We derive the radial distribution function and the static structure factor for the particles in model nanoparticleorganic hybrid materials composed of nanoparticles and attached oligomeric chains in the absence of an intervening solvent. The assumption that the oligomers form an incompressible fluid of bead-chains attached to the particles that is at equilibrium for a given particle configuration allows us to apply a density functional theory for determining the equilibrium configuration of oligomers as well as the distribution function of the particles. A quasi-analytic solution is facilitated by a regular perturbation analysis valid when the oligomer radius of gyration R g is much greater than the particle radius a. The results show that the constraint that each particle carries its own share of the fluid attached to itself yields a static structure factor that approaches zero as the wavenumber approaches zero. This result indicates that each particle excludes exactly one other particle from its neighborhood.

The structure of solvent-free oligomer-grafted nanoparticles has been investigated using molecular dynamics simulations and density-functional theory. At low temperatures and moderate to high oligomer lengths, the qualitative features of the core particle pair probability, structure factor, and the oligomer brush configuration obtained from the simulations can be explained by a density-functional theory that incorporates the configurational entropy of the space-filling oligomers. In particular, the structure factor at small wave numbers attains a value much smaller than the corresponding hardsphere suspension, the first peak of the pair distribution function is enhanced due to entropic attractions among the particles, and the oligomer brush expands with decreasing particle volume fraction to fill the interstitial space. At higher temperatures, the simulations reveal effects that differ from the theory and are likely caused by steric repulsions of the expanded corona chains.

Suspensions of solvent-less, polymer-grafted nanoparticles have previously been reported to exhibit enhanced elasticity, glassy dynamics, and jamming as temperature is increased. This so-called thermal jamming behavior is not predicted by current models for soft glassy materials and is opposite to what is normally observed for polymer melts. Here we report results from a detailed study of structural, dynamic, and rheological transitions in solvent-less silica–poly­(ethylene glycol) methyl ether (SiO2–PEGME) hybrid particles aimed at understanding the molecular origins of the phenomenon. We find that interdigitated PEGME corona chains enforce coupling between SiO2 cores analogous to cross-links in associating polymer networks leading to elastic behavior at low strains and small deformation rates. Pullout and slippage of interdigitated corona chains is thought to produce yielding of the materials in nonlinear shear flow and stretched exponential relaxation following small amplitude step shear. We show with the help of small-angle X-ray scattering, density functional theoretical calculations, and a constitutive model previously reported for deformation and flow of physically associating polymer networks, that thermal jamming of solvent-less polymer-grafted nanoparticles originates from enhanced cross-linking of the cores produced by increased stretching and interpenetration of particle-tethered polymer molecules to satisfy the space-filling constraint on tethered polymer chains.

We investigate the static structure factor S(q) of solvent-free nanoparticle-organic hybrid materials consisting of silica nanocores and space-filling polyethylene glycol coronas using a density-functional theory and small angle X-ray scattering measurements. The theory considers a bidisperse suspension of hard spheres with different radii and tethered bead-spring oligomers with different grafting densities to approximate the polydispersity effects in experiments. The experimental systems studied include pure samples with different silica core volume fractions and the associated mean corona grafting densities, and blends with different mixing ratios of the pure samples, in order to introduce varying polydispersity of corona grafting density. Our scattering experiments and theory show that, compared to the hard-sphere suspension with the same core volume fraction, S(q) for pure samples exhibit both substantially smaller values at small q and stronger particle correlations corresponding to a larger effective hard core at large q, indicating that the tethered incompressible oligomers enforce a more uniform particle distribution, and the densely grafted brush gives rise to an additional exclusionary effect between the nanoparticles. According to the theory, polydispersity in the oligomer grafting density controls the deviation of S(q) from the monodisperse system at smaller q, and the interplay of the enhanced effective core size and the entropic attraction among the particles is responsible for complex variations in the particle correlations at larger q. The successful comparison between the predictions and the measurements for the blends further suggests that S(q) can be used to assess the uniformity of grafting density in polymer-grafted nanoparticle materials.

We present a composite generalized Langevin equation as a unified framework for bridging the hydrodynamic, Brownian, and adhesive spring forces associated with a nanoparticle at different positions from a wall, namely, a bulklike regime, a near-wall regime, and a lubrication regime. The particle velocity autocorrelation function dictates the dynamical interplay between the aforementioned forces, and our proposed methodology successfully captures the well-known hydrodynamic long-time tail with context-dependent scaling exponents and oscillatory behavior due to the binding interaction. Employing the reactive flux formalism, we analyze the effect of hydrodynamic variables on the particle trajectory and characterize the transient kinetics of a particle crossing a predefined milestone. The results suggest that both wall-hydrodynamic interactions and adhesion strength impact the particle kinetics.