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36 CHAPTER2. COMPUTATIONALMETHODS 4. 5. 6. where ∆Ew,water is the electronic adsorption energy, including water in the cell, ∆ZPE is the change in zero point energy from the reactant to the in- termediate state and T∆S is the change in entropy from the reactant to the intermediate state. The expression should also include an enthalpic temper- ature correction, but this contribution is small enough to disregard in many cases2. The electronic adsorption energy of e.g. Cl* can be obtained from an ab initio calculation: 1 ∆Ew,water =E(Cl∗)−E(∗)−E 2Cl2 . (2.46) The effect of an applied potential U is introduced by shifting the free energy of each reaction step that involves transfer of an electron by −ne− eU (see Figure 2.1). The effect of an external electric field on the energy of adsorbates on the electrode surface is usually neglected as the effect is small[108], but can in principle be included as a potential gradient extending from the surface. The free energy of H+ can be calculated at pH different from 0 using the change in free energy as a function of pH G(pH) = −kBT lnH+ (2.47) This leads to a model where free energies for electrochemical reactions can be obtained without having to explicitly model neither the polarization of the elec- trodes nor the charge transfer process. However, the method is limited to mod- eling elementary electrochemical reaction steps that are directly associated with a thermodynamic reversible potential. Still, by coupling e.g. chemical surface reactions and electrochemical adsorption and desorption reactions, multistep pro- cesses can be studied. The advantage of not having to explicitly model polarization or charge transfer does mean that activation energies, which can be used to obtain rate constants by use of Transition-state theory (TST)[109], cannot be calculated for the electrochemical steps. However, Sabatier analysis, which will be intro- duced in the next Section, is still possible based on energetics obtained from the CHE model[188]. This means that predictions regarding which catalysts should be ideal for a certain reaction can still be made, but possible differences in activation energies (and thus kinetics) are not captured fully between different electrocata- lysts. 2As an example, Peterson et al. [187] found that the enthalpic temperature correction, ˆˆ ∆Hcorr = (CpdT)intermediate− (CpdT)reactant, (2.45) for adsorption of O on Cu (at 18.5 ◦C) was 0.015 eV, to be compared with e.g. the entropic correction of 0.192 eV.PDF Image | Studies of Electrode Processes in Industrial Electrosynthesis
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