Zeta potentials shear plane

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.

The electroosmotic pumping is executed when an electric field is applied across the channel. The moving force comes from the ion moves in the double layer at the wall towards the electrode of opposite polarity, which creates motion of the fluid near the walls and transfer of the bulk fluid in convection motion via viscous forces. The potential at the shear plane between the fixed Stem layer and Gouy-Champmon layer is called zeta potential, which is strongly dependent on the chemistry of the two phase system, i.e. the chemical composition of both solution and wall surface. The electroosmotic mobility, xeo, can be defined as follow,... 

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. 

The charge or zeta ( ) potential of the filler particle (i.e. the charge at the plane of shear between the particle s diffuse double layer and the bulk liquid phase) can be obtained by measuring its mobility in an applied electric field of known magnitude. The mobility is a function of the field gradient and is therefore expressed as a speed per unit potential gradient (/im/s/V/cm). Mobility and therefore zeta potential are both a function of pH (Figure 6.4). 

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).

The potential is the potential difference between the plane of shear (or slipping plane) and the bulk solution. From Eq. (4), it is clear that for a given situation of water (electrolyte) in the interstitium, the Ueo is proportional to the zeta potential and to the applied field strength. Also in a real situation of EOD, it is necessary to use the so called length-averaged value of the zeta potential in order to take into account the effect of the axially variable zeta potential on the electroosmotic velocity. 

The electrokinetic potential (zeta potential, Q is the potential drop across the mobile part of the double layer (Fig. 3.2c) that is responsible for electrokinetic phenomena, for example, elecrophoresis (= motion of colloidal particles in an electric field). It is assumed that the liquid adhering to the solid (particle) surface and the mobile liquid are separated by a shear plane (slipping plane). The electrokinetic charge is the charge on the shear plane. 

The surface potential is not accessible by direct experimental measurement it can be calculated from the experimentally determined surface charge (Eqs. 3.1 - 3.3) by Eqs. (3.3a) and (3.3b). The zeta potential, calculated from electrophoretic measurements is typically lower than the surface potential, y, calculated from diffuse double layer theory. The zeta potential reflects the potential difference between the plane of shear and the bulk phase. The distance between the surface and the shear plane cannot be defined rigorously. 

Effect of adsorbed polymer on the double-layer. Because of the presence of adsorbed train segments, the double layer is modified. The zeta-potential, , is displaced because the adsorbed polymer displaces the plane of shear. The parameters for describing adsorbed polymers are the fraction of the first layer covered by segments, 0, and the effective thickness, A, of the polymer layer, The insert gives the distribution of segments over trains and loops for polyvinyl alcohol adsorbed on silver iodide. Results obtained from double layer and electrophoresis measurements. 

The variation of the electric potential in the electric double layer with the distance from the charged surface is depicted in Figure 6.2. The potential at the surface ( /o) linearly decreases in the Stem layer to the value of the zeta potential (0- This is the electric potential at the plane of shear between the Stern layer (and that part of the double layer occupied by the molecules of solvent associated with the adsorbed ions) and the diffuse part of the double layer. The zeta potential decays exponentially from to zero with the distance from the plane of shear between the Stern layer and the diffuse part of the double layer. The location of the plane of shear a small distance further out from the surface than the Stem plane renders the zeta potential marginally smaller in magnitude than the potential at the Stem plane ( /5). However, in order to simplify the mathematical models describing the electric double layer, it is customary to assume the identity of (ti/j) and The bulk experimental evidence indicates that errors introduced through this approximation are usually small. 

In the above equations, h is the film thickness, n is the munber concentration of z z symmetrical electrolyte and is the surface potential. The surface potential is the potential at the interface of stem and diffuse layers and is usually replaced by the zeta potential of the droplet determined from electrophoretic measurements. When the interface has an adsorbed layer of globular proteins, it may be reasonable to assume that the shear plane is located at the interface of protein layer. When xp > 2L, the disjoining pressure 11 / can be evaluated by replacing with potential and taking as (jCf - 2L,). 

At the shear plane, fluid motion relative to the particle surface is zero. For particles with no adsorbed surfactant or ionic atmosphere, this plane is at the particle surface. Adsorbed surfactant or ions that are strongly attracted to the particle, with their accompanying solvent, prevent liquid motion close to the particle, thus moving the shear plane away from the particle surface. The effective potential at the shear plane is called the zeta potential, C,. It is smaller than the potential at the surface, but because it is difficult to determine aj or usua assumption is that V /0 is effectively equal to which can be... 

Figure 1. (Bottom) Diagram of the electrostatic potential adjacent to a membrane bearing a positive charge. The zeta potential is the potential at the hydrodynamic plane of shear, which should be about 2 A from the surface of the membrane. (Top) Schematic of the location of the probe molecules used to detect the potential produced by the adsorption of calcium and other alkaline earth cations to membranes formed from PC. The divalent cation cobalt and the amphipathic, anionic, fluorescent probe TNS will sense the potential at the interface. The non-actin-Rf complex will sense the potential in the center of the membrane.

