Stern potential

Fig. 8. Electrical double layer of a sohd particle and placement of the plane of shear and 2eta potential. = Wall potential, = Stern potential (potential at the plane formed by joining the centers of ions of closest approach to the sohd wall), ] = zeta potential (potential at the shearing surface or plane when the particle and surrounding Hquid move against one another). The particle and surrounding ionic medium satisfy the principle of electroneutrafity.

For Gg (b), a reasonable (although not strictly correct) procedure is to replace the Stern potential in one of the standard equations for Gg by the zeta potential of the polymer-coated particles this assumes that the plane of hydrodynamic shear corresponds to the periphery of the adsorbed layer. 

Figure 9. Formation of Stern plane and diffuse layer on particle surface ( I 0 = surface or Nernst potential, = potential of inner Flelmholtz plane, I 5 = Stern potential, l = thickness of Stern plane, ZP = zeta potential at surface of shear, d = distance from particle surface).

Fig. 5.5 Distribution of electrical charges and potentials in a double layer according to (a) Gouy-Chapman model and (b) Stern model, where /q and are surface and Stern potentials, respectively, and d is the thickness of the Stern layer...

Stern potential in magnitude, and definitely less than the potential at the surface f/0. The relative values of these different potentials are shown in Figure 12.2. 

The potential changes from iffo (the surface or wall potential) to tpd (the Stern potential) in the Stern layer, and decays from iftd to zero in the diffuse double layer. 

For the case of two spherical particles of radii a and a2, Stern potentials, iftdi and i//d2, and a shortest distance, H, between their Stern layers, Healy and co-workers195 have derived the following expressions for constant-potential, V, and constant-charge, Fr, double-layer interactions. The low-potential form of the Poisson-Boltzmann distribution (equation 7.12) is assumed to hold and Kax and xa2 are assumed to be large compared with unity ... 

The reader is referred to Void and Void (1983) for the difference between the zeta and Stern potentials. 

Helmholtz plane Pc = = zeta potential Pb = stern potential... 

Specific adsorption potential 3p0 = Surface potential = Stern potential O = Stern layer charge CJ2 = Diffuse layer charge... 

Figure 5-2 Distribution of + and - ions around the surface of an electrophoretic support. Fixed on the surface of the solid is a layer of - ions, (These may be + ions under suitable conditions.) A second layer of + ions is attracted to the surface. These two layers compose the Stern potentiai.The large, diffuse layer containing mostly + ions is the electro kinetic or zeta (Q potential. Extending farther from the surface of the solid is homogeneous solution.The Stern potential plus the zeta potential equals the electrochemical potential, or epsilon (e) potential.

This is illustrated in Figure 7.5 for two flat plates. The potential ipui2 half-way between the plates is no longer zero (as would be the case for isolated particles at x oo). The potential distribution at an interparticle distance H is depicted schematically by the full Une in Figure 7.5. The stern potential is considered to be independent of the particle distance, and the dashed curves show the potential as a function of distance x to the Helmholtz plane, had the particles been at an infinite distance. 

A high surface or Stern potential (zeta-potential), and high surface charge. As shown in Equation (7.5), the repulsive energy is proportional to... 

Surface potential Stern potential Zeta potential Double>layer thickness (reciprocal Debye length)... 

Fig. 3 Electrostatic repulsive thick line), van der Waals attractive dotted line) and total thin line) interaction energies of two approaching spherical particles. Particle radius, R=100 nm Stern potential, Pd=10 niV Hamaker constant, A=0.5xl0" J...

Inner Potential In the diffuse electric double layer extending outward from a charged interface, the electrical potential at the boundary between the Stern and the diffuse layer is termed the inner electrical potential. Synonyms include the Stern layer potential or Stern potential. See also Electric Double Layer, Zeta Potential. 

When a particle surrounded by an electric double layer is subjected to an electric field, the Stern layer and a part of the diffuse double layer move with the particle. The electrical potential at the plane of shear between the bound and free parts of the double layer is called the zeta potential ( ). It is considered that the shear plane is usually located at a small distance further out from the surface than the Stern plane and that ( is generally marginally smaller in magnitude than the Stern potential (see Figure 21). 

