Energy attractive interaction

FIGURE 6.2 Arrangements of dipoles, (a) and (b) lead to attraction (interaction energy negative) and (c) leads to repulsion (interaction energy positive). 

Dipole-dipole electrostatic interaction perturbs the randomness of orientation. If the dipole on the left is pointing "up," then there is a slightly greater chance that the dipole on the right will point "down" (or vice versa both particles are equivalent in mutual perturbation). By increasing the chances of an attractive mutual orientation, the perturbation creates a net-attractive interaction energy. 

The total attractive interaction energy between molecules is the sum of three contributions dipole-dipole interactions, dipole-induced dipole interactions and induced dipole-induced dipole interactions. The important feature is the dependence of all three types of interaction energy on the inverse of the sixth power of the separation ... 

Thus the behavior of lattice defects bears some analogy to phase separation in fluids, or to the treatment of adsorption on localized sites. At low relative temperatures, the defects adopt a random distribution if they are sufficiently dilute if their concentration exceeds a certain value they segregate into defect-poor and defect-rich regions which can coexist. The concentration at which this occurs, and the relative temperature scale, depend on what can be represented as a nearest-neighbor attraction in the interaction potentials. The magnitude of the attractive interaction energy defines a critical temperature above which no segregation of defects occurs. 

First consider interactions in the pure state (Figure 11-10). Let the attractive interaction energy between a pair of small A molecules be eM and that between a pair of similarly sized B molecules be ea. If we assume that we can simply add the interactions between all pairs, then we can say that the interaction of a chosen A molecule with all its nearest neighbors is where z is the number of... 

Attractive Interaction Energy for Former Coated Particles... 

AVhen the particles are coated with a pol3mier of thickness S, the van der Waals attractive interaction energy is calculated by [13—16]... 

When the van der Waal s attraction brings a particle (molecule) closer to the surface, a repulsive force develops between the core electrons of the particle (molecule) surface and those of the atoms in the surface. The equilibrium separation is determined by a balance between repulsive and the attractive forces and decreases with increasing radius of the particle. Note also that the dielectric constant of the medium separating the particle (molecule) and the surface also affects the magnitude of E in Equations (9.1)-(9.3), as the constant C is inversely proportional to the dielectric constant. The van der Waal s attractive interaction energy is small, and thus the physisorption bands are weak and can be easily broken, especially when cleaning in high dielectric constant liquids. 

C is a coefficient that depends on the nature of the molecule, r the mean distance between the molecules and the total attractive interaction energy. 

Table 2. Comparison between the KSCED (LDA and GGA97) interaction energies with reference (CCSD(T)) results calculated at the same ab initio determined equilibrium geometry. A positive value indicates the attractive interaction. Energies (well depths) are given in kcal/mol. More details can be found in [Wesolowski and Tran, J. Chem. Phys., 118 (2003) 2072].

H.C. Hamaker, in 1937, was the first to treat London dispersion interactions between macroscopic objects. He started with the most basic case, to determine the interaction of a single molecule with a planar solid surface. He considered a molecular pair potential and its relation with the molecules present within the solid surface, to derive the total interaction potential by summing the attractive interaction energies between all pairs of molecules, ignoring multibody perturbations. In this way, he built up the whole from the parts. Thus, Hamaker s method is called the microscopic approach. 

Figure 12.8d shows a liquid neck between solid particles in a fluid, which holds the particles together by capillary forces (see Section 10.6) the attractive interaction energy can be very large. An example is bridging of various particles in cocoa mass (a melted chocolate)—where oil is the continuous phase—induced by tiny water droplets this then gives the cocoa mass a greatly enhanced viscosity. 

Adsorption is cooperative with an attractive interaction energy of YiEl (6 neighbors on the surface, 12 in the liquid / % = Y)-... 

The simplest potential form which exhibits the necessary properties of a core repulsion and an attractive interaction energy at larger separations is the square-well (SW) potential energy function, illustrated in Figure 10. 

It follows from Eqs (1.31) and (1.32) that the predominant contribution to the flexoelectric coefficients is determined by the isotropic intermolecular attraction modulated by the polar molecular shape. Indeed, in the general case the maximum attraction interaction energy V(R) kT where R is the equilibrium distance between the two molecules. It follows then that A ... 

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