TY - JOUR

T1 - Poisson-bracket approach to the dynamics of bent-core molecules

AU - Kung, William

AU - Marchetti, M. Cristina

PY - 2007/7/20

Y1 - 2007/7/20

N2 - We generalize our previous work on the phase stability and hydrodynamic of polar liquid crystals possessing local uniaxial Cv symmetry to biaxial systems exhibiting local C2v symmetry. Our work is motivated by the recently discovered examples of thermotropic biaxial nematic liquid crystals comprising bent-core mesogens, whose molecular structure is characterized by a non-polar-body axis (n) as well as a polar axis (p) along the bisector of the bent mesogenic core which is coincident with a large, transverse dipole moment. The free energy for this system differs from that of biaxial nematic liquid crystals in that it contains terms violating the p→-p symmetry. We show that, in spite of a general splay instability associated with these parity-odd terms, a uniform polarized biaxial state can be stable in a range of parameters. We then derive the hydrodynamic equations of the system, via the Poisson-bracket formalism, in the polarized state and comment on the structure of the corresponding linear hydrodynamic modes. In our Poisson-bracket derivation, we also compute the flow-alignment parameters along the three symmetry axes in terms of microscopic parameters associated with the molecular geometry of the constituent biaxial mesogens.

AB - We generalize our previous work on the phase stability and hydrodynamic of polar liquid crystals possessing local uniaxial Cv symmetry to biaxial systems exhibiting local C2v symmetry. Our work is motivated by the recently discovered examples of thermotropic biaxial nematic liquid crystals comprising bent-core mesogens, whose molecular structure is characterized by a non-polar-body axis (n) as well as a polar axis (p) along the bisector of the bent mesogenic core which is coincident with a large, transverse dipole moment. The free energy for this system differs from that of biaxial nematic liquid crystals in that it contains terms violating the p→-p symmetry. We show that, in spite of a general splay instability associated with these parity-odd terms, a uniform polarized biaxial state can be stable in a range of parameters. We then derive the hydrodynamic equations of the system, via the Poisson-bracket formalism, in the polarized state and comment on the structure of the corresponding linear hydrodynamic modes. In our Poisson-bracket derivation, we also compute the flow-alignment parameters along the three symmetry axes in terms of microscopic parameters associated with the molecular geometry of the constituent biaxial mesogens.

UR - http://www.scopus.com/inward/record.url?scp=34547436184&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34547436184&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.76.011710

DO - 10.1103/PhysRevE.76.011710

M3 - Article

AN - SCOPUS:34547436184

SN - 1063-651X

VL - 76

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

IS - 1

M1 - 011710

ER -