Period Boundary Conditions Illustrated


This is an image of a simulation cube of nitrogen (in cyan) molecules dissolved in poly(dimethylesiloxane) polymer and its periodic neighboring images, viewed head-on. This polymer is amorphous - on the length scale of the primary simulation cube (the central square in the figure), there is no crystallographic order in the structure of the polymer matrix. The surrounding squares (8 of them seen in this head-on view - in 3D, there are a total of 26 neighboring cubes) are exact replicas of the central cube. This is the so-called Periodic Boundary Condition.

On length scales larger than the side length of the primary simulation cube, the structure is exactly periodic, like a crystal. If we are simulating a crystalline system, this is realistic at both short and long length scales. For this amorphous matrix, we must discard the structural information at long length scales, because we have introduced an artificial crystalline order. Structural information on the short length scale, however, is still valid and can be very informative.

Notice that in this polymer simulation, there is only one unique chain conformation (it is highlighted). As it traces a path outside of it primary cube, an "image" chain traces a path into the primary cube. For the purposes of characterizing the simulation, the image chain segment is considered to be from a different polymer molecule.


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