Direct Observation of Diffuse Cone Behavior in de Vries Smectic-$A$ and -$C$ Phases of Organosiloxane Mesogens

Simultaneous and direct x-ray measurements of the smectic layer spacing, molecular tilt, and orientational order in the de Vries smectic $A$ ($\mathrm{Sm}A$) and $C$ ($\mathrm{Sm}C$) phases of two organosiloxane mesogens reveal that (i) the $\mathrm{Sm}C$ (tilt) order parameter exponent $\beta =0.26\pm 0.01$ for 2nd order $\mathrm{Sm}A\mathrm{\text{−}}\mathrm{Sm}C$ transition—in excellent agreement with the tricritical behavior, (ii) the siloxane and hydrocarbon parts of the molecules are segregated and oriented parallel to the director with very different degree of orientational order, and (iii) thermal evolution of the effective molecular length is different in the two phases.

Figure 1

Diffuse-cone model: polar tilt of molecules remains relatively unchanged while the uniform azimuthal distribution of the $\mathrm{Sm}A$ phase gradually loses its degeneracy in the $\mathrm{Sm}C$ phase increasing the effective tilt angle at lower temperatures.

Figure 2

Molecular structures and phase sequence of C4 and C9 compounds. Here, I and Cr are abbreviations for the isotropic and crystal phases, respectively.

Figure 3

Representative diffraction patterns in the $\mathrm{Sm}A$ phase at $57.2°\mathrm{C}$ and the $\mathrm{Sm}C$ phase at $55.7°\mathrm{C}$, of mesogen C4 illustrating a change in molecular tilt from 0° in the $\mathrm{Sm}A$ phase to 9° in the $\mathrm{Sm}C$ phase. The dotted line passing through the large angles peaks of the $\mathrm{Sm}C$ phase represents their orientation in the $\mathrm{Sm}A$ phase.

Figure 4

Temperature dependence of tilt angle for the two compounds. Line (red) graphs represent fits with order parameter exponent $\beta =0.26\pm 0.01$ for the second order $\mathrm{Sm}A\mathrm{\text{−}}\mathrm{Sm}C$ transition of C4 and $\beta =0.21\pm 0.02$ at the first order transition of C9. The inset shows temperature dependence of $d$ for C4 and C9.

Figure 5

Left: $\chi$ scans through the two large angle peaks arising from lateral separation between siloxane and hydrocarbon sections of the C4 molecule in the $\mathrm{Sm}A$ phase. Right: $\chi$ scans through the hydrocarbon peak in the $\mathrm{Sm}C$ phase ($59.7°\mathrm{C}$) of C9. Solid line represents the fit to calculate $S$ for the two domains misoriented by $\sim 45°$ with respect to each other. Fits to the two domains are represented by the dashed (green) and dotted (blue) plots.

Figure 6

Temperature dependence of the orientational order parameter $S$ for C4 and C9 calculated for the hydrocarbon and siloxane peaks at 4.5 and 6.8 Å, respectively. DSC results on top are taken from Ref. 20.

Figure 7

Temperature dependence of the effective molecular length $L$ in the $\mathrm{Sm}A$ and $\mathrm{Sm}C$ phases of C4 and C9. Solid and dashed lies are linear fits to the data.