Dielectric study of a subphase stabilized in an exceptionally wide temperature range by a delicate balance of interlayer interactions and thermal fluctuations

The chiral smectic phases of calamitic liquid crystals, $\mathrm{Sm}{C}^{*}$ and $\mathrm{Sm}{C}_A^{*}$, are characterized by the synclinic ferroelectric $F$ ordering and the anticlinic antiferroelectric $A$ ordering in adjacent layers. Various states with mixed $A$ and $F$ orderings are degenerate at the frustrated phase-transition point. The degeneracy lifting is commonly caused by the long-range interlayer interactions (LRILIs), producing a series of biaxial subphases specified by a relative ratio of both orderings, $q_T=\left[F\right]/(\left[A\right]+\left[F\right])$. Sandhya et al. [Phys. Rev. E 87, 012502 (2013)] established, however, the importance of thermal fluctuations in the degeneracy lifting in some binary mixtures of MC881 and MC452. They observed the most intriguing interplay of thermal fluctuations and LRILIs in the stabilization of an apparently single subphase. Since no other detailed experimental study of the subphase has so far been made, we carry out its dielectric investigations and clarify the following five points: (1) the subphase is surely a single phase from $\approx 80{}^{\circ }\mathrm{C}$ down to room temperature; (2) the imaginary part of complex permittivity ${\epsilon }^{″}$ shows the weak antiphase mode and hence it must be antiferroelectric $q_T=1/2$; (3) ${\epsilon }^{″}$ becomes much stronger above $\approx 80{}^{\circ }\mathrm{C}$, indicating the emergence of ferroelectric and/or ferrielectric states; (4) the dielectric amplitude gradually increases at least just above the 1/2 subphase, suggesting it be due to a continuous increase of $q_T$; and (5) at low temperatures the antiphase relaxation mode shows irregularities that indicate the important role played by the cooperative motion of the layer undulation as well as of the director tilting.

Figure 1

Peculiar bulk phase diagram of MC881-MC452 binary mixture system near the critical concentration $r_{\mathrm{c}}=57.65\pm 0.15$ wt %, reproduced from Figs. 4 and 5 of Ref. [25]. The bulk phase diagram was obtained by observing Bragg reflection spectra due to the director helical structure. Bars indicate the temperature ranges where the full-pitch band gradually grows and circles specify the half-pitch divergence temperatures. An apparently single subphase emerges in a narrow concentration $r\le r_{\mathrm{c}}$ range of less than 3 wt %.

Figure 2

The chemical formula for MC881 and MC452, both of which are ($R$) moieties.

Figure 3

Temperature variation of the imaginary part of complex permittivity ${\epsilon }^{″}\left(f\right)$ in the planar cell. Temperature ranges and steps are (a) $110\mathrm{to}105{}^{\circ }\mathrm{C}$ at a step of $0.5{}^{\circ }\mathrm{C}$, (b) $90\mathrm{to}80{}^{\circ }\text{C}$ at a step of $1^{\circ }\text{C}$ with two additional 84.5 and 83.5, and (c)–(f) $75\mathrm{to}-30{}^{\circ }\mathrm{C}$ at a step of $5{}^{\circ }\mathrm{C}$. The temperature range of $105\mathrm{to}90{}^{\circ }\mathrm{C}$ is not plotted here as the peak intensity and the frequency of the dielectric loss curves do not change much in this temperature range. The steps are so chosen that the lines are not too thick but still show a delicate change clearly. See text for further details.

Figure 4

Temperature variation of the imaginary part of complex permittivity ${\epsilon }^{″}\left(f\right)$ in the homeotropic cell. For plots, a temperature step of $4{}^{\circ }\mathrm{C}$ throughout is chosen such that the lines are not too thick but still a delicate change is shown clearly: (a) $114\mathrm{to}94{}^{\circ }\text{C}$, (b) $94\mathrm{to}70{}^{\circ }\text{C}$, (c) $70\mathrm{to}46{}^{\circ }\text{C}$, (d) $46\mathrm{to}22{}^{\circ }\text{C}$, (e) $22\text{to}-2^{\circ }\mathrm{C}$, and (f) $-2$ to $-{26}^{\circ }\mathrm{C}$. See text for further details.

Figure 5

The relaxation frequency vs temperature $f_{\max }\left(T\right)$ calculated from the measurements (1) triangle, (3) circle, and (4) cross referred to those in Table 1. The high ($H$), medium ($M$), and low ($L$) frequency modes are observed in the $q_T=1/2$ subphase. G and S refer to the Goldstone and soft modes, respectively. See text for details.

Figure 6

The Arrhenius behavior of the $H$ and $L$ relaxation processes observed in measurement (3) of Table 1 and summarized in Fig. 5.

Figure 7

The ORP as a function of temperature in a $30\text{−}\mu \mathrm{m}$-thick cell of MC881 mixture containing 55.09 wt % MC452 measured in the heating and cooling processes at a rate of $4.5{}^{\circ }\mathrm{C}/\mathrm{h}$. The light source used is a He-Ne laser (633 nm).

Figure 8

The dielectric amplitude as a function of temperature, $\mathrm{\Delta }\epsilon \left(T\right)$, in the temperature range of the state with quasicontinuous $q_T$ and its vicinity. The two adjacent phases seem to coexist in the temperature ranges where $\mathrm{\Delta }\epsilon$ is plotted by open circles.

Figure 9

The antiphase mode splitting at the low temperature and frequency range obtained in measurement (3) of Table 1. To make it clear to see the temperature variation by avoiding the excessive overlapping of curves, ${\epsilon }^{″}\left(f\right)$ in two temperature ranges are separately plotted for (a) $-30\text{to}-4{}^{\circ }\mathrm{C}$ and (b) $-10\text{to}28{}^{\circ }\mathrm{C}$. (c) The logarithm of the antiphase mode relaxation frequency ${\log }_{10}(f_{\max }$) is also plotted as a function of temperature. Open circles were obtained by WinFIT on the assumption that the shoulders emerge at temperatures $T\le -4{}^{\circ }\mathrm{C}$ but not for $T\ge -2{}^{\circ }\mathrm{C}$. On the other hand, solid lines are drawn tentatively by considering that the antiphase mode peak gradually splits up over a wide temperature range. See text for further details.

Figure 10

Preliminary data of the temperature dependence of layer spacing obtained in the heating process at a rate of $10{}^{\circ }\mathrm{C}/\mathrm{h}$.

Figure 11

Schematic illustrations of (a) the ordinary antiferroelectric four-layer $q_T=1/2$ subphase and (b) the corresponding one with the hexatic character, where the smectic layers tend to tilt with respect to the fixed $\mathrm{Sm}A$ director and form zigzag structures. The cooperative undulational motion in the antiphase mode which expands the shaded area and reduces the other area produces net spontaneous polarization and plays an important role in dielectric spectroscopy. See text for details.

Figure 12

The $g\text{–}\tilde{T}$ phase diagrams now look completely different from those previously obtained and shown in Fig. 12 of Ref. [27]. Parameters used are $c_{\mathrm{f}}/c_{\mathrm{p}}=1.0$ and (a) $\chi c_{\mathrm{p}}{c}_{\mathrm{f}}/B=0.05$, (b) 0.1, and (c) 0.2, respectively.