Interactions between molecules dispersion

Perturbation theory yields a siim-over-states fomnila for each of the dispersion coefficients. For example, the isotropic coefficient for the interaction between molecules A and B is given by... 

This dispersion interaction must be added to the dipole-dipole interactions between molecules, such as HCl, NH3 and H2O which have a permanent dipole, fi. The magnitude of die dipole moment depends on tire differences in electronegativity of the atoms in the molecule. Here again, the energy of interaction varies as (orientation effect). 

When thinking about chemical reactivity, chemists usually focus their attention on bonds, the covalent interactions between atoms within individual molecules. Also important, hotvever, particularly in large biomolecules like proteins and nucleic acids, are a variety of interactions between molecules that strongly affect molecular properties. Collectively called either intermolecular forces, van der Waals forces, or noncovalent interactions, they are of several different types dipole-dipole forces, dispersion forces, and hydrogen bonds. 

Dispersion force (Section 2.13) A noncovalent interaction between molecules that arises because of constantly changing electron distributions within the molecules. 

Noncovalcnt interaction (Section 2.13) An interaction between molecules, commonly called intermolecular forces or van der VVaals forces. Hydrogen bonds, dipole-dipole forces, and dispersion forces are examples. 

First, it is important to appreciate that all liquid crystal mesophases exist due to non-covalent interactions between molecules, namely the anisotropic dispersion forces mentioned earlier. However, this section will address more specific non-covalent interactions that have been used either to induce liquid-crystalline behaviour or to generate a new species that is liquid crystalline. 

Polar interactions between molecules arise from permanent or Induced dipoles existing in the molecules and do not result from permanent charges as in the case of Ionic interactions. Examples of polar substances having permanent dipoles would be alcohols, ketones, aldehydes etc. Examples of polarizable substances would be aromatic hydrocarbons such as benzene or toluene. It is considered that, when a molecule carrying a permanent dipole comes Into close proximity to a polarizable molecule, the field from the molecule with the permanent dipole induces a dipole in the polarizable molecule and thus electrical interaction can occur. It follows that to selectively retain a polar solute, then the stationary phase must also be polar and contain, perhaps, hydroxyl groups. If the solutes to be separated are strongly polar, then perhaps a polarizable substance such as an aromatic hydrocarbon could be employed as the stationary phase. However, to maintain strong polar interactions with the stationary phase (as opposed to the mobile phase) the mobile phase must be relatively non-polar or dispersive in nature. 

The first term on the right-hand side of Eq. 12.9 or 12.14 describes the short-range, repulsive interaction between molecules as they get very close to one another. The second term accounts for the longer-range, attractive potential (i.e the dispersion interaction between the molecules). The final term is the longest-range interaction, between the dipole moments JTj and JTj of the two molecules. In the case where one or both of the dipole moments are zero, the Stockmayer potential reduces to the Lennard-Jones potential discussed in Sec 12.2.1. 

The electrostatic part, Wg(ft), can be evaluated with the reaction field model. The short-range term, i/r(Tl), could in principle be derived from the pair interactions between molecules [21-23], This kind of approach, which can be very cumbersome, may be necessary in some cases, e.g. for a thorough analysis of the thermodynamic properties of liquid crystals. However, a lower level of detail can be sufficient to predict orientational order parameters. Very effective approaches have been developed, in the sense that they are capable of providing a good account of the anisotropy of short-range intermolecular interactions, at low computational cost [6,22], These are phenomenological models, essentially in the spirit of the popular Maier-Saupe theory [24], wherein the mean-field potential is parameterized in terms of the anisometry of the molecular surface. They rely on the physical insight that the anisotropy of steric and dispersion interactions reflects the molecular shape. 

