  The interaction between two chemically identical charge-regulated surfaces is
studied using the classical density functional theory. In contrast to common
expectations and assumptions, under certain realistic conditions we find a
spontaneous emergence of disparate charge densities on the two surfaces. The
surface charge densities can differ not only in their magnitude, but quite
unexpectedly, even in their sign, implying that the electrostatic interaction
between the two chemically identical surfaces can be attractive instead of
repulsive. Moreover, an initial symmetry with equal charge densities on both
surfaces can also be broken spontaneously upon decreasing the separation
between the two surfaces. The origin of this phenomenon is a competition
between the adsorption of ions from the solution to the surface and the
interaction between the adsorbed ions already on the surface.These findings are
fundamental for the understanding of the forces between colloidal objects and,
in particular, they are bound to strongly influence the present picture of
protein interaction.
