Field-cycling NMR relaxometry of a liquid crystal above $T_{NI}$ in mesoscopic confinement

We measured the proton spin-lattice relaxation times in the isotropic phase of liquid crystal $4^{\prime }\text{−}n\text{-pentyl-}4\text{-cyanobiphenyl}$ (5CB) confined into porous glass (CPG) with the average pore diameter $\sim 72\mathrm{nm}$. The analysis of $T_1^{-1}$ frequency dispersions, spanning over four decades, shows that the main relaxation mechanism induced by the ordered surface layer are molecular reorientations mediated by translational displacements (RMTD). The RMTD contribution to $T_1^{-1}$ is proportional to the inverse square root of Larmor frequency, a consequence of the equipartition of diffusion modes along the surface. Low and high frequency cutoffs of the RMTD mechanism clearly reveal that the surface alignment of liquid crystal is random planar with the size of uniformly oriented patches $\sim 5\mathrm{nm}$, depending on the treatment of the CPG matrix. According to the size of the uniformly oriented patches varies also the thickness of the ordered surface layer and its temperature behavior. The surface-induced order parameter is found to be temperature independent and determined by the local short range surface interactions.

Figure 1

Scanning electron micrograph (SEM) of the controlled-pore-glass (CPG) with average pore diameter $\sim 72\mathrm{nm}$. Micrograph provided by the Ceramics Department, J. Stefan Institute.

Figure 2

Frequency dispersion of proton spin-lattice relaxation rate $T_1^{-1}$ of 5CB in the porous glass (sample 1, open symbols) and in the bulk (solid symbols) at four temperatures above the nematic-isotropic transition temperature $T_{NI}(\Delta T=T-T_{NI})$.

Figure 3

Temperature dependence of proton spin-lattice relaxation rate $T_1^{-1}$ at Larmor frequency $\nu =11\mathrm{kHz}$ for 5CB in porous glass (sample 1 and sample 2) and in the bulk.

Figure 4

Frequency dispersion of proton spin-lattice relaxation rate $T_1^{-1}$ of 5CB in the porous glass (sample 1) at $\sim 1\mathrm{K}$ above $T_{NI}$. The bold solid line is a fit of Eq. (17) to the experimental data. It is a sum of four contributions: conformational changes and molecular local reorientations around the long axis $(C+RL)$, molecular rotations around the short axis and translational self-diffusion $(RS+D)$, order fluctuations (OFs), and reorientations mediated by translational displacements (RMTDs).

Figure 5

Frequency dispersion of proton spin-lattice relaxation rate $T_1^{-1}$ of 5CB in the porous glass (sample 1) at $\sim 10\mathrm{K}$ above $T_{NI}$. The bold solid line is a fit of Eq. (17) to the experimental data. It is a sum of four contributions: conformational changes and molecular local reorientations around the long axis $(C+RL)$, molecular rotations around the short axis and translational self-diffusion $(RS+D)$, order fluctuations (OFs), and reorientations mediated by translational displacements (RMTDs). The contribution of order fluctuations is negligible at this temperature.

Figure 6

Temperature dependence of proton spin-lattice relaxation rate $T_1^{-1}$ of 5CB in the porous glass (sample 1) at Larmor frequency $\nu =11\mathrm{kHz}$. The bold solid line is a fit of Eq. (17) to the experimental data. RMTD is here a thermally activated process, its contribution obeys the Arrhenius law.

Figure 7

Temperature dependence of proton spin-lattice relaxation rate $T_1^{-1}$ of 5CB in the porous glass (sample 2) at Larmor frequency $\nu =11\mathrm{kHz}$. The bold solid line is a fit of Eq. (17) to the experimental data. The temperature dependence of RMTD contribution exhibits a pretransitional increasing superimposed on the Arrhenius-type behavior.