Helmholtz double layer reaction

For many practically relevant material/environment combinations, thennodynamic stability is not provided, since E > E. Hence, a key consideration is how fast the corrosion reaction proceeds. As for other electrochemical reactions, a variety of factors can influence the rate detennining step. In the most straightforward case the reaction is activation energy controlled i.e. the ion transfer tlrrough the surface Helmholtz double layer involving migration and the adjustment of the hydration sphere to electron uptake or donation is rate detennining. The transition state is... 

For moderately doped substrates, when the surface is free of oxide the change of potential is mostly dropped in the space charge layer and in the Helmholtz double layer. The reactions are very sensitive to geometric factors. The reaction that is kinetically limited by the processes in the space charge layer is sensitive to radius of curvature, while that limited by the processes in the Helmholtz layer is sensitive to the orientation of the surface. Depending on the relative effect of each layer the curvature effect versus anisotropic effect can vary. 

For heavily doped materials, either notp type, the surface is degenerated and the material behaves like a metal electrode, meaning that the charge transfer reaction in the Helmholtz double layer is the rate-determining step. This is supported by the lack of an impedance loop associated with the space charge for the heavily doped materials. Also, for heavily doped n-Si large current in the dark is due to electron injection, which is not characterized by a slope of 60 mV/decade. For p-Si, electron injection into the conduction band may also occur during the anodic dissolution. 

Helmholtz layer contains the second water molecule layer. From the Helmholtz double layer toward the bulk electrolyte are the diffusion layer and the hydrodynamic layer. In the diffusion layer, the concentration of species changes from that of the bulk electrolyte to that of the electrode surface. The diffusion layer does not move, but its thickness will decrease with increasing bulk electrolyte flow rate to allow higher reaction rates. The diffusion layer thickness is inversely proportional to the square root of the flow rate. The hydrodynamic layer or Prandtl layer has the same composition as the bulk electrolyte, but the flow of the electrolyte decreases from that of the bulk electrolyte to the stationary diffusion layer. 

In IP, there exist two paths by which current may pass the interface between the solid particle and the electrolyte the faradaic and nonfaradaic paths. Current passage in the faradaic path is the result of electrochemical reactions (redox reactions) and the diffusion of charge toward or off the Helmholtz double layer and aqueous solution interface, that is, Warburg impedance. In the nonfaradaic case, charged particles do not cross the interface. Instead, the current is carried by... 

If the discharge of ions takes place in the Helmholtz double layer, only a fraction x < 1 of the total potential drop is important for the reaction rate. Then... 

Another important electrode reaction type is the electro-de-position of metals from solution. The first elementary step in this reaction is the discharge of ions from the Helmholtz double layer, which is shown to be rate-determining in many cases /159/ A direct... 

TTius, it is quite obvious that purity of the used IL is for many studies and in particular for electrochemical investigations of an enormous importance Water but in particular ionic impurities from the reaction process can lead to a completely different behavior at the interface, because a hard inorganic cation such as sodium or lithium disturb the formation of an ideal, homogeneous Helmholtz-double-layer (Figure 22.2) and should have - even in low concentrations - a significant on fundamental properties. 

In all the above cases, the charge is transferred between the electrode and a species which is ultimately found or ultimately starts from outside the Helmholtz double layer. Of course, reactions involving electron transfer to or from adsorbed species may well occur in relatively complex reaction sequences. While they will be unlikely to be rate determining, they may be expected to influence reaction rates as a function of potential. Since the rate of the overall process may be described by the rate of the rds multiplied by the equilibrium constants for preceding rapid reactions, then, for cathodic processes involving a previous electron transfer, we can write... 

Another important observation is that parallel electrolytic reactions can help to prevent ssaiconductor decomposition. Such parallel reactions are favoured by the presence of surface states with energies below the conduction band or above the valence band edge. Because of their energy position such surface states will prevent the accumulation of electrons or holes at the surface but cause an increasing variation of the voltage drop in the Helmholtz double layer by the accumulation of charge directly on the surface of the semiconductor [l4,27j. 

This is the so-called Tafel equation (Tafel was the first person to find empirically a linear relation between log j and tj). Meanwhile many redox reactions at metal electrodes have been investigated (see, e.g., [1]). One example is shown in Figure 7.4. It should be mentioned that the relevant experiments are performed with electrolytes containing a sufficiently high concentration of a conducting salt so that the externally applied potential occurs only across the Helmholtz double layer. Usually, a values between 0.4 and 0.6 are found. An extrapolation of the linear portions of the log j—tj curves to r/ = 0 yields the exchange current Jq which is concentration dependent. Usually, )q values are given for standard conditions, that is, for = 1 molU For further details on the evaluation of more... 

Having shown that charge is transferred across the interface by the metal cations, not by the electrons, one has to propose a mechanism that would explain the observed behavior, particularly the unexpectedly high reaction rate discussed in Section 19.7.1. In the model presented below it is assumed that the ions cross the interface by migration, under the influence of the high electric field in the Helmholtz double layer, caused by application of an overpotential. This field is given by... 

F r d ic Current. The double layer is a leaky capacitor because Faradaic current flows around it. This leaky nature can be represented by a voltage-dependent resistance placed in parallel and called the charge-transfer resistance. Basically, the electrochemical reaction at the electrode surface consists of four thermodynamically defined states, two each on either side of a transition state. These are (11) (/) oxidized species beyond the diffuse double layer and n electrons in the electrode and (2) oxidized species within the outer Helmholtz plane and n electrons in the electrode, on one side of the transition state and (J) reduced species within the outer Helmholtz plane and (4) reduced species beyond the diffuse double layer, on the other. 

If the electrolyte components can react chemically, it often occurs that, in the absence of current flow, they are in chemical equilibrium, while their formation or consumption during the electrode process results in a chemical reaction leading to renewal of equilibrium. Electroactive substances mostly enter the charge transfer reaction when they approach the electrode to a distance roughly equal to that of the outer Helmholtz plane (Section 5.3.1). It is, however, sometimes necessary that they first be adsorbed. Similarly, adsorption of the products of the electrode reaction affects the electrode reaction and often retards it. Sometimes, the electroinactive components of the solution are also adsorbed, leading to a change in the structure of the electrical double layer which makes the approach of the electroactive substances to the electrode easier or more difficult. Electroactive substances can also be formed through surface reactions of the adsorbed substances. Crystallization processes can also play a role in processes connected with the formation of the solid phase, e.g. in the cathodic deposition of metals. 

The Frumkin theory of the effect of the electrical double layer on the rate of the electrode reaction is a gross simplification. For example, the electrode reaction does not occur only at the outer Helmholtz plane but also at a somewhat greater distance from the electrode surface. More detailed considerations indicate, however, that Eq. (5.3.20) can still be used to describe the effect of the electrical double layer as a good approximation. 

Surface complexation models for the oxide-electrolyte interface are reviewed two models for surface hydrolysis reactions are considered (diprotic surface groups and monoprotic surface groups) and four models for the electric double layer (Helmholtz,... 

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