Electrokinetic curves, shape

Allegedly pure materials often contain specifically adsorbing ions as impurities. These impurities induce a shift in the lEP, and special cleaning methods are necessary to remove them. Most likely some unusual pH values reported as pristine lEP for certain materials (Table 3.1, and 3.3) are caused by specific adsorption of impurities, namely, anionic impurities induce a low lEP and cationic—a high lEP. Lack of coincidence between the lEP and CIP (cf. Fig. 4.12) and unsymmetrical shape of the electrokinetic curves corroborates this assertion. The errors caused by specific adsorption of anionic impurities are more common than the cation effects. The COi and SiOj errors in electrokinetic measurements and difficulties in removal of multivalent anions, which are present in solutions used to prepare monodispersed colloids, can serve as a few examples (cf. Section 3.I.B.1). 

The rest of discussion in this section relates to the shapes of smoothed electrokinetic curves, disregarding the local minima and maxima caused by the scattering of results. 

The idealized curves shown in Figure 1.2 steadily decrease with pH and have no more than one IEP, but numerous electrokinetic curves reported in the literature show different shapes. The electrophoretic mobility of alumina in 0.1 M NaNOj was pH-independent at pH 4-8 [469]. 

Scattered results are reported in [2979], and there are too few data points near the IEP. Also, in [2980,2981], too few data points are available near the IEP to make a reliable estimate. In [2982], at one pH value is reported. In [2983], potentials were measured only at pH 1,4, and 12. The IEP was obtained in [2984] from ESA measurements for two titanias (source or characterization of the powers or experimental details were not reported). The unusually high IEP reported in [2984] may be due to experimental errors the sohd concentration was too low, and the electrolyte background was not subtracted. Among the results from [1726], only the IEP for Nd(Ol I), was used. The other lEPs are based on arbitrary interpolations. The pH reported in the (pH) plot in [208] was not the pH of the dispersion. A home-made apparatus was used in [267], atypical shapes of electrokinetic curves... 

This equation is a reasonable model of electrokinetic behavior, although for theoretical studies many possible corrections must be considered. Correction must always be made for electrokinetic effects at the wall of the cell, since this wall also carries a double layer. There are corrections for the motion of solvated ions through the medium, surface and bulk conductivity of the particles, nonspherical shape of the particles, etc. The parameter zeta, determined by measuring the particle velocity and substituting in the above equation, is a measure of the potential at the so-called surface of shear, ie, the surface dividing the moving particle and its adherent layer of solution from the stationary bulk of the solution. This surface of shear ties at an indeterrninate distance from the tme particle surface. Thus, the measured zeta potential can be related only semiquantitatively to the curves of Figure 3. 

The effect of specific adsorption on electrokinetic behavior of materials is usually presented in form of C(pH) curves at constant initial (total) concentration of a specifically adsorbing salt. The electrophoretic mobility rather than the potential is often plotted as a function of the pH. The mobility (directly measured quantity) is a complicated function involving the C potential on the one hand and particle size and shape, and concentrations of ionic species in the solution on the other (cf. Figs. 3.80 and 3.81), and exact calculation of the potential in real systems (polydispersed and irregularly shaped particles) is practically impossihle. This is a serious difficulty in quantitative interpretation of electrokinetic data obtained in the presence of specific adsorption. On the other hand, the zero electrophoretic mobility corresponds to zero C potential, and the shifts in the lEP along the pH axis can be determined with accuracy on the order of 0.1 pH unit. 

The examples shown is Section D indicate that the shape of calculated uptake curves (slope, ionic strength effect) can be to some degree adjusted by the choice of the model of specific adsorption (electrostatic position of the specifically adsorbed species and the number of protons released per one adsorbed cation or coadsorbed with one adsorbed anion) on the one hand, and by the choice of the model of primary surface charging on the other. Indeed, in some systems, models with one surface species involving only the surface site(s) and the specifically adsorbed ion successfully explain the experimental results. For example, Rietra et al. [103] interpreted uptake, proton stoichiometry and electrokinetic data for sulfate sorption on goethite in terms of one surface species, Monodentate character of this species is supported by the spectroscopic data and by the best-fit charge distribution (/si0,18, vide infra). 

These stirring transverse flows can be generated by channel shapes that stretch, fold, break, and split the laminar flow over the cross-section of the channel. This effect can be achieved using 2D curved [111-113], or 3D convoluted channels [114—116] and by inserting obstacles [117] and bas-reliefs on the channel walls [54,118,119]. It must be noted that such type of chaotic flow could also be achieved by an active mixing strategy such as one using electrokinetic instability (EKl), as described in Sect. 3.2.2. 

The electrokinetic potential may thus be viewed as the potential at some plane, referred to as the plane of shear (the slipping plane), located within the limits of the diffuse part of the double layer. The plane of shear separates the immobilized part of the liquid phase bound to the solid surface from the remaining mobile part in which the displacement takes place. The curve describing the change in the displacement velocity of the layers of liquid as a function of the distance from the wall, u(x), matches the x axis up to the plane of shear, and at x>A has the same shape as the function showing the change in the potential as a function of distance (see Figs. V-7 and V-8). 

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