Segregation and phase inversion of strongly and weakly fluctuating Brownian particle mixtures and a chain of such particle mixtures in spherical containers

We investigate the segregation pattern formation of strongly and weakly fluctuating Brownian particle mixtures confined in a three-dimensional spherical container. We consider systems where the particle motion is restricted by the harmonic external trapping potential and the container edge wall. In such systems, two segregation patterns are observed. When the container radius is sufficiently large, more weakly fluctuating particles accumulate near the center of the container than strongly fluctuating particles. On the other hand, the distributions of the strongly and weakly fluctuating particles are inverted when the container radius is small. With no external trapping potentials, we find similar segregation and phase inversion if the particles construct a chain (heterofluctuating polymer) and are confined in a three-dimensional spherical container. We could apply these phenomena in the study of biopolymer behavior, such as chromosomes in the cell nucleus.

Figure 1

Typical snapshots of the distribution of $S$ particles [gray (red)] and $W$ particles (black) of the hetero-Brownian particles model $\left(N=512\right)$ on the 2D cross section for (a) $R=12$, (b) $R=6.5$, and (c) $P\left(r\right)$ for typical $R$, where $r$ is the distance from the origin.

Figure 2

(a) Plot of $\langle r\rangle /R$ as a function of $R$ for several $k_n$ and (b) $R^{*}-d/2$ as a function of $k_n$ for $n=1$ and 2 in the case of $N=2$. The solid and dashed curves in (b) are the fitted curves for each $n$.

Figure 3

(a) Illustration of the heterofluctuating polymer model, where the black and gray (red) circles indicate weakly and strongly fluctuating particles, respectively. (b) and (c) Typical snapshots of the distributions of $S$ particles and $W$ particles of the heterofluctuating polymer model $\left(N=512\right)$ on the 2D cross section for $R=11$ and 6, respectively, with $L=64$. (d) and (e) Plots of the $P\left(r\right)$ of this model for typical $R$ with $L=64$ and 128, respectively.