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TU Berlin

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Project B.5: Convolution theory for dynamic mechanical systems: bottom-up approach to viscoelastic polymeric networks

We plan to develop a bottom-up theory for the viscoelastic response behavior of polymeric networks. For this three dimensional network theory, we in addition to the spatial response functions have to define angular response functions and cross couplings between angular and spatial degree of freedom at the nodal connection points. For the response functions of semi flexible polymers with parameters mimicking actin filaments, we will use our recently introduced mean-field-type theory that yields dynamic response functions in perfect agreement with simulations including the effects of hydrodynamics over the full frequency range. Results will be checked by explicit simulations of coarse-grained bead-spring models as well. The protein linkers will first be modeled as harmonic springs that act on the positions of the connected filaments. Angular confinement will be taken into account as well, for this we will resolve the differences between linkers that enforce a preferred tangential angle relation between the connected filaments and those that do not, both forms exist in nature and lead to distinctly different viscoelastic responses. We will also model transitions between a bound state and an unbound state of the linker and therefore include stochastic resonance and non-linear phenomena into the equations. The onset of non-linear effects can be estimated by a heuristic criterion introduced recently by us and shall be included into the convolution theory as well. First we will consider ordered network lattices, in which case the resulting equations for the macroscopic viscoelastic behavior involve the inversion of large response matrices, in later refinements disorder effects will be treated as well.

Project leaders: Prof. Dr. R. Netz, Prof. Dr. M. Falcke

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