Charged Particles in a Solution

Electrostatic theory tells us that the force between two point charges 2iS and Z2 at a distance r apart in vacuum is 

For univalent ions, i = z2 = 1, at a distance of 5 A, 7(r) = 66 Kcal/mole, which is of the order of magnitude of most single bonds. The 

The electrical parameters are equally impressive. The electric field intensity E(r) in the neighborhood of a point charge zS is, in vacuo 

SO that again for a univalent ion at a distance of 5 A, JS/ = 5.75 X 10 volts/cm, a field intensity larger by several powers of 10 than anything yet available in a laboratory. 

In a hypothetical, isotropic, structureless, uniform medium of dielectric constant D, the quantities F r)y t/(r), and E r) are all reduced by the factor 1 /D. For water at 25 C with D = 78.5, for the preceding cases we find F(r) = 1.2 X 10 dynes, U(r) = 0.83 Kcal/mole, and E r) = 7.2 X 10 volts/cm, somewhat reduced but still large. In considerations of solvent power it is the ratio U r)/kT which indicates the extent to which the dielectric medium is important (relative to thermal motion) in shielding charges from each other. 

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One of the most successful models for gel electrophoresis is the reptation theory of Lumpkin and Zimm for the migration of double-stranded DNA (Lumpkin, 1982). An in-depth discussion can be found in Zimm and Levene (1992) for a synopsis see Bloomfield et al. (2000). The velocity v of a charged particle in a solution with an electric field E depends on the electrical force Fei = ZqE, in which Z is the number of charges and q is the charge of a proton, and the frictional force l fr = —fv, in which/is the frictional coefficient. At steady state, these forces balance and the velocity is v = ZqE/f. The electrophoretic mobility fi is the velocity relative to the field strength, fi = vE = Zq/f. 

Electroosmosis is one of several electrokinetic effects that deal with phenomena associated with the relative motion of a charged solid and a solution. A related effect is the streaming potential that arises between two electrodes placed as in Figure 9.8.1 when a solution streams down the tube (essentially the inverse of the electroosmotic effect). Another is electrophoresis, where charged particles in a solution move in an electric field. These effects have been studied for a long time (37, 38). Electrophoresis is widely used for separations of proteins and DNA (gel electrophoresis) and many other substances (capillary electrophoresis). 

Electrophoresis refers to the motion of a charged particle in a solution in response to an applied electric field. The electrophoresis technique has been widely used to characterize the electrokinetic properties of charged particle-liquid interfaces. In the electrophoresis method, fine particles (usually of 1 pm in diameter) are dispersed in a solution. Under an applied electric field, the particle electrophoresis mobility, vg, defined as the ratio of particle velocity to electric field strength, is measured using an appropriate microscopic technique. The particle -potential is determined from the measured electrophoresis mobility, ve, by using the Smoluchowski equation expressed as... 

Here, u, is a transport property, known as mobility. It measures how mobile the charged particles are in an electric field. The mobility may be interpreted as the average velocity of a charged particle in a solution when acted upon by a force of one Newton per mole. The unit... 

Electrophoresis An electrochemical process in which macromolecules or colloidal particles with a net electric charge migrate in a solution under the influence of an electric current. 

The question to be discussed is whether saturation of the electric field (asserted by Proposition 2.1) implies saturation of the interparticle force of interaction. Consider for definiteness repulsion between two symmetrically charged particles in a symmetric electrolyte solution. In the onedimensional case (for parallel plates) the answer is known—the force of repulsion per unit area of the plates saturates. (This follows from a direct integration of the Poisson-Boltzmann equation carried out in numerous works, primarily in the colloid stability context, e.g., [9]. Recall that again in vacuum, dielectrics, or an ionic system with a linear screening, the appropriate force grows without bound with the charging of the particles.)... 

B. Deryagin and L. D. Landau, A theory of the stability of strongly charged lyophobic sols and the coalescence of strongly charged particles in electrolytic solutions, Collected Papers by L. D. Landau, D. Ter-Haar, ed., Gordon and Breach, New York, 1967. 

Counter ion — A mobile ion that balances the charge of another charged entity in a solution. It is a charged particle, whose charge is opposite to that of another electrically charged entity (an atom, molecule, micelle, or surface) in question [i]. Counter ions can form electrostatically bound clouds in the proximity of ionic macromolecules and in many cases, determine their electric properties in solution [ii]. 

There is clear evidence that the spectrum of the hydrated electron is best described as a charged particle in a cavity in solution, the simplest anion.The spectrum and the reactivity are very consistent with such an interpretation. However, there is also clear evidence that this is not the best description of the electron. There is no obvious way to reconcile the reaction... 

The same author (McDonald et al. [25]) used a combination of electric and magnetic fields for the separation of neutral and charged particles in free solution. The technique was later perfected by Kolin [27]. Another possibility, namely the application of electric and magnetic fields in perpendicular fashion was used by Kowalczyk and Pompanski [28] for the separation of molecules and charged particles. The electric field used was 20 Vcm and the magnetic field had an intensity of 10000 Gauss. 

Ihe homogenous processes in underground water are dominated reactions of ion association and dissociation, which have very high rates. As in water solution many ions are hydrated, their interaction cannot be considered as interaction of only charged particles in a uniform inert mediimi. Ihe rate of many reactions in the solution depends on the ion strength and pH values. 

A charged particle with a zeta potential of order kTle ( 25 mV e is the elementary electric charge, k is Boltzmann s constant, and T is the absolute temperature) in electrolyte gradients of order 100 kmol/m" (1 M/cm) will move by diffusiophoresis at speeds of several micrometers per second. The typical diffusiophoretic velocity of a particle in a solution of uncharged solute is of the same order of magnitude. 

Ohshima, H., Electrophoretic mobility of a highly charged colloidal particle in a solution of general electrolytes, J. Colloid Interface Set, 275, 665, 2004. 

There are two general situations in which the particles in a solution do not have the same identity as those that are put into the system when a component dissociates and when components can combine to form other species. The first case is commonly identified with salts forming ions with electrostatic charges. In both cases, the reactions need not be complete, so that the solution can have the original species (components) as well as the new species. Further, the speciation need not lead to detectable entities. Thus, the chemical theory of solutions and the solution of... 

The approximate experimental determination of xl), is based on measurement of the velocity of a charged particle in a solvent subjected to an applied voltage. Such a particle experiences an electrical force that initiates motion. Since a hydrodynamic frictional force acts on the particle as it moves, a steady state is reached, with the particle moving with a constant velocity U. To calculate this electrophoretic velocity U theoretically, it is, in general, necessary to solve Poisson s equation (Equation 3.19) and the governing equations for ion transport subject to the condition that the electric field is constant far away from the particle. The appropriate viscous drag on the particle can be calculated from the velocity field and the electrical force on the particle from the electrical potential distribution. The fact that the sum of the two is zero provides the electrophoretic velocity U. Actual solutions are complex, and the electrical properties of the particle (e.g., polarizability, conductivity, surface conductivity, etc.) come into play. Details are given by Levich (1962) (see also Problem 7.8). 

Electrophoresis (EP) is the movement of an electrically charged particle within a solution medium under the influence of an applied electric field. The movement is due to the EP force acting on the particle. The EP force is a type of Coulomb force in its origin and is simply given by... 

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