One-Dimensional Anomalous Diffusion of Gold Nanoparticles in a Polymer Melt

We investigated the dynamics of polymer-grafted gold nanoparticles loaded into polymer melts using x-ray photon correlation spectroscopy. For low molecular weight host matrix polymer chains, normal isotropic diffusion of the gold nanoparticles is observed. For larger molecular weights, anomalous diffusion of the nanoparticles is observed that can be described by ballistic motion and generalized Lévy walks, similar to those often used to discuss the dynamics of jammed systems. Under certain annealing conditions, the diffusion is one-dimensional and related to the direction of heat flow during annealing and is associated with an dynamic alignment of the host polymer chains. Molecular dynamics simulations of a single gold nanoparticle diffusing in a partially aligned polymer network semiquantitatively reproduce the experimental results to a remarkable degree. The results help to showcase how nanoparticles can under certain circumstances move rapidly in polymer networks.

Figure 1

(a) Isotropic ($g_2\text{−}1$) functions for 18 nm gold particle in host Matrix $\mathrm{MW}=30\mathrm{kg}/\mathrm{mol}$ for $T=160°\mathrm{C}$ and $q=9\times {10}^{-3}{\AA }^{-1}$. The curves have been vertically displaced for clarity. (b) $1/\tau$ vs $q$ and (c) $\omega$ vs $q$ for the above mentioned system.

Figure 2

(a) Relaxation dynamics in terms of $g_2\text{−}1$ as a function of $\tau$ at different angles $\varphi$ at $T=160°\mathrm{C}$ and $q=9\times {10}^{-3}{\AA }^{-1}$ for sample of $97\mathrm{kg}/\mathrm{mol}$ host matrix with nanoparticle diameter 18 nm annealed in orientation A ($\circ$) and orientation B ($\star$), plotted with two different timescales as shown. The curves have been vertically displaced for clarity. Dependence of (b) $1/\tau$ and (c) $\omega$ as a function of $q_z(=q\cos \varphi )$ at $T=160°\mathrm{C}$ for 18 nm Au NPs annealed in orientation A. Inset panels in Figs. (b) and (c) represent the cases of samples at orientation B as a function of $q$.

Figure 3

The variations of (a) $v_1$ and $v_2$ for the 13 and 18 nm Au NPs samples with $97\mathrm{kg}/\mathrm{mol}$ host matrix annealed in orientation A, as a function of temperature. Velocity distributions at $T=160°\mathrm{C}$ for NPs in (b) $97\mathrm{kg}/\mathrm{mol}$ and (c) 18 nm Au NPs in the $30\mathrm{kg}/\mathrm{mol}$ host matrices annealed in orientation A.

Figure 4

Mean square displacement (MSD) and ISF computed from simulations. (a) Overall MSD as a function of time and its $x$, $y$, and $z$ components of gold NP in $\mathrm{MW}=13\mathrm{kg}/\mathrm{mol}$ polymer host matrix. (b) Overall MSD and its $x$, $y$, and $z$ components, and (c) ISF modulus square ${|{\mathrm{f}}_{1,z}|}^2$ as a function of $t(\sec )$ of gold NP in $\mathrm{MW}=143\mathrm{kg}/\mathrm{mol}$ polymer host matrix. All $f_1$ curves are normalized and shifted vertically. Here, $q(n)=2\pi n/(55\times 45){\AA }^{-1}$.