Repulsion electrostatic

To calcualte the repulsive force between two plates, we need the local electrostatic potential, ift, which creates a local stress. The local stress can be calculated from the osmotic pressure caused by the local ionic concentration, which is in turn caused by the local electrostatic potential [17]. 

FIGURE 10J. View ofthermodynamici rstem for paraOel plate interaction energy calculation. 

For asymmetric parallel plate cases (i.e., different surface potentials or surface charges), the force has an additional stress term. 

FIGURE 10 Electric potential function between two plates for small interaction. The total potential can be approximated by the svim of the two sin e potentials as shown. 

To determine the potential at the midplane, the Poisson-Boltzmann equation must be solved for the parallel plate geometry. For a z—z electrolyte, the Poisson-Boltzmann equation is given by [18] 

The surfaces of colloidal particles are often charged and these changes can arise from a number of sources. Chemically bound ionogenic species may be found on the surface of particles such as rubber or paint latex particles. Charged species may be physically adsorbed if ionic surface active materials, for example, have been added. A charged surface may occur on a crystal lattice. An example is the isomorphous substitution of lower valency cations such as aluminium for silicon in the lattice structure of clays. A further example is the adsorption of lattice ions 

Unlike charges attract and like charges repel each other, so there is a high concentration of counterions attracted to the particle surface whilst co-ions (those with the same sign charge as that of the surface) are repelled. Thermal motion, i.e. diffusion, opposes this local concentration gradient so that the counterions are in a diffuse cloud around the particle. Of course particles which have a like charge will also repel each other but the interaction of the particle surfaces will be screened by the counterion clouds between the particles. The interaction potential is a function of the surface potential, i]/o, and the permittivity of the fluid phase, e = r80, where r is the relative permittivity.12,27 

The Debye-Hiickel decay parameter, k, which has units of m is a function of the ionic strength, I, and the permittivity  

In practice we use the electrokinetic potential, , in place of the surface potential as it is readily measurable and will reflect the changes to the surface as a result of adsorbed ionic species. 

Values of (l/jc) at various 1 1 electrolyte concentrations are given below  

Combination of van der Waals attraction and double layer repulsion results in the well-known theory of coUoid stability due to Deryaguin- Landau-Verwey- Overbeek (DLVO) theory [5, 6]  

The above presentation is for a system at low electrolyte concentration. At large h, attraction prevails resulting in a shallow minimum on the order of few 

The surface potential T o decreases linearly with (the Stem Potential), which is nearly equal to the measurable zeta (C) potential. 

The energy-distance curve is characterised by two minima, a shallow secondary rninimum (weak and reversible attraction) and a primary deep minimum (strong and irreversible attraction). 

Particles deposited under conditions of secondary minimum will be weakly attached, whereas particles deposited under conditions of primary minimum will be strongly attached. At intermediate distances of separation, an energy maximum is obtained whose height depends on the surface or zeta potential, electrolyte concentration and valency of the ions. This maximum prevents particle deposition. 

Gmax clearly decreases with increasing NaCl concentration and eventually disappears at 10 mol dm . Thus, particle deposition for particles with the same sign as the surface will increase with increasing electrolyte concentrations. 

The above trend was confirmed by Hull and Kitchener [39] using a rotating disc coated with a negative film and negative polystyrene latex particles. The number of polystyrene particles deposited was found to increase with increasing NaCl concentration, reaching a maximum at CnsO 10 mol dm . The ratio of maximum number of particles deposited Nmax to the number deposited at any other NaCl concentration Nj (the so-called stability ratio W) was calculated and plotted versus NaCl concentration. 

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A major advance in force measurement was the development by Tabor, Win-terton and Israelachvili of a surface force apparatus (SFA) involving crossed cylinders coated with molecularly smooth cleaved mica sheets [11, 28]. A current version of an apparatus is shown in Fig. VI-4 from Ref. 29. The separation between surfaces is measured interferometrically to a precision of 0.1 nm the surfaces are driven together with piezoelectric transducers. The combination of a stiff double-cantilever spring with one of a number of measuring leaf springs provides force resolution down to 10 dyn (10 N). Since its development, several groups have used the SFA to measure the retarded and unretarded dispersion forces, electrostatic repulsions in a variety of electrolytes, structural and solvation forces (see below), and numerous studies of polymeric and biological systems. 

The ernes of ionic surfactants are usually depressed by tire addition of inert salts. Electrostatic repulsion between headgroups is screened by tire added electrolyte. This screening effectively makes tire surfactants more hydrophobic and tliis increased hydrophobicity induces micellization at lower concentrations. A linear free energy relationship expressing such a salt effect is given by ... 

