Pretransitional effects near the smectic-$A$–smectic-$C^{*}$ phase transition of hydrophilic and hydrophobic aerosil networks dispersed in ferroelectric liquid crystals

A detailed x-ray scattering and high-resolution ac calorimetric study has been carried out near the smectic-$A$ to chiral smectic-$C$ phase transition of liquid-crystal compounds 4-(2-methyl butyl) phenyl 4-$n$-octylbiphenyl-4-carboxylate (CE8) and $p$-($n$-decyloxy) benzylidene-$p$-amino-(2-methylbutyl) cinnamate (DOBAMBC) confined in hydrophilic and hydrophobic aerosil nanoparticle networks. The character of the transition, which is mean field near a tricritical point in bulk, is changed dramatically with an increase of aerosil-induced disorder. X-ray measurements revealed pretransitional behavior and compression of the smectic layers, phenomena that are strongly pronounced in high aerosil concentrations. A theoretical model that takes into account the interplay of relevant mechanisms is proposed to explain the observed phenomena. The effect of chirality on the interaction of liquid crystals with aerosils is discussed.

Figure 1

The chemical formulas, phase sequences, and transition temperatures of the three liquid crystals CE8, DOBAMBC, and $\overline{8}\mathrm{S}5$.

Figure 2

(a) A wide-range x-ray spectrum of normalized intensity vs the wave vector $q$ for CE8 bulk (solid line) and two hydrophilic aerosil mixtures $x=0.05$ (dashed line) and $x=0.15$ (dotted line) is shown. (b) The first harmonic quasi-Bragg peak for all samples is plotted versus $q-q_o$.

Figure 3

(a) The smectic layer thickness $\left(d\right)$ as a function of temperature (for clarity only selected data sets are shown) for CE8 and hydrophilic aerosil 300. (b) The tilt angle $\left(\theta \right)$ vs temperature is shown for CE8 bulk (solid circles), $x=0.05$ (open circles), $x=0.10$ (open triangles), $x=0.12$ (stars), $x=0.15$ (open squares), and $x=0.25$ (solid squares). The solid line represents the fit of bulk CE8 data using the extended mean-field ansatz.

Figure 4

The tilt angle $\left(\theta \right)$ vs temperature for bulk CE8 (solid circles) and hydrophobic aerosil mixtures $x=0.025$ (open circles), $x=0.05$ (open triangles), and $x=0.15$ (stars). The solid line is a fit of CE8 bulk data using an extended mean-field ansatz.

Figure 5

Heat capacity $\left(C_p\right)$ peak vs temperature for bulk CE8 (solid circles) and hydrophilic mixtures $x=0.05$ (open circles), $x=0.10$ (open triangles), and $x=0.15$ (stars). The solid line is a fit of CE8 bulk data using an extended mean-field ansatz.

Figure 6

Heat capacity $\left(C_p\right)$ peak vs temperature for bulk CE8 (solid circles) and hydrophobic mixtures $x=0.025$ (open rhombus), $x=0.05$ (open circles), and $x=0.15$ (stars). The solid line is a fit of CE8 bulk data using an extended mean-field ansatz.

Figure 7

The enthalpy of the $\mathrm{Sm}\text{−}A$ to $\mathrm{Sm}\text{−}C*$ phase transition for bulk CE8 (solid circles), hydrophilic (solid triangles), and hydrophobic mixtures (open triangles). In the inset, the magnitude of the $C_p$ jump at $T_c$ is shown.

Figure 8

(a) A wide-range x-ray spectrum of normalized intensity vs the wave vector $q$ for bulk DOBAMBC (solid line) and two hydrophobic aerosil mixtures $x=0.03$ (dashed line) and $x=0.15$ (dotted line) is shown. (b) The first harmonic peak for all samples is plotted versus $q-q_o$.

Figure 9

(a) The smectic layer thickness $\left(d\right)$ of bulk DOBAMBC and hydrophobic aerosil mixtures is plotted as a function of $T-T_c$ (for clarity, only selected data sets are shown). (b) The tilt angle $\left(\theta \right)$ vs $T-T_c$ is shown for bulk DOBAMBC (solid circles), $x=0.03$ (open circles), $x=0.08$ (open triangles), $x=0.15$ (solid squares), and $x=0.25$ (stars) mixtures. The solid line represents the fit of bulk DOBAMBC data using the extended mean-field ansatz.

Figure 10

The shift of $T_c$ vs concentration $x$ for the various hydrophobic aerosil dispersions in DOBAMBC. The dotted line is a guide to the eye.

Figure 11

The smectic layer thickness vs $T-T_c$ for $\overline{8}\mathrm{S}5$ and hydrophobic aerosil mixture of $x=0.15$.

Figure 12

The reduced compression of layers for CE8 and hydrophilic/hydrophobic mixtures (solid/open circles), DOBAMBC and hydrophobic mixtures (open squares), and $\overline{8}\mathrm{S}5$ and hydrophobic aerosil mixtures (stars).

Figure 13

The tilt temperature variation for different concentrations $x$. Symbols mark measurements (CE8) and lines represent theoretical predictions. In (a) we take into account only different widths of the distribution Eq. (26), ${\theta }_t=0$. In (b) and (c), we allow a finite pretilt and assume that the aerosil-induced tilt persists over the effective smectic penetration length [see Eq. (22)]. (b) $\Delta d^{\left(o\right)}=0$; $x=0.05$, ${\lambda }_0=1.2\mathrm{nm}$, ${\theta }_t=1.7°$, $\Delta T=1\mathrm{K}$; $x=0.10$, ${\lambda }_0=0.9\mathrm{nm}$, ${\theta }_t=2.8°$, $\Delta T=3\mathrm{K}$; $x=0.15$, ${\lambda }_0=2.4\mathrm{nm}$, ${\theta }_t=9.8°$, $\Delta T=6\mathrm{K}$. (c) In fitting the $x=0.15$ case, the full line and dotted line correspond to the “line” and “point” version of the model described in Sec. 5C. Model parameters are ${\theta }_t=5°$, $\Delta T=5\mathrm{K}$, ${\lambda }_0=1\mathrm{nm}$, and $\Delta d^{\left(o\right)}\sim d_0-d\left(T_{\text{deep}}\right)$, where $T_{\text{deep}}$ corresponds to the temperature deep in the $\mathrm{Sm}\text{−}A$ phase.