Enhancement in the diffusivity of Brownian spheroids in the presence of spheres

Self Assembly of Patchy Anisotropic Particle Forming Free Standing Monolayer Film

“…We have already shown that if the step size is smaller than 0.005 d , the diffusion coefficient of the ellipsoidal particle obtained from BCD agrees with the analytical calculation of Perrin et al. [ 32 ]…”

“…We define $${h}_{i,j}({\mathbf{r}}_{i,j},{\widehat{n}}_{i},{\widehat{n}}_{j})$$ as the distance between the surfaces of the hard cores, calculated by using ellipsoids contact function (ECF). [ 32 ] $$\bm{}{\bm{\sigma}}_{\mathbf{i},\mathbf{j}}$$ and $$\bm{}{\bm{\chi}}_{\mathbf{i},\mathbf{j}}$$ is defined as $$$$\begin{equation} {\sigma}_{i,j}=\left\{ \def\eqcellsep{&}\begin{array}{c} {1\hspace*{28.45274pt}{h}_{i,j}<\varepsilon}\\ {0\hspace*{28.45274pt}\text{Otherwise}}\end{array} \right. \end{equation}$$$$ $$$$\begin{equation} {\chi}_{i,j}=\left\{ \def\eqcellsep{&}\begin{array}{c} {1\hspace*{28.45274pt}|{\widehat{r}}_{\textit{ij}}.$$…”

“…Thus unit of time t 0 is defined as the time taken by the center of mass of an ellipsoids to travel a unit distance. [ 32 ] The orientation of the symmetry axis of the ellipsoid undergoes a random walk on a 2D plane with a step size $${s}_{r}$$ in a random direction which mimic rational motion as shown by Varma et al. [ 32 ] If either of the movement steps leads to the hard core to overlap with other ellipsoidal particles or break an already formed bond then that movement step of that particular ellipsoid is rejected.…”

“…[ 32 ] The orientation of the symmetry axis of the ellipsoid undergoes a random walk on a 2D plane with a step size $${s}_{r}$$ in a random direction which mimic rational motion as shown by Varma et al. [ 32 ] If either of the movement steps leads to the hard core to overlap with other ellipsoidal particles or break an already formed bond then that movement step of that particular ellipsoid is rejected. We have already shown that if the step size is smaller than 0.005 d , the diffusion coefficient of the ellipsoidal particle obtained from BCD agrees with the analytical calculation of Perrin et al.…”

“…Later the BCD was extended to simulate the structure and dynamics for both prolate and oblate particles. [ 32 ] In the present study we have focused on prolate particle with two‐patches placed at the opposite ends of the major axis. Here, we control the valency by controlling the patch angle as we have kept the patch width a constant.…”