Nikzad, Shaghayegh, Noshad, Houshyar. (1395). Electrostatic analysis of the charged surface in a solution via the finite element method: The Poisson-Boltzmann theory. نشریه مهندسی عمران امیرکبیر, 48(1), 11-17. doi: 10.22060/eej.2016.627
Shaghayegh Nikzad; Houshyar Noshad. "Electrostatic analysis of the charged surface in a solution via the finite element method: The Poisson-Boltzmann theory". نشریه مهندسی عمران امیرکبیر, 48, 1, 1395, 11-17. doi: 10.22060/eej.2016.627
Nikzad, Shaghayegh, Noshad, Houshyar. (1395). 'Electrostatic analysis of the charged surface in a solution via the finite element method: The Poisson-Boltzmann theory', نشریه مهندسی عمران امیرکبیر, 48(1), pp. 11-17. doi: 10.22060/eej.2016.627
Nikzad, Shaghayegh, Noshad, Houshyar. Electrostatic analysis of the charged surface in a solution via the finite element method: The Poisson-Boltzmann theory. نشریه مهندسی عمران امیرکبیر, 1395; 48(1): 11-17. doi: 10.22060/eej.2016.627

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، 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
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