Globally Suppressed Dynamics in Ion-Doped Polymers.

We investigate how ion-polymer complexation suppresses molecular motion in conventional polymer electrolytes using molecular dynamics (MD) simulations of lithium hexafluorophosphate in poly(ethylene oxide) and a modified Rouse model. The employed model utilizes an inhomogeneous friction distribution to describe ion-polymer interactions and provides an effective way to examine how ion-polymer interactions affect polymer motion. By characterizing the subdiffusive Li+ transport and polymer relaxation times at several salt concentrations, we observe that increases in local friction due to ion-polymer complexation are significantly smaller than previously assumed. We find that a Rouse-based model that only considers local increases in friction cannot simultaneously capture the magnitude of increased polymer relaxation times and the apparent power-law exponent for Li+ subdiffusion observed in MD simulations. This incompatibility is reconciled by augmenting the modified Rouse model with a term that increases the global friction with the square of the salt concentration; this significantly improves the agreement between the model and MD, indicating the importance of ion-ion interactions and distributions on ion/polymer mobility.

Systematic Computational and Experimental Investigation of Lithium-Ion Transport Mechanisms in Polyester-Based Polymer Electrolytes.

Understanding the mechanisms of lithium-ion transport in polymers is crucial for the design of polymer electrolytes. We combine modular synthesis, electrochemical characterization, and molecular simulation to investigate lithium-ion transport in a new family of polyester-based polymers and in poly(ethylene oxide) (PEO). Theoretical predictions of glass-transition temperatures and ionic conductivities in the polymers agree well with experimental measurements. Interestingly, both the experiments and simulations indicate that the ionic conductivity of PEO, relative to the polyesters, is far higher than would be expected from its relative glass-transition temperature. The simulations reveal that diffusion of the lithium cations in the polyesters proceeds via a different mechanism than in PEO, and analysis of the distribution of available cation solvation sites in the various polymers provides a novel and intuitive way to explain the experimentally observed ionic conductivities. This work provides a platform for the evaluation and prediction of ionic conductivities in polymer electrolyte materials.

Theory of Anisotropic Diffusion of Entangled and Unentangled Polymers in Rod-Sphere Mixtures.

We present a microscopic self-consistent theory for the long-time diffusion of infinitely thin rods in a hard sphere matrix based on the simultaneous dynamical treatment of topological uncrossability and finite excluded volume constraints. Distinctive regimes of coupled anisotropic longitudinal and transverse diffusion are predicted, and steric blocking of the latter leads to a tube-like localization transition largely controlled by the ratio of the sphere diameter to rod length and tube diameter. For entangled polymers, in a limited regime of strongly retarded dynamics a "doubly renormalized" reptation law is predicted where the confinement tube is compressed and longitudinal motion is partially blocked. At high sphere volume fractions, strong suppression of rod motion results in dynamic localization in the unentangled regime. The present advance provides a theoretical foundation to treat differential mobility effects and flexible chain dynamics in diverse polymer-particle mixtures.

Nanoparticle diffusion in polymer nanocomposites.

Large-scale molecular dynamics simulations show that nanoparticle (NP) diffusivity in weakly interacting mixtures of NPs and polymer melts has two very different classes of behavior depending on their size. NP relaxation times and their diffusivities are completely described by the local, Rouse dynamics of the polymer chains for NPs smaller than the polymer entanglement mesh size. The motion of larger NPs, which are comparable to the entanglement mesh size, is significantly slowed by chain entanglements, and is not describable by the Stokes-Einstein relationship. Our results are in essentially quantitative agreement with a force-level generalized Langevin equation theory for all the NP sizes and chain lengths explored, and imply that for these lightly entangled systems, activated NP hopping is not important.

Spatially dependent relative diffusion of nanoparticles in polymer melts.

We formulate and apply a microscopic statistical-mechanical theory for the non-hydrodynamic relative diffusion coefficient of a pair of spherical nanoparticles in entangled polymer melts based on a combination of Brownian motion, mode-coupling, and polymer physics ideas. The focus is on the mesoscopic regime where particles are larger than the entanglement spacing. The dependence of the non-hydrodynamic friction on interparticle separation, degree of entanglement, and tube diameter is systematically studied. The overall magnitude of the relative diffusivity is controlled by the ratio of the particle to tube diameter and the number of entanglements in a manner reminiscent of single-particle self-diffusion and Stokes-Einstein violations. A rich spatial separation dependence of mobility enhancement relative to the hydrodynamic behavior is predicted even for very large particles, and the asymptotic dependence is derived analytically in the small and large separation limits. Particle separations in excess of 100 nm are sometimes required to recover the hydrodynamic limit. The effects of local polymer-particle packing correlations are found to be weak, and the non-hydrodynamic effects are also small for unentangled melts.

Theory of Entanglements and Tube Confinement in Rod-Sphere Nanocomposites.

We formulate a microscopic theory for the polymer transverse confinement length and associated dynamic potential for a mixture of infinitely thin rods and hard spheres based solely on topological entanglements and excluded volume constraints. For fixed spheres, the needle effective tube diameter decreases with particle loading, and is largely controlled by a single dimensionless parameter involving all three key length-scales in the problem. A crossover from polymer entanglement to nanoparticle-controlled tube localization with increased loading is predicted. A preliminary extension to chain melts exhibits reasonable agreement with a recent simulation, and experimentally testable predictions are made. This work establishes a first-principles theoretical foundation to investigate a variety of dynamical problems in entangled polymer nanocomposites.

Theory of nanoparticle diffusion in unentangled and entangled polymer melts.

We propose a statistical dynamical theory for the violation of the hydrodynamic Stokes-Einstein (SE) diffusion law for a spherical nanoparticle in entangled and unentangled polymer melts based on a combination of mode coupling, Brownian motion, and polymer physics ideas. The non-hydrodynamic friction coefficient is related to microscopic equilibrium structure and the length-scale-dependent polymer melt collective density fluctuation relaxation time. When local packing correlations are neglected, analytic scaling laws (with numerical prefactors) in various regimes are derived for the non-hydrodynamic diffusivity as a function of particle size, polymer radius-of-gyration, tube diameter, degree of entanglement, melt density, and temperature. Entanglement effects are the origin of large SE violations (orders of magnitude mobility enhancement) which smoothly increase as the ratio of particle radius to tube diameter decreases. Various crossover conditions for the recovery of the SE law are derived, which are qualitatively distinct for unentangled and entangled melts. The dynamical influence of packing correlations due to both repulsive and interfacial attractive forces is investigated. A central finding is that melt packing fraction, temperature, and interfacial attraction strength all influence the SE violation in qualitatively different directions depending on whether the polymers are entangled or not. Entangled systems exhibit seemingly anomalous trends as a function of these variables as a consequence of the non-diffusive nature of collective density fluctuation relaxation and the different response of polymer-particle structural correlations to adsorption on the mesoscopic entanglement length scale. The theory is in surprisingly good agreement with recent melt experiments, and new parametric studies are suggested.