De Gennes model of the nematic to smectic-A transition: dislocations and gauge properties

Thesis/Dissertation · Sun Jan 01 04:00:00 EST 1984

OSTI ID:5171527

Day, A R

The de Gennes model is used to study the nematic to smectic-A (N-A) transition of liquid crystals. The analogy between the Ginzburg-Landau model for the normal metal to superconducting transition and the role of the splay elastic constant K/sub 1/ is stressed. It is found that, in contrast to what was previously thought, the de Gennes model is gauge invariant, irrespective of the value of k/sub 1/. The model is studied in an arbitrary gauge, and it is shown that the renormalization group recursion relations in the epsilon expansion are independent of gauge. The critical exponent eta, with governs the power law decay of the smectic correlations at the critical point, is found to depend on the gauge, and, in the physical gauge, to diverge at the accessible fixed point, K/sub 1//sup XX.XX/ = 0. This is indicative of the nonpower law decay of the correlation function at the critical point. The author introduces an extension of the de Gennes model that describes a liquid crystal, with negative dielectric anisotropy, in an applied electric field. It is shown that there are at least two possible extensions to 4-epsilon dimensions and that they predict different critical behavior.

• Research Organization: Pennsylvania Univ., Philadelphia (USA)
• OSTI ID: 5171527
• Country of Publication: United States
• Language: English

Related Subjects

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
COMPARATIVE EVALUATIONS
CRYSTALS
ELECTRIC CONDUCTIVITY
ELECTRICAL PROPERTIES
FLUIDS
GAUGE INVARIANCE
INVARIANCE PRINCIPLES
LIQUID CRYSTALS
LIQUIDS
PHASE TRANSFORMATIONS
PHYSICAL PROPERTIES
SUPERCONDUCTIVITY