Dielectric Modes in Antiferroelectric and Ferroelectric Liquid Crystals in a Pure Enantiomeric Version and a Racemic Mixture
Abstract
:1. Introduction
- SmC*
- —ferroelectric synclinic phase with a helical superstructure and its axis of rotation perpendicular to the smectic layers. Molecules in one smectic layer are tilted by the angle .
- SmCA*
- —antiferroelectric synclinic phase with a helical superstructure and its axis of rotation perpendicular to the smectic layers. Molecules in one smectic layer are tilted by the angle , while molecules in the next layer are tilted by the angle .
- SmC
- —synclinic phase without a helical superstructure. Molecules in one smectic layer are tilted by the angle The helical superstructure and ferroelectricity vanish when the SmC phase is built from achiral molecules or SmC is the racemate—the phase is a mixture of 50% S-enantiomer and 50% R-enantiomer.
- SmCA
- —anticlinic phase without a helical superstructure. Molecules in one smectic layer are tilted by the angle , while molecules in the next layer are tilted by the angle . The helical superstructure and antiferroelectricity vanish when the SmCA phase is built from achiral molecules or SmCA is the racemate—the phase is an equimolar mixture of S- and R-enantiomers.
- Goldstone mode
- —collective and strong dielectric mode (molecules move collectively around the cone in the smectic layer) in the same direction. During the rotation the phase angle changes in time, so this mode is called the phason mode.
- S mode
- —molecular dielectric mode when the molecule rotates around its short molecular axis. This mode is observed in isotropic liquid, nematic, or smectic phases. This mode is Arrhenius type: its relaxation frequency decreases with decreasing temperature. The relaxation frequency of the S mode is 1k–10k times lower than the relaxation frequency of the L mode.
- L mode
- —molecular dielectric mode when the molecule rotates around its long molecular axis. This mode is observed in isotropic liquid, nematic, or smectic phases. This mode is also Arrhenius type. It is not usually observed in standard impedance spectroscopy because it is fast.
- PH mode
- —collective and weak (in comparison with the Goldstone mode) dielectric mode detectable in antiferroelectric anticlinic SmCA*. It is also Arrhenius type. Molecules in neighboring layers, in the two-layer unit, rotate in opposite directions around the cone; hence, it is called the anti-phase phason mode. The relaxation frequency of the PH mode is 1k times lower than the relaxation frequency of the S mode and 1k times higher than the relaxation frequency of the PL mode.
- PL mode
- —collective and weak (in comparison with Goldstone mode) dielectric mode detectable in antiferroelectric anticlinic SmCA*. It is also Arrhenius type. Molecules in neighboring layers, in the two-layer unit, rotate in the same direction around the cone; hence, it is called the in-phase phason mode. The relaxation frequency of the PL mode is 1k lower than the relaxation frequency of the PH mode.
- X mode
- —the dielectric mode described in this paper, which is observed in the racemic synclinic SmC phase. It seems to be the continuation of the PL mode from the racemic SmCA phase. Its strength at the SmC-SmCA phase transition is twice weaker than the strength of the PL mode close to the SmCA-SmC phase transition.
- —the strength of the ith dielectric mode.
- —the relaxation frequency of the ith dielectric mode.
- —high-frequency limit of permittivity.
- —low-frequency limit of permittivity.
- and
- —Havriliak–Negami distribution parameters.
- —imaginary unit.
- —ionic conductivity of the sample.
- —parameter describing ion contribution to the imaginary part of permittivity (close to one).
- —capacity in the parallel equivalent circuit.
- —conductivity in the parallel equivalent circuit.
- —empty cell capacity.
- —limit of relaxation frequency at high temperatures (in Arrhenius law).
- —Boltzmann constant.
- —temperature on the thermodynamic scale.
2. Materials and Methods
2.1. Studied Compound
2.2. DSC Measurements
2.3. Microscopy Observations
2.4. Dielectric Spectroscopy
2.5. The Method for Calculating the Parameters of Dielectric Modes
3. Results
3.1. Results of the DSC Measurements and Microscopic Observations Performed for the Pure Enantiomer and Racemate
3.2. Results of the Measurements Performed for the Pure Enantiomer
3.3. Results of the Measurements Performed for the Racemic Mixture
3.4. Results of the Calculations
4. Discussion, Conclusions, and Summary
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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SmCA* | SmC* | |
---|---|---|
Dielectric modes (no DC) | Residual Goldstone mode PL mode PH mode Molecular S mode | Goldstone mode Weak PL mode covered by the Goldstone mode Weak PH mode covered by the Goldstone mode Molecular S mode |
Dielectric modes (with DC) | Residual Goldstone mode PL mode strengthened by the DC field PH mode strengthened by the DC field Molecular S mode weakened by the DC field | Suppressed Goldstone mode PL mode strengthened by the DC field, non-covered by the suppressed Goldstone mode PH mode strengthened by the DC field, non-covered by the suppressed Goldstone mode Molecular S mode weakened by the DC field |
SmCA | SmC | |
---|---|---|
Dielectric modes (no DC) | PL mode Molecular S mode | Weak X(PL) mode Molecular S mode |
Dielectric modes (with DC) | PL mode strengthened by the DC field Molecular S mode weakened by the DC field PL mode strengthened by the DC field PH mode strengthened by the DC field Molecular S mode weakened by the DC field | X(PL) mode strengthened by the DC field Molecular S mode weakened by the DC field PH mode strengthened by the DC field, non-covered by the suppressed Goldstone mode Molecular S mode weakened by the DC field |
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Perkowski, P.; Urbańska, M. Dielectric Modes in Antiferroelectric and Ferroelectric Liquid Crystals in a Pure Enantiomeric Version and a Racemic Mixture. Materials 2024, 17, 3335. https://doi.org/10.3390/ma17133335
Perkowski P, Urbańska M. Dielectric Modes in Antiferroelectric and Ferroelectric Liquid Crystals in a Pure Enantiomeric Version and a Racemic Mixture. Materials. 2024; 17(13):3335. https://doi.org/10.3390/ma17133335
Chicago/Turabian StylePerkowski, Paweł, and Magdalena Urbańska. 2024. "Dielectric Modes in Antiferroelectric and Ferroelectric Liquid Crystals in a Pure Enantiomeric Version and a Racemic Mixture" Materials 17, no. 13: 3335. https://doi.org/10.3390/ma17133335