An electric charge standard with nanoscale resolution is created using the known charge distribution of a single tobacco mosaic virus coat protein combined with the known packing of these proteins in the virus capsid. This advances the ability to measure charge on nanometric samples. Experimental atomic force microscope (AFM) force−distance curves are collected under aqueous conditions with controlled pH and ion concentration. A mathematical model that considers a polarizable dielectric tip immersed in an electrolyte is used to obtain charge density from the AFM measurements. Interactions between the tip and the sample are modeled using theory that includes monopolar electrostatic interactions, dipolar interactions, screening from both the dielectric nature of ambient water and solvated ions as described by the linear Poisson−Boltzmann equation, and hard-core repulsion. It is found that the tip charge density changes on a timescale of hours requiring recalibration of the tip for experiments lasting more than an hour. As an example of how a chargecalibrated tip may be used, the surface charge densities on 20 individual carboxylate-modified polystyrene (PS) beads are measured. The average of these AFM-measured bead charge densities is compared with the value obtained from conventional titration combined with electron microscopy. The two values are found to agree within 20%. While the comparison demonstrates similarity of the two charge measurements, hypotheses are put forward as to why the two techniques might be expected not to provide identical mean charge densities. The considerations used to build these hypotheses thus underscore the relevance of the method performed here if charge information is required on individual nanoparticles.
A theory is presented to obtain surface charge density on nanoscale objects from data in the snap-to-contact portion of an atomic force microscope force–separation curve. The mathematical model takes into account the tip’s dielectric constant using the Self-Consistent Sum of Dipoles theory which includes the charge–charge interaction and the charge–dipole interaction with electrolyte-induced exponentially decaying screening, Debye and London dipolar force, and fluid viscosity including confined fluid layers to account for energy dissipation. Using previously published experimental data, the mathematical model is applied to measure the surface charge density on an individual nanoscale amine-modified polystyrene bead immobilized on the basal plane of highly oriented pyrolytic graphite in buffered aqueous solution. Within the experimental uncertainty, the magnitude of the charge density on a single bead obtained using the new method falls within the distribution of values determined by the manufacturer using titration and electron microscopy.
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