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Article: Nonlinear Poisson - Boltzmann equation in a model of a scanning tunneling microscope

TitleNonlinear Poisson - Boltzmann equation in a model of a scanning tunneling microscope
Authors
Issue Date1994
PublisherJohn Wiley & Sons, Inc. The Journal's web site is located at http://www.interscience.wiley.com/jpages/0749-159X/
Citation
Numerical Methods For Partial Differential Equations, 1994, v. 10 n. 6, p. 689-702 How to Cite?
AbstractThe nonlinear Poisson - Boltzmann equation is solved in the region between a sphere and a plane, which models the electrolyte solution interface between the tip and the substrate in a scanning tunneling microscope. A finite difference method is used with the domain transformed into bispherical coordinates. Picard iteration with relaxation is used to achieve convergence for this highly nonlinear problem. An adsorbed molecule on the substrate can also be modelled by a superposition of a perturbing potential in a small region of the plane. An approximate analytical solution using a superposition of individual solutions for plane, the adsorbed molecule, and the sphere is also attempted. Results for cases of different potential values on the boundary surfaces and different distances of the sphere from the plane are presented. The results of the numerical method, the approximate analytical method, as well as the previous solutions of the linearized equation are compared.
Persistent Identifierhttp://hdl.handle.net/10722/167526
ISSN
2015 Impact Factor: 0.964
2015 SCImago Journal Rankings: 1.153

 

DC FieldValueLanguage
dc.contributor.authorChan, KwongYuen_US
dc.contributor.authorHenderson, Douglasen_US
dc.contributor.authorStenger, Franken_US
dc.date.accessioned2012-10-08T03:08:04Z-
dc.date.available2012-10-08T03:08:04Z-
dc.date.issued1994en_US
dc.identifier.citationNumerical Methods For Partial Differential Equations, 1994, v. 10 n. 6, p. 689-702en_US
dc.identifier.issn0749-159Xen_US
dc.identifier.urihttp://hdl.handle.net/10722/167526-
dc.description.abstractThe nonlinear Poisson - Boltzmann equation is solved in the region between a sphere and a plane, which models the electrolyte solution interface between the tip and the substrate in a scanning tunneling microscope. A finite difference method is used with the domain transformed into bispherical coordinates. Picard iteration with relaxation is used to achieve convergence for this highly nonlinear problem. An adsorbed molecule on the substrate can also be modelled by a superposition of a perturbing potential in a small region of the plane. An approximate analytical solution using a superposition of individual solutions for plane, the adsorbed molecule, and the sphere is also attempted. Results for cases of different potential values on the boundary surfaces and different distances of the sphere from the plane are presented. The results of the numerical method, the approximate analytical method, as well as the previous solutions of the linearized equation are compared.en_US
dc.languageengen_US
dc.publisherJohn Wiley & Sons, Inc. The Journal's web site is located at http://www.interscience.wiley.com/jpages/0749-159X/en_US
dc.relation.ispartofNumerical Methods for Partial Differential Equationsen_US
dc.titleNonlinear Poisson - Boltzmann equation in a model of a scanning tunneling microscopeen_US
dc.typeArticleen_US
dc.identifier.emailChan, KwongYu:hrsccky@hku.hken_US
dc.identifier.authorityChan, KwongYu=rp00662en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1002/num.1690100605-
dc.identifier.scopuseid_2-s2.0-0028545510en_US
dc.identifier.volume10en_US
dc.identifier.issue6en_US
dc.identifier.spage689en_US
dc.identifier.epage702en_US
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridChan, KwongYu=7406034142en_US
dc.identifier.scopusauthoridHenderson, Douglas=7402988756en_US
dc.identifier.scopusauthoridStenger, Frank=7003354565en_US

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