Brownian Diffusion of Hexagonal Boron Nitride Nanosheets and Graphene in Two Dimensions

Two-dimensional (2D) nanomaterials have numerous interesting chemical and physical properties that make them desirable building blocks for the manufacture of macroscopic materials. Liquid-phase processing is a common method for forming macroscopic materials from these building blocks including wet-spinning and vacuum filtration. As such, assembling 2D nanomaterials into ordered functional materials requires an understanding of their solution dynamics. Yet, there are few experimental studies investigating the hydrodynamics of disk-like materials. Herein, we report the lateral diffusion of hexagonal boron nitride nanosheets (h-BN and graphene) in aqueous solution when confined in 2-dimensions. This was done by imaging fluorescent surfactant-tagged nanosheets and visualizing them by using fluorescence microscopy. Spectroscopic studies were conducted to characterize the interactions between h-BN and the fluorescent surfactant, and atomic force microscopy (AFM) was conducted to characterize the quality of the dispersion. The diffusion data under different gap sizes and viscosities displayed a good correlation with Kramers' theory. We propose that the yielded activation energies by Kramers' equation express the magnitude of the interaction between fluorescent surfactant tagged h-BN and glass because the energies remain constant with changing viscosity and decrease with increasing confinement size. The diffusion of graphene presented a similar trend with similar activation energy as the h-BN. This relationship suggests that Kramers' theory can also be applied to simulate the diffusion of other 2D nanomaterials.