The size distribution of particles in dispersions is an important property that is usually measured. In many cases, however, theoretical or semi-empirical models are developed to predict these distributions. The models, none the less, come with subtle constraints that limit the regimes of their applicability. At present, there is no systematic approach for identifying these limitations, which, if ignored, can lead to serious flaws. In this work we introduce an entropy-related property of the dispersion, and demonstrate th at this property, which is intensive, and, therefore, independent of system size and configuration, can be used to pinpoint where these limitations lie.
The solutions to the kinetic equation of coagulation are reviewed particularly from the standpoint of their asymptotic behavior. The coagulation equation is studied theoretically by means of a new similarity transformation. For the case of constant collision frequency factor, the transformed spectrum function approaches a self-preserving form after a sufficiently long time, for a certain class of initial distributions. For Brownian coagulation, approximate solutions are derived in closed form for the upper and the lower end of the self-preserving spectrum, and a numerical solution is given for the whole spectrum. The result of this study indicates that the shape of the self-preserving spectrum is greatly influenced by the form of the collision frequency factor.
We report enhancement of the mechanical stability of graphene through a one-step method to disperse gold nanoparticles on the pristine graphene without any added agent.