Enthalpic consistency

Regarding enthalpic consistency, Grabow et al. [38] have proposed a method in which the enthalpy of adsorption is kept as predicted from DFT, and the heat of surface reaction is adjusted to make the mechanism thermodynamically consistent for each thermodynamic loop. The difference between the corrected (A// and the... 

One of the major issues in developing detailed surface reaction mechanisms is thermodynamic consistency. Even though the recently published reaction mechanisms ensure enthalpic consistency, many of them are not consistent with respect to entropy, which is due to the lack of knowledge about the transition states of the individual reaction steps. Thus, there is not sufficient information for a theory-hased determination of preexponential factors in the rate equations. However, an independent choice of the rate coefficients causes an inconsistent entropy change in the overall reaction, which leads to an incorrect prediction of equilibrium states. There are two approaches to avoid this inconsistency by adjusting the rate expressions, which are described in the Hterature (Deutschmann, 2008 Maier et al., 2011 Mhadeshwar et al., 2003). 

Basic Thermodynamics. Equilibrium-phase behavior of mixtures is governed by the free energy of mixing and how this quantity, consisting of enthalpic... 

The diffusion coefficients of this system were determined for disordered micelles and bcc spheres [47]. They were found to be retarded as compared to the disordered state. This retardation is consistent with a hindered diffusion process, D Do exp(- AxN ), with D0 being the diffusion coefficient in the absence of any interactions (i.e. for y -> 0), and A is a prefactor of order unity. Hence, the diffusion barrier increases with the enthalpic penalty xNa, where N represents the number of monomers in the foreign block. In the simplest description of hindered diffusion, the prefactor A remains constant. This model describes the experimental data poorly as A was found to increase with xNa [47]. 

If the backbone as well as the side chains consist of flexible units, the molecular conformation arises out of the competition of the entropic elasticity of the confined side chains and the backbone [ 153 -155]. In this case, coiling of the side chains can occur only at the expense of the stretching of the backbone. In addition to the excluded volume effects, short range enthalpic interactions may become important. This is particularly the case for densely substituted monoden-dron jacketed polymers, where the molecular conformation can be controlled by the optimum assembly of the dendrons [22-26,156]. If the brush contains io-nizable groups, the conformation and flexibility may be additionally affected by Coulomb forces depending on the ionic strength of the solvent [79,80]. 

In the case of nonionic compounds, the driving forces for adsorption consist of entropy changes and weak enthalpic (bonding) forces. The sorption of these compounds is characterized by an initial rapid rate followed by a much slower approach to an apparent equilibrium. The faster rate is associated with diffusion on the surface, while slower reactions have been related to particle diffusion into micropores. 

Theory. The most widely accepted mechanism of size separation is based on steric exclusion (1). In terms of thermodynamic properties, the distribution coefficient consists of enthalpic and entropic contributions ... 

Extreme cases were reactions of the least stabilized, most reactive carbene (Y = CF3, X = Br) with the more reactive alkene (CH3)2C=C(CH3)2, and the most stabilized, least reactive carbene (Y = CH3O, X = F) with the less reactive alkene (1-hexene). The rate constants, as measured by LFP, were 1.7 x 10 and 5.0 X lO M s, respectively, spanning an interval of 34,000. In agreement with Houk s ideas,the reactions were entropy dominated (A5 —22 to —29e.u.). The AG barriers were 5.0 kcal/mol for the faster reaction and 11 kcal/ mol for the slower reaction, mainly because of entropic contributions the AH components were only —1.6 and +2.5 kcal/mol, respectively. Despite the dominance of entropy in these reactive carbene addition reactions, a kind of de facto enthalpic control operates. The entropies of activation are all very similar, so that in any comparison of the reactivities of alkene pairs (i.e., ferei)> the rate constant ratios reflect differences in AA//t, which ultimately appear in AAG. Thus, car-benic philicity, which is the pattern created by carbenic reactivity, behaves in accord with our qualitative ideas about structure-reactivity relations, as modulated by substiment effects in both the carbene and alkene partners of the addition reactions. " Finally, volumes of activation were measured for the additions of CgHsCCl to (CH3)2C=C(CH3)2 and frani-pentene in both methylcyclohexane and acetonitrile. The measured absolute rate constants increased with increasing pressure Ayf ranged from —10 to —18 cm /mol and were independent of solvent. These results were consistent with an early, and not very polar transition state for the addition reaction. 

The Flory parameter is in essence analogous to the activity coefficient of the HOC in the DOM phase and consists of two components %u and 5Cs> which are the enthalpic and entropic contributions, respectively ... 

Since Ki is expressed as a ratio, any consistent measure of composition in the membrane and external phases may be used in Equation 7.2. When K> 1, the membrane acts as a concentrator that attracts component i from the external phase and makes it available at the membrane surface for transmembrane movement. Intermolecular forces of solvation and mixing that are responsible for the partitioning process may be entropic as well as enthalpic in origin. The balance of these forces acting between the membrane and external phase can cause either a higher or lower concentration of a given solute inside the membrane relative to the external phase. If the tendency to enter the membrane is negligible, the partition coefficient approaches zero, that is, Kj —> 0. 

An alternative procedure to gain deeper insight into the physico-chemical basis of solvation consists of the partitioning of AGsoi into its enthalpic, A//soi, and en-tropic, A.S(o, components. Taken together, these quantities represent a substantial reservoir of information about the interactions between solute and solvent molecules. Moreover, these quantities are state functions and can be rigorously derived by using standard thermodynamic relationships, as noted in Eqs. 4-2 and 4-3. Finally, the availability of experimentally measured data for the enthalpy and entropy of solvation makes it possible to calibrate the reliability of theoretical models to predict those thermodynamic quantities. 

Values for the enthalpy and entropy of activation for the reaction catalyzed by 1F7 were determined from the temperature dependence of kcat. Apparently, the observed rate acceleration is due entirely to a lowering of the enthalpic barrier (15 kcal/mol versus 21 kcal/mol for the uncatalyzed reaction (24)), consistent with the notion that induced strain might be an important component of catalysis. The entropy of activation for the antibody-promoted reaction (-22 eu) is actually less favorable than for the spontaneous reaction (-13 eu) (23). This fact may reflect the need for some conformational change in the antibody binding pocket during catalysis. However, possible solvent effects make the interpretation of AS difficult. 

The ability of copolymers consisting of chemically distinct polymeric segments to undergo microphase separation as a result of enthalpically driven segregation has led... 

In the initial theory, x was taken to be a function only of the nature of the components in a binary mixture. It became apparent, however, that it depends on concentration and to some extent on molecular weight. It is now considered to be a free energy of interaction and thus consists of enthalpic and entropic components with the latter accounting for its temperature dependence. 

According to the Gibbs-Helmholtz equation, the free energy of binding consists of an enthalpic and an entropic contribution ... 

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