An analytical equation of state for describing isotropic-nematic phase equilibria of Lennard-Jones chain fluids with variable degree of molecular flexibility

Abstract

Articles you may be interested inWe develop an equation of state (EoS) for describing isotropic-nematic (IN) phase equilibria of Lennard-Jones (LJ) chain fluids. The EoS is developed by applying a second order Barker-Henderson perturbation theory to a reference fluid of hard chain molecules. The chain molecules consist of tangentially bonded spherical segments and are allowed to be fully flexible, partially flexible (rodcoil), or rigid linear. The hard-chain reference contribution to the EoS is obtained from a Vega-Lago rescaled Onsager theory. For the description of the (attractive) dispersion interactions between molecules, we adopt a segment-segment approach. We show that the perturbation contribution for describing these interactions can be divided into an "isotropic" part, which depends only implicitly on orientational ordering of molecules (through density), and an "anisotropic" part, for which an explicit dependence on orientational ordering is included (through an expansion in the nematic order parameter). The perturbation theory is used to study the effect of chain length, molecular flexibility, and attractive interactions on IN phase equilibria of pure LJ chain fluids. Theoretical results for the IN phase equilibrium of rigid linear LJ 10-mers are compared to results obtained from Monte Carlo simulations in the isobaric-isothermal (N PT) ensemble, and an expanded formulation of the Gibbs-ensemble. Our results show that the anisotropic contribution to the dispersion attractions is irrelevant for LJ chain fluids. Using the isotropic (density-dependent) contribution only (i.e., using a zeroth order expansion of the attractive Helmholtz energy contribution in the nematic order parameter), excellent agreement between theory and simulations is observed. These results suggest that an EoS contribution for describing the attractive part of the dispersion interactions in real LCs can be obtained from conventional theoretical approaches designed for isotropic fluids, such as a Perturbed-Chain Statistical Associating Fluid Theory approach. C 2015 AIP Publishing LLC.[http://dx

Liquid-crystal phase equilibria of Lennard-Jones chains

“…The simulation results presented in this section are extensively compared to a recently developed analytical equation of state of van Westen et al [71]. The equation of state was developed from a perturbation theory based on a hard-chain reference fluid.…”

“…As shown in Ref. [71], this assumption leads to an excellent description of the isotropic-nematic phase behaviour of a linear Lennard-Jones 10-mer fluid. We here provide a more elaborate evaluation of the equation of state comparing it to simulation data, allowing further analysis on the effect of molecular orientation on attractive dispersion interactions.…”

“…In this work, we focus our study on the isotropic-nematic phase behaviour of linear and partially-flexible Lennard-Jones chain fluids. To the best of our knowledge, apart from our recent work [71], there is no other study showing simulation results for the isotropic-nematic phase transition of Lennard-Jones chains. Galindo et al [72] studied the phase behaviour of linear Lennard-Jones chains of 3 and 5 segments; however, in that study, no liquid-crystalline phases were observed due to the short length of the chains.…”

“…Galindo et al [72] studied the phase behaviour of linear Lennard-Jones chains of 3 and 5 segments; however, in that study, no liquid-crystalline phases were observed due to the short length of the chains. The importance of this study is twofold, first to determine the effect of main molecular characteristics (such as chain length, flexibility, attractive interactions, and composition of mixtures) on the isotropic-nematic behaviour of long Lennard-Jones chains, and second to validate the analytical equation of state presented by van Westen et al [71] for Lennard-Jones chain fluids with variable degree of flexibility.…”

“…The equation of state of van Westen et al [71] was developed using a perturbation theory based on a reference fluid of hard-chain molecules. An important assumption in the development of the equation of state was that of orientation-independent attractive interactions.…”