Direct intermolecular forces

The driving force for diffusion is the thermal energy, T, associated with Brownian motion. By contrast, for reactions between ions of charges Zj e and z e, the direct intermolecular potential energy becomes very important and is the Coulomb interaction 

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Introduction.—Most theoretical v> ork on the relation between intermolecular forces and the thermodynamic properties of liquids and liquid mixtures has been limited to potential fields which are independent of the orientation of the particles. This condition, however, is only strictly satisfied by monoatomic substances. For a great many molecular substances directional intermolecular forces are likely to be important and will have a significant effect on the thermodynamic properties of liquids both because of the additional cohesive energy and because of the loss of entropy associated with hindrance to free rotation. Although many of the observed properties of liquids have been attributed to directional forces in a qualitative manner, there has been little in the way of general quantitative theory. 

A topic of abiding interest is the issue of characterizing the order in liquids which may be defined as the entropy deficit due to preferential orientations of molecular multipoles relative to random orientations (orientational order) and nonuniformly directed intermolecular forces (positional order). Phenomenologically, two criteria are often claimed to be relevant for deciding whether or not a liquid is to be viewed as ordered the Trouton entropy of vaporization or Trouton quotient and the Kirkwood correlation factor gK. Strictly speaking, however, both are of limited relevance to the issue. 

Fig. 8.7. (a) Two methane molecules at intermolecular distance (Ti = 1.533 A. All hydrogen atoms belonging to the upper molecule are shown. Hydrogen number 4 is directed toward the center of the second molecule. (The direct intermolecular forces between the two molecules are assumed to be switched off, so that they can penetrate into each other to any chosen distance.) (b) One ethane molecule situated at the same space occupied previously by the two methane molecules. 

A method based on thermodynamic perturbation theory is described which allows strong directional Intermolecular forces to be taken into account when calculating thermodynamic properties. This is applied to the prediction of phase equilibrium and critical loci for mixtures containing polar or quadrupolar constituents. Two applications of the theory are then considered. In the first, the relation between intermolecular forces and the type of phase behavior is explored for binary mixtures in which one component is either polar or quadrupolar. Such systems are shown to give rise to five of the six classes of binary phase diagrams found in nature. The second application Involves comr-parison of theory and experiment for binary and ternary mixtures. 

The pressure tensor can be written as the sum of kinetic and potential terms. The potential part arises from the direct intermolecular forces and is therefore a function of the local fluid microstructure. In a dense liquid the shear viscosity is overwhelmingly dominated by the potential contribution. ... 

Specific intermolecular forces which give rise to the surface tensions do not affect the contact angles directly intermolecular forces determine the surface tensions the surface tensions then determine the contact angle through the Young equation. ... 

One fascinating feature of the physical chemistry of surfaces is the direct influence of intermolecular forces on interfacial phenomena. The calculation of surface tension in section III-2B, for example, is based on the Lennard-Jones potential function illustrated in Fig. III-6. The wide use of this model potential is based in physical analysis of intermolecular forces that we summarize in this chapter. In this chapter, we briefly discuss the fundamental electromagnetic forces. The electrostatic forces between charged species are covered in Chapter V. 

Nesbitt D J 1994 Fligh-resolution, direct infrared-laser absorption-spectroscopy in slit supersonic ]ets—intermolecular forces and unimolecular vibrational dynamics in clusters Ann. Rev. Phys. Chem. 45 367-99... 

Many of these features are interrelated. Finely divided soHds such as talc [14807-96-6] are excellent barriers to mechanical interlocking and interdiffusion. They also reduce the area of contact over which short-range intermolecular forces can interact. Because compatibiUty of different polymers is the exception rather than the rule, preformed sheets of a different polymer usually prevent interdiffusion and are an effective way of controlling adhesion, provided no new strong interfacial interactions are thereby introduced. Surface tension and thermodynamic work of adhesion are interrelated, as shown in equations 1, 2, and 3, and are a direct consequence of the intermolecular forces that also control adsorption and chemical reactivity. 

Ihe boiling points of different molecular substances are directly related to the strength of the intermolecular forces involved. The stronger the intermolecular forces, the higher the boiling point of the substance. In the remainder of this section, we examine the nature of the three different types of intermolecular forces dispersion forces, dipole forces, and hydrogen bonds. 

