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

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

doi:10.1016/j.apm.2017.01.046

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

Full Record
Other Related Research

Abstract

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.

Authors:

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

Publication Date:: Thu Jun 01 00:00:00 EDT 2017

Research Org.:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1340261

Report Number(s):: SAND-2016-12468J
Journal ID: ISSN 0307-904X; 649809

Grant/Contract Number:: AC04-94AL85000

Resource Type:: Accepted Manuscript

Journal Name:: Applied Mathematical Modelling

Additional Journal Information:: Journal Volume: 46; Journal Issue: C; Journal ID: ISSN 0307-904X

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; Percolation; Binary disks; Excluded volume; Percolation threshold estimates

Citation Formats


                    Meeks, Kelsey, Pantoya, Michelle L., Green, Micah, and Berg, Jordan. Extending the excluded volume for percolation threshold estimates in polydisperse systems: The binary disk system.  United States: N. p., 2017. 
Web.  doi:10.1016/j.apm.2017.01.046.

Copy to clipboard


                    Meeks, Kelsey, Pantoya, Michelle L., Green, Micah, & Berg, Jordan. Extending the excluded volume for percolation threshold estimates in polydisperse systems: The binary disk system.  United States.  https://doi.org/10.1016/j.apm.2017.01.046

Copy to clipboard


                    Meeks, Kelsey, Pantoya, Michelle L., Green, Micah, and Berg, Jordan. Thu .  
"Extending the excluded volume for percolation threshold estimates in polydisperse systems: The binary disk system".  United States.  https://doi.org/10.1016/j.apm.2017.01.046.  https://www.osti.gov/servlets/purl/1340261.

Copy to clipboard


                    
@article{osti_1340261,

  title        = {Extending the excluded volume for percolation threshold estimates in polydisperse systems: The binary disk system},

  author       = {Meeks, Kelsey and Pantoya, Michelle L. and Green, Micah and Berg, Jordan},

  abstractNote = {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.},

  doi          = {10.1016/j.apm.2017.01.046},

  journal      = {Applied Mathematical Modelling},

  number       = C,

  volume       = 46,

  place        = {United States},

  year         = {Thu Jun 01 00:00:00 EDT 2017},

  month        = {Thu Jun 01 00:00:00 EDT 2017}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1016/j.apm.2017.01.046

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 14 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Similar Records in DOE PAGES and OSTI.GOV collections:

Percolation of binary disk systems: Modeling and theory

Journal Article Meeks, Kelsey ; Tencer, John ; Pantoya, Michelle L. - Physical Review E

The dispersion and connectivity of particles with a high degree of polydispersity is relevant to problems involving composite material properties and reaction decomposition prediction and has been the subject of much study in the literature. This paper utilizes Monte Carlo models to predict percolation thresholds for a two-dimensional systems containing disks of two different radii. Monte Carlo simulations and spanning probability are used to extend prior models into regions of higher polydispersity than those previously considered. A correlation to predict the percolation threshold for binary disk systems is proposed based on the extended dataset presented in this work and comparedmore »« less
Cited by 12
https://doi.org/10.1103/PhysRevE.95.012118

Full Text Available
Searching for low percolation thresholds within amphiphilic polymer membranes: The effect of side chain branching

Journal Article Dorenbos, G., E-mail: dorenbos@ny.thn.ne.jp - Journal of Chemical Physics

Percolation thresholds for solvent diffusion within hydrated model polymeric membranes are derived from dissipative particle dynamics in combination with Monte Carlo (MC) tracer diffusion calculations. The polymer backbones are composed of hydrophobic A beads to which at regular intervals Y-shaped side chains are attached. Each side chain is composed of eight A beads and contains two identical branches that are each terminated with a pendant hydrophilic C bead. Four types of side chains are considered for which the two branches (each represented as [C], [AC], [AAC], or [AAAC]) are splitting off from the 8th, 6th, 4th, or 2nd A bead,more »« less
https://doi.org/10.1063/1.4922156
Electrical properties of random metal-insulator composite near the percolation threshold

Thesis/Dissertation Chen, I G

The electrical properties of three different systems of metal particles randomly dispersed in an insulator host near the percolation threshold were studied. The effects of the matrix phase as well as the metal-particle shape on the conductivity and dielectric properties of these random composites were investigated and compared as a function of metal-volume fraction and as a function of applied external d.c. field. Particle distribution and cluster shape, as well as the phase nature of the constituents of the composite, have been characterized by using electron microscopy (SEM, TEM, STEM), x-ray spectrum (EDS), and computer-aided image analysis. The results showmore »« less
Evolution of exciton states near the percolation threshold in two-phase systems with II-VI semiconductor quantum dots

Journal Article Bondar, N. V., E-mail: jbond@iop.kiev.ua ; Brodyn, M S - Semiconductors

From studies of two-phase systems (borosilicate matrices containing ZnSe or CdS quantum dots), it was found that the systems exhibit a specific feature associated with the percolation phase transition of charge carriers (excitons). The transition manifests itself as radical changes in the optical spectra of both ZnSe and CdS quantum dot systems and by fluctuations of the emission band intensities near the percolation threshold. These effects are due to microscopic fluctuations of the density of quantum dots. The average spacing between quantum dots is calculated taking into account their finite dimensions and the volume fraction occupied by the quantum dotsmore »« less
https://doi.org/10.1134/S1063782610070109
Structure and dynamics of water-in-oil microemulsions near the critical and percolation points

Journal Article Ku, C Y ; Chen, S H ; Rouch, J ; ... - International Journal of Thermophysics

The three-component ionic microemulsion system consisting of AOT/water/decane shows an interesting phase behavior in the vicinity of room temperature. The phase diagram in the temperature-volume fraction (of the dispersed phase) plane exhibits a lower consolute critical point at about 40{degrees}C and 8% volume fraction. A percolation line, starting from the vicinity of the critical point, cuts across the plane, extending to the high-volume fraction side at progressively lower temperatures. This phase behavior can be understood in terms of a system of polydispersed spherical water droplets, each coated by a monolayer of AOT, dispersed in a continuum of oil. These dropletsmore »« less
https://doi.org/10.1007/BF02081280

Similar Records