Diffusion double-layer

The treatment in the case of a plane charged surface and the resulting diffuse double layer is due mainly to Gouy and Qiapman. Here may be replaced by d /dx since is now only a function of distance normal to the surface. It is convenient to define the quantities y and yo as... 

The quantity 1 /k is thus the distance at which the potential has reached the 1 je fraction of its value at the surface and coincides with the center of action of the space charge. The plane at a = l//c is therefore taken as the effective thickness of the diffuse double layer. As an example, 1/x = 30 A in the case of 0.01 M uni-univalent electrolyte at 25°C. 

By analogy with the Helmholtz condenser formula, for small potentials the diffuse double layer can be likened to an electrical condenser of plate distance /k. For larger yo values, however, a increases more than linearly with o, and the capacity of the double layer also begins to increase. 

Charged surface plus diffuse double layer of ions —>... 

In the case of a charged particle, the total charge is not known, but if the diffuse double layer up to the plane of shear may be regarded as the equivalent of a parallel-plate condenser, one may write... 

Derive the general equation for the differential capacity of the diffuse double layer from the Gouy-Chapman equations. Make a plot of surface charge density tr versus this capacity. Show under what conditions your expressions reduce to the simple Helmholtz formula of Eq. V-17. 

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). 

Fig. 1. Schematic representation of the electrochemical or diffuse double layer showing the inner (IHP) and outer (OHP) Helmholtz planes and the...

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. 

Measurements based on the Gouy-Chapman-Stem theory to determine the diffuse double-layer capacitance 10, 24,72, 74... 

This result was taken as an experimental eonfirmation of the model developed by Sehmiekler [7]. However, it appeared somehow eontradictory with other results obtained with SECM. It was also suggested that eoneentration polarization phenomena occurring at the aqueous side are negligible as the whole potential drop is presumably developed in the benzene phase. This assumption can be qualitatively verified by evaluating a simplified expression for the potential distribution based on a back-to-back diffuse double layer [40,113],... 

The same system has been studied previously by Boguslavsky et al. [29], who also used the drop weight method. While qualitatively the same behavior was observed over the broad concentration range up to the solubility limit, the data were fitted to a Frumkin isotherm, i.e., the ions were supposed to be specifically adsorbed as the interfacial ion pair [29]. The equation of the Frumkin-type isotherm was derived by Krylov et al. [31], on assuming that the electrolyte concentration in each phase is high, so that the potential difference across the diffuse double layer can be neglected. 

FIG. 8 Inverse differential capacity at the zero surface charge vs. inverse capacity Cj of the diffuse double layer for the water-nitrobenzene (O) and water-1,2-dichloroethane (, ), interface. The diffuse layer capacity was evaluated by the GC ( ) or the MPB (0,)> theory. (From Ref. 22.)... 

To evaluate the contribution of the SHG active oriented cation complexes to the ISE potential, the SHG responses were analyzed on the basis of a space-charge model [30,31]. This model, which was proposed to explain the permselectivity behavior of electrically neutral ionophore-based liquid membranes, assumes that a space charge region exists at the membrane boundary the primary function of lipophilic ionophores is to solubilize cations in the boundary region of the membrane, whereas hydrophilic counteranions are excluded from the membrane phase. Theoretical treatments of this model reported so far were essentially based on the assumption of a double-diffuse layer at the organic-aqueous solution interface and used a description of the diffuse double layer based on the classical Gouy-Chapman theory [31,34]. 

It is also possible for ions in the water, especially positively charged ions, or cations, to be attracted to the negatively charged surfaces. This leads to a zone of water and ions surrounding the clay particles, known as the diffuse double layer. 

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 ... 

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