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.
Highlights
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
We consider the problem of measuring charge of nanoparticles in electrolytes from experimental forces; forces obtained with Atomic Force Microscopy (AFM) fitted with microsphere tips
We derive mathematical expressions and propose experimental methods that help in the understanding of surface charges in solid in electrolytes. This mathematical framework considers a charged micron size AFM spherical tip [1] [2] interacting with a charged nanoparticle, both embedded in an electrolyte
Summary
We consider the problem of measuring charge of nanoparticles in electrolytes from experimental forces; forces obtained with Atomic Force Microscopy (AFM) fitted with microsphere tips. We derive mathematical expressions and propose experimental methods that help in the understanding of surface charges in solid in electrolytes This mathematical framework considers a charged micron size AFM spherical tip [1] [2] interacting with a charged nanoparticle, both embedded in an electrolyte. This force will be shown to be a function of the surface charges at both objects. Measurement of surface charge on particles is routinely done using Titration and Zeta-Potential methods. One permanent problem with this technique is that the slip plane is vaguely defined, which translates into an imprecise value of the charge at the surface These techniques, titration and zeta-potential, are the workhorses of charge measurements for particles in the micron range size and below. We propose a quantitative method for experimentally measuring the nanoparticle charge
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