The structures composed of individual polymer nanoparticles are simulated using a molecular dynamics technique. Structures composed of model polyethylene particles consisting of between 3000 and 24,000 monomer units are paired into dimers in a molecular dynamics simulation. The vibrational motion of the polymer particle structures corresponding to the stretching vibration between particles is studied using the time averaged normal coordinate analysis method. The data are fit to an empirical formula based on the expected scaling of the force constants with the surface contact area, yielding a formula which could be extrapolated to large particle structures which can be experimentally generated.