Diffusion of a nanowire rod through an obstacle field

We report the experimental realization of a rod diffusing in a two-dimensional obstacle field following the single rod dynamics. We use a silver nanowire as our rod and two types of obstacles: repelling light beams and polymer pillars. We study the effect of hydrodynamic interactions on the transport of the rod, comparing both experimental realizations and recent simulations. We propose a framework for analyzing the transport through such systems, and we predict a new superdiffusive regime of rod transport at high obstacle concentration and short times.

Figure 1

Two experimental realizations of a rod diffusing in an obstacle field. A silver nanowire suspended in water is subjected to (a) a random field of repelling focused laser beams, and (b) an array of randomly positioned polymer pillars.

Figure 2

The diffusion coefficient of a freely moving rod as a function of rod length $L$, (a) translational diffusion coefficients, $D_{\parallel },D_{\perp }$, and (b) rotational diffusion coefficient $D_r$. Fits to theory [26] with friction coefficient $\gamma =0.8$ (dashed line). Inset: a typical trajectory of a free rod.

Figure 3

Log-log MSD graphs for the trajectories of nanowires 15 $\mu \text{m}$ long diffusing through an optical obstacle field array in three conditions: (a) no flow, $n^{*}\sim 3$; (b) flow, 0.2 $\mu \text{m}/\text{s}, n^{*}\sim 5.3$; and (c) flow, 0.2 $\mu \text{m/s}, n^{*}\sim 3$. The slopes of the graphs are (from bottom to top) 1.4, 1.8, and 1.9. Right: center-of-mass trajectories of nanowires at these three conditions.

Figure 4

The normalized diffusion coefficients of a confined rod as a function of normalized density $n^{*}$, (a) optical scatterers, and (b) polymer pillars, red dashed lines fit for $D\sim {\left(n^{*}\right)}^{-\alpha }$ at high density, green dashed line fit for $D\sim {\left(n^{*}\right)}^{-2}$. (c) Comparison of $D_{\parallel }/D_{\perp }$ for optical and polymer obstacles. (d) Center-of-mass diffusion coefficient for the polymer pillar experiments.

Figure 5

Mean-square displacement of a rod moving ballistically in an obstacle field of our WLC inspired model [Eq. (2)]. (a) Transition from anomalous diffusion to regular diffusion at different $n*$. (b) Mean-square displacement as a function of $t$ and $n^{*}$. At large $t$, the scaling $D_{\text{cm}}\sim \sqrt{n^{*}}$ is recovered (see the black solid line).