Structural and thermodynamic consistency in coarse-grained models of macromolecules

Coarse-grained models of complex liquids are becoming increasingly important in simulations of complex fluids because they substantially reduce computational time while bridging information between simulations performed with atomistic resolution and continuum models. However, to be useful coarse-graining approaches need to provide physically consistent representations of the system under study, independent of the degree of coarse-graining resolution, i.e. they need to ensure consistency in both the thermodynamic and structural properties. Developing coarse-graining approaches that ensure consistency of thermodynamic and structural properties across variable coarse-graining resolution is a challenge. The difficulty is in properly mapping many-body interactions into effective pair interactions, which are input to the fast mesoscale molecular dynamic simulations of the coarse-grained representations. In this paper we review a Coarse-Grained approach, based on Integral Equation theory. This model conserves thermodynamics while accurately reproducing the structure of polymer liquids across variable levels of resolution. As it is solved analytically, it provides a formalism to reconstruct a posteriori the correct dynamics from the accelerated dynamics of the coarse grained simulation. This approach has the advantage of being largely analytically solved and it is useful to highlight some important and general points that need to be considered when developing coarse-graining models.