Theory of light-activated catalytic Janus particles.

We study the dynamics of active Janus particles that self-propel in solution by light-activated catalytic decomposition of chemical "fuel." We develop an analytical model of a photo-active self-phoretic particle that accounts for "self-shadowing" of the light by the opaque catalytic face of the particle. We find that self-shadowing can drive "phototaxis" (rotation of the catalytic cap toward the light source) or "anti-phototaxis," depending on the properties of the particle. Incorporating the effect of thermal noise, we show that the distribution of particle orientations is captured by a Boltzmann distribution with a nonequilibrium effective potential. Furthermore, the mean vertical velocity of phototactic (anti-phototactic) particles exhibits a superlinear (sublinear) dependence on intensity. Overall, our findings show that photo-active particles exhibit a rich "tactic" response to light, which could be harnessed to program complex three-dimensional trajectories.