Top

Colloid and Polymer Science

Published in:

01-04-2013 | Original Contribution

Highly accurate and simple analytical approach to nonlinear Poisson–Boltzmann equation

Authors: S. Zhou, G. Zhang

Published in: Colloid and Polymer Science | Issue 4/2013

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

A novel method is suggested to analytically solve a nonlinear Poisson–Boltzmann (NLPB) equation. The method consists chiefly of reducing the NLPB equation to linear PB equation in several segments by approximating a free term of the NLPB equation by piecewise linear functions, and then, solving analytically the linear PB equation in each segment. Superiority of the method is illustrated by applying the method to solve the NLPB equation describing a colloid sphere immersed in an arbitrary valence and mixed electrolyte solution; extensive test indicates that the resulting analytical expressions for both the electrical potential distribution Ψ (r) and surface charge density/surface potential relationship (σ/Ψ ₀) are characterized with two properties that mathematical structures are much simpler than those previously reported and application scope can be arbitrarily wide by adjusting the linear interpolation range. Finally, it is noted that the method is “universal” in that its applications are not limited to the NLPB equation.

previous article Self-assembly behavior of fluorocarbon-end-capped poly(glycerol methacrylate) in aqueous solution

next article A simple way of preparing large compound vesicles loaded with and without silver nanoparticles based on polystyrene-block-polyacrylonitrile

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Available only for authorised users

Krotova MK, Vasilevskaya VV, Makita N, Yoshikawa K, Khokhlov AR (2010) DNA compaction in a crowded environment with negatively charged proteins. Phys Rev Lett 105:128302CrossRef

Yoshida E (2010) Self-assembly of poly(allylamine hydrochloride) through electrostatic interaction with sodium dodecyl sulfate. Colloid Polym Sci 288:1321–1325CrossRef

Elter P, Lange R, Beck U (2011) Electrostatic and dispersion interactions during protein adsorption on topographic nanostructures. Langmuir 27:8767–8775CrossRef

Honig B, Nicholls A (1995) Classical electrostatics in biology and chemistry. Science 268:1144–1149CrossRef

Ohshima H (2011) Electrostatic interaction between two spherical soft particles at small separations. Colloids Surf A Physicochem Eng Asp 379:18–20CrossRef

Ohshima H (1999) Electrostatic repulsion between two parallel plates covered with polymer brush layers. Colloid Polym Sci 277:535–540CrossRef

Hsu J-P, Huang C-H (2010) Electrical potentials of two identical planar, cylindrical, and spherical colloidal particles in a salt-free medium. J Colloid Interface Sci 348:402–407CrossRef

Ohshima H (1999) Electrostatic interaction between a cylinder and a planar surface. Colloid Polym Sci 277:563–569CrossRef

Ohshima H (2010) Approximate expression for the potential energy of the double-layer interaction between two parallel ion-penetrable membranes at small separations in an electrolyte solution. J Colloid Interface Sci 350:249–252CrossRef

10.

Hsu J-P, Huang C-H, Tseng S (2011) Electrical potentials of two identical particles with fixed surface charge density in a salt-free medium. J Colloid Interface Sci 356:550–556CrossRef

11.

Fixman M (1982) The flexibility of polyelectrolyte molecules. J Chem Phys 76:6346–6353CrossRef

12.

Hingerty BE, Ritchie RH, Ferrel TL, Turner JE (1985) Dielectric effects in biopolymers: the theory of ionic saturation revisited. Biopolymers 24:427–439CrossRef

13.

Misra VK, Draper DE (1999) The interpretation of Mg²⁺ binding isotherms for nucleic acids using Poisson–Boltzmann theory. J Mol Biol 294:1135–1147CrossRef

14.

Tang Z, Scriven LE, Davis HT (1992) J Chem Phys 97:9258CrossRef

15.

Goel T, Patra CN, Ghosh SK, Mukherjee T (2010) Three component model of cylindrical electric double layers containing mixed electrolytes: a systematic study by Monte Carlo simulations and density functional theory. J Chem Phys 132:194706CrossRef

16.

Guerrero-Garcia GI, Gonzalez-Tovar E, Chavez-Paez M, Lozada-Cassou M (2010) Overcharging and charge reversal in the electrical double layer around the point of zero charge. J Chem Phys 132:054903CrossRef

17.

Misra VK, Draper DE (2000) Mg²⁺ binding to tRNA revisited: the nonlinear Poisson–Boltzmann model. J Mol Biol 299:813–825CrossRef

18.

