Modify free energy surface

As we mentioned earlier, in our model the electrode potential modifies the electronic energy of the reactant. This makes it possible to calculate free energy surface for various overpotentials. Figure 3.13b shows the surface for a cathodic overpotential of 200 mV. The activation energy is reduced by about 0.1 eV, indicating an transfer coefficient of a = 0.5. For other systems, we typically found transfer coefficients of the order of 0.4-0.6 for the Volmer reaction, which is in line with typical experimental values. 

Surface free energy (surface tension) of the fillers determines both matrix/filler and particle/particle interaction. The former has a pronounced effect on the mechanical properties, the latter determines aggregation. Both interactions can be modified by surface treatment. 

The shift of the free energy due to interactions with the solid is given by the liquid-solid interaction term (30) minus the lost part of the fluid-fluid interaction term in Eq. (9). We will compute it here for a liquid layer with a sharp interface at 2 = /i parallel to the solid surface at 2 = /i (the diffuse interface theory is discussed in Section 5.2). Setting p = p/ = const at 0 < 2 < /i and neglecting the gas density, the modified free energy integral (9) can be computed by integrating the van der Waals interactions laterally as in Eq. (11). The correction due to the interaction with the solid is computed as... 

For a wide variety of systems, it was found that a value of y = 0.75 A gave satisfactory results for the transition state rates When V(R)=Vq(R) - kT Q(R) is used to evaluate the harrier frequency in (15), the free energy surface gives predictions of the reaction dynamics in the hath density regime in which diffusion control may he important. Of course, solvent packing and stabilization effects may modify V(R). 

Figure 5.7 shows the modified surface free energies y calculated for unreconstructed and reconstmcted Au(lOO) using DFT. The details can be found in [Jacob, 2007a]. The plot shows that the hexagonal reconstructed surface is more stable over... 

Poisoning is caused by chemisorption of compounds in the process stream these compounds block or modify active sites on the catalyst. The poison may cause changes in the surface morphology of the catalyst, either by surface reconstruction or surface relaxation, or may modify the bond between the metal catalyst and the support. The toxicity of a poison (P) depends upon the enthalpy of adsorption for the poison, and the free energy for the adsorption process, which controls the equilibrium constant for chemisorption of the poison (KP). The fraction of sites blocked by a reversibly adsorbed poison (0P) can be calculated using a Langmuir isotherm (equation 8.4-23a) ... 

For now we consider the interaction of two identical blocks of material separated by their own equilibrium vapor. From the point of view of modifying the force of attraction, the vapor is assumed to have a negligible effect, behaving essentially like a vacuum. The facing planes become equilibrium surfaces characterized by an interfacial free energy 7. 

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