Electrical double layer Debye length

Ionic strength of medium, surface structure and non-spherical particles can affect diffusion speed of particles. The thickness of the electric double layer (Debye length) changes with the ions in the medium and the total ionic concentration. An extended double layer of ions around the particle results from a low conductivity medium. So, the diffusion speed reduces and hydrodynamic diameter increases. The diffusion speed can be affected with a change in surface area. The diffusion speed will reduce with an adsorbed polymer layer. Polymer conformation can alter the apparent size. 

In the second group of models, the pc surface consists only of very small crystallites with a linear parameter y, whose sizes are comparable with the electrical double-layer parameters, i.e., with the effective Debye screening length in the bulk of the diffuse layer near the face j.262,263 In the case of such electrodes, inner layers at different monocrystalline areas are considered to be independent, but the diffuse layer is common for the entire surface of a pc electrode and depends on the average charge density <7pc = R ZjOjOj [Fig. 10(b)]. The capacitance Cj al is obtained by the equation... 

The electroviscous effect present with solid particles suspended in ionic liquids, to increase the viscosity over that of the bulk liquid. The primary effect caused by the shear field distorting the electrical double layer surrounding the solid particles in suspension. The secondary effect results from the overlap of the electrical double layers of neighboring particles. The tertiary effect arises from changes in size and shape of the particles caused by the shear field. The primary electroviscous effect has been the subject of much study and has been shown to depend on (a) the size of the Debye length of the electrical double layer compared to the size of the suspended particle (b) the potential at the slipping plane between the particle and the bulk fluid (c) the Peclet number, i.e., diffusive to hydrodynamic forces (d) the Hartmarm number, i.e. electrical to hydrodynamic forces and (e) variations in the Stern layer around the particle (Garcia-Salinas et al. 2000). 

The basic difference between metal-electrolyte and semiconductor-electrolyte interfaces lies primarily in the fact that the concentration of charge carriers is very low in semiconductors (see Section 2.4.1). For this reason and also because the permittivity of a semiconductor is limited, the semiconductor part of the electrical double layer at the semiconductor-electrolyte interface has a marked diffuse character with Debye lengths of the order of 10 4-10 6cm. This layer is termed the space charge region in solid-state physics. 

It is instructive to compare this to the capacitance of a plate capacitor o A/d. Here, A is the cross-sectional area and d is the separation between the two plates. We see that the electric double layer behaves like a plate capacitor, in which the distance between the plates is given by the Debye length The capacity of a double layer — that is the ability to store charge — rises with increasing salt concentration because the Debye length decreases. 

We can observe electro-osmosis directly with an optical microscope using liquids, which contain small, yet visible, particles as markers. Most measurements are made in capillaries. An electric field is tangentially applied and the quantity of liquid transported per unit time is measured (Fig. 5.13). Capillaries have typical diameters from 10 fim up to 1 mm. The diameter is thus much larger than the Debye length. Then the flow rate will change only close to a solid-liquid interface. Some Debye lengths away from the boundary, the flow rate is constant. Neglecting the thickness of the electric double layer, the liquid volume V transported per time is... 

This simple equation is, however, only valid for R Xp- If the radius is not much larger than the Debye length we can no longer treat the particle surface as an almost planar surface. In fact, we can no longer use the Gouy-Chapman theory but have to apply the theory of Debye and Hiickel. Debye and Hiickel explicitly considered the electric double layer of a sphere. A result of their theory is that the total surface charge and surface potential are related by... 

Electrostatic forces, acting when the electric double layers of two drops overlap, play an important role. As mentioned above, oil drops are often negatively charged because anions dissolve in oil somewhat better than cations. Thus, the addition of salt increases the negative charge of the oil drops (thus their electrostatic repulsion). At the same time it reduces the Debye length and weakens the electrostatic force. For this reason, emulsion stability can exhibit a maximum depending on the salt concentration. 

For relatively wide channels with negligible electrical double-layer overlap (r/8 > 10), a nearly flat flow profile is expected. It has often been stated that when the channel size and the Debye length are of similar dimensions (r 8), complete electrical double-layer overlap occurs and the EOF is negligible. However, when r 8, a significant EOF can still be created the EOF velocity in the central part of the channel is approximately 20% of that in an infinitely wide channel. Only at conditions where r/8 1 is the EOF fully inhibited by double-layer overlap [25], It should be noted here that the approximations made by using the Rice and Whitehead theory at r/8 < 10 may lead to significant errors in the calculation of the velocity distribution and magnitude of the EOF [17] compared to more sophisticated models. 

Debye-Hiickel parameter k (the Debye length), which has the dimension of length, serves as a measure for the thickness of the electrical double layer. Figure 1.5 plots the... 

This is a somewhat academic question because the answer depends on the definition of this. Two possibilities for this have been given in fig. 2.6. Nevertheless, for interpretational purposes it is sometimes useful to have some feeling for the thickness t. The issue may be compared with that of defining the thickness of an electric double layer. Strictly speaking such layers are infinitely thick but for many practical purposes, like colloid stability and electrokinetics, it has proved convenient to introduce the Debye length, v" as a representative measure of t. Making this choice for double layers involves three elements ... 

Electrically charged particles in aqueous media are surroimded by ions of opposite charge (counterions) and electrolyte ions, namely, the electrical double layer. The quantity He represents the energy of repulsion caused by the interaction of the electrical double layers. The expression for He depends on the ratio between the particle radius and the thickness of the electrical double layer, k, called the Debye length. For K.a > 5 (Quemada and Berli, 2002) ... 

Experimental results showed that treatment of CAJ with a cationic resin decreased the zeta ( surface) potential of the particles, decreased the ionic strength, and consequently increased the thickness of the electrical double layer surrounding the particles (Debye length), but did not change cloud... 

When charged colloidal particles in a dispersion approach each other such that the double layers begin to overlap (when particle separation becomes less than twice the double layer extension), then repulsion will occur. The individual double layers can no longer develop unrestrictedly, as the limited space does not allow complete potential decay [10, 11]. The potential v j2 half-way between the plates is no longer zero (as would be the case for isolated particles at 00). For two spherical particles of radius R and surface potential and condition x i <3 (where k is the reciprocal Debye length), the expression for the electrical double layer repulsive interaction is given by Deryaguin and Landau [10] and Verwey and Overbeek [11],... 

Electrostatic repulsion has a limitation. It works only for systems that do not contain large quantities of electrolytes. Indeed, the presence of electrolytes reduces the so-called Debye length, which is basically the distance at which electrostatic repulsion is effective. Electrolytes also compress the electrical double layer. The result is a reduction of the electrostatic repulsion, which may become weaker than van der Waals attraction. 

Mathematical treatment of the diffuse portion of the electrical double layer (Adamson, 1976) yields the very useful concept of an effective thickness 1/k of that layer. This is the distance from the charged surface into the solution within which the major portion of electrical interactions with the surface can be considered to occur. The effective thickness, often called the Debye length, is given by... 

Debye Length A parameter in the Debye—Hiickel theory of electrolyte solutions, k-1. For aqueous solutions at 25 °C, k = 3.288y7 in reciprocal nanometers, where I is the ionic strength of the solution. The Debye length is also used in the DLVO theory, where it is referred to as the electric double-layer thickness. See also Electric Double-Layer Thickness. 

Electric Double-Layer Thickness A measure of the decrease of potential with distance in an electric double layer. It is the distance over which the potential falls to 1/e, about one-third, of the value of the surface potential. Also termed the Debye length. 

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