Dispersive interactions forces

With the exception of the last example we have mainly dealt with supramolecular assemblies and structures of polymers which are formed by dispersion interaction forces so far. Self-assembly of polymers by more specific interactions, which justifies the denotation as supramolecular complexes is still limited in number and mostly poorly defined. 

More commonly used descriptors of polymer solubility are the solubility parameters introduced by Hildebrand and Scott for dispersive interaction forces, and extended by Hansen " for dispersive (8 ), polar (8d), and hydrogen bonding contributions (8 ) to interaction energies. An equation sometimes used to estimate the solubility range of Polymer 2 in a solvent (subscript 1) is ... 

FIGURE 8.25 The stability of a sol (a suspension of colloidal particles) may be evaluated from the balance of repulsive (electrostatic) interaction forces and attractive (dispersive) interaction forces, e.g., by applying the DLVO theory (Equation 8.103). If a potential energy barrier exists the system is stable (left). If the barrier is removed, the coagulation of the particles is contolled by diffusion alone. (Courtesy of Jean Le Bell.)... 

It is seen from Eq. (164) that the dispersion interaction force (F = —d Waal dr) is a short-range force and weak. However, when a molecular assembly consists of a large number of nonpolar molecules, then the dispersion interaction force (or energy) between two bodies of such molecular assemblies becomes a long-range force (or interaction energy) (Verywey and Overbeek). ... 

Further studies of the van der Waals interaction among molecules having permanent dipole moments have been carried out using quantum mechanical methods by Dzyaloshinskii et Their approach includes the retardation effect as well as a polarization effect due to molecular dipoles. Then, the total dispersion interaction force (F) acting on a unit area of each of the slabs is given by... 

The solvating strength of plasticizer depends on its chemical structure as it relates to its physical properties. Application of Hansen solubility parameters (64 = dispersion interactive forces, 6p = dipole interactive forces, and 61, = hydrogen bonding forces) is the most successful method of predicting interaction between plasticizers and PVC. Table 3.2 shows values of these parameters for PVC and selected plasticizers. 

The forces of intermolecular interactions are the superposition of the dipole, induction, and disperse interaction forces. They can be expressed as a united function of interactions, such as the sum of two power functions Equation 1.7-39 (the Lennard-Johns potential), the potential pit, etc. 

To first order, the dispersion (a-a) interaction is independent of the structure in a condensed medium and should be approximately pairwise additive. Qualitatively, this is because the dispersion interaction results from a small perturbation of electronic motions so that many such perturbations can add without serious mutual interaction. Because of this simplification and its ubiquity in colloid and surface science, dispersion forces have received the most significant attention in the past half-century. The way dispersion forces lead to long-range interactions is discussed in Section VI-3 below. Before we present this discussion, it is useful to recast the key equations in cgs/esu units and SI units in Tables VI-2 and VI-3. 

In an extensive SFA study of protein receptor-ligand interactions, Leckband and co-workers [114] showed the importance of electrostatic, dispersion, steric, and hydrophobic forces in mediating the strong streptavidin-biotin interaction. Israelachvili and co-workers [66, 115] have measured the Hamaker constant for the dispersion interaction between phospholipid bilayers and find A = 7.5 1.5 X 10 erg in water. 

A thin film of hydrocarbon spread on a horizontal surface of quartz will experience a negative dispersion interaction. Treating these as 1 = quartz, 2 = n-decane, 3 = vacuum, determine the Hamaker constant A123 for the interaction. Balance the negative dispersion force (nonretarded) against the gravitational force to find the equilibrium film thickness. 

Determine the net DLVO interaction (electrostatic plus dispersion forces) for two large colloidal spheres having a surface potential 0 = 51.4 mV and a Hamaker constant of 3 x 10 erg in a 0.002Af solution of 1 1 electrolyte at 25°C. Plot U(x) as a function of x for the individual electrostatic and dispersion interactions as well as the net interaction. 

There are tliree important varieties of long-range forces electrostatic, induction and dispersion. Electrostatic forces are due to classical Coulombic interactions between the static charge distributions of the two molecules. They are strictly pairwise additive, highly anisotropic, and can be either repulsive or attractive. 

Long-range forces are most conveniently expressed as a power series in Mr, the reciprocal of the intemiolecular distance. This series is called the multipole expansion. It is so connnon to use the multipole expansion that the electrostatic, mduction and dispersion energies are referred to as non-expanded if the expansion is not used. In early work it was noted that the multipole expansion did not converge in a conventional way and doubt was cast upon its use in the description of long-range electrostatic, induction and dispersion interactions. However, it is now established [8, 9, 10, H, 12 and 13] that the series is asymptotic in Poincare s sense. The interaction energy can be written as... 

The measurement of surface forces out-of-plane (nonual to the surfaces) represents a central field of use of the SFA teclmique. Besides the ubiquitous van der Waals dispersion interaction between two (mica) surfaces... 

