Stem potential

For present purposes, the electrical double-layer is represented in terms of Stem s model (Figure 5.8) wherein the double-layer is divided into two parts separated by a plane (Stem plane) located at a distance of about one hydrated-ion radius from the surface. The potential changes from xj/o (surface) to x/s8 (Stem potential) in the Stem layer and decays to zero in the diffuse double-layer quantitative treatment of the diffuse double-layer follows the Gouy-Chapman theory(16,17 ... 

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. 

The nature and the thickness of the electrical donble layer are important becanse the interaction between charged particles is governed by the overlap of their diffnse layers. Unfortunately, it is impossible to measure directly the Stem potential Pg. Instead, the zeta potential, which is the potential at the shear plane close to the Stem plane, can be experimentally measured and is often nsed as a measure of the surface potential. 

In this case the notation of the Stem potential is convenient. The Stem potential characterises the potential at the boundary of the Stem and the diffuse layer. If the potential drop across the Stem layer can be neglected the state of the counterions within it can be characterised by the Stem potential too. Thus the charges of Stem and difhise layers can be expressed by one potential. At low electrolyte concentration the diffuse layer thickness exceeds the thickness of the Stem layer which can be estimated as a multiple of the ion dimension. This means that the potential drop across the Stem layer is very small in comparison to the Stem potential and can be neglected. However the neglecting of the potential drop across the Stem layer at high electrolyte concentration, when the diffuse layer thickness is small, is questionable. 

In the Stem-Gouy-Chapman (SGC) theory the double layer is divided into a Stem layer, adjacent to the surface with a thickness d, and a diffuse layer of point charges. The diffuse layer begins at the Stem plane in a distance d, from the surface. In the simplest case the Stem layer is free of charges. In real cases the Stem layer is formed by specifically adsorbed ions. The condition of electroneutrality was given by Eq. (2.59) In addition to and Oj, the surface charge can be represented by the Stem potential. It transforms the conditions of electroneutrality into the equation for the determination of the Stem potential. 

In the theory of adsorption retardation the energy of an ion approaching the interface is described by the very simple law zev /(x), the maximum value of which is proportional to the Stem potential (cf. Chapter 2). Each ion is screened by counterions (Kortum 1966) and ions pass the diffuse part of the DL together with their screening counterions. In Section 7.5. it will be shown, that under certain conditions this effect can be neglected. 

It follows from (7.26) that at small Stem potentials at the bubble surface, the ratio K(vj7s,) / 6 is a quantity of the order of (1/(k8d), i.e., it is much less than unity. The new effect, the electrostatic retardation of kinetics of surfactant anions adsorption becomes visible when the dimensionless parameter exp(-v /sj) equals or exceeds (kSq). ... 

The values V /sk, and r refer to the equilibrium values of the Stem potential and the surface concentration, respectively. To replace the concentration c(0) from Eq. (7.27), the adsorption isotherm (7.10) can be used,... 

In presence of an background electrolyte, the adsorption kinetics can also be controlled by electric retardation effects. This conclusion holds for strongly charged surfaces and high electrolyte concentration. High Stem potentials, of about 200 mV, can be achieved at common surfactant and electrolyte concentrations. This becomes clear from the data in Fig. 7.1 representing results from electrophoresis measurements of n-heptane droplets in water in the presence of sodium dodecylsulphate and 10 M NaCl. 

The importance of electrostatic retardation increases with the surface potential, i.e. with the adsorption surfactant molecules. Especially in some practical systems of high background electrolyte, only at densely packed adsorption layers the electrostatic retardation will set in. This state of adsorption has not been taken into consideration so far. With increasing background electrolyte concentration counterions build the Stem layer. The charge of the adsorption layer is compensated partially by the diffuse layer and the Stem layer (Eq. 2.5) which decrease with the increased amount of counterions in the Stem layer. Simultaneously, the Stem potential is lowered and the electrostatic retardation becomes less effective. This aspect was discussed already by Kretzschmar et al. (1980). Consequently, the electrostatic retardation can exist in NaCl solution while it can disappear under certain conditions in CaCl2 solutions. 

The possibility to realise the second condition (8.101) is considered by Usui et al. (1980), where the Stem potential was calculated together with the sedimentation potential from adsorption data of CTAB. In the region of high concentration 0.7-2.5T0-5 mole/cm and adsorption, C, and coincide. At concentrations lower than 7T0- mole/cm, differences between and become significant. The difference between and T, decreases with decreasing surfactant concentration, reaching a value of the order of 100 mV. 

These results show that at high concentrations (above 7T0- mole/cm ), addition of surfactant increases the degree of retardation of the bubble surface. Thus, under the condition Xb > X th adsorption can considerably deviate from the mean value only in the vicinity of the leading pole of the bubble and the electrokinetic potential can be calculated from the equilibrium adsorption value. When the concentration of the surfactant decreases, retards to a lesser extent the motion of the surface. The condition Xb < Xo is realised when the removal of surfactant to the rear of the bubble is possible, and adsorption is much lower than the equilibrium value over almost the whole bubble surface. This statement needs a confirmation if values of adsorption less than 10 ° mole/cm are taken into account since then a deviation of the electrokinetic potential from Stem potential was observed (Sotskova et al. 1982). Substituting this value and the velocity of the buoyant bubble with a radius of 150 pm condition (8.98) is fulfilled. 

