Zeta measurements

The structure electrical double layer at the silica-aqueous electrolyte interface was one of the earlier examined of the oxide systems. At the beginning the investigations were performed with application of electrokinetic methods next, with potentiometric titrations. The properties of this system were very important for flotation in mineral processing. Measurements proved that pHpZC and pHiep are equal to 3, but presence of some alkaline or acidic contaminants may change the position of these points on pH scale. Few examples, concerning edl parameters are shown in Table 3. Presented data concern a group of systems of different composition of the liquid phase and solid of a different origin. The latest measurements of this system takes into account the kinetics of the silica dissolution [152], and at zeta measurements, also the porosity of dispersed solid [155]. 

In most of the papers, the investigations of zirconia-aqueous electrolyte solutions interface concentrated on zeta measurements and determination of the surface charge by the potentiometric titration [237-240]. The background electrolyte ion adsorption measurements at the interface of the system showed much higher adsorption than predicted from the equilibrium states, described by the reactions of the complexion of the surface hydroxyl groups [241]. 

One can write acid-base equilibrium constants for the species in the inner compact layer and ion pair association constants for the outer compact layer. In these constants, the concentration or activity of an ion is related to that in the bulk by a term e p(-erp/kT), where yp is the potential appropriate to the layer [25]. The charge density in both layers is given by the algebraic sum of the ions present per unit area, which is related to the number of ions removed from solution by, for example, a pH titration. If the capacity of the layers can be estimated, one has a relationship between the charge density and potential and thence to the experimentally measurable zeta potential [26]. 

There are a number of complications in the experimental measurement of the electrophoretic mobility of colloidal particles and its interpretation see Section V-6F. TTie experiment itself may involve a moving boundary type of apparatus, direct microscopic observation of the velocity of a particle in an applied field (the zeta-meter), or measurement of the conductivity of a colloidal suspension. 

Several effects, due to the existence of the double layer on the surface of most particles suspended in Hquids, can be used to measure the so-called zeta potential. Table 1 gives a simplified summary of the effects. 

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). 

The well-known DLVO theory of coUoid stabiUty (10) attributes the state of flocculation to the balance between the van der Waals attractive forces and the repulsive electric double-layer forces at the Hquid—soHd interface. The potential at the double layer, called the zeta potential, is measured indirectly by electrophoretic mobiUty or streaming potential. The bridging flocculation by which polymer molecules are adsorbed on more than one particle results from charge effects, van der Waals forces, or hydrogen bonding (see Colloids). 

Electroultrafiltration (EUF) combines forced-flow electrophoresis (see Electroseparations,electrophoresis) with ultrafiltration to control or eliminate the gel-polarization layer (45—47). Suspended colloidal particles have electrophoretic mobilities measured by a zeta potential (see Colloids Elotation). Most naturally occurring suspensoids (eg, clay, PVC latex, and biological systems), emulsions, and protein solutes are negatively charged. Placing an electric field across an ultrafiltration membrane faciUtates transport of retained species away from the membrane surface. Thus, the retention of partially rejected solutes can be dramatically improved (see Electrodialysis). 

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. 

Not all of the ions in the diffuse layer are necessarily mobile. Sometimes the distinction is made between the location of the tme interface, an intermediate interface called the Stem layer (5) where there are immobilized diffuse layer ions, and a surface of shear where the bulk fluid begins to move freely. The potential at the surface of shear is called the zeta potential. The only methods available to measure the zeta potential involve moving the surface relative to the bulk. Because the zeta potential is defined as the potential at the surface where the bulk fluid may move under shear, this is by definition the potential that is measured by these techniques (3). 

Streaming Current Detectors These units produce a measurement closely related to the zeta potential of a suspension and are used successfully in optimizing the coagulant dose in clarification applications. 

Several devices are available commercially to measure mobihty. One of these (Zeta-Meter Inc., New York) allows direct microscopic measurement of individual particles. Another allows measurement in more concentrated suspensions (Numinco Instrument Corp., Monroeville, Pa.). The state of the charge can also be measured by a streaming-current detecdor (Waters Associates, Inc., Framingham, Mass.). For macromolecules, more elaborate devices such as the Tisehus moving-boundaiy apparatus are used. 

