Progress towards a phenomenological picture and theoretical understanding of glassy dynamics and vitrification near interfaces and under nanoconfinement

Polymers under nanoconfinement: where are we now in understanding local property changes?

Polymers are increasingly being used in applications with nanostructured morphologies where almost all polymer molecules are within a few tens to hundreds of nanometers from some interface. From nearly three decades of study on polymers in simplified nanoconfined systems such as thin films, we have come to understand property changes in these systems as arising from interfacial effects where local dynamical perturbations are propagated deeper into the material. This review provides a summary of local glass transition temperature T_g changes near interfaces, comparing across different types of interfaces: free surface, substrate, liquid, and polymer-polymer. Local versus film-average properties in thin films are discussed, making connections to other related property changes, while highlighting several historically important studies. By experimental necessity, most studies are on high enough molecule weight chains to be well entangled, although aspects that connect to lower molecule weight materials are described. Emphasis is made to identify observations and open questions that have yet to be fully understood such as the evidence of long-ranged interfacial effects, finite domain size, interfacial breadth, and chain connectivity.

A Simple New Way To Account for Free Volume in Glassy Dynamics: Model-Free Estimation of the Close-Packed Volume from PVT Data

In this article we focus on the important role of well-defined free volume (V_free) in dictating the structural relaxation times, τ, of glass-forming liquids and polymer melts. Our definition of V_free = V - V_hc, where V is the total system volume, means the use of V_free depends on determination of V_hc, the system's volume in the limiting closely packed state. Rejecting the historically compromised use of V_free as a dynamics-dependent fitting function, we have successfully applied a clear thermodynamics-based route to V_hc using the locally correlated lattice (LCL) model equation of state (EOS). However, in this work we go further and show that V_hc can be defined without the use of an equation of state by direct linear extrapolation of a V(T) high-pressure isobar down to zero temperature (T). The results from this route, tested on a dozen experimental systems, yield ln τ vs 1/V_free isotherms that are linear with T-dependent slopes, consistent with the general ln τ ∼ f(T) × (1/V_free) form of behavior we have previously described. This functional form also results by implementing a simple mechanistic explanation via the cooperative free volume (CFV) rate model, which assumes that dynamic relaxation is both thermally activated and that it requires molecular segmental cooperativity. With the degree of the latter, and thus the activation energy, being determined by the availability of free volume, the new route we demonstrate here for determination of V_free expands the potential for understanding and predicting local dynamic relaxation in glass-forming materials.

Lateral diffusion of single poly(ethylene oxide) chains on the surfaces of glassy and molten polymer films

Fluorescence correlation spectroscopy was used to show that the temperature-dependent diffusion coefficient of poly(ethylene oxide) (PEO) adsorbed on polystyrene and different poly(alkyl methacrylate) (PAMA) films in aqueous solution exhibited a maximum close to (but below) the surface glass transition temperature, T_gs, of the film. This elevated diffusion was observed over a small range of temperatures below T_gs for these surfaces, and at other temperatures, the diffusion was similar to that on silicon, although the diffusion coefficient for PEO on polystyrene at temperatures above T_gs did not completely decrease to that on silicon, in contrast to the PAMA surfaces. It is concluded that the enhanced surface mobility of the films near the surface glass transition temperature induces conformational changes in the adsorbed PEO. The origin of this narrow and dramatic increase in diffusion coefficient is not clear, but it is proposed that it is caused by a coupling of a dominant capillary mode in the liquid surface layer with the polymer. Friction force microscopy experiments also demonstrate an unexpected increase in friction at the same temperature as the increase in diffusion coefficient.

