TITLE:
Nanoparticle Charge in Fluid from Atomic Force Microscopy Forces within the Nonlinear Poisson-Boltzmann Equation
AUTHORS:
Fredy R. Zypman
KEYWORDS:
Nonlinear Differential Equations, Poisson-Boltzmann equation, Atomic Force Microscopy, Colloidal Interaction, Debye Length
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.6,
June
28,
2018
ABSTRACT: We
consider the problem of measuring the electric charge of nanoparticles immersed
in a fluid electrolyte. We develop a mathematical framework based on the
solution of the nonlinear Poisson-Boltzmann equation to obtain interaction
forces between nanoparticles immersed in a fluid electrolyte and an Atomic
Force Microscopy micro spherical probe. This force-separation information is
shown explicitly to depend on the charge of the nanoparticle. This method overcomes the statistical nature
of extant methods and renders a charge value for an individual single
nanoparticle.