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

Abstract

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 Levy 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 semi-quantitatively reproduce the experimental results to a remarkable degree. The results help to showcase how nanoparticles can under certain circumstances move rapidly in polymer networks.

Diffusion in Heterogenous Media and Sorption—Desorption Processes

“…The fractional time derivative present in Equation ( 18) is directly related to the bulk effects and, in particular, depends on the heterogeneity of the substrate, where the particles diffuse. The solution for Equation (18) by considering Φ(0) = 0, i.e., the particles are initially in bulk may be obtained by considering the Laplace transform (L{ρ(x, t); s} = ∞ 0 dte −st ρ(x, t) = ρ(x, s) and L −1 { ρ(x, s); t} = 1 2πi c+i∞ c−i∞ dse st ρ(x, s)) = ρ(x, t), yielding Φ(s) = Ĩ (s)…”

“…Similarly, during the desorption process (substance is released to the bulk), diffusion compensates for the increase in concentration near the substrate. Therefore, understanding how these two phenomena work together is crucial not only in separation process but in several other systems where diffusion and adsorption occur together, such as biochemical reactions in living systems [9,10], in the electrical response of weak electrolytes [11], in cancer [12] and population dynamics [13,14], and many others [15][16][17][18][19][20][21].…”

Assembly mechanism of surface-functionalized nanocubes

“…In general, the dissociation mechanism involves lineal separation of the nanocubes, while their ensuing progressive association towards the next metastable state follows a combination of sliding and rolling motions. In the future, it would be important to experimentally test these assembly pathway predictions using new, powerful spectroscopy techniques such as multimodal single-molecule FRET 37 and fluorescence correlation spectroscopy, 38 which can measure spatiotemporal changes in the relative location of fluorescent molecules strategically tagged onto the system of interest.…”

Fractional Diffusion with Geometric Constraints: Application to Signal Decay in Magnetic Resonance Imaging (MRI)

“…Mathematical models of diffusion are needed to interpet experimental measurements designed to probe the micro-structure of heterogeneous materials [1][2][3]. For example, identifying the role of diffusion in the electrical response of electrolytic cells, in electrochromic charge transfer in tungsten oxide films [4], in the dispersion of gold nanoparticles in a polymer melt [5], in the neuronal growth on surfaces with controlled geometries [6], and in the movement of proteins in living cells [7,8]. Depending on the interaction between the media and the diffusing particles, these processes manifest different features that promote normal or anomalous diffusion regimes.…”