Nematics with Quenched Disorder: Pinning out the Origin of Memory

Memory effects and glassy behavior have been repeatedly observed in disordered nematic liquid crystals but the connection between these effects and the system topology remained unrevealed. We present an analysis of the local and global topology of the nematic ordering in the presence of quenched disorder and we show that nematics with quenched disorder can be mapped into a system of pinned defect lines and that the memory of the system stems from the pinning of these strings.

Figure 1

Comparison between data obtained by optical measurements [Panel (a)] and SSS MC simulations [Panel (b)] in a ZFC experiment: the system is quenched in the $N$ phase with no external electric field applied. After the equilibration an electric pulse is applied and the data are collected in presence (filled symbols) and after the removal (open symbols) of the applied field $E$. Panel (a) Transmitted intensity normalized to the isotropic value $I/I_0$ measured as a function of the amplitude of 1 kHz electric field applied for 5 seconds. The samples are thermalized at 10 °C below the $I$ to $N$ transition temperature. Circles: $3\mu \mathrm{m}$ Millipore membrane imbibed by 5 CB [11]. Squares: Filled nematic composed by 6 CB and 15% Aerosil [10]. Panel (b) Asymptotic order parameter $⟨P_2⟩$ plotted as a function of electric field strength $\eta$. Data obtained with a ${50}^3$ cube with $p=14\%$. Inset: $⟨P_2⟩$ plotted as a function of the MC cycles for $L=50$ (solid line) and $L=80$ (dashed line). The electric field $\eta =0.03$ is ON in the MC cycles interval $[100000,200000]$ and OFF elsewhere. In the inset three states are defined: the initial state (zero-FC or RIC), the ON asymptotic state in the presence of a field, and the OFF asymptotic state after the removal of the field. The acronyms in the figures indicate the configurations described in the text and in Table .

Figure 2

DL perimeter length distribution for AIC (dots) and RIC (open circles) for $L=80$ and $p=0.14$. Inset: snapshot of the longest DL (2968 lattice units) in a RIC state, $p=0.14$, $L=50$ (blue line). The red line is the longest DL (1392 lattice units) obtained through the domain freezing procedure applied to the same RIC system (see text for details).

Figure 3

Panel (a) Evolution of the relative fraction of long (open circles) and short (filled circles) defect loops, PP (stars), and $R$ fraction (lines) as a function of MC cycles. The data refer to the same MC simulations presented in the inset of Fig. 1b. The blue, green, and orange symbols refer to states where the field is OFF, ON, and OFF again, respectively. Panel (b) Snapshot of DL in a small portion of the simulation cube, comparing the RIC state (blue line), the RIC-ON2 state (green line) and RIC-OFF2 state (orange line).