Double layer theories Helmholtz

In the potential region where nonequilibrium fluctuations are kept stable, subsequent pitting dissolution of the metal is kept to a minimum. In this case, the passive metal apparently can be treated as an ideally polarized electrode. Then, the passive film is thought to repeat more or less stochastically, rupturing and repairing all over the surface. So it can be assumed that the passive film itself (at least at the initial stage of dissolution) behaves just like an adsorption film dynamically formed by adsorbants. This assumption allows us to employ the usual double-layer theory including a diffuse layer and a Helmholtz layer. 

As regards the origin of the double layer the Helmholtz theory gives no information, but several other theories have been formulated. Modem electrical theories suppose every conducting substance to contain large numbers of negatively charged ions, called electrons, which are exactly alike no matter in what substance they are found. When two s.T. 5... 

It is evident now why the Helmholtz and Gouy-Chapman models were retained. While each alone fails completely when compared with experiment, a simple combination of the two yields good agreement. There is room for improvement and refinement of the theory, but we shall not deal with that here. The model of Stem brings theory and experiment close enough for us to believe that it does describe the real situation at the interface. Moreover, the work of Grahame shows that the diffuse-double-layer theory, used in the proper context (i.e., assuming that the two capacitors are effectively connected in series), yields consistent results and can be considered to be correct, within the limits of the approximations used to derive it. 

Chapter 3 deals with theoretical and experimental studies of thermo-osmosis of liquids and gases along with thermo-osmotic concentration differences. Correlation with kinetic theory has also been attempted. Chapter 4 is concerned with experimental and theoretical studies of electro-kinetic phenomena, e.g. electro-osmosis and streaming in a system containing two subsystems separated by a membrane. Relationship with Helmholtz double layer theory has been examined with a view to provide physical interpretation of phenomenological coefficients. Theory and experiment have been compared to assess the range of validity of thermodynamic theory. Chapters 3 and 4 are concerned with discontinuous systems involving a membrane as barrier. 

Comparison with Helmholtz double layer theory... 

The origin of second-order coefficients, particularly L122 and L211, can be easily understood on the basis of Helmholtz double layer theory. It may be noted that local... 

According to Helmholtz double layer theory, streaming current ( )a, =o is given by [15]... 

Based on the classical electrical double layer theory, the potential drop across the inner Helmholtz layer (vj/o-vj/p) is related to the surface charge (0o) by... 

Equations (l)-(4) are the foundations of electrical double layer theory and are often used in modeling the adsorption of metal ions at interfaces of charged solid and electrolyte solutions. In a typieal TLM, the outer layer capacitance is often fixed at a lower value (i.e., C2 = 0.2 F/m ), whereas iimer layer capacitance (Ci) can be adjusted to between 1.0 and 1.4 F/m [25]. It should be noted that the three-plane model (TPM) is a variation of the classical triple-layer model, in which the outer layer eapaeitanee is not fixed. Although the physical presentations of the TLM and TPM are identical as shown in Fig. 2, i.e., both involve a surface layer (0), an inner Helmholtz plane (p), and an outer Helmholtz plane d) where the diffuse double layer starts, a one-step protonation process (i.e., 1 piC approach) is, in general, assumed in the TPM, in eontrast to a two-step protonation process (i.e., 2 p/C approach) in the TLM. Another distinct difference is that pair-forming ions are assumed to be on the outer Helmholtz plane in the TPM but on the inner Helmholtz plane in the TLM. In our study, the outer layer capacitance is allowed to vary while the pair-forming ions are placed on the iimer Helmholtz plane with a complete set of surface eomplexation reactions being considered. Therefore, our approach represents a hybrid of the TPM and TLM. 

The early concept of an electrochemical supercapacitor (ES) was based on the electric double-layer existing at the interface between a conductor and its contacting electrolyte solution. The electric double-layer theory was first proposed by Hermann von Helmholtz and further developed by Gouy, Chapman, Grahame, and Stem. The electric double-layer theory is the foundation of electrochemistry from which fhe electrochemical processes occurring at an electrostatic interface... 

