Dynamics of stiff filaments in size-polydisperse hard sphere fluids

The dynamics of a stiff filament (made by connecting beads) embedded in size-polydisperse hard sphere fluid is investigated by means of molecular dynamics simulations with focus on how the degree of size-polydispersity, characterized by polydispersity index ($\delta$), affects the dynamics in this model heterogeneous system. Polydispersity of the fluid as well as strong coupling of rotational and translational motion of the rods are two of the various hurdles in interpreting the experimental results in a complex fluid environment. Furthermore, influence of volume fraction, $\phi$, and absolute free volume, $V_{\rm free}$, which changes inherently with $\delta$ on the dynamics are not adequately discussed in the literature. Thus, we investigate the dynamical behaviour of the rods under two different conditions: (i) constant pressure (in which $\phi$ changes with $\delta$), and (ii) constant $\phi$. Under constant pressure it is observed that the rotational relaxation time and hence the diffusion constant, $D_R$, varies with rod length as $D_R \sim l^{-\alpha}$, where the value of exponent $\alpha$ increases from $3.0-3.2$ while varying $\delta$ from $0-40\%$. It is observed that the effect of increasing $\phi$ dominates over the effect of increasing $V_{\rm free}$. Also there is minimal effect of hydrodynamic interaction among the beads belonging to a rod during rotation, whereas the presence of partial hydrodynamic screening for the motion of the centre of mass is seen. On the other hand, for fixed $\phi$ systems, increasing $\delta$ results in increasing $V_{\rm free}$ and thus enhances tracer diffusion, an opposite trend compared to the system under constant pressure.