Interaction of Nanoparticles in Electrolyte Solutions

[Image: see text] The interaction between nanoparticles includes several components; however, the most frequently used are electrostatic, caused by overlapping double electrical layers, and London–van der Waals interactions, caused by quantum and thermodynamic fluctuations of electromagnetic fields. Only these two kinds of interaction are considered below. The electrostatic interaction is calculated based on the linearized Poisson–Boltzmann equation for particles with constant electrical potential of the surfaces (constant ζ potentials). An exact solution of the problem is obtained for both identical particles and particles of different sizes. For the London–van der Waals interaction, the screening of static fluctuations and the retardation of electromagnetic fields for the dispersive part of the interaction are taken into account. The total interaction energy for two particles was calculated for a range of possible nanoparticle sizes from 1 to 10(3) nm and electrolyte concentration from 10(–2) to 10(–6) mol/L. The predominance of the London–van der Waals force over the shielded electrostatic repulsion force was found at high electrolyte concentrations in the range from 10(–2) to 10(–3) mol/L at large interparticle distances.