Dispersion forces, illustration

Polar molecules, like nonpolar molecules, are attracted to one another by dispersion forces. In addition, they experience dipole forces as illustrated in Figure 9.9, which shows the orientation of polar molecules, such as Id, in a crystal. Adjacent molecules line up so that the negative pole of one molecule (small Q atom) is as dose as possible to the positive pole (large I atom) of its neighbor. Under these conditions, there is an electrical attractive force, referred to as a dipole force, between adjacent polar molecules. 

The dispersion forces that act between atoms of the noble gases depend on the polarizabilities of their electron clouds. The total electron counts for these atoms are 10 for neon and 54 for xenon. When two atoms approach each other, the smaller electron cloud of neon distorts less than the larger electron cloud of xenon, as a molecular picture illustrates ... 

Fig. 7.5 Illustration of how dispersion forces affect gauche (G) conformations. Compared to structures with gauche forms devoid of dispersion forces (i.e., HF-optimized), structures with gauche forms subject to dispersion forces (MP2 optimized) contract in such a way that the 1. ..5 nonbonded interactions in an attractive part of the van der Waals potential are shortened. Thus, in GG-pentane (shown above), MP2-optimized torsional angles are contracted by several degrees compared to the HF-optimized geometry, causing a reduction in the 1...5 nonbonded distances by several tenths of an A. For additional details and the numerical values see R. F. Frey, M. Cao, S. Q. Newton, and L. Schafer, J. Mol. Struct. 285 (1993) 99.

Combined Electrostatic and Steric Stabilization. The combination of the two mechanisms is illustrated in Figure 4, taken from Shaw s textbook, (13) where the repulsion of the steric barrier during a collision falls off so rapidly as the colliding particles bounce apart that the dispersion force attractions hold the particles together in the "secondary minimum". This is exactly what happens in the system investigated in this paper. 

Figure 3.1 Illustration of the various molecular interactions arising from uneven electron distributions (a) dispersive forces, (b) dipole-induced dipole forces, (c) dipole-dipole forces, (d) electron acceptor-electron donor forces.

Typical potential energy curves for the interaction of two atoms are illustrated in Figure 11.3. There is characteristically a very steeply rising repulsive potential at short interatomic distances as the two atoms approach so closely that there is interpenetration of their electron clouds. This potential approximates to an inverse twelfth-power law. Superimposed upon this is an attractive potential due mainly to the London dispersion forces. This follows an inverse sixth-power law. The total potential energy is given by... 

The extent to which surface tension can be controlled by fluoroalkyl-containing coupling agent type treatments is summarized in Table 1. Its purpose is to simply illustrate the range of control possible detailed comparisons are unwarranted because of differences in sample preparation and choice of substrate, data acquisition and treatment. Some of the critical surface tensions (crc) are obtained with -alkanes, some with other liquids. Some of the dispersion force components (of) and polar components (of) of solid surface tension are derived by use of different equations. The reader is referred to the key references in Table 1 for full details. 

In a thick film, the molecules located at its free surface do not sense the presence of the substrate. In contrast, in a thin film they do interact with the substrate. For the majority of the molecules of a thick film, the range of the interaction forces is smaller than the thickness of the film. In contrast, it is larger for the molecules of a thin film. As a result, the free energy of a thin film depends on its thickness. Considering, for illustrative purposes, London dispersion forces between molecules, the following expression is obtained for the interaction... 

The low-coverage energy data for the adsorption of n-hexane and benzene on various non-porous solids in Table 1.4 illustrate the importance of the surface structure of the adsorbent and the nature of the adsorptive. Since n-hexane is a non-polar molecule, Em > Esp, and therefore the value of E0 is dependent on the overall dispersion forces and hence on the density of the force centres in the outer part of the adsorbent (i.e. its surface structure). Dehydroxylation of a silica surface involves very little change in surface structure and therefore no significant difference in the value of E0 for n-hexane. However, replacement of the surface hydroxyls by alkylsilyl groups... 

We have drawn simple representative curves to illustrate the general form of the potential energy for attractive and repulsive forces in Figure 8-7, but there are various theories and equations that can be used to obtain a more formal description. Repulsive forces are not as well understood as attractive forces, but it is often assumed that the repulsive part of the potential varies as 1/r12, where r is the distance between the molecules or segments of molecules. Attractive forces are better understood and for many of the intennolecular interactions that are commonly encountered in polymers the potential goes as -Hr6. We will be particularly concerned with dispersion forces, dipole/dipole interactions, strong polar forces and hydro-... 

Recall that we already derived a similar expression from the van der Waals theory under a number of restrictive simplifications, see (2.5.44 and 45]. There the geometric mean was related to the same mean of Hamaker constants. This equation can be tested experimentally for liquids like water, in which a variety of forces are operative, y can be established by measuring interfacial tensions against organic liquids in which the interaction is dominated by the dispersion forces. This analysis can be illustrated with the data of table 2.3. In (2.11.19] a is an organic liquid (like a hydrocarbon, he) for which it was assumed that only dispersion forces determined the surface tension y = Consequently, y" is the only unknown. Its value appears to be invariant at about 22 mJ m", comprising 30% of the total tension. 

Adsorption by dispersion forces acting between adsorbent and adsorbate molecules is important as an universal supplementary mechanism in all other types. The effect is illustrated by the ability of surfactants with long hydrocarbon tails to displace equally charged low molecular weight materials and simple inorganic ions from solid substrates [75,76]. 

The origin of the critical point can be traced to the temperature effect on miscibility. Patterson [1982] observed that there are three principal contributions to the binary interaction parameter, the dispersive, free volume and specific interactions. As schematically illustrated in Figure 2.16, the temperature affects them differently. Thus, for low molecular weight systems where the dispersion and free volume interactions dominate, the sum of these two has a U-shape, intersecting the critical value of the binary interaction parameter in two places — hence two critical points, UCST and LCST. By contrast, most polymer blends derive their miscibility from the presence of specific interactions, characterized by a large negative value of the interaction parameter that increases with T. The system is also affected by the free volume contribution, as well as relatively unimportant in this case dispersion forces. The sum of the interactions reaches the critical value only at one temperature — LCST. 

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