  We calculate the force between two spherical metal nanoparticles of charge Q
1 and Q 2 in a dilute 1:1 electrolyte solution. Numerically solving the
non-linear Poisson-Boltzmann equation, we find that metal nanoparticles with
the same sign of charge can attract one another. This is fundamentally
different from what is found for like-charged, non-polarizable, colloidal
particles, the two body interaction potential for which is always repulsive
inside a dilute 1:1 electrolyte. Furthermore, existence of like-charge
attraction between spherical metal nanoparticles is even more surprising in
view of the result that such attraction is impossible between parallel metal
slabs, showing the fundamental importance of curvature. To overcome a slow
convergence of the numerical solution of the full non-linear Poisson-Boltzmann
equation, we developed a modified Derjaguin approximation which allows us to
accurate and rapidly calculate the interaction potential between two metal
nanoparticles, or between a metal nanoparticle and a phospholipid membrane.
