Abstract

Describing properties of mesoscale order in polymeric liquid crystals (LC) has attracted considerable attention [1-4], partially due to unusual behaviour of correlation functions (e.g. “bow-tie” shape of density structure factor). This behaviour stems from coupling between variations in density and orientation of director, induced by polymer chain connectivity. For polymer nematics several analytical theories have been proposed, describing fluctuation spectra and related elastic constants. Intriguingly, some theoretical predictions are very controversial. The dependence of the splay constant on chain length is a well-known example, where linear [2-4] and quadratic [1] growth was predicted. Currently, apart from fundamental scientific interest, understanding mesoscale order and associated material constants, becomes practically important in view of novel applications of polymeric LC mesophases, e.g. in organic electronics [5].

The presentation focuses on validation of theories mentioned above, with efficient Monte Carlo simulations [6]. For this purpose, polymer nematics are described through a worm-like chain model combined with soft anisotropic non-bonded interactions. The latter are motivated by a framework akin to classical density functional theory of liquids. To obtain a realistic model and facilitate comparison with potential experiments, the parameters are chosen to reproduce persistence length and density typical for poly(3-alkylthiophenes) ─ a representative family of conjugated polymers where LC mesophases have been reported [7]. We demonstrate that early analytical theories indeed can describe several features of fluctuation spectra obtained in the simulations. Material constants controlling density and director fluctuations are extracted and compared with theoretical predictions. The simulation results support analytical theories predicting a linear dependence of splay constant on chain length.

References:

[1] P.G. de Gennes, Polymer Liquid Crystals, ch. 5, New York: Academic Press (1982) [2] R.B. Mayer, Polymer Liquid Crystals, ch. 6, New York: Academic Press (1982) [3] D.R. Nelson, Physica A (1991), 177, 220 [4] R.D. Kamien, P. Le Doussal, and D.R. Nelson, Phys. Rev. A (1992), 45, 8727 [5] N. Stingelin, Polym. Int. (2012), 61, 866 [6] P. Gemünden and K.Ch. Daoulas, Soft Matter (2015), 11, 532 [7] V. Ho, B.W. Boudouris, and R.A. Segalman, Macromolecules (2010), 43, 7895