Interaction attractive and repulsive

P/100, surface coverage / , AG/2.303 RT AC, free energy of adsorption R, gas constant T, temperature c, bulk inhibitor concentration n, number of water molecules replaced per inhibitor molecule f, inhibitor interaction parameter (0, no interaction + attraction and repulsion) K, constant and % P = 1 inhibited corrosion rate/uninhibited corrosion rate. 

The DLVO theory is a theoretical construct that has been able to explain many experimental data in at least a semiquantitative manner it illustrates plausibly that at least two types of interactions (attraction and repulsion) are needed to account for the overall interaction energy as a function of distance between the particles. 

Figure 7. Three possible interactions (.attractive and repulsive) between phases in multiple emulsions are shown in the upper diagram, while below those arrangements of the aqueous (W), surfactant (s and Sg) and oil phases are shown which must be taken into account in calculation of attractive and repulsive forces in these interactions. ...

The forces of interaction (attraction and repulsion) depend not only on the properties of the bodies in contact and the layer separating these, but also on the external applied force. This force determines the thickness of the gap between the bodies. If the compressing force is no greater than Fj ax (height of the force barrier) the adhesive force will be relatively small and equal to F nin H the compressive force exceeds F the adhesive force will be equal to F nin ... 

Many-body problems wnth RT potentials are notoriously difficult. It is well known that the Coulomb potential falls off so slowly with distance that mathematical difficulties can arise. The 4-k dependence of the integration volume element, combined with the RT dependence of the potential, produce ill-defined interaction integrals unless attractive and repulsive mteractions are properly combined. The classical or quantum treatment of ionic melts [17], many-body gravitational dynamics [18] and Madelung sums [19] for ionic crystals are all plagued by such difficulties. 

The first term includes the electrostatic attractions and repulsions between the net charges on pairs of atoms, one from each molecule. The second involves interactions between occupied and vacant molecular orbitals on the two molecules. The hypothesis is that the reaction proceeds in a way to produce the most favorable... 

Attractive and Repulsive Forces. The force that causes small particles to stick together after colliding is van der Waals attraction. There are three van der Waals forces (/) Keesom-van der Waals, due to dipole—dipole interactions that have higher probabiUty of attractive orientations than nonattractive (2) Debye-van der Waals, due to dipole-induced dipole interactions (ie, uneven charge distribution is induced in a nonpolar material) and (J) London dispersion forces, which occur between two nonpolar substances. 

In a force-displacement curve, the tip and sample surfaces are brought close to one another, and interact via an attractive potential. This potential is governed by intermolecular and surface forces [18] and contains both attractive and repulsive terms. How well the shape of the measured force-displacement curve reproduces the true potential depends largely on the cantilever spring constant and tip radius. If the spring constant is very low (typical), the tip will experience a mechanical instability when the interaction force gradient (dF/dD) exceeds the... 

As the distance between the two particles varies, they are subject to these long-range r " attractive forces (which some authors refer to collectively as van der Waals forces). Upon very close approach they will experience a repulsive force due to electron-electron repulsion. This repulsive interaction is not theoretically well characterized, and it is usually approximated by an empirical reciprocal power of distance of separation. The net potential energy is then a balance of the attractive and repulsive components, often described by Eq. (8-16), the Lennard-Jones 6-12 potential. 

A measurement of the density of helium gas shows that it is a monatomic gas. Molecules of He2 do not form. What difference between hydrogen atoms and helium atoms accounts for the absence of bonding for helium The answer to this question also must lie in the attractive and repulsive electrical interactions between two helium atoms when they approach each other. Figure 16-4A shows the attractive forces in one of our hypothetical instantaneous snapshots. There are, of course, four electrons and each is attracted to each nucleus. In Figure 16-4B we see the repulsive forces. Taking score, we find in Figure 16-4A eight attractive interactions, four... 

These two complementary mles are intuitively obvious, e.g. can be simply derived by considering the lateral attractive and repulsive interactions of coadsorbed reactants and promoters as already shown in section 4.5.9.2. They can explain all the observed promotionally induced kinetics for more than sixty different catalytic systems (Table 6.1). As an example these two rules can explain all the observed changes in kinetics orders with [Pg.299]

Surface force apparatus has been applied successfully over the past years for measuring normal surface forces as a function of surface gap or film thickness. The results reveal, for example, that the normal forces acting on confined liquid composed of linear-chain molecules exhibit a periodic oscillation between the attractive and repulsive interactions as one surface continuously approaches to another, which is schematically shown in Fig. 19. The period of the oscillation corresponds precisely to the thickness of a molecular chain, and the oscillation amplitude increases exponentially as the film thickness decreases. This oscillatory solvation force originates from the formation of the layering structure in thin liquid films and the change of the ordered structure with the film thickness. The result provides a convincing example that the SFA can be an effective experimental tool to detect fundamental interactions between the surfaces when the gap decreases to nanometre scale. 

