TY - JOUR
T1 - Extending the excluded volume for percolation threshold estimates in polydisperse systems
T2 - The binary disk system
AU - Meeks, Kelsey
AU - Pantoya, Michelle L.
AU - Green, Micah
AU - Berg, Jordan
N1 - Publisher Copyright:
© 2017
PY - 2017/6
Y1 - 2017/6
N2 - 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 paper 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. The result may be computed extremely rapidly and matches key parameters closely enough to be useful for composite material design.
AB - 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 paper 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. The result may be computed extremely rapidly and matches key parameters closely enough to be useful for composite material design.
KW - Binary disks
KW - Excluded volume
KW - Percolation
KW - Percolation threshold estimates
UR - http://www.scopus.com/inward/record.url?scp=85017575082&partnerID=8YFLogxK
U2 - 10.1016/j.apm.2017.01.046
DO - 10.1016/j.apm.2017.01.046
M3 - Article
AN - SCOPUS:85017575082
VL - 46
SP - 116
EP - 125
JO - Applied Mathematical Modelling
JF - Applied Mathematical Modelling
SN - 0307-904X
ER -