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The mean nearest surface for polydispersed sphere radii, lP (r), can be estimated from multiple iterations of void-void spacing measurements. As described in the previous section, 1000 spheres are chosen at regular intervals from the original sorted list of sphere radii. This list also corresponds to the cumulative distribution function of the sphere radii. If the void-void measurements are repeated from many system iterations, averaging the radii in the 500 th entry, for example, will yield an unbiased estimate of the 50 th percentile of the sphere radii distribution. Likewise, the corresponding nearest sphere surface distance in the 500 th entry can be averaged, yielding an estimate of the mean nearest surface for the 50 th percentile.
This process is repeated for all 1000 entries of both sphere radii and void-void distances. Upon averaging over all system iterations, there are 1000 averaged radii and 1000 averaged void-void spacings. The 1000 averaged void-void spacings plotted against the corresponding 1000 averaged radii represents an estimate of lP (r).