Understanding the physics of the auxetic response in a liquid crystal elastomer

Synthetic materials that are auxetic (negative Poisson's ratio) at a molecular level have long been sought after. An auxetic liquid crystal elastomer (LCE) was reported recently, but the physical origin of the behavior has remained unclear. Here, we explain the physics behind the auxetic response of a uniaxial LCE under strain by the emergence of biaxial order. Our study relies on understanding order parameters (OPs), determined via Raman scattering, for LCEs strained either parallel or perpendicular to the director and explaining their relevance in terms of existing LCE theory. In particular, we consider a 3D interpretation of the orientational distribution function. We use uniaxial and biaxial models to deduce that (i) a changing nematic order drives the mechanical Fréedericksz transition (MFT), (ii) the apparent semi-soft elasticity exhibited by this LCE is related to this change in order, (iii) there is also an emergence of biaxial order in the LCE, and (iv) the emergence of biaxiality explains the auxetic response. Uniaxial OPs, ⟨ P 200 ⟩ and ⟨ P 400 ⟩ , initially take values of 0.6 and 0.3 and, for strains parallel to the director, increase by 20%. For perpendicular strains, the OPs reduce dramatically with increasing strain, becoming zero at the MFT, where the director reorients to align with the strain axis; the auxetic behavior emerges in the same strain regime. Our explanation identifies key parameters in determining the requirements for auxetic behavior in LCEs.