Zeta potentials of floe produeed in the plant may also be measured as a means of eontrol. The zeta potential value for optimum eoagulation must be determined for a given wastewater by aetual correlation with jar tests or with plant performance. The control point is generally in the range of 0 to 10 millivolts. If good correlations can be obtained between some zeta potential values and optimum plant performance, then it is possible to make rapid measurements of particle charge to compensate for major variations in wastewater composition due to storm flows or other causes. 

Electrokinetic measurements consisted of measuring the viscosity with and without NaGl (Carlo Erba, Argentine) (Figures 3-a and 3-b), while the isoelectric point (figure 2) and zeta potential (figure 3-c) were measured at different pH (HCl Ciccarelli and NaOH Tetrahedrom, Argentine). 

The calculation of zeta potential from electoviscous effect measures (Rubio-Hernandez et al. 1998 and 2004), is given by the equation... 

An important reason for this lack of experimental work is that the zeta-potential cannot be easily determined independent of the electrophoretic mobility [284] however, in the case of proteins (as well as some other charged colloids), the intrinsic charge obtained by titration is a parameter that can be measured independent of the electrophoretic mobility. The charge obtained from electrophoretic measurements (i.e., the net charge) via the preceding theories is generally not the same as the charge obtained from titration (i.e., the in-... 

The charges present on the insulator surface in contact with the solution give rise to an accumulation of ions of opposite sign in the solution layer next to the surface, and thus formation of an electric double layer. Since straightforward electrochemical measurements are not possible at insulator surfaces, the only way in which this EDL can be characterized quantitatively is by measuring the values of the zeta potential in electrokinetic experiments (see Section 31.2). 

The zeta potential is a measurable indication of the apparent particle charge in the dispersion medium. When its value is relatively high, the repulsive forces usually exceed the attractive forces. Accordingly, the particles are individually dispersed and are said to be deflocculated. Thus, each particle settles separately, and the rate of sedimentation is relatively small. The settling particles have plenty of time to pack tightly by falling over one another to form an impacted bed. The sedimentation volume of such a system is low, and the sediment is difficult to redisperse. The supernatant remains cloudy even when settling is apparent. 

Suspensions are generally evaluated with respect to their particle size, electrokinetic properties (zeta potential), and rheological characteristics. A detailed discussion on the methods/techniques and relevant instrumentation is given in Sec. VII. A number of evaluating methods done specifically with suspension dosage forms, such as sedimentation volume, redispersibility, and specific gravity measurements, will be treated in this section. 

Electrophoresis involves the movement of a charged particle through a liquid under the influence of an applied potential difference. A sample is placed in an electrophoresis cell, usually a horizontal tube of circular cross section, fitted with two electrodes. When a known potential is applied across the electrodes, the particles migrate to the oppositely charged electrode. The direct current voltage applied needs to be adjusted to obtain a particle velocity that is neither too fast nor too slow to allow for errors in measurement and Brownian motion, respectively. It is also important that the measurement is taken reasonably quickly in order to avoid sedimentation in the cell. Prior to each measurement, the apparatus should be calibrated with particles of known zeta potential, such as rabbit erythrocytes. 

The velocity of particle migration, v, across the field is a function of the surface charge or zeta potential and is observed visually by means of an ultramicroscope equipped with a calibrated eyepiece and a scale. The movement is measured by timing the individual particles over a certain distance, and the results of approximately 10-15 timing measurements are then averaged. From the measured particle velocity, the electrophoretic mobility (defined as v/E, where E is the potential gradient) can be calculated. 

Bauerle and Seelig [395] studied the structural aspects of amlodipine (weak base, primary amine pKa 9.26 [162]) and nimodipine (nonionizable) binding to phospholipid bilayers, using NMR, microcalorimetry, and zeta-potential measurements. They were able to see evidence of interactions of amlodipine with the cis double bond in the acyl chains. They saw no clear evidence for (=P—O- 1 H N—) electrostatic interactions. 

The theory described in the previous section is now applied to beryllium metal. Accurate low temperature data was taken from the paper of Larsen and Hansen [20]. (But note that in (20) I used the structure factors multiplied by 1000, as given in then-paper.) For the orthogonalisation, all nearest neighbours we included within the first shell. There were 12 atoms. A triple zeta basis set from Ref. [21] was used. There are 182 basis functions and 361 independent parameters in the wave function, whereas there are 58 experimental measurements. Figure 1 shows a plot of the x2 agreement statistic as a function of the parameter X for k = 0.2. Larger values of k caused... 

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