Author(s)

Fredy R. Zypman

Department of Physics, Yeshiva University, Manhattan, NY, USA.

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.

Nonlinear Differential Equations, Poisson-Boltzmann equation, Atomic Force Microscopy, Colloidal Interaction, Debye Length

Zypman, F. (2018) Nanoparticle Charge in Fluid from Atomic Force Microscopy Forces within the Nonlinear Poisson-Boltzmann Equation. Journal of Applied Mathematics and Physics, 6, 1315-1323. doi: 10.4236/jamp.2018.66110.