Molecularly derived constitutive equation for low-molecular polymer melts from thermodynamically guided simulation

We develop a systematic method for the derivation of closed-form and thermodynamically consistent constitutive equations of complex fluids from microscopic models. The method builds upon our recent work [Ilg et al., Phys. Rev. E 79, 011802 (2009)] on thermodynamically guided simulations within a consistent coarse-graining scheme. These simulations are powerful at low to intermediate flow rates and have the considerable advantage that they do not require flow-adapted boundary conditions, i.e., operate at arbitrary homogeneous flows. The new method for deriving constitutive equations is illustrated for low-molecular polymer melts subjected to imposed, homogeneous flow fields. The differential constitutive equation we obtain for this model system is a simple, nonlinear equation of change for the conformation tensor, from which the stress tensor is readily obtained. The proposed constitutive model shows shear thinning (shear viscosity exhibiting fractional power laws in the range -0.40 to -0.86, the corresponding range for the first viscometric function is -1.20 to -1.43), stress overshoots, normal stress coefficients, and elongational viscosities in agreement with reference results. The constitutive equation can be interpreted as a molecularly derived, modified Giesekus model with conformation-dependent coefficients. (C) 2011 The Society of Rheology. [DOI: 10.1122/1.3523485]