Heterogeneous activation free energy

My conclusion (based on double-layer theory) was that, under the usual experimental conditions, the image term is almost entirely screened off. When this is so, the dielectric contribution to the activation free energy is essentially the same for the homogeneous and the heterogeneous process. 

The final step of the convolution analysis is the determination of the transfer coefficient a. This coefficient, sometimes called the symmetry factor, describes how variations in the reaction free energy affect the activation free energy (equation 26). The value of a does not depend on whether the reaction is a heterogeneous or a homogeneous ET (or even a different type of reaction such as a proton transfer, where a is better known as the Bronsted coefficient). Since the ET rate constant may be described by equation (4), the experimental determination of a is carried out by derivatization of the ln/Chet-AG° and thus of the experimental Inkhei- plots (AG° = F E — E°)) (equation 27). 

For heterogeneous nucleation, activation free energy required for the formation of a stable nucleus... 

The activation free energy for heterogeneous nucleation (AGhet) is lower than that for homogeneous nucleation (AGhom) a demonstrated on the schematic free energy-versus-nucleus radius cm es of Figure 10.6. 

Activation free energy for formation of stable solid particle (heterogeneous nucleation)... 

Equation (56) states that if the liquid completely wets the solid, then (3 = 0, m = —1, and 0 = 1. In this case the heterogeneous situation becomes identical with the homogeneous one. However, if the liquid and vapor are equally attracted to the solid, 0 = 90°, m = 0, and 0 = K-In this case the free energy of activation and the work of forming a nucleus are each reduced to half. If the vapor wets the solid completely, 0 = 180°, m = +1, and 0 = 0. Then AE0 (or PFo) is reduced to zero superheating should be impossible. 

The Marcus treatment for heterogeneous electron transfer at electrodes is analogous to the homogeneous case of redox reactions in solution discussed in Vol. 2, Chap. 4. The free energy of activation can also be expressed by... 

Here asx is the activity of the bound species and ax and as are the activities of the species in the sample and of the binding site in the sensor, respectively. For the purpose of this discussion, the binding site can be thought of as a defined but separate component of the selective layer, such as in heterogeneous selective layers, or it may be a specific part of the uniform matrix, as in homogeneous selective layers. (More on the origins of selectivity are discussed later.) The free energy of interaction for reaction depicted in (1.1) is... 

Adsorption reduces the imbalance of attractive forces which exists at a surface, and, hence, the surface free energy of a heterogeneous system. In this respect, the energy considerations relating to solid surfaces are, in principle, the same as those already discussed for liquid surfaces. The main differences between solid and liquid surfaces arise from the fact that solid surfaces are heterogeneous in respect of activity, with properties dependent, to some extent, on previous environment. 

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