Calculation of the friction, diffusion and sedimentation coefficients of nanoplatelets of arbitrary shape

Abstract

We have developed a computational scheme for the calculation of the hydrodynamic properties of nanoplatelets – or flat sheets – of arbitrary shape based on the bead-modeling methodology. The procedure has been implemented in computer codes that interface with the public-domain HYDRO++ program. When the friction coefficient calculated for the model is normalized to the value of an infinitely thin disk having the same surface area, its dependence on thickness normalized to a characteristic length of the platelet surface is very weak and depends just on the shape of the particle and not on its size. This allows for a simplified, general treatment of the dependence on thickness. In addition to examples with various peculiar shapes, we have calculated the friction coefficient of elliptical particles as well as some regular polygons. The results are presented in the form of simple equations relating the friction coefficient to the particle dimensions. The results for the friction coefficient are applied to the formulation of the experimentally measurable diffusion and sedimentation coefficients. The diffusion coefficient has a very weak dependence on thickness so that it can be employed to analyze the geometry of the surface even if the thickness is not precisely determined. However, the sedimentation coefficient depends appreciably on thickness and can be used for its precise determination. A joint analysis of diffusion and sedimentation can provide a complete determination of the nanoplatelet shape, dimensions and mass.