Analysis of Brownian Dynamics and Molecular Dynamics Data of Unentangled Polymer Melts Using Proper Orthogonal Decomposition

A non-linear Brownian dynamics (BD) model based upon the Rouse model is developed for unentangled polymer melts. The essence of the model is that it includes an equilibrium spring length b, a non-linear force term that is not present in the equation of motion of the Rouse model. The equation of motion is solved numerically with the technique of proper orthogonal decomposition (POD) to obtain the dynamics information. To illustrate that the BD model can be readily implemented on polymers with different molecular structures, it is applied to polyethylene with linear, ring, and star structures. For comparison purpose, the corresponding molecular dynamics (MD) simulation is also carried out on molecules with the same sizes (N = 30-73). To characterize the dynamics, time correlation functions of the end-to-end vector, the m-to-n vector, and the arm vector of the linear, ring, and star polyethylene are determined respectively. It is found that the longest relaxation times (tau(1)s), the relaxation times of the vectors (tau(v)s), as well as zero-shear viscosity (eta(0)s) obtained from the BD and MD simulations agree well with each other. The time correlation functions can be reasonably described using the eigenmodes.