Cotton and Mouton favored the electric double layer theory of Helmholtz. Duclaux, who with Jordis had considered hydrosols of... 

The more detailed analysis by Grahame distinguishes two kinds of molecular condenser (see 4d, p. 134). The distance of closest approach of the cations to the interface is called by Grahame the outer Helmholtz plane We wish to introduce the name limiting Gouy plane thereby expressing the fact that up to this plane the double layer may be treated completely according to the diffuse double layer theory. 

IHP) (the Helmholtz condenser formula is used in connection with it), located at the surface of the layer of Stem adsorbed ions, and an outer Helmholtz plane (OHP), located on the plane of centers of the next layer of ions marking the beginning of the diffuse layer. These planes, marked IHP and OHP in Fig. V-3 are merely planes of average electrical property the actual local potentials, if they could be measured, must vary wildly between locations where there is an adsorbed ion and places where only water resides on the surface. For liquid surfaces, discussed in Section V-7C, the interface will not be smooth due to thermal waves (Section IV-3). Sweeney and co-workers applied gradient theory (see Chapter III) to model the electric double layer and interfacial tension of a hydrocarbon-aqueous electrolyte interface [27]. 

In 1979, a viable theory to explain the mechanism of chromium electroplating from chromic acid baths was developed (176). An initial layer of polychromates, mainly HCr3 0 Q, is formed contiguous to the outer boundary of the cathode s Helmholtz double layer. Electrons move across the Helmholtz layer by quantum mechanical tunneling to the end groups of the polychromate oriented in the direction of the double layer. Cr(VI) is reduced to Cr(III) in one-electron steps and a colloidal film of chromic dichromate is produced. Chromous dichromate is formed in the film by the same tunneling mechanism, and the Cr(II) forms a complex with sulfate. Bright chromium deposits are obtained from this complex. 

The Gouy-Chapman theory for metal-solution interfaces predicts interfacial capacities which are too high for more concentrated electrolyte solutions. It has therefore been amended by introducing an ion-free layer, the so-called Helmholtz layer, in contract with the metal surface. Although the resulting model has been somewhat discredited [30], it has been transferred to liquid-liquid interfaces [31] by postulating a double layer of solvent molecules into which the ions cannot penetrate (see Fig. 17) this is known as the modified Verwey-Niessen model. Since the interfacial capacity of liquid-liquid interfaces is... 

By means of the thermodynamic theory of the double layer and the theory of the diffuse layer it is possible to determine the charge density ox corresponding to the adsorbed ions, i.e. ions in the inner Helmholtz plane, and the potential of the outer Helmholtz plane 2 in the presence of specific adsorption. 

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. 

As a result of these experiments Smith concludes that (a) the simple Helmholtz theory of the double layer is insufficient to account for all the observed facts. The potential difference mercury-electrolyte is not purely electrostatic, but depends on the nature of the ions, as, according to Nemst s theory, it should do. This theory, it will be remembered, involves the " solution pressure of the ions, which varies with their chemical nature. (6) The potential difference mercury-electrolyte is not necessarily zero when the interfacial tension is a maximum, although in the particular case of dilute KC1 this condition is very nearly fulfilled. 

The Helmholtz model was found not to be able to give a satisfactory analysis of measured data. Later, another theory of the diffuse double layer was proposed by Gouy and Chapman. The interfacial region for a system with charged lipid, R-Na+, with NaCl, is shown in Figure 4.10. 

It is noted that the molecular interaction parameter described by Eq. 52 of the improved model is a function of the surfactant concentration. Surprisingly, the dependence is rather significant (Eig. 9) and has been neglected in the conventional theories that use as a fitting parameter independent of the surfactant concentration. Obviously, the resultant force acting in the inner Helmholtz plane of the double layer is attractive and strongly influences the adsorption of the surfactants and binding of the counterions. Note that surface potential f s is the contribution due to the adsorption only, while the experimentally measured surface potential also includes the surface potential of the solvent (water). The effect of the electrical potential of the solvent on adsorption is included in the adsorption constants Ki and K2. 

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