Interaction energy electrostatic repulsion

Schematic forms of the curves of interaction energies (electrostatic repulsion Vr, van der Waals attraction Va, and total (net) interaction Vj) as a function of the distance of surface separation. Summing up repulsive (conventionally considered positive) and attractive energies (considered negative) gives the total energy of interaction. Electrolyte concentration cs is smaller than cj. At very small distances a repulsion between the electronic clouds (Born repulsion) becomes effective. Thus, at the distance of closest approach, a deep potential energy minimum reflecting particle aggregation occurs. A shallow so-called secondary minimum may cause a kind of aggregation that is easily counteracted by stirring.

Figure 1. Schematic illustrating the form of the curve of potential energy vs. distance for the interaction between two spheres. Total interaction involving electrostatic repulsion and van der Waals attraction.

The ion-dipole interaction may be approximately expressed as f = +Aa n - 2Ba-m, where the first term is for Mie repulsions and the second is the effective sum of the ion-permanent dipole (zepa-2) and ion-induced dipole (z2e2a a 4/2EA) interactions and electrostatic repulsions. The latter are dominated by the repulsions in the first and second shells (see later discussion), which are generally proportional to a-3. From the equilibrium condition, nAa0"n = 2rnBa0 m, where a is the equilibrium ion-dipole center distance at < >o, the bottom of the energy well. Writing a = a (l + x/a,) and expanding the powers of (1 + x/a0) to the quadratic terms, the first binomial terms vanish and we obtain ... 

Although the intermolecular interactions are non-additive, we may ask whether individual contributions to the interaction energy (electrostatic, induction, dispersion, or valence repulsion) are additive ... 

The second contribution to the energy arises from the electrostatic repulsion between pairs III electrons. This interaction depends on the electron-electron distance and, as we have seen, is calculated from infegrals such as ... 

When two or more molecular species involved in a separation are both adsorbed, selectivity effects become important because of interaction between the 2eobte and the adsorbate molecule. These interaction energies include dispersion and short-range repulsion energies (( ) and ( )j ), polarization energy (( )p), and components attributed to electrostatic interactions. 

The parameter redundancy is also the reason that care should be exercised when trying to decompose energy differences into individual terms. Although it may be possible to rationalize the preference of one conformation over another by for example increased steric repulsion between certain atom pairs, this is intimately related to the chosen functional form for the non-bonded energy, and the balance between this and the angle bend/torsional terms. The rotational banier in ethane, for example, may be reproduced solely by an HCCH torsional energy term, solely by an H-H van der Waals repulsion or solely by H-H electrostatic repulsion. Different force fields will have (slightly) different balances of these terms, and while one force field may contribute a conformational difference primarily to steric interactions, another may have the... 

Figure 6.3. Schematic potential energy curve describing the interactions between colloidal particles. The overall potential is a sum of an electrostatic repulsive term which arises due to any charged groups on the surface of the particle and the attractive van der Waals term.

The DLVO theory, with the addition of hydration forces, may be used as a first approximation to explain the preceding experimental results. The potential energy of interaction between spherical particles and a plane surface may be plotted as a function of particle-surface separation distance. The total potential energy, Vt, includes contributions from Van der Waals energy of interaction, the Born repulsion, the electrostatic potential, and the hydration force potential. [Israelachvili (13)]. 

Electrostatic repulsion between high-energy electrons -produced from an accelerator, or by photon interaction with substrate atoms - and valency electrons in the polymer cause excitation and ionization. The chemical reactions result from these species. 

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