Revealing spatially heterogeneous relaxation in a model nanocomposite

Dynamics of polylactic acid under ultrafine nanoconfinement: The collective interface effect and the spatial gradient

Polymers under nanoconfinement can exhibit large alterations in dynamics from their bulk values due to an interface effect. However, understanding the interface effect remains a challenge, especially in the ultrafine nanoconfinement region. In this work, we prepare new geometries with ultrafine nanoconfinement ∼10nm through controlled distributions of the crystalline phases and the amorphous phases of a model semi-crystalline polymer, i.e., the polylactic acid. The broadband dielectric spectroscopy measurements show that ultrafine nanoconfinement leads to a large elevation in the glass transition temperature and a strong increment in the polymer fragility index. Moreover, new relaxation time profile analyses demonstrate a spatial gradient that can be well described by either a single-exponential decay or a double-exponential decay functional form near the middle of the film with a collective interface effect. However, the dynamics at the 1-2 nm vicinity of the interface exhibit a power-law decay that is different from the single-exponential decay or double-exponential decay functional forms as predicted by theories. Thus, these results call for further investigations of the interface effect on polymer dynamics, especially for interfaces with perturbed chain packing.

Molecular Mobility and Gas Transport Properties of Mixed Matrix Membranes Based on PIM-1 and a Phosphinine Containing Covalent Organic Framework

Polymers with intrinsic microporosity (PIMs) are gaining attention as gas separation membranes. Nevertheless, they face limitations due to their pronounced physical aging. In this study, a covalent organic framework containing λ5-phosphinine moieties, CPSF-EtO, was incorporated as a nanofiller (concentration range 0-10 wt %) into a PIM-1 matrix forming dense films with a thickness of ca. 100 μm. The aim of the investigation was to investigate possible enhancements of gas transport properties and mitigating effects on physical aging. The incorporation of the nanofiller occurred on an nanoaggregate level with domains up to 100 nm, as observed by T-SEM and confirmed by X-ray scattering. Moreover, the X-ray data show that the structure of the microporous network of the PIM-1 matrix is changed by the nanofiller. As molecular mobility is fundamental for gas transport as well as for physical aging, the study includes dielectric investigations of pure PIM-1 and PIM-1/CPSF-EtO mixed matrix membranes to establish a correlation between the molecular mobility and the gas transport properties. Using the time-lag method, the gas permeability and the permselectivity were determined for N2, O2, CH4, and CO2 for samples with variation in filler content. A significant increase in the permeability of CH4 and CO2 (50% increase compared to pure PIM-1) was observed for a concentration of 5 wt % of the nanofiller. Furthermore, the most pronounced change in the permselectivity was found for the gas pair CO2/N2 at a filler concentration of 7 wt %.

Effect of the nature of the solid substrate on spatially heterogeneous activated dynamics in glass forming supported films

We extend the force-level elastically collective nonlinear Langevin equation theory to treat the spatial gradients of the alpha relaxation time and glass transition temperature, and the corresponding film-averaged quantities, to the geometrically asymmetric case of finite thickness supported films with variable fluid-substrate coupling. The latter typically nonuniversally slows down motion near the solid-liquid interface as modeled via modification of the surface dynamic free energy caging constraints that are spatially transferred into the film and which compete with the accelerated relaxation gradient induced by the vapor interface. Quantitative applications to the foundational hard sphere fluid and a polymer melt are presented. The strength of the effective fluid-substrate coupling has very large consequences for the dynamical gradients and film-averaged quantities in a film thickness and thermodynamic state dependent manner. The interference of the dynamical gradients of opposite nature emanating from the vapor and solid interfaces is determined, including the conditions for the disappearance of a bulk-like region in the film center. The relative importance of surface-induced modification of local caging vs the generic truncation of the long range collective elastic component of the activation barrier is studied. The conditions for the accuracy and failure of a simple superposition approximation for dynamical gradients in thin films are also determined. The emergence of near substrate dead layers, large gradient effects on film-averaged response functions, and a weak non-monotonic evolution of dynamic gradients in thick and cold films are briefly discussed. The connection of our theoretical results to simulations and experiments is briefly discussed, as is the extension to treat more complex glass-forming systems under nanoconfinement.