The available evidence suggests that the plane of shear lies 2 A from the surface of a phospholipid bilayer membrane (7) so the zeta potential should be a good approximation to the electrostatic potential at the... 

In this section we deal with liquids, which flow along charged solid surfaces. In many cases the surface binds one, two, or several layers of liquid molecules and possibly ions more or less tightly. As a result the shear plane is often not directly at the interface. Only at a distance 6 away from the surface do the molecules start to move. The potential at this distance is called the zeta potential . 

The first four methods are described in Refs. [81,253,254] and the electroacoustical methods in [130,255-257]. Of these, electrophoresis finds the most use in industrial practice. The electroacoustic methods are perhaps the best suited to studying concentrated suspensions and emulsions without dilution [258], In all of the electro-kinetic measurements, either liquid is made to move across a solid surface or vice versa. Thus the results can only be interpreted in terms of charge density (a) or potential (zeta potential, ) at the plane of shear. The location of the shear plane is generally not exactly known and is usually taken to be approximately equal to the potential at the Stern plane, = W d), see Figure 4.9. Several methods can be used to calculate zeta potentials [16,81,253], Some of these will be discussed here, in the context of electrophoresis results. 

For an interpretation of the adsorption process it is important to know the so called zeta-potential ( ) that can be calculated from electrokinetic measurements. It may be defined as the potential difference at the shear plane (near to the outer Helmholtz plane) between the diffuse layer outside the slipping plane and the bulk phase, when the solid and liquid phases are moved tangentially to each other. The location of the slipping plane is not exactly known, but it can be assumed that the shear plane is only very little further... 

The inner part of the double layer may include specifically adsorbed ions. In this case, the center of the specifically adsorbed ions is located between the surface and the Stem plane. Specifically adsorbed ions (e.g., surfactants) either lower or elevate the Stem potential and the zeta potential as shown in Figure 4.31. When the specific adsorption of the surface-active or polyvalent counter ions is strong, the charge sign of the Stem potential will be reversed. The Stem potential can be greater than the surface potential if the surface-active co-ions are adsorbed. The adsorption of nonionic surfactants causes the surface of shear to be moved to a much longer distance from the Stem plane. As a result, the zeta potential will be much lower than the Stem potential. 

In another part of this study we wished to see the effects of post-modification treatments on the properties of the modified LDPE surface. Polyethylene samples were photosulfonated for different periods of time. Afterwards they were subjected to an after-treatment by conditioning in an electrolyte solution (aqueous KC1, 10-3 M) for 48 hours and then characterized by zeta potential measurements. This conditioning process resulted in a shift of f to even less negative values (see Fig. 8). This finding may be explained by the swelling of the polymer samples (water adsorption) in water that causes a shift of the shear plane of the electrochemical double layer into the liquid phase. This effect demonstrates that storage conditions and pre-conditioning may exert a pronounced influence on the zeta potential recorded for surface-modified polymers. Phenomena of this kind have already been described in previous literature [26,27],... 

These authors also defined a shear plane, not necessarily coincident with the outer Helmholtz plane, which is extremely important in electrokinetic effects (Section 3.7). The shear plane limits the zone where the rigid holding of ions owing to the electrode charge ceases to operate. The potential of this plane is called the zeta or electrokinetic potential, f. 

The size of the particles that is calculated from these experiments corresponds to particle dimensions plus the double layer thickness, in this case defined by the shear plane inside which the adsorbed species are rigidly held, and outside of which there is free movement. The shear plane can therefore be associated roughly with the outer Helmholtz plane, an approximation often made. The value of the electrostatic potential at the shear plane with respect to the value in bulk solution is called the electrokinetic or zeta potential, 33 (see Section 3.3). 

Here v is the velocity of the particle, E is the electric field strength, eo is the - permittivity of vacuum, eT is the dielectric constant of the electrolyte solution, ( is the equilibrium potential at the plane of shear (- zeta potential), and tj is the -> viscosity. See also -> Smolu-chowski equation (for the case of xr 1). 

Zeta potential — The electrical -> potential difference between the bulk solution and the shear plane or outer limit of the rigid part of the double layer (the limits of the diffuse - double layer) is the electrokinetic potential , often called the Zeta potential ((or more precisely the Zeta potential difference (). 

Microelectrophoresis is used to measure the electrophoretic mobility or, in other words, the movement of liposomes under the influence of an electric field. From the electrophoretic mobility the electrical potential at the plane of shear or (zeta) potential can be determined (by the Helmoholtz-Smoluchowski equation). From the zeta potential values the surface charge density (o) can be calculated. 

FIGURE 9.15 Potential near the surface of a flat platelet particle using linear and nonlinear Poisson-Boltzmann equation with a surface potential of % = 2.0, (51.4 mV), which is the potential at the outer Helmholtz plane in Figure 9.14. Also showing the shear plane where the zeta potential is measured. 

---