The present invention relates to a method for calculating an interaction potential between filler particles in a polymeric material, more particularly to a method for determining parameters of the Lennard-Jones potential between the filler particles.
In recent years, in order to develop or design rubber compositions, various computer simulation methods for evaluating properties of a composite of a polymeric material and filler have been proposed.
In such a simulation method, for example, filler models of filler particles are defined, and the Lennard-Jones potential ULJ given by the following equation (1) (namely, an interaction potential between two filler models) is defined between the filler models.
                                          U            LJ                    ⁡                      (                          r              ij                        )                          =                  4          ⁢                      ɛ            LJ                    ⁢                      {                                                            (                                                            σ                      LJ                                                              r                      ij                                                        )                                12                            -                                                (                                                            σ                      LJ                                                              r                      ij                                                        )                                6                                      }                                              Equation        ⁢                                  ⁢                  (          1          )                    wherein    rij is the distance between two filler models,    ϵLJ is a coefficient for the intensity of the potential between the filler models, and    σLJ corresponds to the diameter of the filler models.
Heretofore, the above-mentioned parameters σLJ and ϵLJ have been determined by an operator based on his/her intuition and experience, therefore, it is difficult to perform the simulation with high accuracy.