Fig. 4, 33 The Drude model for dispersive interactions. (Figure adapted from Rigby M, E B Smith, W A Wakeham and G C Maitland 1986. The Forces Between Molecules. Oxford, Clarendon Press.)...

The strength of dispersion interaction of a solid with a gas molecule is determined not only by the chemical composition of the surface of the solid, but also by the surface density of the force centres. If therefore this surface density can be sufficiently reduced by the pre-adsorption of a suitable substance, the isotherm may be converted from Type II to Type III. An example is rutile, modified by the pre-adsorption of a monolayer of ethanol the isotherm of pentane, which is of Type II on the unmodified rutile (Fig. 5.3, curve A), changes to Type III on the treated sample (cf. Fig. 5.3 curve B). Similar results were found with hexane-l-ol as pre-adsorbate. Another example is the pre-adsorption of amyl alcohol on a quartz powder... 

Dispersive Interactions. For pairs of nonpolar polymers, the intermolecular forces are primarily of the dispersive type, and in such cases the energy of interaction between unlike segments is expected to be closely approximated by the geometric mean of the energies of interaction between the two like pairs (98). In this case, the Flory-Huggins interaction energy between this polymer pair can be expressed in terms of the solubiUty parameters 5 of the pure components. 

Forces Molecules are attracted to surfaces as the result of two types of forces dispersion-repulsion forces (also called London or van der Waals forces) such as described by the Lennard-Jones potential for molecule-molecule interactions and electrostatic forces, which exist as the result of a molecule or surface group having a permanent electric dipole or quadrupole moment or net electric charge. 

The continuum model, in which solvent is regarded as a continuum dielectric, has been used to study solvent effects for a long time [2,3]. Because the electrostatic interaction in a polar system dominates over other forces such as van der Waals interactions, solvation energies can be approximated by a reaction field due to polarization of the dielectric continuum as solvent. Other contributions such as dispersion interactions, which must be explicitly considered for nonpolar solvent systems, have usually been treated with empirical quantity such as macroscopic surface tension of solvent. 

When a gas comes in contact with a solid surface, under suitable conditions of temperature and pressure, the concentration of the gas (the adsorbate) is always found to be greater near the surface (the adsorbent) than in the bulk of the gas phase. This process is known as adsorption. In all solids, the surface atoms are influenced by unbalanced attractive forces normal to the surface plane adsorption of gas molecules at the interface partially restores the balance of forces. Adsorption is spontaneous and is accompanied by a decrease in the free energy of the system. In the gas phase the adsorbate has three degrees of freedom in the adsorbed phase it has only two. This decrease in entropy means that the adsorption process is always exothermic. Adsorption may be either physical or chemical in nature. In the former, the process is dominated by molecular interaction forces, e.g., van der Waals and dispersion forces. The formation of the physically adsorbed layer is analogous to the condensation of a vapor into a liquid in fret, the heat of adsorption for this process is similar to that of liquefoction. 

Dispersion forces are ubiquitous and are present in all molecular interactions. They can occur in isolation, but are always present even when other types of interaction dominate. Typically, the interactions between hydrocarbons are exclusively dispersive and, because of them, hexane, at S.T.P., is a liquid boiling at 68.7°C and is not a gas. Dispersive interactions are sometimes referred to as hydrophobic or lyophobic particularly in the fields of biotechnology and biochemistry. These terms appear to have arisen because dispersive substances, e.g., the aliphatic hydrocarbons, do not dissolve readily in water. Biochemical terms for molecular interactions in relation to the physical chemical terms will be discussed later. 

Charge Fluctuation - the Source of Dispersive Forces and Dispersive Interactions... 

The dipoles are shown interacting directly as would be expected. Nevertheless, it must be emphasized that behind the dipole-dipole interactions will be dispersive interactions from the random charge fluctuations that continuously take place on both molecules. In the example given above, the net molecular interaction will be a combination of both dispersive interactions from the fluctuating random charges and polar interactions from forces between the two dipoles. Examples of substances that contain permanent dipoles and can exhibit polar interactions with other molecules are alcohols, esters, ethers, amines, amides, nitriles, etc. 

The induced counter-dipole can act in a similar manner to a permanent dipole and the electric forces between the two dipoles (permanent and induced) result in strong polar interactions. Typically, polarizable compounds are the aromatic hydrocarbons examples of their separation using induced dipole interactions to affect retention and selectivity will be given later. Dipole-induced dipole interaction is depicted in Figure 12. Just as dipole-dipole interactions occur coincidentally with dispersive interactions, so are dipole-induced dipole interactions accompanied by dispersive interactions. It follows that using an n-alkane stationary phase, aromatic... 

There are three types of interactions that contribute to van der Waals forces. These are interactions between freely rotating permanent dipoles (Keesom interactions), dipole-induced dipole interaction (Debye interactions), and instantaneous dip le-induced dipole (London dispersion interactions), with the total van der Waals force arising from the sum. The total van der Waals interaction between materials arise from the sum of all three of these contributions. 

---