Effect entropic

Third key point NHPI guarantees high selectivity to the catalyzed oxidation process under homogeneous conditions. 

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Monte Carlo simulations are an efficient way of predicting liquid structure, including the preferred orientation of liquid molecules near a surface. This is an efficient method because it is not necessary to compute energy derivatives, thus reducing the time required for each iteration. The statistical nature of these simulations ensures that both enthalpic and entropic effects are included. 

It is evident that many solutions fall between these limiting categories, with both energetic and entropic effects contributing to solution non-ideality. For example, if the energy of interaction between unlike species in a solution is highly favored over like-like interactions, it is obvious that these interactions will be preferred, a fact which in itself will lead to non-randomness of the packing in the solution. 

Weakly absorbed does not mean that the adsorption energy e is small in comparison to k T, since entropic effects are important rather, it means e - ej ed, ed being the absorption energy at the threshold [2]. 

Thus the apparent rate constant (kcat/KM) is determined by the apparent activation barrier Ag. In fact, both Ag and Agjfat should have been written as AG and AGaat, respectively [see eq. (2.11)], but as long as we do not have large entropic effects (see Chapter 9), the approximation given above is reasonable. 

Fig. 5.3. Now the reaction rate is determined by AGcage and Ag age, but AGcage is almost entirely determined by simple concentration factors. Thus a comparison of Ag age and Agfat allows one to explore fundamental catalytic aspects, including real entropic effects, without preoccupation with the rather trivial effective concentration effect, associated with bringing the reactants to the same cage.

FIGURE 9.5. The potential surface for the 0"C = 0— 0-C-0" step in amide hydrolysis in solution, where the surface is given in terms of the angle 0 and the distance b. The heavy contour lines are spaced by fi (at room temperature) and can be used conveniently in estimating entropic effects. The figure also shows the regions (cross hatched) where the potential is less than for the corresponding reaction in the active site of subtilisin. 

The entropic hypothesis seems at first sight to gain strong support from experiments with model compounds of the type listed in Table 9.1. These compounds show a huge rate acceleration when the number of degrees of freedom (i.e., rotation around different bonds) is restricted. Such model compounds have been used repeatedly in attempts to estimate entropic effects in enzyme catalysis. Unfortunately, the information from the available model compounds is not directly transferable to the relevant enzymatic reaction since the observed changes in rate constant reflect interrelated factors (e.g., strain and entropy), which cannot be separated in a unique way by simple experiments. Apparently, model compounds do provide very useful means for verification and calibration of reaction-potential surfaces... 

RHCOOR— R COOCOR" + OR) of Related Model Compounds, Which Can Be Used in Estimating the Importance of Entropic Effects in Solution Reactions (see Ref. 2)... 

In Eq. (6) Ecav represents the energy necessary to create a cavity in the solvent continuum. Eel and Eydw depict the electrostatic and van-der-Waals interactions between solute and the solvent after the solute is brought into the cavity, respectively. The van-der-Waals interactions divide themselves into dispersion and repulsion interactions (Ed sp, Erep). Specific interactions between solute and solvent such as H-bridges and association can only be considered by additional assumptions because the solvent is characterized as a structureless and polarizable medium by macroscopic constants such as dielectric constant, surface tension and volume extension coefficient. The use of macroscopic physical constants in microscopic processes in progress is an approximation. Additional approximations are inherent to the continuum models since the choice of shape and size of the cavity is arbitrary. Entropic effects are considered neither in the continuum models nor in the supermolecule approximation. Despite these numerous approximations, continuum models were developed which produce suitabel estimations of solvation energies and effects (see Refs. 10-30 in 68)). 

Identifying the transition state and the associated energy barrier is essential for understanding the course of a reaction. Of course, details of the shape of the potential material, e.g. steric hindrance and entropic effects, may impede the system from crossing the barrier. The barrier energy (which is not very different from the activa-... 

The elasticity can be related to very different contributions to the energy of the interface. It includes classical and nonclassical (exchange, correlation) electrostatic interactions in ion-electron systems, entropic effects, Lennard-Jones and van der Waals-type interactions between solvent molecules and electrode, etc. Therefore, use of the macroscopic term should not hide its relation to microscopic reality. On the other hand, microscopic behavior could be much richer than the predictions of such simplified electroelastic models. Some of these differences will be discussed below. 

The main problem is to find the free energy of the real interface with nonlocal energetic and entropic effects. For a general multicomponent interface the minimization of the nonlocal HS-B2-functional is a nontrivial numerical problem. Fortunately, the variational nature of the problem lends itself to a stepwise solution where simple para-metrization of the density profiles through the interface upon integration of the functional yields the free energy as a function of the parameters. In fact, if we take the profile to be a step function as in the case of local free energy then with local entropy we get the result... 

Naturally selectivity in a several-component system is primarily influenced by rather strong effects such as the presence or absence of strong H-bonding, but possibly also by much weaker interactions (e.g. of C—H... O type). In this regard, it is interesting to note the similarity between the selectivity exerted by such simple inclusion hosts, e.g. /, and chiral recognition 103). In both cases, weak interactions are of decisive importance in the final outcome of the experiments. Entropic effects have been demonstrated to play a fundamental role in enzymatic reactions 102,107 >. Conceptual similarity of inclusion compounds to more complicated associates is underlined thereby. 

Prausnitz and coworkers [91,92] developed a model which accounts for nonideal entropic effects by deriving a partition function based on a lattice model with three categories of interaction sites hydrogen bond donors, hydrogen bond acceptors, and dispersion force contact sites. A different approach was taken by Marchetti et al. [93,94] and others [95-98], who developed a mean field theory... 

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