Quantification of ordering in active light driven colloids

Light driven diffusioosmosis allows for the controlled self-assembly of colloidal particles. Illuminating of colloidal suspensions built of nanoporous silica microspheres dispersed in aqueous solution containing photosensitive azobenzene cationic surfactant enables manufacturing self-assembled well-ordered 2D colloidal patterns. We conjectured that ordering in this patterns may be quantified with the Voronoi entropy.

Depending on the isomerization state the surfactant either tends to absorb (trans-state) into negatively charged pores or diffuse out (cis-isomer) of the particles generating an excess concentration near the colloids outer surface and thus resulting in the initiation of diffusioosmotic flow. The direction of the flow can be controlled by the wavelength and intensity of irradiation. Under irradiations with blue light the colloids separate within a few seconds forming equidistant particle ensemble where long range diffusioosmotic repulsion acts over distances exceeding several times the particle diameter. Hierarchy of ordering in the studied colloidal systems is distinguished, namely: i) ordering of individual separated colloidal particles; ii) ordering of clusters built of colloidal particles; iii) ordering within clusters of individual colloidal particles.

The study of the temporal change in the Voronoi entropy for the light illuminated colloidal dispersions allowed quantification of ordering evolution on different lateral scales and under different irradiation conditions. Fourier analysis of the time evolution of the Voronoi entropy is presented. Fourier spectrum of the "small-area" (100 × 100 μm) reveals the pronounced peak at f = 1.125 Hz reflecting the oscillations of individual particles at this frequency. Ordering in hierarchical colloidal system emerging on different lateral scales is addressed. The minimal Voronoi entropy is intrinsic for the close packed 2D clusters.