Measuring liquid crystal elastic constants with free energy perturbations

Abstract

A first principles method is proposed to calculate the Frank elastic constants of nematic liquid crystals. These include the constants corresponding to standard splay, twist and bend deformations, and an often-ignored surface-like contribution known as saddle-splay. The proposed approach is implemented on the widely studied Gay-Berne (3, 5, 2, 1) model [J. G. Gay and B. J. Berne, J. Chem. Phys., 1981, 74, 3316], and the effects of temperature and system size on the elastic constants are examined in the nematic phase. The results of simulations for splay, twist, and bend elastic constants are consistent with those from previous literature reports. The method is subsequently applied to the saddle-splay elastic constant k24 which is found to exist at the limits of the Ericksen inequalities governing positive definite free energy. Finally, extensions of the method are discussed that present a new paradigm for in silico measurements of elastic constants.

Reversible Switching of Liquid Crystalline Order Permits Synthesis of Homogeneous Populations of Dipolar Patchy Microparticles

“…Accordingly, we estimate the magnitude of the elastic forces driving the colloid to the defect as: [ 34,35 ] = E Ka elastic (1) in which K is the elastic constant of the LC (using the "one constant" approximation), and a is the radius of the PS colloid (0.5 µm). Using a typical value for an elastic constant for a low molecular weight LC, K = 10 −11 N, [ 20,36 ] we calculate E elastic ≈ 5 × 10 −18 J. As noted above, the force driving transport of the PS colloid across the surface of the LC droplet is opposed by a Stokes' drag force.…”

“…Using a typical value for an elastic constant for a low molecular weight LC, K =10 -11 N, [20, 36] we calculate E elastic ≈ 5×10 -18 J. As noted above, the force driving transport of the PS colloid across the surface of the LC droplet is opposed by a Stokes' drag force.…”

Basis Function Sampling: A New Paradigm for Material Property Computation

“…Expanded ensemble calculations, which extract free energies by enforcing uniform sampling on a small set of thermodynamic quantities, are of particular interest for their efficiency and wide application [24]. These methods may naturally measure the free energetic cost of perturbations [28], codified by material properties defining response to (e.g.) thermal stress, tension, torsion or shear by probing the local free energy topography along a deformation coordinate ξ,…”

“…Obtaining these constants by traditional techniques is notoriously challenging [28,42]. Utilizing the fundamental bend, twist and splay modes (cf.…”

“…Utilizing a recently devised method for generating fundamental bend, twist, and splay elastic perturbations in silico [28], we define an order parameter ξ corresponding to bend, splay, or twist. The resulting free energy profile is F * (ξ) = V * K * ξ 2 /2, with V * the reduced system volume, which is equal to the number of spins.…”