Because in lyophilic colloids there is an attractive interaction between the particles and the medium, the interface between these two phases has a low surface energy and the particles are solvated. There is little reason for particles to clump together under these circumstances thus, the dispersed particles are usually individual macromolecules. The shape of the macromolecule depends on the relative magnitude of the forces within the molecule to those between the molecule and the medium. If the former is larger, the particle will be globular, if the latter is larger, the particles will be extended. In the latter case, there may be some interactions between different dispersed molecules, producing semisolid properties (a gel). 

In the development of the set of intermolecular potentials for the nitramine crystals Sorescu, Rice, and Thompson [112-115] have considered as the starting point the general principles of atom-atom potentials, proven to be successful in modeling a large number of organic crystals [120,123]. Particularly, it was assumed that intermolecular interactions can be separated into dispersive-repulsive interactions of van der Waals and electrostatic interactions. An additional simplification has been made by assuming that the intermolecular interactions depend only on the interatomic distances and that the same type of van der Waals potential parameters can be used for the same type of atoms, independent of their valence state. The non-electric interactions between molecules have been represented by Buckingham exp-6 functions,... 

Dispersional Interaction between Molecules. We still wish to consider briefly energies due to interaction between fluctuating induced electric charge distributions of atoms and molecules. In constrast to electrostatic and induced interactions, these are present even when the molecules do not possess permanent electric moments. These dispersional interactions cannot be dealt with on a classical electrostatics level owing to their relation to London s quantum dispersion theory, they have been termed London dispersional interactions. 

For tliis class of mixtures, interactions between molecules of like species are different in kind for the two species. In particular, two molecules of the polar species experience a direct-electrostatic interaction and a (usually weak) induction interaction, in addition to the usual dispersion interaction here, the attractive forces are stronger than would be observed for a nonpolar species of similar size and geometry. Interactionbetween uiihke species, on the other liand, involves only the dispersion and (weak) induction forces. One therefore expects to be positive, only more so than for otlierwise similar NPNP mixtures. Experiment bears tliis out, on average (Fig. 16.5). 

The viscosity of microemulsions has been studied several times in order to determine hydration and interactions between the dispersed droplets. It was found that an increase in hydration of the surfactant molecules resulted in rheological behavior more similar to that of suspensions containing solid particles in low concentrations. In any case, the microemulsions showed Newtonian flow characteristics. 

In total, there are three different basic types of molecular force, all of which are electrical in nature. These forces are called dispersion forces, polar forces, and ionic forces. Despite there being many different terms used to describe molecular interactions (e.g., hydrophobic forces, 77-77 interactions, hydrogen-bonding, etc.), all interactions between molecules are the result of composites of these three different types of molecular force. 

Particle-particle interaction is central to a wide range of engineering applications and processing industries. Examples include coagulation, flocculation, dispersion, emulsification, and froth flotation. In these applications, the particle size is small, and the overall particulate behavior is determined by forces associated with the surface properties rather than those related to mass or volume. The surface properties of a particle in a liquid medium are the result of a complex interaction between molecules, atoms, and ions at the particle surface and in the surrounding liquid. If a number of particles are present, interactions also take place between particles at short separation distances, and it is this interaction that is of most interest as it can determine the overall stability or instability of dispersions and/or suspensions. 

The interactions between molecules which produce the cohesive energy characteristic of the liquid phase are described in the section entitled Secondary Forces Between Solvent and Solute Molecules. These involve the dispersion forces, dipole-dipole and dipole-induced dipole interactions, and specific interactions, especially hydrogen bonding. If it is assumed that the intermolecular forces are the same in the vapor and liquid states, then -E is the energy of a liquid relative to its ideal vapor at the same temperature. It can be described as the energy required to vaporize 1 mole of liquid to the saturated vapor phase (Af U) plus the energy required for the isothermal expansion of the saturated vapor to infinite volume. Detailed discussion of the theory and derivations is given in the publications by Hildebrand and associates cited above. 

The interaction between molecules that do not form chemical bonds arises from electrostatic, induction and dispersion effects. The energy of interaction... 

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