Phase structure and molecular dynamics of liquid-crystalline side-on organosiloxane tetrapodes

X-ray diffraction and proton NMR relaxation measurements were carried out on two liquid-crystalline organosiloxane tetrapodes with side-on mesogenic groups, exhibiting nematic and smectic-$C$ phases, and on a monomeric analog. Packing models for the mesophases exhibited by these systems are proposed on the basis of x-ray diffraction data. As a consequence of microsegregation, the aromatic cores are packed in between two sublayers formed by a mixture of interdigitated aliphatic and siloxane chains. The mixed sublayers are characteristic for the tetrapodes with side-on mesogenic groups presented in this work and have not been observed in tetrapodes with terminally attached mesogens. The tilt angle in the smectic-$C$ phase is found very large, i.e., $\sim 61°–62°$. Notably, smectic-$C$ clusters are present also in the whole temperature range of the nematic phase. NMR relaxometry yields $T_1^{-1}$ dispersions clearly different from those of conventional calamitics. The influence of molecular tendency to form interdigitated structures is evidenced by frequency-dependent relaxation rate in the isotropic phase—indicating the presence of ordered clusters far above the phase transition—and by the diminished role of molecular self-diffusion in ordered phases. Nematiclike director fluctuations are the dominating relaxation mechanism whereas the translational displacements are strongly hindered by the interdigitation of dendrimer arms.

Figure 1

Chemical formulas of the studied compounds and the corresponding phase sequences.

Figure 2

(Color online) Molecular dimensions of tetrapodes $T_s$ (a) and $T_{as}$ (b) resulting from molecular modeling: ${\ell }_m$—length of the mesogenic unit; ${\ell }_c$—length of the aromatic core; ${\ell }_{ch}$, ${\ell }_{ch1}$, and ${\ell }_{ch2}$—lengths of aliphatic chains; ${\ell }_s$—length of the siloxane chains; ${\ell }_p$—approximate distance from the aliphatic chains end to the oxygen atom at the chemical bond between aromatic core and siloxane chain.

Figure 3

(Color online) Schematic representation of the angular scales and integration limits used in the analysis of XRD diffraction patterns (magnetic-field direction: vertical). Plots as a function of $\theta$ (or the scattering vector magnitude $q=4\pi \text{sin}\theta /\lambda$) are azimuthally integrated from 0 to $2\pi$. Plots of azimuthal variation in the small- or wide-angle regions (variables $\psi$ and $\chi$, respectively) are radially integrated over $\theta$ with integration limits defined by circular crowns as exemplified in the picture.

Figure 4

(Color online) (a) Two-dimensional XRD pattern for $T_s$ in the $\text{Sm}C$ phase at $78°\text{C}$. (b) Fit of the azimuthally integrated XRD pattern (intensity vs scattering vector magnitude, $q=4\pi \text{sin}\theta /\lambda$) for $T_s$ in the $\text{Sm}C$ phase at $78°\text{C}$.

Figure 5

(Color online) Proposed packing models for the $\text{Sm}C$ (a) and $N$ phases (b) of the $T_s$ tetrapod with side-on attached symmetric mesogenic units.

Figure 6

(Color online) Schematic details of the $\text{Sm}C$ phase molecular organization with the indication of the molecular area $\left(\Sigma \right)$, molecular cross-sectional area $\left(\sigma \right)$, and tilt angle of the aromatic core $\left(\psi \right)$.

Figure 7

(Color online) Variation in the layer spacing in the $\text{Sm}C$ phase and the pseudolayer spacing (associated with the cybotactic groups) in the $N$ phase as a function of temperature.

Figure 8

(Color online) (a) Two-dimensional XRD pattern for $T_s$ in the $N$ phase at $104°\text{C}$. (b) Fit of the azimuthally integrated XRD pattern (intensity vs scattering vector magnitude, $q=4\pi \text{sin}\theta /\lambda$) for $T_s$ in the $N$ phase at $104°\text{C}$.