Gradient of Segmental Dynamics in Stereoregular Poly(Methyl Methacrylate) Melts Confined between Pristine or Oxidized Graphene Sheets

Segmental dynamics in unentangled isotactic, syndiotactic, and atactic poly(methyl methacrylate) (i-, a-, and s-PMMA) melts confined between pristine graphene, reduced graphene oxide, RGO, or graphene oxide, GO, sheets is studied at various temperatures, well above glass transition temperature, via atomistic molecular dynamics simulations. The model RGO and GO sheets have different degrees of oxidization. The segmental dynamics is studied through the analysis of backbone torsional motions. In the vicinity of the model nanosheets (distances less than ≈2 nm), the dynamics slows down; the effect becomes significantly stronger with increasing the concentration of the surface functional groups, and hence increasing polymer/surface specific interactions. Upon decreasing temperature, the ratios of the interfacial segmental relaxation times to the respective bulk relaxation times increase, revealing the stronger temperature dependence of the interfacial segmental dynamics relative to the bulk dynamics. This heterogeneity in temperature dependence leads to the shortcoming of the time-temperature superposition principle for describing the segmental dynamics of the model confined melts. The alteration of the segmental dynamics at different distances, d, from the surfaces is described by a temperature shift, ΔTseg(d) (roughly speaking, shift of a characteristic temperature). Next, to a given nanosheet, i-PMMA has a larger value of ΔTseg than a-PMMA and s-PMMA. This trend correlates with the better interfacial packing and longer trains of i-PMMA chains. The backbone torsional autocorrelation functions are shown in the frequency domain and are qualitatively compared to the experimental dielectric loss spectra for the segmental α-relaxation in polymer nanocomposites. The εT″(f) (analogous of dielectric loss, ε″(f), for torsional motion) curves of the model confined melts are broader (toward lower frequencies) and have lower amplitudes relative to the corresponding bulk curves; however, the peak frequencies of the εT″(f) curves are only slightly affected.

Strain Rate and Thickness Dependences of Elastic Modulus of Free-Standing Polymer Nanometer Films

Elastic moduli, E, of free-standing polystyrene (PS) single-layers and polystyrene-polydimethylsiloxane (PS-PDMS) bilayers are measured by uniaxial tensile testing at room temperature under different strain rates, γ̇, and for PS thicknesses, h, from 8 to 130 nm. As γ̇ increases, E increases initially, then approaches the bulk value, E_bulk, when γ̇ exceeds a characteristic value (≡ τ^-1) that decreases with increasing h. The noted variation of E with γ̇ shows that stress relaxation occurs in the films during measurement when γ̇τ ≪ 1, while the noted variation of τ^-1 with h shows that thinner films relax faster. Consequently, E decreases with decreasing h if γ̇ is small, but displays independence of h if γ̇ is large. Visually, the crossover takes place at around γ̇ = 0.0015 s^-1, where at γ̇τ > 1 for all films.

Local Glass Transition Temperature Tg(z) Within Polystyrene Is Strongly Impacted by the Modulus of the Neighboring PDMS Domain

Profiles in the local glass transition temperature T_g(z) within polystyrene (PS) next to polydimethylsiloxane (PDMS) domains were determined using a localized fluorescence method. By changing the base to cross-linker ratio, we varied the cross-link density and, hence, the Young's modulus of PDMS (Sylgard 184). The local T_g(z) in PS at a distance of z = 50 nm away from the PS/PDMS interface was found to shift by 40 K as the PDMS modulus was varied from 0.9 to 2.6 MPa, demonstrating a strong sensitivity of this phenomenon to the rigidity of the neighboring domain. The extent the T_g(z) perturbation persists away from the PS/PDMS interface, z ≈ 65-90 nm before bulk T_g is recovered, is much shorter for this strongly immiscible system compared with the weakly immiscible systems studied previously, which we attribute to a smaller interfacial width, as the χ parameter for PS/PDMS is an order of magnitude larger.

Energy barriers and cooperative motion at the surface of freestanding glassy polystyrene films

We investigate the near-surface relaxation of freestanding atactic polystyrene films with molecular dynamics simulations. As in previous coarse-grained simulations, relaxation times for backbone segments and phenyl rings are linked to their bulk relaxation times via a power-law coupling relation. Variation of the coupling exponent with distance from the surface is consistent with depth-dependent activation barriers. We also quantify a reduction in dynamical heterogeneity at the interface, which can be interpreted in the framework of cooperative models for glassy dynamics.

