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.

Active nematics are microscopically driven liquid crystals that exhibit dynamical steady states characterized by the creation and annihilation of topological defects. Motivated by experimental realizations of such systems made of biopolymer filaments and motor proteins, we describe a largescale simulation study of a particle-based computational model that explicitly incorporates the semiflexibility of the biopolymers. We find that energy injected into the system at the particle scale preferentially excites bend deformations, renormalizing the filament bend modulus to smaller values. The emergent characteristics of the active nematic depend on activity and flexibility only through this activity-renormalized bend modulus, demonstrating that material parameters such as the Frank 'constants' must explicitly depend on activity in a continuum hydrodynamic description of an active nematic. Further, we present a systematic way to estimate these material parameters from observations of deformation fields and defect shapes in experimental or simulation data. arXiv:1711.05714v3 [cond-mat.soft] 1 Sep 2018

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