Multiscale simulations of PS-SiO2 nanocomposites: from melt to glassy state

Dynamics of Polymer Chains in Poly(ethylene oxide)/Silica Nanocomposites via a Combined Computational and Experimental Approach

The dynamics of polymer chains in poly(ethylene oxide)/silica (PEO/SiO₂) nanoparticle nanohybrids have been investigated via a combined computational and experimental approach involving atomistic molecular dynamics simulations and dielectric relaxation spectroscopy (DRS) measurements. The complementarity of the approaches allows us to study systems with different polymer molecular weights, nanoparticle radii, and compositions across a broad range of temperatures. We study the effects of spatial confinement, which is induced by the nanoparticles, and chain adsorption on the polymer's structure and dynamics. The investigation of the static properties of the nanocomposites via detailed atomistic simulations revealed a heterogeneous polymer density layer at the vicinity of the PEO/SiO₂ interface that exhibited an intense maximum close to the inorganic surface, whereas the bulk density was reached for distances ∼1-1.2 nm away from the nanoparticle. For small volume fractions of nanoparticles, the polymer dynamics, probed by the atomistic simulations of low-molecular-weight chains at high temperatures, are consistent with the presence of a thin adsorbed layer that exhibits slow dynamics, with the dynamics far away from the nanoparticle being similar to those in the bulk. However, for high volume fractions of nanoparticles (strong confinement), the dynamics of all polymer chains were predicted slower than that in the bulk. On the other hand, similar dynamics were found experimentally for both the local β-process and the segmental dynamics for high-molecular-weight systems measured at temperatures below the melting temperature of the polymer, which were probed by DRS. These differences can be attributed to various parameters, including systems of different molecular weights and nanoparticle states of dispersion, the different temperature range studied by the different methods, the potential presence of a reduced-mobility PEO/SiO₂ interfacial layer that does not contribute to the dielectric spectrum, and the presence of amorphous-crystalline interfaces in the experimental samples that may lead to a different dynamical behaviors of the PEO chains.

Structure and Dynamics of Highly Attractive Polymer Nanocomposites in the Semi-Dilute Regime: The Role of Interfacial Domains and Bridging Chains

Detailed molecular dynamics (MD) simulations are employed to study how the presence of adsorbed domains and nanoparticle bridging chains affect the structural, conformational, thermodynamic, and dynamic properties of attractive polymer nanocomposite melts in the semi-dilute regime. As a model system we have chosen an unentangled poly(ethylene glycol) (PEG) matrix containing amorphous spherical silica nanoparticles with different diameters and at different concentrations. Emphasis is placed on properties such as the polymer mass density profile around nanoparticles, the compressibility of the system, the mean squared end-to-end distance of PEG chains, their orientational and diffusive dynamics, the single chain form factor, and the scattering functions. Our analysis reveals a significant impact of the adsorbed, interfacial polymer on the microscopic dynamic and conformational properties of the nanocomposite, especially under conditions favoring higher surface-to-volume ratios (e.g., for small nanoparticle sizes at fixed nanoparticle loading, or for higher silica concentrations). Simultaneously, adsorbed polymer chains adopt graft-like conformations, a feature that allows them to considerably extend away from the nanoparticle surface to form bridges with other nanoparticles. These bridges drive the formation of a nanoparticle network whose strength (number of tie chains per nanoparticle) increases substantially with increasing concentration of the polymer matrix in nanoparticles, or with decreasing nanoparticle size at fixed nanoparticle concentration. The presence of hydroxyl groups at the ends of PEG chains plays a key role in the formation of the network. If hydroxyl groups are substituted by methoxy ones, the simulations reveal that the number of bridging chains per nanoparticle decreases dramatically, thus the network formed is less dense and less strong mechanically, and has a smaller impact on the properties of the nanocomposite. Our simulations predict further that the isothermal compressibility and thermal expansion coefficient of PEG-silica nanocomposites are significantly lower than those of pure PEG, with their values decreasing practically linear with increasing concentration of the nanocomposite in nanoparticles.

An Enhanced Scheme for Multiscale Modeling of Thermomechanical Properties of Polymer Bulks

While multiscale modeling significantly enhances the capability of molecular simulations of polymer systems, it is well realized that the systematically derived coarse-grained (CG) models generally underestimate the thermomechanical properties. In this work, a charge-based mapping scheme has been adopted to include explicit electrostatic interactions and benchmarked against two typical polymers, atactic poly(methyl methacrylate) (PMMA) and polystyrene (PS). The CG potentials are parameterized against the oligomer bulks of nine monomers per chain to match the essential structural features and the two basic pressure-volume-temperature (PVT) properties, which are obtained from the all-atomistic (AA) molecular dynamics (MD) simulations at a single elevated temperature. The so-parameterized CG potentials are extended with the MD method to simulate the two polymer bulks of one hundred monomers per chain over a wide temperature range. Without any scaling, all the simulated results, including mass densities and bulk moduli at room temperature, thermal expansion coefficients at rubbery and glassy states, and glass transition temperatures (T_g), compare well with the corresponding experimental data. The proposed scheme not only contributes to realistically simulating various thermomechanical properties of both apolar and polar polymers but also allows for directly simulating their electrical properties.

