TY - JOUR

T1 - Phase transition and director fluctuations in the three-dimensional Lebwohl-Lasher model of liquid crystals

AU - Zhang, Zhengping

AU - Zuckermann, Martin J.

AU - Mouritsen, Ole G.

PY - 1993

Y1 - 1993

N2 - Monte Carlo computer simulation techniques are used to study the orientational phase transition in the three-dimensional Lebwohl-Lasher model which couples molecular rotors placed on a cubic lattice by the potential P2(cosθij). The orientational transition is a model of the nematic-isotropic phase transition in liquid crystals. The simulations involve the determination of energy and order parameter distribution functions which permit free energy functions to be derived. The data have been analysed by finite size scaling methods to reveal the nature of the phase transition which is found to be weakly first order with stability limits of the nematic and isotropic phases being extremely close to the equilibrium transition temperature, in good agreement with experimental studies of room temperature nematogens. Results are reported for the specific heat, the axial and biaxial susceptibilities, as well as the enthalpy and nematic order parameter discontinuity at the transition. It is shown that the inclusion of a term p4(cosθij) in the potential enhances the first-order character of the transition and displaces the stability limits further from the equilibrium transition temperature. The director fluctuations have been analysed, and it is found that, whereas the fluctuations in the isotropic phase follow ordinary Brownian motion, the fluctuations in the nematic phase correspond to fractional Brownian motion. By introducing a symmetry- breaking field, –h2 cosθ2i, a field-induced crossover between fractional and normal Brownian motion is observed in agreement with recent neutron scattering studies on deuterated p-azoxyanisole.

AB - Monte Carlo computer simulation techniques are used to study the orientational phase transition in the three-dimensional Lebwohl-Lasher model which couples molecular rotors placed on a cubic lattice by the potential P2(cosθij). The orientational transition is a model of the nematic-isotropic phase transition in liquid crystals. The simulations involve the determination of energy and order parameter distribution functions which permit free energy functions to be derived. The data have been analysed by finite size scaling methods to reveal the nature of the phase transition which is found to be weakly first order with stability limits of the nematic and isotropic phases being extremely close to the equilibrium transition temperature, in good agreement with experimental studies of room temperature nematogens. Results are reported for the specific heat, the axial and biaxial susceptibilities, as well as the enthalpy and nematic order parameter discontinuity at the transition. It is shown that the inclusion of a term p4(cosθij) in the potential enhances the first-order character of the transition and displaces the stability limits further from the equilibrium transition temperature. The director fluctuations have been analysed, and it is found that, whereas the fluctuations in the isotropic phase follow ordinary Brownian motion, the fluctuations in the nematic phase correspond to fractional Brownian motion. By introducing a symmetry- breaking field, –h2 cosθ2i, a field-induced crossover between fractional and normal Brownian motion is observed in agreement with recent neutron scattering studies on deuterated p-azoxyanisole.

U2 - 10.1080/00268979300102981

DO - 10.1080/00268979300102981

M3 - Journal article

AN - SCOPUS:0001303641

VL - 80

SP - 1195

EP - 1221

JO - Molecular Physics

JF - Molecular Physics

SN - 0026-8976

IS - 5

ER -