Bertonati C, Honig B, Alexov E (2007) Poisson–Boltzmann calculations of nonspecific salt effects on protein-protein binding free energies. Biophys J 92:1891–1899CrossRef

19.

Misra VK, Hecht JL, Sharp KA, Friedman RA, Honig B (1994) Salt effects on protein-DNA interactions. The l-cI repressor and EcoRI endonuclease. J Mol Biol 238:264–280CrossRef

20.

Ben-Tal N, Honig B, Miller C, McLaughlin S (1997) Electrostatic binding of proteins to membranes. Theoretical predictions and experimental results with charybdotoxin and phospholipid vesicles. Biophys J 73:1717–1727CrossRef

21.

Murray D, McLaughlin S, Honig B (2001) The role of electrostatic interactions in the regulation of the membrane association of G protein beta gamma heterodimers. J Biol Chem 276:45153–45159CrossRef

22.

Ohshima H, Healy TW, White LR (1982) Accurate analytic expressions for the surface charge density/surface potential relationship and double-layer potential distribution for a spherical colloidal particle. J Colloid Interface Sci 90:17–26CrossRef

23.

van Aken GA, Lekkerkerker HNW, Overbeek JTG, de Bruyn PL (1990) Adsorption of monovalent ions in thin spherical and cylindrical diffuse electrical double layers. J Phys Chem 94:8468–8472CrossRef

24.

Hsu J-P, Kuo Y-C (1995) Approximate analytical expression for surface potential as a function of surface charge density. J Colloid Interface Sci 170:220–228CrossRef

25.

Ohshima H (1995) Surface charge density/surface potential relationship for a spherical colloidal particle in a solution of general electrolytes. J Colloid Interface Sci 171:525–527CrossRef

26.

Zhou S (1998) An approximate analytic expression for the surface charge density/surface potential relationship for a spherical colloidal particle. J Colloid Interface Sci 208:347–350CrossRef

27.

Tuinier R (2003) Approximate solutions to the Poisson–Boltzmann equation in spherical and cylindrical geometry. J Colloid Interface Sci 258:45–49CrossRef

28.

Lin S-H, Hsu J-P, Tseng S, Chen C-J (2005) Analytical expressions for the electrical potential near planar, cylindrical, and spherical surfaces for symmetric electrolytes. J Colloid Interface Sci 281:255–257CrossRef

29.

Teso A, Filho ED, Neto AA (1997) Solution of the Poisson–Boltzmann equation for a system with four ionic species. J Math Biol 35:814–824CrossRef

30.

Tseng S, Wong N-B, Liu P-C, Hsu J-P (2007) Approximate analytical expressions for the electrical potential in a cavity containing salt-free medium. Langmuir 23:10448–10454CrossRef

31.

Zhou S, Zhang G (2011) Approximate analytical expressions for electrical potential distribution and surface charge density/surface potential relationship for planar, cylindrical, and spherical entities immersed in a general electrolyte solution. Colloids Surf, A Physicochem Eng Asp 385:28–39CrossRef

32.

Zhou S, Wu H Analytical solutions of nonlinear Poisson–Boltzmann equation for colloidal particles immersed in a general electrolyte solution by homotopy perturbation technique. Colloid Polym Sci. doi:10.1007/s00396-012-2622-1

33.

Zhou S, Zhang G Approximate analytic solution of the nonlinear Poisson–Boltzmann equation for spherical colloidal particles immersed in a general electrolyte solution, Colloid Polym Sci doi:10.1007/s00396-012-2683-1

34.

Frenkel D, Smit B (2002) Understanding molecular simulation. Academic, Boston

Title: Highly accurate and simple analytical approach to nonlinear Poisson–Boltzmann equation
Authors: S. Zhou
G. Zhang
Publication date: 01-04-2013
Publisher: Springer-Verlag
Published in: Colloid and Polymer Science / Issue 4/2013
Print ISSN: 0303-402X
Electronic ISSN: 1435-1536
DOI: https://doi.org/10.1007/s00396-012-2805-9

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Other articles of this Issue 4/2013

Synthesis and characterization of well-defined star PLLA with a POSS core and their microspheres for controlled release

Fabrication of polymeric micelles with core–shell–corona structure for applications in controlled drug release

Low molecular weight aromatic compounds possessing nonflammable and flammable characteristics in calcium fluoride nanocomposite matrices after calcination at 800 °C

Generalizing the polymerization conditions for the production of monodisperse polymeric particles via dispersion polymerization

Self-assembly behavior of fluorocarbon-end-capped poly(glycerol methacrylate) in aqueous solution

Xanthan gum-coated soft magnetic carbonyl iron composite particles and their magnetorheology

Premium Partners