Hydrogen Bonding Exchange and Supramolecular Dynamics of Monohydroxy Alcohols

We unravel hydrogen bonding dynamics and their relationship with supramolecular relaxations of monohydroxy alcohols (MAs) at intermediate times. The rheological modulus of MAs exhibits Rouse scaling relaxation of G(t)∼t^{-1/2} switching to G(t)∼t^{-1} at time τ_{m} before their terminal time. Meanwhile, dielectric spectroscopy reveals clear signatures of new supramolecular dynamics matching with τ_{m} from rheology. Interestingly, the characteristic time τ_{m} follows an Arrhenius-like temperature dependence over exceptionally wide temperatures and agrees well with the hydrogen bonding exchange time from nuclear magnetic resonance measurements. These observations demonstrate the presence of Rouse modes and active chain swapping of MAs at intermediate times. Moreover, detailed theoretical analyses point out explicitly that the hydrogen bonding exchange truncates the Rouse dynamics of the supramolecular chains and triggers the chain-swapping processes, supporting a recently proposed living polymer model.

Design of Polymer Nanodielectrics for Capacitive Energy Storage

Polymer nanodielectrics present a particularly challenging materials design problem for capacitive energy storage applications like polymer film capacitors. High permittivity and breakdown strength are needed to achieve high energy density and loss must be low. Strategies that increase permittivity tend to decrease the breakdown strength and increase loss. We hypothesize that a parameter space exists for fillers of modest aspect ratio functionalized with charge-trapping molecules that results in an increase in permittivity and breakdown strength simultaneously, while limiting increases in loss. In this work, we explore this parameter space, using physics-based, multiscale 3D dielectric property simulations, mixed-variable machine learning and Bayesian optimization to identify the compositions and morphologies which lead to the optimization of these competing properties. We employ first principle-based calculations for interface trap densities which are further used in breakdown strength calculations. For permittivity and loss calculations, we use continuum scale modelling and finite difference solution of Poisson's equation for steady-state currents. We propose a design framework for optimizing multiple properties by tuning design variables including the microstructure and interface properties. Finally, we employ mixed-variable global sensitivity analysis to understand the complex interplay between four continuous microstructural and two categorical interface choices to extract further physical knowledge on the design of nanodielectrics.

Kinetics of the Glass Transition of Silica-Filled Styrene-Butadiene Rubber: The Effect of Resins

Resins are important for enhancing both the processability and performance of rubber. Their efficient utilization requires knowledge about their influence on the dynamic glass transition and their miscibility behavior in the specific rubber compound. The resins investigated, poly-(α-methylstyrene) (AMS) and indene-coumarone (IC), differ in molecular rigidity but have a similar aromaticity degree and glass transition temperature. Transmission electron microscopy (TEM) investigations show an accumulation of IC around the silanized silica in styrene–butadiene rubber (SBR) at high contents, while AMS does not show this effect. This higher affinity between IC and the silica surface leads to an increased compactness of the filler network, as determined by dynamic mechanical analysis (DMA). The influence of the resin content on the glass transition of the rubber compounds is evaluated in the sense of the Gordon–Taylor equation and suggests a rigid amorphous fraction for the accumulated IC. Broadband dielectric spectroscopy (BDS) and fast differential scanning calorimetry (FDSC) are applied for the characterization of the dielectric and thermal relaxations as well as for the corresponding vitrification kinetics. The cooling rate dependence of the vitrification process is combined with the thermal and dielectric relaxation time by one single Vogel–Fulcher–Tammann–Hesse equation, showing an increased fragility of the rubber containing AMS.

Rationalizing the Composition Dependence of Glass Transition Temperatures in Amorphous Polymer/POSS Composites

We report that the fractions of "bonded" or "unbonded" monomers at a filler interface dictate the composition dependence of the glass transition temperatures (T_g) of polyhedral oligomeric silsesquioxane (POSS)-containing nanocomposites. T_g is arguably the single most important material property; however, predicting T_g in nanocomposites is often challenging because of confounding interfacial effects. To this end, we design a model nanocomposite to systematically study T_g of nanocomposites by leveraging the "all-interfacial" nature of ultrasmall POSS fillers loaded into random copolymers of styrene and 2-vinylpyridine (2VP). The amine-functionalized POSS forms hydrogen bonds only with 2VP, which behaves as a "bonded" monomer. The influence of copolymer composition and POSS loading on the T_g of this model composite is successfully explained by a Fox equation framework. This model also captures the T_g increase of other POSS-based polymer composites and potentially directs the future design of nanocomposite materials with tailored T_g.

