Thermodynamic parameters entropy

Thermodynamic parameters have been obtained from kinetic HNMR spectroscopic studies of the thermal decomposition of ethyl 2,7-di-to7-butyl-5-methylthiepin-4-carboxylaten and two 1-benzothiepin compounds.12 The activation parameters for sulfur extrusion are AH = 93.7 kJ mol - 1 and AS = — 112.6 J Kmol-1 (in [2H18]Decalin) for the thiepin derivative,11 and AH = 75.3 and 87.9 kJ mol1 and AS = —100.4 and —104.6J Kmol-1 (in [2Hs]toluene) for the benzothiepin compounds.12 The large negative activation entropy values are consistent with a high degree of order in the anticipated thianorcaradiene transition state of the sulfur extrusion reaction. 

Fig. 37. Dependence of the thermodynamic parameters AH and AS of triple-helix formation on the imino acid content of the peptides (obtained by cleavage of calf skin-type I collagene with cyanogene and subequent isolation by column chromatrography)3) and of the native neutral salt-soluble skin collagene of various animals. The entropy values are denoted by dotted lines...

In contrast to the situation observed in the trivalent lanthanide and actinide sulfates, the enthalpies and entropies of complexation for the 1 1 complexes are not constant across this series of tetravalent actinide sulfates. In order to compare these results, the thermodynamic parameters for the reaction between the tetravalent actinide ions and HSOIJ were corrected for the ionization of HSOi as was done above in the discussion of the trivalent complexes. The corrected results are tabulated in Table V. The enthalpies are found to vary from +9.8 to+41.7 kj/m and the entropies from +101 to +213 J/m°K. Both the enthalpy and entropy increase from ll1 "1" to Pu1 with the ThSOfj parameters being similar to those of NpS0 +. Complex stability is derived from a very favorable entropy contribution implying (not surprisingly) that these complexes are inner sphere in nature. 

The nonnuclear chemistry of Fr reduces to studies of coprecipitation in which Fr shows the behavior of the heavier alkali metal. Coprecipitation is followed by ion exchange to concentrate Fr Physical (mp, density, crystal parameters) and chemical (thermodynamics, solvation entropies) properties are theoretically derived or extrapolated from the trends exhibited by the other alkali metals. 

The use of direct electrochemical methods (cyclic voltammetry Pig. 17) has enabled us to measure the thermodynamic parameters of isolated water-soluble fragments of the Rieske proteins of various bci complexes (Table XII)). (55, 92). The values determined for the standard reaction entropy, AS°, for both the mitochondrial and the bacterial Rieske fragments are similar to values obtained for water-soluble cytochromes they are more negative than values measured for other electron transfer proteins (93). Large negative values of AS° have been correlated with a less exposed metal site (93). However, this is opposite to what is observed in Rieske proteins, since the cluster appears to be less exposed in Rieske-type ferredoxins that show less negative values of AS° (see Section V,B). 

A certain ambiguity arises in the proper choice of the thermodynamic parameter p, since entropy changes due to solvent orientation are neglected. The available experimental data (cf. Sect. 4) indicate, however, that the free energy of reaction for systems showing a spin change is close to zero. The numerical analysis has been therefore performed for the specific case p = 0, for which value the rate constant in Fig. 15 has been computed as a function of S and h lkgT. 

Stepwise formation constants have been determined in the system Hg2+/Cl-/diethylenetriamine (dien) and related systems by potentiometry. Thermodynamic parameters have been calculated and the contribution of the entropy term to complex stability discussed.208... 

Regardless of the relative importance of polar and nonpolar interactions in stabilizing the cyclohexaamylose-DFP inclusion complex, the results derived for this system cannot, with any confidence, be extrapolated to the chiral analogs. DFP is peculiar in the sense that the dissociation constant of the cyclohexaamylose-DFP complex exceeds the dissociation constants of related cyclohexaamylose-substrate inclusion complexes by an order of magnitude. This is probably a direct result of the unfavorable entropy change associated with the formation of the DFP complex. Thus, worthwhile speculation about the attractive forces that lead to enantiomeric specificity must await the measurement of thermodynamic parameters for the chiral substrates. 

For several reversible reactions, the thermodynamic parameters for reaction in the quasi-free state are given in Table 10.6 using Eq. (10.16) and the reaction scheme (I). Experimental data for AX°(X = G, H, or S) are taken from Holroyd et al., (1975, 1979) and Holroyd (1977), while Table 10.5A provides data on AX r°, except for TMS (vide supra). The chief uncertainty in these calculations is the experimental determination of V0. It is remarkable that all thermodynamic parameters of reaction in the quasi-free state are negative in the same way as for the overall reaction. In particular, the entropy change is relatively large and probably for the same reason as for the overall reaction (Holroyd, 1977). 

Papisov et al. (1974) performed calorimetric and potentiometric experiments to determine the thermodynamic parameters of the complex formation of PMAA and PAA with PEG. They investigated how temperature and the nature of the solvent affected the complex stability. They found that in aqueous media the enthalpy and entropy associated with the formation of the PMAA/PEG complex are positive while in an aqueous mixture of methanol both of the thermodynamic quantities become negative. The exact values are shown in Table II. The viscosities of aqueous solutions containing complexes of PMAA and PEG increase with decreasing temperature as a result of a breakdown of the complexes. 

