Impact of defects on percolation in random sequential adsorption of linear k-mers on square lattices.
Identifieur interne : 001701 ( PubMed/Curation ); précédent : 001700; suivant : 001702Impact of defects on percolation in random sequential adsorption of linear k-mers on square lattices.
Auteurs : Yuri Yu Tarasevich [Russie] ; Valeri V. Laptev [Russie] ; Nikolai V. Vygornitskii [Ukraine] ; Nikolai I. Lebovka [Ukraine]Source :
- Physical review. E, Statistical, nonlinear, and soft matter physics [ 1550-2376 ] ; 2015.
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Abstract
The effect of defects on the percolation of linear k-mers (particles occupying k adjacent sites) on a square lattice is studied by means of Monte Carlo simulation. The k-mers are deposited using a random sequential adsorption mechanism. Two models L(d) and K(d) are analyzed. In the L(d) model it is assumed that the initial square lattice is nonideal and some fraction of sites d is occupied by nonconducting point defects (impurities). In the K(d) model the initial square lattice is perfect. However, it is assumed that some fraction of the sites in the k-mers d consists of defects, i.e., is nonconducting. The length of the k-mers k varies from 2 to 256. Periodic boundary conditions are applied to the square lattice. The dependences of the percolation threshold concentration of the conducting sites p(c) vs the concentration of defects d are analyzed for different values of k. Above some critical concentration of defects d(m), percolation is blocked in both models, even at the jamming concentration of k-mers. For long k-mers, the values of d(m) are well fitted by the functions d(m)∝k(m)(-α)-k(-α) (α=1.28±0.01 and k(m)=5900±500) and d(m)∝log(10)(k(m)/k) (k(m)=4700±1000) for the L(d) and K(d) models, respectively. Thus, our estimation indicates that the percolation of k-mers on a square lattice is impossible even for a lattice without any defects if k⪆6×10(3).
DOI: 10.1103/PhysRevE.91.012109
PubMed: 25679572
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Laptev</name><affiliation wicri:level="1"><nlm:affiliation>Astrakhan State University, 414056 Astrakhan, Russia and Astrakhan State Technical University, 414056 Astrakhan, Russia.</nlm:affiliation><country xml:lang="fr">Russie</country><wicri:regionArea>Astrakhan State University, 414056 Astrakhan, Russia and Astrakhan State Technical University, 414056 Astrakhan</wicri:regionArea></affiliation></author><author><name sortKey="Vygornitskii, Nikolai V" sort="Vygornitskii, Nikolai V" uniqKey="Vygornitskii N" first="Nikolai V" last="Vygornitskii">Nikolai V. Vygornitskii</name><affiliation wicri:level="1"><nlm:affiliation>F. D. Ovcharenko Institute of Biocolloidal Chemistry, National Academy of Sciences of Ukraine, 03142 Kiev, Ukraine.</nlm:affiliation><country xml:lang="fr">Ukraine</country><wicri:regionArea>F. D. Ovcharenko Institute of Biocolloidal Chemistry, National Academy of Sciences of Ukraine, 03142 Kiev</wicri:regionArea></affiliation></author><author><name sortKey="Lebovka, Nikolai I" sort="Lebovka, Nikolai I" uniqKey="Lebovka N" first="Nikolai I" last="Lebovka">Nikolai I. Lebovka</name><affiliation wicri:level="1"><nlm:affiliation>F. D. Ovcharenko Institute of Biocolloidal Chemistry, National Academy of Sciences of Ukraine, 03142 Kiev, Ukraine.</nlm:affiliation><country xml:lang="fr">Ukraine</country><wicri:regionArea>F. D. Ovcharenko Institute of Biocolloidal Chemistry, National Academy of Sciences of Ukraine, 03142 Kiev</wicri:regionArea></affiliation></author></analytic><series><title level="j">Physical review. E, Statistical, nonlinear, and soft matter physics</title><idno type="eISSN">1550-2376</idno><imprint><date when="2015" type="published">2015</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Adsorption</term><term>Models, Theoretical</term><term>Monte Carlo Method</term></keywords><keywords scheme="KwdFr" xml:lang="fr"><term>Adsorption</term><term>Modèles théoriques</term><term>Méthode de Monte-Carlo</term></keywords><keywords scheme="MESH" xml:lang="en"><term>Adsorption</term><term>Models, Theoretical</term><term>Monte Carlo Method</term></keywords><keywords scheme="MESH" xml:lang="fr"><term>Adsorption</term><term>Modèles théoriques</term><term>Méthode de Monte-Carlo</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">The effect of defects on the percolation of linear k-mers (particles occupying k adjacent sites) on a square lattice is studied by means of Monte Carlo