Spontaneous ordering of magnetic particles in liquid crystals: From chains to biaxial lamellae

Using Monte Carlo computer simulations we explore the self-assembly and ordering behavior of a hybrid, soft magnetic system consisting of small magnetic nanospheres in a liquid-crystalline (LC) matrix. Inspired by recent experiments with colloidal rod matrices, we focus on conditions where the sphere and rod diameters are comparable. Already in the absence of a magnetic field, the nematic ordering of the LC can stabilize the formation of magnetic chains along the nematic or smectic director, yielding a state with local (yet no macroscopic) magnetic order. The chains, in turn, increase the overall nematic order, reflecting the complex interplay of the structure formation of the two components. When increasing the sphere diameter, the spontaneous uniaxial ordering is replaced by biaxial lamellar morphologies characterized by alternating layers of rods and magnetic chains oriented perpendicular to the rod's director. These ordering scenarios at zero field suggest a complex response of the resulting hybrid to external stimuli, such as magnetic fields and shear forces.

Figure 1

(a) State diagram of a mixture of GB rods and dipolar spheres with ${\sigma }_{\text{s}}^{*}=1$ $\left(x_{\text{r}}=0.8\right)$, involving fully miscible isotropic (I), uniaxial nematic $\left({\mathrm{N}}_{\text{u}}\right)$, and uniaxial smectic-$B$ $\left(\mathrm{Sm}B\right)$ states. The symbols indicate state points where the actual simulations were performed. The solid and dashed lines indicate state transformations of the nonmagnetic reference system. (b) Global order parameters as functions of $T^{*}$ at ${\rho }^{*}=0.40$.

Figure 2

Representative simulation snapshots for mixtures with ${\sigma }_{\text{s}}^{*}=1$ and $x_{\text{r}}=0.8$ in (a) the isotropic (I) state $\mathrm{[}(T^{*},{\rho }^{*})=(1.1,0.34)]$, (b) the uniaxial nematic $\left({\mathrm{N}}_{\text{u}}\right)$ state $\mathrm{[}(T^{*},{\rho }^{*})=(1.2,0.40)]$, and (c) the uniaxial smectic-$B$ $\left(\mathrm{Sm}B\right)$ state $\mathrm{[}(T^{*},{\rho }^{*})=(0.9,0.40)]$. In the bottom parts only the MNPs are shown for clarity. The directors ${\widehat{\mathit{n}}}_{\text{r}}$ and ${\widehat{\mathit{n}}}_{\text{s}}$ are indicated by thick lines.

Figure 3

(a) State diagram at size ratio ${\sigma }_{\text{s}}^{*}=2$ $\left(x_{\text{r}}=0.9\right)$, involving fully miscible isotropic (I), biaxial nematic $\left({\mathrm{N}}_{\text{b}}\right)$, and biaxial lamellar $\left({\mathrm{L}}_{\text{b}}\right)$ states. The solid line indicates the I-N transformation of the nonmagnetic reference system. Open symbols indicate defect-rich lamellar states (for ${\rho }^{*}=0.305)$ or hysteresis in cooling-heating series in the I-${\mathrm{N}}_{\text{b}}$ transformation (for ${\rho }^{*}=0.326$ and $0.338)$. (b) Global order parameters as functions of $T^{*}$ at ${\rho }^{*}=0.338$. Cooling: solid symbols; heating: open symbols.

Figure 4

Representative simulation snapshots for mixtures with ${\sigma }_{\text{s}}^{*}=2$ and $x_{\text{r}}=0.9$ in (a) the biaxial nematic $\left({\mathrm{N}}_{\text{b}}\right)$ state $\mathrm{[}(T^{*},{\rho }^{*})=(1.8,0.338)]$ and (b) the biaxial lamellar $\left({\mathrm{L}}_{\text{b}}\right)$ state $\mathrm{[}(T^{*},{\rho }^{*})=(1.2,0.338)]$. On the right sides only the MNPs are shown for clarity. (b) additionally includes a snapshot of the structure in one dipolar layer. The directors ${\widehat{\mathit{n}}}_{\text{r}}$ and ${\widehat{\mathit{n}}}_{\text{s}}$ are indicated by thick lines.