  Recently synthesized colloids and biological systems such as proteins,
viruses and monoclonal antibodies are heterogeneously charged, i.e., different
regions of their surfaces carry different amount of positive or negative
charge. Because of charge anisotropy, the electrostatics interactions between
these units through the surrounding medium are intristically anisotropic,
meaning that they are characterized not only by the attraction between
oppositely-charged regions but also by the repulsion between like-charged
areas. Recent experiments have shown that the liquid-liquid phase separation of
these systems can be driven by anisotropic electrostatics interactions, but it
is not clear how the emerging aggregates are affected by charge imbalance and
charge patchiness. The ability to experimentally control these two quantities
calls for a theoretical understanding of their interplay, which we address here
at the critical point. We consider a coarse grained model of anisotropically
charged hard spheres whose interaction potential is grounded in a robust mean
field theory and perform extensive numerical Monte Carlo simulations to
understand the aggregation behavior of these units at the critical point.
Stemming from the simplicity of the model, we address the interplay between
charge imbalance and charge patchiness with the use of three parameters only
and fully rationalize how these features impact the critical point of the model
by means of thermodynamic-independent pair properties.
