Molecular dynamic study of the self-diffusion scefficient and velocity autocorrelation of a polymer in solution

Abstract

A molecular dynamic computation-experiment was performed on a system of 108 particles composed of a single polymer chain connected Np particles and solvent nature. The state considered was in the immediate neighborhood of the triple point of the system. The polymer itself is an analog to a freely jointed chain. The Lennard-Jones potential was used to represent the interactions between all particles including the interactions between non-nearest particles in the polymer except for the particles forming bonds, for which the interaction was expressed by a harmonic potential law. The self-diffusion coefficients and time-dependent velocity autocorrelation functions of the center of mass of a polymer were calculated at various chain lengths Np, and interaction strengths between solvent molecules and polymer atoms. For self-diffusion coefficients D, the Einstein relation holds goods; as chain length Np increases, the D value decreases at constant $\varepsilon_{cs}$, the interaction strength between solvent and polymer atom; and D also decreases as $\varepsilon_{cs}$ increases at constant chain length. The velocity autocorrelation function decays roughly exponentially during the relaxation time; as chain length increases, the normalized of this function does not change during the relaxation time within statistical errors; and the relaxation time decreases if $\varepsilon_{cs}$ increases, whereas the polymer molecule suffers larger backscattering as $\varepsilon_{cs}$ increases. The diffusion coefficients in various conditions reveal that our systems are in a free-draining limit.