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Die molekulardynamische Simulation ist eine weit verbreitete Methode, die Einblicke in die submikroskopische Ebene von Vielteilchensystemen erlaubt und die Berechnung makroskopischer und struktureller Eigenschaften ermöglicht. Sie kann auch didaktisch hilfreich zur Vermittlung von Wechselwirkungen und den daraus resultierenden molekularen Prozessen sein. Der Umgang mit der Frage, wie eine solche Simulation abläuft, kann zum Verständnis chemischer Inhalte beitragen. Dieses „Wie" erfordert eine Auseinandersetzung mit den Simulationsmethoden und den molekularen Modellen auf der Grundlage einsehbarer Programmcodes. Bei solchen Glass‐Box Simulationen ist der Code Teil der Behandlung chemischer Inhalte. Dabei wird informatisches Denken genutzt, um mit Algorithmen molekulare Vorgänge zu erläutern. In diesem Artikel werden die van der Waals‐Wechselwirkung, die Geschwindigkeitsverteilung sowie die Struktur von Fluiden und Feststoffen behandelt. Neben einer Visualisierung der submikroskopischen Prozesse ermöglicht dieser Ansatz auch Erkenntnisse über die Natur von Modellen. Hinzu kommt, dass Programmierfähigkeiten in den Naturwissenschaften von großer Bedeutung sind und auch im schulischen Bereich für die damit verbundenen Möglichkeiten sensibilisiert werden sollte. [ABSTRACT FROM AUTHOR]

While quantum chemistry is the standard model for treating a chemical bond in chemical science for about one hundred years, its application in secondary education is still limited. Especially the introduction of wave properties of matter is often neglected. The complexity of this topic makes it necessary to treat it exemplary. Simple models with infinitely high potential walls and vanishing potential energy inside can serve as suggestion for teachers to teach the subject. The mathematical modeling is restricted to the sinus function and therefore suitable for the upper secondary level. The foundation of bond formation is the interference of electronic wave functions taking place when waves come close as atoms approach. Interference then leads to a redistribution of the charge. In case, this redistribution takes up more space than available before, the kinetic energy decreases. In addition, the redistribution of the charge leads to changes in the potential energy. This is the background for a series of rules and effects in high school chemistry that are often introduced without relation to each other. Even though the topic is rather located in upper secondary education, in middle secondary education the wave property of matter can be introduced phenomenologically equivalent to particle properties in a preparatory manner. [ABSTRACT FROM AUTHOR]

The observation that high school students often do not recognize the contributions of other subjects such as applied mathematics or informatics to chemistry may be countered by introducing appropriate mathematical modelling in chemistry class. It should be focused on topics which are typically part of the regular curricula. Here chemical kinetics is employed within the introduction of the nucleophilic substitution as an example allowing conjunctions to mathematics and informatics. In this context, kinetics is deepened by quantitative considerations as well as simulations. The time laws for the kinetics of first and second order are derived using mathematical methods that are typically included in present mathematics curricula. In addition, two quantitatively analyzable model experiments can be used to allow a playfully understanding of the differential equations and their solutions. Furthermore, these model experiments can be transformed into concise computer algorithms. In this way, students learn the different methods experiment, analytical derivation, and simulation for gaining chemical knowledge. [ABSTRACT FROM AUTHOR]

Vapor-liquid nucleation in the binary system n-nonane/methane is investigated by molecular dynamics simulation. The supersaturation is achieved by cooling down the system during the expansion in order to closely mimic the real process. Binary clusters formed by nucleation are frequently inhomogeneous objects in which components are not well mixed. By studying high-pressure nucleation and cluster growth in the n-nonane/methane mixture, we demonstrate the role of structuring effects in these processes. At typical simulation conditions—pressure 60 bar, temperature 240 K, and nucleation rate ∼1026 cm−3s−1—the mole fraction of methane in the critical cluster reaches 80 percent, which is much higher than its equilibrium value in the bulk liquid at the same pressure and temperature. These observations are supported by the recently formulated coarse-grained theory for binary nucleation as well as by the experimental observations. [ABSTRACT FROM AUTHOR]

In high school and beyond students regard the subjects often isolated from each other. In contrast, every subject always requires contributions from other subjects. The subject chemistry requires, besides others, mathematical skills. In order to illustrate the relation between chemistry and applied mathematics the principles of mathematical modelling can already be introduced in high school. Here a practical example is employed to show how it is possible to simulate a standard experiment in high school chemistry, namely the titration of monoprotic strong and weak acids with a strong base. The mathematical derivation is merely based on mathematical skills, which are typically taught in 9th grade. The topic fits well in the chemistry curricula as a deepening. This approach of implementing mathematics in chemistry also aims to counteract the possible estrangement of the high school subject chemistry from the university subject chemistry. The mathematical derivations are detailed with focus on the traceability and should be adjusted for application in high school. The way of deriving the equations also allows to teach general methods of mathematical modelling in natural science. [ABSTRACT FROM AUTHOR]

