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. 

Fig. V-5. The repulsive force between crossed cylinders of radius R (1 cm) covered with mica and immersed in propylene carbonate solutions of tetraethylammonium bromide at the indicated concentrations. The dotted lines are from double-layer theory (From Ref. 51).

Weeks J, Chandler D and Anderson H C 1971 Role of repulsive forces in determining the equilibrium structure of simple liquids J. Chem. Phys. 54 5237... 

Figure A3.1.1. Typical pair potentials. Illustrated here are the Lennard-Jones potential, and the Weeks-Chandler- Anderson potential, which gives the same repulsive force as the Leimard-Jones potential.

The van der Waals attraction arises from tlie interaction between instantaneous charge fluctuations m the molecule and surface. The molecule interacts with the surface as a whole. In contrast the repulsive forces are more short-range, localized to just a few surface atoms. The repulsion is, therefore, not homogeneous but depends on the point of impact in the surface plane, that is, the surface is corrugated. 

As the tip is brought towards the surface, there are several forces acting on it. Firstly, there is the spring force due to die cantilever, F, which is given by = -Icz. Secondly, there are the sample forces, which, in the case of AFM, may comprise any number of interactions including (generally attractive) van der Waals forces, chemical bonding interactions, meniscus forces or Bom ( hard-sphere ) repulsion forces. The total force... 

This term describes the repulsive forces keeping two nonbonded atoms apart at close range and the attractive force drawing them together at long range. 

The electrostatic potential at a point is the force acting on a unit positive charge placed at that point. The nuclei give rise to a positive (i.e. repulsive) force, whereas the electrons give rise to a negative potential. The electrostatic potential is an observable quantity that can be determined from a wavefunction using Equations (2.222) and (2.223) ... 

The urigin uf van der Waals repulsive forces is mutual interaction of electrons in atttrn 1 and those in atom 4. 

We assume that the nuclei are so slow moving relative to electrons that we may regard them as fixed masses. This amounts to separation of the Schroedinger equation into two parts, one for nuclei and one for electrons. We then drop the nuclear kinetic energy operator, but we retain the intemuclear repulsion terms, which we know from the nuclear charges and the intemuclear distances. We retain all terms that involve electrons, including the potential energy terms due to attractive forces between nuclei and electrons and those due to repulsive forces... 

On August 29,1982, physicists at the Heavy Ion Research Laboratory, Darmstadt, West Germany made and identified element 109 by bombing a target of Bi-209 with accelerated nuclei of Fe-58. If the combined energy of two nuclei is sufficiently high, the repulsive forces between the nuclei can be overcome. 

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... 

Nonbonded interactions are the forces be tween atoms that aren t bonded to one another they may be either attractive or repulsive It often happens that the shape of a molecule may cause two atoms to be close in space even though they are sep arated from each other by many bonds Induced dipole/induced dipole interactions make van der Waals forces in alkanes weakly attractive at most distances but when two atoms are closer to each other than the sum of their van der Waals radii nuclear-nuclear and electron-electron repulsive forces between them dominate the fvan derwaais term The resulting destabilization is called van der Waals strain... 

Diaxial repulsion (Section 3 10) Repulsive forces between axial substituents on the same side of a cyclohexane nng... 

Van der Waals radius (Section 2 17) A measure of the effec tive size of an atom or a group The repulsive force between two atoms increases rapidly when they approach each other at distances less than the sum of their van der Waals radii Van der Waals strain (Section 3 2) Destabilization that results when two atoms or groups approach each other too closely Also known as van der Waals repulsion Vicinal (Section 6 14) Describing two atoms or groups at tached to adjacent atoms... 

The above potential is referred to as a Lennard-Jones or 6-12 potential and is summed over all nonbonded pairs of atoms ij. The first positive term is the short range repulsion and the second negative term is the long range attraction. The parameters of the interaction are Aj and B... The convenient analytical form of the 6-12 potential means that it is often used, although an exponential repulsion term is usually considered to be a more accurate representation of the repulsive forces (as used in MM-t). 

The forces which bring about adsorption always include dispersion forces, which are attractive, together with short-range repulsive forces. In addition, there will be electrostatic (coulombic) forces if either the solid or the gas is polar in nature. Dispersion forces derive their name from the close connection between their origin and the cause of optical dispersion. First... 

An expression for the short-range repulsive force (which arises from the interpenetration of the electron clouds of the two atoms) can also be derived from quantum-mechanical considerations" as... 

The effect of polarity in enhancing the energy of interaction has been discussed by Kiselev and his associates who distinguish between non-specific adsorption, where only dispersion and repulsive forces are involved 4>d and and specific adsorption, where coulombic contributions (some or all of (p, [Pg.11]

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