Electrolyte electrophoretic velocity

FIG. 12.4 The domain within which most investigations of aqueous colloidal systems lie in terms of particle radii and 1 1 electrolyte concentration. The diagonal lines indicate the limits of the Hiickel and the Helmholtz-Smoluchowski equations. (Redrawn with permission from J. Th. G., Overbeek, Quantitative Interpretation of the Electrophoretic Velocity of Colloids. In Advances in Colloid Science, Vol. 3 (H. Mark and E. J. W. Verwey, Eds.), Wiley, New York, 1950.)... 

Even in the absence of a colloid, an electrolyte solution will display electroosmotic flow through a chamber of small dimensions. Therefore the observed particle velocity is the sum of two superimposed effects, namely, the true electrophoretic velocity relative to the stationary liquid and the velocity of the liquid relative to the stationary chamber. Figure 12.10a shows the results of this superpositioning for particles tracked at different depths in the cell. The particles used in this study are cells of the bacterium Klebsiella aerogenes in phosphate buffer. Rather than calculated velocities or mobilities, Figure 12.10a shows the reciprocal of the time... 

Analytical expression for the electrophoretic velocity of a sphere can be obtained for a thin but distorted double layer. Dukhin [6] first examined the effect of distortion of thin ion cloud on the electrophoresis of a sphere in a symmetric two-species electrolyte. Dukhin s approach was later simplified and extended by O Brien [7] for the case of a general electrolyte and a particle of arbitrary shape. Since 0(k 1) double layer thickness is much smaller than the characteristic particle size L, the ion cloud can be approximated as a structure composed of a charged plane interface and an adjacent diffuse cloud of ions. Within the double layer, the length scales for variation of quantities along the normal and tangential directions are k ] and L, respectively. 

As mentioned in Sec. I, the system in most applications of electrophoresis contains more than one single particle suspended in the electrolyte solution. The interactions between the particles should be taken into account unless the concentration of particles is very low. In this section, studies on particle interactions in electrophoresis will be reviewed. The results for spherical and nonspherical particles will be presented and discussed separately in two respective subsections. Then, we will show how to obtain the average electrophoretic velocity for a dispersion of particles from the interaction results. 

Electrophoretic velocity, i/ep, or rate of migration (in electrophoresis) — The velocity of a charged analyte under the influence of an electric field relative to the -> background (supporting) electrolyte. 

Consider spherical soft particles moving with a velocity U (electrophoretic velocity) in a liquid containing a general electrolyte in an applied electric field E. Each soft particle consists of the particle core of radius a covered with a polyelectrolyte layer of thickness d (Fig. 22.1). The radius of the soft particle as a whole is thus b = a + d. We employ a cell model [8] in which each sphere is surrounded by a concentric spherical shell of an electrolyte solution, having an outer radius of c such that the particle/cell volume ratio in the unit cell is equal to the particle volume fraction (j) throughout the entire suspension (Fig. 22.1), namely,... 

The action of external electric field on the free disperse system results in particle motion (electrophoresis). The electrophoretic velocity, vE, is not a function of ( -potential only, but also depends on the particle radius, r, and the type of electrolyte present in the system. However, it turns out (see fine print further down) that all of these factors can be simultaneously accounted for by the numerical coefficient, kt, introduced into the Helmholtz-Smoluchowski equation (V.26). If the particles are spherical, k, changes from 2/3 for particles smaller compared to the ionic atmosphere thickness (kt 1) to 1 for large particles ( kt 1). Consequently, the particle flux due to the applied electric... 

CapUlary electrophoresis (CE) is a routine analytical technique for fast and efficient separation of charged species. Under the influence of an electric field, the ionic species in a sample that is introduced as a plug (or zone) into an electrolyte at one end of a capillary will be separated into discrete bands when they migrate to the other end of the capillary at different electrophoretic velocities. However, Joule heating is an inevitable phenomenon in CE that limits the performance of electrophoretic separation. 

As a general conclusion one may state that, provided the C potential, and thus the electrophoretic velocity, is small (f < 25 mV, v < I /i cmjVsec) the charge of the particles is directly proportional to f and therefore also to v. The exact indication of the proportionality factor (which also depends on the electrolyte concentrations of the system) still presents difficulties. 

Measurements of the zeta potential of a clay-water suspension in the presence of one or more electrolytes can be performed using a U-shaped tube (Burton tube) in which the suspension is subjected to an electric field appUed between two electrodes. The electrophoretic velocity v of the electrolyte ions is related to the zeta potential. Then, the electric force <7- E (where E = electrostatic field strength) acting on the charged particles is balanced by the frictional force 77 v/d (77 = dynamic viscosity) that is ... 

This, however, is only the case to a very limited extent. In the initial stages of elcctrodialysis, electrodccantation is very slow, because the electrophoretic velocity (sec this chapter, 4 c, p. 78 and chapter V, p. 207) is small. In the later stages, when the major part of the electrolytes has already been removed, clectrodecantation is not helpful to eliminate the remainder of electrolytes, because the electrolytes arc also decanted and the supernatant is practically pure water (see 4 a, p. 73). 

The electrophoretic velocity may be determined in the same waj as the transport number of an electrolyte. A certain current i is sent through a colloid during a time t, and the quantity of colloidal material (g) that has been displaced to anode or cathode is determined analytically. As the charge of a colloidal particle is relatively much smaller t han that of an ion the mass of displaced material is comparatively large and this method of determination is fairly accurate ... 

In electrophoresis in mixtures of electrolytes it is possible to show rather directly the influence of the time-of-rehxation effect Troelstra and Kruyt determined the electrophoretic velocity of silver iodide sol particles, with addition of Ba(N03)2 and of mixtures of Ba(N03)2 KNO3. In small con ... 

The most conspicuous influence of the addition of lyophilic colloids to lyophobic ones is the protective action" A sufficient (usually not very large) quantity of , for instance, gelatin makes a lyophobic sol much less susceptible to flocculation by electrolytes Electrophoresis measurements show that the electrophoretic velocity of the hydrophobic particles has changed by the addition of the gelatin from the value of the pure hydrophobic sol to a value proper to the pure gelatin soL... 

The other physical phenomenon responsible for the reduction of the ionic mobility in the bulk electrolyte solution is the electrophoretic effect, which arises from the motion of an ion in a medium (solvent) not at rest. This electrophoretic correction to the mobility of the ions in the bulk concentrated electrolyte solutions can be calculated by the following arguments. In the steady state of the ionic transport the electrophoretic velocity is the result of the equilibrium between the electric force driving the ionic cloud and the viscous force... 

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