Anchoring-mediated stick-slip winding of cholesteric liquid crystals

The stick-slip phenomenon widely exists in contact mechanics, from the macroscale to the nanoscale. During cholesteric-nematic unwinding by external fields, there is controversy regarding the role of planar surface anchoring, which may induce discontinuous stick-slip behaviors despite the well-known continuous transitions observed in past experiments. Here we observe three regimes, namely, constrained, stick-slip, and sliding-slip, under mechanical winding with different anchoring conditions, and measure the corresponding forces by the surface force balance. These behaviors result from a balance of cholesteric elastic torque and surface torque, reminiscent of the slip morphology on frictional substrates [T. G. Sano et al., Phys. Rev. Lett. 118, 178001 (2017)], and provide evidence of dynamics in static rotational friction.

Figure 1

Forces measured in the surface force balance (SFB). (a) Schematic diagram of cholesterics confined in the crossed cylinders with radius $R$. (b) Force profiles of three regimes, i.e., I: Constrained (red); II: Stick-slip (black): and III: Sliding-slip (blue), during the approach of the surface as the anchoring strength decreases. (c) Force profile (red, light gray) in the first regime fitted by elastic forces (black, dark gray) calculated by Eq. (4) with $K_{22}=3.8$ pN. (d) Force profile (black, dark gray) in the second regime fitted by elastic forces (red, light gray) calculated by Eq. (4) with various integer layers (numbers) and $K_{22}=6$ pN. The slope of the straight blue line in (c,d) is the spring constant of the cantilever spring that connects to the surface $dF/dD=k=125\mathrm{N}/\mathrm{m}$.

Figure 2

Compression ratio of cholesteric layers at the critical jumping distance. (a) First regime. (b) Second regime (premier jumps). (c) The data in the first and second regimes fall on two blue lines that are theoretically calculated by Eq. (7) with $K_{22}=3.8$ and 6 pN, respectively.

Figure 3

Calculation of the anchoring strength. The critical jumping distance $D_c$ as a function of the original distance $D_0$ in (a) the first regime and (b) the second regime (including all the stick-slip jumps); the blue line is the linear trend line. (c) Fitting the force profile (black, upper) in the second regime by Eqs. (4) and (10) with $K_{22}=6$ pN and the critical surface torque and anchoring strength obtained from (b).

Figure 4

Hysteresis of the twist angle in three regimes. The noninteger layer has been deducted to eliminate the difference of easy axes among different experiments. (a) First regime. The twist angle during the jump process is assumed to keep a constant compression ratio but decrease the total twist angle. (b) Second regime. (c) Third regime. The deviation of the anchoring angle is ignored in all three regimes. (d) Three regimes. (e) Approach profiles of I–III three regimes. (f) Retraction profiles of I–III three regimes. Thin and thick lines following the direction of the arrow are approach and retraction profiles, respectively. The red, black, and blue lines denote the three regimes, respectively.