Extending the excluded volume for percolation threshold estimates in polydisperse systems: The binary disk system

Journal Article · Thu Jun 01 00:00:00 EDT 2017 · Applied Mathematical Modelling

DOI:https://doi.org/10.1016/j.apm.2017.01.046· OSTI ID:1340261

Meeks, Kelsey; Pantoya, Michelle L.; Green, Micah; Berg, Jordan

For dispersions containing a single type of particle, it has been observed that the onset of percolation coincides with a critical value of volume fraction. When the volume fraction is calculated based on excluded volume, this critical percolation threshold is nearly invariant to particle shape. The critical threshold has been calculated to high precision for simple geometries using Monte Carlo simulations, but this method is slow at best, and infeasible for complex geometries. This article explores an analytical approach to the prediction of percolation threshold in polydisperse mixtures. Specifically, this paper suggests an extension of the concept of excluded volume, and applies that extension to the 2D binary disk system. The simple analytical expression obtained is compared to Monte Carlo results from the literature. In conclusion, the result may be computed extremely rapidly and matches key parameters closely enough to be useful for composite material design.

• Research Organization: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: AC04-94AL85000
• OSTI ID: 1340261
• Report Number(s): SAND--2016-12468J; 649809
• Journal Information: Applied Mathematical Modelling, Journal Name: Applied Mathematical Modelling Journal Issue: C Vol. 46; ISSN 0307-904X
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
Binary disks
Excluded volume
Percolation
Percolation threshold estimates