Systematic studies of bubble hydrodynamics based on the Dom effect were suggested by Dukhin (1983). A comprehensive study, comprising the measurement of adsorption on immobile surfaces with the calculation of the Stem potential and measurements of sedimentation potentials, should be performed with homologous series of ionic surfactant so that the condition (8.97) is fulfilled by higher homologues and the opposite condition (8.101) by the lower ones. With decreasing surface activity the condition (8.97) will be fulfilled at smaller adsorption values. This means that the lower the surface activity, the smaller should be the deviation of the electrokinetic potential from the Stem potential at respective values of adsorption. And finally, when condition (8.97) is not fulfilled the electrokinetic and Stem potentials must coincide over the whole concentration interval. 

Overbeek (1990) developed non-linear formulations for the calculation of the double layer interaction of divers particles. Kihira et al. (1992) used Overbeek results and established an applicability limit of the HHF approximation. It is not valid if the Stem potential difference is to small and the individual values exceed 25 mV. On the other hand it works well if the ratio of the potential values is sufficiently high even though one of the two potentials is high. 

The literature analysis in Appendix lOD showed that even at high electrolyte concentration (10 -10 M) the absolute values of Stem potentials of bubbles and particles cannot be small and their difference very large. It means that Overbeek s equations have to be used for the estimation of the electrostatic barrier in microflotation and it can be lower than predicted by the HHF approximation. For example in the investigations by Yoon Luttrel (1991) on the role of hydrophobic interaction in microflotation equals -20 mV and = -45mV. The HHF approximation leads to an overestimation of electrostatic repulsion by almost two orders of magnitude according to Fig. 3 of Kihira et al. (1992). 

On the contrary, the HHF approximation can be used for the estimation of the barrier disappearance due to the decrease of the Stem potential caused by cation adsorption. 

The results presented in Figs. 10.7 and 10.8 have to be modified and generalised. The negative complex Hamaker constant and the difference of the Stem potentials of the bubble and the particle have to be incorporated into the calculations. The force of hydrophobic attraction has to be added into the general necessary condition of microflotation. 

The contact angle within the rear stagnant cup can strongly differ from its equilibrium value because surface concentration exceeds the equilibrium value. In particular, difference between surface concentration within the r.s.c. and the equilibrium value causes a difference in the Stem potential too. Here, the absolute value of the Stem potential exceeds its equilibrium value because the surface concentration of OH is higher than at equilibrium. The effect of this difference on the value of the contact angle within r.s.c. can be estimated on the basis of Eq. (10A.6). 

Li Somasundaran (1991, 1992) have established that the absolute value of the negative charge of the water-air interface is sufficiently high already at 10 -10 M NaCl at sufficiently high pH-value. It leads to the conclusion that OH -adsoiption at the water-air interface satisfies condition (8.72) and its value within the r.s.c. exceeds equilibrium. Consequently, the Stem potential also can exceed the equilibrium. Due to the high sensitivity of the contact angle to the Stem potential, this difference can be important. 

Let us assume the absolute value of the Stem potential at the water-air interface T, exceeds that of the mineral particle 1 2> I il > Thus, within the r.s.c. F, - -values are higher than in equilibrium. Taking into account the fourth degree in Eq. (10A.6), even a small increase in l, - 4 21 can cause a big increase of the contact angle within the r.s.c. 

A recharge of the bubble, caused by aluminium adsorption provides an electrokinetic potential value of 15 mV at 0.0 IM NaCl. These new results show that the conditions for the electrostatic attraction remain even at high salt concentration. The additional condition is not a small Stem potential of the particle surface. It is important to take into account that at high electrolyte... 

Vsto = eVsto(x) kT dimensionless equilibrium Stem potential... 

Inner Potential (Stern) 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 Stem potential. See also Electric Double Layer, Zeta Potential. 

Chone (2001) analyzed the favorable impact of moderate water stress on the aromatic potential of Sauvignon Blanc grapes. One initial finding of this research was that stem potential ( Pt), measured in a pressure chamber , provided an earlier indication of moderate water stress than basic leaf potential ( bp) (Chone et al., 2001a). As described in Volume 1, Section 10.4.8, stem potential represents the sap pressure resulting from the difference between leaf transpiration and water absorption by the roots, whereas basic leaf... 

For illustration of the influence of electrolyte coneentra-tion, Stem potential, and particle dimension some calculations of doublet lifetime are made and their results are presented in Fig. 6. The potential well depth increases and in parallel doublet lifetime increases with increasing particle dimension and elec trolyte concentration and decreasing surface potential. 

Figure 6 Dependence of doublet lifetime on the Stem potential for different electrol)fte concentrations and droplet dimensions. Numbers near curves correspond to droplet radius. (1) Curves 1 -4 without accoxmt for retardation of molecular forces of attraction, T = exylkT (2) curves 1 =4 with accoimt for retardation. (From Ref. 26.)...

As distinct from uncharged droplets, flocculation in the range of micrometer-sized droplets is possible. As seen in Fig. 9, even rather large droplets (4 pm) aggregate reversibly if file electrolyte concentration is lower than (1-5) X10 M and the Stem potential is higher than 25 mV. For smaller droplets the domain of flocculation will extend while the domain of coagulation will shrink. For submicrometer droplets, flocculation takes place even at high electrolyte concentrations (0.1 M). 

Fig. 8.4-14 Electrostatic potential as a function of the distance. The potential rises from the value at Z) = 0 within the adsorbed layer to a maximum in the Helmholtz layer followed by a linear decrease to the Stem potential. The Gnoy-Chapman equation describes this decrease in the double layer...

Potential charges + first counter ions (Stem potential outer Helmholtz layer)... 

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