When a (solid) surface moves in a liquid, or vice versa, there is always a layer of liquid adjacent to the surface that moves with the same velocity as the surface. The distance from the surface over which this stagnant liquid layer extends or, in other words, the location of the boundary between the mobile and the stationary phases, the so-called plane of shear or slip plane, is not exactly known. For smooth surfaces, the plane of shear is within a few liquid (water) molecules from the surface (see Figure 9.4), that is, well within the electrical double layer. The stagnant layer is probably somewhat thicker than the Stern layer, so that the plane of shear is located in the diffuse part of the electrical double layer. It follows that the potential at the plane of shear, that is, the electrokinetic potential or the zeta potential is somewhat lower than the Stern potential /j. Because the largest part of the potential drop in the... 

The functionality tanh (x) can be approximated by x for small values of jc and it approaches unity for large x. Hence, for zF iJ43iT < 2, may be replaced by zF iJ43iT and for zF fJ3iT> 8, y reaches unity. In a 1 1 electrolyte solution at room temperature, the first condition applies if /i < 50 mV and the second if /d > 200mV. In the latter case, the interaction between the electrical double layers becomes insensitive for the Stern potentials. 

Figure 11.9 Stern potential indicating the contact layer and the diffuse layer profiles.

Fig. 37a shows the results of measurements of Stern potentials ij/i in dependence on CTAB concentration Co- Calculated using Eq. (42), the corresponding dependence for surface charges, cr = cr(Co), is shown in Fig. 37b [46]. Measurements were performed at pH 6.5 in the background electrolyte, 5 x 10 M KCl. Experimental data are shown in Fig. 37 by points, whereas solid lines are plotted using Langmuir isotherm, which was recommended to describe adsorption data for weakly charged surfaces [52] ...

Measurement of the Stern potentials 1/ 1 in quartz capillaries with radii from 5 to 10 pm were performed in the range of CTAB concentrations C from 10 to 10 M at various pH, from 3 to 9.5. By changing pH values it was possible to obtain concentration dependencies i/ i(Co) and cr(Co) starting from the different initial surface charge (T of quartz surface at Co = 0. Measured values of Stern potentials vary from —105 mV at pH 9.5 to —10 mV at pH 3. 

Measuring electrokinetic potentials before and after polymer adsorption, that is, the Stern potential of the bare quartz surface ij/i and C potential, which reflect a shift in the position of slipping plane, it becomes in principle possible to assess the hydrodynamic thickness 5 of an adsorbed polymer layer. Assuming that presence of polymer does not change significantly the exponential distribution of local potential values il/(x) in the electrical double layer, the hydrodynamic thickness may be calculated from the Gouy equation... 

However, correct determination of the <5 value is possible when the surface potential of quartz preserves its initial magnitude ipi and is not influenced by formation of hydrogen bonds between quartz surface and polymer molecules. It was shown in Refs. 47, 56 and 57 that potential of quartz surface under an adsorbed polymer layer, ij/iQ, is lower than Stern potential i/ i of a bare quartz surface. 

In Fig. 38 are shown results of measurements of C potentials of quartz capillaries, the surface of which was covered with adsorbed layers of PEO, in dependence on KCl concentration. Equilibrium adsorption layers are formed by pumping PEO solutions of various concentrations Cp = 0.1 (curve 1), 10 to 10 (curve 2), and 10 " (curve 3) g/dm. By curve 4 are shown the results of measurements of Stern potentials i/ i for bare quartz capillaries in KCl solutions before adsorption of PEO. 

The double layer is characterised by the surface charge (cro), the charge in the Stern layer (o-g), the charge of the diffuse layer era (note that ao = as+ aa) the surface potential ( T)q and the Stern potential Ta ( zeta potential). 

Note that W increases as G j increases. The stability of colloidal dispersions can be quantitatively assessed from plots of log W versus log C, as illustrated in Fig. 3.23. Two main criteria for electrostatic stabilization can be considered (i) High surface or Stern potential (zeta potential) [78], high surface charge, (ii) Low electrolyte concentration and low valency of counter- and co-ions. One should ensure that an energy maximum... 

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