Ionic spacing

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,... 

X-ray diffraction—Measurement of atomic and ionic spacings in crystal structures and thicknesses of thin metal films. 

The electrochemical interface has a very large electrical capacity (— 10"s F cm-2) compared with the solid—gas or solid—vacuum interface due to the existence of an ionic space charge localized at a short distance from the electrode. 

All of this is based on the linearization procedure in Equation 11. If one examines this condition, the restriction turns out to be quite tight. We may approximate by e/4irtr0, where r0 is the ionic spacing (19). Then Equation 11 takes the form ... 

Thus for an electron beam with v = 1.46 x 106 m/s, Eq. (7-2) gives A. = 5.0 A, comparable to the ionic spacing in a crystal. In 1920, it was found that a crystal would indeed diffract an electron beam, and de Broglie s crazy idea was proven ... 

J - J + iuP at low frequencies, and In many cases of biological interest, there is the more serious problem of "electrode polarization" resulting from accumulation of ionic space charge. 

Interconnect The property requirements for the interconnect ceramic are the most demanding. The conductivity should be as high as possible and, ideally, 100% electronic. This is necessary to reduce internal resistance and to avoid severe problems which would arise were ionic space-charge polarization (see Section 2.7.1) to develop. 

Example 13.4 Determine the field strength for the sampler in Example 13.3 considering ionic space charge. The precipitator voltage is 20 kV. Assume 20°C, standard pressure, f = 0.6. Use Z = 2.2 cm2/(Vs ). 

When the charge on the center wire is relatively low, the ionic space charge density is assumed to be negligible, and Laplace s equation is... 

Figure 30. Ionic space charge effects at grain boundaries in Frenkel disordered materials, (a) Theoretical profiles if u, > u .120 (b) The enhanced grain boundary conductivity can be verified by point electrode impedance spectroscopy.121 The number given are in units of nS / cm and refer to room temperature.

Murray has demonstrated that soluble metallic clusters exhibit coulomb staircase-type behaviour [102]. The ionic space charge formed around the dissolved MFCs is reported to contribute to its capacitance, upon charging of the metal core. It is well known that small metal particles exhibit double layer charging (capacitive charging) properties in liquid electrolytes [104]. The sub-attofarad capacitance associated with the MFCs leads to charging of the tiny capacitor by single electron processes in potential intervals of A V that surpass ke T where is the Boltzmann constant and T is the temperature [102, 105]. 

Figure 11. Ionic spacing S, crystallinity Xc, H20 uptake per a membrane (W) and per an ionic site (N) for the sulfonic acid (-9-), and carboxylic acid (- -Q>- -) membranes as a function of EW.

Equations (14) and (16) assume that the potential distribution is entirely due to the back-to-back ionic space charge regions in each phase. In the early... 

Kluger K, Lohrengel MM (1991) Mobility of ionic space charges in thin insulating films. Ber Bimsenges Physik Chem 95 1458-1461... 

A thorough theoretical treatment together with various verified examples can be found in previous works of the author [4-9]. It is particularly important to note that all carriers that are mobile feel the field effect even if their contribution to it is marginal (fellow traveler effect) [4]. For that reason ionic space charge effects are also crucial for electronic conductors. 

Nanoionics at High Temperatures, Fig. 3 A collection of ionic space charge effects at interfaces involving solids (Reprinted from Ref. [8] by permission of ElseviCT)... 

So far the ionic space charge concepts have been mainly applied to transport and storage. An area that is not adequately addressed but expected to be greatly influenced by such effects is the area of interfacial transfer and reactions including reaction kinetics, catalysis, or in particular the electrochemical transfer reaction. In many of these processes, defect concentrations are involved in the rate determining steps and not only will space charge considerations help understand them but more importantly lead to a targeted improvement of electrochemical performance. 

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