Charged Spherical Particles

Marmur [12] has presented a guide to the appropriate choice of approximate solution to the Poisson-Boltzmann equation (Eq. V-5) for planar surfaces in an asymmetrical electrolyte. The solution to the Poisson-Boltzmann equation around a spherical charged particle is very important to colloid science. Explicit solutions cannot be obtained but there are extensive tabulations, known as the LOW tables [13]. For small values of o, an approximate equation is [9, 14]... 

In addition, Dirac s theory provides a direct explanation for the fact that the electron magnetic dipole moment is about twice the value expected classically on the basis of a spherical charged particle rotating around one... 

The reason is that Ag and Cl are both essentially spherical charged particles. However, collision orientation may be important in reactions that involve nonspherical molecules (assumption 3). Consider the following hypothetical reaction ... 

The friction drag force over a spherical charge particle moving through a liquid electrolyte is given based on Stake s law as... 

Therefore, the potential on the surface of a spherical-charged particle is the sum of the potential from its charge and that from its ion cloud, as a spherical shell with the opposite charge of the particle, located at the Debye length (/c ) away from the surface of the macroion. We shall use this result in describing the mobility of macroions in electrolyte solutions. 

Turbidity. Turbidity in water is removed by ozonation (0.5—2 ppm) through a combination of chemical oxidation and charge neutralization. GoUoidal particles that cause turbidity are maintained in suspension by negatively charged particles which are neutralized by ozone. Ozone further alters the surface properties of coUoidal materials by oxidizing the organic materials that occur on the surface of the coUoidal spherical particles. 

The simulations to investigate electro-osmosis were carried out using the molecular dynamics method of Murad and Powles [22] described earher. For nonionic polar fluids the solvent molecule was modeled as a rigid homo-nuclear diatomic with charges q and —q on the two active LJ sites. The solute molecules were modeled as spherical LJ particles [26], as were the molecules that constituted the single molecular layer membrane. The effect of uniform external fields with directions either perpendicular to the membrane or along the diagonal direction (i.e. Ex = Ey = E ) was monitored. The simulation system is shown in Fig. 2. The density profiles, mean squared displacement, and movement of the solvent molecules across the membrane were examined, with and without an external held, to establish whether electro-osmosis can take place in polar systems. The results clearly estab-hshed that electro-osmosis can indeed take place in such solutions. 

Loeb, AL Overbeek, JTG Wiersema, PH, The Electrical Double Layer Around a Spherical Colloid Particle, Computation of the Potential, Charge Density, and Free Energy of the Electrical Double Layer Around a sperical Colloid Particle M.I.T. Press Cambridge, MA, 1961. Lorentz, HA, Wied, Ann. 11, 70, 1880. 

Gl) have also derived a similar modified equation for the case of a drop of conducting liquid surrounded by a gaseous suspension of both neutral and charged particles, enclosed in a spherical container. 

Molecules consist of electrons and nuclei the principal difference between a molecule and an atom is that the latter has only one particle of the nuclear sort. Classical potential theory, which in this case works for quantirm mechanics, says that Coulomb s law operates between charged particles. This asserts that the potential energy of a pair of spherical, charged objects is... 

Electrostatic interactions between a spherical charged protein particle and an oppositely charged, deformable interface can be estimated by evaluating the electrostatic force on a small segment of the interface as that produced by an adjacent flaf section on the protein surface. The strength of this interaction is dependent on the separation distance (b) between those two segments, and so will be a function of the position of the interfacial segment ... 

Calculation of Coagulation Rate. Here we discuss an interaction potential of two charged particles in a liquid within a framework of DLVO theory. Following this theory, the overall interaction potential U, of charged spherical particles of the same radius R and surface distance d is a sum of a coulombic repulsive force of charged particles and a van der Waals attractive force given by the equation (28) ... 

Spherical latex particles with a reasonably well-defined number of charges per particle can be synthesized and used to study the non-Newtonian behavior of charged dispersions and related electroviscous phenomena (described in Chapter 4). The surface... 

Considering the track structures as spherical or cylindrical formations and using the methods of diffusion kinetics, it proved to be possible to explain many experimental facts concerning the radiolysis of water solutions, in particular, the dependence of yields on LET.361 It is owing to this that the LET was considered to be a universal qualitative characteristic of radiation, and the concentration of active particles was considered to be in direct dependence on the LET with no regard for the type of charged particle. 

Figure 7.13 Electrophoretic mobility and zeta potential for spherical colloidal particles in electrolyte solutions containing polyvalent ions (A+lz+ = A /z = 70 ft cm2 mol -1). Electrolyte type is numbered with counter-ion charge number first ...

Ohshima, H. (2002). Electrophoretic mobility of a charged spherical colloidal particle covered with an uncharged polymer layer. Electrophoresis 23,1993-2000. 

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