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A microscopic theory for coarse graining diblock copolymers into dumbbells ofinteracting soft colloidal particles has been developed, based on the solutionof liquid-state integral equations. The Ornstein-Zernike equation is solved toprovide a mesoscopic description of the diblock copolymer system at the levelof 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 ofstructurally symmetric diblock copolymers as a function of temperature,density, chain length, and chain composition. The theory correctly predictsthermodynamically-driven segregation of diblocks into microdomains as afunction of temperature ($chi$ parameter). The coarse-grained descriptioncontains contributions from density and concentration fluctuations, with thelatter becoming dominant as temperature decreases. Numerical calculations forthe block coarse-grained total correlation functions, as a function of theproximity of the system to its phase transition, are presented. Comparison withunited atom molecular dynamics simulations are carried out in the athermalregime, where simulations and theory quantitatively agree with no need ofadjustable parameters.

Theoretical coarse-graining approach to bridge length scales in diblock copolymer liquids