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Charged surfaces in contact with liquids containing ions are accompanied inequilibrium by an electric double layer consisting of a layer of electriccharge on the surface that is screened by a diffuse ion cloud in the bulkfluid. This screening cloud determines not only the interactions betweencharged colloidal particles or polyelectrolytes and their self-assembly intoordered structures, but it is also pivotal in understanding energy storagedevices, such as electrochemical cells and supercapacitors. However, little isknown to what spatial complexity the electric double layers can be designed.Here, we show that electric double layers of non-trivial topology and geometry-including tori, multi-tori and knots- can be realised in charged topologicalcolloidal particles, using numerical modelling within a mean-fieldPoisson-Boltzmann theory. We show that the complexity of double layers-including geometry and topology- can be tuned by changing the Debye screeninglength of the medium, or by changing the shape and topology of the (colloidal)particle. More generally, this work is an attempt to introduce concepts oftopology in the field of charged colloids, which could lead to novel excitingmaterial design paradigms.

Complex electric double layers in charged topological colloids