Heterogeneity of the Segmental Dynamics in Lamellar Phases of Diblock Copolymers

Glass formation and dynamics of model polymer films with one versus two active interfaces

Polymers and other glass-forming liquids can exhibit profound alterations in dynamics in the nanoscale vicinity of interfaces, over a range appreciably exceeding that of typical interfacial thermodynamic gradients. The understanding of these dynamical gradients is particularly complicated in systems with internal or external nanoscale dimensions, where a gradient nucleated at one interface can impinge on a second, potentially distinct, interface. To better understand the interactions that govern system dynamics and glass formation in these cases, here we simulate the baseline case of a glass-forming polymer film, over a wide range of thickness, supported on a dynamically neutral substrate that has little effect on nearby dynamics. We compare these results to our prior simulations of freestanding films. Results indicate that dynamical gradients in our simulated systems, as measured based upon translational relaxation, are simply truncated when they impinge on a secondary surface that is locally dynamically neutral. Altered film behavior can be described almost entirely by gradient effects down to the thinnest films probed, with no evidence for finite-size effects sometimes posited to play a role in these systems. Finally, our simulations predict that linear gradient overlap effects in the presence of symmetric dynamically active interfaces yield a non-monotonic variation of the whole free standing film stretching exponent (relaxation time distribution breadth). The maximum relaxation time distribution breadth in simulation is found at a film thickness of 4-5 times the interfacial gradient range. Observation of this maximum in experiment would provide an important validation that the gradient behavior observed in simulation persists to experimental timescales. If validated, observation of this maximum would potentially also enable determination of the dynamic gradient range from experimental mean-film measurements of film dynamics.

Nature of dynamic gradients, glass formation, and collective effects in ultrathin freestanding films

Molecular, polymeric, colloidal, and other classes of liquids can exhibit very large, spatially heterogeneous alterations of their dynamics and glass transition temperature when confined to nanoscale domains. Considerable progress has been made in understanding the related problem of near-interface relaxation and diffusion in thick films. However, the origin of "nanoconfinement effects" on the glassy dynamics of thin films, where gradients from different interfaces interact and genuine collective finite size effects may emerge, remains a longstanding open question. Here, we combine molecular dynamics simulations, probing 5 decades of relaxation, and the Elastically Cooperative Nonlinear Langevin Equation (ECNLE) theory, addressing 14 decades in timescale, to establish a microscopic and mechanistic understanding of the key features of altered dynamics in freestanding films spanning the full range from ultrathin to thick films. Simulations and theory are in qualitative and near-quantitative agreement without use of any adjustable parameters. For films of intermediate thickness, the dynamical behavior is well predicted to leading order using a simple linear superposition of thick-film exponential barrier gradients, including a remarkable suppression and flattening of various dynamical gradients in thin films. However, in sufficiently thin films the superposition approximation breaks down due to the emergence of genuine finite size confinement effects. ECNLE theory extended to treat thin films captures the phenomenology found in simulation, without invocation of any critical-like phenomena, on the basis of interface-nucleated gradients of local caging constraints, combined with interfacial and finite size-induced alterations of the collective elastic component of the structural relaxation process.

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

The nature of alterations to dynamics and vitrification in the nanoscale vicinity of interfaces-commonly referred to as "nanoconfinement" effects on the glass transition-has been an open question for a quarter century. We first analyze experimental and simulation results over the last decade to construct an overall phenomenological picture. Key features include the following: after a metrology- and chemistry-dependent onset, near-interface relaxation times obey a fractional power law decoupling relation with bulk relaxation; relaxation times vary in a double-exponential manner with distance from the interface, with an intrinsic dynamical length scale appearing to saturate at low temperatures; the activation barrier and vitrification temperature T_g approach bulk behavior in a spatially exponential manner; and all these behaviors depend quantitatively on the nature of the interface. We demonstrate that the thickness dependence of film-averaged T_g for individual systems provides a poor basis for discrimination between different theories, and thus we assess their merits based on the above dynamical gradient properties. Entropy-based theories appear to exhibit significant inconsistencies with the phenomenology. Diverse free-volume-motivated theories vary in their agreement with observations, with approaches invoking cooperative motion exhibiting the most promise. The elastically cooperative nonlinear Langevin equation theory appears to capture the largest portion of the phenomenology, although important aspects remain to be addressed. A full theoretical understanding requires improved confrontation with simulations and experiments that probe spatially heterogeneous dynamics within the accessible 1-ps to 1-year time window, minimal use of adjustable parameters, and recognition of the rich quantitative dependence on chemistry and interface.

Temperature-Independent Rescaling of the Local Activation Barrier Drives Free Surface Nanoconfinement Effects on Segmental-Scale Translational Dynamics near Tg

Near-interface alterations in dynamics and glass formation behavior have been the subject of extensive study for the past two decades, both because of their practical importance and in the hope of revealing underlying correlation lengths underpinning glass transition more generally. Here we employ molecular dynamics simulations of thick films to demonstrate that these effects emerge, for segmental-scale translational dynamics at low temperature, from a temperature-independent rescaling of the local activation barrier. This rescaling manifests as a fractional power law decoupling relationship of local dynamics relative to the bulk, with a transition from a regime of weak decoupling at high temperatures to a regime of strong decoupling at low temperatures. The range of this effect saturates at low temperatures, with 90% of the surface perturbation in the barrier lost over a range of 12 segmental diameters. These findings reduce the phenomenology of T_g nanoconfinement effects to two properties-a position-dependent, temperature independent, barrier rescaling factor and an onset time scale-while substantially constraining the predictions required from any theoretical explanation of this phenomenon.

Dielectric relaxation of polymers: segmental dynamics under structural constraints

In this article we review the recent polymer literature where dielectric spectroscopy has been used to investigate the segmental dynamics of polymers under the constraints produced by self-structuring. Specifically, we consider three cases: (i) semicrystalline polymers, (ii) segregated block-copolymers, and (iii) asymmetric miscible polymer blends. In these three situations the characteristics of the dielectric relaxation associated with the polymer segmental dynamics are markedly affected by the constraints imposed by the corresponding structural features. After reviewing in detail each of the polymer systems, the most common aspects are discussed in the context of the use of dielectric relaxation as a sensitive tool for analyzing structural features in nanostructured polymer systems.

Combined Dependence of Nanoconfined Tg on Interfacial Energy and Softness of Confinement

We employ molecular dynamics simulations of nanolayered polymers to systematically quantify the dependence of T_g nanoconfinement effects on interfacial energy and the "softness" of confinement. Results indicate that nanoconfined T_g depends linearly on interfacial adhesion energy, with a slope that scales exponentially with the ratio of the bulk Debye-Waller factors ⟨u²⟩ of the confined and confining materials. These trends, together with a convergence at low interfacial adhesion energy to the T_g of an equivalent freestanding film, are captured in a single functional form, with only three parameters explicitly referring to the confined state. The observed dependence on ⟨u²⟩ indicates that softness of nanoconfinement should be defined in terms of the relative high frequency shear moduli, rather than low frequency moduli or relaxation times, of the confined and confining materials.