simulation. The k-mers are deposited using a random sequential adsorption mechanism. Two models L(d) and K(d) are analyzed. In the L(d) model it is assumed that the initial square lattice is nonideal and some fraction of sites d is occupied by nonconducting point defects (impurities). In the K(d) model the initial square lattice is perfect. However, it is assumed that some fraction of the sites in the k-mers d consists of defects, i.e., is nonconducting. The length of the k-mers k varies from 2 to 256. Periodic boundary conditions are applied to the square lattice. The dependences of the percolation threshold concentration of the conducting sites p(c) vs the concentration of defects d are analyzed for different values of k. Above some critical concentration of defects d(m), percolation is blocked in both models, even at the jamming concentration of k-mers. For long k-mers, the values of d(m) are well fitted by the functions d(m)∝k(m)(-α)-k(-α) (α=1.28±0.01 and k(m)=5900±500) and d(m)∝log(10)(k(m)/k) (k(m)=4700±1000) for the L(d) and K(d) models, respectively. Thus, our estimation indicates that the percolation of k-mers on a square lattice is impossible even for a lattice without any defects if k⪆6×10(3).</div></front></TEI><pubmed><MedlineCitation Status="MEDLINE" Owner="NLM"><PMID Version="1">25679572</PMID><DateCompleted><Year>2016</Year><Month>01</Month><Day>04</Day></DateCompleted><DateRevised><Year>2015</Year><Month>02</Month><Day>14</Day></DateRevised><Article PubModel="Print-Electronic"><Journal><ISSN IssnType="Electronic">1550-2376</ISSN><JournalIssue CitedMedium="Internet"><Volume>91</Volume><Issue>1</Issue><PubDate><Year>2015</Year><Month>Jan</Month></PubDate></JournalIssue><Title>Physical review. E, Statistical, nonlinear, and soft matter physics</Title><ISOAbbreviation>Phys Rev E Stat Nonlin Soft Matter Phys</ISOAbbreviation></Journal><ArticleTitle>Impact of defects on percolation in random sequential adsorption of linear k-mers on square lattices.</ArticleTitle><Pagination><MedlinePgn>012109</MedlinePgn></Pagination><Abstract><AbstractText>The effect of defects on the percolation of linear k-mers (particles occupying k adjacent sites) on a square lattice is studied by means of Monte Carlo simulation. The k-mers are deposited using a random sequential adsorption mechanism. Two models L(d) and K(d) are analyzed. In the L(d) model it is assumed that the initial square lattice is nonideal and some fraction of sites d is occupied by nonconducting point defects (impurities). In the K(d) model the initial square lattice is perfect. However, it is assumed that some fraction of the sites in the k-mers d consists of defects, i.e., is nonconducting. The length of the k-mers k varies from 2 to 256. Periodic boundary conditions are applied to the square lattice. The dependences of the percolation threshold concentration of the conducting sites p(c) vs the concentration of defects d are analyzed for different values of k. Above some critical concentration of defects d(m), percolation is blocked in both models, even at the jamming concentration of k-mers. For long k-mers, the values of d(m) are well fitted by the functions d(m)∝k(m)(-α)-k(-α) (α=1.28±0.01 and k(m)=5900±500) and d(m)∝log(10)(k(m)/k) (k(m)=4700±1000) for the L(d) and K(d) models, respectively. Thus, our estimation indicates that the percolation of k-mers on a square lattice is impossible even for a lattice without any defects if k⪆6×10(3).</AbstractText></Abstract><AuthorList CompleteYN="Y"><Author ValidYN="Y"><LastName>Tarasevich</LastName><ForeName>Yuri Yu</ForeName><Initials>YY</Initials><AffiliationInfo><Affiliation>Astrakhan State University, 414056 Astrakhan, Russia.</Affiliation></AffiliationInfo></Author><Author ValidYN="Y"><LastName>Laptev</LastName><ForeName>Valeri V</ForeName><Initials>VV</Initials><AffiliationInfo><Affiliation>Astrakhan State University, 414056 Astrakhan, Russia and Astrakhan State Technical University, 414056 Astrakhan, Russia.</Affiliation></AffiliationInfo></Author><Author ValidYN="Y"><LastName>Vygornitskii</LastName><ForeName>Nikolai V</ForeName><Initials>NV</Initials><AffiliationInfo><Affiliation>F. D. Ovcharenko Institute of Biocolloidal Chemistry, National Academy of Sciences of Ukraine, 03142 Kiev, Ukraine.</Affiliation></AffiliationInfo></Author><Author ValidYN="Y"><LastName>Lebovka</LastName><ForeName>Nikolai I</ForeName><Initials>NI</Initials><AffiliationInfo><Affiliation>F. D. 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