Adsorbed hydrogen atoms, chemical potential

The chemistry of electrochemical reaction mechanisms is the most hampered and therefore most in need of catalytic acceleration. Therefore, we understand that electrochemical catalysis does not, in principle, differ much fundamentally and mechanistically from chemical catalysis. In addition, apart from the fact that charge-transfer rates and electrosorption equilibria do depend exponentially on electrode potential—a fact that has no comparable counterpart in chemical heterogeneous catalysis—in many cases electrocatalysis and catalysis of electrochemical and chemical oxidation or reduction processes follow very similar if not the same pathways. For instance as electrochemical hydrogen oxidation and generation is coupled to the chemical splitting of the H2 molecule or its formation from adsorbed hydrogen atoms, respectively, electrocatalysts for cathodic hydrogen evolution—... 

The method can, however, be refined since we have made some serious approximations concerning the prefactors for the adsorption process. This is also the method typically used for microkinetic modeling of catalytic reactions. Here the dissociation of hydrogen is typically in quasi-equUibrium and, therefore, we can neglect the transition state and only concentrate on the initial and final state of the adsorption process. If we have equilibrium the chemical potentials for molecular hydrogen will be equal to the chemical potential of the two resulting adsorbed hydrogen atoms... 

Eq. (9-5) describes the pure chemical dimerization of two adsorbed hydrogen atoms, the chemical recombination, which should not be directly affected by the electrode potential. 

However, this problem does not affect the thermodynamics of electrochemical reactions. The free energy of the solvated proton can be obtained from a thermodynamic argument, that of the adsorbed hydrogen atom from standard DFT, with or without a few water molecules. In this way, the free energy balance for the reaction can be calculated, and from this, the equilibrium potential can be obtained. The same principle can be employed for complicated reactions such as oxygen reduction, which contain many possible intermediate states. Chemical steps not involving charge transfer, such as the recombination reaction H2, can be treated by pure DFT, and for... 

In the previous section, we have referred to the way in which the overall rate of the reaction depends on the chemical potential of the transition state when rates for identical processes are compared under identical conditions on different substrates. It was also implied that an equilibrium could be assumed between processes taking place before the rate-determining step in simple cases. This concept will be examined in more detail in this section for the case of more complex processes in which parallel reaction pathways can and do occur. One of the most characteristic (and one of the simplest and most studied) of such processes is that of hydrogen evolution, where three possible steps involving adsorbed species are generally considered to occur. " These are known respectively as the discharge or Volmer process, the electrochemical desorption or Heyrovsky process, and the hydrogen atom combination (Tafel) reaction, as follows (written in the cathodic direction) ... 

The dipole density profile p (z) indicates ordered dipoles in the adsorbate layer. The orientation is largely due to the anisotropy of the water-metal interaction potential, which favors configurations in which the oxygen atom is closer to the surface. Most quantum chemical calculations of water near metal surfaces to date predict a significant preference of oxygen-down configurations over hydrogen-down ones at zero electric field (e.g., [48,124,141-145]). The dipole orientation in the second layer is only weakly anisotropic (see also Fig. 7). 

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