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Systematic and thermodynamically consistent coarse graining the flow of complex fluids

Final Report Summary - CGCOMPLEXFLUIDFLOW (Systematic and thermodynamically consistent coarse graining the flow of complex fluids)

Derivation of macroscopic constitutive equations from underlying microscopic model systems is at the core of nonequilibrium statistical mechanics. In the context of soft matter in general and polymer and liquid-crystal physics in particular, this classical problem has seen renewed interest not least due to new and fascinating applications in smart materials.

In this project, we investigate coarse-graining approaches for two microscopic model systems of nematic liquid crystals: the Lebwohl-Lasher spin lattice system as well as an off-lattice systems of rigid ellipsoids interacting via the Gay-Berne potential. As collective variable, we choose the orientational order parameter tensor. A cornerstone of the macroscopic theory of liquid crystals is the Landau-de Gennes free energy.
Rather than postulating the Landau-de Gennes free energy, we were able to establish a link between this effective free energy and a large deviation function. Using Chernoff's formula allows us to determine the latter numerically and to reduce the numerical uncertainties compared to earlier approaches. Furthermore, we showed for the Lebwohl-Lasher model the equivalence of the projection operator approach to a more traditional, Kirkwood-like method of coarse graining. Special emphasis we paid on the resulting time correlation functions of fluctuations that play a central part in determining macroscopic properties. Interestingly, we find propagating modes and long-time tails in the angular momentum correlations.

More information and the corresponding publications can be found under or directly contacting Patrick Ilg via email: