Accelerated Local Dynamics in Matrix-Free Polymer Grafted Nanoparticles

The tracer diffusion coefficient of six different permanent gases in polymer-grafted nanoparticle (GNP) membranes, i.e., neat GNP constructs with no solvent, show a maximum as a function of the grafted chain length at fixed grafting density. This trend is reproduced for two different NP sizes and three different polymer chemistries. We postulate that nonmonotonic changes in local, segmental friction as a function of graft chain length (at fixed grafting density) must underpin these effects, and use quasielastic neutron scattering to probe the self-motions of polymer chains at the relevant segmental scale (i.e., sampling local friction or viscosity). These data, when interpreted with a jump diffusion model, show that, in addition to the speeding-up in local chain dynamics, the elementary distance over which segments hop is strongly dependent on graft chain length. We therefore conclude that transport modifications in these GNP layers, which are underpinned by a structural transition from a concentrated brush to semidilute polymer brush, are a consequence of both spatial and temporal changes, both of which are likely driven by the lower polymer densities of the GNPs relative to the neat polymer.

Figure 1

(a) Dynamic structure factors measured on HFBS for a composite with $M_n\approx 88\mathrm{kDa}$ (red star) and bulk PMA (black square) at $q=11.1{\mathrm{nm}}^{-1}$ showing differences in broadening. The maximum value of the scattering function was normalized to unity in each case to account for differences in the sample thickness and total scattering. (b) Intermediate scattering functions for the $M_n\approx 88\mathrm{kDa}$ composite from $q=2{\mathrm{nm}}^{-1}$ to $14.2{\mathrm{nm}}^{-1}$ at 420 K. Red lines are fits to a stretched exponential function. (c) Stretching exponents $\beta$ for the grafted chains. The gray region defines the range of stretching exponents observed for the bulk polymer with its corresponding error estimate. The stretching exponents are all within error of each other.

Figure 2

(a) Comparison of the $q$ dispersion curves for a composite with $M_n\approx 88\mathrm{kDa}$ (black square) and a bulk polymer with $M_n\approx 96\mathrm{kDa}$ (green circle). (b) Crossover $q$’s (empty circle) for the two asymptotic behaviors observed for the different grafted samples. The gray band corresponds to the crossover wave vectors for the bulk polymer. The $M_n\approx 29\mathrm{kDa}$ (HFBS) and $M_n\approx 80\mathrm{kDa}$ (SPHERES) have no evidence for a crossover within instrument parameters—the error bars extending to zero on the $y$ axis point to this fact. The point at zero molecular weight is the pure PMA (with no NPs). (c) Relaxation times of the composites normalized to the bulk polymer after summing across all wave vectors. The dashed line is a guide to the eye. Data were measured on HFBS.

Figure 3

(a) ${\tau }^{\beta }$ vs $q$ with fits to the jump diffusion model (solid line). (b) Jump length $l_0$ extracted from the model for all composites tested. The gray band corresponds to the jump length for the reference polymer melt (no NPs). (c) Relaxation time ${\tau }_0$ for the diffusive jumps. The bands represent the corresponding fit values for the reference polymer melt. (d) Normalized segmental diffusivity for the composites (black circle). Normalized diffusivities of ${\mathrm{CO}}_2$ in the GNPs are plotted (red symbols) as a function of $M_n$. Similar nonmonotonic behavior is observed for the two, although quantitative differences persist.