Structural Transitions in Glassy Atactic Polystyrene Using Transition-State Theory

Transition pathways on the energy landscape of atactic polystyrene (aPS) glassy specimens are probed below its glass-transition temperature. Each of these transitions is considered an elementary structural relaxation event, whose corresponding rate constant is calculated by applying multidimensional transition-state theory. Initially, a wide spectrum of first-order saddle points surrounding local minima on the energy landscape is discovered by a stabilized hybrid eigenmode-following method. Then, (minimal-energy) “reaction paths” to the adjacent minima are constructed by a quadratic descent method. The heights of the free energy, the potential energy, and the entropy barriers are estimated for every connected triplet of transition state and minima. The resulting distribution of free energy barriers is asymmetric and extremely broad, extending to very high barrier heights (over 50 k_BT); the corresponding distribution of rate constants extends over 30 orders of magnitude, with well-defined peaks at the time scales corresponding to the subglass relaxations of polystyrene. Analysis of the curvature along the reaction paths reveals a multitude of different rearrangement mechanisms; some of them bearing multiple distinct phases. Finally, connections to theoretical models of the glass phenomenology allows for the prediction, based on first-principles, of the “ideal” glass-transition temperature entering the Vogel–Fulcher–Tammann (VFT) equation describing the super-Arrhenius temperature dependence of glassy dynamics. Our predictions of the time scales of the subglass relaxations and the VFT temperature are in favorable agreement with available experimental literature data for systems of similar molecular weight under the same conditions.

Insights from modeling into structure, entanglements, and dynamics in attractive polymer nanocomposites

Conformations, entanglements and dynamics in attractive polymer nanocomposites are investigated in this work by means of coarse-grained molecular dynamics simulation, for both weak and strong confinements, in the presence of nanoparticles (NPs) at NP volume fractions φ up to 60%. We show that the behavior of the apparent tube diameter dapp in such nanocomposites can be greatly different from nanocomposites with nonattractive interactions. We find that this effect originates, based on a mean field argument, from the geometric confinement length dgeo at strong confinement (large φ) and not from the bound polymer layer on NPs (interparticle distance ID <2Rg) as proposed recently based on experimental measurements. Close to the NP surface, the entangled polymer mobility is reduced in attractive nanocomposites but still faster than the NP mobility for volume fractions beyond 20%. Furthermore, entangled polymer dynamics is hindered dramatically by the strong confinement created by NPs. For the first time using simulations, we show that the entangled polymer conformation, characterized by the polymer radius of gyration Rg and form factor, remains basically unperturbed by the presence of NPs up to the highest volume fractions studied, in agreement with various experiments on attractive nanocomposites. As a side-result we demonstrate that the loose concept of ID can be made a microscopically well defined quantity using the mean pore size of the NP arrangement.

Structure and thermodynamics of grafted silica/polystyrene dilute nanocomposites investigated through self-consistent field theory

Polymer/matrix nanocomposites (PNCs) are materials with exceptional properties. They offer a plethora of promising applications in key industrial sectors. In most cases, it is preferable to disperse the nanoparticles (NPs) homogeneously across the matrix phase. However, under certain conditions NPs might lump together and lead to a composite material with undesirable properties. A common strategy to stabilize the NPs is to graft on their surface polymer chains of the same chemical constitution as the matrix chains. There are several unresolved issues concerning the optimal molar mass and areal density of grafted chains that would ensure best dispersion, given the nanoparticles and the polymer matrix. We propose a model for the prediction of key structural and thermodynamic properties of PNC and apply it to a single spherical silica (SiO2) nanoparticle or planar surface grafted with polystyrene chains embedded at low concentration in a matrix phase of the same chemical constitution. Our model is based on self-consistent field theory, formulated in terms of the Edwards diffusion equation. The properties of the PNC are explored across a broad parameter space, spanning the mushroom regime (low grafting densities, small NPs and chain lengths), the dense brush regime, and the crowding regime (large grafting densities, NP diameters, and chain lengths). We extract several key quantities regarding the distributions and the configurations of the polymer chains, such as the radial density profiles and their decomposition into contributions of adsorbed and free chains, the chains/area profiles, and the tendency of end segments to segregate at the interfaces. Based on our predictions concerning the brush thickness, we revisit the scaling behaviors proposed in the literature and we compare our findings with experiment, relevant simulations, and analytic models, such as Alexander's model for incompressible brushes.

