Memory effects in nematics with quenched disorder

We present a combined experimental and Monte Carlo study of a nematic phase in the presence of quenched disorder. The turbidity of a nematic liquid crystal embedded in a porous polymer membrane is measured under different applied field conditions for field-cooled and zero-field-cooled samples. We find that a significant permanent alignment of the nematic can be induced by fields as low as $0.1\mathrm{V}∕\mathrm{\mu }\mathrm{m}$ applied during the isotropic to nematic transition. An analogous effect and dependence on sample history is found by studying the order parameter of a sprinkled disorder Lebwohl-Lasher spin model, indicating that dilute quenched randomness is sufficient to produce memory effects in nematics. The large memory induced by field cooling appears to be written in the system during the transition as a result of the field action on freely oriented nematic nuclei. At lower temperature the nuclei consolidate into permanent nematic textures developed from the interaction with quenched disorder.

Figure 1

Experimental ZFC procedure and response to the electric field. (a) The temperature was decreased linearly from the $I$ phase to the $N$ phase, and then held constant. (b) The electric field applied to the sample was turned on after the equilibration in the $N$ phase and removed after $6\min$. (c) The turbidity of the sample increases as the temperature decreases in the $N$ phase. The application of an electric field in the $N$ phase induces a pronounced decrease of the turbidity which is partially $\left(\mathrm{\Delta }{\tau }_r\right)$ recovered after the removal of the field. The unrecovered part $\left(\mathrm{\Delta }{\tau }_p\right)$ is ascribed to permanent reconfiguration of the system. The vertical dotted lines are drawn as a guide to the eye in correspondence of temperature gradient changes and field transitions.

Figure 2

Experimental FC procedure and response to the electric field. (a) Similar to the ZFC procedure, the temperature of the sample was decreased linearly to bring the sample from the $I$ phase to the $N$ phase, and then held constant. (b) The electric field applied to the sample was turned on in the $I$ phase and maintained until the sample was equilibrated in the $N$ phase. The field was kept off for $5000\sec$ and then turned on again. (c) The turbidity of the sample in the $I$ phase is not influenced by the application of the electric field. In the $N$ phase the sample turbidity is low because of the aligning effect of the applied field. Upon removal of the field the high turbidity measured in the unperturbed ZFC state (dashed horizontal line at $\tau =0.375\mathrm{\mu }{\mathrm{m}}^{-1}$) is partially recovered $\left(\mathrm{\Delta }{\tau }_r\right)$. The unrecovered part $\left(\mathrm{\Delta }{\tau }_p\right)$ is ascribed to permanent reconfiguration induced by the field. The subsequent application of an electric field induces a pronounced decrease of the turbidity. The vertical dotted lines are drawn as a guide to the eye for temperature gradient changes and field transitions.

Figure 3

Turbidity measured at $25°\mathrm{C}$ as a function of the amplitude of an external electric field $E$. (a) Turbidity measured in presence of the applied field. Full dots: ZFC:ON states. These data have been taken by applying consecutive bursts of the electric field having increasing amplitude. The burst duration is $6\min$, with a time interval of $6\min$ between two consecutive bursts. Open dots: FC:ON1 states. Dotted line: FC:ON2 states. Each point refers to an independent FC measure following the field $E$ and temperature state sequence ON1-OFF-ON2 as shown in Fig. 2. (b) Turbidity measured after the removal of the electric field. Full dots: ZFC:OFF2 states. These data have been taken after the application of consecutive burst of duration $6\min$. Each value of turbidity has been measured $6\min$ after the removal of the field. Open dots: FC:OFF states. Each point refers to an independent FC measure following the field and temperature state sequence ON1-OFF-ON2 as shown in Fig. 2.

Figure 4

A schematic example of ZFC and FC procedure adopted in the MC simulations of the SSS model as a function of the Monte Carlo (MC) kcycles. (a) In the ZFC procedure the system was brought from the $I$ phase to the $N$ phase with $\eta =0$, then the field was turned on at $1\times {10}^5$ cycles and removed again at $2\times {10}^5$ cycles. (b) In the FC procedure the system was equilibrated in the $N$ phase with $\eta =0.01$, then the field was removed at $1\times {10}^5$ cycles and turned on again at $2\times {10}^5$ cycles. (c) Nematic order parameter $⟨P_2⟩$ versus MC cycles as obtained from the simulation using the ZFC procedure (black points) and the FC procedure (gray points) with $p=0.14$ at $T_N^{*}=0.2$. The MC cycles are counted starting from the temperature change $T_I^{*}\to T_N^{*}$. The vertical dotted lines are drawn as a guide to the eye for the field transitions.

Figure 5

Order parameter $⟨P_2⟩$ obtained from MC simulations as a function of an external field of strength $\eta$. (a) Order parameter obtained in presence of the external field. Full dots joined by the dashed line: ZFC:ON states. These data have been obtained by applying consecutive pulses of field of increasing amplitude $\eta$ and letting equilibrate after each field transition (see Fig. 4). Open dots joined by the dashed line: FC:ON1 states. Dotted line: FC:ON2 states calculated for $\eta \ge 0.1$. Each points refers to an independent FC simulation, following the field state sequence ON1-OFF-ON2 as shown in Fig. 4. (b) Order parameter obtained after the removal of the external field. Full dots: ZFC:OFF2 states. These data represent the residual $⟨P_2⟩$ computed after the removal of a field of strength $\eta$ (see Fig. 4). Open dots: FC:OFF states. Each point refers to an independent FC simulation, following the field state sequence ON1-OFF-ON2 as shown in Fig. 4.

Figure 6

Experimental $\left(m_{exp}\right)$ and simulated $\left(m_{sim}\right)$ memory coefficient as a function of the external field. (a) $m_{exp}$ measured for fields applied during ZFC (full dots) and FC (open dots) procedures. Points at very low fields (below $0.25\mathrm{V}∕\mathrm{\mu }\mathrm{m}$ for ZFC and below $0.1\mathrm{V}∕\mathrm{\mu }\mathrm{m}$ for FC) are not shown since the low values of $\mathrm{\Delta }{\tau }_p$ and $\mathrm{\Delta }{\tau }_r$ lead to high experimental uncertainty in the extraction of $m_{exp}$. (b) $m_{sim}$ calculated for fields $\eta$ applied during ZFC (full dots) and FC (open dots) procedures.