  Charged surfaces in contact with liquids containing ions are accompanied in
equilibrium by an electric double layer consisting of a layer of electric
charge on the surface that is screened by a diffuse ion cloud in the bulk
fluid. This screening cloud determines not only the interactions between
charged colloidal particles or polyelectrolytes and their self-assembly into
ordered structures, but it is also pivotal in understanding energy storage
devices, such as electrochemical cells and supercapacitors. However, little is
known 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 topological
colloidal particles, using numerical modelling within a mean-field
Poisson-Boltzmann theory. We show that the complexity of double layers
-including geometry and topology- can be tuned by changing the Debye screening
length of the medium, or by changing the shape and topology of the (colloidal)
particle. More generally, this work is an attempt to introduce concepts of
topology in the field of charged colloids, which could lead to novel exciting
material design paradigms.
