Kauzmann entropy

There has been a wealth of activity based on the idea that glassy dynamics is due to some underlying thermodynamic transition [1-25], If a glass former shows a jump in some an appropriate order parameter without the evolution of latent heat, then such a system is said to exhibit a random first-order transition [94,95]. Models of this kind, which include the p-spin glasses [110], and the random energy model [111], do not have symmetry between states but do have quenched random long-range interactions and exhibit the so-called Kauzmann entropy crisis. 

Gibbs and Di Marzio [18] used the above spH,dis (g) to demonstrate the entropy crisis in polymers (see Ref [52] for details). This calculation was the first one of its kind to demonstrate the entropy crisis. Despite its limitation, to be discussed below, the work by Gibbs and Di Marzio has played a pivotal role in elevating the Kauzmann entropy crisis from a mere curious observation to probably the most important mechanism behind the glass transition, even though the demonstration was only for long molecules. 

Let us now turn to a discussion of the relation of the temperature dependence of the polymer melt s configurational entropy with its glass transition and address the famous paradox of the Kauzmann temperature of glass-forming systems.90 It had been found experimentally that the excess entropy of super-cooled liquids, compared with the crystalline state, seemed... 

Johari G.P. (2000) An equilibrium supercooled liquid s entropy and enthalpy in the Kauzmann and the third law extrapolations, and a proposed experimental resolution. /. Chem. Phys. 113, 751-761. 

Ito et al. observed a remarkable similarity between kinetic fragility plot and normalized entropy data, namely, Kauzmann plot, exhibited in a scaled- / , form sheds considerable light into the role of excess entropy... 

Here, Cv h(T) and Svlh(T) are the vibrational contributions to the heat capacity and the entropy, respectively. Note that the slope of the replica symmetry-breaking parameter with respect to temperature is not unity as predicted by one-step replica symmetry breaking. Rather, the slope is governed by three factors the Narayanaswamy-Moynihan nonlinearity parameter x, the Kauzmann temperature, and the ratio of the Kauzmann temperature to the glass transition temperature. 

The interest in hydrophobic interactions was stimulated by their unusual thermodynamic properties it was argued and believed that they are governed, not by enthalpic, but by entropic features, characterized by the undesirable entropy decrease of water in the vicinity of nonpolar groups (Frank and Evans, 1945 Kauzmann, 1959 Franks, 1975 Tanford, 1980). This conclusion was reached largely from consideration of solvation effects at room temperature. 

If apolar hydration is characterized by the conditions that AG° > 0, TAS < 0 and AH < 0, then a process which minimizes exposure of apolar groups to water should be a thermodynamically favoured process. Then if two apolar groups of either the same or different molecules come together in water, AS for this process will be positive because some of the structured water is released into the bulk solvent. Such association is called hydrophobic, hydrophobic bonding or hydrophobic interaction (Kauzmann, 1959). The term bond is probably inappropriate because the association is due to entropy rather than to enthalpy effects, a consequence of the disruption of the clathrate structure around the apolar solute (Jolicoeur and Friedman, 1974). Despite the general acceptance of the concept of hydrophobic association, there are different approaches to the problem of understanding this phenomenon. 

The first theoretician of the vitrification process was Simon (1930), who pointed out that it can be interpreted as a "freezing-in" process. Simon measured specific heats and entropies of glycerol in the liquid, crystalline and glassy state below Tg the entropy of the supercooled liquid could, as a matter of fact, only be estimated. Linear extrapolation would lead to a negative entropy at zero temperature (paradox of Kauzmann, 1948) which would be in contradiction with Nernst s theorem. So one has to assume a sharp change in the slope of the entropy, which suggested a second order transition as defined by Ehrenfest. 

The Kauzmann temperature plays an important role in the most widely applied phenomenological theories, namely the configurational entropy [100] and the free-volume theories [101,102]. In the entropy theory, the excess entropy ASex obtained from thermodynamic studies is related to the temperature dependence of the structural relaxation time xa. A similar relation is derived in the free-volume theory, connecting xa with the excess free volume AVex. In both cases, the excess quantity becomes zero at a distinguished temperature where, as a consequence, xa(T) diverges. Although consistent data analyses are sometimes possible, the predictive power of these phenomenological theories is limited. In particular, no predictions about the evolution of relaxation spectra are made. Essentially, they are theories for the temperature dependence of x.-jT) and r (T). 

V)(dV/dT)p is the coefficient of thermal expansion for the pure solvent. The additional temperature derivative is d ne/dT)p —4.3 x 10 (Uematsu and Eranck, 1980), at the standard point indicated above, and ap 3x 10 " K (Eisenberg and Kauzmann, 1969). This entropy contribution is negative and has a magnitude of a small multiple of lcalK mol This magnitude is about a power of ten smaller than typical experimental results. Again, notice that this doesn t make a comparison that would warrant detailed discussion of a standard state for a particular experiment (Friedman and Krishnan, 1973). 

Kauzmann lists some —A//and —AS values for denaturation. Their range is 60-150 kcal/mole and 200-400 e.u. for several proteins. The entropy change is very large, hence denaturation involves a gross gain of entropy in a series of many small increments. In many instances the molecule cannot return to the previous orderly arrangement, and irreversible denaturation is observed. 

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