Molecular simulations provide a very useful tool for understanding the structure-property relations of various materials. Application of these techniques to polymeric materials, however, is not straight forward due to the broad range of length and time scales characterizing them [1]. For this reason multi-scale modeling techniques that are using information from different length and time scales are needed.

We develop hierarchical simulation approaches that combines microscopic (atomistic) and mesoscopic (coarse grained) simulations, which can generally be applied to polymeric materials. The general procedure involves the following steps:

First a coarse-grained (CG) model for the specific polymer is chosen. The CG force field bonded parameters are obtained from detailed atomistic simulations of random walks.  based on data obtained from atomistic simulations of isolated PS dimers, are chosen in a way which allows differentiating between meso- and racemic dyads. Nonbonded interactions between coarse-grained beads can be obtained either as purely repulsive or from potentials of mean force.


Then mesoscopic dynamic simulations in the CG level are performed. The proposed CG is tested along a different number of structural properties, i.e. on the monomeric level (distribution function of bonds, bending and dihedral angles) as well as on the level of the whole chain (internal distances, radius of gyration, end-to-end distance). This approach also allows to distinguish stereoregular polymer systems.


 Quantitative study of dynamics can be performed by comparing short chain atomistic and coarse-grained simulations. Then the time mapping constant is determined. This allows the prediction of dynamical and rheological properties in range of molecular weight close to polymer processing without any adjustable parameter.


An important advantage of the present methodology is the capability to obtain well-equilibrated atomistic configurations of long polymer melts. To achieve this, a rigorous approach for reinserting the atomistic detail, that combined minimization and short MD runs, has been developed. The methodology has been successfully tested for short PS chains and the structure was found to be exactly similar with the one obtained directly from very long atomistic MD runs as well as from experimental measurements.










1.  V.A. Harmandaris, V.G. Mavrantzas, D.N. Theodorou, M. Kröger, J. Ramírez, H.C. Öttinger, D. Vlassopoulos, “Dynamic crossover from Rouse to entangled polymer melt regime: Signals from long, detailed atomistic molecular dynamics simulations, supported by rheological experiments”, Macromolecules, 2003, 36, 1376-1387.

2. V.A. Harmandaris, N. Adhikari, N.F.A. van der Vegt, K. Kremer “Hierarchical modeling of polystyrene: From atomistic to coarse-grained simulations”, Macromolecules 2006, 39, 6708.

3.  V.A. Harmandaris, D. Reith, N.F.A. van der Vegt, K. Kremer, “Comparison between coarse-graining models for polymer systems: Two mapping schemes for polystyrene”, Macrom. Chem. and Phys. 2007, 208, 2109.

4. 4. V.A. Harmandaris, K. Kremer, “Quantitative study of polymer dynamics through hierarchical dynamic simulations”, submitted.

Hierarchical Multi-Scale Modeling of Polymers