Two-Dimensional Dynamics of Metal Nanoparticles on the Surface of Thin Polymer Films Studied with Coherent X Rays

X-ray photon-correlation spectroscopy is used to measure the dynamic structure factor $f(q,\tau )$ of gold particles moving on the surface of thin polymer films. Above the glass transition of the polymer the peculiar form $f(q,\tau )\sim \exp [-(\Gamma \tau {)}^{\alpha }]$ is found with $0.7<\alpha <1.5$, depending on sample age and temperature. The relaxation rates $\Gamma$ scale linearly with $q$, excluding a simple Brownian diffusive motion. This type of behavior, already observed in aging bulk soft matter systems, is explained by a power law distribution of particle velocities due to ballistic motion.

Figure 1

Average in-plane radius of the gold clusters as a function of temperature as extracted from the incoherent GISAXS data. The inset presents two $q_{\parallel }$ scans taken at 300 and 450 K (down and up triangles, respectively) together with their best fits.

Figure 2

CCD images of the coherent GISAXS patterns. The left picture was taken well below and the right above the glass transition, each one resulting from an accumulation of 400 frames of 10 s each.

Figure 3

Correlation functions $g_2(\tau )$ measured at 440 (circles), 420 (squares), and 400 K (triangles), respectively, for $q_{||}=0.051{\AA }^{-1}$ and a sample age of 2462–3693 s. The curves are shifted vertically for reasons of clarity. The solid lines represent the fits according to Eq. (2). The inset shows the correlation functions for all measured wave vector transfers $q_{||}$ at 420 K for the same sample age.

Figure 4

Dispersion relations (relaxation rate $\Gamma$ vs $q_{||}$) at 400 (left) and 440 K (right) presented for three different ages: 0–1231 s (circles), 1231–2462 s (squares), and 2462–3693 s (triangles). The solid lines are linear fits to the data.