We report results on nucleation, growth, and structure formation of methane/n-nonane clusters in an expanding system investigated by molecular dynamics simulation. From bulk phase equilibria data, it is expected that the concentration of the less volatile substance n-nonane in the clusters is very high. However, analyses of experimental data in the literature suggest somewhat higher methane content at onset of nucleation. Our simulations show that the methane mole fraction is actually very high and increases even further at the beginning of the cluster growth. On the other hand, in this transient state after nucleation the methane mole fraction in the cluster core decreases, leaving a n-nonane rich core, i.e., we observe the phase separation inside the growing cluster. Methane is squeezed out from the core to the surface and then evaporates from the surface shell during expansion of the system. [ABSTRACT FROM AUTHOR]

The stability limits in binary fluid mixtures are investigated on the basis of the global phase diagram approach employing a model for the attracting hard-sphere fluid. In addition to the diffusion spinodals the mechanical spinodals are included. As a result one finds topologically different types of the diffusion spinodals while only one shape exists for the mechanical spinodals which are present in the region of liquid-vapor equilibria only. The diffusion spinodals represent the underlying properties of the phase behavior. The types of stable phase behavior therefore resemble that of the spinodal behavior. The different shapes of the spinodals can be important for nonequilibrium processes in nature and technology. [ABSTRACT FROM AUTHOR]

The dependence of the critical volume fraction at constant pressure as a function of the chain length of a polymer/solvent system can be described by a power law. The exponent of this power law is investigated based on an equation of state model and experimental data for various chain-molecule solutions here. The results are compared to recent molecular simulation data taken from the literature and analytical models. The theoretical models, simulation, and experimental data show that the exponent depends on the chain length of the dissolved chain molecules. The power law with a constant exponent is therefore not a universal relationship for this dependence. Based on the investigation of the chain length dependence a correlation for the critical volume fraction is proposed here. This function generalizes the Flory and a renormalization group model and is applied to the correlation of the experimental data. This more general relationship includes the power law with the exponent obtained from the Flory theory as limiting behavior. Some additional experimental data for oligomer solutions which are necessary for an investigation of the short chain length limit have been measured. [ABSTRACT FROM AUTHOR]

Proposes hard-sphere equations which in combination with a van der Waals attraction term lead to a biquadratic equation of state. Limiting behavior at low and high densities shown by the equations; Proximity of the poles to the physical packing fraction of hard spheres.

Today quantum mechanics plays a significant role in chemistry. Program packages are available that allow quantum mechanical calculations in many areas of chemistry as well as material and engineering science. Doubtless quantum mechanics is part of university education, nevertheless, it is possible to teach the main features in the final year of high school chemistry. Here, one can merely focus on the principles related to topics which are already part of the curricula. The model of a particle in a one dimensional box discussed here is taught in German high school physics with a different focus but on a similar level and hence pupils are in principle not overtaxed by this topic. This model relatively simply allows to present the basic features of quantum mechanics and it is approximately applicable to linear and cyclic π electron systems. The major approximation is that the potential energy in the box is zero while the potential energy of the atoms in actually given by a periodic Coulomb potential. The approximation employed here aims on the application of the simple model, that itself is solved exactly, to more complex molecules. Deviations in the electron distribution between the box potential and the periodic Coulomb potential are discussed. [ABSTRACT FROM AUTHOR]

Phase diagrams of binary fluid mixtures have been calculated from the Carnahan–Starling–Redlich–Kwong equation of state in connection with standard quadratic mixing rules. The phase diagrams were classified according to the system of van Konynenburg and Scott and then used to construct global phase diagrams showing the extent of the various phase diagram classes in the space of the parameters of the equation of state. For molecules of equal size, the global phase diagram is rather similar to that of the Redlich–Kwong or the van der Waals equation. For molecules of different sizes, however, a new tricritical line appears. Such a behavior is observed for cubic equations of state only if nonadditive covolumes are assumed. Along this new tricritical line, some unusual phase diagrams involving four-phase states and high-density instabilities can be found. The influence of molecular size ratios on the global phase diagrams and the relationship of the equation of state of this work to the ternary symmetric lattice gas and the van der Waals lattice gas are discussed. [ABSTRACT FROM AUTHOR]

Presents an association theory for the formation of ion oligomers. Basis for the development of the theory; Association constants of the equilibria; Employment of the dielectric constant of the pure solvent; Replacement of the exponential low density pair correlation function; Approximation of the covolumes of clusters; Description of Coulomb interaction.