Extending the excluded volume for percolation threshold estimates in polydisperse systems: The binary disk system
•A new method for prediction of percolation thresholds is presented.•An extension of the concept of excluded volume to polydisperse systems is proposed.•Percolation threshold estimates for the 2D binary disk system. For dispersions containing a single type of particle, it has been observed that the...
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| Veröffentlicht in: | Applied Mathematical Modelling 2017-06, Vol.46 (C), p.116-125 |
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| creator | Meeks, Kelsey Pantoya, Michelle L. Green, Micah Berg, Jordan |
| description | •A new method for prediction of percolation thresholds is presented.•An extension of the concept of excluded volume to polydisperse systems is proposed.•Percolation threshold estimates for the 2D binary disk system.
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. |
| doi_str_mv | 10.1016/j.apm.2017.01.046 |
| format | Article |
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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.</description><subject>Binary disks</subject><subject>Composite materials</subject><subject>Computer simulation</subject><subject>Concentration (composition)</subject><subject>Dispersion</subject><subject>Dispersions</subject><subject>Excluded volume</subject><subject>Extreme values</subject><subject>Geometry</subject><subject>Mathematical analysis</subject><subject>MATHEMATICS AND COMPUTING</subject><subject>Monte Carlo simulation</subject><subject>Particle shape</subject><subject>Percolation</subject><subject>Percolation threshold estimates</subject><subject>Studies</subject><issn>0307-904X</issn><issn>1088-8691</issn><issn>0307-904X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp9kMtOwzAQRSMEEuXxAewsWDeMm8RpYIUqXhISG5DYWY49oS6pndouon_PVO2CFauxZ84d3blZdsEh58DF9SJXwzKfAK9z4DmU4iAbQQH1uIHy4_DP-zg7iXEBABX9Rtnq_iehM9Z9sjRHhj-6Xxs07Nv36yWyzgc2YNC-V8l6R0zAOPe9YRiTXaqEkVnHBt9vjI1ERmRxExMu4w17o4WtdSpsGA2_9oOz7KhTfcTzfT3N3h_u32ZP45fXx-fZ3ctYF02VxkXVKtN0U62piCkXJaimNAWoSVXzUrStRlGpKdG87hRX1DOtKkGjqhsNxWl2udvryamM2ibUc-2dQ50kL0qYCE7Q1Q4agl-t6Sa58OvgyJfkTTHhRS1ERRTfUTr4GAN2cgh0fNhIDnIbv1xIil9u45fAJcVPmtudBunGb4thawGdRmPD1oHx9h_1L_EKj7k</recordid><startdate>201706</startdate><enddate>201706</enddate><creator>Meeks, Kelsey</creator><creator>Pantoya, Michelle L.</creator><creator>Green, Micah</creator><creator>Berg, Jordan</creator><general>Elsevier Inc</general><general>Elsevier BV</general><general>Elsevier</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>OIOZB</scope><scope>OTOTI</scope><orcidid>https://orcid.org/0000-0001-9279-3412</orcidid><orcidid>https://orcid.org/0000000192793412</orcidid></search><sort><creationdate>201706</creationdate><title>Extending the excluded volume for percolation threshold estimates in polydisperse systems: The binary disk system</title><author>Meeks, Kelsey ; Pantoya, Michelle L. ; Green, Micah ; Berg, Jordan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c395t-35bad9f8ccad9681640a94d30a257146bbce65a8c3917fa1a146dba40cea79c03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Binary disks</topic><topic>Composite materials</topic><topic>Computer simulation</topic><topic>Concentration (composition)</topic><topic>Dispersion</topic><topic>Dispersions</topic><topic>Excluded volume</topic><topic>Extreme values</topic><topic>Geometry</topic><topic>Mathematical analysis</topic><topic>MATHEMATICS AND COMPUTING</topic><topic>Monte Carlo simulation</topic><topic>Particle shape</topic><topic>Percolation</topic><topic>Percolation threshold estimates</topic><topic>Studies</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Meeks, Kelsey</creatorcontrib><creatorcontrib>Pantoya, Michelle L.</creatorcontrib><creatorcontrib>Green, Micah</creatorcontrib><creatorcontrib>Berg, Jordan</creatorcontrib><creatorcontrib>Sandia National Lab. 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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.</abstract><cop>New York</cop><pub>Elsevier Inc</pub><doi>10.1016/j.apm.2017.01.046</doi><tpages>10</tpages><orcidid>https://orcid.org/0000-0001-9279-3412</orcidid><orcidid>https://orcid.org/0000000192793412</orcidid><oa>free_for_read</oa></addata></record> |
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| source | Elsevier ScienceDirect Journals; EBSCOhost Business Source Complete; Education Source; EZB-FREE-00999 freely available EZB journals |
| subjects | Binary disks Composite materials Computer simulation Concentration (composition) Dispersion Dispersions Excluded volume Extreme values Geometry Mathematical analysis MATHEMATICS AND COMPUTING Monte Carlo simulation Particle shape Percolation Percolation threshold estimates Studies |
| title | Extending the excluded volume for percolation threshold estimates in polydisperse systems: The binary disk system |
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