Gibbs energy electrical contribution

Here a° and yr° are the surface charge (density) and surface potential, respectively. The primes Indicate the variable values when the double layer is reversibly charged from cr° =0 to its final value, cr°. As y/° and a° have the same signs, AG°(el) > 0, so a non-electric contribution is needed to make the overall Gibbs energy change negative, as required for a spontaneous process. For relaxed... 

The standard molar Gibbs energy of adsorption now contains electric and non-electric contributions. Formally, we can write... 

The chemical term contains the intrinsic contribution of the dissociation and the electrical term, the additional Gibbs energy to remove the proton from the charged site to infinity (where the electric field is zero). In the simple case that all titratable groups belong to one class... 

FIGURE 20.7 Gibbs energy of adhesion of a particle at a brush-coated, charged substratum surface as a function of separation distance (—), made up of four types of contributions (1) short-range particle-substratum attraction (2) dispersive attraction (3) electrostatic repulsion due to overlap of Uke-charged electrical double layers and (4) osmotic repulsion due to compression of the polymer brush. 

The term in parenthesis in the left-hand side of Equation 11.14 is the Gibbs free energy change of reaction 11.8. The next term is the electrical contribution to the electrochemical Gibbs free energy change of reaction 11.8 ... 

Although one automatically couples double layers to electrostatics, it is obvious that their formation cannot be of a purely coulombic nature. Accumulation of many charges of the same sign on a solid surface is electrostatically unfavorable. In thermodynamic terms, the electrical part of the Gibbs energy of formation, AG(el) > 0. Hence, a non-coulombic contribution, AG (non-coul) < 0, must also be present and exceed the electrical contribution. This basic statement requires at least two specifications. 

Here, is the quantity (mass) of component i in phase a with Gibbs free energy G . Electrochemical potentials are separated in a chemical and electrical contribution... 

All these experimental results have been recently complemented by a very useful theoretical study by Kharkats and Ulstrup," who calculated analytically the electrostatic Gibbs energy profile of an ion between two dielectric phases separated by a planar boundary, incorporating both the ionic finite size and the dielectric image interactions. The profile obtained, illustrated in Fig. 4, shows that there is no discontinuity as the ion traverses the boundary and that cation and anion concentration distribution will differ if they have different ionic radii, as they will penetrate the boundary to a different extent. This has important repercussions on the Poisson-Boltzman equation as the work term is not only the electrical energy, —but also an electrostatic contribution to the Gibbs energy of solvation as the ion... 

Of practical importance are electrochemical systems with electrodes. Electrical and gravitational systems may be of a pseudo first order with respect to charge and mass additions, when only the contribution of the external field to the energy is considered. However, this does not mean that these electrical and gravitational contributions should be included into the Gibbs -Duhem equation [16]. Of course, it is a matter of definition of the thermodynamic variables, whether the thermodynamic similarity exists or not. 

AG° is the electrochemical standard Gibbs free energy change (or electrochemical free energy for short), AG is the chemical contribution, and AG°a is the electrical... 

---