presence of an interfacial dynamical gradient alter the dynamic heterogeneity present in bulk? How does the presence of heterogeneity in turn alter near-interface dynamics in and out of equilibrium? How is the anisotropy of dynamics altered near interfaces? By employing simulations in the isoconfigurational ensemble, here we provide insight into the answers to these questions.