Two kinds of smectic-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>C</mml:mi><mml:mi>α</mml:mi><mml:mo>*</mml:mo></mml:msubsup></mml:math>subphases in a liquid crystal and their relative stability dependent on the enantiomeric excess as elucidated by electric-field-induced birefringence experiment

Abstract

The electric-field-induced birefringence has been investigated by using a photoelastic modulator, with a view to obtaining a molecular model for the subphases produced by the frustration between ferroelectricity and antiferroelectricity in the chiral smectic liquid crystals. It has been found that even in the bulk, there exist two subphases in the smectic-C(alpha)* (Sm-C(alpha)*) temperature range. By extending the Emelyanenko-Osipov model [Phys. Rev. E 68, 051703 (2003)] to include the temperature dependence of the tilt angle, we have alluded to a possible lifting of the degeneracy at the frustration point P(alpha) , where Sm-C(A)*, Sm-C*, and Sm-A have the same free energy. This leads to the appearance of uniaxial Sm-C(alpha)* characterized by short-pitch helical structures and consequently with a pitch much lower than the optical wavelength. The numerical calculations indicate that the short pitch may generally increase or decrease monotonically with temperature. Depending on the parameter value that represents the relative strength of ferroelectricity and antiferroelectricity, the short-pitch temperature variation may abruptly change from increase to decrease at a temperature; this can be assigned to the observed phase transition between the two Sm-C(alpha)* subphases.