Generation and Structural Characterization for Randomly Dispersed Non-overlapping Spheres by Lennard-Jones Potential Based on Molecular Dynamics Simulations and the Two-Point Correlation Functions

Random dispersion of spheres are useful and appropriate models for a wide class of particulate random materials. In order to evaluate the effective properties of building composites materials. A means of generating a representative elemental volume (RVE) is desirable. The considerations of this problem are motivated by direct applications, namely the estimation of mechanical, thermal and electrical properties of inclusion-reinforced composites. An impenetrable spherical particles distributed randomly is an essential step towards the study of random materials. Recent advances in Molecular Dynamics (MD) methodology have made it possible to study routinely the microscopic details of inclusion-reinforced building composites materials using computers. Thus, a structure generated by an MD model is made to provide a pedagogical treatment of the microscopic details. On the “Two-point” level, a convenient integral formula is derived which interconnects the radial distribution function of the spheres with two-point correlation of the said characteristic function and used to characterize the internal structure generated by the MD model. First, the standard Newtonian or Hamiltonian dynamics based method is presented. It is followed by a discussion of theoretical advances related to MD. Next, the probability distributions for one-particle kinetic energy, momentum, and velocity for finite systems of classical impenetrable spheres with constant total energy and identical masses are derived. The novel Liouville operator factorization approach to numerical integration is reviewed. Since the results of an MD simulations depend on the inter-particle interactions employed in the calculations, modern empirical force fields based on Lennard-Jones (LJ) potential and Periodic Boundary Conditions (PBC) approaches are discussed.