Interplay of Particle Morphology and Director Distortions in Nematic Fluids Davide Revignas and Alberta Ferrarini * Universit ` a di Padova, Dipartimento di Scienze Chimiche, via Marzolo 1, 35131 Padova, Italy (Received 10 August 2020; revised 16 October 2020; accepted 26 October 2020; published 23 December 2020) The existing microscopic theories for elasticity of nematics are challenged by recent findings on systems, whether bent molecules or semiflexible polymers, which do not comply with the model of rigid rodlike particles. Here, we propose an extension of Onsager-Straley second-virial theory, based on a model for the orientational distribution function that, through explicit account of the director profile along a particle, changes in the presence of deformations. The elastic constants reveal specific effects of particle morphology, which are not captured by the existing theories. This paves the way to microscopic modeling of the elastic properties of semiflexible liquid crystal polymers, which is a longstanding issue. DOI: 10.1103/PhysRevLett.125.267802 A major consequence of orientational order in nematics is their curvature elasticity: they oppose a restoring force to distortions of the director and this property is crucial for their meso- and macroscale behavior. It plays a role in prac- tically any application of liquid crystals, from the pervasive electro-optic devices to emerging applications in a variety of fields [1]. Moreover, it underlies fundamental questions of geometry and topology [2–5]. Curvature deformations in a nematic fluid are described by the director field ˆ nðRÞ and, in macroscopic terms, the bulk deformation free energy (Frank free energy) is expressed as [6] A def ¼ 1 2 Z V dRfK 11 ð∇ · ˆ nÞ 2 þ K 22 ð ˆ n · ∇ × ˆ nÞ 2 þ K 33 j ˆ n × ð∇ × ˆ nÞj 2 g; ð1Þ where K ii (i ¼ 1, 2, 3) are material parameters (Frank elastic constants), which quantify the energetic cost for splay, twist, and bend deformations, respectively. The typical textbook behavior is K ii ∼ 1 ÷ 10 pN, with K 22 the smallest of the three moduli and K 33 ranging from slightly lower to 2–3 times higher than K 11 [7]. This is the typical trend for conventional thermotropic nematics made of low molar mass mesogens. Liquid crystal polymers (LCPs) have much larger differences between their elastic constants (elastic anisotropy), with a significant depend- ence on the chain flexibility [8,9]. Recent interest in the continuously expanding variety of nematic systems [10–13] has brought to light several examples of unconven- tional elasticity. These include supramolecular polymers, such as chromonics [14–16] and DNA oligomers [17], bent molecules [18–21], and actin-based filaments [22–24]. The experimental results challenge the microscopic theories of nematic elasticity, which predict a general trend for the elastic constants scarcely dependent on the structure of their constituents. Within such theories, expressions for the elastic constants are obtained as averages of suitable quantities over the orientational distribution function (ODF) of particles in the undeformed nematic phase. The underlying assumption is that the ODF is the same as in the undeformed system, but referred to the local director at the center of mass (c.m.) of the particle (“local” model). Such an approximation is justified by the very slow variation in space of the director field, on the scale of the particle size. This is the approach used in the seminal Straley paper [25], where the elastic constants of hard rods are calculated within an Onsager-like second-virial frame- work [26]. The typical experimental trend is correctly predicted: K 22 <K 11 <K 33 , with the elastic constants that increase with increasing order. In a couple of studies, dealing with the specific case of particles of polar sym- metry [27,28], the assumption that the ODF is unaffected by deformation was relaxed; it was shown that the unrelaxed elastic constants are upper bounds and that the coupling of director distortion and polar order can lead to a significant decrease of K 11 and K 33 , which can explain experimental findings for bent mesogens [18–21]. For LCPs there have been efforts to take into account the flexibility [29] and the conformation dependence of the chain morphology [30], using models that are essentially based on the concept of effective rod, whose ODF is unaffected by director distortions. This turns out to be insufficient to capture important aspects of experiments [14,15,17] and computer simulations [30]; hence the demand of novel interpretation tools [14,17,31]. Motivated by the experimental findings and by the need of broadening the theoretical understanding, we propose here an extension of Onsager-Straley second-virial theory that overcomes the limitations of the existing microscopic approaches to nematic elasticity. The key point is the definition of an ODF that takes into account the director profile along a particle (“nonlocal” model). In this way, the coupling of particle morphology and director deformation PHYSICAL REVIEW LETTERS 125, 267802 (2020) 0031-9007=20=125(26)=267802(6) 267802-1 © 2020 American Physical Society