The formation of pharmaceutical particles by the rapid expansion of a supercritical solution is investigated by molecular dynamics simulation. As a pharmaceutical model substance naproxen, a pain reliever and anti-inflammatory drug, is used. The expansion process is modeled in the simulation method by stepwise increasing the size of the simulation box. Comparison with an accurate reference equation of state for the pure solvent carbon dioxide shows that the simulation system follows an adiabatic expansion path. The expansion of a solution of naproxen in supercritical carbon dioxide leads to a highly supersaturated system that starts to form particles. The nucleation and growth kinetics of this particle formation process is investigated and the effect on the particle structure is analyzed.

In the context of the investigation of particle formation, a potential model by means of the embedded atom method is developed for the hexagonal close packed metal zinc. This type of model includes many-body interactions caused by delocalised electrons in metals. The effective core charge as function of the distance is calculated here by an integral over the electron distribution function rather than fitting it to experimental data. In addition, the dimer potential is included in the parameterisation because we focus on the formation of nanoparticles from the vapour phase. With this potential model, the growth of zinc clusters consisting of 125 to 1000 atoms is investigated, which takes place at elevated temperatures in a liquid-like cluster state. The growing clusters are embedded in an argon carrier gas atmosphere which regulates the cluster temperature. The average thermal expansion of the clusters and the different lattice constants are analysed. For the determination of the cluster structure, the common-neighbour analysis method is extended to hexagonal close packed surface structures. During growth, small clusters with less than approximately 60 atoms develop transient icosahedral structure before transforming into hexagonal close-packed structure. The surface of the clusters exhibits a transformation from planes with high surface energy to the most stable ones. Besides ambiguous surface structures the final clusters are almost completely in an hexagonal close packed structure.

An extension of a recently proposed method for the calculation of the spinodals in pure fluid systems from the interfacial properties is elaborated, which requires the density profile as only input. The foundation of this approach is the so-called Fuchs-transformation which gives an estimate for the tangential pressure profile from the density profile. Using molecular dynamics simulation data for argon and carbon dioxide as well as lattice Boltzmann simulation data for the argon-like Shan–Chen fluid, the accuracy of the approach is analyzed. The Fuchs-transformation is qualitative, however it is possible to estimate the temperature–density projection of the spinodal. Depending on the underlying correlation function for the interfacial density profile reasonable results are obtained for the liquid and the vapor spinodal. The advantage of this method is that equilibrium data can be used to estimate the spinodal which is experimentally impossible to access because it is a highly non-equilibrium property. In the final consequence of this approach only the coexistence vapor and liquid densities are required to estimate the temperature–density projection of the spinodals.

The formation of naphthalene particles by expansion of a supercritical solution is investigated by molecular dynamics simulation. Supercritical carbon dioxide is chosen as solvent. A method for the successive expansion of the simulation box is developed which allows expanding the system very closely to the adiabatic curve obtained form a reference equation of state. During the expansion the solubility decreases and naphthalene particles precipitate. The heat of formation is compensated by the Joule−Thomson effect of the expanding solvent. Therefore, no influence of a molecular dynamics simulation thermostat is involved. Here the method is proposed and analyzed in extensive studies. Results are presented for the formation of naphthalene particles using a realistic model for the molecular interaction. In addition, a simplified potential model is employed to analyze finite size effects.

The limit of metastability, the so-called spinodal, is calculated for pure carbon dioxide by molecular dynamics simulation. The determination of the spinodal is based on properties of the liquid vapor interface using a recently developed method. This method relates the tangential pressure component through the vapor−liquid interface to the van der Waals loop in the two-phase region of the phase diagram. By application of the thermodynamic stability criteria, the location of the spinodal can be determined. The spinodal determined in this way is called interface spinodal here. Furthermore, the simulation provides equation of state properties in the complete metastable region of the phase diagram. The performance of different correlation equations for the density and the pressure tensor profiles with respect to the estimation of the spinodal is compared. It has been found that the interface spinodal coincides with the thermodynamic mean field spinodal within some reasonable deviation. Finally the influence of the size of the simulation box on the spinodal properties is investigated showing that the temperature-density spinodal data are independent of the interface thickness. Additional simulations using a Lennard-Jones fluid confirm these results over a range of 1.5 orders of magnitude for the systems size. A further result is that interface systems require a very long simulation time in order to obtain reliable results.

