Frequency-domain nonlinear dielectric relaxation spectroscopy
Application to chiral smectic liquid crystals
Yasuyuki Kimura
Department of Applied Physics, School of Engineering, University of Tokyo,
7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
Response to external field becomes easily nonlinear in soft condensed matters such as
liquid crystals and polymers. We can obtain more detailed information on their structure and
dynamics by their nonlinear response. Dielectric relaxation spectroscopy is one of the basic and
powerful methods to investigate the dynamics of soft condensed matters, but it has been
restricted only to linear regime. Recently, dielectric relaxation spectroscopy in frequency
domain has been extended to nonlinear regime and called nonlinear dielectric relaxation
spectroscopy (NDRS). In this study, we have applied this method to chiral smectic liquid
crystals in ferroelectric (SmC*), antiferroelectric (SmCA*) and paraelectric (SmA) phases.
(1) Nonlinear dielectric spectrum of ferroelectric Goldstone mode in SmC* phase
The linear spectrum 1* shows a single relaxation of Debye type corresponding to ferroelectric
Goldstone mode. The third-order nonlinear spectrum 3* has negative increment and exhibits a
more complicated profile than that of 1* [1]. The negative increment of 3* indicates that the
observed nonlinear response originates from the saturation in alignment of spontaneous
polarization by applied field. We also study the nonlinear dielectric spectra of Goldstone mode
theoretically and the calculated spectrum of 3* is found to make good agreement with the
measured one. From the obtained values of the linear and the third-order dielectric increment
and relaxation time, we have succeeded in the simultaneous evaluation of material constants
such as spontaneous polarization and rotational viscosity [2].
(2) Nonlinear dielectric spectrum of antiferroelectric Goldstone mode in SmCA* phase
In the SmCA* phase, we cannot observe antiferroelectric Goldstone mode in 1* because of the
anti-parallel alignment of spontaneous polarization. But, we can detect it by NDRS because
nonlinear response also appears due to nonlinear coupling between liquid crystals and electric
field. The obtained spectrum 3* shows a single relaxation of Debye type with positive
increment, which is also supported by the theoretical calculation [3].
(3) Nonlinear dielectric relaxation spectrum of ferroelectric soft mode in SmA phase
At the vicinity of SmA-SmC* (para-ferroelectric) phase transition, we can observe the critical
behavior of soft mode not only in 1* but also 3* in SmA phase. The linear permittivity shows
Curie-Weiss type critical behavior and third-order permittivity also shows the critical behavior
with critical exponent of 4. We also study the nonlinear dielectric spectra theoretically by
Landau theory and find the sign of 3* depends on the order of transition [4].
1.
2.
3.
4.
Y. Kimura and R. Hayakawa, Experimental study of nonlinear dielectric relaxation spectra of ferroelectric
liquid crystals in the smectic C* phase, Jpn. J. Appl. Phys. 32, 4571 (1993).
Y. Kimura, S. Hara and R. Hayakawa, Nonlinear dielectric relaxation spectroscopy of ferroelectric liquid
crystals, Phys. Rev. E62, R5907 (2000).
Y. Kimura, R. Hayakawa, N. Okabe and Y. Suzuki, Nonlinear dielectric relaxation spectroscopy of the
antiferroelectric liquid crystal 4-(1-trifluoromethyl-pheptyloxy carbonyl) phenyl
4'-octyloxybiphenyl-4-carboxylate, Phys. Rev. E53, 6080 (1996).
Y. Kimura, H. Isono and R. Hayakawa, Critical behavior of nonlinear permittivity in the smectic-A phase of
chiral liquid crystals, Phys. Rev. E64, 060701(R) (2001).