Unlike the forces between ions which are electrostatic and without direction, covalent bonds are directed in space. For a simple molecule or covalently bonded ion made up of typical elements the shape is nearly always decided by the number of bonding electron pairs and the number of lone pairs (pairs of electrons not involved in bonding) around the central metal atom, which arrange themselves so as to be as far apart as possible because of electrostatic repulsion between the electron pairs. Table 2.8 shows the essential shape assumed by simple molecules or ions with one central atom X. Carbon is able to form a great many covalently bonded compounds in which there are chains of carbon atoms linked by single covalent bonds. In each case where the carbon atoms are joined to four other atoms the essential orientation around each carbon atom is tetrahedral. 

The Exclusion Prin cip le is t ii an tn ni mechanical in nature, and outside the realm ofeveryday, classical" experience. Think ofii as iheinherent tendency of electron s to slay away from oneanoiher, to be m n tnally excluded. Excbi sion is due to lb c an lisymmdry of the wave function and nol to electrostatic coulomb repulsion between two electrons. Exclusion exists even m the absence of electrostatic repulsions. 

Tire total energy equals the sum of the nuclear energy (the electrostatic repulsion between the positively charged nuclei) and the electronic energy. The electronic energy comprises... 

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 ... 

Ihc complete neglect of differential overlap (CNDO) approach of Pople, Santry and Segal u as the first method to implement the zero-differential overlap approximation in a practical fashion [Pople et al. 1965]. To overcome the problems of rotational invariance, the two-clectron integrals (/c/c AA), where fi and A are on different atoms A and B, were set equal to. 1 parameter which depends only on the nature of the atoms A and B and the ii ilcniuclear distance, and not on the type of orbital. The parameter can be considered 1.0 be the average electrostatic repulsion between an electron on atom A and an electron on atom B. When both atomic orbitals are on the same atom the parameter is written , A tiiid represents the average electron-electron repulsion between two electrons on an aiom A. 

In PPP-SCF calculations, we make the Bom-Oppenheimer, a-rr separation, and single-electron approximations just as we did in Huckel theor y (see section on approximate solutions in Chapter 6) but we take into account mutual electrostatic repulsion of n electrons, which was not done in Huckel theory. We write the modified Schroedinger equation in a form similar to Eq. 6.2.6... 

In the Huckel theory of simple hydrocarbons, one assumes that the election density on a carbon atom and the order of bonds connected to it (which is an election density between atoms) are uninfluenced by election densities and bond orders elsewhere in the molecule. In PPP-SCF theory, exchange and electrostatic repulsion among electrons are specifically built into the method by including exchange and electrostatic terms in the elements of the F matrix. A simple example is the 1,3 element of the matrix for the allyl anion, which is zero in the Huckel method but is 1.44 eV due to election repulsion between the 1 and 3 carbon atoms in one implementation of the PPP-SCF method. 

Wheland intermediate (see below) as its model for the transition state. In this form it is illustrated by the case mentioned above, that of nitration of the phenyltrimethylammonium ion. For this case the transition state for -nitration is represented by (v) and that for p-substitution by (vi). It is argued that electrostatic repulsions in the former are smaller than in the latter, so that m-nitration is favoured, though it is associated rvith deactivation. Similar descriptions can be given for the gross effects of other substituents upon orientation. 

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. 

In an aqueous system with large particles weU-separated by a distance, s, (D and 5 > t ) the electrostatic repulsion energy between two identical charged spheres may be approximated (1) ... 

Response to Electric and Acoustic Fields. If the stabilization of a suspension is primarily due to electrostatic repulsion, measurement of the zeta potential, can detect whether there is adequate electrostatic repulsion to overcome polarizabiUty attraction. A common guideline is that the dispersion should be stable if > 30 mV. In electrophoresis the appHed electric field is held constant and particle velocity is monitored using a microscope and video camera. In the electrosonic ampHtude technique the electric field is pulsed, and the sudden motion of the charged particles relative to their counterion atmospheres generates an acoustic pulse which can be related to the charge on the particles and the concentration of ions in solution (18). 

In the absence of a suitable soHd phase for deposition and in supersaturated solutions of pH values from 7 to 10, monosilicic acid polymerizes to form discrete particles. Electrostatic repulsion of the particles prevents aggregation if the concentration of electrolyte is below ca 0.2 N. The particle size that can be attained is dependent on the temperature. Particle size increases significantly with increasing temperature. For example, particles of 4—8 nm in diameter are obtained at 50—100°C, whereas particles of up to 150 nm in diameter are formed at 350°C in an autoclave. However, the size of the particles obtained in an autoclave is limited by the conversion of amorphous siUca to quartz at high temperatures. Particle size influences the stabiUty of the sol because particles <7 nm in diameter tend to grow spontaneously in storage, which may affect the sol properties. However, sols can be stabilized by the addition of sufficient alkaU (1,33). 

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