The theory of elastic constants

Abstract

The elastic theory of liquid crystals can be traced back to the early 1930s, but the origin of the molecular theory of elastic constants must be postponed to more than 30 years later, when Alfred Saupe wrote his famous papers on this subject. At approximately the same time, the seminal works by Priest and Straley also appeared. Since then, several theories have been developed to connect intermolecular interactions to curvature deformations, on a quite different length-scale, in liquid crystals. This field was particularly alive between the end of the 1970s and the beginning of the 1980s, in parallel with experimental investigations. In more recent times, a renewed interest was aroused by the controversy about the second-order splay-bend contribution, which appears in the Nehring-Saupe expression for the deformation energy density. In the first part of the present contribution the molecular theory of elastic constants is briefly reviewed. This paper focuses on the effects of molecular structure on the elastic constants of thermotropic nematics and the ability of different models to account for them. A few classical examples are discussed to illustrate these issues. The second part of this paper is dedicated to our recent 'Surface Interaction' model, a molecular field approach based on the Maier-Saupe theory, implemented into a framework allowing for atomistic molecular modelling. The theoretical background is outlined, then some new results are reported and the insights derived from a realistic molecular representation are discussed. We conclude that, after about 40 years of theoretical investigations, there is a general consensus on the importance of the molecular shape in determining the elastic constants of nematics: for fairly rigid compounds these can be simply related to the length-to-width ratio, but for the general case of non-rigid mesogens the molecular flexibility and shape curvature have to be taken into account

From the Molecular Structure to Spectroscopic and Material Properties: Computational Investigation of a Bent‐Core Nematic Liquid Crystal

“…K 3 is unusually low and its temperature dependence cannot be described by the relationship K 3 / S zz 2 , customarily assumed for rod-like mesogens. [42] Using our computational methodology, which allows us to take into account the real molecular shape, we already showed that there may be significant deviations from such a relationship. [20,41] The special sensitivity of K 3 to the molecular curvature has already been evidenced for bent-core systems [20,21,32] and for bent mesogenic Figure 5.…”

“…Here we used the experimental chemical shifts of C5 to define the relation between e and temperature, to report our results as a function of temperature, which makes the comparison with experimental data easier. [42] Using our computational methodology, which allows us to take into account the real molecular shape, we already showed that there may be significant deviations from such a relationship. Therefore the results shown in Figure 5 can be taken as an assessment of the adequacy of our description of the molecular structure and our account of the conformational and orientational distribution for A131.…”

“…[20,21,32,[40][41][42][43] Of course, a detailed molecular-level description is a necessary requirement also for the prediction of NMR We present a computational investigation of the nematic phase of the bent-core liquid crystal A131. This has been shown to be important for the elastic properties, and crucial for the bend-elastic constant.…”

“…This has been shown to be important for the elastic properties, and crucial for the bend-elastic constant. [20,21,32,[40][41][42][43] Of course, a detailed molecular-level description is a necessary requirement also for the prediction of NMR We present a computational investigation of the nematic phase of the bent-core liquid crystal A131. We use an integrated approach that bridges density functional theory calculations of molecular geometry and torsional potentials to elastic properties through the molecular conformational and orientational distribution function.…”

Polymorphism of stable collagen fibrils

“…We use a leading order gradient expansion for the elastic contributions. The elastic free energy density 24 of a chiral liquid crystal system with no external stress is f el = 1 2 K 11 (∇ · n n n) 2 + 1 2 K 22 n n n · ∇ × n n n + k 2 K 22 2 + 1 2 K 33 (n n n × (∇ × n n n)) 2 + k 13 ∇ · (∇ · n n n) n n n − 1 2 (K 22 + k 24 )∇ · (n n n × (∇ × n n n) + n n n(∇ · n n n)) ,…”