Manipulation of cholesteric liquid crystal phase behavior and molecular assembly by molecular chirality

Molecular simulation is used to study the effect of molecular chirality on liquid crystalline phase transition and molecular assembly behavior. Based on a flexible chain (FCh) model with helical arrangement of side beads, the phase behavior of FCh models with various molecular chiralities are studied as functions of pressure (or density). By modifying the molecular chirality of FCh, we can manipulate the relative stability of the nematic and cholesteric phases continuously; and we found that increasing molecular chirality may destabilize cholesteric order due to the effective reduction of chiral interactions. A semismectic phase is identified in the high-density region, in which the two-dimensional fluid layers overlap due to shift alignment formed by FCh particles. The global phase diagram of the FCh model is constructed and the potential energy surface is calculated to elucidate the formation of cholesteric phase in terms of two-body interactions.

Figure 1

(a) Schematic of flexible chains with helical Lennard-Jones interactions (FCh) with molecular chiralities ${\varphi }_0=0^{\circ }$ and ${\varphi }_0={60}^{\circ }$, and the orientation of FCh particle $\mathbf{u}$, is aligned with the principal axis of a FCh particle. (b) Decomposition of center-of-mass separation $\mathbf{r}$ into parallel ${\mathbf{r}}_{\parallel }$ and perpendicular ${\mathbf{r}}_{\perp }$ components, with respect to director $\widehat{\mathbf{n}}$. (c) Internal azimuthal angle $\psi$.

Figure 2

Phase behavior of FCh with $m=10$, molecular chirality ${\varphi }_0=0^{\circ }$ at $T^{*}=1.0$. (a) Pressure $P^{*}$-packing fraction $\eta =\rho V_{\mathrm{mol}}$ equation-of-state for isotropic-nematic transition; (b) dependence of orientational order parameter $S_2$ on $\eta$.

Figure 3

Snapshots of FCh with $m=10$, molecular chirality ${\varphi }_0=0^{\circ }$ at $T^{*}=1.0$: isotropic state at $P^{*}=0.05$ and $P^{*}=0.18$, nematic state at $P^{*}=0.20$, and the semismectic (s-smectic) state at $P^{*}=0.26$. FCh particles are color coded according to their orientations in the isotropic and nematic phases.

Figure 4

Pair distribution function g(r) of FCh with $m=10$, molecular chirality ${\varphi }_0=0^{\circ }$ with increasing $P^{*}$, (a) region of $1.0<r<2.0$, and (b) enlargement of $0.6<g\left(r\right)<1.6$. The inset in (a) shows the overall shapes of g(r). (c) Orientational correlation function $g_2\left(r\right)$.

Figure 5

(a) Transverse $g_{\perp }\left(r_{\perp }\right)$ and (b) longitudinal $g_{\parallel }\left(r_{\parallel }\right)$ pair correlation functions of FCh molecules with $m=10$, molecular chirality ${\varphi }_0=0^{\circ }$.

Figure 6

Left column: $P^{*}-\eta$ equation-of-state for isotropic-cholesteric phase behavior of FCh with $m=10$, and varying molecular chiralities ${\varphi }_0={10}^{\circ },{20}^{\circ },{30}^{\circ }$ at $T^{*}=1.0$. The corresponding $S_2-\eta$ curves are also shown in right column.

Figure 7

Radial distribution function (RDF) of FCh with $m=10$, and varying molecular chiralities ${\varphi }_0={10}^{\circ },{20}^{\circ },{30}^{\circ }$ at $P^{*}=0.1$ (left-hand side column) and $P^{*}=0.2$ (right-hand side column). (a, b) $g\left(r\right)$, (c, d) $g_{\perp }\left(r_{\perp }\right)$, and (e, f) $g_{\parallel }\left(r_{\parallel }\right)$.

Figure 8

Right-hand-side column: configuration snapshots of lowest-density cholesteric phase formed at $T^{*}=1.0$ for FCh with $m=10$, and varying molecular chiralities ${\varphi }_0={10}^{\circ },{20}^{\circ },{30}^{\circ }$. Left-hand-side column: corresponding local orientational order parameters $S_2\left(z\right)$, $S_{\text{m}}\left(z\right)$, and $S_{\text{l}}\left(z\right)$, and twist angle profile $cos{\alpha }_0\left(z\right)$.

Figure 9

(a) Chiral pitch $P_{\text{chiral}}$ as a function of packing fraction $\eta =\rho V_{\mathrm{mol}}$ of FCh particle with $m=10$, and varying molecular chiralities ${\varphi }_0={10}^{\circ },{20}^{\circ },{30}^{\circ }$ at $T^{*}=1.0$. (b) Dependence of the prefactor $C\left({\varphi }_0\right)$ on ${\varphi }_0$.

Figure 10

(a) Pressure ($P^{*}$)-packing fraction ($\eta$) equation-of-state for FCh with $m=10$, and molecular chirality ${\varphi }_0={60}^{\circ }$ at $T^{*}=1.0$. The $\eta \text{−}{S}_2$ (orientational order parameter) is plotted in the inset. (b) Density dependence of chiral pitch $P_{\text{chiral}}/\sigma$ at $T^{*}=1.0$

Figure 11

(a) Orientational order distribution $S_2\left(z\right)$ and (b) twist angle profile $cos{\alpha }_0\left(z\right)$ of the isotropic (iso, $P^{*}=0.09$), cholesteric (chole, $P^{*}=0.16$), and nematic (nem, $P^{*}=0.20$) states in the FCh with $m=10$ and molecular chirality ${\varphi }_0={60}^{\circ }$ at $T^{*}=1.0$; (c) configuration snapshots for the corresponding isotropic, cholesteric, and nematic states.

Figure 12

Structure of FCh with $m=10$, and molecular chirality ${\varphi }_0={60}^{\circ }$ under pressure $P^{*}=0.05–0.32$ and $T^{*}=1.0$. (a) pair correlation function (PCF) $g\left(r\right)$, (b) orientational correlation function $g_2\left(r\right)$, (c) transverse PCF $g_{\perp }\left(r_{\perp }\right)$, and (d) longitudinal PCF $g_{\parallel }\left(r_{\parallel }\right)$.

Figure 13

Global phase diagram of FCh with $m=10$, and molecular chiralities ${\varphi }_0=0^{\circ }–{60}^{\circ }$ at $T^{*}=1.0$. The gray dash curve represents phase boundary between isotropic, cholesteric, and nematic phases. The representative configurations are shown in the right-hand-side column.

Figure 14

Minimum potential energy surface $U_{\min }(r_{\mathrm{CoM}},\theta )$ of FCh model with $m=10$ and ${\varphi }_0=0^{\circ }–{60}^{\circ }$ as a function of center-of-mass separation ($r_{\mathrm{CoM}}$) and relative orientation ($\theta$). The arrows indicate two split local minima (sub-1, sub-2) in the $U_{\min }(r_{\mathrm{CoM}},\theta )$ surface of FCh with ${\varphi }_0={60}^{\circ }$.