Gibbs energy barriers

The Gibbs energy barrier involved in an electron transfer reaction is shown in fig. 7.3. As a result of random thermal processes the reactants achieve the neces-... 

Fig. 7.15 Gibbs energy barrier for an outer sphere electron transfer process with a standard Gibbs energy change of AG°(A). Interaction of the surfaces for reactants and products leads to electronic coupling and creates an energy gap IJ at the point where they intersect (B).

Fig. 7.1 7 Plot of the Gibbs activation energy A G° against the Gibbs energy barrier AG° for an electron transfer reaction with Ex equal to lOOkJmoP. ...

The study of static medium effects is obviously important because it provides direct information regarding the factors which influence the Gibbs energy barrier for the reaction. These factors are important in deciding the mechanism of complex reactions. As a result, medium effects are often used by the synthetic chemist to determine the final product of a reaction in solution. 

In this limit, the dynamic solvent effect can also be treated as a diffusion process using the Smoluchowski equation. This emphasizes the fact that the friction leads to multiple crossings of the Gibbs energy barrier. The diffusion coefficient associated with this process is given by... 

Figure 4.11. Hypothetical reactivity-selectivity profile for the interaction of a weakly reactive digitalis compound (D,) or a strongly reactive digitalis compound (Ds) with Na lJC-ATPase isoenzymes or Eg, which differ in the chemotopography of the digitalis binding matrix. Selectivity is shown to be a reflection of the differential height of the activation Gibbs energy barrier, which is equivalent to the association rate constant. In other words, the inhibitor D, will preferentially bind to the isoenzyme Eg, whereas inhibitor D2 will equally bind to both isoenzymes. Eg and Eg (adapted from [251]).

FIGURE 10.9 Ratio of Gibbs energy barrier for heterogeneous and homogeneous nucle-ation as a function of the membrane porosity and the contact angle of lysozyme solution (protein 40 mg/ml NaCl as precipitant 2% w/v). Lines are from Equation 10.15 abbreviations as in Table 10.2. (Adapted with permission from Curcio et al., J. Phys. Chem. B, 114, 13650-13655. Copyright 2006 American Chemical Society.)... 

For the same system, as mentioned earlier, in a 10 M solution of a 1 1 electrolyte (so that K = 10" nm" ) but now with a Gibbs energy barrier of 201 Br between the particles, we find that the half time of aggregation goes up to more than three weeks. Depending on acceptable storage time or shelf life, the system may now be regarded as stable or not. 

Transport of a solute from one side (1) of the membrane to the other side (2) may be considered as the net result of adsorption and desorption at both sides of the membrane, combined with a permeation step. Permeation of ion i involves the passage of a Gibbs energy barrier that is determined by the profile of d(p, + z,F /)/dx 0. In our model, the barrier is the highest in the apolar center of the lipid bilayer, as shown in Figure 19.5. From the laws of conservation for the permeating ion i it follows that... 

The extension of the glycocalyx decreases with inCTcasing ionic strength. The existence of a membrane potential lowers the Gibbs energy barrier for ions to traverse the membrane. 

Table 1.1 Gibbs energy barriers [Pd(R)2(PMe3)(L)] complexes [61] (in kcal mol ) for the reductive elimination from cis-...

From the quantitative perspective, the results collected in Fig. 4.9 show a reasonable match between the computed and experimental values for the stabiUties of the reagents and products in equilibrium (with energy differences about 1 kcal mol ). On the other hand, the computed Gibbs energy barriers show an excellent fit with the experimental value for the transmetalation of 1 to 2 (with a difference of less than 0.5 kcal moP ), but not so good for the transmetalation to 3 (calculations underestimates the Gibbs energy barrier by 5 kcal mol ). 

The quantitative comparison of experimental and theoretical Gibbs energy barriers can be only strictly made for the concerted mechanisms, since only the lower (for 5+) and higher (for 4+) limits for the ionic mechanisms could be estimated experimentally. Thus, according to the computed barriers for the concerted mechanisms... 

Table 5.4 Global Gibbs energy barriers in DCM (AGdcm, kcal mol ) at 298 K for the cationic and anionic mechanisms with the different 4-substituted phenylacetylenes (R = H, CF3, OMe, NMei)...

The Gibbs energy barriers for the lowest-energy deprotonation pathways with the different R... 

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