Thermodynamic singularity

Speedy, R.J. and Angell, C.A. Isothermal compressibility of supercooled water and evidence for a thermodynamic singularity at -45°C, /. Chem. Phys., 65, 851, 1976. 

In considering the kinetics of crystallization of supercooled water and representing the domelike eurve 1 for the crystallization rate we left aside the question of the spinodal of supercooled liquid. If such a spinodal exists, it means that, at least, a part of eurve 1 (on the left) does not conform to the actual possibility of nucleation in a homogeneous system. The decrease of the inverse isothermal eompressibility of water with a temperature decrease below 319 K is interpreted by the authors as a trace of thermodynamic singularity at 228 K (curve 3"). However, it does not agree with the liquid capacity for much greater supercoolings established by experiment. 

Rouch, J., Lai, C. C., Chen, C. H. (1977) High frequency sound velocity and sound absorption in supercooled water and thermodynamics singularity at 228 K. J. Chem. Phys. 66, 5031-5034... 

In the absence of any interceding phenomena, it seems necessary only to allow the supercooled liquid longer and longer periods of equilibration to ensure that its entropy will fall below that of the crystal at the temperature Jk (denoted Fj and in Refs. 58 and 106, respectively). Such an occurrence, though not actually in violation of the third law at finite temperatures, would imply a contradiction of the Nemst heat theorem on the approach to 0°K. This seems unlikely and raises the question of the existence of a thermodynamic singularity underlying the glass transition at or above the Kauzmann temperature T. ... 

In contrast, closed association may lead to a sharp change in the number of micelles, but the transition is continuous as far as the size of micelles remains finite. There is no thermodynamic singularity because the number of molecules involved in the clusters remains finite. 

The percolation models discussed so far undergo piuely geometrical transitions because the objects treated have no center of mass translational motion. They are only randomly placed either on the lattices or in the continuum space. Therefore, they don t reveal any thermodynamic singularities. If particles are moving in a space, however, the entropy associated with the translational motion may partly vanish at the percolation point since the mass center of the infinite cluster (gel) ceases to move. If its derivative with respect to the concentration across the percolation point has a discontinuity, the transition becomes a real thermodynamic one. 

The Singularity Free Hypothesis Sastry et al. [60] proposed that a minimal scenario that was consistent with the salient anomalies did not require recourse to any thermodynamic singularities, such as a critical point or a retracing spinodal. They analyzed the interrelationship between the locus of density and the compressibility extrema and showed that the change of slope of the locus of density maxima (TMD) was associated with an intersection with the locus of compressibility extrema (TEC) (Fig. 3c). The relationship between the temperature dependence of isothermal compressibility at the TMD and the slope of the TMD is given by... 

A key concept within the studies of asymptotic decay is the Fisher-Widom (FW) line [199]. The latter is the locus of points in the (p T) plane (or in the (p, T) plane) signaling the crossover of the h (R) decay from monotonic to exponentially damped oscillatory. Although no thermodynamic singularities are related to the FW Une, and despite the fact that it may not exist for some models of fluids (e.g., classical hard spheres), the FW line is very useful in that it marks the change in the decay regime which may be characteristic of certain fluid properties (e.g., monotonic in the vicinity of the critical point) [201]. Furthermore, these two general decay behaviors are connected with interfacial properties, such as the liquid-vapor interface structure, or the wetting transitions at wall-fluid interfaces [188, 200, 201],... 

Similarly, there is no singularity in Xoid or (aord(T) at Tm- Thus, the thermodynamic singularity in the equilibrium free energy does not necessarily create a singularity in tt>dis(T) or cOord(T) at Tm, as was discussed. The existence of a singularity at some other temperature is a different issue with which we are not concerned here. 

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