Nearest neighbor distances in uniform–random poly-dispersed microstructures

Nearest neighbor distributions are systematically studied in uniform–random microstructures containing impenetrable poly-dispersed spherical particles using computer simulation. The simulations are based on random sequential adsorption (RSA) algorithm. The computed nearest neighbor distance distributions and the mean nearest neighbor distances are unbiased and free of any edge effects. In the simulated microstructures, there are no spatial correlations among the spheres of different sizes. It is shown that the mean nearest neighbor distance 〈D〉 depends only on the sphere volume fraction f, number density NV, and coefficient of variation (CV) of the sphere size distribution CV; it is not sensitive to the other attributes of the size distribution function such as skewness. The mean nearest neighbor distance can be calculated using the following simple equation, which is deduced from large number of simulation. 〈 D 〉 N V 1 / 3 = K 1 + B f f 0 2 / 3 − ( 1 − exp ( − C V ⋅ f ) ) where K = ( 4 / 3 π ) − 1 / 3 Γ ( 4 / 3 ) ≈ 0.55396 , B = 2 − 1 / 6 ( 4 3 π ) − 1 / 3 Γ ( 4 3 ) − 1 ≈ 1.02625 , and f0 is the volume fraction in a closed pack structure (i.e., π / 18 or ∼0.74).