Nanoparticles confined to a spherical surface in the presence of an external field: Interaction forces and induced...

The structural response of a set of charged nanoparticles confined to move on a spherical surface under the influence of an external field is studied by Brownian Dynamics (BD) simulations and by an integral equation approach (IEA). Considering an identical nanoparticle as the source of the external field, we analyze the force exerted by the N confined particles on the external one, as well as the corresponding potential energy, focusing on their dependence on the distance of the external particle to the center of the sphere r₀. The connection of the force and potential to the equilibrium local distribution of the adsorbed particles, that is, the microstructure within the spherical monolayer induced by the external nanoparticle, which is also dependent on r₀, is elucidated by this analysis. It is found that the external particle needs to surmount a considerable potential barrier when moving toward the spherical surface, although much smaller than the one generated by a uniform surface distribution with an equivalent amount of charge. This is understood in terms of the correlation hole within the confined monolayer induced by the external particle. Another interesting conclusion is that the IEA provides an accurate, almost quantitative, description of the main features observed in the BD results, yet it is much less computationally demanding. The connection of these results with the overall chemical equilibrium of charged surfactant nanoparticles in the context of Pickering emulsions is also briefly discussed.