Ostwald ripening is an important growth process in many scientific disciplines ranging from material science, geology, biophysics, and product formulation. Here ripening of argon clusters in a vapor phase is observed directly in constant energy molecular dynamics simulations serving as a model system for large-time scale ripening processes. Starting from an initial metastable equilibrium between the vapor phase and two clusters Ostwald ripening is initiated by the addition of kinetic energy. This mimics local thermal fluctuations in a larger system. It appears that there is not necessarily a close encounter of two clusters before ripening sets in. Also no static density bridge between two ripening clusters is observed. The onset of ripening is rather related to the different evaporation dynamics of clusters of different size. It can start at the moment energy is added or with some delay, depending on the difference in cluster size and dynamics.

An easy applicable and accurate method for the correlation of the infinite dilution diffusion coefficient of organic solutes in supercritical fluids is proposed. The method is applicable to all supercritical fluids; in this work, however, only supercritical carbon dioxide is considered. The infinite dilution diffusion coefficient is calculated from the solvent viscosity by means of a modified Stokes–Einstein relation. The viscosity is calculated from an equation of state using friction theory. Here two equations of state are used, namely the short form of the Span–Wagner reference equation for carbon dioxide and the Peng–Robinson equation of state.

The influence of the phase behaviour of the solvent–antisolvent system on the process conditions for the gas–antisolvent process is investigated. The two fluids are modelled by the Peng–Robinson equation of state while the dissolved solid is described by a Clapeyron-type approach. Based on the correlation of the ternary system, a liquid–liquid immiscibility region has been found which hinders the proper crystallisation of the solute. A thorough investigation of the binary solvent–antisolvent system by the global phase diagram methods yields a criterion for the proper choice of the solvent. The crucial property turns out to be the distance of the solvent–antisolvent system from the tricritical curve in the global phase diagram.

In this paper, we combine experimental investigations and a newly developed correlation to elucidate the high-pressure solubility behavior in CO2 and the saturation pressure of three anthraquinone-based disperse dyestuffs. For modeling pVT-data of the supercritical solvent CO2, an accurate semiempirical equation of state has been developed. Furthermore, this equation of state has been extended to dilute solutions of the low-volatile anthraquinone derivatives by adapting a fugacity approach. The required saturation pressure of the pure solute has been described by a Clausius–Clapeyron type equation with two adjustable parameters. We have compared the saturation pressures deduced from the sequence of solubility isotherms with those reported in the literature. Besides, the consequences of the choice of saturation pressure on our calculations, especially on the coordinates of solubility extremes, are discussed. The results from our model demonstrate a substantial agreement between measured and calculated solubility data, even for a large solvent density region in its entirety.

A new simplified form of an equation of state suitable for the correlation of pVT-data is presented. The new equation of state is capable to model pVT-data in the low- and high-pressure regions as well as in the critical region. Taking a fugacity approach as a basis, we have calculated the solubility of several low-volatile solid organic compounds, in particular of the globular molecule adamantane in CO2 and the natural dyestuff β-carotene in three compressed gases, i.e. CO2, CClF3, and N2O. For all systems except β-carotene+N2O solubility data measured up to 100 MPa and more (180 MPa for β-carotene+CO2 and+CClF3) are available. Experimental results for the systems β-carotene+CO2 and+CClF3 are also reported. Here, adamantane serves as an example for a relatively high-soluble substance, while β-carotene represents low-soluble solutes. Solubility maxima, which have been found experimentally as a function of pressure or density at constant temperature, are considered in the correlations.

In the context of the investigation of particle formation, a potential model by means of the embedded atom method is developed for the hexagonal close packed metal zinc. This type of model includes many-body interactions caused by delocalised electrons in metals. The effective core charge as function of the distance is calculated here by an integral over the electron distribution function rather than fitting it to experimental data. In addition, the dimer potential is included in the parameterisation because we focus on the formation of nanoparticles from the vapour phase. With this potential model, the growth of zinc clusters consisting of 125 to 1000 atoms is investigated, which takes place at elevated temperatures in a liquid-like cluster state. The growing clusters are embedded in an argon carrier gas atmosphere which regulates the cluster temperature. The average thermal expansion of the clusters and the different lattice constants are analysed. For the determination of the cluster structure, the common-neighbour analysis method is extended to hexagonal close packed surface structures. During growth, small clusters with less than approximately 60 atoms develop transient icosahedral structure before transforming into hexagonal close-packed structure. The surface of the clusters exhibits a transformation from planes with high surface energy to the most stable ones. Besides ambiguous surface structures the final clusters are almost completely in an hexagonal close packed structure.