Interactions dispersion

In the case of a loosely structured, highly solvated train-loop-tail-like conformation of the adsorbed layer, as is the case with flexible polymers, the density of the adsorbed layer approaches that of the bulk solution and, hence, the contribution from dispersion (London-van der Waals) interactions may be negligibly small. However, for the formation of a compact adsorbed protein layer, dispersion interactions have to be taken into account. 

For a sphere interacting with a planar surface, the contribution from dispersion interaction to the Gibbs energy of adsorption can be approximated by 

32 is the Hamaker constant for the interaction between the flat snrface (1) and the spherical protein molecule (2) across the (aqueous) medium (3) a is the radius of the sphere 

Under most conditions, ft a, so that Equation 15.11 simplifies to 

Values for Hamaker constants (of the individual components) are given in several references and a compilation is also made in Table 16.1. The Hamaker constant for the system can be derived from the individual ones according to  

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Eq. IV-9 would use the surface tensions that liquids A and B would have if their inter-molecular potentials contained only the same kinds of interactions as those involved between A and B (see Refs. 20, 22-24). For the hydrocarbon-water system, Fowkes [20] assumed that Uh arose solely from dispersion interactions leaving... 

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. 

These equations imply that A132 will exceed A12 if A33 is larger than A13 + A23. This effect, termed lyophobic bonding, occurs if the solvent-surface interaction is weaker than that between the solvent molecules. More interestingly, the dispersion interaction will be repulsive (A 132 < 0) when An and/or A23 are sufficiently large. Israelachvili [1] tabulates a number of Am values Awhw Ahwh 0-4X 10 erg, Apwp 1 x 10" erg, and Aqwq = O.SX -IO erg, where W, H, P, and Q denote water, hydrocarbon, polystyrene and quartz respectively. 

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. 

Just as with interaction energies, II can be regarded as the sum of several components. These include Ilm due to dispersion interaction, Ilf due to electrostatic interactions between charged surfaces, 11 due to overlapping adsorbed layers of neutral... 

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. 

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... 

Hence, the same teclmiques used to calculate are also used for Cg. Note that equation (A1.5.28) has a geometrical factor whose sign depends upon the geometry, and that, unlike tlie case of the two-body dispersion interaction, the triple-dipole dispersion energy has no minus sign in front of the positive coefficient Cg. For example, for an equilateral triangle configuration the triple-dipole dispersion is repulsive and varies... 

Once the models for the charge distributions are in hand, the electrostatic interaction is computed as the interaction between the sets of point charges or distributed nuiltipoles, and added to an atom-atom, exp-6 fonn that represents the repulsion and dispersion interactions. Different exp-6 parameters, often from [140. 

We discuss classical non-ideal liquids before treating solids. The strongly interacting fluid systems of interest are hard spheres characterized by their harsh repulsions, atoms and molecules with dispersion interactions responsible for the liquid-vapour transitions of the rare gases, ionic systems including strong and weak electrolytes, simple and not quite so simple polar fluids like water. The solid phase systems discussed are ferroniagnets and alloys. 

The parameters a and b are characteristic of the substance, and represent corrections to the ideal gas law dne to the attractive (dispersion) interactions between the atoms and the volnme they occupy dne to their repulsive cores. We will discnss van der Waals equation in some detail as a typical example of a mean-field theory. 

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... 

The dispersion interaction arises between the fluctuating multipoles and the moments they induce and can occur even between spherically synuuetric ions and neutrals. Thus,... 

Qualitatively, the first term of Eq. (27) represents the electron exchange repulsion as a result of the Pauli principle, and the second long-range term accounts for the attractive dispersion interaction. The [12-6] formulation is only qualitatively... 

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.)...

Irude model thus predicts that the dispersion interaction varies as 1//. wo-dimensional Drude model can be extended to three dimensions, the result being ... 

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