Influence of virtual surfaces on Frank elastic constants in a polymer-stabilized bent-core nematic liquid crystal

Effect of a polymer network on the threshold voltage of the Fréedericksz transition, Frank elastic constants, switching speed, and the rotational viscosity are investigated in a polymer-stabilized bent-core nematic liquid crystal with different polymer concentrations. These polymer networks form virtual surfaces with a finite anchoring energy. The studies bring out several differences in comparison to similar studies with a calamitic liquid crystal as the nematic host. For example, on varying the polymer content the threshold voltage decreases initially, but exhibits a drastic increase above a critical concentration. A similar feature—reaching a minimum before rising—is seen for the bend elastic constant, which gets enhanced by an order of magnitude for a polymer content of 2.5 wt %. In contrast, the splay elastic constant has a monotonic variation although the overall enhancement is comparable to that of the bend elastic constant. The behavior changing at a critical concentration is also seen for the switching time and the associated rotational viscosity. The presence of the polymer also induces a shape change in the thermal dependence of the bend elastic constant. We explain the features observed here on the basis of images obtained from the optical and atomic force microscopy.

Figure 1

Chemical structures and transition temperatures of the components employed.

Figure 2

Schematic of the cell geometry showing the polymer bundles and the LC molecules, in the (a) field-off and (b) field-on conditions. Polymers remain in the direction of the substrate plane even when the LC molecules (at least the nontrapped ones) are reoriented normal to the substrate plane by the applied electric field. The bundles have trapped a sizable $\left(\sim 1000\right)$ LC molecules along the cross section.

Figure 3

Temperature dependence of permittivity in the planar configuration at 1 kHz for pure 6OCN $\left(X=0\right)$ and representative polymer-stabilized mixtures (concentrations of the polymer indicated against each curve). For the purpose of better presentation the data are normalized with respect to ${\varepsilon }_{NI}$, the value at the isotropic-nematic transition temperature $\left(T_{NI}\right)$. Inset: Polymer stabilization is seen to lower $T_{NI}$ as well as $\delta \varepsilon$, the difference in permittivity at $T_{NI}$ and ${\varepsilon }_{\perp }$ in the nematic at a reduced temperature of $\mathrm{\Delta }T=T_{NI}\text{–}6\mathrm{K}$.

Figure 4

Raw profiles of reduced capacitance with voltage at $\mathrm{\Delta }T=20\mathrm{K}$ for the pure LC and the different mixtures. The numbers against the data sets indicate the concentration of RM82. Inset shows a raw profile taken with the ALC apparatus for $X=1.5$ concentration mixture. The lines through the data for $X=0$, 0.5, and 1 represent the fitting to Eq. (2)).

Figure 5

Concentration dependence of the reduced threshold voltage $v=V_{\mathrm{th}}/V_{\mathrm{o}}$, where $V_{\mathrm{th}}$ and $V_{\mathrm{o}}$ are the Fréedericksz threshold voltage for, respectively, the corresponding polymer composite and pure 6OCN at the same $\mathrm{\Delta }T$. The value shows a lowering until a critical concentration $X_c=0.9$, and then rapidly rises. The solid line represents a fit to Eq. (3)) and the dashed line, a fit to Eq. (6).

Figure 6

Polarizing optical microscopy images taken in the isotropic phase of the mixture with concentrations $X=1$, 1.5, 2, and 2.5. While the polymer fibrils are well developed for the latter three materials, the $X=1$ mixture exhibits a few stray fibrils. It may also be noted in all the cases the fibrils are along the director direction (indicated by the arrow) of the host nematic. The network is seen to become denser with increasing concentration of RM82.

Figure 7

AFM images of the $X=1.5$ (left panel) and $X=2$ (right panel) mixtures exhibiting well developed polymer strands. The diameter of the strands is more for the higher concentration mixture. The twisting of the strands seen in both the images is a surprising feature since neither the host nematic nor the polymerizing monomer is chiral in nature.

