Electrical double layer charge density

Eq. (3.92) implies a linear relation between cosh Y0 and cosh Ym. Therefore, values for go., and Fo, can be assessed by extrapolating this relation to cosh Ym = 1. This is demonstrated in Fig. 3.46 where a plot of cosh Yg versus cosh Ym is shown. Making use of least-squares analysis we obtain a slope of 1.01 0.01 and an intercept of 1.80 0.4. Furthermore, in conformity with Eq. (3.92) the intercept yields Fo, = 119 0.03 or, respectively, (po = 30.5 0.7 mV and <70i = 1.29 0.04 mC m 2 for the diffuse electric layer potential and diffuse double layer charge density at infinite separation. These values are in... 

In simulations of the full electric double layer, ionic density profiles are oscillatory in the concentration range between 1 and 3 mol/1. Surface charges are screened by free ions over a distance of several Debye lengths. 

In accord with Eqs. (IV.4) and (IV.5), the double-layer charge density and the electrical component of adhesion may be changed by changing the work function of one of the members of the contacting pair. It is usually easier to change the work function of the surface that is being exposed to dust. 

Let us examine the relationship between the electrical and molecular components of adhesive interaction. Such an analysis has been made starting from various premises. In [154], account was taken of the elastic properties of the contact surfaces in [151-153], the analysis was based on the relationship between the double-layer charge density in the contact zone and the adhesion... 

In detaching the particles, the force of adhesion is overcome. If the adhesion is determined by the electrical component, the adhesive force will be completely dependent on the double-layer charge density. Since each force of detachment corresponds to an adhesion number and a specific double-layer charge density, we can express the mathematical expectation for the electrical component of adhesion as follows ... 

The double-layer charge density og may assume its maximum value then the force of detachment will be equal to the electrical component of adhesive force, and the adhesion number will be a function of the maximum double-layer charge density, i.e., yp =f(of ). 

The arrangement of particles on a rough surface is random a particle may occupy any site relative to the peaks on the surface. Depending on the particle position, the double-layer charge density Og may vary, as well as the mathematical expectation of the electrical component of adhesive force Fg. 

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... 

Loeb, AL Overbeek, JTG Wiersema, PH, The Electrical Double Layer Around a Spherical Colloid Particle, Computation of the Potential, Charge Density, and Free Energy of the Electrical Double Layer Around a sperical Colloid Particle M.I.T. Press Cambridge, MA, 1961. Lorentz, HA, Wied, Ann. 11, 70, 1880. 

Studies of theadsorption of surface-active electrolytes at the oil,water interface provide a convenient method for testing electrical double-layer theory and for determining the state of water and ions in the neighborhood of an interface. The change in the surface amount of the large ions modifies the surface charge density. For instance, a surface ionic area of 100 per ion corresponds to 16 pC per square centimeter. " " ... 

According to the model proposed by Verwey and Niessen (1939), an electric double layer is formed at an ITIES, which consists of two ionic space charge regions. As a whole the electric double layer is electrically neutral, so for the excess charge density in the part of the double layer in the aqueous phase, and for the part in the organic phase,... 

Of the quantities connected with the electrical double layer, the interfacial tension y, the potential of the electrocapillary maximum Epzc, the differential capacity C of the double layer and the surface charge density q(m) can be measured directly. The latter quantity can be measured only in extremely pure solutions. The great majority of measurements has been carried out at mercury electrodes. 

The description of the sorption of charged molecules at a charged interface includes an electrostatic term, which is dependent upon the interfacial potential difference, Ai//(V). This term is in turn related to the surface charge density, electric double layer model. The surface charge density is calculated from the concentrations of charged molecules at the interface under the assumption that the membrane itself has a net zero charge, as is the case, for example, for membranes constructed from the zwitterionic lecithin. Moreover,... 

The Lippmann Equation. It can be shown thermodynamically that the slope of the electrocapillary curve is equal to the charge density, a, in the electric double layer (First Lippmann Equation). 

ECs are another promising electrical energy storage device with a higher energy density than electrical capacitors, and a better rate capability and cycling stability than LIBs [32]. Carbon-based electric double layer capacitors and metal oxide- or polymer-based pseudocapacitors are two main types of ECs. The charge-... 

---