Activation free energy gradient controls interfacial mobility gradient in thin polymer films

We examine the mobility gradient in the interfacial region of substrate-supported polymer films using molecular dynamics simulations and interpret these gradients within the string model of glass-formation. No large gradients in the extent of collective motion exist in these simulated films, and an analysis of the mobility gradient on a layer-by-layer basis indicates that the string model provides a quantitative description of the relaxation time gradient. Consequently, the string model indicates that the interfacial mobility gradient derives mainly from a gradient in the high-temperature activation enthalpy ΔH₀ and entropy ΔS₀ as a function of depth z, an effect that exists even in the high-temperature Arrhenius relaxation regime far above the glass transition temperature. To gain insight into the interfacial mobility gradient, we examined various material properties suggested previously to influence ΔH₀ in condensed materials, including density, potential and cohesive energy density, and a local measure of stiffness or u²(z)^-3/2, where u²(z) is the average mean squared particle displacement at a caging time (on the order of a ps). We find that changes in local stiffness best correlate with changes in ΔH₀(z) and that ΔS₀(z) also contributes significantly to the interfacial mobility gradient, so it must not be neglected.

Confinement Effects on Glass-Forming Aqueous Dimethyl Sulfoxide Solutions

Combining broadband dielectric spectroscopy and nuclear magnetic resonance studies, we analyze the reorientation dynamics and the translational diffusion associated with the glassy slowdown of the eutectic aqueous dimethyl sulfoxide solution in nano-sized confinements, explicitly, in silica pores with different diameters and in ficoll and lysozyme matrices at different concentrations. We observe that both rotational and diffusive dynamics are slower and more heterogeneous in the confinements than in the bulk but the degree of these effects depends on the properties of the confinement and differs for the components of the solution. For the hard and the soft matrices, the slowdown and the heterogeneity become more prominent when the size of the confinement is reduced. In addition, the dynamics are more retarded for dimethyl sulfoxide than for water, implying specific guest-host interactions. Moreover, we find that the temperature dependence of the reorientation dynamics and of the translational diffusion differs in severe confinements, indicating a breakdown of the Stokes-Einstein-Debye relation. It is discussed to what extent these confinement effects can be rationalized in the framework of core-shell models, which assume bulk-like and slowed-down motions in central and interfacial confinement regions, respectively.

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.

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.

Initial Solvent-Driven Nonequilibrium Effect on Structure, Properties, and Dynamics of Polymer Nanocomposites

Unusual structures and dynamic properties found in polymer nanocomposites (PNCs) are often attributed to immobilized (adsorbed) polymers at nanoparticle-polymer interfaces, which are responsible for reducing the intrinsic incompatibility between nanoparticles and polymers in PNCs. Although tremendous effort has been made to characterize the presence of immobilized polymers, a systematic understanding of the structure and dynamics under different processing conditions is still lacking. Here, we report that the initial dispersing solvent, which is not present after producing PNCs, drives these nonequilibrium effects on polymer chain dynamics at interfaces. Employing extensive small-angle scattering, proton NMR spectroscopy, and rheometry experiments, we found that the thickness of the immobilized layer can be dependent on the initial solvent, changing the structure and the properties of the PNC significantly. In addition, we show that the outcome of the initial solvent effect becomes more effective at particle volume fractions where the immobile layers begin to interact.