Exploring a unified description of the super-Arrhenius region above and below the glass transition temperature

A new approach is presented in order to check whether the hypothesis of an Arrhenius component surviving in the α-relaxation region is consistent with experimental data. The temperature dependence of the dynamics in the whole glassy regime is described by an equation which assumes an Arrhenius component in the cooperative diffusion. Based on thermodynamic arguments, the dynamic heterogeneities close to the glass transition region are related to structural heterogeneities in a manner consistent with the idea of a sigmoidal shape in the cohesion energy. By doing so, a characteristic temperature which can be identified as the glass transition temperature (T_g) emerges, while an additional parameter for the extension of the super-Arrhenius region is introduced. In the analysis of experimental data, the activation energy parameter, determined from the temperature dependence of the β-relaxation, is fixed, and the relation between the experimental and the predicted glass transition temperature is examined. The results of this comparison support the idea that dynamics above and below T_g can be described in a unified manner. The proposed model is tested against experimental data of glass-forming liquids, polymers and polymer composites. In the latter systems, it is shown that the Arrhenius-like behavior characterizing the dynamics of the polymeric bound-layer can be accounted for by such an extension of the super-Arrhenius region.

Molecular Simulations and Mechanistic Analysis of the Effect of CO2 Sorption on Thermodynamics, Structure, and Local Dynamics of Molten Atactic Polystyrene

A simulation strategy encompassing different scales was applied to the systematic study of the effects of CO₂ uptake on the properties of atactic polystyrene (aPS) melts. The analysis accounted for the influence of temperature between 450 and 550 K, polymer molecular weights (M _w) between 2100 and 31000 g/mol, and CO₂ pressures up to 20 MPa on the volumetric, swelling, structural, and dynamic properties of the polymer as well as on the CO₂ solubility and diffusivity by performing molecular dynamics (MD) simulations of the system in a fully atomistic representation. A hierarchical scheme was used for the generation of the higher M _w polymer systems, which consisted of equilibration at a coarse-grained level of representation through efficient connectivity-altering Monte Carlo simulations, and reverse-mapping back to the atomistic representation, obtaining the configurations used for subsequent MD simulations. Sorption isotherms and associated swelling effects were determined by using an iterative procedure that incorporated a series of MD simulations in the NPT ensemble and the Widom test particle insertion method, while CO₂ diffusion coefficients were extracted from long MD runs in the NVE ensemble. Solubility and diffusivity compared favorably with experimental results and with predictions of the Sanchez-Lacombe equation of state, which was reparametrized to capture the M _w dependence of polymer properties with greater accuracy. Structural features of the polymer matrix were correctly reproduced by the simulations, and the effects of gas concentration and M _w on structure and local dynamics were thoroughly investigated. In the presence of CO₂, a significant acceleration of the segmental dynamics of the polymer occurred, more pronouncedly at low M _w. The speed-up effect caused by the swelling agent was not limited to the chain ends but affected the whole chain in a similar fashion.

Modelling Mixed-Gas Sorption in Glassy Polymers for CO₂ Removal: A Sensitivity Analysis of the Dual Mode Sorption Model

In an effort to reduce the experimental tests required to characterize the mixed-gas solubility and solubility-selectivity of materials for membrane separation processes, there is a need for reliable models which involve a minimum number of adjustable parameters. In this work, the ability of the Dual Mode Sorption (DMS) model to represent the sorption of CO₂/CH₄ mixtures in three high free volume glassy polymers, poly(trimethylsilyl propyne) (PTMSP), the first reported polymer of intrinsic microporosity (PIM-1) and tetrazole-modified PIM-1 (TZ-PIM), was tested. The sorption of gas mixtures in these materials suitable for CO₂ separation has been characterized experimentally in previous works, which showed that these systems exhibit rather marked deviations from the ideal pure-gas behavior, especially due to competitive effects. The accuracy of the DMS model in representing the non-idealities that arise during mixed-gas sorption was assessed in a wide range of temperatures, pressures and compositions, by comparing with the experimental results available. Using the parameters obtained from the best fit of pure-gas sorption isotherms, the agreement between the mixed-gas calculations and the experimental data varied greatly in the different cases inspected, especially in the case of CH₄ absorbed in mixed-gas conditions. A sensitivity analysis revealed that pure-gas data can be represented with the same accuracy by several different parameter sets, which, however, yield markedly different mixed-gas predictions, that, in some cases, agree with the experimental data only qualitatively. However, the multicomponent calculations with the DMS model yield more reliable results than the use of pure-gas data in the estimation of the solubility-selectivity of the material.

Multiscale Molecular Simulations of Polymer-Matrix Nanocomposites: or What Molecular Simulations Have Taught us About the Fascinating Nanoworld

Following the substantial progress in molecular simulations of polymer-matrix nanocomposites, now is the time to reconsider this topic from a critical point of view. A comprehensive survey is reported herein providing an overview of classical molecular simulations, reviewing their major achievements in modeling polymer matrix nanocomposites, and identifying several open challenges. Molecular simulations at multiple length and time scales, working hand-in-hand with sensitive experiments, have enhanced our understanding of how nanofillers alter the structure, dynamics, thermodynamics, rheology and mechanical properties of the surrounding polymer matrices.