Entropy control

Two extreme situations should be noted. If p =0, then 8AG = — 78A5, and the reaction series is entirely entropy controlled it is said to be isoenthalpic. If I/p = 0, then 8AG = 8A//, and the series is enthalpy controlled, or isoentropic. All of these relationships apply also to equilibria, but we will be concerned with kinetic quantities. 

A comparison of the effects of increasing selectivity of sorption of organic counterions and the entropy control of the replacement of small ions by large organic ions in CP is a rational explanation of these phenomena. 

One may conclude that the rate-determining step of the renaturation is at least partly influenced by the cis-trans isomerization of the peptide bond the secondary nitrogen atom of which arises from proline. Otherwise, only the entropy-controlled slow nuclea-tion should be observed kinetically. The covalent bridging through Lys-Lys, therefore, gives rise not only to thermodynamic stabilization of the triple helix but also to kinetic properties which have hitherto been observed in the case of type III procollagen146) and its aminoterminal fragment Col 1-3144). 

The restricted access principle is based on the concept of diffusion-based exclusion of matrix components and allows peptides, which are able to access the internal surface of the particle, to interact with a functionalized surface (Figure 9.2). The diffusion barrier can be accomplished in two ways (i) the porous adsorbent particles have a topochemically different surface functionalization between the outer particle surface and the internal surface. The diffusion barrier is then determined by an entropy controlled size exclusion mechanism of the particle depending on the pore size of adsorbent (Pinkerton, 1991) and (ii) the diffusion barrier is accomplished by a dense hydrophilic polymer layer with a given network size over the essentially functionalized surface. In other words, the diffusion barrier is moved as a layer to the interfacial... 

Not only the formation of these insertion by-products but also the ring-formation described in Section Hf (see also Table 6) proved that the activation of the a C-H bond by a vicinal negative charge for the carbene insertion is more effective than the non-ionic as well as entropy-controlled formation of five-membered rings. 

The 5,6-dihydropyrimidine-6-yl radicals discussed above behave, in their reactions with nitrobenzenes, like the simpler radicals CH2OH and CH(al-kyl)Oalkyl do, i.e. they react exclusively by addition to give nitroxyl radicals and uncatalyzed heterolysis is not observed (khs < 10 s ). If, however, a methyl group is introduced at C(6) (= CJ of the pyrimidine-6-yl radical, the corresponding nitroxyl radicals heterolyze with rate constants at 20 °C of 10 to 5 X 10 s depending on the structure of the pyrimidine and of the nitrobenzene (Eq. 16). This SnI type reaction is characterized by activation enthalpies of 30-40 kJ mol and activation entropies of — 89 to — 7 Jmol K (entropy control) [27]. The rate-enhancing effect of the methyl group is, of course, due to... 

The activation parameters for the (bimolecular) addition and the (unim-olecular) heterolysis steps have been determined [28] for the case of Ri, R2, R3 = H or CH3 and the results are shown in Fig. 1. It is obvious that the heterolysis reaction is entropy controlled which is the consequence of the highly ionic transition state which leads to freezing of water molecules with the concomitant loss of entropy. 

FIGURE 16.4 Three stages of the engagement of a macromolecule with apore. Schematic representation of the entropy controlled exclusion process. 

Peak inversions may arise at different temperatures as the result of enthalpy versus entropy control of chiral recognition. Thus, changes in the elution order of enantiomers below or above the isoenantioselective temperature Tis0 have indeed been observed199-201, for example, with (l-methylethyl)oxirane (Figure 23). 

K. N. Houk, N. G. Randan, and J. Mareda, Theoretical Studies of Halocarbene Cycloaddition Selectivities. A New Interpretation of Negative Activation Energies and Entropy Control of Selectivity, Tetrahedron, 1985, 41, 1555. 

It has been shown recently (1) that the transfer of urea from water to water-rich water-tetrahydrofuran (THF) mixtures is an entropy-controlled phenomenon (T AS°t > AH°t ), but from water to water-THF mixtures of mole fraction Z2 > 0.20 it is an enthalpy-controlled phenomenon ( AH°t > T AS°t ) moreover, the transfer is energetically favorable in the former case and unfavorable in the latter. A minimum in the standard free energy transfer... 

The process of complexation is believed to occur through the stepwise incorporation of the ligand, i.e. stepwise replacement of the existing solvation, or hydration, sheath. The process is likely to be entropy controlled and entropy increases have been noted in thermodynamic studies on these systems.33... 

Negative activation energies for cycloaddition reactions of some carbenes are reported60 and they confirm the presence of a pre-association equilibrium on the reaction pathway. In addition, the entropy control of the cycloaddition of halocarbenes to the C=C double bond was extensively reported61 and explained by the presence of a weakly bound intermediate complex (25), which is reversibly formed and is probably a CT complex62. Its presence is also supported by direct kinetic data59,63. 

Petkov and Stoineva (12) have more recently reported that the relative rate of the o-chymotrypsin-catalyzed hydrolysis of p-alkoxycarbonyl anilide derivatives 35 of N-acetyl-(.-phenylalanine is enhanced with an increase in the size of the R alkyl group of the leaving group. This rate enhancement specificity appears to be entropy controlled the bulky alkyl groups increase both enthalpy and entropy of activation. These kinetic and thermodynamic data were interpreted in the following way the bulky -alkoxycarbonyl... 

Temperature is also an important parameter for controlling the resolution of enantiomers in HPLC. The enthalpy and entropy control of chiral resolution on antibiotic CSPs is similar to the case of polysaccharide-based CSPs (Chapter 2). Armstrong et al. [1] have studied the effect of temperature on the resolution behavior of proglumide, 5-methyl-5-phenylhydantoin and A-carbamyl-D-pheny-lalanine on the vancomycin column. The experiments were carried out from 0°C to 45°C. These results are given in Table 6 for three chiral compounds. It has been observed that the values of k, a, and Rs for the three studied molecules have decreased with the increase in temperature, indicating the enhancement of chiral resolution at low temperature. In another work, the same workers [22] have also studied the effect of temperature on the resolution of certain amino acid derivatives on the teicoplanin chiral stationary phase. They further observed poor resolution at ambient temperature, whereas the resolution increased at low... 

If TA S > AH, the spontaneous process is said to be entropy-controlled. The free energy of an ideal solution of species x is given by... 

Jagannadham V, Steenken S (1988a) Reactivity of cx-heteroatom-substituted alkyl radicals with nitrobenzenes in aqueous solution an entropy-controlled electron-transfer/addition mechanism. J Am Chem Soc 110 2188-2192... 

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