1 Dielectric response of a ferroelectric nematic liquid crystalline phase in thin cells

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Dielectric response of a ferroelectric nematic liquid crystalline phase in thin

cells

Nataša Vaupotič,1,2 Damian Pociecha,3,* Paulina Rybak,3 Joanna Matraszek,3 Mojca Čepič,2

Joanna M. Wolska,3 and Ewa Gorecka3

1 Department of Physics, Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška 160,

2000 Maribor, Slovenia

2 Jozef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia

3 Faculty of Chemistry, University of Warsaw, Żwirki i Wigury 101, 02-089 Warsaw, Poland

4 Faculty of Education, University of Ljubljana, Kardeljeva ploščad 16, 1000 Ljubljana, Slovenia

Abstract

We studied dielectric properties of a polar nematic phase (NF) sandwiched between two gold or ITO

electrodes, serving as a cell surfaces. In bulk, NF is expected to exhibit a Goldstone mode (phason),

because polarization can uniformly rotate with no energy cost. However, because the coupling between

the direction of nematic director and polarization is finite, and the confinement, even in the absence of

the aligning surface layer, induces some energy cost for a reorientation of polarization, the phason

dielectric relaxation frequency is measured in a kHz regime. The phason mode is easily quenched by a

bias electric field, which enables fluctuations in the magnitude of polarization to be followed in both,

the ferronematic and nematic phases. This amplitude (soft) mode is also influenced by boundary

conditions. A theory describing the phase and amplitude fluctuations in the NF phase shows that the free

energy of the system and, consequently, the dielectric response are dominated by polarization-related

terms with the flexoelectricity being relevant only at a very weak surface anchoring. Contributions due

to the nematic elastic terms are always negligible. The model relates the observed low frequency mode

to the director fluctuations weakly coupled to polarization fluctuations.

Introduction

The discovery of a ferroelectric fluid (ferronematic phase, NF) few years ago immediately caught a lot

of attention [1-7]; the spontaneous electric polarization in the NF phase is comparable to that of solid

ferroelectrics and is of the order of 10-6 C/cm2 [8], which, combined with fluidity, makes the ferroelectric

nematics potentially very attractive for future applications. In the NF phase, the longitudinal molecular

dipole moments align in the same direction, which breaks the up/down symmetry of the average

direction of the long molecular axis (given by a unit vector - director). The NF phase is a very interesting

topic also for fundamental studies, because a full understanding of the ferroelectric order in soft

materials is still at an early stage. Namely, for decades it was believed that the dipole order in soft matter

is a secondary effect induced by steric interactions and requires at least some degree of a positional order

[9]. For a fluid phase having a high electric polarization one can expect a giant low-frequency dielectric

permittivity due to two dielectrically active relaxation modes, which can be regarded as a Goldstone-

like (phason) and Higgs-like (amplitude) modes, the modes that are inherent to the Mexican-hat-form

of the displacement potential [10].

Experimental

The dielectric permittivity was measured in 1 Hz – 10 MHz frequency () range using a Solatron 1260

impedance analyzer, which enabled application of bias field up to 40 V. The amplitude of the ac

measuring field was 0.01 V/µm or less, and it was checked optically that this voltage is below

the Fréedericksz transition threshold. Material was placed in 3 to 10 µm-thick glass cells with ITO or

gold electrodes with no polymer alignment layer. The relaxation frequency, , and dielectric strength,

, of the mode were evaluated by fitting the complex dielectric permittivity to the Cole-Cole formula,





  

, where  is a high frequency dielectric constant,  is a distribution

parameter of the mode and  is a low frequency conductivity.

Results and Discussion

To explore collective motions of molecules in the ferroelectric nematic phase, the dielectric dispersion

measurements were performed in a broad temperature range for homologues of a model ferronematogen,

RM-734 [1], differing in the length of the lateral chain (Figure 1) [11].

Figure 1. Molecular structure of the studied nematogens;  = 3, 4 and 5.

