Ionic drift

There are also models assuming the electrostrictive input of incorporated anions into the breakdown initiation,285,299 ionic drift models,300 and many others reviewed elsewhere.283,293 However, the majority of specialists agree that further work is necessary in order to properly understand the physics of the electric breakdown in growing oxide films and that caused by electric stress in thin-film structures. 

FIGURE 8.11 Arrangement ofan experiment to demonstrate ionic drift. 

If we place an ionic conductor between parallel-plate blocking electrodes that produce an electric field E parallel to the x-axis, the electrostatic potential varies as — xE on passing from one electrode at x = 0 to the other. At equilibrium, the mobile-ion concentration Cj(x) is proportional to exp(qEx/kT), and the ionic drift-current density (7(E in the field is balanced by a diffusion current due to the concentration gradient (Fick s law) ... 

Fig. 7.18. As the electrode reaction consumes ions from the OHP, their concentration is bound to decrease because the ionic drift diffusion from the bulk of the solution can start only after a certain concentration gradient is established.

IONIC DRIFT UNDER A CHEMICAL-POTENTIAL GRADIENT DIFFUSION... 

IONIC DRIFT UNDER AN ELECTRIC HELD CONDUCTION... 

When a potential gradient, i.e., electric field, exists in an electrolytic solution, the positive ions drift toward the negative electrode and the negative ions drift in the opposite direction. What is the effect of this ionic drift on the state of charge of an electrolytic solution ... 

The occurrence of a reaction at each electrode is tantamount to removal of equal amounts of positive and negative charge from the solution. Hence, when electron-transfer reactions occur at the electrodes, ionic drift does not lead to segregation of charges and the building up of an electroneutrality field (opposite to the applied field). Thus, the flow of charge can continue i.e., the solution conducts. It is an ionic conductor. 

The driving force for ionic drift, i.e., the electric field X, not only has a particular magnitude, it also acts in a particular direction. It is a vector. Since the ionic current density j, i.e., the flow of electric charge, is proportional to the electric field operating in a solution [Eq. (4.128)],... 

Another way of looking at ionic drift is to consider the fate of any particular ion under the field. The electric force field would impart to it an accelaation according to Newton s second law. Were the ion completely isolated (e.g., in vacuum), it would accelerate indefinitely until it collided with the electrode. In an electrolytic solution, however, the ion very soon collides with some other ion or solvent molecule that crosses its path. This collision introduces a discontinuity in its speed and direction. The motion of the ion is not smooth it is as if the medium offers resistance to the motion of the ion. Thus, the ion stops and starts and zigzags. However, the applied electric field imparts to the ion a direction (that of the oppositely charged electrode), and the ion gradually works its way, though erratically, in the direction of this electrode. The ion drifts in a preferred direction. 

Current Density Associated with the Directed Movement of Ions in Solution, in Terms of Ionic Drift Velocities... 

By recalling that the ionic drift velodlies are related through the force operating on the ions to the ionic mobilities [Eq. (4.151)], it will be realized that Eq. (4.157) is the basic expression from which may be derived the expressions for conductance, equivalent conductivity, specific conductivity, etc. 

A stimulating approach to the problem of the interdependence of ionic drifts can... 

If, however, the solvent is considered fixed, i.e., the solvent is taken as the coordinate system or the frame of reference, then one can consider ionic fluxes relative to the solvent. Under this condition, Jq = 0, and one has only two ionic fluxes. Thus, one can describe the interacting and independent ionic drifts by the following... 

Attention should be drawn to the fact that there has been a degree of inconsistency in the treatments of ionic clouds (Chapter 3) and the elementary theory of ionic drift (Section 4.4.2). When the ion atmosphere was described, the central ion was considered—from a time-averaged point of view—at rest. To the extent that one seeks to interpret the equilibrium properties of electrolytic solutions, this picture of a static central ion is quite reasonable. This is because in the absence of a spatially directed field acting on the ions, the only ionic motion to be considered is random walk, the characteristic of which is that the mean distance traveled by an ion (not the mean square distance see Section 4.2.5) is zero. The central ion can therefore be considered to remain where it is, i.e., to be at rest. 

When, however, the elementary picture of ionic drift (Section 4.4.2) was sketched, the ionic cloud around the central ion was ignored. This approximation isjustified only when the ion atmosphere is so tenuous that its effects on the movement of ions can be neglected. This condition of extreme tenuosity (in which there is a negligible coupling between ions) obtains increasingly as the solution tends to infinite dilution. Hence, the simple, unclouded picture of conduction (Section 4.4) is valid only at infinite dilution. 

All transport processes (viscous flow, diffusion, conduction of electricity) involve ionic movements and ionic drift in a preferred direction they must therefore be interrelated. A relationship between the phenomena of diffusion and viscosity is contained in the Stokes-Einstein equation (4.179). 

Distance between electrodes in APPJ is usually about 1 mm, which is much smaller than the size of the electrodes (about 10 cm x 10 cm). Therefore, the discharge can be considered one-dimensional, and effects of the boundaries on the discharge can be neglected. The electric current in the discharge is the sum of the current due to the drift of electrons and ions, and the displacement current. Since mobility of the ions is usually 100 times smaller than the electron mobility, the current in the discharge is mostly due to electrons. Considering that the typical ionic drift velocity in APPJ discharge conditions is about 3 x 10" cm/s, the time needed for ions to cross the gap is about 3 ps, which corresponds to a frequency of... 

By comparing the F//curve of the segmented MEA with the reference curve it can be seen in Figure 7-15 that the patterning process of 200 xm isolating lines can be performed without degradation of the MEA, and ionic drift currents between cells can be neglected. 

Hayamizu, K. and Aihara, Y, Correlating the ionic drift under Pt/Pt electrodes for ionic liquids measured by low-voltage electrophoretic NMR with chronoanperometry, J. Phys. Chem. Lett. 1, 2055-2058 (2010). 

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