Abstract
A simple algorithm is presented for obtaining an approximate analytic solution to the cylindrical Poisson-Boltzmann equation for the electric double layer potential distribution in a charged cylindrical narrow pore filled with an electrolyte solution. Agreement with the exact numerical solution is excellent for low-to-moderate values of the pore surface potential when the pore radius is less than the Debye length. The obtained results are thus considerably better approximations than those previously obtained by Martynov and Avdeev (Colloid J 44: 626–632 (1983)). Approximate analytic expressions are also derived for the relationship between the pore surface charge density and the pore surface potential.
References
Derjaguin BV, Landau L (1941) Theory of the stability of strongly charged lyophobic sols and of the adhesion of strongly charged particles in solutions of electrolytes. Acta Physicochim USSR 14:633–662
Verwey EJW, Overbeek JTG (1948) Theory of the stability of lyophobic colloids. Elsevier/Academic Press, Amsterdam
Dukhin SS (1993) Non-equilibrium electric surface phenomena. Adv Colloid Interf Sci 44:1–134
Ohshima H, Furusawa K (eds) (1998) Electrical phenomena at interfaces, fundamentals, measurements, and applications, 2nd edition, revised and expanded. Dekker, New York
Delgado AV (ed) (2000) Electrokinetics and electrophoresis. Dekker, New York
Lyklema J (2005) Fundamentals of interface and colloid science, volume IV, chapter 3. Elsevier/Academic Press, Amsterdam
Ohshima H (2006) Theory of colloid and interfacial electric phenomena. Elsevier/Academic Press, Amsterdam
Ohshima H (2010) Biophysical chemistry of biointerfaces. John Wiley & Sons, Hoboken
Ohshima H (ed) (2012) Electrical phenomena at interfaces and biointerfaces: fundamentals and applications in nano-, bio-, and environmental sciences. John Wiley & Sons, Hoboken
Olivares W, Croxton TL, McQuarrie DA (1980) Electrokinetic flow in a narrow cylindrical capillary. J Phys Chem 84:867–869
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 90:17–26
Martynov GA, Avdeev SM (1983) Solution of the nonlinear Poisson-Boltzmann equation 1. Outer and inner problems for a cylinder. Colloid J 44:626–632 Translated from Kolloidn Zh (1982) 44: 702-708
Olivares W, McQuarrie DA (1985) Comments on the calculation of the potential inside a charged microcapillary. J Phys Chem 89:2966–2967
Hawkins Cwirko E, Carbonell RG (1989) Transport of electrolytes in charged pores: analysis using the method of spatial averaging. J Colloid Interface Sci 129:513–531
Vlachy V, Haymet ADJ (1989) Electrolytes in charged micropores. J Am Chem Soc 111:477–481
van Keulen H, Smit JAM (1992) Analytical approximations for potential profiles in charged micropores originating from the Poisson-Boltzmann equation. J Colloid Interface Sci 151:546–554
Ohshima H (1995) Surface charge density/surface potential relationship for a spherical colloidal particle in a solution of general electrolytes surface charge density/surface potential relationship for a spherical colloidal particle in a solution of general electrolytes. J Colloid Interface Sci 171:525–527
Ohshima H (1998) Surface charge density/surface potential relationship for a cylindrical particle in an electrolyte solution. J Colloid Interface Sci 200:291–297
Lamm G (2003) The Poisson-Boltzmann equation. In: Lipkowitz KB, Larter R, Cundari TR, Boyd DB (eds) Reviews in computational chemistry, Vol 19, chapter 4. John Wiley & Sons, Hoboken, pp. 147–365
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The author declares that he has no conflict of interest.
Source of funding
The author declares no sources of funding.
Rights and permissions
About this article
Cite this article
Ohshima, H. A simple algorithm for the calculation of the electric double layer potential distribution in a charged cylindrical narrow pore. Colloid Polym Sci 294, 1871–1875 (2016). https://doi.org/10.1007/s00396-016-3943-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00396-016-3943-2