Numerical study of light-induced phase behavior of smectic solids

By the chemical cross-linking of rigid molecules, liquid crystal polymer (LCP) has been envisaged as a novel heterogeneous material due to the fact that various optical and geometric states of the liquid crystalline (LC) phases are projected onto the polymeric constituents. The phase behavior, which refers to the macroscopic shape change of LCP under thermotropic phase change, is a compelling example of such optical-mechanical coupling. In this study, the photomechanical behavior, which broadly refers to the thermal- or light-induced actuation of smectic solids, is investigated using three-dimensional nonlinear finite element analysis (FEA). First, the various phases of LC are considered as well as their relation to polymeric conformation defined by the strain energy of the smectic polymer; a comprehensive constitutive equation that bridges the strong, optomechanical coupling is then derived. Such photomechanical coupling is incorporated in the FEA considering geometric nonlinearity, which is vital to understanding the large-scale light-induced bending behavior of the smectic solid.To demonstrate the simulation capability of the present model, numerous examples of photomechanical deformations are investigated parametrically, either by changing the operating conditions such as stimuli (postsynthesis) or the intrinsic properties (presynthesis). When compared to nematic solids, distinguished behaviors due to smectic substances are found herein and discussed through experiments. The quasisoftness that bidirectionally couples microscopic variables to mechanical behavior is also explained, while considering the effect of nonlinearity. In addition to providing a comprehensive measure that could deepen the knowledge of photomechanical coupling, the use of the proposed finite element framework offers an insight into the design of light-responsive actuating systems made of smectic solids.

Figure 1

Order parameter $s^{*},{\rho }_o^{*},q_0^{*}$ with increasing temperature; first order phase transition is observed due to assumed Landau form of free energy.

Figure 2

Uniaxial shrinkage due to phase change of the smectic solids with different layer modulus $D$: (a) Length change vs changing shape parameter $r$; (b) length change vs operating temperature. Nonmonotonic shrinkage is observed, as shown in the experiment [19, 20].

Figure 3

Flowchart of the photomechanical analysis on smectic solids, which is a combination of microscopic polymeric conformation and finite element analysis (marked by deformations).

Figure 4

Profile of light-induced derivatives in out-of-plane direction. (a) Decay of the light intensity depending on Beer's law; (b) steady-state cis population $n_{\mathrm{cis}}$; (c) shape parameter $r$, wherein monotonicity is observed.

Figure 5

Temperature dependence of photoresponsive behavior with increasing light intensity in terms of curvature. (a) Temperature variation with fixed penetration depth $\left(d/h=0.4\right)$ and (b) variation of penetration depth $d$ with fixed temperature $\left(T=330\mathrm{K}\right)$.

Figure 6

(a) Deformed profile and the local rotation $\varphi$ of the smectic solid with given stimuli $(T=360\mathrm{K},I^{\mathrm{eff}}=2$), and (b) profile of the rotation with increasing light intensity and greater nonlinearity.

Figure 7

Alternation of the bending curvature depending on the uniformly deviated angle $\theta$ between layer normal $\vec{n}$ and the longitudinal direction, with fixed temperature $T=330\mathrm{K}$. The bending direction is found to be strongly dependent on intensity and $\theta$.

Figure 8

Effect of nonlinearity depending on the temperature and intensity (inset) of the bent geometry of the smectic solid, where the rotation $\varphi$ is marked by the color on the surface. The overestimation of the curvature and rotation is observed when nonlinearity is not taken into account.