Potential gradients double layer

IHP) (the Helmholtz condenser formula is used in connection with it), located at the surface of the layer of Stem adsorbed ions, and an outer Helmholtz plane (OHP), located on the plane of centers of the next layer of ions marking the beginning of the diffuse layer. These planes, marked IHP and OHP in Fig. V-3 are merely planes of average electrical property the actual local potentials, if they could be measured, must vary wildly between locations where there is an adsorbed ion and places where only water resides on the surface. For liquid surfaces, discussed in Section V-7C, the interface will not be smooth due to thermal waves (Section IV-3). Sweeney and co-workers applied gradient theory (see Chapter III) to model the electric double layer and interfacial tension of a hydrocarbon-aqueous electrolyte interface [27]. 

Ohmic potential gradients are established practically instantaneously across conductors, certainly within times shorter than the response time of the fastest measuring devices, which is about 1 ns. They are caused by formation of a double layer, the charge of which is located on the opposite faces of the conductor in question. 

The potential governing these electrokinetic effects is clearly at the boundary (the face of shear) between the stationary phase (the fixed double layer) and the moving phase (the solution). This potential is called the electrokinetic potential or the zeta potential. An electrokinetic phenomenon in soil involves coupling between electrical, chemical, and hydraulic gradients. 

The concentration overpotential i/c is the component of the overpotential due to concentration gradients in the electrolyte solution near the electrode, not including the electric double layer. The concentration overpotential is usually identified with the Nernst potential of the working electrode with respect to the reference electrode that is, the thermodynamic electromotive force (emf) of a concentration cell formed between the working electrode (immersed in electrolyte depleted of reacting species) and the reference electrode (of the same kind but immersed in bulk electrolyte solution) ... 

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). 

Equations (6.4.43a-c) yield the central result of this section—the following expression for the electro-osmotic slip velocity ua under an applied potential and concentration gradient, in the Debye-Hiickel approximation for a thin double layer... 

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. 

In general, the flow of water due to a chemical potential gradient is called chemical osmosis. When compacted, clay can act as a semi-permeable membrane due to overlapping diffuse double layers. This means that the movement of solute particles is restricted across the membrane, while solvent is free to flow. To attain chemical equilibrium in case of an initial concentration gradient across the clay, water flows from low to high salt concentration. The degree of semi-permeability is described by the reflection coefficient a, which ranges from 0 (no osmosis) to 1 (no solute transport). 

If D is the dielectric constant of the parallel plate condenser formed by these two plane layers of opposite charges, r their distance apart, or the thickness of the double layer , then the capacity of the double layer per square centimetre is Djterr if a is the amount of charge in each layer per square centimetre, the potential difference between the two sides of this idealized double layer is = terra ID. The force on the charge a in a field of potential gradient X is Xa but the resistance to motion of the layer of liquid at the distance from the solid surface where the outer side of this double layer is situated, is rj(v[r), where y is the viscosity and v the velocity with which the liquid moves. At steady motion the driving force and viscous resistance to motion... 

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