The overall dielectric response is similar for all the studied materials (Figure 2), although the frequency

range in which the dielectric modes are active decreases with an increasing lateral chain length, due to

an increasing material viscosity. The dielectric response was studied in cells with gold or ITO electrodes,

which were not covered with polymer layers. Such cells were chosen purposely, because cells with

dielectric layers on electrodes, although commonly used to obtain a proper alignment of liquid

crystalline (LC) phases and to block charge injections to the sample, cause additional effects in dielectric

measurements [12]. Thin dielectric layers (polymer) act as an additional, large capacitance in a serial

connection with the capacitor filled with a liquid crystal material. However, it should be noted that the

capacitance of the LC layer becomes comparable to that of polymer layers when studying giant dielectric

constant materials. In such a case the interpretation of dielectric measurements become complicated, as

the impedance analyzer detects the apparent conductance and capacitance of the whole electric circuit

and thus the dielectric constant determined from the equivalent capacitance and dielectric loss

determined from equivalent conductance are strongly affected by the presence of polymer layers.

Another problem may appear when the studied LC samples exhibit a low resistivity or a high electric

polarization. If the polarization vector follows the applied electric field without a time delay (real

Goldstone-type relaxation), the apparent resistivity of the LC slab, , may be as low as 1 Ohm, so only

dielectric layers are charged and their capacitance, , is measured, yielding a relaxation mode (-

mode) with a characteristic time . Even when using cells with gold or ITO electrodes

without dielectric layers, one has to be very careful when interpreting experimental results, because a

thin layer of the studied LC material close to the surface, over which polarization will rotate from the

direction preferred by the surface to the direction preferred by bulk, can cause a similar effect as surface

coating. Thus, dielectric permittivity components,  and  on Figure 2 (and then also on Figure 3)

should be understood as apparent values, which are related to the real and imaginary part of the dielectric

constant of the liquid crystal in a complex way, as given in Appendix A.

In the paraelectric nematic phase a single relaxation mode is detected. The mode relaxation frequency

() decreases and its strength () increases critically when the temperature is lowered, which is a

typical behavior for the dielectric relaxation mode originating in the collective excitation of the local

electric polarization, i.e. from the excitation of the order parameter of the lower temperature ferroelectric

phase (soft mode). Because the correlation length of such fluctuations grows near the phase transition

temperature, the mode frequency critically decreases and its strength increases reaching a maximum at

the Curie temperature, (Figures 2a and 2c).

Figure 2. Dielectric properties of the compound with  measured in a -thick cell with gold electrodes and without

aligning polymer layers. The real () and imaginary () part of the dielectric permittivity vs. temperature () and frequency

(freq) measured on cooling a) without a bias field and b) under applied bias field 0.4 V m-1. The relaxation frequency, 

(black circles), and dielectric strength,  (blue squares), of the relaxation mode c) without the bias field and d) under applied

bias field, evaluated from the data presented in (a) and (b), respectively.

The dielectric response in the NF phase is dominated by a very strong mode, the origin of which can be

attributed either to the director fluctuations (phason mode) as will be discussed in detail in the next

section, or to the -mode proposed in [12]. The dielectric strength of this mode, exceeding 104, is

nearly temperature independent below . A small decrease of the mode relaxation frequency near is

caused by a contribution of the amplitude mode, because near  it is expected that also the amplitude

mode should strongly affect the dielectric response. A non-critical decrease of the mode relaxation

frequency far from  is due to a gradual increase of viscosity of the system on cooling. By applying a

bias electric field, it was possible to observe that in the NF phase, close to the transition to the paraelectric

phase, indeed two modes contribute to the dielectric response: a strong phason (or possibly ) mode

and a much weaker amplitude mode (Figure 3). Interestingly, while the relaxation frequency of the

amplitude mode slightly increases with increasing bias field, the relaxation frequency of the strong, low-

frequency mode decreases, which is opposite to the typical behavior observed in the ferroelectric smectic

C* phase [13], but similar to the behavior found previously in the ferroelectric smectic A (SmAPF) phase

[14]. By increasing the bias electric field, the low frequency mode can be completely suppressed and

the critical voltage that quenches the mode increases as temperature is lowered. When the dielectric

permittivity dispersion measurements are performed under a sufficiently strong bias field, the

temperature evolution of the amplitude mode is clearly seen in both the N and NF phases (Fig. 2b and

2d).

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摘要：

1DielectricresponseofaferroelectricnematicliquidcrystallinephaseinthincellsNatašaVaupotič,1,2DamianPociecha,3,*PaulinaRybak,3JoannaMatraszek,3MojcaČepič,2JoannaM.Wolska,3andEwaGorecka31DepartmentofPhysics,FacultyofNaturalSciencesandMathematics,UniversityofMaribor,Koroška160,2000Maribor,Slovenia2Joze...

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1 Dielectric response of a ferroelectric nematic liquid crystalline phase in thin cells

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