Shear-enhanced elasticity in the cubic blue phase I

We present results of the linear and nonlinear rheology of the cubic blue phase I (BPI). The elasticity of BPI is dominated by double-twist cylinders assembled in a body-centered cubic lattice, which can be specified by disclination lines. We find that the elasticity of BPI is enhanced by an order of magnitude by applying pre-shear. The shear-enhanced elasticity is attributed to a rearrangement of the disclination lines that are arrested in a metastable state. Our results are relevant for the understanding of the dynamics of disclinations in the cubic blue phases.

Figure 1

Temperature dependence of the viscosity at $\dot{\gamma }$ = 1 ${\mathrm{s}}^{-1}$. The different symbols correspond to measurements during the cooling and heating processes. The temperature was changed at a constant rate of $\dot{T}$ = 0.1 ${}^{\circ }\mathrm{C}$/min.

Figure 2

Polarized microscope images during cooling (a) and heating (b) in the quiescent state. The scale bar corresponds to 10 $\mu \mathrm{m}$. In each process, the temperature was changed at a constant rate of 0.1 ${}^{\circ }\mathrm{C}$/min. In microscope observations, the sample was sandwiched between a slide glass and a cover slip as a thin film.

Figure 3

Shear moduli $G^{\prime }$ and $G^{\prime \prime }$ as a function of angular frequency $\omega$ at different temperatures. The shear moduli measured during the heating and cooling process are compared in the same figure. Filled and open symbols indicate the storage and loss modulus, respectively.

Figure 4

Shear moduli of BPI/iso biphase at $T$ = 31.0 ${}^{\circ }\mathrm{C}$ as a function of angular frequency $\omega$: Shear moduli measured before and after applying pre-shear rate of ${\dot{\gamma }}_{\mathrm{pre}}$ = 500 ${\mathrm{s}}^{-1}$ are compared in panel (a). Solid lines indicate the slope of the shear moduli ${\omega }^{0.5}, {\omega }^{1.0}$, and ${\omega }^{2.0}$ for reference, respectively. Shear moduli measured at different elapsed times $\mathrm{\Delta }t$ = 2000 s and 4000 s after pre-shear are also shown in panel (b). Filled and open symbols are storage and loss shear modulus, respectively. Solid and dashed lines correspond to the shear moduli after pre-shearing at ${\dot{\gamma }}_{\mathrm{pre}}$ = 500 ${\mathrm{s}}^{-1}$.

Figure 5

Shear moduli of homogeneous BPI at $T$ = 29.5 ${}^{\circ }\mathrm{C}$ as a function of $\omega$ measured before and after applying pre-shear rate of $\dot{\gamma }$ = 50 and 500 ${\mathrm{s}}^{-1}$: (a) Representative results of the pre-shear effect on the shear moduli are summarized. (b) Shear moduli measured at $\mathrm{\Delta }t$ = 2000 s and 4000 s after pre-shearing at ${\dot{\gamma }}_{\mathrm{pre}}$ = 500 ${\mathrm{s}}^{-1}$ are shown. Filled and open symbols are storage and loss shear modulus, respectively. Solid and curved lines correspond to the shear moduli after pre-shear at ${\dot{\gamma }}_{\mathrm{pre}}$ = 500 ${\mathrm{s}}^{-1}$.

Figure 6

Polarized microscopy images of BPI and BPI/iso biphase taken after a quench from shear rates of $\dot{\gamma }$ = 500 ${\mathrm{s}}^{-1}$ to 0 ${\mathrm{s}}^{-1}$. The images in the upper row show results at $T$ = 31.0 ${}^{\circ }\mathrm{C}$, whereas those in the lower row give results at $T$ = 29.5 ${}^{\circ }\mathrm{C}$. The scale bar corresponds to 10 $\mu \mathrm{m}$ and the flow is along the vertical direction.

Figure 7

Effect of the pre-shear treatment on the shear modulus $G^{\prime }$ and relaxation time in BPI at $T$ = 29.5 ${}^{\circ }\mathrm{C}$. Here, the shear modulus at a representative frequency of $\omega$ = 0.1 ${\mathrm{s}}^{-1}$ is shown. The relaxation time $\tau$ was estimated as the inverse frequency where the peak in the loss shear modulus $G^{\prime \prime }$ was observed.

Figure 8

(a) Flow curves at different temperatures. The apparent yield stress can be estimated from the flow curves. (b) Second plateau modulus $G_{0.1}^{\prime }$ at $\omega$ = 0.1 ${\mathrm{s}}^{-1}$ and apparent yield stress ${\sigma }_{\mathrm{Y}}$ as a function of temperature.