Free energy balance

The main features of the chemiluminescence mechanism are exemplarily illustrated in Scheme 11 for the reaction of bis(2,4,6-trichlorophenyl)oxalate (TCPO) with hydrogen peroxide in the presence of imidazole (IMI-H) as base catalyst and the chemiluminescent activators (ACT) anthracene, 9,10-diphenylanthracene, 2,5-diphenyloxazole, perylene and rubrene. In this mechanism, the replacement of the phenolic substituents in TCPO by IMI-H constitutes the slow step, whereas the nucleophilic attack of hydrogen peroxide on the intermediary l,l -oxalyl diimidazole (ODI) is fast. This rate difference is manifested by a two-exponential behavior of the chemiluminescence kinetics. The observed dependence of the chemiexcitation yield on the electrochemical characteristics of the activator has been rationalized in terms of the intermolecular CIEEL mechanism (Scheme 12), in which the free-energy balance for the electron back-transfer (BET) determines whether the singlet-excited activator, the species responsible for the light emission, is formed ... 

Basic equations for calculation of free energy-distance curves Vincent et al (8) showed that the net free energy balance... 

Furthermore, the redox chemistry of doped ceria is dependent on the ionic radius of the doped cation. The energy due to lattice stresses resulting from mismatch of the host and dopant cation sizes will also go into the free energy balance as briefly described below. 

Olson, M.A. (2001) Electrostatic effects on the free-energy balance in folding a ribosome-inactivating protein. Biophys Chem, 91, 219-229. 

This equation is a free energy balance for the ion-exchange reaction ... 

For a liquid that rests on a smooth surface with a finite contact angle, one can determine the relationship between the interfacial tensions at the different interfaces from consideration of the balance of surface forces at the line of contact of the three phases (solid, liquid, and gas). Remembering that the interfacial tension always exerts a pressure tangentially along the surface, the surface free-energy balance (a... 

Whatever the detailed free energy balance involved in transferring a solute from outside to a micellar solution, four microenvironments have to be considered, i.e. bulk solvent, polar region, palisade layer and core of the micelles. The two intermediate regions shown... 

As it has been outlined in chapter 2 the widely accepted meaning of photocatalysis is that both light and a catalyst are necessary to bring about an appropriate reaction. The term catalyst is used somewhat different than in the classical thermal catalysis. First of all, here the term catalyst includes both catalytically active species able to effect repeatedly the conversion of a substrate S to a product P and nominal catalysts or initiators to be activated by light. Secondly, despite the classical meaning, a catalyst may well influence the free energy balance of the parent thermal reaction from S to P due to the participation of electronically excited species in photocatalytic reactions.The different features of photocatalysis when compared with thermal catalysis arise from the constituent "photo", indicating that a photon has to be absorbed by either the substrate or the catalyst prior to or within... 

Each of the elementary reactions has a corresponding standard equilibrium potential, the value of which could be obtained from first-principles calculations. The free energy balance at equilibrium, written for each elementary reaction step, leads to a simple relation between these standard equilibrium potentials. For the four electron sequence that follows the first pathway, involving Equation 3.43, this relation is... 

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... 

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