Entropy convergence

The simplicity and accuracy of such models for the hydration of small molecule solutes has been surprising, as well as extensively scrutinized (Pratt, 2002). In the context of biophysical applications, these models can be viewed as providing a basis for considering specific physical mechanisms that contribute to hydrophobicity in more complex systems. For example, a natural explanation of entropy convergence in the temperature dependence of hydrophobic hydration and the heat denaturation of proteins emerges from this model (Garde et al., 1996), as well as a mechanistic description of the pressure dependence of hydrophobic... 

L. Fu and E. Freire, On the origin of the enthalpy and entropy convergence temperatures in protein folding, Proc. Natl. Acad. Sci. USA 1992, 89, 9335-9338. 

Entropies calculated as the temperature derivative of along the saturation cmwe are shown in Fig. 8.7. As expected, these entropies are large and negative at room temperature, and increase with temperature. The entropies of hydration for these solutes converge in a temperature region aroimd 400 K, close to the temperature at which they are zero. The observed entropy convergence for transfer of simple nonpolar species from the dilute gas to water (Harvey et al, 1991) is similar. 

For hard-sphere solutes this entropy convergence point has a nontrivial size dependence that isn t apparent from Fig. 8.7 (Huang and Chandler, 2000 Ashbaugh and Pratt, 2004). Figure 8.9 gives a current estimate of those entropy... 

Figure 8.9 Variation of the entropy convergence temperature with increasing hard-sphere radius. The thin solid line is the convergence temperature determined under the assumption that the heat capacity is independent of temperature, and the thick solid line is the exact entropy convergence temperature for spheres smaller than R < (Tww/2 (Ashbaugh and Pratt, 2004). The dashed line smoothly interpolates between the exact and constant heat capacity curves at 1.25 A and 3.3 A, respectively. The filled circle indicates the entropy convergence temperature of a methane-sized solute (7), = 382K). The open circle indicates the entropy convergence temperature based on the information model = 420 K) (Ashbaugh and Pratt, 2004).

Figure 8.10 The distribution of the number of oxygen atoms within 5.1 A of the Kr atom in aqueous solution at an elevated temperature in the region of the entropy convergence temperature (LaViolette et al, 2003). These results were obtained to investigate the possibilities of clathrate nucleation upon quenching see Filipponi etal. (1997) and Bowron etal. (1998). Note that the coordination numbers n = 20 or n = 24, which are associated with clathrate cages, are unexceptional in this distribution for the liquid solution. The subtle structure in this distribution for n below the mode may be reflective of possibilities for alternative thermodynamic phases, e.g. the coexisting gas phase, or structures with commodious cages.

Crutchfield, J.P., Feldman, D.P. Regularities unseen, randomness observed Levels of entropy convergence. Chaos 13, 25-54 (2003)... 

The two-moment ITM applied to hard sphere solutes predicts entropy convergence for those cases. Additionally, test particle simulation methods used to study more realistic, Lennard-Jones models of inert gas atoms in water also provide a reliable description of the temperature dependence of the solvation free-energy. This theoretical success permits a simpler understanding of entropy convergence. We argue as follows a continuous Gaussian distribution reliably approximates the two-moment information model,exhibits the entropy convergence, and produces an explicit result for the excess chemical potential ... 

S. Garde, G. Hummer, A. E. Garda, M. E. Paulaitis, and L. R. Pratt, Phys. Rev. Lett., 77,4966 (1996). Origin of Entropy Convergence in Hydrophobic Hydration and Protein Folding. 

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