Thesis--Wisconsin. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1983. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Köln, Universiẗat, Diss., 2001.

No description available.

The van der Waals forces, which are forces between neutral atoms and molecules, play an important role in physics (e.g. in phase transitions), chemistry (e.g. in chemical reactions) and biology (e.g. in determining properties of DNA). These forces are of quantum nature and it is long being conjectured and experimentally verified that they have universal behaviour at large separations: they are attractive and decay as the inverse sixth power of the pairwise distance between the atoms or molecules. In this thesis we prove the van der Waals law under the technical condition that ionization energies (energies of removing electrons) of atoms are larger than electron affinities (energies released when adding electrons). This condition is well justified experimentally as can be seen from the table, \newline \begin{tabular}{|c|c|c|c|} \hline Atomic number & Element & Ionization energy (kcal/mol)& Electron affinity (kcal/mol) \\ \hline 1 & H & 313.5 & 17.3 \\ \hline 6 & C & 259.6 & 29 \\ \hline 8 & O & 314.0 & 34 \\ \hline 9 & F & 401.8 & 79.5 \\ \hline 16 & S & 238.9 & 47 \\ \hline 17 & Cl & 300.0 & 83.4 \\ \hline \end{tabular} \newline where we give ionization energies and electron affinities for a small sample of atoms, and is obvious from heuristic considerations (the attraction of an electron to a positive ion is much stronger than to a neutral atom), however it is not proved so far rigorously. We verify this condition for systems of hydrogen atoms. With an informal definition of the cohesive energy $W(y),\ y=(y_1,...,y_M)$ between $M$ atoms as the difference between the lowest (ground state) energy, $E(y)$, of the system of the atoms with their nuclei fixed at the positions $y_1,...,y_M$ and the sum, $\sum_{j=1}^M E_j$, of lowest (ground state) energies of the non-interacting atoms, we show that for $|y_i-y_j|,\ i,j \in \{1,...,M\}, i \neq j,$ large enough, $$W(y)=-\sum_{i<j}^{1,M} \frac{\sigma_{ij}}{|y_i-y_j|^6}+O(\sum_{i<j}^{1,M} \frac{1}{|y_i-y_j|^7})$$ where $\sigma_{ij}$ are in principle computable positive constants depending on the nature of the atoms $i$ and $j$.

The van der Waals forces, which are forces between neutral atoms and molecules, play an important role in physics (e.g. in phase transitions), chemistry (e.g. in chemical reactions) and biology (e.g. in determining properties of DNA). These forces are of quantum nature and it is long being conjectured and experimentally verified that they have universal behaviour at large separations: they are attractive and decay as the inverse sixth power of the pairwise distance between the atoms or molecules. In this thesis we prove the van der Waals law under the technical condition that ionization energies (energies of removing electrons) of atoms are larger than electron affinities (energies released when adding electrons). This condition is well justified experimentally as can be seen from the table, \newline \begin{tabular}{|c|c|c|c|} \hline Atomic number & Element & Ionization energy (kcal/mol)& Electron affinity (kcal/mol) \\ \hline 1 & H & 313.5 & 17.3 \\ \hline 6 & C & 259.6 & 29 \\ \hline 8 & O & 314.0 & 34 \\ \hline 9 & F & 401.8 & 79.5 \\ \hline 16 & S & 238.9 & 47 \\ \hline 17 & Cl & 300.0 & 83.4 \\ \hline \end{tabular} \newline where we give ionization energies and electron affinities for a small sample of atoms, and is obvious from heuristic considerations (the attraction of an electron to a positive ion is much stronger than to a neutral atom), however it is not proved so far rigorously. We verify this condition for systems of hydrogen atoms. With an informal definition of the cohesive energy $W(y),\ y=(y_1,...,y_M)$ between $M$ atoms as the difference between the lowest (ground state) energy, $E(y)$, of the system of the atoms with their nuclei fixed at the positions $y_1,...,y_M$ and the sum, $\sum_{j=1}^M E_j$, of lowest (ground state) energies of the non-interacting atoms, we show that for $|y_i-y_j|,\ i,j \in \{1,...,M\}, i \neq j,$ large enough, $$W(y)=-\sum_{i<j}^{1,M} \frac{\sigma_{ij}}{|y_i-y_j|^6}+O(\sum_{i<j}^{1,M} \frac{1}{|y_i-y_j|^7})$$ where $\sigma_{ij}$ are in principle computable positive constants depending on the nature of the atoms $i$ and $j$.

Thesis (Master)--İzmir Institute of Technology, İzmir, 2006. / Keywords: particle, collection, liquid droplets. Includes bibliographical references (leaves 65-67).

No description available.

Some equilibrium and non-equilibrium properties of a gas of hard spheres with a long range attractive potential are investigated by considering the properties of an equation, proposed by deSobrino (1967), for a one-particle distribution function for the gas model considered. The solutions of this equation obey an H-theorem indicating that our gas model approaches local equilibrium. Equilibrium solutions of the kinetic equation are studied; they satisfy an equation for the density η(r) for which space dependent solutions exist and correspond to a mixture of gas and liquid phases. The kinetic equation is next linearized and the linearized equation is applied to the study of the stability of the uniform density stationary states of a Van der Waals gas. A brief asymptotic analysis of sound propagation in dilute gases is presented in view of introducing an approximation of the linearized Boltzmann collision integral due to Gross and Jackson (1959). To first order, the dispersion in the speed of sound at low frequencies is the same as the Burnett and Wang Chang-Uhlenbeck values while the absorption of sound is slightly less than the Burnett value and slightly greater than the Wang Chang-Uhlenbeck value; all three are in good agreement with experiment. Finally, using the method developed in the previous section, an approximation for the linearized Enskog collision integral is obtained; a dispersion relation is derived and used to show that the uniform density states which correspond to local minima of the free energy and traditionally called metastable, are in fact stable against sufficiently small perturbations. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

No description available.