Both of the above approaches rely in most cases on classical ideas that picture the atoms and molecules in the system interacting via ordinary electrical and steric forces. These interactions between the species are expressed in terms of force fields, i.e., sets of mathematical equations that describe the attractions and repulsions between the atomic charges, the forces needed to stretch or compress the chemical bonds, repulsions between the atoms due to then-excluded volumes, etc. A variety of different force fields have been developed by different workers to represent the forces present in chemical systems, and although these differ in their details, they generally tend to include the same aspects of the molecular interactions. Some are directed more specifically at the forces important for, say, protein structure, while others focus more on features important in liquids. With time more and more sophisticated force fields are continually being introduced to include additional aspects of the interatomic interactions, e.g., polarizations of the atomic charge clouds and more subtle effects associated with quantum chemical effects. Naturally, inclusion of these additional features requires greater computational effort, so that a compromise between sophistication and practicality is required. 

Figure 7.10. Distribution of two adsorbates A and B over a surface with different combinations of attractive and repulsive interactions, as predicted by a Monte Carlo simulation. (Courtesy A.P. van Bavel, Eindhoven.)...

If the substituents are nonpolar, such as an alkyl or aryl group, the control is exerted mainly by steric effects. In particular, for a-substituted aldehydes, the Felkin TS model can be taken as the starting point for analysis, in combination with the cyclic TS. (See Section 2.4.1.3, Part A to review the Felkin model.) The analysis and prediction of the direction of the preferred reaction depends on the same principles as for simple diastereoselectivity and are done by consideration of the attractive and repulsive interactions in the presumed TS. In the Felkin model for nucleophilic addition to carbonyl centers the larger a-substituent is aligned anti to the approaching enolate and yields the 3,4-syn product. If reaction occurs by an alternative approach, the stereochemistry is reversed, and this is called an anti-Felkin approach. 

The interactions between similar particles, dissimilar particles, and the dispersion medium constitute a complex but essential part of dispersion technology. Such interparticle interactions include both attractive and repulsive forces. These forces depend upon the nature, size, and orientation of the species, as well as on the distance of separation between and among the particles of the dispersed phase and the dispersion medium, respectively. The balance between these forces determines the overall characteristics of the system. 

Despite these modifications there remain a number of well-documented problems with the AM1/PM3 core-repulsion function [37] which has resulted in further refinements. For example, Jorgensen and co-workers have developed the PDDG (pair-wise distance directed Gaussian) PM3 and MNDO methods which display improved accuracy over standard NDDO parameterisations [38], However, for methods which include d-orbitals (e.g. MNDO/d [23,24], AMl/d [25] and AMI [39,40]) it has been found that to obtain the correct balance between attractive and repulsive Coulomb interactions requires an additional adjustable parameter p (previously evaluated using the one-centre two-electron integral Gss, Eq. 5-7), which is used in the evaluation of the two-centre two-electron integrals (Eq. 5-8). 

Again, we are reminded that Nature provides the ultimate model for emulation in the use of cooperative interactions of an enormous number of small structural components through many weak, reversible attractions and repulsions to produce such complex microstructures as proteins, enzymes, viruses, and cells with virtually perfect fidelity (Whitesides, 1991). One important strategy for producing ultra-thin films of promise for microelectronics... 

The fact that the nuclei do not get closer together does not mean that the forces of attraction and repulsion are equal. The minimum distance is that distance where the total energy (attraction and repulsion) is most favorable. Because the molecule has some vibrational energy, the internuclear distance is not constant, but the equilibrium distance is Ra. Figure 3.2 shows how the energy of interaction between two hydrogen atoms varies with internuclear distance. 

When the two atoms are relatively far apart, there is essentially no interaction at all between them both the attractive and repulsive forces are about zero. As the two atoms get closer, the attractive forces dominate, and the potential energy decreases to a minimum at a distance of 0.74 A, which is the H-H bond length. At distances less than 0.74 A, the repulsive forces become more important and the energy increases sharply. 

The discussion thus far has focused on the forces between an array of atoms connected together through covalent bonds and their angles. Important interactions occur between atoms not directly bonded together. The theoretical explanation for attractive and repulsive forces for nonbonded atoms i and j is based on electron distributions. The motion of electrons about a nucleus creates instantaneous dipoles. The instantaneous dipoles on atom i induce dipoles of opposite polarity on atom j. The interactions between the instantaneous dipole on atom i with the induced instantaneous dipole on atom j of the two electron clouds of nonbonded atoms are responsible for attractive interactions. The attractive interactions are know as London Dispersion forces,70 which are related to r 6, where r is the distance between nonbonded atoms i and j. As the two electron clouds of nonbonded atoms i and j approach one another, they start to overlap. There is a point where electron-electron and nuclear-nuclear repulsion of like charges overwhelms the London Dispersion forces.33 The repulsive... 

In MM3, the two types of nonbonded interactions which are included in the program are handled separately. The first includes attractive and repulsive forces between nonbonded atoms, their origins are described above, and the second is hydrogen bonding. 

The interaction between atoms separated by more than two bonds is described in terms of potentials that represent non-bonded or Van der Waals interaction. A variety of potentials are being used, but all of them correspond to attractive and repulsive components balanced to produce a minimum at an interatomic distance corresponding to the sum of the Van der Waals radii, V b = R — A. The attractive component may be viewed as a dispersive interaction between induced dipoles, A = c/r -. The repulsive component is often modelled in terms of either a Lennard-Jones potential, R = a/rlj2, or Buckingham potential R = aexp(—6r ). 

Factors that would affect the slope of this straight line are related to deviations real gases exhibit from ideality. At higher pressures, real gases tend to interact more, exerting forces of attraction and repulsion that Boyle s Law does not take into account. 

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