Unusual geometric percolation of hard nanorods in the uniaxial nematic liquid crystalline phase

Abstract

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 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.

Continuum percolation in colloidal dispersions of hard nanorods in external axial and planar fields

“…This has been shown analytically and was confirmed by Monte Carlo simulations by Finner et al, in the absence of an external field. 65,66 Noting that quadrupole fields always inhibit the formation of percolating clusters to some extent, we conclude that this finding remains valid in the presence of an external field.…”

“…However, it may be justified on the grounds that it makes sense to make use of the same renormalisation of the excluded volume term of the free energy as that in the direct connectedness function, which in effect is a connectedness volume. 66 Perhaps more convincingly, it turns out that this approximation yields very accurate results for aspect ratios L/D 4 10. 66 By the same methods described in Section 3, we solve the connectedness Ornstein-Zernike equation and find the cluster size as function of the volume fraction j, aspect ratio L/D, connectedness criterion l/D, and external field strength K. We summarise our findings in the percolation diagrams shown in Fig.…”

“…Actually, the theory discussed above should be expected to become quantitatively correct for aspect ratios exceeding a few hundred. 66 Even though that this covers many practical applications, involving, e.g., carbon nanotubes, we need to ask ourselves the question if our main conclusions remain valid if we correct for finite aspect ratios. This we investigate next.…”

“…45,67,68 This approach is similar in spirit to the Parsons-Lee approach, yet has been shown to yield results that are in better agreement with Monte Carlo simulations of percolation, and in fact remains nearly quantitative, even down to aspect ratios of L/D = 5. 66,69,70 We briefly present the main ingredients of the theory, and proceed to apply it to percolation of rods in external fields.…”

“…At K = 0, our results show excellent agreement with earlier simulations and numerical work. 72 To apply SPT to our calculation of the cluster size, we closely follow the procedure presented in Finner et al 66 We rescale our contact volume with the same parameter G that we used to rescale our excluded volume, given by eqn (10), and explicitly include the contributions due to the end-effects to the excluded volume. The closure of the connectedness Ornstein-Zernike eqn (5) now becomes…”