Criteria ruling particle agglomeration

• Dieter Vollath

Beilstein J. Nanotechnol. 2021, 12, 1093–1100, doi:10.3762/bjnano.12.81

• principle of a minimum of free enthalpy. This means that one has to introduce additional criteria for a complete description of the system. The principle of maximum entropy is based on either the Boltzmann entropy or the Gibbs entropy of mixing. In the description of the thermodynamics of sufficiently large

• discussions, for simplicity, instead of the entropy S, a reduced entropy S* = S/k is used. After applying Stirling’s equation, for large numbers of particles, the Boltzmann entropy may be rewritten as: Setting ni/N = pi, one obtains the Gibbs entropy of mixing: Equation 2 and Equation 3 demonstrate that, in

Agglomerates of nanoparticles

• Dieter Vollath

Beilstein J. Nanotechnol. 2020, 11, 854–857, doi:10.3762/bjnano.11.70

• . The exact determination of the size distribution of the agglomerates also gives the maximum size of the agglomerates. These considerations lead to an improved understanding of ensembles of agglomerated nanoparticles. Keywords: agglomeration; enthalpy; entropy; Gibbs entropy; nanoparticles; size

• showed a maximum at i = 1 or i = Nmax. In both cases, the entropy values were identical. Looking at the equation for the Gibbs entropy (Equation 5) one realizes that the summands are independent on the index i. Therefore, one may write For the following discussions, F(1) is attributed to f(1) = 1 and F(2