Calculation of zeta potential

Although measurement of particle mobility is fairly simple (particularly with the development of automated instmments), interpretation of the results is not simple. The calculation of zeta potential from particle mobility is not straightforward since this depends on the particle size and shape as well as the electrolyte concentration. For simplicity we will assume that the particles are spherical. 

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

Figure 7.29 Schematic drawing of a microelectrophoresis apparatus showing the positioning of the anode and cathode and the capillary in which the velocity of particulates is monitored to allow calculation of zeta potential.

Spanos, N. and Koutsoukos, P.C., Calculation of zeta potential from electrokinetic measurements on titania plugs, J. Colloid Interf. Sci., 214, 85, 1999. 

Instrumentation. A Rank Bros, micro-electrophoresis unit was used in those studies, with a specially made quartz cell having a 6 cm. path length of rectangular inside cross-section (l mm thick, 10 mm deep) in which the Komagata equation (25) predicts zero mobility of the liquid phase in planes located at 0.612 of the distance b from the center plane of the cell to the wall. In electrophoresis experiments 300 to 1200 volts were applied to the cell and mobilities measured in planes a distance h from the center plane. The results were graphed as observed velocity versus (h/b)z as proposed by van Gils (26J, and if the straight lines characteristic of perfect parabolic flow resulted, the electrophoretic mobilities (v ) observed at h/b=0.612 were considered acceptable for calculation of zeta-potential. Zeta-potentials were calculated by the Huckel equation (27) ... 

The zeta potential is the parameter used to characterize a nanostructure s surface charge. Although zeta potential is not measurable directly, it can be calculated using theoretical models applied to the data provided by experimentally determined electrophoretic mobility or dynamic electrophoretic mobility, electrokinetic phenomena and electroacoustic phenomena being the usual sources of data for the calculation of zeta potential. Keeping the zeta potential far from a neutral value is important in order to avoid stability problems in systems once electrostatic repulsion is favored. Indeed, zeta potentials close to neutral result in a tendency to aggregate, and a high zeta potential (in module) is usually associated with stable systems. 

There are two more parameters in the calculation of zeta potential - the viscosity and dielectric constant of the medium. The accuracy of zeta potential is very difficult to estimate since it is not an experimentally determined quantity. Its accuracy depends heavily on the suitability of the model used in the calculation and the biases of the model as it relates to real particles. Because the interpretation of zeta potential is not accurate to the same level as the present experimental accuracy, any motivation to fiirther improve experimental accuracy is not great if the ultimate parameter one wants to obtain is zeta potential. 

A measurement of electrophoretic mobility /v, gives x = 0.02 cm s-1, where v is the velocity observed under a field, and x the mobility. Calculate the zeta potential of the colloid concerned. (Bockris)... 

It follows from a comparison of Eqs. 1.51 and 1.52 that in the calculation of the actual EOF mobility, the effect of tortuosity is taken into account so that peo, packed can be used to calculate the zeta potential of the packing. In the literature of electroki-netic phenomena in porous media [44], constriction factor is employed to describe the effect arising from the variability of cross-section along a given flow path. However, in packed CEC columns this factor is estimated to be in the range 0.93-1.0 and so may be neglected in the following treatment. 

The method given above for calculating the zeta-potential at a diffuse double layer may be applied to the diffuse portion of the Stern double layer. If charge density on the solid and ai and are the corresponding values on the solution sides of the fixed and diffuse layers, respectively, then the condition of electrical neutrality requires that... 

A glass particle suspended in water (tj = 0.01 poise) was observed to move with a velocity of 21.0 X 10 cm. per sec. under a potential gradient of 6.0 volts per cm. Calculate the zeta-potential at the glass-water interface. 

For calculating the zeta potential the following theoretical assumptions are necessary In the modified Stokes equation, the electrical field is the driving force for the movement of the particles ... 

The anomalous surface conduction was studied extensively by O Brien and by Hunter, and they could show that the Stem layer conduction is about thirty times larger than the diffuse layer conduction at low salt concentration. This explains substantial discrepancies between the electrophoresis and the conductance estimates of zeta potential. For thin double-layer systems such as this, the zeta potential is usually calculated from the electrophoretic mobility using Smoluchowski s formula, which in O Brien s case corresponds to a zeta potential of 50 mV [8]. Complex conductivity measurements result in f = —160 mV. 

For example, dissolved carbonate species present in our 0.02 I buflFer system, predominantly CO2, H2CO3 , HCOa, COa, and various car-bonato complexes, had a marked elfect concerning adsorption to transition metal oxides. The zeta potential of CuO in 0.02 I buffer was —17.6 6.1 mV, while in 0.02M NaCl that contained only traces of total dissolved carbonate (approximately lO M), it was -f32.0 it 5.8 mV. This shows marked alteration of the electrical structure of double layers by some carbonate species. The same effects were seen to lesser extents on Fc203 and Mn02 (8). Double-layer interaction potentials calculated with zeta potentials measured in 0.02 I reaction buffers matched adsorption free energy differences well, and these potentials included the effects of carbonate species. Where effects of dissolved constituents have not been accounted for intrinsically, predictions made on the basis of the DLVO-Lifshitz considerations alone must be made with care. 

The zeta potential of a particle is calculated from electro kinetic phenomena such as electrophoresis, streaming potential, electro-osmosis and sedimentation potential. Each of these phenomena and the determination of zeta potential by using each technique will be discussed briefly in this section. 

Sedimentation potential This is the creation of an electric field when charged particles move relative to a stationary fluid. This technique is the least commonly used for the determination of zeta potential, because of several limitations associated with the measurement and calculation of the zeta potential. 

The average velocity of the liquid during electroosmosis is determined by Eq. 28. Using the measured average velocity data, the method described earlier can be used to calculate the zeta potential The measured total current... 

FIGURE 3.8 Full calculation of the sedimentation field ( sed) of spherical particles of 100 nm radius as compared with Smoluchowski formula, as a function of zeta potential for the na values indicated. 

FIGURE 3.18 Frequency dependence of the relative dielectric increment of 265-nm radius polystyrene spheres in 0.1 nunol/1 KCl solution. Symbols experimental data soUd line classical calculation dashed line DSL calculation. In both calculations, the zeta potential used was the one best-fitting simultaneously electrophoretic mobility and dielectric dispersion data. 

This equation can be used to simply calculate the zeta potential from the measured electrophoretic mobility. For small values of k , Eq. (7) becomes... 

By contrast, there is considerable evidence to suggest that the Nernst equation, used to calculate the surface potential and thus AG%iec,n is inappropriate in the case of hydrous metal oxides [84,85], Crawford et al. [25,26,28] proposed the use of zeta potentials rather than surface potential to calculate AG iec,/ (and also AG°soiv,/) and this forms the basis of the modified model used throughout this chapter. 

The thickness of the adsorbed polymer layer may also be calculated from electrophoretic mobility measurements by calculating the zeta-potential at the plane of shear of the particle. This potential corresponds to the potential at the periphery of the adsorbed layer. By also measuring the zeta-potential of the bare particle and assuming a value of 4 A for the Stern layer, use of Eq. 15 allows the calculation of be, the electrokinetic thickness of the adsorbed layer (13). 

Figure 2. True surface concentration of SDS, versus value calculated from Zeta potential,...

As mentioned above, one of the main criteria for electrostatic stabflity is the high surface or zeta potential, which can be experimentally measured (vide infra). Before describing the experimental techniques for measuring the zeta potential it is essential to consider the electrokinetic effects in some detail, describing the theories that can be used to calculate the zeta potential from the particle electrophoretic mobility [21]. 

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