A general theory of Van der Waals forces developed by Lifshitz based on quantum electrodynamics theory is applied in the range R《λ0 (where the Casimir effects may be neglected) to construct Van der Waals attractive potential between identical dielectric molecules in rarefied media in order that the effective attractive potential between the like-molecules (including the repeat units) is offered. A closed form solution for the integral formulation of the attractive potential between like-particles is first obtained based on certain assumptions made in this work. On the basis of the theory of electric polarization, the derived expression in terms of bulk properties is then compared with the well-known London formula, the former differs from the latter only by the factor4. The validity of the effective potential can be verified by testing cases composed of several types of dielectric materials. The computed results are presented in this paper, and comparisons with the results computed by London dispersion formula, as well as the recommended values in virtue of the experimental and theoretical techniques, are also presented. The effective potential of polyethylene is also computed to demonstrate the effectiveness of the developed model, and it is found that the computed well depth fall within a reasonable range of accuracy.