Thermal expansion — as elasticity — depends directly upon the strength of the intermolecular forces in the material. Strongly bonded materials usually expand little when heated, whereas the expansion of weak materials may be a hundred times as large. This general trend is confirmed by Table 5.1. The coefficient of thermal expansion a was found to be lower in the crosslinked polymers and higher in the less crosslinked or thermoplastic materials as observed by Nielsen [1], In addition, Table 5.1 presents the Young s moduli E of the polymers at ambient temperatures as well as the products a2E. The values of oc2E are all close to 13.1 Pa K 2 with a coefficient of variation of 1.6%. 

The effect of molecular interactions on the distribution coefficient of a solute has already been mentioned in Chapter 1. Molecular interactions are the direct effect of intermolecular forces between the solute and solvent molecules and the nature of these molecular forces will now be discussed in some detail. There are basically four types of molecular forces that can control the distribution coefficient of a solute between two phases. They are chemical forces, ionic forces, polar forces and dispersive forces. Hydrogen bonding is another type of molecular force that has been proposed, but for simplicity in this discussion, hydrogen bonding will be considered as the result of very strong polar forces. These four types of molecular forces that can occur between the solute and the two phases are those that the analyst must modify by choice of the phase system to achieve the necessary separation. Consequently, each type of molecular force enjoins some discussion. 

In the interior of a liquid bottom), each molecule experiences equal forces in all directions. A molecule at the surface of a liquid top) is pulled back into the liquid by intermolecular forces. 

In the liquid state, the molecules are still free to move in three dimensions but stiU have to be confined in a container in the same manner as the gaseous state if we expect to be able to measure them. However, there are important differences. Since the molecules in the liquid state have had energy removed from them in order to get them to condense, the translational degrees of freedom are found to be restricted. This is due to the fact that the molecules are much closer together and can interact with one another. It is this interaction that gives the Uquid state its unique properties. Thus, the molecules of a liquid are not free to flow in any of the three directions, but are bound by intermolecular forces. These forces depend upon the electronic structure of the molecule. In the case of water, which has two electrons on the ojQ gen atom which do not participate in the bonding structure, the molecule has an electronic moment, i.e.- is a "dipole". 

The nature of intermolecular force is essentially no different from that which participates in the chemical bond or chemical reaction. The factor which determines the stable shape of a molecule, the influence on the reaction of an atom or group which does not take any direct part in the reaction, and various other sterically controlling factors might also be comprehended by a consideration based on the same theoretical foundation. 

Figure 5.2 (a) Electron density contour map of the CI2 molecule (see Chapter 6) showing that the chlorine atoms in a CI2 molecule are not portions of spheres rather, the atoms are slightly flattened at the ends of the molecule. So the molecule has two van der Waals radii a smaller van der Waals radius, r2 = 190 pm, in the direction of the bond axis and a larger radius, r =215 pm, in the perpendicular direction, (b) Portion of the crystal structure of solid chlorine showing the packing of CI2 molecules in the (100) plane. In the solid the two contact distances ry + ry and ry + r2 have the values 342 pm and 328 pm, so the two radii are r 1 = 171 pm and r2 = 157, pm which are appreciably smaller than the radii for the free CI2 molecule showing that the molecule is compressed by the intermolecular forces in the solid state. 

Chapter 6. The outer contour in this map is for a density of 0.001 au, which has been found to represent fairly well the outer surface of a free molecule in the gas phase, giving a value of 190 pm for the radius in the direction opposite the bond and 215 pm in the perpendicular direction. In the solid state molecules are squashed together by intermolecular forces giving smaller van der Waals radii. Figure 5.2b shows a diagram of the packing of the Cl2 molecules in one layer of the solid state structure of chlorine. From the intermolecular distances in the direction opposite the bond direction and perpendicular to this direction we can derive values of 157 pm and 171 pm for the two radii of a chlorine atom in the CI2 molecule in the solid state. These values are much smaller than the values for the free molecule in the gas phase. Clearly the Cl2 molecule is substantially compressed in the solid state. This example show clearly that the van der Waals of an atom radius is not a well defined concept because, as we have stated, atoms in molecules are not spherical and are also compressible. 

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