All Title Author
Keywords Abstract


Interaction Energy between an Atomic Force Microscope Tip and a Charged Particle in Electrolyte

DOI: 10.4236/jamp.2016.411199, PP. 1989-1997

Keywords: Atomic Force Microscopy, Colloids, Electrostatics in Liquids

Full-Text   Cite this paper   Add to My Lib

Abstract:

A variational principle to the nonlinear Poisson-Boltzmann equation (PB) in three dimensions is used to first obtain solutions to the electrostatic potential surrounding a pair of spherical colloidal particles, one of them modeling the tip of an Atomic Force Microscope. Specifically, we consider the PB action integral for the electrostatic potential produced by charged colloidal particles and propose an analytical ansatz solution. This solution introduces the density and its corresponding electrostatic potential parametrically. The PB action is then minimized with respect to the parameter. Polynomial-exponential approximations for the parameters as functions of tip-particle separation and boundary electrostatic potential are obtained. With that information, tip-particle energy-separation curves are computed as well. Finally, based on the shape of the energy-separation curves, we study the stability properties predicted by this theory.

References

[1]  Zypman, F.R. and Eppell, S.J. (2013) Electrostatic Force Curves in Finite-Size-Ion Electrolytes. Langmuir, 29, 11908-11914.
http://dx.doi.org/10.1021/la402344m
[2]  McLaughlin, S. (1989) The Electrostatic Properties of Membranes. Annual Review of Biophysics and Biophysical Chemistry, 18, 113-136.
http://dx.doi.org/10.1146/annurev.bb.18.060189.000553
[3]  Maver, U., Velnar, T., Gaberscek, M., Planinsek, O. and Finsgar, M. (2016) Recent Progressive Use of Atomic Force Microscopy in Biomedical Applications. TrAC Trends in Analytical Chemistry, 80, 96-111.
http://dx.doi.org/10.1016/j.trac.2016.03.014
[4]  Jarmusik, K.E., Eppell, S.J., Lacks, D.J. and Zypman, F.R. (2011) Obtaining Charge Distributions on Geometrically Generic Nanostructures Using Scanning Force Microscopy. Langmuir, 27, 1803-1810.
http://dx.doi.org/10.1021/la104153p
[5]  Napper, D.H. (1970) Colloid Stability. Product R&D, 9, 467-477.
[6]  Israelachvili, J.N. (1997) Intermolecular and Surface Forces. Academic Press, London.
[7]  Birdi, K.S. (2016) Handbook of Surface and Colloid Chemistry. 4th Edition, Chapter 1, CRC Press, Taylor and Francis, London, New York, Boca Raton, 1-144.
[8]  Evans, F. and Wennerström, H. (1994) The Colloidal Domain: Where Physics, Chemistry, Biology, and Technology Meet. VCH Publishers, New York.
[9]  Verwey, J. and Overbeek, J.Th.G. (1984) Theory of Stability of Lyophobic Colloids. Elsevier Publishing Company, New York, 22-30.
[10]  Davis, M.E. and McCammon, J.A. (1990) Electrostatics in Biomolecular Structure and Dynamics. Chemical Reviews, 90, 509-521.
http://dx.doi.org/10.1021/cr00101a005
[11]  Brenner, S.L. and Roberts, R.E. (1973) Variational Solution of the Poisson-Boltzmann Equation for a Spherical Colloidal Particle. The Journal of Physical Chemistry, 77, 2367-2370.
http://dx.doi.org/10.1021/j100639a001
[12]  Bohinc, K., Iglic, A. and Slivnik, T. (2008) Linearized Poisson Boltzmann Theory in Cylindrical Geometry. Elektrotechniskivestnik, 75, 82-84.
[13]  Henderson, D. and Chan, K.Y. (1992) Potential Distribution in the Solution Interface of a Scanning Tunneling Microscope. Journal of Electroanalytical Chemistry, 330, 395-406.
http://dx.doi.org/10.1016/0022-0728(92)80320-4
[14]  Chan, K.Y., Henderson, D. and Stenger, F. (1994) Nonlinear Poisson-Boltzmann Equation in a Model of a Scanning Tunneling Microscope. Numerical Methods for Partial Differential Equations, 10, 689-702.
[15]  Pecina, O., Schmickler, W., Chan, K.Y., Henderson, D.J. (1995) A Model for the Effective Barrier Height Observed with a Scanning Tunneling Microscope. Journal of Electroanalytical Chemistry, 396, 303-307.
http://dx.doi.org/10.1016/0022-0728(95)03853-9
[16]  Zypman, F. (2006) Exact Expressions for Colloidal Plane-Particle Interaction Forces and Energies with Applications to Atomic Force Microscopy. Journal of Physics: Condensed Matter, 18, 2795-2803.
http://dx.doi.org/10.1088/0953-8984/18/10/005
[17]  Jackson, D. (1998) Classical Electrodynamics. John Wiley, New York.
[18]  Hill, L. (1960) An Introduction to Statistical Thermodynamics. Addison Wesley, Reading.
[19]  Israelachvili, J.N. and Adams, G.E. (1978) Measurement of Forces between Two Mica Surfaces in Aqueous Electrolyte Solutions in the Range 0 - 100 nm. Journal of the Chemical Society, Faraday Transactions, 74, 975-1001.
http://dx.doi.org/10.1039/f19787400975

Full-Text

comments powered by Disqus