Influence of nanoconfinement on the nematic behavior of liquid crystals

We explore the nematic ordering of the rodlike liquid crystals 5CB and 6CB, embedded into parallel-aligned nanochannels in mesoporous silicon and silica membranes as a function of mean channel radius ($4.7\le R\le 8.3$ nm), and, thus, geometrical confinement strength, by optical birefringence measurements in the infrared region. The orientational order inside the nanochannels results in an excess birefringence, which is proportional to the nematic order parameter. It evolves continuously on cooling with a precursor behavior, typical of a paranematic state at high temperatures. These observations are compared with the bulk behavior and analyzed within a phenomenological model. Such an approach indicates that the strength of the nematic ordering fields $\sigma$ is beyond a critical threshold ${\sigma }_c=$ 1/2 that separates discontinuous from continuous paranematic-to-nematic behavior. In agreement with the predictions of the phenomenological approach, a linear dependency of $\sigma$ on the inverse channel radius is found and we can infer therefrom the critical channel radii, $R_c$, separating continuous from discontinuous paranematic-to-isotropic behavior, for 5CB (12.1 nm) and 6CB (14.0 nm). Our analysis suggests that the tangential anchoring at the channel walls is of similar strength in mesoporous silicon and mesoporous silica membranes. A comparison with the bulk phase behavior reveals that the nematic order in nanoconfinement is significantly affected by channel wall roughness, leading to a reduction of the effective nematic ordering.

Figure 1

Orientational ordering of a nematogen LC inside a cylindric channel. Panels (a) and (b) sketch the nematic ($T<T_{IN}^{*}$) and paranematic ($T>T_{IN}^{*}$) ordering, respectively, that develop in channels with smooth walls. Panels (c) and (d) depict the nematic ordering in broad and narrow channel with rough pore wall, respectively; dash-dot rectangles (red online color) mark the core region of the channel filling, with relatively well-developed nematic ordering in comparison to the considerably orientationally disordered near-interface region. Panel (e) shows the order parameter $q_e$ in the KKLZ model as a function of reduced temperature $t$ for several effective surface fields $\sigma$; traces 1-4,4${}^{\prime }$ correspond to a case of smooth channel wall; channel wall roughness reduces the effective ordering as sketched by trace 4${}^{\prime \prime }$.

Figure 2

Measured optical birefringence $\Delta n$ ($\lambda =1342$ nm) of nematogen 5CB (left panels) and 6CB (right panels) embedded in parallel-aligned nanochannels of several porous membranes: [(a) and (d)] $p$Si ($P=68$$\%$, $R=8.3$ nm); [(b) and (e)] $p$SiO${}_2$ ($P=50$$\%$, $R=6.3$ nm); [(c) and (f)] $p$Si ($P=60$$\%$, $R=4.7$ nm). The broken line (red online color) represents the best fit obtained within the KKLZ model based on a free energy expansion (1). Completion of the free energy by higher-order terms (up to 10th order) describes the saturation of the order parameter at lower temperatures more accurately; see solid line (red online color). The base line corresponding to the thermooptic contribution (dash-dot line, gray online color) is obtained within the same fitting procedure. The values of the effective nematic ordering field $\sigma$ and quenched disorder factor $\kappa$ are quoted for each LC-porous matrix combination.

Figure 3

Nematic ordering field $\sigma$ vs inverse mean channel radius $R^{-1}$. Square symbols correspond to $\sigma$ values as extracted within the fitting analysis of the $\Delta n\left(T\right)$ dependencies shown in Fig. 2. Solid lines are the best linear fits of the $\sigma$ data points. Their intersections with a horizontal line, $\sigma ={\sigma }_c=1/2$ (see solid circles), yield coordinates of the critical points ${\sigma }_c(R_c=12.1$ nm$)$ (5CB) and ${\sigma }_c(R_c=14.0$ nm$)$ (6CB) as discussed in the text.

Figure 4

Normalized excess birefringence $\Delta n_{\mathrm{nex}}$ vs temperature $T$ (blue, green and red colors) of nematogen 5CB (a) and 6CB (b) embedded into mesoporous membranes, as calculated from the data presented in Fig. 2. The traces $\Delta n_{\mathrm{nex}}\left(T\right)$ for $p$SiO${}_2$ (6.3 nm, blue color) and $p$Si (8.3 nm, green color) are shifted vertically by 0.015 and 0.03, respectively, in order to avoid their overlap; horizontal broken lines with relevant labels marks 0 levels for these traces. Bulk birefringence (black circles) is given for comparison.

Figure 5

$\Delta n_{\mathrm{nex}}/\Delta n^{\left(\max \right)}$ vs $R^{-1}$ as determined for both LCs at $T=T_{IN}^{*}-10$ K using the normalized excess birefringence, $\Delta n_{\mathrm{nex}}\left(T\right)$, and bulk birefringence, $\Delta n\left(T\right)$, data in Fig. 4.