Tilt angles and spontaneous polarization in induced S*_c phases

Abstract

Induced S*_c phases can be obtained by doping several non-chiral S_c-host phases (H) with chiral polar compounds (G). The tilt angle θ of such systems and their spontaneous polarization P _s were measured as a function of the mole fraction, x _G, of the optically active compounds.

In the S*_c phase of a pure compound P _s and θ are expected to be closely related to each other. Consequently, a material constant P ₀ can be defined as P _s = P ₀ sin θ. In induced S*_c-phases P _s depends on the concentration of the optically active guest compound. In several cases P _s(x _G) deviates considerably from linearity. To investigate the origin of this non-linearity we measured θ and P _s as function of x _G. The question arises if P ₀ depends on x _G and/or on the molecular structure of G and H: P _s(x _G) = P ₀(x _G) sin θ (x _G). Comparing the results of P ₀(x _G) for mixed systems with the same optically active dopant G we can make the following statements.

arabic	The polarization is directly proportional to sin θ.
arabic	P 0(x G) is linear within experimental error in the measured concentration range referred to a temperature 5 K below the transition S*c to chol or SA.
arabic	P 0(x G) only depends on the molecular structure of the optically active guest compound, but there is no dependence on the structure of the host phase.

As a result we can define a material constant, the polarization power ∂_p:

which is an inherent material constant for a given polar chiral dopant.