Intermolecular potentials polar molecules

What Do We Need to Know Already This chapter uses the concepts of potential energy (Section A), coulombic interactions (Section 2.4), polar molecules and dipoles (Section 3.3), and intermolecular forces in gases (Section 4.12). 

The first terms of the power series obtained by the multipole expansion of the Coulomb intermolecular potential account for dipole-dipole interactions prevailing in systems of polar molecules. As an adequate approximation for ensembles of... 

The model presented here develops these ideas and introduces features which make the calculation of mixture properties simple. For a polar fluid with approximately central dispersion forces together with a strong angle dependent electrostatic force we may separate the intermolecular potential into two parts so that the virial coefficients, B, C, D, etc. of the fluid can be written as the sum of two terms. The first terms B°, C°, D°, etc, arise from dispersion forces and may include a contribution arising from the permanent dipole of the molecule. The second terms contain equilibrium constants K2, K, K, etc. which describe the formation... 

The "force of interaction , F, between two spherical non-polar molecules is a function of the intermolecular separation , r. For most purposes, however, it is more convenient to use the "potential energy of interaction , 0(r), rather than the force of interaction F(r). These two functions are simply related ... 

For non-polar molecules, a commonly used "intermolecular potential energy factor is the Lennard-Jones (6-12) Potential ... 

For polar molecules, the most widely used intermolecular potential energy is the Stockmayer Potential ... 

Another useful intermolecular potential is the Stockmayer potential [178,379], which can be used to describe the interaction between polar molecules. The functional form of the Stockmayer potential is... 

A more realistic interpretation of the quenching efficiencies may be sought in terms of the magnitude of the intermolecular potential between 02(1E9+) and the quencher.44 Thus polar molecules might be expected to be better quenchers than nonpolar molecules, in agreement with the experimental data, and quantitative calculation of the intermolecular potentials indicates a strong correlation between the potential and quenching efficiency. 

One of the simplest orientational-dependent potentials that has been used for polar molecules is the Stockmayer potential.48 It consists of a spherically symmetric Lennard-Jones potential plus a term representing the interaction between two point dipoles. This latter term contains the orientational dependence. Carbon monoxide and nitrogen both have permanent quadrupole moments. Therefore, an obvious generalization of Stockmayer potential is a Lennard-Jones potential plus terms involving quadrupole-quadrupole, dipole-dipole interactions. That is, the orientational part of the potential is derived from a multipole expansion of the electrostatic interaction between the charge distributions on two different molecules and only permanent (not induced) multipoles are considered. Further, the expansion is truncated at the quadrupole-quadrupole term. In all of the simulations discussed here, we have used potentials of this type. The components of the intermolecular potentials we considered are given by ... 

This section presents a fundamental development of Sections V and VI. Here a linear dielectric response of liquid H20 is investigated in terms of two processes characterized by two correlation times. One process involves reorientation of a single polar molecule, and the second one involves a cooperative process, namely, damped vibrations of H-bonded molecules. For the studies of the reorientation process the hat-curved model is employed, which was considered in detail in Section V. In this model a hat-like intermolecular potential comprises a flat bottom and parabolic walls followed by a constant potential. For the studies of vibration process two variants are employed. 

A) Reorientation of a single polar molecule during the mean lifetime ror in a rather narrow intermolecular potential well considered in Section V in terms of the hat-curved (HC) model. 

The realisation that lattice theories of liquids were getting nowhere came only slowly from about 1950 onwards. A key paper for chemists was that of Longuet-Higgins on what he called conformal solutions in 1951. In this he avoided the assumption that a liquid had a lattice (or any other particular) structure but treated the different strengths of the intermolecular potentials in a mixture as a first-order perturbation of the physical properties of one of the components. In practice, if not formally in principle, his treatment was restricted to molecules that could be assumed to be spherical, but it was so successful for many mixtures of non-polar liquids that this and later derivatives drove lattice theories of liquid mixtures from the field. 

The forces of attraction and repulsion between molecules must be considered for a more accurate and rigorous representation of the gas flow. Chapman and Enskog proposed a well-known theory in which they use a distribution function, the Boltzmann equation, instead of the mean free path. Using this approach, for a pair of non-polar molecules, an intermolecular potential, V (r), is given in the potential function proposed by the Lennard-Jones potential ... 

Molecules that have permanent dipole or quadrupole moments generate an electric field that induces an attractive response in nonpolar molecules by polarizing the nonpolar molecule so that it exhibits a temporary dipole. In fact, polar molecules can also have induced dipoles due to the electric field effect of another polar molecule in close proximity. The simplified expression for these induced intermolecular potential energies is... 

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