Atomistic Molecular Dynamics Simulation of Stress Relaxation upon Cessation of Steady-State Uniaxial Elongational Flow

Abstract

A new approach is presented for predicting the linear viscoelastic properties of a polymer melt through a series of molecular dynamics (MD) simulations of the relaxation of well-equilibrated, preoriented, strained configurations. Such strained configurations have been accumulated (Mavrantzas and Theodorou, 1998) by employing the end-bridging Monte Carlo (EBMC) algorithm in the presence of a small tensorial field Rxx which orients the chains. They are representative of a melt under conditions of steady-state, uniaxial elongational flow. In the dynamic studies presented in this work, the tensorial field Rxx is removed and the relaxation of the system back toward its field-free, equilibrium state is monitored with MD. All simulations are performed in the NTLxUyyUzz statistical ensemble (Yang et al., 1997), where the following variables are kept constant: the number of particles N, the temperature T, the length Lx of the simulation box in the direction of flow, and the average stress (Uyy + Uzz)/2 in the other two (lateral) directions. The physical experiment modeled through these NTLxUyyUzz MD simulations is one of stress relaxation upon cessation of a steady-state, uniaxial elongational flow. The relaxation of the melt is quantified by monitoring the temporal evolution of the normal stress Uxx in the x direction, of the volume V, and of certain descriptors of the short- and long-length scale conformation of chains. These include the diagonal components cxx, cyy, and czz of the conformation tensor and the chain mean-square end-to-end distance 〈R 2 〉, all as functions of time t. Results for the aforementioned properties, accumulated as statistical averages over many initial configurations subjected to NTLxUyyUzz MD simulations, are presented for two PE melt systems, C24 and C78, both of which have been studied extensively in the past. By invoking the Rouse model, analytical expressions are derived for the functions Uxx(t) and cxx(t) corresponding to the experiment simulated. By mapping the simulation results on these expressions, the longest relaxation times UR of the melts are extracted in excellent agreement with previous equilibrium computer experiments (Harmandaris et al., 1998). The stress relaxation modulus G(t) is computed from the equilibrium shear stress autocorrelation function at short times and from the spectrum of relaxation times extracted by mapping the MD results on the Rouse model at long times, yielding consistent and physically meaningful results.