8 research outputs found
Unusual geometric percolation of hard nanorods in the uniaxial nematic liquid crystalline phase
We investigate by means of continuum percolation theory and Monte Carlo
simulations how spontaneous uniaxial symmetry breaking affects geometric
percolation in dispersions of hard rod-like particles. If the particle aspect
ratio exceeds about twenty, percolation in the nematic phase can be lost upon
adding particles to the dispersion. This contrasts with percolation in the
isotropic phase, where a minimum particle loading is always required to obtain
system-spanning clusters. For sufficiently short rods, percolation in the
uniaxial nematic mimics that of the isotropic phase, where the addition of
particles always aids percolation. For aspect ratios between twenty and
infinity, but not including infinity, we find re-entrance behavior: percolation
in the low-density nematic may be lost upon increasing the amount of
nanofillers but can be re-gained by the addition of even more particles to the
suspension. Our simulation results for aspect ratios of 5, 10, 20, 50 and 100
strongly support our theoretical predictions, with almost quantitative
agreement. We show that a new closure of the connectedness Ornstein-Zernike
equation, inspired by Scaled Particle Theory, is more accurate than the
Lee-Parsons closure that effectively describes the impact of many-body direct
contacts
Simulation study of the electrical tunneling network conductivity of suspensions of hard spherocylinders
Using Monte Carlo simulations, we investigate the electrical conductivity of networks of hard rods with aspect ratios 10 and 20 as a function of the volume fraction for two tunneling conductance models. For a simple, orientationally independent tunneling model, we observe nonmonotonic behavior of the bulk conductivity as a function of volume fraction at the isotropic-nematic transition. However, this effect is lost if one allows for anisotropic tunneling. The relative conductivity enhancement increases exponentially with volume fraction in the nematic phase. Moreover, we observe that the orientational ordering of the rods in the nematic phase induces an anisotropy in the conductivity, i.e., enhanced values in the direction of the nematic director field. We also compute the mesh number of the Kirchhoff network, which turns out to be a simple alternative to the computationally expensive conductivity of large systems in order to get a qualitative estimate
Unusual geometric percolation of hard nanorods in the uniaxial nematic liquid crystalline phase
We investigate by means of continuum percolation theory and Monte Carlo simulations how spontaneous uniaxial symmetry breaking affects geometric percolation in dispersions of hard rodlike particles. If the particle aspect ratio exceeds about 20, percolation in the nematic phase can be lost upon adding particles to the dispersion. This contrasts with percolation in the isotropic phase, where a minimum particle loading is always required to obtain system-spanning clusters. For sufficiently short rods, percolation in the uniaxial nematic mimics that of the isotropic phase, where the addition of particles always aids percolation. For aspect ratios between 20 and infinity, but not including infinity, we find reentrance behavior: percolation in the low-density nematic may be lost upon increasing the amount of nanofillers but can be regained by the addition of even more particles to the suspension. Our simulation results for aspect ratios of 5, 10, 20, 50, and 100 strongly support our theoretical predictions, with almost quantitative agreement. We show that a different closure of the connectedness Ornstein-Zernike equation, inspired by scaled particle theory, is as least as accurate in predicting the percolation threshold as the Parsons-Lee closure, which effectively describes the impact of many-body direct contacts
Unusual geometric percolation of hard nanorods in the uniaxial nematic liquid crystalline phase
\u3cp\u3eWe investigate by means of continuum percolation theory and Monte Carlo simulations how spontaneous uniaxial symmetry breaking affects geometric percolation in dispersions of hard rodlike particles. If the particle aspect ratio exceeds about 20, percolation in the nematic phase can be lost upon adding particles to the dispersion. This contrasts with percolation in the isotropic phase, where a minimum particle loading is always required to obtain system-spanning clusters. For sufficiently short rods, percolation in the uniaxial nematic mimics that of the isotropic phase, where the addition of particles always aids percolation. For aspect ratios between 20 and infinity, but not including infinity, we find reentrance behavior: percolation in the low-density nematic may be lost upon increasing the amount of nanofillers but can be regained by the addition of even more particles to the suspension. Our simulation results for aspect ratios of 5, 10, 20, 50, and 100 strongly support our theoretical predictions, with almost quantitative agreement. We show that a different closure of the connectedness Ornstein-Zernike equation, inspired by scaled particle theory, is as least as accurate in predicting the percolation threshold as the Parsons-Lee closure, which effectively describes the impact of many-body direct contacts.\u3c/p\u3