Diffusion double layers and

Rheology. Flow properties of latices are important during processing and in many latex appHcations such as dipped goods, paint, inks (qv), and fabric coatings. For dilute, nonionic latices, the relative latex viscosity is a power—law expansion of the particle volume fraction. The terms in the expansion account for flow around the particles and particle—particle interactions. For ionic latices, electrostatic contributions to the flow around the diffuse double layer and enhanced particle—particle interactions must be considered (92). A relative viscosity relationship for concentrated latices was first presented in 1972 (93). A review of empirical relative viscosity models is available (92). In practice, latex viscosity measurements are carried out with rotational viscometers (see Rpleologicalmeasurement). 

F r d ic Current. The double layer is a leaky capacitor because Faradaic current flows around it. This leaky nature can be represented by a voltage-dependent resistance placed in parallel and called the charge-transfer resistance. Basically, the electrochemical reaction at the electrode surface consists of four thermodynamically defined states, two each on either side of a transition state. These are (11) (/) oxidized species beyond the diffuse double layer and n electrons in the electrode and (2) oxidized species within the outer Helmholtz plane and n electrons in the electrode, on one side of the transition state and (J) reduced species within the outer Helmholtz plane and (4) reduced species beyond the diffuse double layer, on the other. 

When an aqueous solution containing an irreducible cation M+ is electrolyzed, H2 evolves at the cathode with the overall reaction Haq+ + e(cathode) — (l/2)H2(gas). The detailed mechanism of this reaction is somewhat ambiguous, as it could be attributed either to absorbed H atoms or absorbed H2+ ions. According to Walker (1966, 1967), the basic cathodic reaction is (6.II) followed by (6.1) to give H2. There are several possibilities for reaction (6.II) (Walker, 1968) (1) direct electron donation by the cathodic metal to water, (2) electron liberation from the diffuse double layer, and (3) neutralization of the irreducible cation M+ (e.g., Na+) at the cathode, followed by the reaction of the neutral atom with water ... 

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). 

In addition to the diffuse double layer and the constant capacitance model dis-... 

A corrected and more general analysis of the primary electroviscous effect for weak flows, i.e., for low Pe numbers (for small distortions of the diffuse double layer), and for small zeta potentials, i.e., f < 25 mV, was carried out by Booth in 1950. The result of the analysis leads to the following result for the intrinsic viscosity [rj] for charged particles in a 1 1 electrolyte ... 

FIG. 11.4 Two models for the double layer (a) a diffuse double layer and (b) charge neutralization due partly to a parallel plate charge distribution and partly to a diffuse layer. 

How must the expressions derived in the sections above be modified to take into account the variation in rj and the finite distance over which it increases The answer is that rj — the viscosity within the double layer —must be written as a function of location. Our objective in discussing this variation is not to examine in detail the efforts that have been directed along these lines. Instead, it is to arrive at a better understanding of the relationship between f and the potential at the inner limit of the diffuse double layer and a better appreciation of the physical significance of the surface of shear. 

The structure of the double layer can be altered if there is interaction of concentration gradients, due to chemical reactions or diffusion processes, and the diffuse ionic double layer. These effects may be important in very fast reactions where relaxation techniques are used and high current densities flow through the interface. From the work of Levich, only in very dilute solutions and at electrode potentials far from the pzc are superposition of concentration gradients due to diffuse double layer and diffusion expected [25]. It has been found that, even at high current densities, no difficulties arise in the use of the equilibrium double layer conditions in the analysis of electrode kinetics, as will be discussed in Sect. 3.5. 

It is postulated that one of the ions of the adsorbed 1 1 electrolyte is surface active and that it forms an ionized monolayer at the solid/liquid interface. All counterions are assumed located in the diffuse double layer (no specific adsorption). Similions are negatively adsorbed in the diffuse double layer. Since the surface-containing region must be electrically neutral, the total moles of electrolyte adsorbed, n2a, equals the total moles of counterions in the diffuse double layer which must be equal to the sum of the moles of similions in the diffuse double layer and the charged surface, A[Pg.158]

There is a range of equations used describing the experimental data for the interactions of a substance as liquid and solid phases. They extend from simple empirical equations (sorption isotherms) to complicated mechanistic models based on surface complexation for the determination of electric potentials, e.g. constant-capacitance, diffuse-double layer and triple-layer model. 

On this basis, three models will be discussed, which enable a calculation of the electrical potential, namely the constant-capacitance, the diffuse-double-layer, and the triple-layer model. 

Grahame, D. C. 1950. Effects of dielectric saturation upon the diffuse double layer and the free energy of hydration of ion. J. Chem. Phys. 18 903-909. 

Iv) combine site binding models with purely diffuse double layers and/or with Stem layers. 

The local Ohmic impedance involves the potential of a reference electrode 4>o(r) located at the outer limit of the diffuse double layer and the potential of a reference electrode located far from the electrode 4>(oo) = 0 see Figure 7.10. Thus, the local Ohmic impedance is given by... 

Stability of Microemulsions. The first attempt to describe the microemulsion stability in terms of different free energy components was made by Ruckenstein and Chi (55) who evaluated the enthalpic (Van der Waals potential, interfacial free energy and the potential due to the compression of the diffuse double layer) and entropic... 

Zeta potential is defined as the potential difference between the shearing surface in the diffuse double layer and the pore water that is moving and ranges from +50 to -50 mV. The sign indicates the relative abundance of cations and anions. If the cation concentration is high relative to anion concentration, the sign will be negative... 

Figure 12.5 Particle with surface charge (consisting of an intrinsic particle charge and charge of specifically adsorbed ions), Helmholtz layer HL, part of the diffuse double layer and the shear plane SP of the zeta-potential measurement (schematic representation).

FIGURE 5.2. Classic models of the interface for charged surfaces include, (a) the early Helmholtz model of a molecular capacitor, (b) the Gouy-Chapman model of the diffuse double layer, and (c) the Stem model. 

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