Density-functional theory and Monte Carlo simulations of the phase behavior of a simple model liquid crystal

Abstract

We consider the phase behavior of a simple model of a liquid crystal by means of modified mean-field density-functional theory (MMF DFT) and Monte Carlo simulations in the grand canonical ensemble (GCEMC). The pairwise additive interactions between liquid-crystal molecules are modeled via a Lennard-Jones potential in which the attractive contribution depends on the orientation of the molecules. We derive the form of this orientation dependence through an expansion in terms of rotational invariants. Our MMF DFT predicts two topologically different phase diagrams. At weak to intermediate coupling of the orientation dependent attraction, there is a discontinuous isotropic-nematic liquid-liquid phase transition in addition to the gas-isotropic liquid one. In the limit of strong coupling, the gas-isotropic liquid critical point is suppressed in favor of a fluid- (gas- or isotropic-) nematic phase transition which is always discontinuous. By considering three representative isotherms in parallel GCEMC simulations, we confirm the general topology of the phase diagram predicted by MMF DFT at intermediate coupling strength. From the combined MMF DFT-GCEMC approach, we conclude that the isotropic-nematic phase transition is very weakly first order, thus confirming earlier computer simulation results for the same model [see M. Greschek and M. Schoen, Phys. Rev. E 83, 011704 (2011)].

Defect topologies in chiral liquid crystals confined to mesoscopic channels

“…IV B, this brings the pitch p of helical structures forming under the conditions adopted here well within reach of p ≈ 100 nm observed in the recent experiments of Oo et al 11 Nevertheless, it needs to be emphasized that this p is typically two or three orders of magnitude smaller than typical values found traditionally in experimental studies. 46,47 To treat the anisotropic part of ϕ mm , we follow Giura and Schoen 48 and expand ϕ anis in the basis of rotational invariants Φ l i l j l according to…”

“…Because of the definition of rotational invariants in terms of spherical harmonics and because of the parity rule 49 for the latter set of functions, l i and l j are immediately restricted to zero or even integers. 48 However, integers l i , l j , and l are not independent of each other. In fact, Φ l i l j l 0 only if the triangle inequality l i − l j ≤ l ≤ l i + l j is satisfied.…”

“…In fact, Φ l i l j l 0 only if the triangle inequality l i − l j ≤ l ≤ l i + l j is satisfied. 48 Because of this selection rule and because we intend to restrict the discussion to the leading terms in the expansion Eq. (3.5) for the sake of simplicity, only terms proportional to Φ 000 , Φ 220 , Φ 221 , Φ 202 and Φ 022 will be considered.…”

“…50 Based upon this truncation of the expansion in Eq. (3.5) and grouping individual terms according to the criteria of Giura and Schoen, 48 we cast ϕ anis as…”

“…(3.7) for a liquid crystal that exhibits a nematic besides the more conventional isotropic liquid and gaseous phases. However, unlike Giura and Schoen, 48 Hess and Su base their derivation of Ψ on an expansion of ϕ anis in terms of irreducible Cartesian tensors.…”