Wolfram Vogelsberger

Thermodynamics of finite systems: a possibility for interpretation of nucleation and condensation experiments

Abstract Nucleation and condensation processes are investigated in finite systems by means of the Helmholtz free energy of formation of microclusters. The radius of clusters and the number of clusters are related to each other in such a system. A maximum of the free energy i.e., the critical state and a minimum i.e., the metastable state are found to be dependent on the number of microclusters present in the system. For a given number of particles (i.e., supersaturation) a maximum number of clusters exists. In this state the maximum and the minimum of the free energy are equal. This condition defines the first metastable state of the system. Condensation may start at this point and proceed along a line in the “valley” of the free energy until the equilibrium between bulk liquid and vapor is reached. Kinetic equations are derived for the condensation process using this thermodynamic concept. The relations obtained differ significantly from the classical ones. Data for water vapor condensation from the literature are used to test the validity of the theory presented. Sufficient agreement is found. The present theory appears to correlate condensation experiments obtained by different techniques.

Theory of nucleation in finite systems—Illustrated by ethanol condensation

Abstract A complete thermodynamic and kinetic model for nucleation and condensation in an isothermalisocoric finite system is presented, which allows exact calculation of all characteristic data of the condensation process. The main difference between classical isobaric nucleation theory and the condensation theory in finite systems is the existence of critical states, maxima of the Helmholtz free energy of condensation, besides metastable states, minima of the Helmholtz free energy of condensation in a finite system whereas only a critical state is found under isobaric conditions. Dependent on the initial supersaturation a first critical and a first metastable droplet size exist in a finite system, and a complete condensation curve is obtained for one single supersaturation. This curve describes the path from supersaturated vapor to the stable equilibrium of bulk liquid at saturation vapor pressure. Different definitions of nucleation rate, condensation rate, and droplet growth rate are compared with each other. Relations between these quantities are derived. Comparison of the present theory to experimental results of ethanol condensation shows good quantitative agreement.

On the use of chemical potentials in the condensation of a pure vapour

Abstract The thermodynamic relations valid for the condensation of a pure vapour at constant temperature have been derived using appropriate chemical potentials. The results are discussed for an imperfect gas and curvature dependent surface tension of the liquid.

Influence of curvature-dependent surface tension on the free energy of formation of microclusters

Abstract The Helmholtz free energy of formation of a spherical microcluster in a finite system is computed using different relations for the curvature dependence of the surface tension. Comparison between computer simulation results of Rao et al. and macroscopic thermodynamics shows relative close agreement.

Thermodynamic considerations on the contribution of the dissociation of silanol groups to the stability of silica sols

Abstract A new relationship for the free energy of silanol-group dissociation on silica sol particles is derived, including both an electrical and a chemical part. Using an equation for the calculation of the dissociation equilibrium based on the simple Gouy-Chapman model of the electrochemical double layer, we discuss the contribution of this term to stabilization of silica sol in a weak alkaline aqueous dispersion. We find minima of the Helmholtz free energy in dependence on dispersion composition. They are identified as stable states in a thermodynamic sense. Relation results between sol composition and particle size of thermodynamic stable states.

Kinetics of nucleation and condensation of supersaturated argon vapour in a finite system. application of curvature-dependent surface tension

Abstract The description of condensation kinetics in finite systems differs from classical nucleation theory The condensation rate of argon calculated with curvature-dependent surface tension is smaller than when calculated with constant surface tension, but no fundamental difference is found

Kinetic Size Effect During Dissolution of a Synthetic γ-Alumina

Abstract The dissolution process of a technical, nanodispersed γ-alumina in water was studied at 25 °C in the pH range 3.0 ≤ pH ≤ 11.5. Thereby, especial attention was paid to the influence of supersaturation on the dissolution behaviour observed. In conclusion, we were able to verify a size effect during the dissolution process, in the whole pH range investigated. In addition, we observed that changing supersaturation under identical conditions, leads to a shift of the maximum in the concentration profiles both, in absolute value and in time, when the maximum occurs. X-ray powder diffraction analysis and nitrogen adsorption measurements were used to identify the solid material collected during selected dissolution experiments. As a result, the formation of the aluminium phase -bayerite/gibbsite- could be excluded as a possible reason for the observed dissolution behaviour. The rate constants of the dissolution process were evaluated using the model of Gibbs free energy of cluster formation, which considers size effect among other factors. As a result, we were able to prove that the observed maxima in the concentration profiles were due to a kinetic size effect, caused by the size of the primary particles of the starting material, surface tension, and supersaturation in the system.

Solubility kinetics of a synthetic uranium(VI) oxide at different pH and controlled O2 partial pressure and evaluation of substantial interface properties

The solubility behaviour of a synthetic uranium(VI) oxide was studied under inert conditions in aqueous NaClO4 solution at 25 ± 2 °C. The dissolution kinetics were investigated in respect of pH in solution and O2 partial pressure in the atmosphere. The actual uranium concentration was determined by ICP-MS measurements. Under acidic conditions we observed a moderate solubility which increases by lowering of the pH of solution yielding to a solubility constant of log10Ksp = −24.38 ± 0.07. The influence of the ionic strength, I, on the dissolution kinetics could be observed which was evaluated using a theoretical model considering the electrical double layer at the surface of the oxide as well as all possible reaction pathways. As a result we could determine the acid-base equilibrium constants of the surface groups and the overall reaction rate, k+, of dissolution process as a function of pH and I. On this basis we are able to determine the pzc of the uranium oxide, to be 7.28. It is in good accordance with a minimum in the tendency of the solid to dissolve which was observed in the pH range 6 to 8.