Attraction and repulsion forces

Madeluag constant For an ionic crystal composed of cations and anions of respective change z + and z, the la ttice energy Vq may be derived as the balance between the coulombic attractive and repulsive forces. This approach yields the Born-Lande equation,... 

The equation of state for an ideal gas, that is a gas in which the volume of the gas molecules is insignificant, attractive and repulsive forces between molecules are ignored, and molecules maintain their energy when they collide with each other. 

The small differences m stability between branched and unbranched alkanes result from an interplay between attractive and repulsive forces within a molecule (intramo lecular forces) These forces are nucleus-nucleus repulsions electron-electron repul sions and nucleus-electron attractions the same set of fundamental forces we met when... 

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. 

DLVO Theory. The overall stabiUty of a particle dispersion depends on the sum of the attractive and repulsive forces as a function of the distance separating the particles. DLVO theory, named for Derjaguin and Landau (11) and Verwey and Overbeek (12), encompasses van der Waals attraction and electrostatic repulsion between particles, but does not consider steric stabilization. The net energy, AGp between two particles at a given distance is the sum of the repulsive and attractive forces ... 

Fig. 16-4. Attractive and repulsive forces when helium atoms approach.

Equation (1.15) states that the internal energy of the ideal gas does not change with volume. This is true when the attractive and repulsive forces between the molecules in the gas are zero. 

The molecular separation in gases is large only if the pressure is small. At high pressures, attractive and repulsive forces become important in gases. 

The presence of intermolecular forces also accounts for the variation in the compression factor. Thus, for gases under conditions of pressure and temperature such that Z > 1, the repulsions are more important than the attractions. Their molar volumes are greater than expected for an ideal gas because repulsions tend to drive the molecules apart. For example, a hydrogen molecule has so few electrons that the its molecules are only very weakly attracted to one another. For gases under conditions of pressure and temperature such that Z < 1, the attractions are more important than the repulsions, and the molar volume is smaller than for an ideal gas because attractions tend to draw molecules together. To improve our model of a gas, we need to add to it that the molecules of a real gas exert attractive and repulsive forces on one another. 

The effectiveness of these forces differs and, furthermore, they change to a different degree as a function of the interatomic distance. The last-mentioned repulsion force is by far the most effective at short distances, but its range is rather restricted at somewhat bigger distances the other forces dominate. At some definite interatomic distance attractive and repulsive forces are balanced. This equilibrium distance corresponds to the minimum in a graph in which the potential energy is plotted as a function of the atomic distance ( potential curve , cf. Fig. 5.1, p. 42). 

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. 

The particles in a disperse system with a liquid or gas being the dispersion medium are thermally mobile and occasionally collide as a result of the Brownian motion. As the particles approach one another, both attractive and repulsive forces are operative. If the attractive forces prevail, agglomerates result indicating an instability of the system. If repulsive forces dominate, a homogeneously dispersed or stable dispersion remains. 

AFM has been used to image surfaces by probing both the attractive and repulsive forces experienced by the tip as a result of its proximity to the sample surface. In both modes, the probe tip is mounted on a cantilever spring. Three main designs have been employed metal foil with a splinter of diamond, a shaped tungsten wire that acts both as spring and tip, and microfabricated tip/cantilever composites. 

The elastic properties of materials can be understood, at least qualitatively, by considering the attractive and repulsive forces between atoms and molecules. 

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. 

While a nucleus attracts the electrons of another atom there are also repulsions both between the electrons and the nuclei of the atoms. When the attractive forces are greater than the repulsive forces the atoms get closer. When the attractive and repulsive forces become equal the electrons start to rotate around both nuclei (not only around the nucleus of their atom) and a bond is formed. 

Which of the many suggested laws of force i.e., what dependence of the attractive and repulsive forces on the distance between the particles concerned) should be chosen for the calculation ... 

Inert Gases. The calculation of 7 should be relatively straightforward for crystals of inert gases, in which only one kind of interaction may be expected. These crystals have a face-centered cubic structure. If each atom is treated as a point source of attractive and repulsive forces, only the forces between the nearest pairs of atoms are considered, the zero point energy is neglected, and no re-arrangement of atoms in the surface region is permitted, then the calculated 7 still depends on the equation selected to represent the interatomic potential U. 

Figure 2.10 Morse curve. Inter-atomic attractive and repulsive forces result in the formation of a bond length with a minimum energy level.

The increase in i>p 0 is due to a progressive increase in the coupling of M-0 and P-0 vibrations with an increasing atomic number of the lanthanide ion. Similarly, McRae and Karraker (201) have found that the Pp 0 increases with decreasing ionic radius in the complexes of TPP with lanthanide nitrates. This trend has, however, been explained by them in terms of relative influence of attractive and repulsive forces in these complexes. As the size of the lanthanide ion decreases, the repulsive forces in-... 

The force resolution is generally of the order of 10 N. One of the main advantages of the SFA technique compared to the two others presented here is that it allows the measurement of both attractive and repulsive forces. 

Part of a molecule or macromolecule endowed with sufficient anisotropy in both attractive and repulsive forces to contribute strongly to LC mesophase, or, in particular, to LC mesophase formation in low-molar-mass and polymeric substances. 

Air at room temperature and pressure consists of 99.9% void and 0.1% molecules of nitrogen and oxygen. In such a dilute gas, each individual molecule is free to travel at great speed without interference, except during brief moments when it undertakes a collision with another molecule or with the container walls. The intermolecular attractive and repulsive forces are assumed in the hard sphere model to be zero when two molecules are not in contact, but they rise to infinite repulsion upon contact. This model is applicable when the gas density is low, encountered at low pressure and high temperature. This model predicts that, even at very low temperature and high pressure, the ideal gas does not condense into a liquid and eventually a solid. 

The van der Waals equation is not a particularly accurate tool for prediction of compressibility Z, but it is the first theory to illuminate the nature of the attractive and repulsive forces that lead to departure from the perfect gas law. There are many more accurate equations of state that use more parameters, including the Benedict-Webb-Rubin equation, the Redlich-Kwong equation, and the Peng-Robinson equation. The compressibility factor can also be expanded into the virial form... 

Different distance dependences of attraction and repulsion forces at a molecular level [83]. 

The same kind of attractive and repulsive forces responsible for the tertiary structure operate to hold together and stabilize the subunit of the quaternary structure. 

The rheological characteristics of cement pastes are related to the nature of the attractive and repulsive forces which exist between cement and cement hydration product particles and can be categorized as follows ... 

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