Enthalpy-entropy compensation temperature

Enthalpy-entropy compensation has been investigated in reversed-phase HPLC with octylsilica stationary phase [77]. The compensation temperatures were determined for this system, and the results show that their change with the composition of the mobile phase is almost similar to that with octadecylsilica stationary phase. It can be concluded that the retention mechanisms of the separation of alkyl benzenes is the same in both systems with the mobile phase exceeding 20% water content. 

Enthalpy-entropy compensation, is expected to occur only if unity of mechanism exists. From the slope of the enthalpy vs entre y plot the so-called compensation temperature, which is chm teristic for the type of transformation under investigation, can be calculated. 

This temperature effect is the usual one for a regular or enthalpy-entropy compensated chromatographic separation, suggesting that the retention of each... 

It would be somewhat surprising that the enthalpy-entropy compensation, though never derived from the fundamental thermodynamic relationships, is found so abundantly in various reactions and equilibria and that the reaction rate and equilibrium are independent of any perturbing factors at the specific temperature. However, it seems natural at the same time that chemical events are not controlled exclusively by a single factor but are rather governed by multiple factors correlating each other. 

Fig. 1. Enthalpy-entropy compensation for nonenzymatic prolyl isomerization (see Table I for literature references). 9, Proline-containing oligopeptides A, dipeptide , Gly-Gly-Lys-Phe-Pro. 1, Suc-Ala-Leu-Pro-Phe-pNA 2, Suc-Ala-Ala-Pro-Phe-pNA 3, Gly-Gly-Pro-Ala 4,N,N-dimethylacetamide 5,Suc-Ala-Trp-Pro-Phe-pNA 6, Suc-Ala-Gly-Pro-Phe-pNA 7, Gly-Pro 8, Ala-Pro 9, Val-Pro 10, His-Pro 11, Gly-Gly-Lys-Phe-Pro. Linear regression analysis of the data for compounds 1—6 yields a slope or critical temperature, T, of 232 29 K analysis of the data for compounds 7-11 yields = 212 27 K.

A fundamental limitation for fhe apphcation of geometric fitting procedures is that fhe complexation free energies are fhe sum of enthalpic and entropic contributions, with the consequence that selectivity can be inversed at different temperatures. Positive cooperativity between different interactions in a complex will usually lead to tighter association at fhe expense of motional freedom and fhus of entropy [51]. The interplay and often observed compensation of enthalpic and entropic contributions have been discussed in several reviews [10, 52, 53], particularly with emphasis on biological systems, and cannot be dealt with in detail here. Unfortunately, many published enthalpy-entropy compensations are blurred by possible artifacts, as the two underlying parameters do not represent independent variables [54]. 

Plots of the standard entropy, or better standard free energy, against the standard enthalpy referred to as enthalpy-entropy compensation plots, are a useful tool for establishing the similarity of the retention mechanism for different solutes [25,79,83,95,96]. When enthalpy-entropy compensation occurs the plots are linear and the slope is called the compensation temperature. All compounds have the same retention at the compensation temperature, although their temperature dependence may differ. This is most likely to occur for processes governed by a single retention mechanism. All related processes... 

If such effects are absent, the van t Hoff plots of related analytes, such as homologous series, exhibit a common focal point at a specific temperature. This point of enthalpy-entropy compensation can be characterized by a specific temperature, file compensation temperature % and the free energy of adsorption at this temperature With the concept of the compensation temperature. Equation (10.8) can be written as... 

FIG U RE 10.4 Comparison between experimental (o) and calculated (solid lines) solubilities of phenacetin (S is the mole fraction of phenacetin) in the mixed solvent water/dioxane is the mole fraction of dioxane) at room temperature. The solubility was calculated using Equation 10.29. 1-activity coefficients expressed via the Flory-Huggins equation, 2-activity coefficients expressed via the Wilson equation. (From C. Bustamante, and P. Bustamante, 1996, Nonlinear Enthalpy-Entropy Compensation for the Solubility of Phenacetin in Dioxane-Water Solvent Mixtures, Journal of Pharmaceutical Sciences, 85, 1109. Reprinted from E. Ruckenstein, and I. L. Shulgin, 2003c, Solubility of Drugs in Aqueous Solutions. Part 2 Binary Nonideal Mixed Solvent, International Journal of Pharmaceutics, 260, 283, With permission from Elsevier.)... 

Temperature Dependence, k(T), Water Activity, a v, and Enthalpy/Entropy Compensation... 

Figure 5.7. Enthalpy/entropy plot (AH /AS ) according to Equ. 5.11 exhibiting a linear relationship ( linear enthalpy/entropy compensation law ). From the slope of the line the isokinetic temperature Tp can be estimated.

The slope of this straight line is referred to as the isokinetic temperature, Tp (Barnes, Vogel, and Gordon, 1969 Leffler, 1966). This relationship with a linear thermodynamic compensation of rates is called enthalpy/entropy compensation it is important for the physiological stability of proteins (Lumry and Eyring, 1954). The value Tp is generally between 270°K and 320°K for the thermal destruction of cells Tp is between 320°K and 350°K. The importance of this fact is the possible implication of a uniform mechanism for cell death through protein denaturation. 

Despite the fact that, in some cases, small differences in AH and A5 can be observed (for various solutes, but on the same column with the same mobile phase), these differences could be found to be essentially insignificant when compared to a change in stationary-phase bonding density using enthalpy-entropy compensation. Enthalpy-entropy compensation is a term used to describe a compensation temperature, which is system independent for a class of similar experimental systems.Melander et have used the enthalpy-entropy compensation method in studies of hydrophobic interactions and separation mechanisms in reversed phase HPLC. Mathematically, enthalpy-entropy compensation can be expressed by the formula 9 ... 

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