{"title":"A mean field theory for diffusion-limited cluster formation","authors":"M. Muthukumar","doi":"10.1002/polc.5070730115","DOIUrl":null,"url":null,"abstract":"<p>A mean field theory for diffusion-controlled cluster formation is presented by considering the competition among the different protions of a growing cluster for the incoming diffusive particles. This competition is shown to introduce a screening length that depends inversely on the density of the cluster. The Hausdorff dimensionality <i>D</i> of these clusters is shown to be (d<sup>2</sup> + 1)/(d + 1), where <i>d</i>is the eudidean dimensionality. This result is in excellent agreement with that of the computer simulations of Witten and Sander and Meakin. The theory also predicts that the growth of these clusters occurs on their periphery in any <i>d</i>.</p><p>PACS nos: 68.70,+ w, 82.70.Dd, 05.70.-a</p>","PeriodicalId":16867,"journal":{"name":"Journal of Polymer Science: Polymer Symposia","volume":"73 1","pages":"105-112"},"PeriodicalIF":0.0000,"publicationDate":"1985-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/polc.5070730115","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Polymer Science: Polymer Symposia","FirstCategoryId":"1085","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/polc.5070730115","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
Abstract
A mean field theory for diffusion-controlled cluster formation is presented by considering the competition among the different protions of a growing cluster for the incoming diffusive particles. This competition is shown to introduce a screening length that depends inversely on the density of the cluster. The Hausdorff dimensionality D of these clusters is shown to be (d2 + 1)/(d + 1), where dis the eudidean dimensionality. This result is in excellent agreement with that of the computer simulations of Witten and Sander and Meakin. The theory also predicts that the growth of these clusters occurs on their periphery in any d.
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