Repulsion between particles

Quantum mechanical calculations view a molecule as a collection of point nuclei and electrons with fixed masses and charges. The energy terms include the kinetic energy of each particle and the coulombic energies between the particles (repulsion between nuclei, attraction between the nucleus and an electron, and repulsion between electrons). Here we will review some basic equations of quantum mechanics to understand quantum mechanical methods, such as Hartree-Fock, semiempirical, and density functional theory methods, that have been most widely used for the clay mineral modeling where simulation size is greater than the molecular cluster with several atoms. 

The repulsion between two double layers is important in determining the stability of colloidal particles against coagulation and in setting the thickness of a soap film (see Section VI-5B). The situation for two planar surfaces, separated by a distance 2d, is illustrated in Fig. V-4, where two versus x curves are shown along with the actual potential. 

An additional method for increasing particle size deserves mention. When a precipitate s particles are electrically neutral, they tend to coagulate into larger particles. Surface adsorption of excess lattice ions, however, provides the precipitate s particles with a net positive or negative surface charge. Electrostatic repulsion between the particles prevents them from coagulating into larger particles. 

Because the electrically charged droplets retain their charge but get smaller, their electric field increases. At some point, mutual repulsion between like charges causes charged particles (ions) to leave the surface of the droplet (ion evaporation). These ions can be detected by the mass spectrometer. 

The stmcture of the particles inside the nucleus was the next question to be addressed. One step in this direction was the discovery of the neutron in 1932 by Chadwick, and the deterrnination that the nucleus was made up of positively charged protons and uncharged neutrons. The number of protons in the nucleus is known as the atomic number, Z. The number of neutrons is denoted by A/, and the atomic mass is thus A = Z - - N. Another step toward describing the particles inside the nucleus was the introduction of two forces, namely the strong force that holds the protons and neutrons together in spite of the repulsion between the positive charges of the protons, and the weak force that produces the transmutation by P decay. 

As shown in Figure 2, adsorption of dispersants on particle surfaces can increase 2eta potential further, enhancing electrostatic repulsion. Increased repulsion between particles is evidenced by lower viscosity in concentrated slurries, or decreased settling rates in dilute suspensions. The effect of added dispersants on settling of (anhydrous) iron oxide particles is shown in Figure 3. 

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 ... 

When clay or similar material is dried, often a pressure gradient is developed by the forces of repulsion between particles as shrinkage brings the particles close together (25). This gradient forces Hquid toward the surface and the resulting moisture profile resembles that characteristic of Hquid diffusion. 

Another example of phase transitions in two-dimensional systems with purely repulsive interaction is a system of hard discs (of diameter d) with particles of type A and particles of type B in volume V and interaction potential U U ri2) = oo for < 4,51 and zero otherwise, is the distance of two particles, j l, A, B] are their species and = d B = d, AB = d A- A/2). The total number of particles N = N A- Nb and the total volume V is fixed and thus the average density p = p d = Nd /V. Due to the additional repulsion between A and B type particles one can expect a phase separation into an -rich and a 5-rich fluid phase for large values of A > Ac. In a Gibbs ensemble Monte Carlo (GEMC) [192] simulation a system is simulated in two boxes with periodic boundary conditions, particles can be exchanged between the boxes and the volume of both boxes can... 

The Orientation of Water Molecules Adjacent to an Ion. Order and Disorder in the Vicinity of Solute Particles. Coulomb Attraction and Repulsion between Ions. Activity Coefficients. The Distance of Closest Approach. Activity Coefficients of Various Solutes. Forces Superimposed on the Coulomb Forces. 

Electrical repulsion between protons should cause a nucleus that contains more than one proton to fly apart. In Section 2H. we describe how the third type of fundamental force, called the strong nuclear force, acts within nuclei and generates enough attraction among nuclear particles to hold nuclei together. 

Neutrons readily induce nuclear reactions, but they always produce nuclides on the high neutron-proton side of the belt of stability. Protons must be added to the nucleus to produce an unstable nuclide with a low neutron-proton ratio. Because protons have positive charges, this means that the bombarding particle must have a positive charge. Nuclear reactions with positively charged particles require projectile particles that possess enough kinetic energy to overcome the electrical repulsion between two positive particles. 

The major impediment to fusion reactions is that the reacting nuclei must have very high kinetic energies to overcome the electrical repulsion between positive particles. The fusion of two hydrogen nuclei has the lowest possible repulsion barrier because it involves two Z — I nuclei. Even so, this reaction requires kinetic energies... 

Ionic compounds such as halides, carboxylates or polyoxoanions, dissolved in (generally aqueous) solution can generate electrostatic stabilization. The adsorption of these compounds and their related counter ions on the metallic surface will generate an electrical double-layer around the particles (Fig. 1). The result is a coulombic repulsion between the particles. If the electric potential associated with the double layer is high enough, then the electrostatic repulsion will prevent particle aggregation [27,30]. 

Values of the calibration curves for the various column sets are given in Table IV. The corves themselves are shown in Figure 5. The slope of the calibration curves decrease with increasing ionic strength. This is the result of reduced electrostatic repulsion between particles and substrate which permits greater penetration of the porous matrix. 

Prieve, D. C. (1986) Hydrodynamic measurement of double-layer repulsion between colloidal particle and flat plate. Science, 231, 1269-1270. 

The polycationic ammonium salt PEU can be chosen for increasing the ionic cloud in the electrical double layer, thus raising the electric repulsion between the gold particles in the sol. Small particles can be obtained (mean diameters between 3.1 and 4.2 nm) [24]. 

The first two tenns in Eq. (2) represent the kinetic energy of the nuclei and the electrons, respectively. The remaining three terms specify the potential energy as a function of the interaction between the particles. Equation (3) expresses the potential function for the interaction of each pair of nuclei. In general, this sum is composed of terms that are given by Coulomb s law for the repulsion between particles of like charge. Similarly, Eq. (4) corresponds to the electron-electron repulsion. Finally, Eq. (5) is the potential function for the attraction between a given electron (<) and a nucleus (j). 

Figure 9.61 QDs containing carboxylate groups can be coupled to amine-containing proteins or other molecules using the EDC/sulfo-NHS reaction to form amide bond linkages. The intermediate sulfo-NHS ester is negatively charged and will help maintain particle stability due to like charge repulsion between particles.

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