Intermolecular Energies and Excluded Volume Force of Cohesion and Internal Energy in the Condensed Phase

Abstract

Intermolecular forces are responsible for most of the physical and chemical properties of materials. This explains the number of works devoted to such studies. The first attempt to explain intermolecular forces was made by Keesom (1912) based on the interaction between permanent dipoles. Debye in 1920 extended the dipole theory to take into account the induction effect in which a permanent dipole induces a dipole in another molecule and a mutual attraction results. This interaction depends on the polarizability R and on the dipole moment µ of the molecule. The cause of the attractive forces between neutral molecules is the dispersion interaction: the quantum mechanical treatment of this interaction was given by London in 1930. These different works furnished much very interesting information, were based on the potential energies of the Lennard-Jones type, and were very often limited to isolated molecules. It has since become necessary to propose new formulations to better describe the interaction energies. One important development was via quantum mechanical calculations which call upon complex considerations. In this case, the interactions are described in terms of a multidimensional potential energy which describes the energy as a function of the configuration of the separated molecules, their relative orientations, and the intermolecular distances. Very little information concerns the interactions of diatomic and polyatomic molecules, and the potential energies were always of the types developed by Lennard-Jones, Morse, Buckingham, Stockmeyer, and Kihara. Another development exploited the reaction field technique which considers that the dispersion forces are linked to the frequency-dependent polarizabilities by averaging over the fluctuating instantaneous dipole-induced dipole interaction. In this approach both quantum mechanical and statistical mechanical fluctuations are simultaneously averaged. For many practical problems it is necessary to understand forces between molecules in liquids. This is a very difficult problem since it involves the detailed packing of the molecules in a liquid as well as the many-body forces between neighboring molecules. A complete and well-documented development can be found in refs 1 and 2 for the interested reader. To go further in our understanding of molecular interactions, much recent research calls upon molecular dynamics simulations. 3–5 The computational methods are used in molecular modeling to compute the energy of an assembly of molecules and to perform a molecular simulation. These simulations are carried out using Lennard-Jones or Buckingham potentials and require taking into account a very large number of atomic and molecular parameters, the estimation of which may be delicate. This paper exploits a new equation of state developed previously 6 which allows proposing a new expression for the cohesive forces and internal energy. On the basis of this expression, it becomes easy to obtain the interaction energy of polar and nonpolar molecules under various pressures and temperatures in the gaseous and liquid states by simply following the variation of excluded volume according to the physical conditions to which the considered fluid is subjected. This excluded volume Vτ appears as the average volume occupied by the considered molecule which in the liquid forbids the presence of any other molecule. The molecule in perpetual translational, rotational, and vibrational movement undergoes a countless number of shocks with its neighbors and as a result remains confined within a volume which on the average over time can be considered as a sphere whatever the molecule under consideration. This volume thus represents the fictive volume of the molecule which will become its true volume under very high pressure. If the temperature is increased, the intermolecular movements are more rapid, the collisions more frequent, and the distances between successive collisions lower, and thus the excluded volume diminishes. So both increased pressure and temperature lead to the same result.