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Electrostatic analysis of the charged surface in a solution via the finite element method: The Poisson-Boltzmann theory | ||
| AUT Journal of Electrical Engineering | ||
| مقاله 2، دوره 48، شماره 1، شهریور 2016، صفحه 11-17 اصل مقاله (589.82 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22060/eej.2016.627 | ||
| نویسندگان | ||
| Shaghayegh Nikzad1؛ Houshyar Noshad* 2 | ||
| 1Department of Energy Engineering and Physics, Amirkabir University of Technology (Tehran Polytechnic), Hafez Avenue, Tehran, Iran | ||
| 2Amirkabir University of Technology | ||
| چکیده | ||
| Electrostatic potential as well as the local volume charge density are computed for a macromolecule by solving the Poisson-Boltzmann equation (PBE) using the finite element method (FEM). As a verification, our numerical results for a one dimensional PBE, which corresponds to an infinite-length macromolecule, are compared with the existing analytical solution and good agreement is found. As a macromolecule has a rod-like shape with a finite length, a much more real case is considered, which leads to a two dimensional PBE. Furthermore, it is demonstrated that the potential and charge density decrease as the distance from the axis of the macromolecule increases. Moreover, it is concluded that the absolute value of the electrostatic field obtained from the nonlinear PBE subject to the boundary condition with a fixed charge differs from that of the linear PBE at fixed potential by an order of magnitude in the vicinity of the finite rod-like macromolecule. On the other hand, excellent agreement is observed between the electric fields calculated from the aforementioned equations at far distances. | ||
| کلیدواژهها | ||
| Poisson-Boltzmann equation؛ finite element method؛ polyelectrolyte؛ reduced electrostatic potential | ||
| عنوان مقاله [English] | ||
| Electrostatic analysis of the charged surface in a solution via the finite element method: The Poisson-Boltzmann theory | ||
| نویسندگان [English] | ||
| Shaghayegh Nikzad1؛ Houshyar Noshad2 | ||
| 1Department of Energy Engineering and Physics, Amirkabir University of Technology (Tehran Polytechnic), Hafez Avenue, Tehran, Iran | ||
| 2Amirkabir University of Technology | ||
| چکیده [English] | ||
| Electrostatic potential as well as the local volume charge density are computed for a macromolecule by solving the Poisson-Boltzmann equation (PBE) using the finite element method (FEM). As a verification, our numerical results for a one dimensional PBE, which corresponds to an infinite-length macromolecule, are compared with the existing analytical solution and good agreement is found. As a macromolecule has a rod-like shape with a finite length, a much more real case is considered, which leads to a two dimensional PBE. Furthermore, it is demonstrated that the potential and charge density decrease as the distance from the axis of the macromolecule increases. Moreover, it is concluded that the absolute value of the electrostatic field obtained from the nonlinear PBE subject to the boundary condition with a fixed charge differs from that of the linear PBE at fixed potential by an order of magnitude in the vicinity of the finite rod-like macromolecule. On the other hand, excellent agreement is observed between the electric fields calculated from the aforementioned equations at far distances. | ||
| کلیدواژهها [English] | ||
| Poisson-Boltzmann equation, finite element method, polyelectrolyte, reduced electrostatic potential | ||
| مراجع | ||
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