Criteria ruling particle agglomeration.

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.

Agglomerates of nanoparticles.

Nanoparticles tend to agglomerate. The process of agglomeration is ruled by thermodynamics. Depending on the sign of the enthalpy of interaction, ensembles consist of (repelling) poorly agglomerated or (attracting) highly agglomerated particles. For these two cases different distribution functions for the agglomerates were found. The size distribution of the agglomerates is ruled by the maximum of the entropy of the ensemble of agglomerates, which is calculated using Gibbs formula of entropy. 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.

Surface Energy of Au Nanoparticles Depending on Their Size and Shape.

Motivated by often contradictory literature reports on the dependence of the surface energy of gold nanoparticles on the variety of its size and shape, we performed an atomistic study combining molecular mechanics and ab initio calculations. We show that, in the case of Au nanocubes, their surface energy converges to a value for ( 0 0 1 ) facets of bulk crystals. A fast convergence to a single valued surface energy is predicted also for nanospheres. However, the value of the surface energy is larger in this case than that of any low-index surface facet of bulk Au crystal. This fact can be explained by the complex structure of the surface with an extensive number of broken bonds due to edge and corner atoms. A similar trend was obtained also for the case of cuboctahedrons. Since the exact surface area of the nanoparticles is an ill-defined quantity, we have introduced the surface-induced excess energy and discuss this quantity as a function of (i) number of atoms forming the nano-object or (ii) characteristic size of the nano-object. In case (i), a universal power-law behaviour was obtained independent of the nanoparticle shape. Importantly, we show that the size-dependence of the surface is hugely reduced if the surface area correction is considered due to its expansion by the electronic cloud, a phenomenon specifically important for small nanoparticles.

Energy distribution in an ensemble of nanoparticles and its consequences.

In general, considerations about isothermal ensembles of nanoparticles assume that each one of the particles is at the same temperature. However, there are experimental indications that such an isothermal ensemble does not exist. Therefore, it is advised to analyze phenomena connected to the temperature distribution within such an ensemble. The detailed analysis presented in this work led to the assumption of a normal distribution of the energy within an ensemble of nanoparticles where basic properties of such an "isothermal" ensemble can be predicted. The width of the energy distribution decreases with increasing particle size. This particle size dependence of the energy per particle controls phase fluctuations in the vicinity of the transformation temperature. Additionally, applying the temperature profile of a phase transformation, it is possible to calculate the particle size distribution of the ensemble with a precision within the scattering range of the experimental data. This is the most important application of this analysis and coincidently a proof of the basic premise. The basic quantity determining the width of the energy distribution is the heat capacity of the particles. For these calculations, bulk data for the heat capacity were successfully applied. This leads to the conclusion that the data for heat capacity of nanoparticles are very close to the bulk values.

Surface energy of nanoparticles - influence of particle size and structure.

The surface energy, particularly for nanoparticles, is one of the most important quantities in understanding the thermodynamics of particles. Therefore, it is astonishing that there is still great uncertainty about its value. The uncertainty increases if one questions its dependence on particle size. Different approaches, such as classical thermodynamics calculations, molecular dynamics simulations, and ab initio calculations, exist to predict this quantity. Generally, considerations based on classical thermodynamics lead to the prediction of decreasing values of the surface energy with decreasing particle size. This phenomenon is caused by the reduced number of next neighbors of surface atoms with decreasing particle size, a phenomenon that is partly compensated by the reduction of the binding energy between the atoms with decreasing particle size. Furthermore, this compensating effect may be expected by the formation of a disordered or quasi-liquid layer at the surface. The atomistic approach, based either on molecular dynamics simulations or ab initio calculations, generally leads to values with an opposite tendency. However, it is shown that this result is based on an insufficient definition of the particle size. A more realistic definition of the particle size is possible only by a detailed analysis of the electronic structure obtained from initio calculations. Except for minor variations caused by changes in the structure, only a minor dependence of the surface energy on the particle size is found. The main conclusion of this work is that surface energy values for the equivalent bulk materials should be used if detailed data for nanoparticles are not available.

Au55, a stable glassy cluster: results of ab initio calculations.

Structure and properties of small nanoparticles are still under discussion. Moreover, some thermodynamic properties and the structural behavior still remain partially unknown. One of the best investigated nanoparticles is the Au55 cluster, which has been analyzed experimentally and theoretically. However, up to now, the results of these studies are still inconsistent. Consequently, we have carried out the present ab initio study of the Au55 cluster, using up-to-date computational concepts, in order to clarify these issues. Our calculations have confirmed the experimental result that the thermodynamically most stable structure is not crystalline, but it is glassy. The non-crystalline structure of this cluster was validated by comparison of the coordination numbers with those of a crystalline cluster. It was found that, in contrast to bulk materials, glass formation is connected to an energy release that is close to the melting enthalpy of bulk gold. Additionally, the surface energy of this cluster was calculated using two different theoretical approaches resulting in values close to the surface energy for bulk gold. It shall be emphasized that it is now possible to give a confidence interval for the value of the surface energy.

Bifunctional nanocomposites with magnetic and luminescence properties.

Many applications require nanoparticles that exhibit high magnetic moment and luminescence. Compounds exhibiting this combination of properties do not exist. However, this combination of properties may be obtained by nanocomposites. There are two possible configurations for these composites: the core-shell design, leading to the smallest composite particles, and agglomerates containing separated particles with the properties in question. The magnetic core is, in most cases, maghemite or magnetite, whereas the luminescence carrier is either an organic molecule or an inorganic quantum dot. One of the basic problems in designing such composites, to be overcome by the appropriate layout choice, is the potential incompatibility between the magnetic core and the lumophore. Experimentally realized solutions of these problems are presented.