In the Present Contribution the Atomistic Structure of the Polymer Melt at 300 K Is Simulated by Means of Molecular Dynamics. the Agreement with an Experimental Density Is Obtained with a Deviation Lower than 1%. the Free Volume Is Analyzed in 1,000 Structures and 6.5 X 108 Cubic Å of Molecular Space. a Model for the Free Volume Cavities Is Proposed. in the Model the Size and Number of the Cavities Can Be Scaled by Three Parameters: Probe Radius, Cavity Depth and Cavity Threshold Volume. the Experimental Values of the Nano-Sized Cavity Volumes as Well as Ortho-Positronium Lifetimes Are Obtained, as Compared to Models with Cylindrical and Spherical Geometry. a Typical Value of the Number Density of Free Volume Cavities at 0.001 Å-3 Is Obtained. the Cavities Have Typically Elongated Shape with a Side-to-Length Ratio 1:2.