  A microscopic theory for coarse graining diblock copolymers into dumbbells of
interacting soft colloidal particles has been developed, based on the solution
of liquid-state integral equations. The Ornstein-Zernike equation is solved to
provide a mesoscopic description of the diblock copolymer system at the level
of block centers of mass, and at the level of polymer centers of mass.
Analytical forms of the total correlation functions for block-block,
block-monomer, and center-of-mass pairs are obtained for a liquid of
structurally symmetric diblock copolymers as a function of temperature,
density, chain length, and chain composition. The theory correctly predicts
thermodynamically-driven segregation of diblocks into microdomains as a
function of temperature ($chi$ parameter). The coarse-grained description
contains contributions from density and concentration fluctuations, with the
latter becoming dominant as temperature decreases. Numerical calculations for
the block coarse-grained total correlation functions, as a function of the
proximity of the system to its phase transition, are presented. Comparison with
united atom molecular dynamics simulations are carried out in the athermal
regime, where simulations and theory quantitatively agree with no need of
adjustable parameters.
