پیوندهای مفید
آمار
| تعداد نشریات | 7 |
| تعداد شماره‌ها | 399 |
| تعداد مقالات | 5,389 |
| تعداد مشاهده مقاله | 5,288,194 |
| تعداد دریافت فایل اصل مقاله | 4,882,937 |
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 | ||
|
[1] Holm, C., Kekicheff, P., Podgornik, R.,“Electrostatic Effects in Soft Matter and Biophysics”, Kluwer Academic, Dordrecht, 2001. [2] Poon, W.C.K., Andelman, D., “Soft condensed matter physics in molecular and cell biology”, Taylor & Francis, New York: London, 2006. [3] Oosawa, F., “Polyelectrolytes”, Marcel Dekker, New York, 1971. [4] Naji, A., Kanduc, M., Netz, R.R., Podgornik, R., “Exotic Electrostatics: Unusual Features of Electrostatic Interactions between Macroions. In:Andelman D and Reiter G (eds) Understanding Soft Condensed Matter via Modeling and Computation”,World Scientific, Singapore, 2010. [5] Mandel, M., “The electric polarization of rod-like,charged Macromolecules”, J. Mol. Phys, 4: pp 489- 496, 1961. [6] French, R.H et al., “Long range interactions innanoscale science”, Rev. Mod. Phys, 82: pp 1887- 1944, 2010. [7] Li, Y., Yang, M.J., She, Y., “Humidity sensitiveproperties of crosslinked and quaternized Poly (4- vinylpyridine-co-butyl methacrylate)”, Sensors andActuators B, 107: pp 252–257, 2005. [8] Harrey, P.M., Ramsey, B.J., Evans, P.S.A., Harrison,D.J., “Capacitive-type humidity sensors fabricated using the offset lithographic printing process”,Sensors and Actuators B, 87: pp 226–232, 2002. [9] Hossain, R., Adamiak, K., “Dynamic properties ofthe electric double layer in electrolytes”, J. Electrost, 71: pp 829-838, 2010. [10] Honig, B., Nicholls, A., “Classical electrostatics inbiology and chemistry”, Science, 268: pp 1144- 1149, 1995. [11] Rocchia, W., Alexov, E., Honig, B., “Extending theApplicability of the Nonlinear Poisson−Boltzmann Equation: Multiple Dielectric Constants andMultivalent Ions”, J. Phys. Chem, 105: pp 6507- 6514, 2001. [12] Butt, H-J., Graf, K., Kappl, M., “Physics andChemistry of Interfaces”, Weinheim: Wiley-VCH, 2003. [13] Israelachvili, J.N., “Intermolecular and SurfaceForces: With Applications to Colloidal and Biological Systems”, Academic Press, London,1985. [14] Vander Vorst, A., Rosen, A., Kotsuka, Y.,“RF/Microwave Interaction with BiologicalTissues”, IEEE Press, 2006. [15] Shestakov, A. I., Milovich, J. L., Noy, A., “Solutionof the nonlinear Poisson–Boltzmann equation using pseudo-transient continuation and the finite elementmethod”, J. Colloid Interface Sci, 247: pp 62–79, 2002. [16] Chapot, D., Bocquet, L., Trizac, E., “Electrostaticpotential around charged finite rod-like macromolecules: nonlinear Poisson–Boltzmann theory”, J. Colloid Interface Sci, 285: pp 609-618, 2005. [17] Sadiku, M.N.O., “A simple introduction to finite element analysis of electromagnetic problems,” IEEE Trans. Educ, 32: pp 85–93, 1989. [18] Le Bret, M., Zimm, B.H., “Distribution of counter ions around a cylindrical polyelectrolyte and Manning‟s condensation theory”, Biopolymers, 23: pp 287-312, 1984. [19] Zangwill, A., “Modern electrodynamics”, Cambridge University Press, 2012. [20] Yoshida, M., Kikuchi, K., Maekawa, T., Watanabe, H., “Electric polarization of rod-like polyions investigated by Monte Carlo simulations”, J. Phys. Chem, 96: pp 2365-2371, 1992. [21] Washizu, H., Kikuchi, K., “Electric polarizability of DNA in aqueous salt solution”, J. Phys. Chem. B, 110: pp 2855-2861, 2006. [22] Deserno, M., Holm, C., May, S., “The fraction of condensed counter ions around a charged rod: Comparison of Poisson-Boltzmann theory and computer simulations”, Macromolecules, 33: pp 199-206, 2000. [23] Fuoss, R., Katchalsky, A., Lifson, S., “The potential of an infinite rod-like molecule and the distribution of the counter ions”, Proc Natl Acad Sci (Wash), 37: pp 579-589, 1951. [24] Alfrey, T., Berg, P., Morawetz, H., “The Counter ion Distribution in Solutions of Rod-Shaped Polyelectrolytes”, J. Polym. Sci, 7: pp 543-547, 1951. [25] Bocquet, L., Trizac, E., Aubouy, M., “Effective charge saturation in colloidal suspensions”, J. Chem. Phys, 117: pp 8138-8152, 2002. [26] Trizac, E., Bocquet, L., Aubouy, M., “Simple approach for charge renormalization in highly charged macroions”, Phys. Rev. Lett, 89: pp 248301(1)-4, 2002. | ||
|
آمار تعداد مشاهده مقاله: 1,628 تعداد دریافت فایل اصل مقاله: 1,704 |
||