Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userUnusual geometric percolation of hard nanorods in the uniaxial nematic liquid crystalline phase
57
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic 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 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.
rate research
Read More
Based on simplifications of previous numerical calculations [Graf and L{o}wen, Phys. Rev. E textbf{59}, 1932 (1999)], we propose algebraic free energy expressions for the smectic-A liquid crystal phase and the crystal phases of hard spherocylinders. Quantitative agreement with simulations is found for the resulting equations of state. The free energy expressions can be used to straightforwardly compute the full phase behavior for all aspect ratios and to provide a suitable benchmark for exploring how attractive interrod interactions mediate the phase stability through perturbation approaches such as free-volume or van der Waals theory.
We investigate the connections between some simple Maier-Saupe lattice models, with a discrete choice of orientations of the microscopic directors, and a recent proposal of a two-tensor formalism to describe the phase diagrams of nematic liquid-crystalline systems. This two-tensor proposal is used to formulate the statistical problem in terms of fully-connected lattice Hamiltonians, with the local nematic directors restricted to the Cartesian axes. Depending on the choice of interaction parameters, we regain all of the main features of the original mean-field two-tensor calculations. With a standard choice of parameters, we obtain the well-known sequence of isotropic, uniaxial, and biaxial nematic structures, with a Landau multicritical point. With another suitably chosen set of parameters, we obtain two tricritical points, according to some recent predictions of the two-tensor calculations. The simple statistical lattice models are quite easy to work with, for all values of parameters, and the present calculations can be carried out beyond the mean-field level.
Percolation of carbon nanotubes (CNTs) in liquid crystals (LCs) opens way for a unique class of anisotropic hybrid materials with a complex dielectric constant widely controlled by CNT concentration. Percolation in such systems is commonly described as a one-step process starting at a very low loading of CNTs. In the present study the two-step percolation was observed in the samples of thickness 250 $mu$m obtained by pressing the suspension between two substrates. The percolation concentrations for the first and second percolation processes were $C_n^{p_1}approx 0.0002$ wt. % and $C_n^{p_2}approx 0.5$ wt. %, respectively. The two-stage nature of percolation was explained on a base of mean field theory assuming core-shell structure of CNTs.
Topological defects resulted from boundary constraints in confined liquid crystals have attracted extensive research interests. In this paper, we use numerical simulation to study the phase transition dynamics in the context of stochastic resonance in a bistable liquid crystal device containing defects. This device is made of nematic liquid crystals confined in a shallow square well, and is described by the planar Lebwohl-Lasher model. The stochastic phase transition processes of the system in the presence of a weak oscillating potential is simulated using an over-damped Langevin dynamics. Our simulation results reveal that, depending on system size, the phase transition may follow two distinct pathways: in small systems the pre-existing defect structures at the corners hold until the last stage and there is no newly formed defect point in the bulk during the phase transition, In large systems new defect points appear spontaneously in the bulk and eventually merge with the pre-existing defects at the corners. For both transition pathways stochastic resonance can be observed, but show dramatic difference in their responses to the boundary anchoring strength. In small systems we observe a sticky-boundary effect for a certain range of anchoring strength in which the phase transition gets stuck and stochastic resonance becomes de-activated. Our work demonstrates the dynamical interplay among defects, noises, and boundary conditions in confined liquid crystals.
Using computer simulations we investigate the microscopic structure of the singular director field within a nematic droplet. As a theoretical model for nematic liquid crystals we take hard spherocylinders. To induce an overall topological charge, the particles are either confined to a two-dimensional circular cavity with homeotropic boundary or to the surface of a three-dimensional sphere. Both systems exhibit half-integer topological point defects. The isotropic defect core has a radius of the order of one particle length and is surrounded by free-standing density oscillations. The effective interaction between two defects is investigated. All results should be experimentally observable in thin sheets of colloidal liquid crystals.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
