  The stability of colloidal suspensions is crucial in a wide variety of
processes including the fabrication of photonic materials and scaffolds for
biological assemblies. The ionic strength of the electrolyte that suspends
charged colloids is widely used to control the physical properties of colloidal
suspensions. The extensively used two-body Derjaguin-Landau-Verwey-Overbeek
(DLVO) approach allows for a quantitative analysis of the effective
electrostatic forces between colloidal particles. DLVO relates the ionic
double-layers, which enclose the particles, to their effective electrostatic
repulsion. Nevertheless, the double layer is distorted at high macroion volume
fractions. Therefore, DLVO cannot describe the many-body effects that arise in
concentrated suspensions. We show that this problem can be largely resolved by
identifying effective point charges for the macroions using cell theory. This
extrapolated point charge (EPC) method assigns effective point charges in a
consistent way, taking into account the excluded volume of highly charged
macroions at any concentration, and thereby naturally accounting for high
volume fractions in both salt-free and added-salt conditions. We provide an
analytical expression for the effective pair potential and validate the EPC
method by comparing molecular dynamics simulations of macroions and monovalent
microions that interact via Coulombic potentials to simulations of macroions
interacting via the derived EPC effective potential. The simulations reproduce
the macroion-macroion spatial correlation and the virial pressure obtained with
the EPC model. Our findings provide a route to relate the physical properties
such as pressure in systems of screened-Coulomb particles to experimental
measurements.
