Supersoft elasticity and slow dynamics of isotropic-genesis polydomain liquid crystal elastomers investigated by loading- and strain-rate-controlled tests

The supersoft elasticity and slow dynamics of isotropic-genesis polydomain nematic elastomers are investigated by loading- and strain-rate-controlled tests. Loading-controlled tests reveal the stretching-driven polydomain-to-monodomain (PM) transition under true equilibrium condition without viscoelastic (time) effect. The equilibrium PM transition is observed as a discontinuous dimensional change at a threshold stress with extremely small magnitude (${\sigma }_{\mathrm{PM}}^{\infty }\approx 1\mathrm{kPa}$). The mechanical work required for 80% elongation of the elastomer accompanying the PM transition is only 2% of that required in the high-temperature isotropic state, reflecting the supersoft elasticity effect. The dimensional growth rate ($R$) under constant loading becomes low as the imposed stress (${\sigma }_0$) approaches ${\sigma }_{\mathrm{PM}}^{\infty }$. The dependency of the dimension on the reduced time ($\mathit{Rt}$) is, however, independent of ${\sigma }_0$. In the strain-rate ($\dot{\varepsilon }$) controlled tests, the stress-stretch curves show a plateau region characteristic of the PM transition in a finite range of stretch, which is equivalent to the discontinuous stretch in the loading-controlled tests. The plateau stress ${\sigma }_{\mathrm{pl}}$ significantly decreases with decreasing $\dot{\varepsilon },$ whereas the ${\sigma }_{\mathrm{pl}}$ at the practically accessible low strain rate (on the order of ${10}^{-4}{\mathrm{s}}^{-1}$ ) is still significantly higher than ${\sigma }_{\mathrm{PM}}^{\infty }$. The dependency of ${\sigma }_{\mathrm{pl}}$ on $\dot{\varepsilon }$ is almost similar to the dependency of ${\sigma }_0$ on $R$ in the loading-controlled tests. This similarity signifies that the two types of tests with different controlled stimuli are governed by the same dynamics of the local director.

Figure 1

Chemical structures of diacrylate mesogen, dithiol flexible spacer, and tetrathiol cross-linker.

Figure 2

Equilibrium elongation $\left({\lambda }_{\infty }\right)$ as a function of imposed constant nominal stress (${\sigma }_0$) obtained by the loading-controlled experiments. Inset shows the magnification of the small ${\sigma }_0$ region. A discontinuous dimensional change is an indication of the PM transition, and the equilibrium threshold stress for the transition (${\sigma }_{\mathrm{PM}}^{\infty }$) is evaluated to be 1.0 kPa. The photographs show the turbid and semitransparent appearances in the undeformed and loaded states at ${\sigma }_0=2.8\mathrm{kPa}$, respectively.

Figure 3

(a) Time development of longitudinal strain ε($t$) under various degrees of constant stress (${\sigma }_0$). The strain is reduced by the equilibrium strain $\left({\varepsilon }_{\infty }\right)$ at each loading. Solid lines represent the fitted curves of Eq. (2) with $c=0.038$ using $R$ as an adjustable parameter. (b) Appearance as a function of elapsed time after load imposition of ${\sigma }_0=2.0\mathrm{kPa}$. (c) Time development of the nematic order parameter for the network backbone ($S_B$) estimated from the data in (a) at ${\sigma }_0=2.0\mathrm{kPa}$ with the anisotropic Gaussian network model.

Figure 4

(a) Reduced time course of $\varepsilon \left(t\right)/{\varepsilon }_{\infty }$ under various degrees of constant stress (${\sigma }_0$). The elapsed time at each loading is reduced by the characteristic growth rate ($R$) obtained by the fitting of Eq. (2) to the ε($t$)-$t$ data in Fig. 3. (b) Double logarithmic plots of $R$ against ${\sigma }_0$. The relation is approximated by $R$ ∼ ${\sigma }_0^{1.9}$. The base of the log in each axis is 10.

Figure 5

(a) Nominal stress (σ)–elongation (λ) relations at various nominal strain rates ($\dot{\varepsilon }$) in the nematic and isotropic states. The transparent appearance at λ = 2.3 in the stretching of $\dot{\varepsilon }=0.00016{\mathrm{s}}^{-1}$ shows the monodomain alignment. The appearance at λ = 2.3 in the high-speed stretching of $\dot{\varepsilon }$ remains turbid, indicating that definite PM transition does not occur. (b) Comparison of the stress-stretch relation obtained by the $\dot{\varepsilon }$-controlled experiment of the slowest strain rate [$0.00016{\mathrm{s}}^{-1}$ in (a)] with the equilibrium relation (Fig. 2) obtained by the ${\sigma }_0$-controlled experiments.

Figure 6

Plateau stress (${\sigma }_{\mathrm{pl}}$ at λ = 1.5) and stress in the monodomain state (${\sigma }_{\mathrm{pl}}$ at λ = 2.4) as a function of the nominal strain rate ($\dot{\varepsilon }$). The open symbols denote the data at high-speed stretching, which induces no definite PM transition. The strain rate required to equilibrate the stress during stretching was estimated to be $2\times {10}^{-5}{\mathrm{s}}^{-1}$ by extrapolating the power law behavior of ${\sigma }_{\mathrm{pl}}\sim {\dot{\varepsilon }}^{0.46}$ to the equilibrium value (${\sigma }_{\mathrm{PM}}^{\infty }=1\mathrm{kPa}$) obtained by the loading-controlled tests.

Figure 7

(a) Nominal stress (σ)–elongation (λ) relations in the loading and unloading processes at the slowest strain rate of $\dot{\varepsilon }=0.00016{\mathrm{s}}^{-1}$ at 20 °C. (b) Immediately after unloading, the specimen exhibits a residual stretch of λ = 1.85 which is close to the stretch at the end of the plateau region. The portions at both ends correspond to the clamped parts in tensile tests. (c) The residual stretch for the unloaded specimen remains unchanged after 20 days at 20 °C, while the visual appearance changes from transparent to slightly translucent, indicating a monodomain state with low orientational order near the PM transition threshold. (d) The unloaded specimen completely recovers the initial dimension after heating at 100 °C beyond the nematic-isotropic transition temperature (about 80 °C). (e) The turbid specimen with the initial dimension and polydomain texture is obtained by cooling at 20 °C.