Table 6.1 summarizes the thermodynamic parameters relating to the macrocyclic effect for the high-spin Ni(n) complexes of four tetraaza-macrocyclic ligands and their open-chain analogues (the open-chain derivative which yields the most stable nickel complex was used in each case) (Micheloni, Paoletti Sabatini, 1983). Clearly, the enthalpy and entropy terms make substantially different contributions to complex stability along the series. Thus, the small macrocyclic effect which occurs for the first complex results from a favourable entropy term which overrides an unfavourable enthalpy term. Similar trends are apparent for the next two systems but, for these, entropy terms are larger and a more pronounced macrocyclic effect is evident. For the fourth (cyclam) system, the considerable macrocyclic effect is a reflection of both a favourable entropy term and a favourable enthalpy term. 

The interaction between 4-(4-hydroxybut-2-ynyloxy)-3-(phenylsulfonyl)-l,2,5-oxadiazole-2-oxide 16 and bovine serum albumin (BSA) was studied by spectroscopic methods including fluorescence and UV-Vis absorption spectroscopy. The results indicate that molecules 16 bind with BSA forming 1 1 complex. Thermodynamic parameters, such as AH, AG, and A.Y, were calculated. The results indicate that the binding reaction is mainly entropy driven and hydrophobic forces play a major role in this reaction <2006CHJ1050>. 

Table 5 lists equilibrium data for a new hypothetical gas-phase cyclisation series, for which the required thermodynamic quantities are available from either direct calorimetric measurements or statistical mechanical calculations. Compounds whose tabulated data were obtained by means of methods involving group contributions were not considered. Calculations were carried out by using S%g8 values based on a 1 M standard state. These were obtained by subtracting 6.35 e.u. from tabulated S g-values, which are based on a 1 Atm standard state. Equilibrium constants and thermodynamic parameters for these hypothetical reactions are not meaningful as such. More significant are the EM-values, and the corresponding contributions from the enthalpy and entropy terms. 

It has been suggested that an increase in the coordination number of vanadium from 4 to 5 already takes place in the second protonation step, i.e. when [H2V04] is formed (21). For reactions (1) and (2), however, the protonation constants and thermodynamic parameters are comparable with those reported for P04 and As04 , providing firm evidence that reaction (2) is not accompanied by incorporation of water in the vanadate ion (15, 17). Further, the estimated thermodynamic quantities for reaction (6), AH° = -39 kJ/mol and AS0 = —51 J/(mol K), obtained by extrapolation from the experimental values for reactions (1) and (2) and those for the three protonation steps of P04 and As04 , are not typical of a simple protonation reaction (17). For such a reaction the entropy change is normally a positive quantity often amounting to 100 50 J/(mol K) and the enthalpy... 

Exchange of unimers between two different types of block copolymer micelles has often been referred to as hybridization. This situation is more complex than for the case described above because thermodynamic parameters now come into play in addition to the kinetic ones. A typical example of such hybridization is related to the mixing of micelles formed by two different copolymers of the same chemical nature but with different composition and/or length for the constituent blocks. Tuzar et al. [41] studied the mixing of PS-PMAA micelles with different sizes in water-dioxane mixtures by sedimentation velocity measurements. These authors concluded that the different chains were mixing with time, the driving force being to reach the maximum entropy. 

As seen in Table 2, A//yS = 9.42 kcal mol-1 and AAxS = 13.9 e.u., and so the free energy of transition state stabilization (approximately 5 kcal mol-1) results from a favourable enthalpy change, partly offset by an unfavourable entropy change. A similar situation pertains to binding of the substrate also (Table 2). Thus, the similarity between transition state binding and substrate binding, pointed out above from the correlation of p/fTS with pKs, is evident in thermodynamic parameters as well. 

The thermodynamic theories [7,8] deny the pure kinetic nature of the glass transition and link it directly to thermodynamic quantities like the configurational entropy of the material. Some recent results suggest a correlation between kinetic quantities and thermodynamic parameters [9]. Also recently, this theory was successfully merged with a potential landscape approach [10]. The thermodynamic approach is interesting since it reflects the different configurations that are allowed not only for the whole ensemble but also for the internal conformations... 

Hilvert s group used the same hapten [26] with a different spacer to generate an antibody catalyst which has very different thermodynamic parameters. It has a high entropy of activation but an enthalpy lower than that of the wild-type enzyme (Table 1, Antibody 1F7, Appendix entry 13.2a) (Hilvert et al., 1988 Hilvert and Nared, 1988). Wilson has determined an X-ray crystal structure for the Fab fragment of this antibody in a binary complex with its TSA (Haynes et al., 1994) which shows that amino acid residues in the active site of the antibody catalyst faithfully complement the components of the conformationally ordered transition state analogue (Fig. 11) while a trapped water molecule is probably responsible for the adverse entropy of activation. Thus it appears that antibodies have emulated enzymes in finding contrasting solutions to the same catalytic problem. 

On the contrary, a more advanced methodology makes use of nonlinear chromatography experiments If the adsorption isotherms are measured under variable temperatures, the corresponding thermodynamic parameters for each site can be obtained in view of the van t Hoff dependency (site-selective thermodynamics measurements) [51,54]. Thus, the adsorption equilibrium constants of the distinct sites bi a = ns, s) are related to the enthalpy (A// ) and entropy (A5j) according to the following equation [54] ... 

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