Figure 9

(Color online) (a) Fit of the radially integrated XRD pattern in the small-angle region for $T_s$ in the $N$ phase at $104°\text{C}$. (b) Tilt angle of molecules with respect to the normal to the pseudolayers associated with the local $\text{Sm}C$-like molecular organization in the $N$ phase as a function of temperature.

Figure 10

(Color online) (a) Two-dimensional XRD pattern for $T_{as}$ in the $N$ phase at $25°\text{C}$. (b) Fit of the azimuthally integrated XRD pattern (intensity vs scattering vector magnitude, $q=4\pi \text{sin}\theta /\lambda$) for $T_{as}$ in the $N$ phase at $25°\text{C}$.

Figure 11

(Color online) (a) Fit of the radially integrated XRD pattern in the small-angle region for $T_{as}$ in the $N$ phase at $25°\text{C}$. (b) Tilt angle of molecules with respect to the normal to the pseudolayers associated with the local $\text{Sm}C$-like molecular organization in the $N$ phase as a function of temperature.

Figure 12

(Color online) Comparison between local molecular packing for the $T_s$ and $T_{as}$ tetrapodes. The symmetry of $T_s$ mesogenic units allows for an effective segregation between aromatic and aliphatic/siloxane sublayers. The asymmetric mesogenic units of $T_{as}$, with chains of different lengths in each side of the aromatic core, hinder the formation of aromatic and aliphatic sublayers of uniform thickness.

Figure 13

(Color online) $T_1^{-1}$ dispersion curves in the isotropic, nematic, and smectic-$C$ phases of the studied compounds: (a) low-molecular-weight symmetric mesogen, $M_s$; (b) organosiloxane tetrapode with side-on attached symmetric mesogens, $T_s$; (c) organosiloxane tetrapode with side-on attached asymmetric mesogens, $T_{as}$.

Figure 14

(Color online) Frequency dispersions of the proton spin-lattice rate $T_1^{-1}$ for the $M_s$ system in the (a) isotropic phase $\left(130°\text{C}\right)$ and (b) nematic phase $\left(90°\text{C}\right)$. The solid lines were obtained by fitting Eqs. (5, 6, 7) to the experimental data and represent the sum of contributions of ODF, SD, and molecular reorientations of the BPP type.

Figure 15

(Color online) Frequency dispersions of the proton spin-lattice rate $T_1^{-1}$ for the $T_s$ tetrapode in the (a) isotropic phase $\left(138°\text{C}\right)$, (b) nematic phase $\left(112°\text{C}\right)$, and (c) $\text{Sm}C$ phase $\left(78°\text{C}\right)$. The solid lines were obtained by fitting Eqs. (5, 6, 7) to the experimental data and represent the sum of contributions of ODF, SD, and BPP-type reorientations of mesogenic units.

Figure 16

(Color online) Fit of the radially integrated x-ray pattern in the wide-angle region in the isotropic phase of the $T_s$ tetrapode $5°\text{C}$ above the $N\text{−}I$ transition. It reveals the presence of cybotactic clusters.

Figure 17

(Color online) Frequency dispersions of the proton spin-lattice rate $T_1^{-1}$ for the $T_{as}$ tetrapode in the (a) isotropic phase $\left(60°\text{C}\right)$ and (b) nematic phase $\left(27°\text{C}\right)$. The solid lines are the fit of Eqs. (5, 6, 7) to the experimental data and represent the sum of contributions of ODF and reorientations of mesogenic units of the BPP type. The contribution of self-diffusion is negligible.

Figure 18

Plot of the fitted rotations/reorientations correlation time ${\tau }_R$ for the $T_s$ and $T_{as}$ tetrapodes as a function of the inverse temperature. The solid line represents the fit of the Arrhenius expression to the experimental values. The activation energy and ${\tau }_{\infty }$ are the same for both tetrapodes: 15 kJ/mol and $\sim 2.5\times {10}^{-12}\text{s}$, respectively.