Reorientation behavior in the helical motility of light-responsive spiral droplets

Abstract

The physico-chemical processes supporting life's purposeful movement remain essentially unknown. Self-propelling chiral droplets offer a minimalistic model of swimming cells and, in surfactant-rich water, droplets of chiral nematic liquid crystals follow the threads of a screw. We demonstrate that the geometry of their trajectory is determined by both the number of turns in, and the handedness of, their spiral organization. Using molecular motors as photo-invertible chiral dopants allows converting between right-handed and left-handed trajectories dynamically, and droplets subjected to such an inversion reorient in a direction that is also encoded by the number of spiral turns. This motile behavior stems from dynamic transmission of chirality, from the artificial molecular motors to the liquid crystal in confinement and eventually to the helical trajectory, in analogy with the chirality-operated motion and reorientation of swimming cells and unicellular organisms.

Fig. 1

Spiral droplets reorient their swim in response to light-induced helix inversion. The molecular chirality of motor m and its light-induced isomer m* is transmitted across increasing length scales, from a chiral center in the motor, to the helical shape of the motor and eventually to liquid crystal chirality (left-handed in red, right-handed in blue). In spherical confinement and with the liquid crystal molecules aligning perpendicularly to the interface, a double spiral disclination line forms at the surface of the droplet. This disclination line is visible under polarized optical microscopy (scale bar 50 μm) and is also shown in the model of the droplet (red for left-handed and blue for right-handed). These chiral droplets are propelled along helical trajectories with a handedness that is opposite to that of the droplets. Upon illumination, the molecular motors invert the handedness of their helical shape, in a process that drives their rotation and leads to inversion of liquid crystal handedness. This light-induced inversion is associated with inversion of the helical trajectory and with a deterministic reorientation

Fig. 2

Helical motion of spiral droplets. a Two-dimensional projection of the trajectory of a chiral droplet. The chirality of the droplet is expressed as a spiral pattern and the axis of the droplet (indicated by a black arrow) undergoes a precession along its helical trajectory. The data acquisition is done by manual z-tracking. b Representation of a left-handed droplet moving along a right-handed helical trajectory. The geometry of the motion is characterized by its radius R and pitch P. c Chiral molecules used as dopants to induce a cholesteric liquid crystal. CB15 is an enantiomerically pure chiral molecule. Me-m and Ph-m are molecular motors that modify the pitch of the liquid crystal helix and invert its handedness upon illumination. Ph-m induces larger twists than Me-m. d Complete trajectories for chiral droplets doped with CB15 (left), Me-m (center), and Ph-m (right). e Evolution of the confinement ratio N in time (number of spiral turns on the surface of the droplet), for droplets incorporating chiral dopant CB15 (black square, initial pitch is 1.5 μm), Me-m (red circles, initial pitch is 4.3 μm) and Ph-m (blue triangle, initial pitch is 1.6 μm). In the case of Me-m and Ph-m, the concentration of dopant increases over time and eventually the droplet becomes isotropic. The solid lines are guides for the eye. The data are ensemble averaged and error bars correspond to the standard deviation. f Dependence of radius R (circles) and pitch P (squares) from the chirality confinement N. The error bars correspond to standard deviation. The data are ensemble averaged for six droplets doped with CB15

Fig. 3

Swimming velocity in time and against the size of the droplets. a The velocity of a chiral droplet doped with CB15 evolves in time. Here, the initial diameter of the droplet was ca. 19 μm (data shown for one individual droplet). b Velocity of motile droplets as a function of their diameter. These data correspond to a collection of drops, and was acquired during their motion

Fig. 4

Reorientation of spiral droplets in response to light. a Three-dimensional motion of a droplet incorporating Me-m motor. Upon strong illumination, the helix inversion operates a sharp reorientation. b A sharp directional change is operated by the spiral droplets upon helix inversion. A chiral droplet follows a right-handed helical trajectory (in blue) and upon strong illumination helix inversion in the droplet inverts the handedness of the trajectory (in red) and modifies the direction of droplet motion. The direction of reorientation is characterized by the angle θ. c Two-dimensional trajectory of a droplet that undergoes directional change upon rapid helix inversion. The angle θ is defined as the angle between the helical axis of motion before (black arrow) and after illumination (red arrow). d Measured reorientation angle θ for N = 32. These angle values are meaningful only between 0 and 180, which means that a cone of deterministic reorientation is associated to each reorientation angle θ. e, Dependence of θ from the chirality confinement ratio N. The angle of photo-stimulated re-direction increases with N. The error bars indicate standard deviation, the dashed line is a guide for the eye

Fig. 5

Influence of kinetics of chirality inversion on the reorientation. The spiral droplet shown here is doped with Me-m. When the light power is sufficiently low, the helical trajectory unwinds slowly and then rewinds with helix inversion. The insets show the structure of the droplet during motion, with straight motion being associated with the disappearance of the spiral organization in the compensated state. The direction of the motion is not modified significantly upon transition from helical to straight