Criteria ruling particle agglomeration

Abstract

Most of the technically important properties of nanomaterials, such as superparamagnetism or luminescence, depend on the particle size. During synthesis and handling of nanoparticles, agglomeration may occur. Agglomeration of nanoparticles may be controlled by different mechanisms. During synthesis one observes agglomeration controlled by the geometry and electrical charges of the particles. Additionally, one may find agglomeration controlled by thermodynamic interaction of the particles in the direction of a minimum of the free enthalpy. In this context, one may observe mechanisms leading to a reduction of the surface energy or controlled by the van der Waals interaction. Additionally, the ensemble may arrange in the direction of a maximum of the entropy. Simulations based on Monte Carlo methods teach that, in case of any energetic interaction of the particles, the influence of the entropy is minor or even negligible. Complementary to the simulations, the extremum of the entropy was determined using the Lagrange method. Both approaches yielded identical result for the particle size distribution of an agglomerated ensemble, that is, an exponential function characterized by two parameters. In this context, it is important to realize that one has to take care of fluctuations of the entropy.

Agglomeration and Aggregation of Nanoparticles

“…There is a strict exponential relationship between the particle size and the number of particles. It can be shown that this relationship is related to a maximum of entropy [10,11]. This exponential relation is valid regardless of the number of iterations.…”

“…Therefore, for these calculations, the particles are not localized; they are just identified by a number. This basic assumption leads to an arrangement characterized by a maximum of entropy, provided that the probability or energy of interaction is neglected [10,11]. As explained in the section 'Theoretical background', this arrangement allows us to consider the interaction between the particles.…”

“…Other papers discuss different criteria based on theoretical considerations or experimental results that rule out agglomeration [8,9]. A different approach is the application of Monte Carlo simulations based on Markov chains [10] or these calculations combined with thermodynamic considerations [11]. Results based on Monte Carlo calculations, with to estimateicle distributions obtained by different gas phase processes, were published by Vollath [12].…”