Polymer dynamics under confinement

We review recent neutron scattering work and related results from simulation and complementary techniques focusing on the microscopic dynamics of polymers under confinement. Confinement is either realized in model porous materials or in polymer nanocomposites (PNC). The dynamics of such confined polymers is affected on the local segmental level, the level of entanglements as well as on global levels: (i) at the segmental level the interaction with the surface is of key importance. At locally repulsive surfaces compared to the bulk the segmental dynamics is not altered. Attractive surfaces slow down the segmental dynamics in their neighborhood but do not give rise to dead, glassy layers. (ii) Confinement generally has little effect on the inter-chain entanglements: both for weakly as well as for marginally confined polymers the reptation tube size is not changed. Only for strongly confined polymers disentanglement takes place. Similarly, in PNC at higher NP loading disentanglement phenomena are observed; in addition, at very high loading a transition from polymer caused topological constraints to purely geometrical constraints is observed. (iii) On the more global scale NSE experiments revealed important information on the nature of the interphase between adsorbed layer and bulk polymer. (iv) Polymer grafts at NP mutually confine each other, an effect that is most pronounced for one component NP. (v) Global diffusion of entangled polymers both in weakly and strongly attractive PNC is governed by the ratio of bottle-neck to chain size that characterizes the 'entropic barrier' for global diffusion.

Theory of the spatial transfer of interface-nucleated changes of dynamical constraints and its consequences in glass-forming films

We formulate a new theory for how caging constraints in glass-forming liquids at a surface or interface are modified and then spatially transferred, in a layer-by-layer bootstrapped manner, into the film interior in the context of the dynamic free energy concept of the Nonlinear Langevin Equation (NLE) theory approach. The dynamic free energy at any mean location (cage center) involves contributions from two adjacent layers where confining forces are not the same. At the most fundamental level of the theory, the caging component of the dynamic free energy varies essentially exponentially with distance from the interface, saturating deep enough into the film with a correlation length of modest size and weak sensitivity to the thermodynamic state. This imparts a roughly exponential spatial variation of all the key features of the dynamic free energy required to compute gradients of dynamical quantities including the localization length, jump distance, cage barrier, collective elastic barrier, and alpha relaxation time. The spatial gradients are entirely of dynamical, not structural or thermodynamic, origin. The theory is implemented for the hard sphere fluid and diverse interfaces which can be a vapor, a rough pinned particle solid, a vibrating (softened) pinned particle solid, or a smooth hard wall. Their basic description at the level of the spatially heterogeneous dynamic free energy is identical, with the crucial difference arising from the first layer where dynamical constraints can be weakened, softened, or hardly changed depending on the specific interface. Numerical calculations establish the spatial dependence and fluid volume fraction sensitivity of the key dynamical property gradients for five different model interfaces. A comparison of the theoretical predictions for the dynamic localization length and glassy modulus with simulations and experiments for systems with a vapor interface reveals good agreement. The present advance sets the stage for using the Elastically Collective NLE theory to make quantitative predictions for the alpha relaxation time gradient, decoupling phenomena, T_g gradient, and many film-averaged properties of both model and experimental (colloids, molecules, and polymers) systems with diverse interfaces and chemical makeup.

Polymer Chain Conformation and Dynamical Confinement in a Model One-Component Nanocomposite

We report a neutron-scattering investigation on the structure and dynamics of a single-component nanocomposite based on SiO_{2} particles that were grafted with polyisoprene chains at the entanglement limit. By skillful labeling, we access both the monomer density in the corona as well as the conformation of the grafted chains. While the corona profile follows a r^{-1} power law, the conformation of a grafted chain is identical to that of a chain in a reference melt, implying a high mutual penetration of the coronas from different particles. The brush crowding leads to topological confinement of the chain dynamics: (i) At local scales, the segmental dynamics is unchanged compared to the reference melt, while (ii) at the scale of the chain, the dynamics appears to be slowed down; (iii) by performing a mode analysis in terms of end-fixed Rouse chains, the slower dynamics is tracked to topological confinement within the cone spanned by the adjacent grafts; (iv) by adding 50% matrix chains, the topological confinement sensed by the grafted chain is lifted partially and the apparent chain motion is accelerated. We observe a crossover from pure Rouse motion at short times to topological confined motion beyond the time when the segmental mean squared displacement has reached the distance to the next graft.