Figure 8

POM images in the nematic phase of the $X=1$ (top images) and $X=2$ (bottom images) mixtures (a,d) in the absence of, and upon application of electric field with (b,e) 20 V and (c,f) 60 V magnitude, respectively. For $X=1$, the reorientation of the host molecules drives the polymer strands also to reorient resulting in essentially a dark field of view. In contrast for the higher concentration mixture even at the highest field applied, the reorientation of the host molecules is not strong enough to reorient the polymer strands resulting in the field of view looking quite similar to the image in the isotropic phase (without any field), shown in Fig. 6.

Figure 9

Polymer fibrils aligned parallel to the nematic director n that is along the $z$ axis in the absence of the electric field. The fibrils are assumed to be perfectly straight and the director domains bounded by rectangles of dimensions $a$ and $b$. For saturating electric field, n reorients to point along the $x$ axis. The average distance between the centers of the polymer fibrils depends on the concentration as $\alpha /\surd X$. The diameter of a fibril is $\beta$ and the characteristic length is $\xi$ (adapted from Ref. [19]).

Figure 10

Temperature dependence of the splay elastic constant $K_{11}$ for pure 6OCN and a few mixtures, whose concentration is indicated against each curve. In all cases the thermal dependence is monotonic. The magnitude of $K_{11}$ increases by more than an order of magnitude over the concentration range $X=0$ to 2.5, as seen from the data taken at a reduced temperature of $\mathrm{\Delta }T=20\mathrm{K}$, presented in the inset.

Figure 11

Thermal variation of the bend elastic constant $K_{33}$ for pure 6OCN and the mixtures in the concentration regime (concentration $X$ is indicated against each curve). While pure 6OCN $\left(X=0\right)$ has a monotonic variation, the mixtures have a convex-shaped profile. The strong increase in the value for pure 6OCN at low temperatures is due to the development of smectic correlations. The inset shows the reciprocal of the slope $S_{\mathrm{LFC}}$ of the capacitance vs voltage curves (such as those presented in Fig. 4) in the region immediately above $V_{\mathrm{th}}$, taken at a reduced temperature of $\mathrm{\Delta }T=20\mathrm{K}$. This parameter is considered as a measure of $K_{33}$ over the entire concentration range studied, and exhibits a drastic increase.

Figure 12

Transient capacitance response when the applied voltage is abruptly removed at a reduced temperature of $\mathrm{\Delta }T=5\mathrm{K}$ for 6OCN $\left(X=0\right)$ and different mixtures; the data are normalized with respect to the zero-time value for 6OCN. The higher $\left(X>1\right)$ concentration mixtures show a single relaxation, whereas the materials with $X\le 1$ have two relaxations. The lines through the data for 6OCN and $X=2$ represent fits to Eqs. (10) and (8), respectively.

Figure 13

Semilogarithmic representation of the inverse temperature dependence of (a) ${\tau }_{\mathrm{off}}$ and (b) the associated rotational viscosity for representative materials (open circle: $X=0$, filled circle: $X=1$, and triangle: $X=1.5$) studied. The essentially linear variation of both the parameters in such a representation suggests Arrhenius behavior. Both parameters exhibit a nonmonotonic dependence on the concentration of RM82, with a maximum at $X\sim 1$, as seen from the insets.

Figure 14

Differential scanning calorimetric profiles in the vicinity of the isotropic-nematic transition for pure 6OCN and the mixture $X=1.5$. While the former exhibits a single sharp peak, the profile for the mixture showing a shoulder can be resolved into two peaks, as depicted on an enlarged scale in the inset. The lower temperature peak is connected with the transition occurring for molecules in the vicinity of the polymer strands. Also to be noted is that although the peak height is greatly reduced for the mixture, the peak area, corresponding to the enthalpy of the transition, is comparable for the two materials.