The coarse-graining of a simple all-atom 2D microscopic model of graphene, in terms of "blobs" described by center of mass variables, is presented. The equations of motion of the coarse-grained variables take the form of dissipative particle dynamics (DPD). The coarse-grained conservative forces and the friction of the DPD model are obtained via a bottom-up procedure from molecular dynamics (MD) simulations. The separation of timescales for blobs of 24 and 96 carbon atoms is sufficiently pronounced for the Markovian assumption, inherent to the DPD model, to provide satisfactory results. In particular, the MD velocity autocorrelation function of the blobs is well reproduced by the DPD model, provided that the effect of friction and noise is taken into account. However, DPD cross-correlations between neighbor blobs show appreciable discrepancies with respect to the MD results. Possible extensions to mend these discrepancies are briefly outlined.

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The determination of relevant rheological properties and parameters in a very broad frequency range can be achieved for a number of thermoplastic polymers, for example, polystyrene, by applying the time-temperature-superposition principle. In contrast, polyethylene can only be explored rheologically in a limited frequency range, due to its fast crystallization below the crystallization temperature and its weak viscosity temperature-dependence. In this paper, various commercially available polydisperse and narrowly distributed linear and branched polyethylenes and ethylene-vinylacetate-copolymers were characterized. A piezoelectric- and a new quartz (crystal resonator) rheometer (QR) with an extended frequency range were utilized for the characterization. Introduction of high frequency rheological techniques and implementation of these new measurement methods are shown. For the first time, the entanglement relaxation time in the higher MHz frequency range was determined by applying the QR-technique and compared with those obtained by an alternative experimental method and numerical calculations.

We obtain Markovian equations of motion for a many body system of interacting coarse-grained (CG) variables and additional fluxes. The investigated CG variables belong to the special family of linear combinations of atomistic degrees of freedom. The system of Markovian equations of motion approximates Mori's exact non-Markovian generalized Langevin equation and is easy to solve by computer simulation. All parameters of the equations can be obtained from equilibrium molecular dynamics simulations of the investigated microscopic system. These parameters are either equal to the famous static covariances from Mori's continued fraction or they represent generalized constant friction matrices. We propose two different ways to compute these friction matrices based on Mori's continued fraction. Finally, some of the parameters are computed numerically for the special case of centre of mass 6

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