Big Effect of Small Nanoparticles: A Shift in Paradigm for Polymer Nanocomposites

Polymer nanocomposites (PNCs) are important materials that are widely used in many current technologies and potentially have broader applications in the future due to their excellent property tunability, light weight, and low cost. However, expanding the limits in property enhancement remains a fundamental scientific challenge. Here, we demonstrate that well-dispersed, small (diameter ∼1.8 nm) nanoparticles with attractive interactions lead to unexpectedly large and qualitatively different changes in PNC structural dynamics in comparison to conventional nanocomposites based on particles of diameters ∼10-50 nm. At the same time, the zero-shear viscosity at high temperatures remains comparable to that of the neat polymer, thereby retaining good processability and resolving a major challenge in PNC applications. Our results suggest that the nanoparticle mobility and relatively short lifetimes of nanoparticle-polymer associations open qualitatively different horizons in the tunability of macroscopic properties in nanocomposites with a high potential for the development of advanced functional materials.

Influence of the Bound Polymer Layer on Nanoparticle Diffusion in Polymer Melts

We measure the center-of-mass diffusion of silica nanoparticles (NPs) in entangled poly(2-vinylpyridine) (P2VP) melts using Rutherford backscattering spectrometry. While these NPs are well within the size regime where enhanced, nonhydrodynamic NP transport is theoretically predicted and has been observed experimentally (2R_NP/d_tube ≈ 3, where 2R_NP is the NP diameter and d_tube is the tube diameter), we find that the diffusion of these NPs in P2VP is in fact well-described by the hydrodynamic Stokes-Einstein relation. The effective NP diameter 2R_eff is significantly larger than 2R_NP and strongly dependent on P2VP molecular weight, consistent with the presence of a bound polymer layer on the NP surface with thickness h_eff ≈ 1.1R_g. Our results show that the bound polymer layer significantly augments the NP hydrodynamic size in polymer melts with attractive polymer-NP interactions and effectively transitions the mechanism of NP diffusion from the nonhydrodynamic to hydrodynamic regime, particularly at high molecular weights where NP transport is expected to be notably enhanced. Furthermore, these results provide the first experimental demonstration that hydrodynamic NP transport in polymer melts requires particles of size ≳5d_tube, consistent with recent theoretical predictions.

Controlling Interfacial Dynamics: Covalent Bonding versus Physical Adsorption in Polymer Nanocomposites

It is generally believed that the strength of the polymer-nanoparticle interaction controls the modification of near-interface segmental mobility in polymer nanocomposites (PNCs). However, little is known about the effect of covalent bonding on the segmental dynamics and glass transition of matrix-free polymer-grafted nanoparticles (PGNs), especially when compared to PNCs. In this article, we directly compare the static and dynamic properties of poly(2-vinylpyridine)/silica-based nanocomposites with polymer chains either physically adsorbed (PNCs) or covalently bonded (PGNs) to identical silica nanoparticles (RNP = 12.5 nm) for three different molecular weight (MW) systems. Interestingly, when the MW of the matrix is as low as 6 kg/mol (RNP/Rg = 5.4) or as high as 140 kg/mol (RNP/Rg= 1.13), both small-angle X-ray scattering and broadband dielectric spectroscopy show similar static and dynamic properties for PNCs and PGNs. However, for the intermediate MW of 18 kg/mol (RNP/Rg = 3.16), the difference between physical adsorption and covalent bonding can be clearly identified in the static and dynamic properties of the interfacial layer. We ascribe the differences in the interfacial properties of PNCs and PGNs to changes in chain stretching, as quantified by self-consistent field theory calculations. These results demonstrate that the dynamic suppression at the interface is affected by the chain stretching; that is, it depends on the anisotropy of the segmental conformations, more so than the strength of the interaction, which suggests that the interfacial dynamics can be effectively tuned by the degree of stretching-a parameter accessible from the MW or grafting density.

Unexpected Molecular Weight Effect in Polymer Nanocomposites

The properties of the interfacial layer between the polymer matrix and nanoparticles largely determine the macroscopic properties of polymer nanocomposites (PNCs). Although the static thickness of the interfacial layer was found to increase with the molecular weight (MW), the influence of MW on segmental relaxation and the glass transition in this layer remains to be explored. In this Letter, we show an unexpected MW dependence of the interfacial properties in PNC with attractive polymer-nanoparticle interactions: the thickness of the interfacial layer with hindered segmental relaxation decreases as MW increases, in sharp contrast to theoretical predictions. Further analyses reveal a reduction in mass density of the interfacial layer with increasing MW, which can elucidate these unexpected dynamic effects. Our observations call for a significant revision of the current understandings of PNCs and suggest interesting ways to tailor their properties.