Dynamic phase transitions in freestanding polymer thin films

After more than two decades of study, many fundamental questions remain unanswered about the dynamics of glass-forming materials confined to thin films. Experiments and simulations indicate that free interfaces enhance dynamics over length scales larger than molecular sizes, and this effect strengthens at lower temperatures. The nature of the influence of interfaces, however, remains a point of significant debate. In this work, we explore the properties of the nonequilibrium phase transition in dynamics that occurs in trajectory space between high- and low-mobility basins in a set of model polymer freestanding films. In thick films, the film-averaged mobility transition is broader than the bulk mobility transition, while in thin films it is a variant of the bulk result shifted toward a higher bias. Plotting this transition's local coexistence points against the distance from the films' surface shows thick films have surface and film-center transitions, while thin films practically have a single transition throughout the film. These observations are reminiscent of thermodynamic capillary condensation of a vapor-liquid phase between parallel plates, suggesting they constitute a demonstration of such an effect in a trajectory phase transition in the dynamics of a structural glass former. Moreover, this transition bears similarities to several experiments exhibiting anomalous behavior in the glass transition upon reducing film thickness below a material-dependent onset, including the broadening of the glass transition and the homogenization of surface and bulk glass transition temperatures.

To Understand Film Dynamics Look to the Bulk

We show that shifts in dynamics of confined systems relative to that of the bulk material originate in the properties of bulk alone, and exhibit the same form of behavior as when different bulk isobars are compared. For bulk material, pressure-dependent structural relaxation times follow τ(T,V)∝exp[f(T)×g(V)]. When two states (isobars) of the material, "1" and "2", are compared at the same temperature this leads to a form τ_{2}∝τ_{1}^{c}, where c=g[V_{2}(T)]/g[V_{1}(T)]. Using equation of state analysis and two models for P-dependent dynamics, we show that c is approximately T independent, and that it can be very simply expressed in terms of either the (free) volume above the close packed state (V_{free}) or the activation energy for cooperative motion. The effect of changing state through a shift in pressure (P_{1} to P_{2}) is thus mechanistically traceable to cooperativity changing with density, through V_{free}. The connection with confined dynamics follows when 1 and 2 are taken as bulk and film at ambient P, differing in density only due to the film surface. The general form for τ(T,V) also illuminates why samples in different states (film vs bulk, high P vs low) trend toward the same relaxation behavior at high T.

Surface diffusion in glasses of rod-like molecules posaconazole and itraconazole: effect of interfacial molecular alignment and bulk penetration

The method of surface grating decay has been used to measure surface diffusion in the glasses of two rod-like molecules posaconazole (POS) and itraconazole (ITZ). Although structurally similar antifungal medicines, ITZ forms liquid-crystalline phases while POS does not. Surface diffusion in these systems is significantly slower than in the glasses of quasi-spherical molecules of similar volume when compared at the glass transition temperature T_g. Between the two systems, ITZ has slower surface diffusion. These results are explained on the basis of the near-vertical orientation of the rod-like molecules at the surface and their deep penetration into the bulk where mobility is low. For molecular glasses without extensive hydrogen bonds, we find that the surface diffusion coefficient at T_g decreases smoothly with the penetration depth of surface molecules and the trend has the double-exponential form for the surface mobility gradient observed in simulations. This supports the view that these molecular glasses have a similar mobility vs. depth profile and their different surface diffusion rates arise simply from the different depths at which molecules are anchored. Our results also provide support for a previously observed correlation between the rate of surface diffusion and the fragility of the bulk liquid.

Theory of Spatial Gradients of Relaxation, Vitrification Temperature and Fragility of Glass-Forming Polymer Liquids Near Solid Substrates

We employ a new force-level statistical mechanical theory to predict spatial gradients of the structural relaxation time and T_g of polymer liquids near microscopically rough and smooth hard surfaces and contrast the results with vapor interface systems. Repulsive rough (smooth) surfaces induce large slowing down (modest speeding up) of the relaxation time compared to the bulk. Nevertheless, a remarkable degree of universality of distinctive dynamical behaviors is predicted for different polymer chemistries and all interfaces, including a double exponential form of the alpha time gradient, power law decoupling of the relaxation time from its bulk value with exponential spatial variation of the exponent, exponential spatial gradient of T_g, weak dependence of normalized T_g gradients on vitrification criterion, and near linear growth with cooling of the slowed down layer thickness near a rough hard interface. The results appear consistent with simulations and experiments, and multiple testable predictions are made.