Elastic constants from direct correlation functions in nematic liquid crystals: A computer simulation study

Abstract

Density functional theories such as the Poniewierski-Stecki theory relate the elastic properties of nematic liquid crystals with their local liquid structure, i.e., with the direct correlation function ͑DCF͒ of the particles. We propose a way to determine the DCF in the nematic state from simulations without any approximations, taking into account the dependence of pair correlations on the orientation of the director explicitly. Using this scheme, we evaluate the Frank elastic constants K 11 , K 22 , and K 33 in a system of soft ellipsoids. The values are in good agreement with those obtained directly from an analysis of order fluctuations. Our method thus establishes a reliable way to calculate elastic constants from pair distributions in computer simulations.

Colloidal particles in liquid crystal films and at interfaces

“…It has been used to simulate various bulk properties of liquid crystals, such as bulk elastic constants [10][11][12][13][14][15][16], viscosities [17,18], helical twisting power [19,20], parameters of the isotropicnematic interface [21]. Moreover, recent works have also proved that computer simulations can be effectively applied to the study of confined geometries [22,23].…”

Simultaneous calculation of the helical pitch and the twist elastic constant in chiral liquid crystals from intermolecular torques

“…Arrows indicate the two values Π c k,0 /V (with k = 0 or k = 0) and Π a k,0 /V (with k = 0) which in the case of weak chirality may be measured in the achiral system to yield the same quantities through eqns (30) and (31). Notation as for Fig.…”

“…[26][27][28][29][30] The route to q λ and K 2 through Π λ is more convenient than with thermodynamic integration or order fluctuation because the data analysis is easier and the computational effort smaller. With respect to thermodynamic integration there is the additional advantage that the simulation giving h λ = K 2 q λ can be done with k = 0 and thus in a fairly small box; we have confirmed the practicality of the approach proposed in Refs 8-10.…”

“…These calculations yielded K 2 q λ from thermodynamic integration, eqn (4), and from our new method, eqn (12) or, in the special case of weak chirality, eqn (30).…”

Calculation of flexoelectric coefficients for a nematic liquid crystal by atomistic simulation

“…Combining the density functional method used in Refs. 37 and 38 with a more accurate method for determining the direct correlation function, such as that recently used by Schmid and co-workers for the calculation of nematic elastic constants 62 could provide an alternative route to the flexoelectric coefficients.…”